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Summary of Chapter 12

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finance 4e

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finance 4e
Marcia Millon Cornett
Bentley University
Troy A. Adair Jr.
Harvard Business School
John Nofsinger
University of Alaska Anchorage

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M: FINANCE, FOURTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2019 by McGraw-Hill Education. All rights reserved. Printed in
the United States of America. Previous editions © 2016, 2014 and 2012. No part of this publication may be reproduced or distributed in any form or by any
means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any
network or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 0 LMN 21 20 19 18
ISBN 978-1-259-91963-3
MHID 1-259-91963-3
All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Portfolio Manager: Noelle Bathurst
Lead Product Developers: Michele Janicek, Kristine Tibbetts
Product Developer: Allison McCabe
Marketing Manager: Trina Maurer
Content Project Managers: Brian Nacik
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Design: Jessica Cuevas
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Cover Image: ©Uber Images/ Shutterstock RF
Compositor: SPi Global
Library of Congress Control Number: 2017043716
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors
or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

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a note from the authors
“There is a lot to cover in this course so I focus on the core concepts, theories, and problems.”
“I like to teach the course by using examples from their own individual lives.”
“My students come into this course with varying levels of math skills.”
How many of these quotes might you have said while teaching the undergraduate corporate finance course? Our
many years of teaching certainly reflect such sentiments, and as we prepared to write this book, we conducted many
market research studies that confirm just how much these statements—or ones similar—are common across the
country. This critical course covers so many crucial topics that instructors need to focus on core ideas to ensure that
students are getting the preparation they need for future classes—and for their lives beyond college.
We did not set out to write this book to change the way finance is taught, but rather to parallel and support the
way that instructors from across the country currently teach finance. Well over 600 instructors teaching this course
have shared their class experiences and ideas via a variety of research methods that we used to develop the
framework for this text. We are excited to have authored a book that we think you will find fits your classroom style
perfectly.
KEY THEMES
This book’s framework emphasizes three themes. See the next section in this preface for a description of features in
our book that support these themes.
Finance is about connecting core concepts. We all struggle with fitting so many topics into this course, so this
text strives to make it easier for you by getting back to the core concepts, key research, and current topics. We
realize that today’s students expect to learn more in class from lectures than in closely studying their textbooks, so
we’ve created brief chapters that clearly lead students to crucial material that they need to review if they are to
understand how to approach core financial concepts. The text is also organized around learning goals, making it
easier for you to prep your course and for students to study the right topics.
Finance can be taught using a personal perspective. Most long-term finance instructors have often heard
students ask “How is this course relevant to me?” on the first day of class. We no longer teach classes dedicated
solely to finance majors; many of us now must teach the first finance course to a mix of business majors. We need
to give finance majors the rigor they need while not overwhelming class members from other majors. For
years, instructors have used individual examples to help teach these concepts, but this is the first text to
integrate this personal way of teaching into the chapters.
Finance focuses on solving problems and decision making. This isn’t to say that concepts and theories aren’t
important, but students will typically need to solve some kind of mathematical problem—or at least understand the
impact of different numerical scenarios—to make the right decision on common finance issues. If you, as an
instructor, either assign problems for homework or create exams made up almost entirely of mathematical material,
you understand the need for good problems (and plenty of them). You also understand from experience the number
of office hours you spend tutoring students and grading homework. Students have different learning styles, and this
text aims to address that challenge to allow you more time in class to get through the critical topics.

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changes in the fourth edition
Based on feedback from users and reviewers, we undertook an ambitious revision in order to make the book follow
your teaching strategy even more closely. Below are the changes we made for this fourth edition, broken out by
chapter.
OVERALL
Simplified figures where appropriate and added captions to emphasize the main “takeaways”
Updated data, company names, and scenarios to reflect latest available data and real-world changes
Cross-referenced numbered examples with similar end-of-chapter problems and self-test problems so students can
easily model their homework
Updated the numbers in the end-of-chapter problems to provide variety and limit the transfer of answers from
previous classes
chapter one
INTRODUCTION TO FINANCIAL MANAGEMENT
Updated the Personal Application with information on firms that have filed for bankruptcy more recently
Changed Learning Goal 1-9 to address the ramifications of China’s slowdown and the drop in the price of oil
Revised the Finance at Work—Markets box to discuss quantitative easing in the United States and around the
world
Revised the Finance at Work—Corporate box to cover the proposed merger of AB InBev and SABMiller
Updated the data in Example 1-2 on executive compensation
Replaced Section 1.7 on the financial crisis with a new Section 1.7: Big Picture Environment, including discussions
of the ramifications of plummeting oil prices and China’s economic slowdown
chapter two
REVIEWING FINANCIAL STATEMENTS
Added a discussion of difference between EBIT and operating income
Included extended definitions of net sales, cost of goods sold, and operating expenses
Added a discussion of the interpretation of a cash-based income statement
Added a new Finance at Work box

chapter three
ANALYZING FINANCIAL STATEMENTS
Added more discussion of debt ratios
chapter four
TIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS
Updated the data in Figure 4.5 on gold prices
Added equation functions to Table 4.2 and Table 4.4
Revised the data for the end-of-chapter Excel problem

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Added a new end-of-chapter Excel problem
chapter five
TIME VALUE OF MONEY 2: ANALYZING ANNUITY CASH FLOWS
Revised the chapter introduction to discuss Boeing
Added equation functions to Tables 5.1, 5.2, 5.5, and 5.6
Updated the present value of multiple annuities example to discuss the new David Price contract with the Boston
Red Sox
Changed the Finance at Work—Behavioral box to address the record Powerball jackpot of $1.5 billion on January
12, 2016
Added a new end-of-chapter Excel problem
chapter six
UNDERSTANDING FINANCIAL MARKETS AND INSTITUTIONS
Updated all figures, tables, and values in the body of the chapter
Added a section on the loanable funds theory/determination of equilibrium interest rates
Added new end-of-chapter problems
Decreased the coverage of the financial crisis (detailed information is available in the Web Appendix for Chapter 6
available in Connect or at mhhe.com/Cornett4e)
chapter seven
VALUING BONDS
Updated the Personal Application with new data
Updated Figures 7.1–7.5 on bond issuance, interest rate path, yield to maturities, new bond quotes, and a summary
of the bond market
Added equation functions to Tables 7.3 and 7.5
Revised the data for the end-of-chapter Excel problem
Added a new end-of-chapter Excel problem

chapter eight
VALUING STOCKS
Updated all table and figure values in the body of the chapter
Updated the coverage of the stock market exchange in Section 8.2 to discuss the changes that have occurred in the
NYSE and elsewhere
Revised Example 8-1 to include new Coca-Cola data
Updated Example 8-4 with new P/E data for Caterpillar
Added a new end-of-chapter Excel problem
chapter nine
CHARACTERIZING RISK AND RETURN
Revised the example that runs throughout the chapter to discuss Staples
Updated all table and figure values in the body of the chapter
Added equation functions to Table 9.3 and Table 9.5

http://www.mhhe.com/Cornett4e

page x
Updated Example 9-2 to include new Mattel data
Updated the data in the Finance at Work—Markets box
Revised the data for the end-of-chapter Excel problem
Added a new end-of-chapter Excel problem
chapter ten
ESTIMATING RISK AND RETURN
Updated values and data in Tables 10.1–10.4
Added a new end-of-chapter Excel problem
chapter eleven
CALCULATING THE COST OF CAPITAL
Clarified and expanded the discussion of use of market values versus book values in the calculation of WACC
Expanded the discussion of when to use CAPM versus the constant-growth model when estimating the cost of
equity
Expanded the discussion of computation of marginal tax rate for WACC
Enhanced the discussion of use of firm versus project WACCs
Enhanced the discussion of appropriateness of divisional WACCs
chapter twelve
ESTIMATING CASH FLOWS ON CAPITAL BUDGETING PROJECTS
Clarified the definition of salvage value
Expanded the discussion of substitutionary and complementary effects
Enhanced the discussion of income tax shield from a project having taxable losses
Enhanced the discussion of NWC changes “leading” changes in sales
Expanded the discussion of the half-year convention in depreciation
chapter thirteen
WEIGHING NET PRESENT VALUE AND OTHER CAPITAL BUDGETING CRITERIA
Clarified the discussion of the goal of capital budgeting decision rules and the differing environments of
investment and capital budgeting decisions
Expanded the discussion of why using rate-based and time-based decision statistics to choose across projects can
be misleading with regards to NPV
chapter fourteen
WORKING CAPITAL MANAGEMENT AND POLICIES
Expanded the discussion of the rationale for NWC and the tradeoffs inherent in having too little or too much
Refined discussion of cash flows vs. the cash account

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brief contents
part one
INTRODUCTION 3
chapter 1 Introduction to Financial Management 3
part two
FINANCIAL STATEMENTS 27
chapter 2 Reviewing Financial Statements 27
chapter 3 Analyzing Financial Statements 59
part three
VALUING OF FUTURE CASH FLOWS 89
chapter 4 Time Value of Money 1: Analyzing Single Cash Flows 89
chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows 115
part four
VALUING OF BONDS AND STOCKS 147

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chapter 6 Understanding Financial Markets and Institutions 147
Appendix 6A: The Financial Crisis: The Failure of Financial Institution Specialness (located at
www.mhhe.com/Cornett4e) 186
chapter 7 Valuing Bonds 199
chapter 8 Valuing Stocks 233
part five
RISK AND RETURN 261
chapter 9 Characterizing Risk and Return 261
chapter 10 Estimating Risk and Return 289

part six
CAPITAL BUDGETING 315
chapter 11 Calculating the Cost of Capital 315
chapter 12 Estimating Cash Flows on Capital Budgeting Projects 339
Appendix 12A: MACRS Depreciation Tables 362
chapter 13 Weighing Net Present Value and Other Capital Budgeting Criteria 369
part seven
WORKING CAPITAL MANAGEMENT AND FINANCIAL PLANNING 399
chapter 14 Working Capital Management and Policies 399
Appendix 14A: The Cash Budget 422

http://www.mhhe.com/Cornett4e

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contents
CHAPTER 1 INTRODUCTION TO FINANCIAL MANAGEMENT 3
1.1 • FINANCE IN BUSINESS AND IN LIFE 4
What Is Finance? 5
Subareas of Finance 8
Application and Theory for Financial Decisions 9
Finance versus Accounting 10
1.2 • THE FINANCIAL FUNCTION 11
The Financial Manager 11
Finance in Other Business Functions 11
Finance in Your Personal Life 12
1.3 • BUSINESS ORGANIZATION 12
Sole Proprietorships 12
Partnerships 13
Corporations 14
Hybrid Organizations 15
1.4 • FIRM GOALS 15
1.5 • AGENCY THEORY 17
Agency Problem 17
Corporate Governance 18
The Role of Ethics 19
1.6 • FINANCIAL MARKETS, INTERMEDIARIES, AND THE FIRM 21
1.7 • BIG PICTURE ENVIRONMENT 21
Oil Prices Plummet 21
China Slows Down 22
CHAPTER 2 REVIEWING FINANCIAL STATEMENTS 27
2.1 • BALANCE SHEET 28
Assets 29
Liabilities and Stockholders’ Equity 29

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Managing the Balance Sheet 30
2.2 • INCOME STATEMENT 33
Debt versus Equity Financing 35
Corporate Income Taxes 36
2.3 • STATEMENT OF CASH FLOWS 38
GAAP Accounting Principles 39
Noncash Income Statement Entries 39
Sources and Uses of Cash 40
2.4 • FREE CASH FLOW 42
2.5 • STATEMENT OF RETAINED EARNINGS 44
2.6 • CAUTIONS IN INTERPRETING FINANCIAL STATEMENTS 44
CHAPTER 3 ANALYZING FINANCIAL STATEMENTS 59
3.1 • LIQUIDITY RATIOS 60
3.2 • ASSET MANAGEMENT RATIOS 62
Inventory Management 62
Accounts Receivable Management 63
Accounts Payable Management 63
Fixed Asset and Working Capital Management 64
Total Asset Management 64
3.3 • DEBT MANAGEMENT RATIOS 66
Debt versus Equity Financing 66
Coverage Ratios 67
3.4 • PROFITABILITY RATIOS 68
3.5 • MARKET VALUE RATIOS 70
3.6 • DUPONT ANALYSIS 71

3.7 • OTHER RATIOS 75
Spreading the Financial Statements 75
Internal and Sustainable Growth Rates 76
3.8 • TIME SERIES AND CROSS-SECTIONAL ANALYSES 77
3.9 • CAUTIONS IN USING RATIOS TO EVALUATE FIRM PERFORMANCE 78
CHAPTER 4 TIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS 89
4.1 • ORGANIZING CASH FLOWS 90
4.2 • FUTURE VALUE 91
Single-Period Future Value 91
Compounding and Future Value 92
4.3 • PRESENT VALUE 98
Discounting 98
4.4 • USING PRESENT VALUE AND FUTURE VALUE 101
Moving Cash Flows 101
4.5 • COMPUTING INTEREST RATES 103
Return Asymmetries 105
4.6 • SOLVING FOR TIME 105
CHAPTER 5 TIME VALUE OF MONEY 2: ANALYZING ANNUITY CASH FLOWS 115
5.1 • FUTURE VALUE OF MULTIPLE CASH FLOWS 116
Finding the Future Value of Several Cash Flows 116
Future Value of Level Cash Flows 118
Future Value of Multiple Annuities 119
5.2 • PRESENT VALUE OF MULTIPLE CASH FLOWS 122

Finding the Present Value of Several Cash Flows 122
Present Value of Level Cash Flows 123
Present Value of Multiple Annuities 124
Perpetuity—A Special Annuity 127
5.3 • ORDINARY ANNUITIES VERSUS ANNUITIES DUE 127
5.4 • COMPOUNDING FREQUENCY 129
Effect of Compounding Frequency 129
5.5 • ANNUITY LOANS 133
What Is the Interest Rate? 133
Finding Payments on an Amortized Loan 134
CHAPTER 6 UNDERSTANDING FINANCIAL MARKETS AND INSTITUTIONS 147
6.1 • FINANCIAL MARKETS 148
Primary Markets versus Secondary Markets 148
Money Markets versus Capital Markets 151
Other Markets 153
6.2 • FINANCIAL INSTITUTIONS 155
Unique Economic Functions Performed by Financial Institutions 156
6.3 • INTEREST RATES AND THE LOANABLE FUNDS THEORY 159
Supply of Loanable Funds 161
Demand for Loanable Funds 162
Equilibrium Interest Rate 163
Factors That Cause the Supply and Demand Curves for Loanable Funds to Shift 163
Movement of Interest Rates over Time 167
6.4 • FACTORS THAT INFLUENCE INTEREST RATES FOR INDIVIDUAL SECURITIES 167
Inflation 168
Real Risk-Free Rate 168
Default or Credit Risk 169
Liquidity Risk 170
Special Provisions or Covenants 171
Term to Maturity 171
6.5 • THEORIES EXPLAINING THE SHAPE OF THE TERM STRUCTURE OF INTEREST RATES 174
Unbiased Expectations Theory 174
Liquidity Premium Theory 176
Market Segmentation Theory 177
6.6 • FORECASTING INTEREST RATES 179
Appendix 6A The financial Crisis: The Failure of Financial Institution Specialness 186
CHAPTER 7 VALUING BONDS 199
7.1 • BOND MARKET OVERVIEW 200
Bond Characteristics 200
Bond Issuers 202
Other Bonds and Bond-Based Securities 204
Reading Bond Quotes 207
7.2 • BOND VALUATION 209
Present Value of Bond Cash Flows 209
Bond Prices and Interest Rate Risk 211

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7.3 • BOND YIELDS 213
Current Yield 213
Yield to Maturity 214
Yield to Call 215
Municipal Bonds and Yield 217
Summarizing Yields 218
7.4 • CREDIT RISK 219
Bond Ratings 219
Credit Risk and Yield 221
7.5 • BOND MARKETS 222
Following the Bond Market 223
CHAPTER 8 VALUING STOCKS 233
8.1 • COMMON STOCK 234
8.2 • STOCK MARKETS 235
Tracking the Stock Market 238
Trading Stocks 240
8.3 • BASIC STOCK VALUATION 241
Cash Flows 241
Dividend Discount Models 243
Preferred Stock 245
Expected Return 246
8.4 • ADDITIONAL VALUATION METHODS 248
Variable-Growth Techniques 248
The P/E Model 251
Estimating Future Stock Prices 254
CHAPTER 9 CHARACTERIZING RISK AND RETURN 261
9.1 • HISTORICAL RETURNS 262
Computing Returns 262
Performance of Asset Classes 265
9.2 • HISTORICAL RISKS 266
Computing Volatility 266
Risk of Asset Classes 269

Risk versus Return 270
9.3 • FORMING PORTFOLIOS 271
Diversifying to Reduce Risk 271
Modern Portfolio Theory 274
CHAPTER 10 ESTIMATING RISK AND RETURN 289
10.1 • EXPECTED RETURNS 290
Expected Return and Risk 290
Risk Premiums 292
10.2 • MARKET RISK 294
The Market Portfolio 294
Beta, a Measure of Market Risk 295
The Security Market Line 296
Finding Beta 298
Concerns about Beta 300
10.3 • CAPITAL MARKET EFFICIENCY 301
Efficient Market Hypothesis 302
Behavioral Finance 303
10.4 • IMPLICATIONS FOR FINANCIAL MANAGERS 304
Using the Constant-Growth Model for Required Return 304
CHAPTER 11 CALCULATING THE COST OF CAPITAL 315
11.1 • THE WACC FORMULA 316
Calculating the Component Cost of Equity 317
Calculating the Component Cost of Preferred Stock 318
Calculating the Component Cost of Debt 318
Choosing Tax Rates 319
Calculating the Weights 321
11.2 • FIRM WACC VERSUS PROJECT WACC 322
Project Cost Numbers to Take from the Firm 323
Project Cost Numbers to Find Elsewhere: The Pure-Play Approach 324
11.3 • DIVISIONAL WACC 326
Pros and Cons of a Divisional WACC 326
Subjective versus Objective Approaches 328
11.4 • FLOTATION COSTS 330
Adjusting the WACC 331
CHAPTER 12 ESTIMATING CASH FLOWS ON CAPITAL BUDGETING PROJECTS
339
12.1 • SAMPLE PROJECT DESCRIPTION 340
12.2 • GUIDING PRINCIPLES FOR CASH FLOW ESTIMATION 341
Opportunity Costs 342
Sunk Costs 342
Substitutionary and Complementary Effects 342
Stock Dividends and Bond Interest 343
12.3 • TOTAL PROJECT CASH FLOW 343
Calculating Depreciation 343
Calculating Operating Cash Flow 344
Calculating Changes in Gross Fixed Assets 345
Calculating Changes in Net Working Capital 346
Bringing It All Together 348
12.4 • ACCELERATED DEPRECIATION AND THE HALF-YEAR CONVENTION 349
MACRS Depreciation Calculation 349
Section 179 Deductions 350

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Impact of Accelerated Depreciation 351
12.5 • “SPECIAL” CASES AREN’T REALLY THAT SPECIAL 352
12.6 • CHOOSING BETWEEN ALTERNATIVE ASSETS WITH DIFFERING LIVES: EAC 354
12.7 • FLOTATION COSTS REVISITED 356
APPENDIX 12A: MACRS DEPRECIATION TABLES 362

CHAPTER 13 WEIGHING NET PRESENT VALUE AND OTHER CAPITAL
BUDGETING CRITERIA 369
13.1 • THE SET OF CAPITAL BUDGETING TECHNIQUES 371
13.2 • THE CHOICE OF DECISION STATISTIC FORMAT 372
13.3 • PROCESSING CAPITAL BUDGETING DECISIONS 373
13.4 • PAYBACK AND DISCOUNTED PAYBACK 374
Payback Statistic 374
Payback Benchmark 375
Discounted Payback Statistic 375
Discounted Payback Benchmark 376
Payback and Discounted Payback Strengths and Weaknesses 378
13.5 • NET PRESENT VALUE 378
NPV Statistic 378
NPV Benchmark 378
NPV Strengths and Weaknesses 380
13.6 • INTERNAL RATE OF RETURN AND MODIFIED INTERNAL RATE OF RETURN 381
Internal Rate of Return Statistic 382
Internal Rate of Return Benchmark 382
Problems with Internal Rate of Return 383
IRR and NPV Profiles with Non-Normal Cash Flows 384
Differing Reinvestment Rate Assumptions of NPV and IRR 385
Modified Internal Rate of Return Statistic 385
IRRs, MIRRs, and NPV Profiles with Mutually Exclusive Projects 385
MIRR Strengths and Weaknesses 389
13.7 • PROFITABILITY INDEX 390
Profitability Index Statistic 390
Profitability Index Benchmark 390
CHAPTER 14 WORKING CAPITAL MANAGEMENT AND POLICIES 399
14.1 • REVISITING THE BALANCE-SHEET MODEL OF THE FIRM 400
14.2 • TRACING CASH AND NET WORKING CAPITAL 401
The Operating Cycle 402
The Cash Cycle 402
14.3 • SOME ASPECTS OF SHORT-TERM FINANCIAL POLICY 403
The Size of the Current Assets Investment 403
Alternative Financing Policies for Current Assets 404
14.4 • THE SHORT-TERM FINANCIAL PLAN 407
Unsecured Loans 407
Secured Loans 408
Other Sources 408
14.5 • CASH MANAGEMENT 409
Reasons for Holding Cash 409
Determining the Target Cash Balance: The Baumol Model 409
Determining the Target Cash Balance: The Miller-Orr Model 410
Other Factors Influencing the Target Cash Balance 411
14.6 • FLOAT CONTROL: MANAGING THE COLLECTION AND DISBURSEMENT OF CASH 413

Accelerating Collections 414
Delaying Disbursements 414
Ethical and Legal Questions 415
14.7 • INVESTING IDLE CASH 415
Why Firms Have Surplus Cash 416
What to Do with Surplus Cash 416
14.8 • CREDIT MANAGEMENT 416
Credit Policy: Terms of the Sale 416
Credit Analysis 416
Collection Policy 417
APPENDIX 14A THE CASH BUDGET 422
VIEWPOINTS REVISITED 426
CHAPTER EQUATIONS 434
INDEX 439

page 1
finance 4e

Part One

page 2
page 3

D
chapter one
introduction to
financial management
© John Lamb/Getty Images/Photodisc
o you know: What finance entails? How financial management functions within the business world?
Why you might benefit from studying financial principles? This chapter is the ideal place to get
answers to those questions. Finance is the study of applying specific value to things we own, services
we use, and decisions we make. Examples are as varied as shares of stock in a company, payments on a
home mortgage, the purchase of an entire firm, and the personal decision to retire early. In this text, we
focus primarily on one area of finance, financial management, which concentrates on valuing things from the
perspective of a company, or firm.
finance The study of applying specific value to things we own, services we use, and decisions we make.
financial management The process for and the analysis of making financial decisions in the business context.

page 4
LEARNING GOALS
LG1-1 Define the major areas of finance as they apply to corporate financial management.
LG1-2 Show how finance is at the heart of sound business decisions.
LG1-3 Learn the financial principles that govern your personal decisions.
LG1-4 Examine the three most common forms of business organization in the United States today.
LG1-5 Distinguish among appropriate and inappropriate goals for financial managers.
LG1-6 Identify a firm’s primary agency relationship and discuss the possible conflicts that may arise.
LG1-7 Discuss how ethical decision making is part of the study of financial management.
LG1-8 Describe the complex, necessary relationships among firms, financial institutions, and financial markets.
LG1-9 Explain the business ramifications of the decline in the price of oil and China’s economic slowdown.

viewpoints
business APPLICATION
Caleb has worked very hard to create and expand his juice stand at the mall. He has finally perfected his products and feels that he is
offering the right combination of juice and food. As a result, the stand is making a nice profit. Caleb would like to open more stands at
malls all over his state and eventually all over the country.
Caleb knows he needs more money to expand. He needs money to buy more equipment, buy more inventory, and hire and train
more people. How can Caleb get the capital he needs to expand? (See the solution at the end of the book.)
Financial management is critically important to the success of any business organization, and
throughout the text we concentrate on describing the key financial concepts in corporate finance. As a
bonus, you will find that many tools and techniques for handling the financial management of a firm also
apply to broader types of financial problems, such as personal finance decisions.
In finance, cash flow is the term that describes the process of paying and receiving money. It makes
sense to start our discussion of finance with an illustration of various financial cash flows. We use simple
graphics to help explain the nature of finance and to demonstrate the different subareas of the field of
finance.
After we have an overall picture of finance, we will discuss three important variables in the business
environment that can and do have significant impact on the firm’s financial decisions. These are (1) the
organizational form of the business, (2) the agency relationship between the managers and owners of a
firm, and (3) ethical considerations as finance is applied in the real world.
1.1 • FINANCE IN BUSINESS AND IN LIFE LG1-1
If your career leads you to making financial decisions, then this book will be indispensable. If not, it is likely that
your activities in a business will involve interacting with the finance functions. After all, the important investments
of a firm involve capital and, therefore, finance. Expanding marketing channels, developing new products, and
upgrading a factory all cost money. A firm spends its capital on these projects to foster growth. Understanding how
finance professionals evaluate those projects will help you be successful in your business focus. In addition,
everyone will benefit in their personal life from learning finance and understanding financial decisions.
And what exactly makes up this engine of financial decision making? Successful application of financial theories
helps money flow from individuals who want to improve their financial future to businesses that want to expand the
scale or scope of their operations. These exchanges lead to a growing economy and more employment opportunities
for people at all income levels. So, two important things result from this simple exchange: The economy will be
more productive, and individuals’ wealth will grow into the future.

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page 5
personal APPLICATION
Dagmar is becoming interested in investing some of her money. However, she has heard about several corporations in which the
investors lost all of their money. Recently, Dagmar has heard that RadioShack (2015), Wet Seal (2015), and THQ (2013) have all filed
for bankruptcy. These firms’ stockholders lost their entire investments in these firms.
Many of the stockholders who lost money were employees of these companies who had invested some of their retirement money in
the company stock. Dagmar wonders what guarantee she has as an investor against losing her money. (See the solution at the end
of the book.)
What is the best way for Dagmar to ensure a happy retirement?
In this first section, we develop a comprehensive description of finance and its subareas, and we look at the specific
decisions that professionals in each subarea must make. As you will see, all areas of finance share a common set of
ideas and application tools.
What Is Finance?
To get the clearest possible picture of how finance works, let’s begin by grouping all of an economy’s participants
along two dimensions. The first dimension is made up of those who may have “extra” money (i.e., money above and
beyond their current spending needs) for investment. The second dimension is made up of those who have an ability
to develop viable business ideas, a sense of business creativity. Both money and ideas are fuel for the financial
engine. In our simple model, these two dimensions result in four groups representing economic roles in society, as
shown in Figure 1.1. Of course, people can move from one group to another over time.
Type 1 people in our model do not lend significant sums of money (capital) or spend much money in a business
context, so they play no direct role in financial markets, the mechanisms by which capital is exchanged. Although
these people probably play indirect roles by providing labor to economic enterprises or by consuming their products,
for simplicity we focus on those who play direct roles. Therefore, type 1 participants will be asked to step aside.
financial markets The arenas through which funds flow.
Type 4 people use financial tools to evaluate their own business concepts and then choose the ideas with the most
potential. From there, they create their own enterprises to implement their best ideas efficiently and effectively.
Type 4 individuals, however, are self-funded and do not need financial markets. The financial tools they use and the
types of decisions they make are narrowly focused or specific to their own purposes. For our discussion,
then, type 4 individuals also are asked to move to the sidelines.
FIGURE 1-1 Participants in Our Hypothetical Economy
No Extra Money Extra Money
No Economically Viable Business Ideas Type 1: No money and no ideas Type 2: Money but no ideas
Economically Viable Business Ideas Type 3: No money but ideas Type 4: Both money and ideas
Four groups form according to the availability of money and ideas.
Now for our financial role players, the type 2 and type 3 people. Financial markets and financial institutions allow
these people to participate in a mutually advantageous exchange. Type 2 people temporarily lend their money to
type 3 people, who put that money to use with their good business ideas.
In most developed economies, type 2 participants are usually individual investors. You will likely be an individual
investor for most of your life. Each of us separately may not have a lot of extra money at any one time, but by
aggregating our available funds, we can provide sizable amounts for investment.



page 7
investors Those who buy securities or other assets in hopes of earning a return and getting more money back in the future.
Type 3 participants, the idea generators, may be individuals, but they are more commonly corporations or other
types of companies with research and development (R&D) departments dedicated to developing innovative ideas.
It’s easy to see that investors and companies can help one another. If investors lend their “extra” capital to
companies, as shown in Figure 1.2, then companies can use this capital to fund expansion projects. Economically
successful projects will eventually be able to repay the money (plus profit) to investors, as Figure 1.3 shows.
FIGURE 1-2 Capital flow from Investors to Companies
Investors are people or groups who need ideas to make more money, and companies are groups who need money to develop the ideas
they do have.
FIGURE 1-3 Return of Capital to Investors
In this basic process, the company can expand its business, hire more employees, and create a promising future for its own growth.
Meanwhile, the investor can increase wealth for the future.

finance at work //: markets
Quantitative Easing in the United States and around the World

page 8
©DAJ/Getty Images
The Financial Crisis of 2007 to 2008 led to a global recession that ended in the United States in 2009. The severe recession is often
referred to as the “Great Recession” to give it a Great Depression flavor. However, the ensuing economic recovery was slow. It did not
have the typical bounce-back that often occurs after an acute recession.
To foster economic growth and give the financial sector time to recover, the U.S. Federal Reserve embarked on a grand experiment
called quantitative easing (QE). QE is a monetary policy designed to increase the money supply in the economy through buying
securities in the market and lowering short-term interest rates. The first round of QE involved the Fed buying potentially toxic mortgage-
backed securities (see Chapter 7), primarily from banks. This removed the suspect securities from the banks’ balance sheets and
allowed them time to get financially stronger. Also, short-term interest rates were cut to zero.
This initial round of QE ended in early 2010 after the Fed had purchased $1.25 trillion of mortgage-backed securities. Chapter 6
discusses QE’s impact on the financial system. By the end of 2010, the economy was still not as strong as desired. The Fed’s mission
has been to foster maximum employment in an environment of 2 percent inflation. But the employment market was still lackluster and
inflation was near zero in 2010.
In the fourth quarter of 2010 the Fed began QE 2, in which it bought $600 billion of long-term U.S. Treasury securities over the
ensuing nine months. This was an attempt to lower long-term interest rates. It did not have the desired impact on long-term rates, so QE
3 was implemented in late 2012 and continued through 2013. For QE 3, the Fed sold short-term bonds in order to purchase more long-
term securities. Short-term interest rates were kept near zero. The low interest rates had profound impacts on the bond market (see
Chapter 7) and companies’ cost of capital (see Chapter 11).
Instead of ending QE 3, the Fed decided to reduce its purchases each month through most of 2014. This QE taper was an attempt to
wean the economy from the constant Fed influence. QE 3 finally tapered out at the end of 2014. Speculation then grew about when the
Fed would start raising interest rates. The Fed finally raised its key interest rate to 0.25% on December 16, 2015. It was the first rate hike
in nearly 10 years.
One ramification of declining interest rates, or near zero rates, is that a country’s currency weakens against foreign currencies (see
Chapter 19). This is likely to increase exports and decrease imports.
The economies of other countries and regions have also struggled to grow since the Financial Crisis, and many of them have also
implemented quantitative easing programs—two notable examples are the European Central Bank and Japan. With the U.S. ending its
QE programs and raising interest rates while these other countries are continuing their monetary expansion, the U.S. dollar is likely to
strengthen. That would make exports more expensive and imports cheaper.
Want to know more?
Key Words to Search for Updates: quantitative easing, zero rate environment, QE taper, currency exchange rates
Of course, not all of the cash will return to the investors. In reality, sources of friction arise in this system, and the
amount of capital returned to investors is reduced. Two primary sources of friction are retained earnings, which are
basically funds the firm keeps for its ongoing operations, and taxes, which the government imposes on the company
and individuals to help fund public services. Figure 1.4 shows an analysis of cash flows with the associated retained
earnings and tax payments. In a very simple way, this figure provides an intuitive overall explanation of finance and
of its major subareas. For example, individuals must assess which investment opportunities are right for their
needs and risk tolerance; financial institutions and markets must efficiently distribute the capital; and


companies must evaluate their potential projects and wisely decide which projects to fund, what kind of capital to
use, and how much capital to return to investors. All of these types of decisions deal with the basic cash flows of
finance shown in Figure 1.4, but from different perspectives.
retained earnings The portion of company profits that are kept by the company rather than distributed to the stockholders as cash
dividends.
Subareas of Finance
Investments is the subarea of finance that involves methods and techniques for making decisions about what kinds of
securities to own (e.g., bonds or stocks), which firms’ securities to buy, and how to pay the investor back in the form
that the investor wishes (e.g., the timing and certainty of the promised cash flows). Figure 1.5 models cash flows
from the investor’s perspective. The concerns of the investments subarea of finance are shown (with the movement
of red arrows) from the investor’s viewpoint (seen as the blue box).
investment The analysis and process of choosing securities and other assets to purchase.
Financial management is the subarea that deals with a firm’s decisions in acquiring and using the cash that is
received from investors or from retained earnings. Figure 1.6 depicts the financial management process very simply.
As we know, this text focuses primarily on financial management. We’ll see that this critical area of finance
involves decisions about
How to organize the firm in a manner that will attract capital.
How to raise capital (e.g., bonds versus stocks).
Which projects to fund.
How much capital to retain for ongoing operations and new projects.
How to minimize taxation.
How to pay back capital providers.
All of these decisions are quite involved, and we will discuss them throughout later chapters.
FIGURE 1-4 The Complete Cash Flows of Finance
All the subareas of the financial system interact, with retained earnings and taxes playing a role in the flows.


page 9
FIGURE 1-5 Investments
Investors mark the start and end of the financial process; they put money in and reap the rewards (or take the risk).

Financial institutions and markets make up another major subarea of finance. These two dynamic entities work in
different ways to facilitate capital flows between investors and companies. Figure 1.7 illustrates the process in which
the firm acquires capital and investors take part in ongoing securities trading to increase that capital. Financial
institutions, such as banks and pension administrators, are vital players that contribute to the dynamics of interest
rates.
financial institutions and markets The organizations that facilitate the flow of capital between investors and companies.
International finance is the final major subarea of finance we will study. As the world has transformed into a global
economy, finance has had to become much more innovative and sensitive to changes in other countries. Investors,
companies, business operations, and capital markets may all be located in different countries. Adapting to this
environment requires understanding of international dynamics, as Figure 1.8 shows. In the past, international
financial decisions were considered to be a straightforward application of the other three financial subareas. But
experience has shown that the uncertainty about future exchange rates, political risk, and changing business laws
across the globe adds enough complexity to these decisions to classify international finance as a subarea of finance
in its own right.
international finance The use of finance theory in a global business environment.
Application and Theory for Financial Decisions
Cash flows are neither instantaneous nor guaranteed. We need to keep this in mind as we begin to apply finance
theory to real decisions. Future cash flows are uncertain in terms of both timing and size, and we refer to this
uncertainty as risk. Investors experience risk about the return of their capital. Companies experience risk in funding
and operating their business projects. Most financial decisions involve comparing the rewards of a decision to the
risks that decision may generate.
risk A potential future negative impact to value and/or cash flows. It is often discussed in terms of the probability of loss and the
expected magnitude of the loss.

page 10


Comparing rewards with risks frequently involves assessing the value today of cash flows that we expect to receive
in the future. For example, the price of a financial asset, something worth money, such as a stock or a bond, should
depend on the cash flows you expect to receive from that asset in the future. A stock that’s expected to deliver high
cash flows in the future will be more valuable today than a stock with low expected future cash flows. Of
course, investors would like to buy stocks whose market prices are currently lower than their actual values.
They want to get stocks on sale! Similarly, a firm’s goal is to fund projects that will give them more value than their
costs.
financial asset A general term for securities like stocks, bonds, and other assets that represent ownership in a cash flow.
FIGURE 1-6 Financial Management
Financial managers make decisions that should benefit both the company and the investor.
FIGURE 1-7 Financial Institutions and Markets

Financial institutions and markets facilitate the flows of money between investors and companies.
Financial assets are normally grouped into asset classes according to their risk and return characteristics. The most
commonly accepted groups of asset classes are stocks, bonds, money market instruments, real estate, and derivative
securities, all of which we will discuss in more detail later in the book. As the risk and return profiles of each of
these asset classes differ widely between classes, the mathematical models, terminology, and expertise of each class
tend to be very specialized and trading tends to happen in distinct, separate financial markets for each asset class.
asset classes A group of securities that exhibit similar characteristics, behave similarly in the marketplace, and are subject to the same
laws and regulations.
Despite the large number of stories about investors who’ve struck it rich in the stock market, it’s actually more
likely that a firm will find “bargain” projects, projects that may yield profit for a reasonable investment, than
investors will find underpriced stocks. Firms can find bargains because business projects involve real assets trading
in real markets (markets in tangible assets). In the real environment, some level of monopoly power, special
knowledge, and expertise possibly can make such projects worth more than they cost. Investors, however, are
trading financial assets in financial markets, where the assets are more likely to be worth, on average, exactly what
they cost.
real assets Physical property like gold, machinery, equipment, or real estate.
real markets The places and processes that facilitate the trading of real assets.
The method for relating expected or future cash flows to today’s value, called present value, is known as time value of
money (TVM). Chapters 4 and 5 cover this critical financial concept in detail and apply it to the financial world (as
well as daily life). Since the expected cash flows of either a business project or an investment are likely to be
uncertain, any TVM analysis must account for both the timing and the risk level of the cash flows.
time value of money (TVM) The theory and application of valuing cash flows at various points in time.

page 11

Risk tolerance varies among individuals.
©Purestock/Superstock
Finance versus Accounting
In most companies, the financial function is usually closely associated with the accounting function. In a very rough
sense, the accountant’s job is to keep track of what happened in the past to the firm’s money, while the finance job
uses these historical figures with current information to determine what should happen now and in the
future with the firm’s money. The results of financial decisions will eventually appear in accounting
statements, so this close association makes sense. Nevertheless, accounting tends to focus on and characterize the
past, while finance focuses on the present and future.
FIGURE 1-8 International Finance

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Laws, risks, and business relationships are variable across different countries but can interact profitably.
time out!
1-1 What are the main subareas of finance and how do they interact?
1.2 • THE FINANCIAL FUNCTION LG1-2
As we said previously, this text focuses primarily on financial management, so we will discuss the particular
functions and responsibilities of the firm’s financial manager. We will also explain how the financial function fits in
and interacts with the other areas of the firm. Finally, to make this study as interesting and as relevant as possible,
we will make the connections that allow you to see how the concepts covered in this book are important in your own
personal finances.
The Financial Manager
The firm’s highest-level financial manager is usually the chief financial officer, or CFO. Both the company treasurer
and the controller report to the CFO. The treasurer is typically responsible for
Managing cash and credit.
Issuing and repurchasing financial securities such as stocks and bonds.
Deciding how and when to spend capital for new and existing projects.
Hedging (reducing the firm’s potential risk) against changes in foreign exchange and interest rates.
In larger corporations, the treasurer may also oversee other areas, such as purchasing insurance or managing the
firm’s pension fund investments. The controller oversees the accounting function, usually managing the tax, cost
accounting, financial accounting, and data processing functions.
Finance in Other Business Functions
Although the CFO and treasurer positions tend to be the firm’s most visible finance-related positions, finance affects
the firm in many ways and throughout all levels of a company’s organizational chart. Finance permeates the
entire business organization, providing guidance for both strategic and day-to-day decisions of the firm and
collecting information for control and feedback about the firm’s financial decisions.

EXAMPLE
1-1 Finance Applications LG1-3
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
Chloe realizes how important finance will be for her future business career.
However, some of the ways that she will see financial applications seem way
off in the future. She is curious about how the theory applies to her personal
life, both in the near term and in the long term.
SOLUTION:
Chloe will quickly find that her financial health now and in the future will
depend upon many decisions she makes as she goes through life—starting
now! For example, she will learn that the same tools that she applies to a
business loan analysis can be applied to her own personal debt. After this
course, Chloe will be able to evaluate credit card offers and select one that
could save her hundreds of dollars per year. When she buys a new car and
the dealership offers her a low-interest-rate loan or a higher-rate loan with
cash back, she will be able to pick the option that will truly cost her the least.
Also, when Chloe gets her first professional job, she will know how to direct
her retirement account so that she can earn millions of dollars for her future.
(Of course, inflation between now and when she retires will imply that Chloe’s
millions won’t be worth as much as they would today.)
Operational managers use finance daily to determine how much overtime labor to use, or to perform cost/benefit
analysis when they consider new production lines or methods. Marketing managers use finance to assess the cost
effectiveness of doing follow-up marketing surveys. Human resource managers use finance to evaluate the
company’s cost for various employee benefit packages. No matter where you work in business, finance can help you
do your job better.
Finance in Your Personal Life LG1-3
Finance can help you make good financial decisions in your personal life. Consider these common activities you
will probably face in your life:
Borrowing money to buy a new car.
Refinancing your home mortgage at a lower rate.
Making credit card or student loan payments.
Saving for retirement.
You will be able to perform all of these tasks better after learning about finance. Recent changes throughout our
economy and the U.S. business environment make knowledge of finance even more valuable to you than before. For
example, most companies have switched from providing defined benefit retirement plans to employees to offering
defined contribution plans (such as 401k plans) and self-funded plans like Individual Retirement Accounts (IRAs). Tax
changes in the early 1980s made this switch more or less inevitable. It appears that each of us will have to ensure
adequate funds for our own retirement—much more so than previous generations.
defined benefit plan A retirement plan in which the employer funds a pension generally based on each employee’s years of service and
salary.
defined contribution plan A retirement plan in which the employee contributes money and directs its investment. The amount of
retirement benefits are directly related to the amount of money contributed and the success of its investment.
401k plan A defined contribution plan that is sponsored by corporate employers.
Individual Retirement Account (IRA) A self-sponsored retirement program.

http://mhhe.com/CornettM4e

page 13
time out!
1-2 How might the application of finance improve your professional and personal decisions?
1.3 • BUSINESS ORGANIZATION LG1-4
In the United States, people can structure businesses in any of several ways; the number of owners is the key to how
business structures are classified. Traditionally, single owners, partners, and corporations operate businesses. We
can express the advantages and disadvantages of each organizational form through several dimensions:
Who controls the firm.
Who owns the firm.
What are the owners’ risks.
What access to capital exists.
What are the tax ramifications.
Recently, small businesses have adopted hybrid structures that capture the benefits from multiple organizational
forms. We’ll discuss those hybrid structures after we cover the more common, traditional types of business
organizations.
Sole Proprietorships
The sole proprietorship represents, by far, the most common type of business in the United States.1 A sole
proprietorship is defined as any unincorporated business owned by a single individual.2 Perhaps these businesses are
so popular because they are relatively easy to start, and they’re subject to a much lighter regulatory and paperwork
burden than other business forms. The owner, or sole proprietor, of the business has complete control of the firm’s
activities. The owner also receives all of the firm’s profits and is solely responsible for all losses.
sole proprietorship A business entity that is not legally separate from its owner.

page 14
Venture capital helped Starbucks become a success story.
©McGraw-Hill Education/Jon Flournoy, photographer
The biggest disadvantage that sole proprietorships carry relative to other organizational forms is that they have
unlimited liability for their companies’ debts and actions. The owner’s personal assets may be confiscated if the
business fails. The law recognizes no distinction between the owner’s business assets and personal assets. The
income of the business is also added to the owner’s personal income and taxed by the government at the appropriate
personal tax rate. Finally, sole proprietors have a difficult time obtaining capital to expand their business operations.
Banks and other lenders are not typically interested in lending much money to sole proprietors because small firms
have only one person liable for paying back the debt. A sole proprietor could raise capital by issuing equity to
another investor. Angel investors and venture capitalists exchange capital for ownership in a business. But this requires
re-forming the business as a partnership and the sole proprietor must give up some of the ownership (and thus
control) of the firm. Table 1.1 summarizes sole proprietorships’ characteristics, along with those of the three other
business organizations we will study.
unlimited liability A situation in which a person’s personal assets are at risk from a business liability.
equity An ownership interest in a business enterprise.
angel investors Individuals who provide small amounts of capital and expert business advice to small firms in exchange for an
ownership stake in the firm.
venture capitalists Similar to angel investors except that they are organized as groups of investors and can provide larger amounts of
capital.
Partnerships
A general partnership, or as it is more commonly known, a partnership, is an organizational form that features
multiple individual owners. Each partner can own a different percentage of the firm. Firm control is typically
determined by the size of partners’ ownership stakes. Business profits are split among the partners according to a
prearranged agreement, usually by the percentage of firm ownership. Received profits are added to each
partner’s personal income and taxed at personal income tax rates.
general partnership A form of business organization where the partners own the business together and are personally liable for legal
actions and debts of the firm.
▼ TABLE 1.1 Characteristics of Business Organization
Ownership Control Ownership Risk
Access
to
Capital Taxes
Sole
Proprietor Single individual Proprietor Unlimited liability Very limited Paid by owner
Partnership Multiple people Shared by
partners
Unlimited liability Limited Paid by partners
Corporation
Public investors
who own the
stock
Company
managers
Stockholders can only
lose their investment in
the firm
Easy access
Corporation pays income tax and
stockholders pay taxes on
dividends
Hybrids: S-
corp, LLP,
LLC, LP
Partners or
shareholders Shared Mostly limited
Limited by
firm size
restrictions
Paid by partners or shareholders
finance at work //: corporate
More Beer

page 15
©Steven Cukrov/123RF
In November 2015, Anheuser-Busch InBev NV agreed to buy SABMiller for $107 billion. AB InBev produces the popular beer brands
Budweiser, Corona, Stella Artois, Beck’s, Hoegaarden, and Leffe. SABMiller is known for Miller, Foster’s, and Grolsch, among others.
These are the two largest brewing companies in the world. The combined firm would produce nearly a third of the beer worldwide.
InBev will pay 44 pounds sterling (nearly $63) in cash per share for a majority of SABMiller shares. This is a 50 percent increase, or
premium, over the market price of SABMiller stock. This proposed merger raises many interesting finance questions. For example, why
does InBev believe that SABMiller should be valued at least 50 percent more than the market does? Why are they paying cash for the
shares instead of exchanging their stock for SABMiller stock? What are the business opportunities and cost-cutting cash flows of the
combined firm that are not available as separate firms?
This book describes the theories and tools needed to make these judgments. The practice of finance isn’t just about numbers, it’s
about real valuation and cash flow—the results of the financial analysis are very dynamic and exciting!
This proposed merger will have significant hurdles to overcome in order to be completed. Governments regulate mergers to ensure
competition in consumer markets. For example, in many regions of the United States, Budweiser and Miller together make up a high
percentage of the market. Thus, if one firm owned both brands, a near monopoly would occur. The U.S. regulatory system would not
allow that. So to prevent this objection, SABMiller is selling its stake in this brand to Molson Coors Brewing for $12 billion. Other
countries may have similar concerns. This proposed mega merger may take an entire year to gain the needed regulatory approval
around the world.
Want to know more?
Key Words to Search for Updates: InBev, SABMiller, beer
The partners jointly share unlimited personal liability for the debts of the firm and all are obligated for contracts
agreed to by any one of the partners. Banks are more willing to lend to partnerships than to sole proprietorships,
because all partners are liable for repaying the debt. Partners would have to give up some ownership and control in
the firm to raise more equity capital. In order to raise enough capital for substantial growth, a partnership often
changes into a public corporation.
Corporations
A public corporation is a legally independent entity entirely separate from its owners. This independence dramatically
alters the firm’s characteristics. Corporations hold many rights and obligations of individual persons, such as the
ability to own property, sign binding contracts, and pay taxes. Federal and state governments tax corporate
income once at the corporate level. Then shareholders pay taxes again at the personal level when corporate

profits are paid out as dividends. This practice is generally known as double taxation.
public corporation A company owned by a large number of stockholders from the general public.
double taxation A situation in which two taxes must be paid on the same income.
Corporate owners are stockholders, also called shareholders. Public corporations typically have thousands of
stockholders. The firm must hire managers to direct the firm, since thousands of individual shareholders could not
direct day-to-day operations under any sort of consensus. As a result, managers control the company. Strong
possibilities of conflicts of interests arise when one group of people owns the business, but another group controls it.
We’ll discuss conflicts of interest and their resolution later in the chapter.
As individual legal entities, corporations assume liability for their own debts, so the shareholders have only limited
liability. That is, corporate shareholders cannot lose more money than they originally paid for their shares of stock.
This limited liability is one reason that many people feel comfortable owning stock. Corporations are thus able to
raise incredible amounts of money by selling stock (equity) and borrowing money. The largest businesses in the
world are organized as corporations.
limited liability Limitation of a person’s financial liability to a fixed sum or investment.
Hybrid Organizations
To promote the growth of small businesses, the U.S. government allows for several types of business organizations
that simultaneously offer limited personal liability for the owners and provide a pass-through of all firm earnings to
the owners, so that the earnings are subject only to single taxation.
Hybrid organizations offer single taxation and limited liability to all owners. Examples are S corporations, limited
liability partnerships (LLPs), and limited liability companies (LLCs). Others, called limited partnerships (LPs), offer
single taxation and limited liability to the limited partners, but also have general partners, who benefit from single
taxation but also must bear personal liability for the firm’s debts.
hybrid organizations Business forms that have some attributes of corporations and some of proprietorships/partnerships.
The U.S. government typically restricts hybrid organization status to relatively small firms. The government limits
the maximum number of shareholders or partners involved,3 the maximum amount of investment capital allowed,
and the lines of business permitted. These restrictions are consistent with the government’s stated reason for
allowing the formation of these forms of business organization—to encourage the formation and growth of small
businesses.
time out!
1-3 Why must an entrepreneur give up some control of the business as it grows into a public corporation?
1-4 What advantages does the corporate form of organization hold over a partnership?
1.4 • FIRM GOALS LG1-5
Tens of thousands of public corporations operate in the United States. Many of them are the largest business
organizations in the world. Because U.S. corporations are so large and because there are so many of them,
corporations have a tremendous impact on society. Given the power that these huge firms wield, many people
question what the corporate goals should be. Two different, well-developed viewpoints have arisen concerning what
the goal of the firm should be. The owners’ perspective holds that the only appropriate goal is to maximize shareholder
wealth. The competing viewpoint is from the stakeholders’ perspective, which emphasizes social responsibility over

page 16
profitability. This view maintains that managers must maximize the total satisfaction of all stakeholders in a
business. These stakeholders include the owners and shareholders, but also include the business’s customers,
employees, and local communities.
maximization of shareholder wealth A view that management should first and foremost consider the interests of shareholders in its
business decisions.
stakeholder A person or organization that has a legitimate interest in a corporation.
While strong arguments speak in favor of both perspectives, financial practitioners and academics now tend to
believe that the manager’s primary responsibility should be to maximize shareholder wealth and give only secondary
consideration to other stakeholders’ welfare. One of the first, and most well known, proponents of this
viewpoint was Adam Smith, an 18th-century economist who argued that, in capitalism, an individual
pursuing his own interests tends also to promote the good of his community.4
Smith argued that the invisible hand of the market, acting through competition and the free price system, would
ensure that only those activities most efficient and beneficial to society as a whole would survive in the long run.
Thus, those same activities would also profit the individual most. When companies try to implement a goal other
than profit maximization, their efforts tend to backfire. Consider the firm that tries to maximize employment. The
high number of employees raises costs. Soon the firm will find that its costs are too high to allow it to compete
against more efficient firms, especially in a global business environment. When the firm fails, all employees are let
go and employment ends up being minimized, not maximized.
invisible hand A metaphor used to illustrate how an individual pursuing his own interests also tends to promote the good of the
community.
Regardless of whether you believe Smith’s assertion or not, a more pragmatic reason supports the argument that
maximizing owners’ wealth is an admirable goal. As we will discuss, the owners of the firm hire managers to work
on their behalf, so the manager is morally, ethically, and legally required to act in the owners’ best interests. Any
relationships between the manager and other firm stakeholders are necessarily secondary to the goal that
shareholders give to their hired managers.
Maximizing owners’ equity value means carefully considering
How best to bring additional funds into the firm.
Which projects to invest in.
How best to return the profits from those projects to the owners over time.
For corporations, maximizing the value of owners’ equity can also be stated as maximizing the current value per
share, or stock price, of existing shares. To the extent that the current stock price can be expected to include the
present value of any future expected cash flows accruing to the owners, the goal of maximizing stock price provides
us with a single, concrete, measurable gauge of value. You may be tempted to choose several other potential goals
over maximizing the value of owners’ equity. Common alternatives are
Maximizing net income or profit.
Minimizing costs.
Maximizing market share.
Although these may look appealing, each of these goals has some potentially serious shortcomings. For example, net
income is measured on a year-by-year or quarter-by-quarter basis. When we say that we want to maximize profits, to
which net income figure are we referring? We can maximize this year’s net income in several legitimate ways, but
many of these ways impose costs that will reduce future income. Or, current net income can be pushed into future
years. Neither of these two extremes will likely encourage the firm’s short-term and long-term stability. One more
likely goal would be to maximize today’s value of all future years of net income. Of course, this possible goal is
very close to maximizing the current stock price, without the convenient market-oriented measure of the stock price.
Another problem with considering maximizing all future profits as the goal is that net income (for reasons we’ll go
into later) does not really measure how much money the firm is actually earning.

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time out!
1-5 Describe why the primary objective of maximizing shareholder value may actually be the most beneficial for society in the
long run.
Minimizing costs and maximizing market share also have fundamental problems as potential goals. Certainly
minimizing costs would not make some stakeholders, such as employees, very happy. In addition, without spending
the money on R&D and new product development, many companies would not survive long in the ever-evolving
economy without improving their products. A firm can always increase market share by lowering price. But if a firm
loses money on every product sold, then selling more products will simply drive the firm into fiscal distress.

1.5 • AGENCY THEORY LG1-6
Whenever one party (the principal) hires someone else (the agent) to work for him or her, their interaction is called
an agency relationship. The agent is always supposed to act in the principal’s best interests. For example, an
apartment complex manager should ensure that tenants aren’t doing willful damage to the property, that fire codes
are enforced, and that the vacancy rate is kept as low as possible, because these are best for the apartment owner.
Agency Problem
In the context of a public corporation, we have already noted that stockholders hire managers to run the firm.
Ideally, managers will operate the firm so that the shareholders realize maximum value for their equity. But
managers may be tempted to operate the firm to serve their own best interests. Managers could spend company
money to improve their own lifestyle instead of earning more profits for shareholders. Sometimes the manager’s
best interest does not necessarily align with shareholder goals. This creates a situation that we refer to as the agency
problem.
Perks can range from extra vacation to private transportation.
©Digital Vision/Getty Images
agency problem The difficulties that arise when a principal hires an agent and cannot fully monitor the agent’s actions.
For example, suppose it is time to buy a new corporate car for the firm’s chief executive officer (CEO). Assuming that
the CEO has no extraordinary driving requirements, shareholders might wish for the CEO to buy a nice,
conservative domestic sedan. But suppose that the CEO demands the newest, biggest luxury car available. It’s

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tempting to say that the shareholders could just tell the CEO which car to buy. But remember, the CEO has most of
the control in a public corporation. Organizational behavior specialists have identified three basic approaches to
minimize this conflict of interest. First, ignore it. If the amount of money involved is small enough relative to the
firm’s cash flows, or if the suitability of the purchase in question is ambiguous enough, shareholders might be best
served to simply overlook the problem. A good deal of research literature suggests that allowing the manager a
certain amount of such perks (perquisites) might actually enhance owner value, in that such items may boost
managers’ productivity.5
chief executive officer (CEO) The highest-ranking corporate manager.
perks/perquisites Nonwage compensation, often in the form of company car, golf club membership, etc.
The second approach to mitigating this conflict is to monitor managers’ actions. Monitoring at too fine a level of
detail is probably counterproductive and prohibitively expensive. However, major firm decisions are usually
monitored at least roughly through the accounting auditing process.
In addition, concentrated ownership in the firm by large stakeholders such as financial institutions, investment
companies, individual block holders, or debt holders give those large stakeholders increased incentives to monitor
the activities of management. These incentives are often driven by both economies of scale in monitoring and by the
claim of the stakeholder having a different risk/return profile than the claim of other stakeholders.
economies of scale Cost advantages when fixed costs are spread over a large number of units.
To see the impact of economies of scale in monitoring costs, consider a simple example: Suppose that it costs $3
each way (i.e., $6 round-trip) for a shareholder in a firm to hop on the subway and ride down to the firm’s offices in
order to go through the firm’s financial statements, and that the most savings to shareholders that could possibly
result from this monitoring would be $5 per share. Would anyone owning a single share ever take the ride to check
up on the firm? No, because it would cost a certain $6 in order to save a possible $5. However, someone owning 100
shares in the firm would find it worthwhile to pay for the subway ride, assuming that the chance of saving $5 × 100
= $500 is large enough.
To envision the effect of one stakeholder having a different claim than others, consider the position of a bondholder
in a firm where there isn’t much free cash flow in the firm above and beyond that which is needed to make the
interest payments on her bond. If the manager of the firm is going to spend an extra $20,000 to buy an
unnecessarily luxurious company car, that $20,000 is very likely to come out of the bondholder’s pocket, so
she will definitely have a heightened incentive to monitor the manager’s company car purchase. On the other hand,
if the firm had so much free cash flow available that the expenditure of the extra $20,000 is unlikely to affect the
payment of the bond interest, then the bondholder would have much less incentive to monitor.6
The final approach for aligning managers’ personal interests with those of owners is to make the managers owners—
that is, to offer managers an equity stake in the firm so that management participates in any equity value increase.
Many corporations take this approach, either through explicitly granting shares to managers, by awarding them
options on the firm’s stock, or by allowing them to purchase shares at a subsidized price through an employee stock
option plan (ESOP). When firm managers are also firm owners, their incentives are more likely to align with
stockholders’ best interests.
option The opportunity to buy stock at a fixed price over a specific period of time.
employee stock option plan (ESOP) An incentive program that grants options to employees (typically managers) as compensation.
Corporate Governance
We refer to the process of monitoring managers and aligning their incentives with shareholder goals as corporate
governance. Theoretically, managers work for shareholders. In reality, because shareholders are usually inactive, the
firm actually seems to belong to management. Generally speaking, the investing public does not know what goes on
at the firm’s operational level. Managers handle day-to-day operations, and they know that their work is mostly
unknown to investors. This lack of supervision demonstrates the need for monitors. Figure 1.9 shows the people and
organizations that help monitor corporate activities.


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corporate governance The set of laws, policies, incentives, and monitors designed to handle the issues arising from the separation of
ownership and control.
FIGURE 1-9 Corporate Governance Monitors
Corporate governance balances the needs of stockholders and managers. Inside the public firm, the members of the board of directors
monitor how the firm is run. Outside the firm, auditors, analysts, investment banks, and credit rating agencies act as monitors.

EXAMPLE
1-2 Executive Compensation LG1-6
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
In 2014, the largest 350 firms in terms of sales paid their CEOs, on average,
$16.3 million—a 3.9 percent increase over the previous year and a 54.3
percent increase since the end of the financial crisis in 2009. The average
CEO compensation was 303 times the average employee’s compensation.
Every year, the controversy over CEO pay arises again. What arguments
could be made for each side?
SOLUTION:
Many people believe that CEOs are paid too much for the services they
provide. They receive compensation that is far higher than workers’ pay within
their firms. Over the years, executive compensation has also increased at a
faster rate than has the value of the stockholders’ wealth. For example, the

http://mhhe.com/CornettM4e

Economic Policy Institute reports that after adjusting for inflation, CEO pay
increased nearly 1,000% between 1978 and 2014. As a comparison, the
typical worker’s inflation adjusted pay increased less than 11 percent during
the same period. Each firm’s board of directors sets CEO compensation.
However, CEOs may have undue influence over director selection, tenure,
and committee assignments—even over selecting the compensation advisors.
This practice creates an unhealthy conflict of interest.
Others believe that a skilled CEO can positively affect company performance
and that, therefore, the firm needs to offer high compensation and a bundle of
perquisites to attract the best talent. To overcome agency problems,
managers must be given incentives that pay very well when the company
performs very well. If CEOs create a substantial amount of shareholder
wealth, then who is to say that they are overpaid?
The monitors inside a public firm are the board of directors, who are appointed to represent shareholders’ interests.
The board hires the CEO, evaluates management, and can also design compensation contracts to tie management’s
salaries to firm performance.
board of directors The group of directors elected by stockholders to oversee management in a corporation.
The monitors outside the firm include auditors, analysts, investment banks, and credit rating agencies. Auditors
examine the firm’s accounting systems and comment on whether financial statements fairly represent the firm’s
financial position. Investment analysts follow a firm, conduct their own evaluations of the company’s business
activities, and report to the investment community. Investment banks, which help firms access capital markets and
advise managers about how to interact with those capital markets, also monitor firm performance. Credit analysts
examine a firm’s financial strength for its debt holders. The government also monitors business activities through
the Securities and Exchange Commission (SEC) and the Internal Revenue Service (IRS).
auditor A person who performs an independent assessment of the fairness of a firm’s financial statements.
investment analyst A person who analyzes a company’s business prospects and gives opinions about its future success.
investment banks Banks that help companies and governments raise capital.
credit analyst A person who analyzes a company’s ability to repay its debts and reports the findings as a grade.
The Role of Ethics LG1-7
Ethics must play a strong role in any practice of finance. Finance professionals commonly manage other people’s
money. For example, corporate managers control the stockholder’s firm, bank employees manage deposits, and
investment advisors manage people’s investment portfolios. These fiduciary relationships create tempting
opportunities for finance professionals to make decisions that either benefit the client or benefit the advisors
themselves. Professional associations (such as for treasurers, bank executives, investment professionals, etc.) place a
strong emphasis on ethical behavior and provide ethics training and standards. Nevertheless, as with any profession
with millions of practitioners, a few are bound to act unethically.
ethics The study of values, morals, and morality.
fiduciary A legal duty between two parties where one party must act in the interest of the other party.
The agency relationship between corporate managers and stockholders can create ethical dilemmas. Sometimes the
corporate governance system has failed to prevent unethical managers from stealing from firms, which ultimately
means stealing from shareholders. Governments all over the world have passed laws and regulations meant to ensure
compliance with ethical codes of behavior.7 And if professionals don’t act appropriately, governments have set up
strong punishments for financial malfeasance. In the end, financial managers must realize that they not only owe
their shareholders the very best decisions to further shareholder interests, but they also have a broader obligation to
society as a whole.

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finance at work //: corporate
The Amazing Story of Apple Inc. and Steve Jobs
©McGraw-Hill Education/Christopher Kerrigan, photographer
Steven Jobs and Stephen Wozniak started Apple Computer in 1976 as an equal partnership. Together, they built 50 computers in a
garage using money borrowed from family, the proceeds from the sale of a VW bus, and credit from the parts distributor.
Jobs and Wozniak then designed the Apple II computer. But a higher production level to make more than 50 computers required
more space and employees. They needed much more capital. They could not get a loan until angel investor Mike Markkula (an Intel
executive) became a partner in the firm. He invested $92,000 and his personal guarantee induced a bank to loan Apple $250,000. As
production ramped up in 1977, Apple Computer incorporated. Most shares were owned by Jobs, Wozniak, and Markkula, but the
principals made some shares available to employees. They also hired an experienced manager (Mike Scott) to be the CEO and run the
firm. Note that as the firm expanded, Jobs’s ownership level and control got diluted. By 1980, Apple Computer had sold a total of
121,000 computers—against a potential demand of millions more. Apple needed even more capital.
At the end of 1980, Apple became a public corporation and sold $65 million worth of stock to public investors. Steve Jobs, cofounder
of Apple, still owned more shares than anyone else (7.5 million), but he owned less than half of the firm. He gave up a great deal of
ownership to new investors in exchange for the capital to expand the firm. Unhappy with Mike Scott’s leadership, Steve Jobs also
became CEO of Apple.
After a couple of years, Apple’s board of directors felt that Jobs was not experienced enough to steer the firm through its rapid
expansion. They hired John Sculley as CEO in 1983. In 1985, a power struggle ensued for control of the firm, and the board backed
Sculley over Jobs. Jobs was forced out of Apple and no longer had a say in business operations, even though he was the largest
shareholder and an original cofounder of the firm.
So, Steve Jobs bought Pixar in 1986 for $5 million and founded NeXT Computer. Over the next 10 years, Jobs’s Pixar produced
mega hit movies like Toy Story, A Bug’s Life, and Monsters, Inc. This time, he kept 53 percent ownership of Pixar to ensure keeping full
control. In the meantime, Apple Computer began to struggle, with losses of $800 million in 1996 and $1 billion in 1997. To get Steve
Jobs back into the firm, Apple bought NeXT for $400 million and hired him as Apple’s CEO. Over the next few years, Jobs introduced the
iMac, iPod, and iTunes, and Apple became very profitable again! Jobs was given the use of a $90 million Gulfstream jet as a perk. To
realign his incentives, he became an Apple owner again via compensation that included options on 10 million shares of stock and 30
million shares of restricted stock. Then in 2006, Disney bought Pixar by swapping $7.4 billion worth of Disney stock for Pixar stock.
When the deal closed, Steve Jobs became the largest owner of Disney stock (7 percent) and joined Disney’s board of directors.
Wow! What a story of accessing capital, business organizational form, company control, and corporate governance.
Want to know more?
Key Words to Search for Updates: Steve Jobs, Apple Computer, Pixar
restricted stock A special type of stock that is not transferable from the current holder to others until specific conditions are satisfied.


1.6 • FINANCIAL MARKETS, INTERMEDIARIES, AND THE
FIRM LG1-8
Astute readers will note that our emphasis on the role of financial markets and intermediaries grew throughout this
chapter. This emphasis is intentional, as we feel that you must understand the role and impact of these institutions on
the firm if you are to grasp the context in which professionals make financial management decisions.
time out!
1-6 What unethical activities might managers engage in because of the agency problem?
1-7 Explain how the corporate governance system reduces the agency problem.
We want to emphasize one other important point about these financial institutions (FI). Very astute readers may
wonder how, if financial markets are competitive, investment banks and other financial institutions are able to make
such impressive profits. Although FIs assist others with transactions involving financial assets in the financial
markets, they do so as paid services. Successful execution of those services takes unique assets and expertise. As
shown in Figure 1.10, it’s the use of those unique assets and expertise that provides financial institutions with their
high profit margins.
1.7 • BIG PICTURE ENVIRONMENT LG1-9
The business world is constantly changing. Companies must constantly adapt in order to succeed. These changes
and adaptations include the field of finance. For example, when interest rates increase in an economy, then the cost
of capital increases for companies. This could make some projects that were worthy of corporate investment become
too costly. In other words, changes in interest rates directly lead to changes in the amount of expansion projects
taken on by companies. Similarly, changes in currency exchange rates between countries directly impact the
attractiveness of expansion into foreign markets. Therefore, while managers often direct most of their focus to their
own firms, it is useful to keep an eye on the big picture.
time out!
1-8 What is the role of financial institutions in a capitalist economy?
Oil Prices Plummet
In early 2009, the price of oil was around $40 per barrel. During the next two years, that price more than doubled to
over $100. It then hovered near $100 into 2014. The steady high price of oil caused much investment in oil
exploration and production in the United States and around the world. The oil that is easy and cheap to pump out of
the ground has already been found. New wells are expensive due to their location (under the Arctic Ocean) or the
status of the oil (trapped in shale deposits).
FIGURE 1-10 Financial Institutions’ Cash Flows

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The unique services and products that financial institutions provide allow them to make money.
Because of these high oil prices, new technologies were created to find and develop new oil wells. One example is
the procedure to extract oil from shale formations, called fracking. A company might estimate that the cost of
finding and drilling a new oil well using fracking is $60 per barrel. This is significantly lower than the many
years of oil priced at $100 per barrel and has therefore caused much activity in the oil industry. Between
2010 and 2015, U.S. oil production increased from 5.6 million barrels a day to 9.3 million barrels in 2015. This was
a huge boon for the economy and added jobs in states from North Dakota to Texas. This characterizes one of the key
financial concepts presented in this book—capital budgeting. Specifically, how firms define different new projects,
decide which ones are worthy of investment, and determine how to finance them.
Similarly, increases in production occurred all over the world. Simple supply and demand economics forecasts that
large increases in supply cause prices to fall. And boy did they! Starting in mid-2014, oil prices fell to $50 in only
six months. By the end of 2015, oil prices were below $30. There is a saying that “a decline in oil prices is like a tax
cut.” This comes from the idea that consumers pay much less on gas for their cars and can spend that money
elsewhere. It is meant to describe a positive event for the overall U.S. economy. But times have changed.
The U.S. no longer imports most of its oil. It was nice when foreign oil producers paid for U.S. consumer savings.
But now, the U.S. produces most of its own oil demand needs. Any savings by consumers at the pump are lost
income to the U.S. oil industry. Oil producing areas of the U.S. are experiencing slowing economies and job losses.
So oil price changes may no longer have net impacts on the U.S. economy overall. But oil companies are affected.
The stock prices of oil companies are way down. Some small oil companies have declared bankruptcy and defaulted
on their bonds and other debts. This will, in turn, impact the banks, mutual funds, pension funds, and other investors
that own these securities.
China Slows Down
For the last two decades, China was the growth engine for the global economy. It went from a minor player in
international trade to the second largest economy in the world, largely through exporting goods to the more
developed markets like the United States and Europe. Chinese production included economic interaction with
nearby countries like Vietnam and Laos. This development included hundreds of millions of rural Chinese moving
to the economic city centers. An enormous amount of infrastructure was built: roads, trains, housing, hydroelectric
dams, and so on. This required massive quantities of basic materials and energy, which China imported from places

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like Australia, Russia, and several African countries. A new Chinese middle class was created. These newly affluent
people want the same material luxuries and services as others around the world. China is trying to increase its
service-based industries to satisfy this new demand. However, this aspect of China’s growth will not create many
international trade opportunities.
Although China’s economy is expected to grow, that growth seems to be slowing down. This will have many
implications throughout the global economy. For example, those companies that produce basic materials such as
steel, iron ore, and copper will see a lower demand than expected. Indeed, we have already seen falling commodity
prices. Of course, this lower commodity cost is good for companies that use these basic materials in their own
products.
The more interesting impacts of the slowdown occur in the second order dynamics. For example, the real estate
market in Sydney, Australia, has declined as a result of China needing less of the basic materials that Australia
produces. However, some capital is leaving China in search of better investment opportunities. Some of the money
is going to Manhattan, New York, which has seen a spike in real estate prices. This shifting global environment will
create new winners and losers all over the world. How companies react and plan for these changes will determine
their level of success or failure.

Get Online
©JGI/ Jamie Grill/ Blend Images LLC.
Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…

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Questions
1. Describe the type of people who use the financial markets. (LG1-1)
2. What is the purpose of financial management? Describe the kinds of activities that financial management
involves. (LG1-1)
3. What is the difference in perspective between finance and accounting? (LG1-2)
4. What personal decisions can you think of that will benefit from your learning finance? (LG1-3)
5. What are the three basic forms of business ownership? What are the advantages and disadvantages to each?
(LG1-4)
6. Among the three basic forms of business ownership, describe the ability of each form to access capital. (LG1-4)
7. Explain how the founder of a business can eventually lose control of the firm. How can the founder ensure this
will not happen? (LG1-4)
8. Explain the shareholder wealth maximization goal of the firm and how it can be measured. Make an argument
for why it is a better goal than maximizing profit. (LG1-5)
9. Name and describe as many corporate stakeholders as you can. (LG1-5)
10. What conflicts of interest can arise between managers and stockholders? (LG1-6)
11. Figure 1.9 shows firm monitors. In your opinion, which group is in the best position to monitor the
firm? Explain. Which group has the potential to be the weakest monitor? Explain. (LG1-6)
12. In recent years, governments all over the world have passed laws that increased the penalties for executives’
crimes. Do you think this will deter unethical corporate managers? Explain. (LG1-6)
13. Every year, the media report on the vast amounts of money (sometimes hundreds of millions of dollars) that
some CEOs earn from the companies they manage. Are these CEOs worth it? Give examples. (LG1-6)
14. Why is ethical behavior so important in the field of finance? (LG1-7)
15. Does the goal of shareholder wealth maximization conflict with behaving ethically? Explain. (LG1-7)
16. Describe how financial institutions and markets facilitate the expansion of a company’s business. (LG1-8)

Notes
CHAPTER 1
1. According to the Small Business Administration, over 70 percent of all businesses in the U.S. were sole proprietorships.
2. However, if you are the sole member of a domestic limited liability company (LLC, discussed below), you are not a sole proprietor if you
elect to treat the LLC as a corporation.
3. For example, current federal regulations limit the number of shareholders in an S corporation to no more than 100.
4. See Book IV of his The Wealth of Nations.
5. See, for example, Raghuram Rajan and Julie Wulf, “Are Perks Really Managerial Excess?” Journal of Financial Economics 79(1),
2006, 1–33.
6. In case you are wondering why the stockholders—who would be the eventual recipients of such “extra” free cash flow—wouldn’t then
have increased incentives to monitor, they would. But, considering that the typical bond sells for $1,000 or more while the typical share
of stock sells for much less, and taking into account that bond ownership tends to be much more concentrated than stock ownership in
many firms, ask yourself whether bondholders or stockholders are more likely to enjoy economies of scale in monitoring.
7. The Sarbanes-Oxley Act of 2002 was passed in response to a number of recent major corporate accounting scandals including those
affecting Enron, Tyco International, and WorldCom. The goal of the act was to make the accounting and auditing procedures more
transparent and trustworthy.

Part Two

page 26
page 27

C
chapter two
reviewing
financial statements
©Photographer’s Choice/ Getty Images
orporate managers must issue many reports to the public. Most stockholders, analysts, government
entities, and other interested parties pay particular attention to annual reports. An annual report
provides four basic financial statements: the balance sheet, the income statement, the statement of
cash flows, and the statement of retained earnings. A financial statement provides an accounting-based
picture of a firm’s financial condition.
financial statement Statement that provides an accounting-based picture of a firm’s financial position.
Whereas accountants use reports to present a picture of what happened in the past, finance
professionals use financial statements to draw inferences about the future. The four statements function
to provide key information to managers, who make financial decisions, and to investors, who will accept
or reject possible future investments in the firm. When you encountered these four financial statements in
accounting classes, you learned how they function to place the right information in the right places. In this
chapter, you will see how understanding these statements, which are the “right places” for crucial
information, creates a solid base for your understanding of decision-making processes in managerial
finance.
Financial statements of publicly traded firms can be found in a number of places. For example, all
quarterly and annual financial statements can be found at a firm’s website (often under a section titled
“investor relations”). Financial statements of publicly traded companies are reported to the Securities and

page 28
Exchange Commission (SEC), who makes them publicly available at their website (www.sec.gov); annual
reports are listed under the term 10-K, and quarterly financial statements are listed as 10-Qs. Finally, a
number of websites exist (e.g., finance.yahoo.com) where one can view and download financial
statements of publicly traded companies. Nonpublic firms are not required to submit financial statements
to the SEC. Thus, it can be quite difficult to find detailed financial information about these
firms. This is one reason why some large firms (Cargill, Toys “R” Us, Fidelity) hesitate to
become publicly traded; they prefer to keep their financial statement information private.
LEARNING GOALS
LG2-1 Recall the major financial statements that firms must prepare and provide.
LG2-2 Differentiate between book (or accounting) value and market value.
LG2-3 Explain how taxes influence corporate managers’ and investors’ decisions.
LG2-4 Differentiate between accounting income and cash flows.
LG2-5 Demonstrate how to use a firm’s financial statements to calculate its cash flows.
LG2-6 Observe cautions that should be taken when examining financial statements.
viewpoints
business APPLICATION
The managers of DPH Tree Farm, Inc., believe the firm could double its sales if it had additional factory space and acreage. If DPH
purchased the factory space and acreage in 2019, these new assets would cost $27 million to build and would require an additional
$1 million in cash, $5 million in accounts receivable, $6 million in inventory, and $4 million in accounts payable. In addition to accounts
payable, DPH Tree Farm would finance the new assets with the sale of a combination of long-term debt (40 percent of the total) and
common stock (60 percent of the total). Assuming all else stays constant, what will these changes do to DPH Tree Farm’s 2019
balance sheet assets, liabilities, and equity? (See 2018 balance sheet in Table 2.1.) (See the solution at the end of the book.)
It should also be noted that this chapter presents a basic set of financial statements; enough so that,
from a financial manager’s viewpoint, we can identify the basic categories on each statement and
relationships across statements. Individual firms’ financial statements may look different from those
presented in the chapter, depending on the level of detail and accounting methods used. Further, financial
statements may be presented in various formats, e.g., in a pdf file or in an Excel spreadsheet.
Appendix 2A to the chapter (available online in Connect) presents the 2015 financial statements for
Colgate-Palmolive Company as listed in its Annual Report, in its 10-K statement, and in an Excel
spreadsheet. While the numbers are the same in all formats, the presentation of the numbers can vary
greatly.
This chapter examines each statement to clarify its major features and uses. We highlight the
differences between the accounting-based (book) value of a firm (reflected in these statements) and the
true market value of a firm, which we will come to understand more fully. We also make a clear distinction
between accounting-based income and actual cash flows, a topic further explored in Chapter 3, where we
see how important cash flows are to the study of finance.
We also open a discussion in this chapter about how firms choose to represent their earnings. We’ll
see that managers have substantial discretion in preparing their firms’ financial statements, depending on
strategic plans for the organization’s future. This is worth looking into as we keep the discipline of finance
grounded in a real-world context. Finally, leading into Chapter 3, we discuss some cautions to bear in
mind when reviewing and analyzing financial statements. ■
*See Appendix 2A: Various Formats for Financial Statements in Connect or online at mhhe.com/Cornett4e.

http://www.sec.gov

http://finance.yahoo.com

http://mhhe.com/Cornett4e

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2.1 • BALANCE SHEET LG2-1
The balance sheet reports a firm’s assets, liabilities, and equity at a particular point in time. It is a picture of the assets
the firm owns and who has claims on these assets as of a given date, for example, December 31, 2018. A firm’s
assets must equal (balance) the liabilities and equity used to purchase the assets (hence the term balance sheet):
balance sheet The financial statement that reports a firm’s assets, liabilities, and equity at a particular point in time.
(2-1)

personal APPLICATION
Chris Ryan is looking to invest in DPH Tree Farm, Inc. Chris has the most recent set of financial statements from DPH Tree Farm’s
annual report but is not sure how to read them or what they mean. What are the four financial statements that Chris should pay most
attention to? What information will these key financial statements contain? (See the solution at the end of the book.)
Thinking of starting your own business?
Figure 2.1 illustrates a basic balance sheet and Table 2.1 presents a simple balance sheet for DPH Tree Farm, Inc., as
of December 31, 2018 and 2017. The left side of the balance sheet lists assets of the firm and the right side lists
liabilities and equity. Both assets and liabilities are listed in descending order of liquidity, that is, the time and effort
needed to convert the accounts to cash. The most liquid assets—called current assets —appear first on the asset side
of the balance sheet. The least liquid, called fixed assets, appear last. Similarly, current liabilities—those obligations
that the firm must pay within a year—appear first on the right side of the balance sheet. Stockholders’ equity, which
never matures, appears last on the balance sheet.
liquidity The ease with which an asset can be converted into cash.
Assets
Figure 2.1 shows that assets fall into two major categories: current assets and fixed assets. Current assets will
normally convert to cash within one year. They include cash and marketable securities (short-term, low-rate
investment securities held by the firm for liquidity purposes), accounts receivable, and inventory. Fixed assets have a
useful life exceeding one year. This class of assets includes physical (tangible) assets, such as net plant and
equipment, and other, less tangible, long-term assets, such as patents and trademarks. We find the value of net plant
and equipment by taking the difference between gross plant and equipment (or the fixed assets’ original value) and
the depreciation accumulated against the fixed assets since their purchase.
current assets Assets that will normally convert to cash within one year.
marketable securities Short-term, low-rate investment securities held by the firm for liquidity purposes.
fixed assets Assets with a useful life exceeding one year.
Liabilities and Stockholders’ Equity
Lenders provide funds, which become liabilities, to the firm. Liabilities fall into two categories as well: current or
long-term. Current liabilities constitute the firm’s obligations due within one year, including accrued wages and taxes,
accounts payable, and notes payable. Long-term debt includes long-term loans and bonds with maturities of more than
one year.

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liabilities Funds provided by lenders to the firm.
current liabilities Obligations of the firm that are due within one year.
long-term debt Obligations of the firm that are due in more than one year.
The difference between total assets and total liabilities of a firm is the stockholders’ (or owners’) equity. The firm’s
preferred and common stock owners provide the funds known as stockholders’ equity. Preferred stock is a hybrid
security that has characteristics of both long-term debt and common stock. Preferred stock is similar to common
stock in that it represents an ownership interest in the issuing firm but, like long-term debt, it pays a fixed
periodic (dividend) payment. Preferred stock appears on the balance sheet as the cash proceeds when the
firm sells preferred stock in a public offering. Common stock and paid-in surplus is the fundamental ownership claim in
a public or private company. The proceeds from common stock and paid-in surplus appear as the other component
of stockholders’ equity. If the firm’s managers decide to reinvest cumulative earnings (recorded on the firm’s
income statement) rather than pay the dividends to stockholders, the balance sheet will record these funds as retained
earnings.
stockholders’ equity Funds provided by the firm’s preferred and common stock owners.
preferred stock A hybrid security that has characteristics of both long-term debt and common stock.
common stock and paid-in surplus The fundamental ownership claim in a public or private company.
retained earnings The portion of company profits that are kept by the company rather than distributed to the stockholders as cash
dividends.
FIGURE 2-1 The Basic Balance Sheet
Total Assets Total Liabilities and Equity
Current assets Current liabilities
Cash and marketable securities Accrued wages and taxes
Accounts receivable Accounts payable
Inventory Notes payable
Fixed assets Long-term debt
Gross plant and equipment Stockholders’ equity
Less: Accumulated depreciation Preferred stock
Net plant and equipment Common stock and paid-in surplus
Other long-term assets Retained earnings
Managing the Balance Sheet
Managers must monitor a number of issues underlying items reported on their firms’ balance sheets. We examine
these issues in detail throughout the text. In this chapter, we briefly introduce them. These issues include the
Accounting method for fixed asset depreciation.
Level of net working capital.
Liquidity position of the firm.
Method for financing the firm’s assets—equity or debt.
Difference between the book value reported on the balance sheet and the true market value of the firm.
Accounting Method for Fixed Asset Depreciation Managers can choose the accounting method they use to
record depreciation against their fixed assets. Recall from accounting that depreciation is the charge against income
that reflects the estimated dollar cost of the firm’s fixed assets. The straight-line method and the MACRS (modified
accelerated cost recovery system) are two choices. Companies commonly choose MACRS when computing the
firm’s taxes and the straight-line method when reporting income to the firm’s stockholders. The MACRS method
accelerates depreciation, which results in higher depreciation expenses and lower taxable income, thus lower taxes,
in the early years of a project’s life. Regardless of the depreciation method used, over time both the straight-line and
MACRS methods result in the same amount of depreciation and therefore tax (cash) outflows. However, because the
MACRS method defers the payment of taxes to later periods, firms often favor it over the straight-line method of

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depreciation. We discuss this choice further in Chapter 12.
Net Working Capital We arrive at a net working capital figure by taking the difference between a firm’s current
assets and current liabilities.
(2-2)
net working capital The difference between a firm’s current assets and current liabilities.
So, clearly, net working capital is positive when the firm has more current assets than current liabilities. Table 2.1
shows the 2018 and 2017 year-end balance sheets for DPH Tree Farm, Inc. At year-end 2018, the firm had $205
million of current assets and $123 million of current liabilities. So the firm’s net working capital was $82 million. A
firm needs cash and other liquid assets to pay its bills as expenses come due. As described in more detail in Chapter
14, liability holders monitor net working capital as a measure of a firm’s ability to pay its obligations. Positive net
working capital values are usually a sign of a healthy firm.
Liquidity As we noted previously, any firm needs cash and other liquid assets to pay its bills as debts come due.
Liquidity actually refers to two dimensions: the ease with which the firm can convert an asset to cash, and the degree
to which such a conversion takes place at a fair market value. You can convert any asset to cash quickly if you price
the asset low enough. But clearly, you will wish to convert the asset without giving up a great portion of its value.
So a highly liquid asset can be sold quickly at its fair market value. An illiquid asset, on the other hand, cannot be
sold quickly unless you reduce the price far below fair value.
Current assets, by definition, remain relatively liquid, including cash and assets that will convert to cash
within the next year. Inventory is the least liquid of the current assets. Fixed assets, then, remain relatively
illiquid. In the normal course of business, the firm would have no plans to liquefy or convert these tangible assets
such as buildings and equipment into cash.
Liquidity presents a double-edged sword on a balance sheet. The more liquid assets a firm holds, the less likely the
firm will be to experience financial distress. However, liquid assets generate little or no profits for a firm. For
example, cash is the most liquid of all assets, but it earns little, if any, for the firm. In contrast, fixed assets are
illiquid, but provide the means to generate revenue. Thus, managers must consider the trade-off between the
advantages of liquidity on the balance sheet and the disadvantages of having money sitting idle rather than
generating profits.
Debt versus Equity Financing You learned in your high school physics class that levers are very useful and
powerful machines—given a long enough lever, you can move almost anything. Financial leverage is likewise very
powerful. Leverage in the financial sense refers to the extent to which a firm chooses to finance its ventures or assets
by issuing debt securities. The more debt a firm issues as a percentage of its total assets, the greater its financial
leverage. We discuss in later chapters why financial leverage can greatly magnify the firm’s gains and losses for the
firm’s stockholders.
financial leverage The extent to which debt securities are used by a firm.
When a firm issues debt securities—usually bonds—to finance its activities and assets, debt holders usually demand
first claim to a fixed amount of the firm’s cash flows. Their claims are fixed because the firm must only pay the
interest owed to bondholders and any principal repayments that come due within any given period. Stockholders—
who buy equity securities or stocks—claim any cash flows left after debt holders are paid. When a firm does well,
financial leverage increases shareholders’ rewards, since the share of the firm’s profits promised to debt holders is
set and predictable.
▼ TABLE 2.1 Balance Sheet for DPH Tree Farm, Inc.
DPH TREE FARM, INC.
Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)

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2018 2017 2018 2017
Assets Liabilities and Equity
Current assets Current liabilities
Cash and marketable
securities
$ 24 $ 25 Accrued wages and taxes $ 20 $ 15
Accounts receivable 70 65 Accounts payable 55 50
Inventory 111 100 Notes payable  48  45
Total $205 $190 Total $123 $110
Fixed assets Long-term debt 192 190
Gross plant and equipment $368 $300 Total debt 315 300
Less: Accumulated
depreciation
 53  40 Stockholders’ equity
Net plant and equipment $315 $260 Preferred stock (5 million shares) $ 5 $ 5
Other long-term assets 50 50 Common stock and paid-in surplus (20
million shares)
40 40
      Retained earnings 210 155
Total $365 $310 Total $255 $200
Total assets $570 $500 Total liabilities and equity $570 $500
However, financial leverage also increases risk. Leverage can create the potential for the firm to experience
financial distress and even bankruptcy. If the firm has a bad year and cannot make its scheduled debt
payments, debt holders can force the firm into bankruptcy. As described in more detail in Chapter 16, managers
often walk a fine line as they decide upon the firm’s capital structure—the amount of debt versus equity financing
held on the balance sheet—because it can determine whether the firm stays in business or goes bankrupt.
capital structure The amount of debt versus equity financing held on the balance sheet.
Book Value versus Market Value LG2-2 Beginning finance students usually have already taken accounting,
so they are familiar with the accounting point of view. For example, a firm’s balance sheet shows its book (or
historical cost) value based on generally accepted accounting principles (GAAP). Under GAAP, assets appear on the
balance sheet at what the firm paid for them, regardless of what those assets might be worth today if the firm were to
sell them. Inflation and market forces make many assets worth more now than they were worth when the firm
bought them. So in many cases, book values differ widely from market values for the same assets—the amount that
the assets would fetch if the firm actually sold them. For the firm’s current assets—those that mature within a year—
the book value and market value of any particular asset will remain very close. For example, the balance sheet lists
cash and marketable securities at their market value. Similarly, firms acquire accounts receivable and inventory and
then convert these short-term assets into cash fairly quickly, so the book value of these assets is generally close to
their market value.
book (or historical cost) value The amount the firm paid for the assets.
market value The amount the firm would get if it sold the assets.
The “book value versus market value” issue really arises when we try to determine how much a firm’s fixed assets
are worth. In this case, book value is often very different from market value. For example, if a firm owns land for
100 years, this asset appears on the balance sheet at its historical cost (of 100 years ago). Most likely, the firm would
reap a much higher price on the land upon its sale than the historical price would indicate.
EXAMPLE Calculating Book versus Market

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2-1 Value LG2-2
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example, log in to
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EZ Toy, Inc., lists fixed assets of $25 million on its balance sheet. The firm’s
fixed assets were recently appraised at $32 million. EZ Toy, Inc.’s, balance
sheet also lists current assets at $10 million. Current assets were appraised at
$11 million. Current liabilities’ book and market values stand at $6 million and
the book and market value of the firm’s long-term debt is $15 million.
Calculate the book and market values of the firm’s stockholders’ equity.
Construct the book value and market value balance sheets for EZ Toy, Inc.
SOLUTION:
Recall the balance sheet identity in equation 2-1: Assets = Liabilities + Equity.
Rearranging this equation: Equity = Assets – Liabilities. Thus, the balance
sheets would appear as follows:

Book
Value
Market
Value
Book
Value
Market
Value
Assets Liabilities andEquity
Current
assets
$10m $11m Current liabilities $ 6m $ 6m
Fixed
assets
25m 32m Accrued wages and
taxes
15m 15m
Stockholders’ equity 14m 14m
Total $35m $43m Total $35m $43m
Similar to Problems 2-17, 2-18, Self-Test Problem 2
Again, accounting tools reflect the past: Balance sheet assets are listed at historical cost. Managers would
thus see little relation between the total asset value listed on the balance sheet and the current market value
of the firm’s assets. Similarly, the stockholders’ equity listed on the balance sheet generally differs from the true
market value of the equity. In this case, the market value may be higher or lower than the value listed on the firm’s
accounting books. So financial managers and investors often find that balance sheet values are not always the most
relevant numbers. The following example illustrates the difference between the book value and the market value of a
firm’s assets.

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The book value and market value of a classic car can be very different.
©Sreedhar Yedlapati/Getty Images
time out!
2-1 What is a balance sheet?
2-2 Which are the most liquid assets and liabilities on a balance sheet?
2.2 • INCOME STATEMENT LG2-1
You will recall that income statements show the total revenues that a firm earns and the total expenses the firm incurs
to generate those revenues over a specific period of time, for example, the year 2018. Remember that while the
balance sheet reports a firm’s position at a point in time, the income statement reports performance over a period of
time, for example, over the last year. Figure 2.2 illustrates a basic income statement and Table 2.2 shows a simple
income statement for DPH Tree Farm, Inc., for the years ended December 31, 2018 and 2017. DPH’s revenues (or
net sales) appear at the top of the income statement. Net sales are defined as gross sales minus any discounts and/or
returns. The income statement then shows various expenses (cost of goods sold [e.g., raw material costs], other
operating expenses [e.g., utilities], depreciation, interest, and taxes) subtracted from revenues to arrive at profit or
income measures.
income statement Financial statement that reports the total revenues and expenses over a specific period of time.
FIGURE 2-2 The Basic Income Statement
Net sales
Less: Cost of goods sold
Gross profits
Less: Other operating expenses
Earnings before interest, taxes, depreciation, and amortization (EBITDA)
Less: Depreciation and amortization
Earnings before interest and taxes (EBIT)
Operating income
Less: Interest
Earnings before taxes (EBT)
Financing and tax considerations

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page 35
Less: Taxes
Net income before preferred dividends
Less: Preferred stock dividends
Net income available to common stockholders
The top part of the income statement reports the firm’s operating income. First, we subtract the cost of goods sold
(the direct costs of producing the firm’s product) from net sales to get gross profit (so, DPH Tree Farm enjoyed gross
profits of $155 million in 2017 and $182 million in 2018). Next, we deduct other operating expenses from gross
profits to get earnings before interest, taxes, depreciation, and amortization (EBITDA); DPH Tree Farm’s EBITDA
was $140 million in 2017 and $165 million in 2018. Other operating expenses include marketing and selling
expenses as well as general and administrative expenses. Finally, we subtract depreciation and amortization from
EBITDA to get operating income or earnings before interest and taxes (EBIT)1 (so DPH Tree Farm’s EBIT
was $128 million in 2017 and $152 million in 2018). The EBIT figure represents the profit earned from the sale of
the product without any financing cost or tax considerations.
gross profit Net sales minus cost of goods sold.
EBITDA Earnings before interest, taxes, depreciation, and amortization.
EBIT Earnings before interest and taxes.
The bottom part of the income statement summarizes the firm’s financial and tax structure. First, we subtract interest
expense (the cost to service the firm’s debt) from EBIT to get earnings before taxes (EBT). So, as we follow our
sample income statement, DPH Tree Farm had EBT of $110 million in 2017 and $136 million in 2018. Of course,
firms differ in their financial structures and tax situations. These differences can cause two firms with identical
operating income to report differing levels of net income. For example, one firm may finance its assets with only
debt, while another finances with only common equity. The company with no debt would have no interest expense.
Thus, even though EBIT for the two firms is identical, the firm with all-equity financing and no debt would report
higher net income. We subtract taxes from EBT to get the last item on the income statement (the “bottom line”), or
net income. DPH Tree Farm, Inc., reported net income of $70 million in 2017 and $90 million in 2018.
EBT Earnings before taxes.
net income The bottom line on the income statement.
Below the net income, or bottom line, on the income statement, firms often report additional information
summarizing income and firm value. For example, with its $90 million of net income in 2018, DPH Tree Farm, Inc.,
paid its preferred stockholders cash dividends of $10 million and its common stockholders cash dividends of $25
million, and added the remaining $55 million to retained earnings. Table 2.1 shows that retained earnings on the
balance sheet increased from $155 million in 2017 to $210 million in 2018. Other items reported below the
bottom line include:
▼ TABLE 2.2 Income Statement for DPH Tree Farm, Inc.
DPH TREE FARM, INC.
Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)
2018 2017
Net sales (all credit) $ 315 $ 275
Less: Cost of goods sold   133   120
Gross profits $ 182 $ 155
Less: Other operating expenses   17   15

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Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 165 $ 140
Less: Depreciation and amortization   13   12
Earnings before interest and taxes (EBIT) $ 152 $ 128
Less: Interest   16   18
Earnings before taxes (EBT) $ 136 $ 110
Less: Taxes   46   40
Net income $  90 $  70
Less: Preferred stock dividends $  10 $  10
Net income available to common stockholders $  80 $  60
Less: Common stock dividends   25   25
Addition to retained earnings $  55 $  35
Per (common) share data:
Earnings per share (EPS) $ 4.00 $ 3.00
Dividends per share (DPS) 1.25 1.25
Book value per share (BVPS) 12.50 9.75
Market value (price) per share (MVPS) 17.25 15.60
(2-3)
(2-4)
(2-5)
(2-6)
We discuss these items further in Chapter 3.
Debt versus Equity Financing
As mentioned earlier, when a firm issues debt to finance its assets, it gives the debt holders first claim to a fixed
amount of its cash flows. Stockholders are entitled to any residual cash flows, or net income. Thus, when a firm
alters its capital structure to include more or less debt (and, in turn, less or more equity), it impacts the residual cash
flows available for the stockholders, i.e., the numerator of the EPS equation. Further, as the firm alters its capital
structure, it will issue more shares of stock when it increases equity to reduce debt, or it will buy back shares of
stock when it decreases equity to increase debt, i.e., the denominator of the EPS equation. Thus, a change in capital
structure will cause a firm’s stockholders’ EPS to change. The question is: Will the reduction (increase) in financial
distress and bankruptcy risk from the reduction (increase) in financial leverage appease the stockholders
who have lost (gained) earnings per share, and ultimately, how will the change affect stockholder wealth?
EXAMPLE
2-2
Impact of Capital Structure on a
Firm’s EPS LG2-1
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Consider a firm with an EBIT of $750,000. The firm finances its assets with

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$1,600,000 debt (costing 5 percent) and 200,000 shares of stock selling at
$6.00 per share. To reduce the firm’s risk associated with this financial
leverage, the firm is considering reducing its debt by $600,000 by selling an
additional 100,000 shares of stock. The firm is in the 40 percent tax bracket.
The change in capital structure will have no effect on the operations of the
firm. Thus, EBIT will remain at $750,000. Calculate the dilution in the firm’s
EPS from this change in capital structure.
SOLUTION:
The EPS before and after this change in capital structure is illustrated below:
Change
Before Capital
Structure Change
After Capital
Structure Change
EBIT $750,000 $750,000
Less: Interest ($1,600,000
× 0.05)
 80,000 ($1,000,000
× 0.05)
 50,000
EBT $670,000 $700,000
Less: Taxes
(40%)
268,000 280,000
Net income $402,000 $420,000
Divided by # of
shares
200,000 300,000
EPS $  2.01 $  1.40
The change in capital structure would dilute the stockholders’ EPS by $0.61.
Similar to Problems 2-5, 2-6, 2-23, 2-24
Corporate Income Taxes LG2-3
Firms pay out a large portion of their earnings in taxes. For example, in 2015, Walmart had EBT of $24.80 billion.
Of this amount, Walmart paid $8.50 billion (over 34 percent of EBT) in taxes. Firms may also defer taxes, e.g., in
2015, Walmart listed a provision for deferred taxes of $0.52 billion. Deferred taxes occur when a company
postpones paying taxes on profits earned in a particular period. For example, some expenses, such as those
associated with research and development or incurred in mergers, may be written off over a fixed number of years.
In these cases, the firm’s current year profits for tax purposes would be lower than the profits computed for
accounting purposes. Thus, the company ends up postponing part of its tax liability on this year’s profits to future
years.
Congress oversees the U.S. tax code, which determines corporate tax obligations. Corporate taxes can thus change
with changes of administration or other changes in the business or public environment. As you might expect, the
U.S. tax system is extremely complicated, so we do not attempt to cover it in detail here. However, firms recognize
taxes as a major expense item and many financial decisions arise from tax considerations. In this section we provide

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page 37
a general overview of the U.S. corporate tax system.
▼ TABLE 2.3 Corporate Tax Rates as of 2018
Taxable Income Pay This Amount on Base Income Plus This Percentage on Anything over the Base
$0–$50,000 $  0 15%
$50,001–$75,000 7,500 25
$75,001–$100,000 13,750 34
$100,001–$335,000 22,250 39
$335,001–$10,000,000 113,900 34
$10,000,001–$15,000,000 3,400,000 35
$15,000,001–$18,333,333 5,150,000 38
Over $18,333,333 $6,416,667 35
The 2018 corporate tax schedule appears in Table 2.3. Note from this table that the U.S. tax structure is progressive,
meaning that the larger the income, the higher the taxes assessed and the higher the taxes paid per dollar of
income. However, corporate tax rates do not increase in any kind of linear way based on this progressive
nature: They rise from a low of 15 percent to a high of 39 percent, then drop to 34 percent, rise to 38 percent, and
finally drop to 35 percent.
EXAMPLE
2-3
Calculation of Corporate Taxes LG2-
3
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example, log in to
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Indian Point Kennels, Inc., earned $16.5 million taxable income (EBT) in
2018. Use the tax schedule in Table 2.3 to determine the firm’s 2018 tax
liability, its average tax rate, and its marginal tax rate.
SOLUTION:
From Table 2.3, the $16.5 million of taxable income puts Indian Point Kennels
in the 38 percent marginal tax bracket. Thus,
Note that the base amount is the maximum dollar value listed in the previous
tax bracket. In this example, we take the highest dollar value ($15,000,000) in
the preceding tax bracket (35 percent). The additional percentage owed
results from multiplying the income above and beyond the $15,000,000 (or
$1,500,000) by the marginal tax rate (38 percent). The average tax rate for
Indian Point Kennels, Inc., comes to:
If Indian Point Kennels earned $1 more of taxable income, it would pay 38
cents (its tax rate of 38 percent) more in taxes. Thus, the firm’s marginal tax

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rate is 38 percent.
Similar to Problems 2-7, 2-8, 2-25, 2-26, Self-Test Problem 3
In addition to calculating their tax liability, firms also want to know their average tax rate and marginal tax rate. You
can figure the average tax rate as the percentage of each dollar of taxable income that the firm pays in taxes.
average tax rate The percentage of each dollar of taxable income that the firm pays in taxes.
marginal tax rate The amount of additional taxes a firm must pay out for every additional dollar of taxable income it earns.
(2-7)
From your economics classes, you can probably guess that the firm’s marginal tax rate is the amount of additional
taxes a firm must pay out for every additional dollar of taxable income it earns.
Interest and Dividends Received by Corporations Any interest that corporations receive is taxable, although
a notable exception arises: Interest on state and local government bonds is exempt from federal taxes. The U.S. tax
code allows this exception to encourage corporations to be better community citizens by supporting local
governments. Another exception of sorts arises when one corporation owns stock in another corporation. Seventy
percent of any dividends received from other corporations is tax exempt. Only the remaining 30 percent is taxed at
the receiving corporation’s tax rate.2
EXAMPLE
2-4
Corporate Taxes with Interest and
Dividend Income LG2-3
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In the previous example, suppose that in addition to the $16.5 million of
taxable income, Indian Point Kennels, Inc., received $250,000 of interest on
state-issued bonds and $500,000 of dividends on common stock it owns in
DPH Tree Farm, Inc. How do these items affect Indian Point Kennel’s tax
liability, average tax rate, and marginal tax rate?
SOLUTION:
In this case, interest on the state-issued bonds is not taxable and should not
be included in taxable income. Further, the first 70 percent of the dividends
received from DPH Tree Farm is not taxable. Thus, only 30 percent of the
dividends received are taxed, so:
Taxable income = $16,500,000 + (0.3)$500,000 = $16,650,000
Now Indian Point Kennel’s tax liability will be:
Tax liability = $5,150,000 + 0.38($16,650,000 − $15,000,000) = $5,777,000
The $500,000 of dividend income increased Indian Point Kennel’s tax liability
by $57,000. Indian Point Kennels, Inc.’s, resulting average tax rate is now:
Average tax rate = $5,777,000 / $16,650,000 = 34.70%
Finally, if Indian Point Kennels earned $1 more of taxable income, it would still
pay 38 cents (based upon its marginal tax rate of 38 percent) more in taxes.

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page 38
page 39
Similar to Problems 2-8, 2-25, 2-26
Interest and Dividends Paid by Corporations Corporate interest payments appear on the income statement as
an expense item, so we deduct interest payments from operating income when the firm calculates taxable income.
But any dividends paid by corporations to their shareholders are not tax deductible. This is one factor that
encourages managers to finance projects with debt financing rather than to sell more stock. Suppose one firm uses
mainly debt financing and another firm, with identical operations, uses mainly equity financing. The equity-
financed firm will have very little interest expense to deduct for tax purposes. Thus, it will have higher
taxable income and pay more taxes than the debt-financed firm. The debt-financed firm will pay fewer taxes and be
able to pay more of its operating income to asset funders, that is, its bondholders and stockholders. So, all else
constant, even stockholders prefer that firms finance assets primarily with debt rather than with stock. However, as
mentioned earlier, increasing the amount of debt financing of the firm’s assets also increases risks. So these affects
must be balanced when selecting the optimal capital structure for a firm. The debt-versus-equity financing issue is
called capital structure.
time out!
2-3 What is an income statement?
2-4 When a corporation owns stock in another corporation, what percentage of dividends received on the stock is taxed?
2.3 • STATEMENT OF CASH FLOWS LG2-4
Income statements and balance sheets are the most common financial documents available to the public. However,
managers who make financial decisions need more than these two statements—reports of past performance—on
which to base their decisions for today and into the future. A very important distinction between the accounting
point of view and the finance point of view is that financial managers and investors are far more interested in actual
cash flows than in the backward-looking profit listed on the income statement.
The statement of cash flows is a financial statement that shows the firm’s cash flows over a given period of time. This
statement reports the amounts of cash the firm has generated and distributed during a particular time period.
The bottom line on the statement of cash flows—the difference between cash sources and uses—equals the
change in cash and marketable securities on the firm’s balance sheet over a period of time. That is, the statement of
cash flows reconciles noncash balance sheet items and income statement items to show changes in the cash and
marketable securities account on the balance sheet over the particular analysis period.
statement of cash flows Financial statement that shows the firm’s cash flows over a period of time.
EXAMPLE
2-5
Effect of Debt-versus-Equity
Financing on Funders’ Returns LG2-
1
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Suppose that you are considering a stock investment in one of two firms
(AllDebt, Inc., and AllEquity, Inc.), both of which operate in the same industry
and have identical operating incomes of $5 million. AllDebt, Inc., finances its
$12 million in assets with $11 million in debt (on which it pays 10 percent

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interest) and $1 million in equity. AllEquity, Inc., finances its $12 million in
assets with no debt and $12 million in equity. Both firms pay 30 percent tax on
their taxable income. Calculate the income that each firm has available to pay
its debt and stockholders (the firms’ asset funders) and the resulting returns to
these asset funders for the two firms.
SOLUTION:
AllDebt AllEquity
Operating income $5.00m $5.00m
Less: Interest 1.10m 0.00m
Taxable income $3.90m $5.00m
Less: Taxes (30%) 1.17m 1.50m
Net income $2.73m $3.50m
Income available for asset
funders
(= Operating income −
Taxes)
$3.83m $3.50m
Return on asset-funders’
investment
$3.83m/$12.00m =
31.92%
$3.50m/$12.00m =
29.17%
By financing most of its assets with debt and receiving the associated tax
benefits from the interest paid on this debt, All Debt, Inc., is able to pay more
of its operating income to the funders of its assets, i.e., its debt holders and
stockholders, than All Equity, Inc.
Similar to Problems 2-19, 2-20
To clarify why this statement is so crucial, it helps to understand that figures on an income statement may not
represent the actual cash inflows and outflows for a firm during a given period of time. There are two main issues,
GAAP accounting principles and noncash income statement entries.
GAAP Accounting Principles
Company accountants must prepare firm income statements following GAAP principles. GAAP procedures require
that the firm recognize revenue at the time of sale. But sometimes the company receives the cash before or after the
time of sale. Likewise, GAAP counsels the firm to show production and other expenses on the income statement as
the sales of those goods take place. So production and other expenses associated with a particular product’s sale
appear on the income statement (for example, cost of goods sold and depreciation) only when that product sells. Of
course, just as with revenue recognition, actual cash outflows incurred with production may occur at a very different
point in time—usually much earlier than GAAP principles allow the firm to formally recognize the expenses.
Noncash Income Statement Entries
Further, income statements contain several noncash entries, the largest of which is depreciation. Depreciation

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attempts to capture the noncash expense incurred as fixed assets deteriorate from the time of purchase to the point
when those assets must be replaced.
Let’s illustrate the effect of depreciation: Suppose a firm purchases a machine for $100,000. The machine has an
expected life of five years and at the end of those five years, the machine will have no expected salvage value. The
firm incurs a $100,000 cash outflow at the time of purchase. But the entire $100,000 does not appear on the income
statement in the year that the firm purchases the machine—in accounting terms, the machine is not expensed in the
year of purchase. Rather, if the firm’s accounting department uses the straight-line depreciation method, it deducts
only $100,000/5, or $20,000, each year as an expense. This $20,000 equipment expense is not a cash outflow for the
firm. The person in charge of buying the machine knows that the cash flow occurred at the time of purchase—and it
totaled $100,000 rather than $20,000.
In conclusion, even though a company may report a large amount of net income on its income statement during a
year, the firm may actually receive a positive, negative, or zero amount of cash. For example, DPH Tree Farm, Inc.,
reported net income of $90 million on its income statement (in Table 2.2), yet reported a net change in cash and
marketable securities of −$1 million on its balance sheet (in Table 2.1). Accounting rules under GAAP create this
sense of discord: Net income is the result of accounting rules, or GAAP, that do not necessarily reflect the firm’s
cash flows. Finance professionals know that the firm needs cash, not accounting profits, to pay the firm’s obligations
as they come due, to fund the firm’s operations and growth, and to compensate the firm’s ultimate owners: its
shareholders. While the income statement shows a firm’s accounting-based income, the statement of cash flows
more often reflects reality today and is thus more important to managers and investors as they seek to answer such
important questions as
Does the firm generate sufficient cash to pay its obligations, thus avoiding financial distress?
Does the firm generate sufficient cash to purchase assets needed for sustained growth?
Does the firm generate sufficient cash to pay down its outstanding debt obligations?

Sources and Uses of Cash LG2-5
In general, some activities increase cash (cash sources) and some decrease cash (cash uses). Figure 2.3 classifies the
firm’s basic cash sources and uses. Cash sources include decreasing noncash assets or increasing liabilities (or
equity). For example, a drop in accounts receivable means that the firm has collected cash from its credit sales—a
cash source. Likewise, if a firm sells new common stock, the firm has used primary markets to raise cash. In
contrast, a firm uses cash when it increases noncash assets (buying inventory) or decreases a liability (paying off a
bank loan). The statement of cash flows separates these cash flows into four categories or sections:
1. Cash flows from operating activities.
2. Cash flows from investing activities.
3. Cash flows from financing activities.
4. Net change in cash and marketable securities.
The basic setup of a statement of cash flows is shown in Figure 2.4, and a more detailed statement of cash flows for
DPH Tree Farm for the year ending December 31, 2018, appears as Table 2.4.
Cash flows from operations (Section A in Figure 2.4 and Table 2.4) are those cash inflows and outflows that result
directly from producing and selling the firm’s products over a period of time. These cash flows include
cash flows from operations Cash flows that are the direct result of the production and sale of the firm’s products.
Net income (adding back depreciation,3 a noncash expense item that is included in net income).
Change in working capital accounts other than cash and operations-related short-term debt.
Most finance professionals consider this top section of the statement of cash flows to be the most important. It
shows quickly and compactly the firm’s cash flows generated by and used for the production process. For example,
DPH Tree Farm, Inc., generated $97 million in cash flows from its 2018 production. That is, producing and selling
the firm’s product resulted in a net cash inflow for the firm. Managers and investors look for positive cash flows
from operations as a sign of a successful firm—positive cash flows from the firm’s operations is precisely what
gives the firm value. Unless the firm has a stable, healthy pattern in its cash flows from operations, it is not


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financially healthy no matter what its level of cash flow from investing activities or cash flows from financing
activities.
FIGURE 2-3 Sources and uses of Cash
Sources of Cash Uses of Cash
Net income Net losses
Depreciation Increase a noncash current asset
Decrease a noncash current assetIncrease a fixed asset
Decrease a fixed asset Decrease a current liability
Increase a current liability Decrease long-term debt
Increase long-term debt Repurchase common or preferred stock
Sell common or preferred stock Pay dividends
Cash flows from investing activities (Section B in Figure 2.4 and Table 2.4) are cash flows associated with the buying or
selling of fixed or other long-term assets. This section of the statement of cash flows shows cash inflows and
outflows from changes in long-term investing activities—most significantly the firm’s investment in fixed assets.
For example, DPH Tree Farm, Inc., used $68 million in cash to purchase fixed and other long-term assets in 2018.
DPH funded this $68 million cash outflow with the $97 million cash surplus DPH Tree Farm produced from its
operations.
cash flows from investing activities Cash flows associated with the purchase or sale of fixed or other long-term assets.
Cash flows from financing activities (Section C in Figure 2.4 and Table 2.4) are cash flows that result from changes in
debt and equity financing. These include raising cash by
cash flows from financing activities Cash flows that result from debt and equity financing transactions.
Issuing short-term debt
Issuing long-term debt
Issuing stock

or using cash to
Pay dividends
Pay off debt
Buy back stock
In 2018, DPH Tree Farm, Inc.’s, financing activities produced a net cash outflow of $30 million. As we saw with
cash flows from financing activities, this $30 million cash outflow was funded (at least partially) with the $97
million cash surplus DPH Tree Farm produced from its operations. Managers, investors, and analysts normally
expect the cash flows from financing activities to include small amounts of net borrowing along with dividend
payments. If, however, a firm is going through a major period of expansion, net borrowing could reasonably be
much higher.
Net change in cash and marketable securities (Section D in Figure 2.4 and Table 2.4), the bottom line of the statement of
cash flows, shows the sum of cash flows from operations, investing activities, and financing activities. This sum will
reconcile to the net change in cash and marketable securities account on the balance sheet over the period of
analysis. For example, the bottom line of the statement of cash flows for DPH Tree Farm is −$1 million.
This is also the change in the cash and marketable securities account on the balance sheet (in Table 2.1) between
2017 and 2018 ($24 million – $25 million = −$1 million). In this case, the firm’s operating, investing, and financing
activities combined to produce a net drain on the firm’s cash during 2018—cash outflows were greater than cash
inflows, largely because of the $68 million investment in long-term and fixed assets. Of course, when the bottom
line is positive, a firm’s cash inflows exceed cash outflows for the period.
net change in cash and marketable securities The sum of the cash flows from operations, investing activities, and financing activities.

▼FIGURE 2-4 The Statement of Cash Flows
Section A. Cash flows from operating activities
Net income
Additions:
Depreciation
Decrease in noncash current assets (e.g., decrease in accounts receivable)
Increase in accrued wages and taxes
Increase in accounts payable
Subtractions:
Increase in noncash current assets (e.g., increase in inventory)
Decrease in accrued wages and taxes
Decrease in accounts payable
Section B. Cash flows from investing activities
Additions:
Decrease in fixed assets
Decrease in other long-term assets
Subtractions:
Increase in fixed assets
Increase in other long-term assets
Section C. Cash flows from financing activities
Additions:
Increase in notes payable
Increase in long-term debt
Increase in common and preferred stock
Subtractions:
Decrease in notes payable
Decrease in long-term debt
Decrease in common and preferred stock
Dividends paid
Section D. Net change in cash and marketable securities
▼ TABLE 2.4 Characteristics of Business Organization
DPH TREE FARM, INC.
Statement of Cash Flows for Year Ending December 31, 2018
(in millions of dollars)
2018
Section A. Cash flows from operating activities
Net income $90
Additions:
Depreciation 13

Increase in accrued wages and taxes ($20 − $15) 5
Increase in accounts payable ($55 − $50) 5
Subtractions:
Increase in accounts receivable ($65 − $70) −5
Increase in inventory ($100 − $111) −11
Net cash flow from operating activities $97
Section B. Cash flows from investing activities
Subtractions:
Increase in fixed assets ($300 − $368) −$68
Increase in other long-term assets ($50 − $50)   ;0
Net cash flow from investing activities −$68
Section C. Cash flows from financing activities
Additions:
Increase in notes payable ($48 − $45) $ 3
Increase in long-term debt ($192 − $190) 2
Increase in common and preferred stock ($40 − $40) + ($5 − $5) 0
Subtractions:
Preferred stock dividends paid − 10
Common stock dividends paid − 25
Net cash flow from financing activities −$30
Section D. Net change in cash and marketable securities −$ 1
When evaluating the statement of cash flows, the overall change in the cash account should be evaluated with care.
For example, a negative cash flow could be the result when a growing firm invests in new fixed assets, inventory,
and so on. Cash expenditures used to expand firm capacity would drain cash during the expansion period. However,
if utilized efficiently, would result in increases in cash flows through time. Thus, the cash flow statement assists
financial professionals to identify where cash is generated and where cash is dispersed over a time period. These
cash inflows and outflows should then be evaluated based on how they added to the value of the firm to its
stockholders.
time out!
2-5 What is a statement of cash flows?
2-6 What are the main sections on the statement of cash flows?
2.4 • FREE CASH FLOW LG2-5
The statement of cash flows measures net cash flow as net income plus noncash adjustments. However, to maintain
cash flows over time, firms must continually replace working capital and fixed assets and develop new products.
Thus, firm managers cannot use the available cash flows any way they please. Specifically, the value of a firm’s
operations depends on the future expected free cash flows, defined as after-tax operating profit minus the amount of
new investment in working capital, fixed assets, and the development of new products. Thus, free cash flow
represents the cash that is actually available for distribution to the investors in the firm—the firm’s debt holders and

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stockholders—after the investments that are necessary to sustain the firm’s ongoing operations are made.
free cash flows The cash that is actually available for distribution to the investors in the firm after the investments that are necessary to
sustain the firm’s ongoing operations are made.
DPH Tree Farm reported net income of $90 million yet reported a net change in cash and marketable securities of −$1 million on its
statement of cash flows.
Source: USDA Natural Resources Conservation Service
To calculate free cash flow (FCF), we use the mathematical equation that appears below:
(2-8)
Notice from this equation that free cash flow merges information from the income statement (performance) with
information from the balance sheet (resources used to produce performance).
To calculate free cash flow, we start with operating cash flow. Firms generate operating cash flow (OCF) after they
have paid necessary operating expenses and taxes. This net operating profit after taxes (NOPAT) is the net profit
a firm earns after taxes, but before any financing costs. It is the profit available for debt holders and
stockholders if the firm does not replace existing or invest in new working capital or fixed assets. Depreciation, a
noncash charge, is added back to NOPAT to determine total OCF. We add other relevant noncash charges, such as
amortization and depletion, back as well. Firms either buy physical assets or earmark funds for eventual equipment
replacement to sustain firm operations; this is called investment in operating capital (IOC). In accounting terms,
IOC includes the firm’s gross investments (or changes) in fixed assets, current assets, and spontaneous current
liabilities (such as accounts payable and accrued wages). Thus, free cash flow measures how well managers utilize
the resources of the company to increase firm performance and, thus, enhance shareholder wealth.
net operating profit after taxes (NOPAT) Net profit a firm earns after taxes but before any financing costs.
Like the bottom line shown on the statement of cash flows, the level of free cash flow can be positive, zero, or
negative. A positive free cash flow value means that the firm may distribute funds to its investors (debt holders and
stockholders). When the firm’s free cash flows come in as zero or negative, however, the firm’s operations produce
no cash flows available for investors. Of course, if free cash flow is negative because operating cash flow is
negative, investors are likely to take up the issue with the firm’s management. Negative free cash flows as a result of
negative operating cash flows generally indicate that the firm is experiencing operating or managerial problems. A

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firm with positive operating cash flows, but negative free cash flows, however, is not necessarily a poorly managed
firm. Firms that invest heavily in operating capital to support growth often have positive operating cash flows but
negative free cash flows. But in this case, the negative free cash flow will likely result in growing future profits.
EXAMPLE
2-6
Calculating Free Cash Flow LG2-5
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
From Tables 2.1 and 2.2, in 2018, DPH Tree Farm, Inc., had EBIT of $152
million, a tax rate of 33.82 percent ($46m/$136m), and depreciation expense
of $13 million. Therefore, DPH Tree Farm’s operating cash flow was:
DPH Tree Farm’s gross fixed assets increased by $68 million between 2017
and 2018. The firm’s current assets increased by $15 million and
spontaneous current liabilities increased by $10 million ($5 million in accrued
wages and taxes and $5 million in accounts payable). Therefore, DPH’s
investment in operating capital for 2018 was:
Accordingly, what was DPH Tree Farm’s free cash flow for 2018?
SOLUTION:
In other words, in 2018, DPH Tree Farm, Inc., had cash flows of $41 million
available to pay its stockholders and debt holders.
Similar to Problems 2-11, 2-12, Self-Test Problem 4

2.5 • STATEMENT OF RETAINED EARNINGS LG2-1
The statement of retained earnings provides additional details about changes in retained earnings during a reporting
period. This financial statement reconciles net income earned during a given period and any cash dividends paid
within that period on one side with the change in retained earnings between the beginning and ending of the period
on the other. Table 2.5 presents DPH Tree Farm, Inc.’s, statement of retained earnings as of December 31, 2018.
The statement shows that DPH Tree Farms brought in a net income of $90 million during 2018. The firm paid out
$10 million in dividends to preferred stockholders and another $25 million to common stockholders. The firm then
had $55 million to reinvest back into the firm, which shows as an increase in retained earnings. Thus, the retained
earnings account on the balance sheet (Table 2.1) increased from $155 million at year-end 2017 to $210 million at
year-end 2018.
statement of retained earnings Financial statement that reconciles net income earned during a given period and any cash dividends
paid with the change in retained earnings over the period.

http://mhhe.com/CornettM4e

time out!
2-7 What is a statement of retained earnings?
2-8 If, during a given period, a firm pays out more in dividends than it has net income, what happens to the firm’s retained
earnings?
Increases in retained earnings occur not just because a firm has net income, but also because the firm’s common
stockholders agree to let management reinvest net income back into the firm rather than pay it out as dividends. If
the shareholders disagreed with the firm’s policy, they would simply sell their shares. Reinvesting earnings is less
expensive than raising capital from outside sources (equity markets). Further, reinvesting net income into retained
earnings allows the firm to grow by providing additional funds that can be spent on plant and equipment, inventory,
and other assets needed to generate even more profit. So, retained earnings represent a claim against all of the firm’s
assets and not against a particular asset.
EXAMPLE
2-7
Statement of Retained
Earnings LG2-1
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
Indian Point Kennels, Inc., earned net income in 2018 of $10.78 million. The
firm paid out $1 million in cash dividends to its preferred stockholders and
$2.5 million in cash dividends to its common stockholders. The firm ended
2017 with $135.75 million in retained earnings. Construct a statement of
retained earnings to calculate the year-end 2018 balance of retained
earnings.
SOLUTION:
The statement of retained earnings for 2018 is as follows:
INDIAN POINT KENNELS, INC.
Statement of Retained Earnings as of December 31, 2018
(in millions of dollars)
Balance of retained earnings, December 31, 2017 $135.75
Plus: Net income for 2018 10.78
Less: Cash dividends paid
Preferred stock $1.0
Common stock  2.5
Total cash dividends paid   3.50
Balance of retained earnings, December 31, 2018 $143.03

http://mhhe.com/CornettM4e

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Similar to Problems 2-13, 2-14, Self-Test Problem 1

2.6 • CAUTIONS IN INTERPRETING FINANCIAL
STATEMENTS LG2-6
As we mentioned earlier in the chapter, firms must prepare their financial statements according to GAAP. GAAP
provides a common set of standards intended to produce objective and precise financial statements. But recall also
that managers have significant discretion over their reported earnings. Managers and financial analysts have
recognized for years that firms use considerable latitude in using accounting rules to manage their reported earnings
in a wide variety of contexts. Indeed, within the GAAP framework, firms can “smooth” earnings. That is, firms
often take steps to over- or understate earnings at various times. Managers may choose to smooth earnings to show
investors that firm assets are growing steadily. Similarly, one firm may be using straight-line depreciation for its
fixed assets, while another is using a modified accelerated cost recovery method (MACRS), which causes
depreciation to accrue quickly. If the firm uses MACRS accounting methods, its managers write fixed asset values
down quickly; assets will thus have lower book values than if the firm used straight-line depreciation methods.
Managers’ choices in these areas make comparisons of such measures as EPS and BVPS across firms difficult.
time out!
2-9 What is earnings management?
This process of controlling a firm’s earnings is called earnings management. At the extreme, earnings management has
resulted in some widely reported accounting scandals involving Enron, Merck, WorldCom, and other major U.S.
corporations that tried to artificially influence their earnings by manipulating accounting rules. Congress responded
to the spate of corporate scandals that emerged after 2001 with the Sarbanes-Oxley Act, passed in June 2002.
Sarbanes-Oxley requires public companies to ensure that their corporate boards’ audit committees have considerable
experience applying generally accepted accounting principles (GAAP) for financial statements. The act also requires
that a firm’s senior management must sign off on the financial statements of the firm, certifying the statements as
accurate and representative of the firm’s financial condition during the period covered. If a firm’s board of directors
or senior managers fail to comply with Sarbanes-Oxley (SOX), the firm may be delisted from stock exchanges.
earnings management The process of controlling a firm’s earnings.
Sarbanes-Oxley Act of 2002 Requires that a firm’s senior management must sign off on the financial statements of the firm, certifying
the statements as accurate and representative of the firm’s financial condition during the period covered.
American Spectrum Realty failed to file quarterly and annual reports in 2013 and 2014 in a timely manner. As a
result, as discussed in the nearby Finance at Work box, the firm’s common stock became subject to delisting.
Congress’s goal in passing SOX was to prevent deceptive accounting and management practices and to bring
stability to jittery stock markets battered in 2002 by accounting and managerial scandals that cost employees their
life savings and harmed many innocent shareholders as well. See also the discussion of the role of ethics in finance
in Chapter 1.
▼ TABLE 2.5 Statement of Retained Earnings for DPH Tree Farm, Inc.
DPH TREE FARM, INC.
Statement of Retained Earnings as of December 31, 2018

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(in millions of dollars)
Balance of retained earnings, December 31, 2017 $155
Plus: Net income for 2018 90
Less: Cash dividends paid
Preferred stock $10
Common stock 25
Total cash dividends paid  35
Balance of retained earnings, December 31, 2018 $210

finance at work //: markets
American Spectrum Realty Receives Letter from the NYSE MKT That It Has Determined to
Initiate Delisting Proceedings
©jmks/Getty Images
American Spectrum Realty, Inc.–a real estate investment management and leasing company–announced that it has received a letter
indicating that the staff of NYSE Regulation, Inc. has determined to commence proceedings to delist the Company’s common stock from
the NYSE MKT LLC. Trading in the Company’s common stock was halted on a continuous basis since NYSE Regulation initiated a
trading halt on April 15, 2014. Trading in the Company’s common stock was immediately suspended intraday on February 19, 2015. As
determined by NYSE Regulation, the suspension is the result of
the Company’s inability to complete its outstanding SEC filings, per Sections 134 and 1101 of the NYSE MKT Company Guide;
the financial condition of the Company, which is so impaired that it appears questionable, in the opinion of the NYSE MKT, as to
whether the Company will be able to continue operations and/or meet its obligations as they mature, per Section 1003(a)(iv) of the
Company Guide; and
the Company’s failure to timely disclose corporate events per Section 1003(d) of the Company Guide.
As disclosed on November 14, 2014, and January 8, 2015, the Company had submitted plans to the NYSE MKT outlining steps to
regain compliance with the requirements of the Company Guide, and the NYSE MKT had granted the Company a period through
February 19, 2016, for the Company to regain compliance as outlined in its plans of compliance, so long as the Company made progress
consistent with such plans. However, due to the financial condition of the Company, the Company was unable to make progress
consistent with such plans, and accordingly, the Board determined it to be in the best interest of the Company and its shareholders to not
appeal NYSE Regulation’s delisting determination.
American Spectrum Realty, Inc., is a real estate investment company that owns, through an operating partnership, interests in office,
industrial/commercial, retail, self-storage, retail, multi-family properties and undeveloped land throughout the United States. American
Spectrum Management Group, Inc., a wholly owned subsidiary of the Company, manages and leases all properties owned by American
Spectrum Realty, Inc. as well as for third-party clients, totaling 7 million square feet in multiple states.

page 47
Source: “American Spectrum Realty Receives Letter from the NYSE MKT That It Has Determined to Initiate Delisting Proceedings,”
Business Wire, February 25, 2015. Reprinted with permission from Business Wire.
Want to know more?
Key Words to Search For Updates: Sarbanes-Oxley Act of 2002, stock delistings, 10Q filing, 10K filing

Get Online
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Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. List and describe the four major financial statements. (LG2-1)
2. On which of the four major financial statements (balance sheet, income statement, statement of cash flows, or
statement of retained earnings) would you find the following items? (LG2-1)
a. Earnings before taxes.
b. Net plant and equipment.
c. Increase in fixed assets.

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d. Gross profits.
e. Balance of retained earnings, December 31, 20xx.
f. Common stock and paid-in surplus.
g. Net cash flow from investing activities.
h. Accrued wages and taxes.
i. Increase in inventory.
3. What is the difference between current liabilities and long-term debt? (LG2-1)
4. How does the choice of accounting method used to record fixed asset depreciation affect management of the
balance sheet? (LG2-1)
5. What are the costs and benefits of holding liquid securities on a firm’s balance sheet? (LG2-1)
6. Why can the book value and market value of a firm differ? (LG2-1)
7. From a firm manager’s or investor’s point of view, which is more important—the book value of a firm or the
market value of the firm? (LG2-2)
8. What do we mean by a progressive tax structure? (LG2-3)
9. What is the difference between an average tax rate and a marginal tax rate? (LG2-3)
10. How does the payment of interest on debt affect the amount of taxes the firm must pay? (LG2-4)
11. The income statement is prepared using GAAP. How does this affect the reported revenue and expense
measures listed on the balance sheet? (LG2-4)
12. Why do financial managers and investors find cash flows to be more important than accounting profit? (LG2-4)
13. Which of the following activities result in an increase (decrease) in a firm’s cash? (LG2-5)
a. Decrease fixed assets.
b. Decrease accounts payable.
c. Pay dividends.
d. Sell common stock.
e. Decrease accounts receivable.
f. Increase notes payable.
14. What is the difference between cash flows from operating activities, cash flows from investing activities, and
cash flows from financing activities? (LG2-5)
15. What are free cash flows for a firm? What does it mean when a firm’s free cash flow is negative? (LG2-5)
16. What is earnings management? (LG2-6)
17. What does the Sarbanes-Oxley Act require of firm managers? (LG2-6)

Problems
BASIC PROBLEMS
2-1 Balance Sheet You are evaluating the balance sheet for Goodman Bees Corporation. From the balance
sheet you find the following balances: cash and marketable securities = $400,000, accounts receivable =
$1,200,000, inventory = $2,100,000, accrued wages and taxes = $500,000, accounts payable = $800,000,
and notes payable = $600,000. Calculate Goodman Bees’ net working capital. (LG2-1)
2-2 Balance Sheet Casello Mowing & Landscaping’s year-end 2018 balance sheet lists current assets of
$435,200, fixed assets of $550,800, current liabilities of $416,600, and long-term debt of $314,500.
Calculate Casello’s total stockholders’ equity. (LG2-1)
2-3 Income Statement The Fitness Studio, Inc.’s, 2018 income statement lists the following income and

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expenses: EBIT = $538,000, interest expense = $63,000, and net income = $435,000. Calculate the 2018
taxes reported on the income statement. (LG2-1)

2-4 Income Statement The Fitness Studio, Inc.’s, 2018 income statement lists the following income and
expenses: EBIT = $773,500, interest expense = $100,000, and taxes = $234,500. The firm has no preferred
stock outstanding and 100,000 shares of common stock outstanding. Calculate the 2018 earnings per share.
(LG2-1)
2-5 Income Statement Consider a firm with an EBIT of $850,000. The firm finances its assets with
$2,500,000 debt (costing 7.5 percent) and 400,000 shares of stock selling at $5.00 per share. To reduce the
firm’s risk associated with this financial leverage, the firm is considering reducing its debt by $1,000,000
by selling an additional 200,000 shares of stock. The firm is in the 40 percent tax bracket. The change in
capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $850,000.
Calculate the change in the firm’s EPS from this change in capital structure. (LG2-1)
2-6 Income Statement Consider a firm with an EBIT of $550,000. The firm finances its assets with
$1,000,000 debt (costing 5.5 percent) and 200,000 shares of stock selling at $12.00 per share. The firm is
considering increasing its debt by $900,000, using the proceeds to buy back 75,000 shares of stock. The
firm is in the 40 percent tax bracket. The change in capital structure will have no effect on the operations of
the firm. Thus, EBIT will remain at $550,000. Calculate the change in the firm’s EPS from this change in
capital structure. (LG2-1)
2-7 Corporate Taxes Oakdale Fashions, Inc., had $245,000 in 2018 taxable income. Using the tax schedule in
Table 2.3, calculate the company’s 2018 income taxes. What is the average tax rate? What is the marginal
tax rate? (LG2-3)
2-8 Corporate Taxes Hunt Taxidermy, Inc., is concerned about the taxes paid by the company in 2018. In
addition to $42.4 million of taxable income, the firm received $2,975,000 of interest on state-issued bonds
and $1,000,000 of dividends on common stock it owns in Oakdale Fashions, Inc. Calculate Hunt
Taxidermy’s tax liability, average tax rate, and marginal tax rate. (LG2-3)
2-9 Statement of Cash Flows Ramakrishnan, Inc., reported 2018 net income of $15 million and depreciation
of $2,650,000. The top part of Ramakrishnan, Inc.’s, 2018 and 2017 balance sheets is reproduced below (in
millions of dollars):
Calculate the 2018 net cash flow from operating activities for Ramakrishnan, Inc. (LG2-4)
2018 2017 2018 2017
Current assets: Current liabilities:
Cash and marketable
securities
$ 20 $ 15 Accrued wages and
taxes
$ 19 $ 18
Accounts receivable 84 75 Accounts payable 51 45
Inventory 121 110 Notes payable  45  40
  Total $225 $200   Total $115 $103
2-10 Statement of Cash Flows In 2018, Usher Sports Shop had cash flows from investing activities of –
$4,364,000 and cash flows from financing activities of −5,880,000. The balance in the firm’s cash
account was $1,615,000 at the beginning of 2018 and $1,742,000 at year-end. Calculate Usher Sports
Shop’s cash flow from operations for 2018. (LG2-4)

2-11 Free Cash Flow You are considering an investment in Fields and Struthers, Inc., and want to evaluate
the firm’s free cash flow. From the income statement, you see that Fields and Struthers earned an
EBIT of $62 million, had a tax rate of 30 percent, and its depreciation expense was $5 million. Fields
and Struthers’s NOPAT gross fixed assets increased by $32 million from 2017 and 2018. The firm’s
current assets increased by $20 million and spontaneous current liabilities increased by $12 million.

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Calculate Fields and Struthers’s NOPAT operating cash flow, investment in operating capital, and free
cash flow for 2018. (LG2-5)
2-12 Free Cash Flow Tater and Pepper Corp. reported free cash flows for 2018 of $39.1 million and
investment in operating capital of $22.1 million. Tater and Pepper incurred $13.6 million in
depreciation expense and paid $28.9 million in taxes on EBIT in 2018. Calculate Tater and Pepper’s
2018 EBIT. (LG2-5)
2-13 Statement of Retained Earnings Mr. Husker’s Tuxedos Corp. began the year 2018 with $256 million
in retained earnings. The firm earned net income of $33 million in 2018 and paid dividends of $5
million to its preferred stockholders and $10 million to its common stockholders. What is the year-end
2018 balance in retained earnings for Mr. Husker’s Tuxedos? (LG2-1)
2-14 Statement of Retained Earnings Use the following information to find dividends paid to common
stockholders during 2018. (LG2-1)
Balance of retained earnings, December 31, 2017 $ 462m
Plus: Net income for 2018 15m
Less: Cash dividends paid
Preferred stock $ 1m
Common stock
Total cash dividends paid $
Balance of retained earnings, December 31, 2018 $ 470m
INTERMEDIATE PROBLEMS
2-15 Balance Sheet Brenda’s Bar and Grill has total assets of $15 million, of which $5 million are current
assets. Cash makes up 10 percent of the current assets and accounts receivable makes up another 40
percent of current assets. Brenda’s gross plant and equipment has a book value of $11.5 million, and
other long-term assets have a book value of $500,000. Using this information, what is the balance of
inventory and the balance of depreciation on Brenda’s Bar and Grill’s balance sheet? (LG2-1)
2-16 Balance Sheet Glen’s Tobacco Shop has total assets of $91.8 million. Fifty percent of these assets are
financed with debt of which $28.9 million is current liabilities. The firm has no preferred stock but the
balance in common stock and paid-in surplus is $20.4 million. Using this information, what is the
balance for long-term debt and retained earnings on Glen’s Tobacco Shop’s balance sheet? (LG2-1)
2-17 Market Value versus Book Value Muffin’s Masonry, Inc.’s, balance sheet lists net fixed assets as
$14 million. The fixed assets could currently be sold for $19 million. Muffin’s current balance sheet
shows current liabilities of $5.5 million and net working capital of $4.5 million. If all the current
accounts were liquidated today, the company would receive $7.25 million cash after paying the $5.5
million in current liabilities. What is the book value of Muffin’s Masonry’s assets today? What is the
market value of these assets? (LG2-2)

2-18 Market Value versus Book Value Ava’s SpinBall Corp. lists fixed assets of $12 million on its
balance sheet. The firm’s fixed assets have recently been appraised at $16 million. Ava’s SpinBall
Corp.’s balance sheet also lists current assets at $5 million. Current assets were appraised at $6
million. Current liabilities’ book and market values stand at $3 million, and the firm’s book and
market values of long-term debt are $7 million. Calculate the book and market values of the firm’s
stockholders’ equity. Construct the book value and market value balance sheets for Ava’s SpinBall
Corp. (LG2-2)
2-19 Debt versus Equity Financing You are considering a stock investment in one of two firms
(NoEquity, Inc., and NoDebt, Inc.), both of which operate in the same industry and have identical
operating income of $32.5 million. NoEquity, Inc., finances its $65 million in assets with $64 million
in debt (on which it pays 10 percent interest annually) and $1 million in equity. NoDebt, Inc., finances
its $65 million in assets with no debt and $65 million in equity. Both firms pay a tax rate of 30 percent
on their taxable income. Calculate the net income and return on assets for the two firms. (LG2-1)

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2-20 Debt versus Equity Financing You are considering a stock investment in one of two firms (AllDebt,
Inc., and AllEquity, Inc.), both of which operate in the same industry and have identical operating
income of $12.5 million. AllDebt, Inc., finances its $25 million in assets with $24 million in debt (on
which it pays 10 percent interest annually) and $1 million in equity. AllEquity, Inc., finances its $25
million in assets with no debt and $25 million in equity. Both firms pay a tax rate of 30 percent on
their taxable income. Calculate the income available to pay the asset funders (the debt holders and
stockholders) and resulting return on assets for the two firms. (LG2-1)
2-21 Income Statement You have been given the following information for Corky’s Bedding Corp.:
a. Net sales = $11,250,000.
b. Cost of goods sold = $7,500,000.
c. Other operating expenses = $250,000.
d. Addition to retained earnings = $1,000,000.
e. Dividends paid to preferred and common stockholders = $495,000.
f. Interest expense = $850,000.
2-22 Income Statement You have been given the following information for Moore’s HoneyBee Corp.:
a. Net sales = $32,000,000.
b. Gross profit = $18,700,000.
c. Other operating expenses = $2,500,000.
d. Addition to retained earnings = $4,700,000.
e. Dividends paid to preferred and common stockholders = $2,900,000.
f. Depreciation expense = $2,800,000.
The firm’s tax rate is 35 percent. Calculate the cost of goods sold and the interest expense for
Moore’s HoneyBee Corp. (LG2-1)
2-23 Income Statement Consider a firm with an EBIT of $1,000,000. The firm finances its assets with
$4,500,000 debt (costing 8 percent) and 200,000 shares of stock selling at $16.00 per share. To reduce
risk associated with this financial leverage, the firm is considering reducing its debt by $2,500,000 by
selling additional shares of stock. The firm is in the 40 percent tax bracket. The change in capital
structure will have no effect on the operations of the firm. Thus, EBIT will remain at $1,000,000.
Calculate the change in the firm’s EPS from this change in capital structure. (LG2-1)

2-24 Income Statement Consider a firm with an EBIT of $10,500,000. The firm finances its assets with
$50,000,000 debt (costing 6.5 percent) and 10,000,000 shares of stock selling at $10.00 per share. The
firm is considering increasing its debt by $25,000,000, using the proceeds to buy back shares of stock.
The firm is in the 40 percent tax bracket. The change in capital structure will have no effect on the
operations of the firm. Thus, EBIT will remain at $10,500,000. Calculate the change in the firm’s EPS
from this change in capital structure. (LG2-1)
2-25 Corporate Taxes The Dakota Corporation had a 2018 taxable income of $33,365,000 from operations
after all operating costs but before (1) interest charges of $8,500,000; (2) dividends received of
$750,000; (3) dividends paid of $5,250,000; and (4) income taxes. (LG2-3)
a. Use the tax schedule in Table 2.3 to calculate Dakota’s income tax liability
b. What are Dakota’s average and marginal tax rates on taxable income?
2-26 Corporate Taxes Suppose that in addition to $17.85 million of taxable income, Texas Taco, Inc.,
received $1,105,000 of interest on state-issued bonds and $760,000 of dividends on common stock it
owns in Arizona Taco, Inc. (LG2-3)
a. Use the tax schedule in Table 2.3 to calculate Texas Taco’s income tax liability.
b. What are Texas Taco’s average and marginal tax rates on taxable income?
2-27 Statement of Cash Flows Use the balance sheet and income statement below to construct a statement
of cash flows for Clancy’s Dog Biscuit Corporation. (LG2-5)

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CLANCY’S DOG BISCUIT CORPORATION
Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)
2018 2017 2018 2017
Assets Liabilities and Equity
Current assets: Current liabilities:
Cash and marketable
securities
$ 5 $ 5 Accrued wages and taxes $ 10 $ 6
Accounts receivable 20 19 Accounts payable 16 15
Inventory  36  29 Notes payable  14  13
Total $ 61 $ 53 Total $ 40 $ 34
Fixed assets: Long-term debt: $ 57 $ 53
Gross plant and
equipment
$106 $ 88
Less: Accumulated
depreciation
 15  11 Stockholders’ equity:
$ 91 $ 77 Preferred stock (2 million shares) $ 2 $ 2
Net plant and
equipment
Common stock and paid-in
surplus (5 million shares)
11 11
Other long-term
assets
  15   15 Retained earnings  57  45
Total $106 $ 92 Total $ 70 $ 58
Total assets $167 $145 Total liabilities and equity $167 $145

CLANCY’S DOG BISCUIT CORPORATION
Income Statement for Years Ending December 31, 2018 and 2017
(in millions of dollars)
2018 2017
Net sales $ 76 $ 80
Less: Cost of goods sold   38   34
Gross profits $ 38 $ 46
Less: Other operating expenses    6    5
Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 32 $ 41
Less: Depreciation    4    4
Earnings before interest and taxes (EBIT) $  28 $ 37
Less: Interest    5    5
Earnings before taxes (EBT) $  23 $ 32

Less: Taxes    7   10
Net income $  16 $  22
Less: Preferred stock dividends $  1 $  1
Net income available to common stockholders $  15 $ 21
Less: Common stock dividends    3    3
Addition to retained earnings $  12 $ 18
Per (common) share data:
Earnings per share (EPS) $ 3.00 $ 4.20
Dividends per share (DPS) $ 0.60 $ 0.60
Book value per share (BVPS) $13.60 $11.20
Market value (price) per share (MVPS) $14.25 $14.60
2-28 Statement of Cash Flows Use the balance sheet and income statement below to construct a statement
of cash flows for Valium’s Medical Supply Corporation. (LG2-5)
VALIUM’S MEDICAL SUPPLY CORPORATION Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)
2018 2017 2018 2017
Assets Liabilities and Equity
Current assets Current liabilities
Cash and
marketable
securities
$ 74 $ 73 Accrued wages and taxes $ 58 $  45
Accounts
receivable
199 189 Accounts payable 159 145
Inventory  322  291 Notes payable  131  131
Total $ 595 $ 553 Total $ 348 $ 321
Fixed assets Long-term debt $ 565 $ 549
Gross plant and
equipment
$1,084 $ 886
Less:
Accumulated
depreciation
 153  116 Stockholders’ equity
Net plant and
equipment
$ 931 770 Preferred stock (6 thousand
shares)
$  6 $  6
Common stock and paid-in
surplus (100 thousand
shares)
120 120
Other long-term
assets
  130  130 Retained earnings   617   457
Total $1,061 $ 900 Total $ 743 $ 583

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Total assets $1,656 $1,453 Total liabilities and equity $1,656 $1,453

VALIUM’S MEDICAL SUPPLY CORPORATION
Income Statement for Years Ending December 31, 2018 and 2017
(in thousands of dollars)
2018 2017
Net sales $ 888 $ 798
Less: Cost of goods sold  387  350
Gross profits $ 501 $ 448
Less: Other operating expenses   48   42
Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 453 $ 406
Less: Depreciation   37   35
Earnings before interest and taxes (EBIT) $ 416 $ 371
Less: Interest   46   40
Earnings before taxes (EBT) $ 370 $ 331
Less: Taxes  129  112
Net income $ 241 $ 219
Less: Preferred stock dividends $  6 $  6
Net income available to common stockholders $ 235 $ 213
Less: Common stock dividends   75   75
Addition to retained earnings $ 160 $ 138
Per (common) share data:
Earnings per share (EPS) $2.35 $2.13
Dividends per share (DPS) $0.75 $0.75
Book value per share (BVPS) $7.37 $5.77
Market value (price) per share (MVPS) $8.40 $6.25
2-29 Statement of Cash Flows Chris’s Outdoor Furniture, Inc., has net cash flows from operating
activities for the last year of $340 million. The income statement shows that net income is $315
million and depreciation expense is $46 million. During the year, the change in inventory on the
balance sheet was $38 million, change in accrued wages and taxes was $15 million, and change in
accounts payable was $20 million. At the beginning of the year, the balance of accounts receivable
was $50 million. Calculate the end-of-year balance for accounts receivable. (LG2-5)
2-30 Statement of Cash Flows Dogs 4 U Corporation has net cash flow from financing activities for the
last year of $34 million. The company paid $178 million in dividends last year. During the year, the
change in notes payable on the balance sheet was $39 million and change in common and preferred
stock was $0. The end-of-year balance for long-term debt was $315 million. Calculate the beginning-
of-year balance for long-term debt. (LG2-5)

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2-31 Free Cash Flow The 2018 income statement for Duffy’s Pest Control shows that depreciation
expense was $197 million, EBIT was $494 million, and the tax rate was 30 percent. At the beginning
of the year, the balance of gross fixed assets was $1,562 million and net operating working capital was
$417 million. At the end of the year, gross fixed assets was $1,803 million. Duffy’s free cash flow for
the year was $424 million. Calculate the end-of-year balance for net operating working capital. (LG2-
5)
2-32 Free Cash Flow The 2018 income statement for Egyptian Noise Blasters shows that depreciation
expense is $85 million, NOPAT is $246 million. At the end of the year, the balance of gross fixed
assets was $655 million. The change in net operating working capital during the year was $73 million.
Egyptian’s free cash flow for the year was $190 million. Calculate the beginning-of-year balance for
gross fixed assets. (LG2-5)

2-33 Statement of Retained Earnings Thelma and Louie, Inc., started the year with a balance of retained
earnings of $543 million and ended the year with retained earnings of $589 million. The company paid
dividends of $35 million to the preferred stockholders and $88 million to common stockholders.
Calculate Thelma and Louie’s net income for the year. (LG2-1)
2-34 Statement of Retained Earnings Jamaica Tours, Inc., started the year with a balance of retained
earnings of $1,780 million. The company reported net income for the year of $284 million and paid
dividends of $17 million to the preferred stockholders and $59 million to common stockholders.
Calculate Jamaica Tour’s end-of-year balance in retained earnings. (LG2-1)
ADVANCED PROBLEMS
2-35 Income Statement Listed below is the 2018 income statement for Tom and Sue Travels, Inc. (LG2-5)
TOM AND SUE TRAVELS, INC.
Income Statement for Year Ending December 31, 2018
(in millions of dollars)
Net sales $16.500
Less: Cost of goods sold  7.100
Gross profits $ 9.400
Less: Other operating expenses  3.200
Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 6.200
Less: Depreciation  2.900
Earnings before interest and taxes (EBIT) $ 3.300
Less: Interest  0.950
Earnings before taxes (EBT) $ 2.350
Less: Taxes  0.705
Net income $ 1.645
The CEO of Tom and Sue’s wants the company to earn a net income of $2.250 million in 2019. Cost of
goods sold is expected to be 60 percent of net sales, depreciation and other operating expenses are not
expected to change, interest expense is expected to increase to $1.050 million, and the firm’s tax rate will
be 30 percent. Calculate the net sales needed to produce net income of $2.250 million. (LG2-1)
2-36 Income Statement You have been given the following information for PattyCake’s Athletic Wear
Corp. for the year 2018:
a. Net sales = $38,250,000.

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b. Cost of goods sold = $22,070,000.
c. Other operating expenses = $5,300,000.
d. Addition to retained earnings = $1,195,500.
e. Dividends paid to preferred and common stockholders = $1,912,000.
f. Interest expense = $1,785,000.
g. The firm’s tax rate is 30 percent.
In 2019:
h. Net sales are expected to increase by $9.75 million.
i. Cost of goods sold is expected to be 60 percent of net sales.
j. Depreciation and other operating expenses are expected to be the same as in 2018.
k. Interest expense is expected to be $2,004,286.
l. The tax rate is expected to be 30 percent of EBT.
m. Dividends paid to preferred and common stockholders will not change.
Calculate the addition to retained earnings expected in 2019. (LG2-1)
2-37 Free Cash Flow Rebecky’s Flowers 4U, Inc., had free cash flows during 2018 of $43 million,
NOPAT of $85 million, and depreciation of $14 million. Using this information, fill in the blanks on
Rebecky’s balance sheet below. (LG2-5)
REBECKY’S FLOWERS 4U, INC.
Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)
2018 2017 2018 2017
Assets Liabilities and Equity
Current assets: Current liabilities:
Cash and
marketable
securities
$ 28 $ 25 Accrued wages and taxes $ 17 $ 15
Accounts receivable 75 65 Accounts payable 50
Inventory  118 100 Notes payable  45 45
Total $221 $190 Total $ $110
Fixed assets: Long-term debt: $ $190
Gross plant and
equipment
$333 $300
Less: Accumulated
depreciation
54 40 Stockholders’ equity:
Net plant and
equipment
$279 $260 Preferred stock (5 million
shares)
$ 5 $ 5
Common stock and paid-in
surplus (20 million shares)
40 40
Other long-term
assets
50 50 Retained earnings  192  
155
Total $329 $310 Total $237 $200
Total assets $550 $500 Total liabilities and equity $550 $500

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2-38 Free Cash Flow Vinny’s Overhead Construction had free cash flow during 2018 of $25.4 million.
The change in gross fixed assets on Vinny’s balance sheet during 2018 was $7.0 million and the
change in net operating working capital was $8.4 million. Using this information, fill in the blanks on
Vinny’s income statement below. (LG2-5)
VINNY’S OVERHEAD CONSTRUCTION CORP.
Income Statement for Year Ending December 31, 2018
(in millions of dollars)
Net sales $
Less: Cost of goods sold 116.10
Gross profits $66.00
Less: Other operating expenses 12.40
Earnings before interest, taxes, depreciation, and amortization (EBITDA) $53.60
Less: Depreciation 10.20
Earnings before interest and taxes (EBIT)
Less: Interest
Earnings before taxes (EBT) $
Less: Taxes
Net income $27.64

Notes
CHAPTER 2
1. Technically operating income and EBIT are different. Specifically, operating income is considered an official financial measure under
GAAP, while EBIT is a non-GAAP measure. EBIT makes adjustment for items that are not accounted for in operating income. In a
majority of cases, these differences are minimal and not crucially important to individual investors who are reviewing financial
statements. As a result, operating income and EBIT are used interchangeably across much of the accounting and finance world.
2. This tax code provision prevents or reduces any triple taxation that could occur: Income could be taxed at three levels: (1) on the
income from the dividend-paying firm, (2) as income for the dividend-receiving firm, and (3) finally, on the personal income of
stockholders who receive dividends.
3. Any other noncash expense (e.g., amortization) would also be added back to net income and any noncash revenue would be
subtracted.

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chapter three
analyzing
financial statements
©Zigzag Mountain Art/Shutterstock

W
page 60
e reviewed the major financial statements in Chapter 2. These financial statements provide
information on a firm’s financial position at a point in time or its operations over some past period
of time. But the real value of these financial statements lies in the fact that managers, investors,
and analysts can use the information the statements contain to analyze the current financial performance
or condition of the firm. More importantly, managers can use this information to plan changes that will
improve the firm’s future performance and, ultimately, its market value. Managers, investors, and analysts
universally use ratios to evaluate financial statements. Ratio analysis involves calculating and analyzing
financial ratios to assess a firm’s performance and to identify actions that could improve firm performance.
The most frequently used ratios fall into five groups: (1) liquidity ratios, (2) asset management ratios, (3)
debt management ratios, (4) profitability ratios, and (5) market value ratios. Each of the five groups
focuses on a specific area of the financial statements that managers, investors, and analysts assess.
ratio analysis The process of calculating and analyzing financial ratios to assess the firm’s performance and to identify actions needed
to improve firm performance.
LEARNING GOALS
LG3-1 Calculate and interpret major liquidity ratios.
LG3-2 Calculate and interpret major asset management ratios.
LG3-3 Calculate and interpret major debt management ratios.
LG3-4 Calculate and interpret major profitability ratios.
LG3-5 Calculate and interpret major market value ratios.
LG3-6 Appreciate how various ratios relate to one another.
LG3-7 Understand the differences between time series and cross-sectional ratio analyses.
LG3-8 Explain cautions that should be taken when examining financial ratios.

viewpoints
business APPLICATION
The managers of DPH Tree Farm, Inc., have released public statements that the firm’s performance surpasses that of other firms in
the industry. They cite the firm’s liquidity and asset management positions as particularly strong. DPH’s superior performance in these
areas has resulted in superior overall returns for their stockholders. What are the key financial ratios that DPH Tree Farm, Inc., needs
to calculate and evaluate in order to justify these statements? (See the solution at the end of the book.)
In this chapter, we review these ratios, describe what each ratio means, and identify the general trend
(higher or lower) that managers and investment analysts look for in each ratio. Note as we review the
ratios that the number calculated for a ratio is not always good or bad and that extreme values (either
high or low) can be a bad sign for a firm. We will discuss how a ratio that seems too good can actually be
bad for a company. We will also see how ratios interrelate—how a change in one ratio may affect the
value of several ratios. It is often hard to make sense of a set of performance ratios. Thus, when
managers or investors review a firm’s financial position through ratio analysis, they often start by
evaluating trends in the firm’s financial ratios over time and by comparing their firm’s ratios with that of
other firms in the same industry. Finally, we discuss cautions that you should take when using ratio
analysis to evaluate firm performance. As we go through the chapter, we show sample ratio analysis
using the financial statements for DPH Tree Farm, Inc., listed in Tables 2.1 and 2.2.
3.1 • LIQUIDITY RATIOS LG3-1

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As we stated in Chapter 2, firms need cash and other liquid assets (or current assets) to pay their bills (or current
liabilities) as they come due. Liquidity ratios measure the relationship between a firm’s liquid (or current) assets and
its current liabilities. The three most commonly used liquidity ratios are the current ratio, the quick (or acid-test)
ratio, and the cash ratio.
liquidity ratios Measure the relationship between a firm’s liquid (or current) assets and its current liabilities.
(3-1)
The broadest liquidity measure, the current ratio, measures the dollars of current assets available to pay each dollar
of current liabilities.
(3-2)
Inventories are generally the least liquid of a firm’s current assets. Further, inventory is the current asset for which
book values are the least reliable measures of market value. In practical terms, what this means is that if the firm
must sell inventory to pay upcoming bills, the firm will most likely have to discount inventory items in order to
liquidate them, and thus they are the current assets on which losses are most likely to occur. Therefore, the
quick (or acid-test) ratio measures a firm’s ability to pay off short-term obligations without relying on
inventory sales. The quick ratio measures the dollars of more liquid assets (cash and marketable securities and
accounts receivable) available to pay each dollar of current liabilities.
personal APPLICATION
Chris Ryan is looking to invest in DPH Tree Farm, Inc. Chris has the most recent set of financial statements from DPH Tree Farm’s
annual report but is not sure how to evaluate them or measure the firm’s performance relative to other firms in the industry. What are
the financial ratios with which Chris should measure the performance of DPH Tree Farm, Inc.? How can Chris use these ratios to
evaluate the firm’s performance? (See the solution at the end of the book.)
So how can these financial ratios work in your life?
(3-3)
If the firm sells accounts receivable to pay upcoming bills, the firm must often discount the accounts receivable to
sell them—the assets once again bring less than their book value. Therefore, the cash ratio measures a firm’s ability
to pay short-term obligations with its available cash and marketable securities.
Of course, liquidity on the balance sheet is important. The more liquid assets a firm holds, the less likely the firm is
to experience financial distress. Thus, the higher the liquidity ratios, the less liquidity risk a firm has. But as
with everything else in business, high liquidity represents a painful trade-off for the firm. Liquid assets
generate little, if any, profits for the firm. In contrast, fixed assets are illiquid, but generate revenue for the firm.
Thus, extremely high levels of liquidity guard against liquidity crises, but at the cost of lower returns on assets. High
liquidity levels may actually show bad or indecisive firm management. Thus, in deciding the appropriate level of
current assets to hold on the balance sheet, managers must consider the trade-off between the advantages of being
liquid versus the disadvantages of reduced profits. Note that a company with very predictable cash flows can
maintain low levels of liquidity without incurring much liquidity risk.
EXAMPLE 3-1 Calculating Liquidity Ratios LG3-
1

For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.
SOLUTION:
The liquidity ratios for DPH Tree Farm, Inc., are calculated as follows.
The industry average is reported alongside each ratio.
Industry average =
1.50 times
Industry average =
0.50 times
Industry average =
0.15 times
All three liquidity ratios show that DPH Tree Farm, Inc., has more
liquidity on its balance sheet than the industry average (we discuss the
process used to develop an industry average in section 3.8). Thus,
DPH Tree Farm has more cash and other liquid assets (or current
assets) available to pay its bills (or current liabilities) as they come due
than does the average firm in the tree farm industry.
Similar to Problems 3-1, 3-2, Self-Test Problem 1
3.2 • ASSET MANAGEMENT RATIOS LG3-2
Asset management ratios measure how efficiently a firm uses its assets (inventory, accounts receivable, and fixed
assets), as well as how efficiently the firm manages its accounts payable. The specific ratios allow managers and
investors to evaluate whether a firm is holding a reasonable amount of each type of asset and whether management
uses each type of asset to effectively generate sales. The most frequently used asset management ratios are listed in
the following sections, grouped by type of asset.
asset management ratios Measure how efficiently a firm uses its assets (inventory, accounts receivable, and fixed assets), as well as
its accounts payable.

http://mhhe.com/CornettM4e

The inventory turnover ratio measures the number of dollars of sales produced per dollar of inventory.
©Ryan McVay/Getty Images
time out!
3-1 What are the three major liquidity ratios used in evaluating financial statements?
3-2 How do the three major liquidity ratios used in evaluating financial statements differ?
3-3 Does a firm generally want to have high or low liquidity ratios? Why?
Inventory Management
As they decide the optimal inventory level to hold on the balance sheet, managers must consider the trade-off
between the advantages of holding sufficient levels of inventory to keep the production process going versus the
costs of holding large amounts of inventory. Two frequently used ratios are the inventory turnover and days’ sales in
inventory.
(3-4)
The inventory turnover ratio measures the number of dollars of sales produced per dollar of inventory. Cost of goods
sold is used in the numerator when managers want to emphasize that inventory is listed on the balance sheet at cost,
that is, the cost of sales generated per dollar of inventory.

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(3-5)
The days’ sales in inventory ratio measures the number of days that inventory is held before the final product is sold.
In general, a firm wants to produce a high level of sales per dollar of inventory; that is, it wants to turn inventory
over (from raw materials to finished goods to sold goods) as quickly as possible. A high level of sales per dollar of
inventory implies reduced warehousing, monitoring, insurance, and any other costs of servicing the inventory. So, a
high inventory turnover ratio or a low days’ sales in inventory is generally a sign of good management.
However, if the inventory turnover ratio is extremely high and the days’ sales in inventory is extremely low, the firm
may not be holding sufficient inventory to prevent running out (or stocking out) of the raw materials needed to keep
the production process going. Thus, production and sales stop, which wastes the firm’s fixed resources. So,
extremely high levels for the inventory turnover ratio and low levels for the days’ sales in inventory ratio may
actually be a sign of bad firm or production management. Note that companies with very good supply chain
relations can maintain lower levels of inventory without incurring as much risk of stockouts.
Accounts Receivable Management
As they decide the level of accounts receivable to hold on the firm’s balance sheet, managers must consider the
trade-off between the advantages of increased sales by offering customers better terms versus the disadvantages of
financing large amounts of accounts receivable. Two ratios used here are the accounts receivable turnover and
average collection period.
(3-6)
The accounts receivable turnover measures the number of dollars of sales produced per dollar of accounts
receivable.
(3-7)
The average collection period (ACP) measures the number of days accounts receivable are held before the firm
collects cash from the sale. This ratio is also sometimes termed the days’ sales outstanding (DSO).
In general, a firm wants to produce a high level of sales per dollar of accounts receivable; that is, it wants to collect
its accounts receivable as quickly as possible to reduce any cost of financing accounts receivable, including interest
expense on liabilities used to finance accounts receivable and defaults associated with accounts receivable. In
general, a high accounts receivable turnover or a low ACP is a sign of good management, which is well aware of
financing costs and customer remittance habits.
However, if the accounts receivable turnover is extremely high and the ACP is extremely low, the firm’s accounts
receivable policy may be so strict that customers prefer to do business with competing firms. Firms offer accounts
receivable terms as an incentive to get customers to buy products from their firm rather than a competing firm. By
offering customers the accounts receivable privilege, management allows them to buy (more) now and pay later.
Without this incentive, customers may choose to buy the goods from the firm’s competitors who offer better credit
terms. So extremely high accounts receivable turnover levels and low ACP levels may be a sign of bad firm
management.
Accounts Payable Management
As they decide the accounts payable level to hold on the balance sheet, managers must consider the trade-off
between maximizing the use of free financing that raw material suppliers offer versus the risk of losing the
opportunity to buy on account. Two ratios commonly used are the accounts payable turnover and average payment
period.

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(3-8)
The accounts payable turnover ratio measures the dollar cost of goods sold per dollar of accounts payable.
(3-9)
The average payment period (APP) measures the number of days that the firm holds accounts payable before it has
to extend cash to pay for its purchases.

In general, a firm wants to pay for its purchases as slowly as possible. The slower the firm pays for its supply
purchases, the longer it can avoid obtaining other costly sources of financing such as notes payable or long-term
debt. Thus, a low accounts payable turnover or a high APP is generally a sign of good management.
However, if the accounts payable turnover is extremely low and the APP is extremely high, the firm may be abusing
the credit terms that its raw materials suppliers offer. At some point, the firm’s suppliers may revoke its ability to
buy raw materials on account and the firm will lose this source of free financing. If this situation is developing,
extremely low levels for the accounts receivable turnover and high levels for the APP may point to bad firm
management.
Fixed Asset and Working Capital Management
Two ratios that summarize the efficiency in a firm’s overall asset management are the fixed asset turnover and sales
to working capital ratios.
(3-10)
The fixed asset turnover ratio measures the number of dollars of sales produced per dollar of net fixed assets.
(3-11)
Similarly, the sales to working capital ratio measures the number of dollars of sales produced per dollar of net
working capital (current assets minus current liabilities).
In general, the higher the level of sales per dollar of fixed assets and working capital, the more efficiently the firm is
being run. Thus, high fixed asset turnover and sales to working capital ratios are generally signs of good
management. However, if either the fixed asset turnover or sales to working capital ratio is extremely high, the firm
may be close to its maximum production capacity. If capacity is hit, the firm cannot increase production or sales.
Accordingly, extremely high fixed asset turnover and sales to working capital ratio levels may actually indicate bad
firm management if managers have allowed the company to approach maximum capacity without making any
accommodations for growth.
Note a word of caution here. The age of a firm’s fixed assets will affect the fixed asset turnover ratio level. A firm
with older fixed assets, listed on its balance sheet at historical cost, will tend to have a higher fixed asset turnover
ratio than will a firm that has just replaced its fixed assets and lists them on its balance sheet at a (most likely) higher
value. Accordingly, the firm with newer fixed assets would have a lower fixed asset turnover ratio. But this is
because it has updated its fixed assets, while the other firm has not. It is not correct to conclude that the firm with
new assets is underperforming relative to the firm with older fixed assets listed on its balance sheet. Similarly, for
firms that are in an expansion phase, a lower fixed asset turnover is actually a good sign. It is not correct to conclude
that a firm with expanding assets is underperforming relative to a firm with no growth.

page 65
time out!
3-4 What are the major asset management ratios?
3-5 Does a firm generally want to have high or low values for each of these ratios?
3-6 Explain why many of these ratios are mirror images of one another.
Total Asset Management
The final two asset management ratios put it all together. They are the total asset turnover and capital intensity
ratios.
(3-12)
The total asset turnover ratio measures the number of dollars of sales produced per dollar of total assets.
(3-13)
Similarly, the capital intensity ratio measures the dollars of total assets needed to produce a dollar of sales.
In general, a well-managed firm produces many dollars of sales per dollar of total assets, or uses few dollars of
assets per dollar of sales. Thus, in general, the higher the total asset turnover and lower the capital intensity
ratio, the more efficient the overall asset management of the firm will be. However, if the total asset
turnover is extremely high and the capital intensity ratio is extremely low, the firm may actually have an asset
management problem. As described above, inventory stockouts, capacity problems, or tight account receivables
policies can all lead to a high total asset turnover and may actually be signs of poor firm management.
EXAMPLE 3-2
Calculating Asset Management
Ratios LG3-2
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.
SOLUTION:
We calculate the asset management ratios for DPH Tree Farm, Inc., as
follows. The industry average is reported alongside each ratio.
Industry average =
2.15 times
Industry average =
170 days
Industry average =
3.84 times

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Industry average =
95 days
Industry average =
3.55 times
Industry average =
102 days
Industry average =
0.85 times
Industry average =
3.20 times
Industry average =
0.40 times
Industry average =
2.50 times
In all cases, asset management ratios show that DPH Tree Farm, Inc.,
is outperforming the industry average. The firm is turning over its
inventory faster than the average firm in the tree farm industry, thus
producing more dollars of sales per dollar of inventory. It is also
collecting its accounts receivable faster and paying its accounts
payable slower than the average firm. Further, DPH Tree Farm is
producing more sales per dollar of fixed assets, working capital, and
total assets than the average firm in the industry.
Similar to Problems 3-3, 3-4, Self-Test Problem 1

3.3 • DEBT MANAGEMENT RATIOS LG3-3
As we discussed in Chapter 2, financial leverage refers to the extent to which the firm uses debt securities in its
capital structure. The more debt a firm uses as a percentage of its total assets, the greater is its financial leverage.
Debt management ratios measure the extent to which the firm uses debt (or financial leverage) versus equity to finance
its assets as well as how well the firm can pay off its debt. The specific ratios allow managers and investors to
evaluate whether a firm is financing its assets with a reasonable amount of debt versus equity financing, as well as
whether the firm is generating sufficient earnings or cash to make the promised payments on its debt. The most
commonly used debt management ratios are listed in the following sections.
debt management ratios Measure the extent to which the firm uses debt (or financial leverage) versus equity to finance its assets as
well as how well the firm can pay off its debt.
Debt versus Equity Financing

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Managers’ choice of capital structure—the amount of debt versus equity to issue—affects the firm’s viability as a
long-term entity. In deciding the level of debt versus equity financing to hold on the balance sheet, managers must
consider the trade-off between maximizing cash flows to the firm’s stockholders versus the risk of being unable to
make promised debt payments. Ratios that are commonly used are the debt ratio, debt-to-equity, and equity
multiplier.
capital structure The amount of debt versus equity financing held on the balance sheet.
(3-14)
The debt ratio measures the percentage of total assets financed with debt.
(3-15)
The debt-to-equity ratio measures the dollars of debt financing used for every dollar of equity financing.
(3-16)
The equity multiplier ratio measures the dollars of assets on the balance sheet for every dollar of equity (or just
common stockholders’ equity) financing.
As you might suspect, all three measures are related.1 Specifically

Notice in all three ratios, the less debt (and more equity) a firm uses, the lower the value of the ratio. Conversely, the
lower the debt, debt-to-equity, or equity multiplier, the less debt and more equity the firm uses to finance its assets
(i.e., the bigger the firm’s equity cushion).
When a firm issues debt to finance its assets, it gives the debt holders first claim to a fixed amount of its cash flows.
Stockholders are entitled to any residual cash flows—those left after debt holders are paid. When a firm does well,
financial leverage increases the reward to shareholders since the amount of cash flows promised to debt holders is
constant and capped. So when firms do well, financial leverage creates more cash flows to share with stockholders
—it magnifies the return to the stockholders of the firm (recall Example 2-5). This magnification is one reason that
stockholders encourage the use of debt financing.
However, financial leverage also increases the firm’s potential for financial distress and even failure. If the firm has
a bad year and cannot make promised debt payments, debt holders can force the firm into bankruptcy. Thus,
a firm’s current and potential debt holders (and even stockholders) look at equity financing as a safety
cushion that can absorb fluctuations in the firm’s earnings and asset values and guarantee debt service payments.
Clearly, the larger the fluctuations or variability of a firm’s cash flows, the greater the need for an equity cushion.
Coverage Ratios
Three additional debt management ratios are the times interest earned, fixed charge coverage, and cash coverage
ratios. These ratios are different measures of a firm’s ability to meet its debt obligations.
(3-17)
The times interest earned ratio measures the number of dollars of operating earnings available to meet each dollar of
interest obligations on the firm’s debt.

(3-18)
EXAMPLE 3-3
Calculating Debt Management
Ratios LG3-3
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.
SOLUTION:
The debt management ratios for DPH Tree Farm, Inc., are calculated
as follows. The industry average is reported alongside each ratio.
Industry average =
68.50%
Industry average =
2.17 times
Industry average =
4.10 times
              Industry average =
4.14 times
Industry average =
5.15 times
Industry average =
5.70 times
Industry average =
7.78 times
In all cases, debt management ratios show that DPH Tree Farm, Inc.,
holds less debt on its balance sheet than the average firm in the tree
farm industry. Further, the firm has more dollars of operating earnings
and cash available to meet each dollar of interest obligations (there are
no other fixed charges listed on DPH Tree Farm’s income statement)
on the firm’s debt. This lack of financial leverage decreases the firm’s
potential for financial distress and even failure, but may also decrease
equity shareholders’ chance for magnified earnings. If the firm has a
bad year, it has promised relatively few payments to debt holders.
Thus, the risk of bankruptcy is small. However, when DPH Tree Farm,
Inc., does well, the low level of financial leverage dilutes the return to
the stockholders of the firm. This dilution of profit is likely to upset
common stockholders of the firm.

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page 68
Similar to Problems 3-5, 3-6, Self-Test Problem 1

The fixed-charge coverage ratio measures the number of dollars of operating earnings available to meet the firm’s
interest obligations and other fixed charges.
(3-19)
The cash coverage ratio measures the number of dollars of operating cash available to meet each dollar of interest
and other fixed charges that the firm owes.
With the help of the times interest earned, fixed-charge coverage, and cash coverage ratios, managers, investors, and
analysts can determine whether a firm has taken on a debt burden that is too large. These ratios measure the dollars
available to meet debt and other fixed-charge obligations. A value of one for these ratios means that $1 of earnings
or cash is available to meet each dollar of interest or fixed-charge obligations. A value of less (greater) than one
means that the firm has less (more) than $1 of earnings or cash available to pay each dollar of interest or fixed-
charge obligations.2 Further, the higher the times interest earned, fixed-charge coverage, and cash coverage ratios,
the more equity and less debt the firm uses to finance its assets. Thus, low levels of debt will lead to a dilution of the
return to stockholders due to increased use of equity as well as to not taking advantage of the tax deductibility of
interest expense.
time out!
3-7 What are the major debt management ratios?
3-8 Does a firm generally want to have high or low values for each of these ratios?
3-9 What is the trade-off between using too much financial leverage and not using enough leverage? Who is likely to complain
the most in each case?
3.4 • PROFITABILITY RATIOS LG3-4
The liquidity, asset management, and debt management ratios examined so far allow for an isolated or narrow look
at a firm’s performance. Profitability ratios show the combined effects of liquidity, asset management, and debt
management on the overall operating results of the firm. Profitability ratios are among the most watched and best
known of the financial ratios. Indeed, firm values (or stock prices) react quickly to unexpected changes in these
ratios. The most commonly used profitability ratios are listed below.
profitability ratios Ratios that show the combined effect of liquidity, asset management, and debt management on the firm’s overall
operating results.
(3-20)
The gross profit margin is the percent of sales left after costs of goods sold are deducted.
(3-21)
The operating profit margin is the percent of sales left after all operating expenses are deducted.
(3-22)

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A company’s profit margin is inversely related to its sales.
©B.O’Kane/Alamy Stock Photo
The profit margin is the percentage of sales left after all firm expenses are deducted. Thus, this ratio provides the net
profit margin of the firm, as opposed to the gross profit or operating profit margin.
(3-23)
The basic earnings power ratio measures the operating return on the firm’s assets, regardless of financial leverage
and taxes. This ratio measures the operating profit (EBIT) earned per dollar of assets on the firm’s balance sheet.
(3-24)

Return on assets (ROA) measures the overall return on the firm’s assets, including financial leverage and taxes. This
ratio is the net income earned per dollar of assets on the firm’s balance sheet.
(3-25)
Return on equity (ROE) measures the return on the common stockholders’ investment in the assets of the firm. ROE
is the net income earned per dollar of common stockholders’ equity. The value of a firm’s ROE is affected not only
by net income, but also by the amount of financial leverage or debt that firm uses. As stated previously, financial
leverage magnifies the return to the stockholders of the firm. However, financial leverage also increases the
firm’s potential for financial distress and even failure. Generally, a high ROE is considered to be a positive
sign of firm performance. However, if performance comes from a high degree of financial leverage, a high ROE can
indicate a firm with an unacceptably high level of bankruptcy risk as well.
EXAMPLE 3-4
Calculating Profitability
Ratios LG3-4
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.

http://mhhe.com/CornettM4e

SOLUTION:
The profitability ratios for DPH Tree Farm, Inc., are calculated as
follows. The industry average is reported alongside each ratio.
Industry average =
56.65%
Industry average =
46.88%
Industry average =
23.25%
Industry average =
22.85%
Industry average =
9.30%
Industry average =
38.00%
Industry average =
30.90%
These ratios show that DPH Tree Farm, Inc., is more profitable than
the average firm in the tree farm industry. The profit margin, gross profit
margin, operating profit margin, BEP, and ROA are all higher than
industry figures. Despite this, the ROE for DPH Tree Farm is much
lower than the industry average. DPH’s low debt level and high equity
level relative to the industry is the main reason for DPH’s strong figures
relative to the industry. As we mentioned above, DPH’s managerial
decisions about capital structure dilute its returns, which will likely upset
its common stockholders. To counteract common stockholders’
discontent, DPH Tree Farm pays out a slightly larger percentage of its
income to its common stockholders as cash dividends. Of course, this
slightly high dividend payout ratio means that DPH Tree Farm retains
less of its profits to reinvest into the business. A profitable firm that
retains its earnings increases its equity capital level as well as its own
value.
Similar to Problems 3-7, 3-8, Self-Test Problem 1
(3-26)
Finally, the dividend payout ratio is the percentage of net income available to common stockholders that the firm
actually pays as cash to these investors.
For all but the dividend payout, the higher the value of the ratio, the higher the profitability of the firm. But just as
has been the case previously in this chapter, high profitability ratio levels may result from poor management in other
areas of the firm as much as superior financial management. A high profit (and gross profit or operating profit)
margin means that the firm has low expenses relative to sales. The BEP reflects how much the firm’s assets earn

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from operations, regardless of financial leverage and taxes. It follows logically that managers, investors, and
analysts find BEP a useful ratio when they compare firms that differ in financial leverage and taxes. In contrast,
ROA measures the firm’s overall performance. It shows how the firm’s assets generate a return that includes
financial leverage and tax decisions made by management.
ROE measures the return on common stockholders’ investment. Since managers seek to maximize common stock
price, managers, investors, and analysts monitor ROE above all other ratios. The dividend payout ratio measures
how much of the profit the firm retains versus how much it pays out to common stockholders as dividends. The
lower the dividend payout ratio, the more profits the firm retains for future growth or other projects. A profitable
firm that retains its earnings increases its level of equity capital as well as its own value.
time out!
3-10 What are the major profitability ratios?
3-11 Does a firm generally want to have high or low values for each of these ratios?
3-12 What are the trade-offs to having especially high or low values for ROE?
3.5 • MARKET VALUE RATIOS LG3-5
As noted, ROE is a most important financial statement ratio for managers and investors to monitor. Generally, a
high ROE is considered to be a positive sign of firm performance. However, if a high ROE results from a highly
leveraged position, it can signal a firm with a high level of bankruptcy risk. While ROE does not directly incorporate
this risk, for publicly traded firms, market prices of the firm’s stock do. (We look at stock valuation in Chapter 8.)
Since the firm’s stockholders earn their returns primarily from the firm’s stock market value, ratios that incorporate
stock market values are equally, and arguably more, important than other financial statement ratios.
The final group of ratios is market value ratios. Market value ratios relate a firm’s stock price to its earnings and its
book value. For publicly traded firms, market value ratios measure what investors think of the company’s future
performance and risk.
market value ratios Ratios that relate a firm’s stock price to its earnings and book value.
(3-27)
The market-to-book ratio measures the amount that investors will pay for the firm’s stock per dollar of equity used
to finance the firm’s assets. Book value per share is an accounting-based number reflecting the firm’s assets’
historical costs, and hence historical value. The market-to-book ratio compares the market (current) value of the
firm’s equity to its historical cost. In general, the higher the market-to-book ratio, the better the firm. If liquidity,
asset management, debt management, and accounting profitability are good for a firm, then the market-to-book ratio
will be high. A market-to-book ratio greater than one (or 100 percent) means that stockholders will pay a
premium over book value for their equity investment in the firm.
EXAMPLE 3-5
Calculating Market Value
Ratios LG3-5
For interactive versions
of this example, log in
to Connect or go to
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the

mhhe.com/CornettM4e. asset management ratios.
SOLUTION:
The profitability ratios for DPH Tree Farm, Inc., are calculated as
follows. The industry average is reported alongside each ratio.
Industry average =
2.15 times
Industry average =
6.25 times
These ratios show that DPH Tree Farm’s investors will not pay as
much for a share of DPH’s stock per dollar of book value and earnings
as the average for the industry. DPH’s low leverage level and high
reliance on equity relative to the industry are likely the main reason for
investors’ disinterest. As mentioned previously, DPH’s seemingly
intentional return dilution will likely upset the firm’s common
stockholders. Accordingly, stockholders lower the amount they are
willing to invest per dollar of book value and EPS.
Similar to Problems 3-9, 3-10, Self-Test Problem 1
(3-28)
One of the best known and most often quoted figures, the price-earnings (or PE) ratio measures how much investors
are willing to pay for each dollar the firm earns per share of its stock. PE ratios are often quoted in multiples—the
number of dollars per share—that fund managers, investors, and analysts compare within industry classes. Managers
and investors often use PE ratios to evaluate the relative financial performance of the firm’s stock. Generally, the
higher the PE ratio, the better the firm’s performance. Analysts and investors, as well as managers, expect
companies with high PE ratios to experience future growth, to have rapid future dividend increases, or both, because
retained earnings will support the company’s goals. However, for value-seeking investors, high-PE firms indicate
expensive companies. Further, higher PE ratios carry greater risk because investors are willing to pay higher prices
today for a stock in anticipation of higher earnings in the future. These earnings may or may not materialize. Low-
PE firms are generally companies with little expected growth or low earnings. However, note that earnings depend
on many factors (such as financial leverage or taxes) that have nothing to do directly with firm operations.
time out!
3-13 What are the major market value ratios?
3-14 Does a firm generally want to have high or low values for each of these ratios?
3-15 Discuss the price-earnings ratio and explain why it assumes particular importance among all of the other ratios we have
presented.
3.6 • DUPONT ANALYSIS LG3-6
Table 3.1 lists the ratios we discuss, their values for DPH Tree Farm, Inc., as of 2018, and the corresponding values
for the tree farm industry. The value of each ratio for DPH Tree Farm is highlighted in green if it is generally
stronger than the industry and is highlighted in red if it is generally a negative sign for the firm. As we noted in this

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chapter’s introduction, many of the ratios we have discussed thus far are interrelated. So a change in one ratio may
well affect the value of several ratios. Often these interrelations can help evaluate firm performance. Managers and
investors often perform a detailed analysis of ROA (return on assets) and ROE (return on equity) using the DuPont
system of analysis. Popularized by the DuPont Corporation, the DuPont system of analysis uses the balance sheet and
income statement to break the ROA and ROE ratios into component pieces.
DuPont system of analysis An analytical method that uses the balance sheet and income statement to break the ROA and ROE ratios
into component pieces.

▼ TABLE 3.1 Summary of Ratios and their values for DPH Tree Farm, Inc., and the Tree Farm Industry
Ratio Value for DPH TreeFarm, Inc.
Value for the Tree
Farm Industry
Liquidity ratios:
1.67 times 1.50 times
0.76 times 0.50 times
0.20 times 0.15 times
Asset management ratios:
2.84 times 2.15 times
129 days 170 days
4.50 times 3.84 times
81 days 95 days
2.42 times 3.55 times
151 days 102 days
1.00 times 0.85 times
3.71 times 3.20 times
0.55 times 0.40 times
1.81 times 2.50 times
Debt management ratios:
55.26% 68.50%

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1.24 times 2.17 times
2.24 times 4.10 times
2.28 times 4.14 times
9.50 times 5.15 times
9.50 times 5.70 times
10.31 times
7.78 times

Profitability ratios:
57.78% 56.65%
48.25% 46.88%
25.40% 23.25%
26.67% 22.85%
14.04% 9.30%
32.00% 38.00%
31.25% 30.90%
Market value ratios:
1.38 times 2.15 times
4.31 times 6.25 times
The basic DuPont equation looks at ROA as the product of the profit margin and the total asset turnover ratios:
(3-29)
The basic DuPont equation looks at the firm’s overall profitability as a function of the profit the firm earns per dollar
of sales (operating efficiency) and the dollar of sales produced per dollar of assets on the balance sheet (efficiency in


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asset use). With this tool, managers can see the reason for any changes in ROA in more detail. For example, if ROA
increases, the DuPont equation may show that the net profit margin was constant, but the total asset turnover
(efficiency in using assets) increased, or that total asset turnover remained constant, but profit margins (operating
efficiency) increased. Managers can identify the reasons for an ROA change more specifically by using the ratios
described above to further break down operating efficiency and efficiency in asset use.

FIGURE 3-1 DuPont System Analysis Breakdown of ROA and ROE
Next, the DuPont system looks at ROE as the product of ROA and the equity multiplier.
(3-30)
Notice that this version of the equity multiplier uses the return to common stockholders (the firm’s owners) only. So
the DuPont equity multiplier uses common stockholders’ equity only, rather than total equity (which includes
preferred stock).
Taking this breakdown one step further, the DuPont system breaks ROE into the product of the profit margin, the
total asset turnover, and the equity multiplier.
(3-31)
This presentation of ROE allows managers, analysts, and investors to look at the return on equity as a function of the
net profit margin (profit per dollar of sales from the income statement), the total asset turnover (efficiency in the use
of assets from the balance sheet), and the equity multiplier (financial leverage from the balance sheet). Again, we

page 75
can break these components down to identify possible causes for an ROE change more specifically. Figure 3.1
illustrates the DuPont system of analysis breakdown of ROA and ROE. The figure highlights how many of the ratios
discussed in this chapter are linked.
time out!
3-16 What are the DuPont ROA and ROE equations?
3-17 How do each of these equations help to explain firm performance and pinpoint areas for improvement?

EXAMPLE 3-6
Application of DuPont
Analysis LG3-6
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.
SOLUTION:
The ROA and ROE DuPont equations for DPH Tree Farm, Inc., are
calculated as follows. The industry average is reported below each
ratio.
As we saw with profitability ratios, DPH Tree Farm, Inc., is more
profitable than the average firm in the tree farm industry when it comes
to overall efficiency expressed as return on assets, or ROA. The
DuPont equation highlights that this superior performance comes from
both profit margin (operating efficiency) and total asset turnover
(efficiency in asset use). Despite this, the ROE for DPH Tree Farm lags
the average industry ROE. The DuPont equation highlights that this

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inferior performance is due solely to the low level of debt and high level
of equity used by DPH Tree Farm relative to the industry.
Similar to Problems 3-11, 3-12
3.7 • OTHER RATIOS
Spreading the Financial Statements LG3-6
In addition to the many ratios listed, managers, analysts, and investors can also compute additional ratios by
dividing all balance sheet amounts by total assets and all income statement amounts by net sales. These calculations,
sometimes called spreading the financial statements, yield what we call common-size financial statements that correct
for sizes. Year-to-year growth rates in common-size balance sheets and income statement balances provide useful
ratios for identifying trends. They also allow for an easy comparison of balance sheets and income statements across
firms in the industry. Common-size financial statements may provide quantitative clues about the direction that the
firm (and perhaps the industry) is moving. They may thus provide roadmaps for managers’ next moves.
common-size financial statements Dividing all balance sheet amounts by total assets and all income statement amounts by net sales.

Internal and Sustainable Growth Rates
Remember again that any firm manager’s job is to maximize the firm’s market value. The firm’s ROA and ROE can
be used to evaluate the firm’s ability to grow and its market value to be maximized. Specifically, managers, analysts,
and investors use these ratios to calculate two growth measures: the internal growth rate and the sustainable growth
rate.
The internal growth rate is the growth rate a firm can sustain if it uses only internal financing—that is, retained
earnings—to finance future growth. Mathematically, the internal growth rate is
internal growth rate The growth rate a firm can sustain if it finances growth using only internal financing, that is, retained earnings
growth.
(3-32)
where RR is the firm’s earnings retention ratio. The retention ratio represents the portion of net income that the firm
reinvests as retained earnings:
(3-33)
Since a firm either pays its net income as dividends to its stockholders or reinvests those funds as retained earnings,
the dividend payout and the retention ratios must always add to one:
(3-34)
EXAMPLE 3-7
Calculating Internal and
Sustainable Growth Rates LG3-6

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For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Use the balance sheet (Table 2.1) and income statement (Table 2.2)
for DPH Tree Farm, Inc., to calculate the firm’s 2018 values for the
asset management ratios.
SOLUTION:
The internal and sustainable growth rates for DPH Tree Farm, Inc., are
calculated as follows. The industry average is reported alongside each
ratio.
These ratios show that DPH Tree Farm, Inc., can grow faster than the
industry if the firm uses only retained earnings to finance the growth.
However, if DPH grows while keeping the debt ratio constant (e.g., both
debt and retained earnings are used to finance the growth), industry
firms can grow much faster than DPH Tree Farm. Once again, DPH’s
low debt level and high equity level relative to the industry creates this
disparity. Therefore, DPH Tree Farm limits its growth as a result of its
managerial decisions.
Similar to Problems 3-13, 3-14, Self-Test Problem 2

the Math Coach on…
“When putting values into the equation, enter them in decimal format,
not percentage format:
CORRECT: 1 – (0.1404 X 0.6875)
NOT CORRECT: 1 – (14.04 X 68.75)„
A problem arises when a firm relies only on internal financing to support asset growth: Through time, its debt ratio
will fall because as asset values grow, total debt stays constant—only retained earnings finance asset growth. If total
debt remains constant as assets grow, the debt ratio decreases. As we noted above, shareholders often become
disgruntled if, as the firm grows, a decreasing debt ratio (increasing equity financing) dilutes their return. So as firms
grow, managers must often try to maintain a debt ratio that they view as optimal. In this case, managers finance asset

http://mhhe.com/CornettM4e

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growth with new debt and retained earnings. The maximum growth rate that can be achieved this way is the
sustainable growth rate. Mathematically, the sustainable growth rate is
sustainable growth rate The growth rate a firm can sustain if it finances growth using both debt and internal financing such that the
debt ratio remains constant.
(3-35)
Maximizing the sustainable growth rate helps firm managers maximize firm value. When applying the DuPont ROE
equation (3-31) here (i.e., ROE = Profit margin × Total asset turnover × Equity multiplier), notice that a firm’s
sustainable growth depends on four factors:
1. The profit margin (operating efficiency).
2. The total asset turnover (efficiency in asset use).
3. Financial leverage (the use of debt versus equity to finance assets).
4. Profit retention (reinvestment of net income into the firm rather than paying it out as dividends).
Increasing any of these factors increases the firm’s sustainable growth rate and hence helps to maximize firm value.
Managers, analysts, and investors will want to focus on these areas as they evaluate firm performance and market
value.
time out!
3-18 What does “spreading the financial statements” mean?
3-19 What are retention rates and internal and sustainable growth rates?
3-20 What factors enter into sustainable growth rates?
3.8 • TIME SERIES AND CROSS-SECTIONAL
ANALYSES LG3-7
We have explored many ratios that allow managers and investors to examine firm performance. But to really analyze
performance in a meaningful way, we must interpret our ratio results against some kind of standard or benchmark.
To interpret financial ratios, managers, analysts, and investors use two major types of benchmarks: (1) performance
of the firm over time (time series analysis) and (2) performance of the firm against one or more companies in the same
industry (cross-sectional analysis).
time series analysis Analyzing firm performance by monitoring ratio trends.
cross-sectional analysis Analyzing the performance of a firm against one or more companies in the same industry.

Analyzing ratio trends over time, along with absolute ratio levels, gives managers, analysts, and investors
information about whether a firm’s financial condition is improving or deteriorating. For example, ratio analysis
may reveal that the days’ sales in inventory is increasing. This suggests that inventories, relative to the sales they
support, are not being used as well as they were in the past. If this increase is the result of a deliberate policy to
increase inventories to offer customers a wider choice and if it results in higher future sales volumes or increased
margins that more than compensate for increased capital tied up in inventory, the increased relative size of the
inventories is good for the firm. Managers and investors should be concerned, on the other hand, if increased
inventories result from declining sales but steady purchases of supplies and production.
Looking at one firm’s financial ratios, even through time, gives managers, analysts, and investors only a limited

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picture of firm performance. Ratio analysis almost always includes a comparison of one firm’s ratios relative to the
ratios of other firms in the industry, or cross-sectional analysis. The key to cross-sectional analysis is identifying
similar firms that compete in the same markets, have similar asset sizes, and operate in a similar manner to the firm
being analyzed. Since no two firms are identical, obtaining such a comparison group is no easy task. Thus, the
choice of which companies to use in a cross-sectional analysis is at best subjective. Note that as we calculated the
financial ratios for DPH Tree Farm, Inc., throughout the chapter, we compared them to the industry average.
Comparative ratios that can be used in cross-sectional analysis are available from many sources. For example, Value
Line Investment Surveys, Robert Morris Associates, Hoover’s Online (at www.hoovers.com), and MSN Money
website (at moneycentral.msn.com) are examples of four major sources of financial ratios for numerous industries
that operate within the United States and worldwide.
time out!
3-21 What is time series analysis of a firm’s operations?
3-22 What is cross-sectional analysis of a firm’s operations?
3-23 How do time series and cross-sectional analyses differ, and what information would you expect to gain from each?
3.9 • CAUTIONS IN USING RATIOS TO EVALUATE FIRM
PERFORMANCE LG3-8
Financial statement analysis allows managers, analysts, and investors to better understand a firm’s performance.
However, data from financial statements should not be received without certain cautions. These include
1. Financial statement data are historical. Historical data may not reflect future performance. While we can make projections using
historical data, we must also remember that projections may be inaccurate if historical performance does not persist.
2. As we discussed in Chapter 2, firms use different accounting procedures. For example, inventory methods can vary. One firm may use
FIFO (first-in, first-out), transferring inventory at the first purchase price, while another uses LIFO (last-in, first-out), transferring
inventory at the last purchase price. Likewise, the depreciation method used to value a firm’s fixed assets over time may vary across
firms. One firm may use straight-line depreciation, while another may use an accelerated depreciation method (e.g., MACRS).
Particularly when reviewing cross-sectional ratios, differences in accounting rules can affect balance sheet values and financial ratios.
It is important to know which accounting rules the firms under consideration are using before making any conclusions about their
performance from ratio analysis.
3. Similarly, a firm’s cross-sectional competitors may often be located around the world. Financial statements for firms based outside the
United States do not necessarily conform to GAAP. Even beyond inventory pricing and depreciation methods, different accounting
standards and procedures make it hard to compare financial statements and ratios of firms based in different countries.
4. Sales and expenses vary throughout the year. Managers, analysts, and investors need to note the timing of these fund flows when
performing cross-sectional analysis. Otherwise they may draw conclusions from comparisons that are actually the result of seasonal
cash flow differences. Similarly, firms end their fiscal years at different dates. For cross-sectional analysis, this complicates
any comparison of balance sheets during the year. Likewise, one-time events, such as a merger, may affect a firm’s
financial performance. Cross-sectional analysis involving these events can result in misleading conclusions.
5. Large firms often have multiple divisions or business units engaged in different lines of business. In this case, it is difficult to truly
compare a set of firms with which managers and investors can perform cross-sectional analysis.
6. Firms often window dress their financial statements to make annual results look better. For example, to improve liquidity ratios
calculated with year-end balance sheets, firms often delay payments for raw materials, equipment, loans, and so on to build up their
liquid accounts and thus their liquidity ratios. If possible, it is often more accurate to use something other than year-end financial
statements to conduct ratio analysis.
7. Individual analysts may calculate ratios in modified forms. For example, one analyst may calculate ratios using year-end balance sheet
data, while another may use the average of the beginning- and end-of-year balance sheet data. If the firm’s balance sheet has
changed significantly during the year, this difference in the way the ratio is calculated can cause large variations in ratio values for a
given period of analysis and large variations in any conclusions drawn from these ratios regarding the financial health of the firm.
Financial statement ratio analysis is a major part of evaluating a firm’s performance. If managers, analysts, or
investors ignore the issues noted here, they may well draw faulty conclusions from their analysis. However, used
intelligently and with good judgment, ratio analysis can provide useful information on a firm’s current position and
hint at future performance.

http://www.hoovers.com

http://moneycentral.msn.com

page 80
time out!
3-24 What cautions should managers and investors take when using ratio analysis to evaluate a firm?
Get Online
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Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.

Your Turn…
Questions
1. Classify each of the following ratios according to a ratio category (liquidity ratio, asset management ratio, debt
management ratio, profitability ratio, or market value ratio). (LG3-1 through LG3-5)
a. Current ratio
b. Inventory turnover
c. Return on assets
d. Average payment period

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e. Times interest earned
f. Capital intensity
g. Equity multiplier
h. Basic earnings power
2. For each of the following actions, determine what would happen to the current ratio. Assume nothing else on
the balance sheet changes and that net working capital is positive. (LG3-1)
a. Accounts receivable are paid in cash.
b. Notes payable are paid off with cash.
c. Inventory is sold on account.
d. Inventory is purchased on account.
e. Accrued wages and taxes increase.
f. Long-term debt is paid with cash.
g. Cash from a short-term bank loan is received.
3. Explain the meaning and significance of the following ratios. (LG3-1 through LG3-5)
a. Quick ratio
b. Average collection period
c. Return on equity
d. Days’ sales in inventory
e. Debt ratio
f. Profit margin
g. Accounts payable turnover
h. Market-to-book ratio
4. A firm has an average collection period of 10 days. The industry average ACP is 25 days. Is this a good or poor
sign about the management of the firm’s accounts receivable? (LG3-2)
5. A firm has a debt ratio of 20 percent. The industry average debt ratio is 65 percent. Is this a good or poor sign
about the management of the firm’s financial leverage? (LG3-3)
6. A firm has an ROE of 20 percent. The industry average ROE is 12 percent. Is this a good or poor sign about the
management of the firm? (LG3-4)
7. Why is the DuPont system of analysis an important tool when evaluating firm performance? (LG3-6)
8. A firm has an ROE of 10 percent. The industry average ROE is 15 percent. How can the DuPont system of
analysis help the firm’s managers identify the reasons for this difference? (LG3-6)
9. What is the difference between the internal growth rate and the sustainable growth rate? (LG3-6)
10. What is the difference between time series analysis and cross-sectional analysis? (LG3-7)
11. What information do time series and cross-sectional analyses provide for firm managers, analysts, and
investors? (LG3-7)
12. Why is it important to know a firm’s accounting rules before making any conclusions about its performance
from ratios analysis? (LG3-8)
13. What does it mean when a firm window dresses its financial statements? (LG3-8)

Problems
BASIC PROBLEMS

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3-1  Liquidity Ratios You are evaluating the balance sheet for PattyCake’s Corporation. From the balance
sheet you find the following balances: cash and marketable securities = $400,000; accounts receivable =
$1,200,000; inventory = $2,100,000; accrued wages and taxes = $500,000; accounts payable = $800,000;
and notes payable = $600,000. Calculate PattyCake’s current ratio, quick ratio, and cash ratio. (LG3-1)
3-2  Liquidity Ratios The top part of Ramakrishnan, Inc.’s, 2018 and 2017 balance sheets is listed below (in
millions of dollars). Calculate Ramakrishnan, Inc.’s, current ratio, quick ratio, and cash ratio for 2018 and
2017. (LG3-1)
2018 2017 2018 2017
Current assets Current liabilities
 Cash and marketable securities $ 34 $ 25  Accrued wages and taxes $ 32 $ 31
 Accounts receivable 143 128  Accounts payable 87 76
 Inventory 206 187  Notes payable 76 68
  Total $383 $340   Total $195 $175
3-3 Asset Management Ratios Tater and Pepper Corp. reported sales for 2018 of $23 million. Tater and
Pepper listed $5.6 million of inventory on its balance sheet. Using a 365-day year, how many days did
Tater and Pepper’s inventory stay on the premises? How many times per year did Tater and Pepper’s
inventory turn over? (LG3-2)
3-4 Asset Management Ratios Mr. Husker’s Tuxedos Corp. ended the year 2018 with an average collection
period of 32 days. The firm’s credit sales for 2018 were $56.1 million. What is the year-end 2018 balance
in accounts receivable for Mr. Husker’s Tuxedos? (LG3-2)
3-5 Debt Management Ratios Tiggie’s Dog Toys, Inc., reported a debt-to-equity ratio of 1.75 times at the end
of 2018. If the firm’s total debt at year-end was $25 million, how much equity does Tiggie’s have on its
balance sheet? (LG3-3)
3-6 Debt Management Ratios You are considering a stock investment in one of two firms (LotsofDebt, Inc.,
and LotsofEquity, Inc.), both of which operate in the same industry. LotsofDebt, Inc., finances its $30
million in assets with $29 million in debt and $1 million in equity. LotsofEquity, Inc., finances its $30
million in assets with $1 million in debt and $29 million in equity. Calculate the debt ratio, equity
multiplier, and debt-to-equity ratio for the two firms. (LG3-3)
3-7 Profitability Ratios Maggie’s Skunk Removal Corp.’s 2018 income statement listed net sales of $12.5
million, gross profit of $6.9 million, EBIT of $5.6 million, net income available to common stockholders
of $3.2 million, and common stock dividends of $1.2 million. The 2018 year-end balance sheet listed total
assets of $52.5 million and common stockholders’ equity of $21 million with 2 million shares
outstanding. Calculate the gross profit margin, operating profit margin, profit margin, basic earnings
power, ROA, ROE, and dividend payout. (LG3-4)
3-8 Profitability Ratios In 2018, Jake’s Jamming Music, Inc., announced an ROA of 8.56 percent, ROE of
14.5 percent, and profit margin of 20.5 percent. The firm had total assets of $9.5 million at year-end 2018.
Calculate the 2018 values of net income available to common stockholders, common stockholders’ equity,
and net sales for Jake’s Jamming Music, Inc. (LG3-4)
3-9 Market Value Ratios You are considering an investment in Roxie’s Bed & Breakfast Corp. During the
last year, the firm’s income statement listed an addition to retained earnings of $4.8 million and common
stock dividends of $2.2 million. Roxie’s year-end balance sheet shows common stockholders’ equity of
$35 million with 10 million shares of common stock outstanding. The common stock’s market price per
share was $9.00. What is Roxie’s Bed & Breakfast’s book value per share and earnings per share?
Calculate the market-to-book ratio and PE ratio. (LG3-5)
3-10 Market Value Ratios Dudley Hill Golf Club’s market-to-book ratio is currently 2.5 times and the PE
ratio is 6.75 times. If Dudley Hill Golf Club’s common stock is currently selling at $22.50 per share,
what are the book value per share and earnings per share? (LG3-5)
3-11 DuPont Analysis If Silas 4-Wheeler, Inc., has an ROE of 18 percent, equity multiplier of 2, and a
profit margin of 18.75 percent, what are the total asset turnover and the capital intensity? (LG3-6)

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3-12 DuPont Analysis Last year, Hassan’s Madhatter, Inc., had an ROA of 7.5 percent, a profit margin of
12 percent, and sales of $25 million. Calculate Hassan’s Madhatter’s total assets. (LG3-6)
3-13 Internal Growth Rate Last year, Lakesha’s Lounge Furniture Corporation had an ROA of 7.5
percent and a dividend payout ratio of 25 percent. What is the internal growth rate? (LG3-6)
3-14 Sustainable Growth Rate Last year Lakesha’s Lounge Furniture Corporation had an ROE of 17.5
percent and a dividend payout ratio of 20 percent. What is the sustainable growth rate? (LG3-6)
INTERMEDIATE PROBLEMS
3-15 Liquidity Ratios Brenda’s Bar and Grill has current liabilities of $15 million. Cash makes up 10
percent of the current assets and accounts receivable makes up another 40 percent of current assets.
Brenda’s current ratio is 2.1 times. Calculate the value of inventory listed on the firm’s balance sheet.
(LG3-1)
3-16 Liquidity and Asset Management Ratios Mandesa, Inc., has current liabilities of $8 million, current
ratio of 2 times, inventory turnover of 12 times, average collection period of 30 days, and credit sales
of $64 million. Calculate the value of cash and marketable securities. (LG3-1, LG3-2)
3-17 Asset Management and Profitability Ratios You have the following information on Els’ Putters,
Inc.: Sales to working capital is 4.6 times, profit margin is 20 percent, net income available to
common stockholders is $5 million, and current liabilities are $6 million. What is the firm’s balance of
current assets? (LG3-2, LG3-4)
3-18 Asset Management and Debt Management Ratios Use the following information to complete the
following balance sheet. Sales are $8.8 million, capital intensity ratio is 2.10 times, debt ratio is 55
percent, and fixed asset turnover is 1.2 times. (LG3-2, LG3-3)

Assets Liabilities and Equity
Current assets $   Total liabilities $  
Fixed assets    Total equity   
Total assets $   Total liabilities and equity $  
3-19 Debt Management Ratios Tiggie’s Dog Toys, Inc., reported a debt-to-equity ratio of 1.75 times at
the end of 2018. If the firm’s total assets at year-end were $25 million, how much of their assets are
financed with debt and how much with equity? (LG3-3)
3-20 Debt Management Ratios Calculate the times interest earned ratio for LaTonya’s Flop Shops, Inc.,
using the following information. Sales are $1.5 million, cost of goods sold is $600,000, depreciation
expense is $150,000, other operating expenses is $300,000, addition to retained earnings is $146,250,
dividends per share is $1, tax rate is 30 percent, and number of shares of common stock outstanding is
90,000. LaTonya’s Flop Shops has no preferred stock outstanding. (LG3-3)
3-21 Profitability and Asset Management Ratios You are thinking of investing in Nikki T’s, Inc. You
have only the following information on the firm at year-end 2018: Net income is $250,000, total debt
is $2.5 million, and debt ratio is 55 percent. What is Nikki T’s ROE for 2018? (LG3-2, LG3-4)
3-22 Profitability Ratios Rick’s Travel Service has asked you to help piece together financial information
on the firm for the most current year. Managers give you the following information: Sales are $8.2
million, total debt is $2.1 million, debt ratio is 40 percent, and ROE is 18 percent. Using this
information, calculate Rick’s ROA. (LG3-4)
3-23 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $35. The firm has total
assets of $50 million, debt ratio of 65 percent, no preferred stock, and 3 million shares of common
stock outstanding. Calculate the market-to-book ratio for Leonatti Labs. (LG3-5)
3-24 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $15. The firm has a profit
margin of 8 percent, total assets of $42 million, a total asset turnover of 0.75, no preferred stock, and 3
million shares of common stock outstanding. Calculate the PE ratio for Leonatti Labs. (LG3-5)
3-25 DuPont Analysis Last year, Stumble-on-Inn, Inc., reported an ROE of 18 percent. The firm’s debt

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ratio was 55 percent, sales were $15 million, and the capital intensity was 1.25 times. Calculate the net
income for Stumble-on-Inn last year. (LG3-6)
3-26 DuPont Analysis You are considering investing in Nuran Security Services. You have been able to
locate the following information on the firm: Total assets are $24 million, accounts receivable are $3.3
million, ACP is 25 days, net income is $3.5 million, and debt-to-equity is 1.2 times. Calculate the
ROE for the firm. (LG3-6)
3-27 Internal Growth Rate Dogs R Us reported a profit margin of 10.5 percent, total asset turnover of
0.75 times, debt-to-equity of 0.80 times, net income of $500,000, and dividends paid to common
stockholders of $200,000. The firm has no preferred stock outstanding. What is Dogs R Us’s internal
growth rate? (LG3-6)
3-28 Sustainable Growth Rate You have located the following information on Webb’s Heating & Air
Conditioning: Debt ratio is 54 percent, capital intensity is 1.10 times, profit margin is 12.5 percent,
and the dividend payout is 25 percent. Calculate the sustainable growth rate for Webb. (LG3-6)

Use the following financial statements for Lake of Egypt Marina, Inc., to answer Problems 3-29 through 3-33.
LAKE OF EGYPT MARINA, INC.
Balance Sheet as of December 31, 2018 and 2017
(in millions of dollars)
2018 2017 2018 2017
Assets Liabilities and Equity
Current assets Current liabilities
Cash and marketable
securities
$ 75 $ 65 Accrued wages and taxes $ 40 $ 43
Accounts receivable 115 110 Accounts payable 90 80
Inventory 200 190 Notes payable   80   70
Total $ 390 $ 365 Total $ 210 $ 193
Fixed assets Long-term debt $ 300 $ 280
Gross plant and equipment $ 580 $ 471
Less: Depreciation  110  100 Stockholders’ equity
Net plant and equipment $ 470 $ 371 Preferred stock (5 million shares) $ 5 $ 5
Common stock and paid-in surplus (65
million shares)
65 65
Other long-term assets   50   49 Retained earnings  330  242
Total $ 520 $ 420 Total $ 400 $ 312
Total assets $ 910 $ 785 Total liabilities and equity $ 910 $ 785
LAKE OF EGYPT MARINA, INC.
Income Statement for Years Ending December 31, 2018 and 2017
(in millions of dollars)
2018 2017
Net sales (all credit) $ 515 $ 432
Less: Cost of goods sold   230   175
Gross profits $ 285 $ 257

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Less: Other operating expenses    30    25
Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 255 $ 232
Less: Depreciation    22    20
Earnings before interest and taxes (EBIT) $ 233 $ 212
Less: Interest    33    30
Earnings before taxes (EBT) $ 200 $ 182
Less: Taxes    57    55
Net income $ 143 $ 127
Less: Preferred stock dividends $ 5 $ 5
Net income available to common stockholders $ 138 $ 122
Less: Common stock dividends 65 65
Addition to retained earnings $ 73 $ 57
Per (common) share data:
 Earnings per share (EPS) $ 2.123 $ 1.877
 Dividends per share (DPS) $ 1.000 $ 1.000
 Book value per share (BVPS) $ 6.077 $ 4.723
 Market value (price) per share (MVPS) $14.750 $12.550

3-29 Spreading the Financial Statements Spread the balance sheets and income statements of Lake of
Egypt Marina, Inc., for 2018 and 2017. (LG3-6)
3-30 Calculating Ratios Calculate the following ratios for Lake of Egypt Marina, Inc., as of year-end
2018. (LG3-1 through LG3-5)
Lake of Egypt Marina, Inc. Industry
a. Current ratio 2.00 times
b. Quick ratio 1.20 times
c. Cash ratio 0.25 times
d. Inventory turnover 3.60 times
e. Days’ sales in inventory 101.39 days
f. Average collection period 32.50 days
g. Average payment period 45.00 days
h. Fixed asset turnover 1.25 times
i. Sales to working capital 4.25 times
j. Total asset turnover 0.85 times
k. Capital intensity 1.18 times
l. Debt ratio 62.50%
m. Debt-to-equity 1.67 times
n. Equity multiplier (total equity) 2.67 times
o. Times interest earned 8.50 times
p. Cash coverage 8.75 times
q. Profit margin 28.75%
r. Gross profit margin 56.45%
s. Operating profit margin 46.78%

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t. Basic earnings power 32.50%
u. ROA 19.75%
v. ROE 36.88%
w. Dividend payout 35.00%
x. Market-to-book ratio 2.55 times
y. PE ratio 15.60 times
3-31 DuPont Analysis Construct the DuPont ROA and ROE breakdowns for Lake of Egypt Marina, Inc.
(LG3-6)
3-32 Internal and Sustainable Growth Rates Calculate the internal and sustainable growth rate for Lake
of Egypt Marina, Inc. (LG3-6)
3-33 Cross-Sectional Analysis Using the ratios from Problem 3-30 for Lake of Egypt Marina, Inc., and the
industry, what can you conclude about Lake of Egypt Marina’s financial performance for 2018? (LG3-
7)
ADVANCED PROBLEMS
3-34 Ratio Analysis Use the following information to complete the balance sheet below. (LG3-1 through
LG3-5)
Current ratio = 2.5 times
Profit margin = 10%
Sales = $1,200m
ROE = 20%

Long-term debt to long-term debt and equity = 55%
Current assets $   Current liabilities $ 210
Fixed assets    Long-term debt   
Stockholders’ equity   
Total assets $   Total liabilities and equity $  
3-35 Ratio Analysis Use the following information to complete the balance sheet below. (LG3-1 through
LG3-5)
Current ratio = 2.20 times
Credit sales = $1,200m
Average collection period = 60 days
Inventory turnover = 1.50 times
Total asset turnover = 0.75 times
Debt ratio = 60%
Cash $  
Accounts receivable     Current liabilities $500m
Inventory     Long-term debt    
Current assets $   Total Debt $  
Fixed assets     Stockholders’ equity    
Total assets $    Total liabilities and equity $   
3-36 DuPont Analysis Last year, K9 WebbWear, Inc., reported an ROE of 20 percent. The firm’s debt
ratio was 55 percent, sales were $20 million, and the capital intensity was 1.25 times. Calculate the net
income and profit margin for K9 WebbWear last year. This year, K9 WebbWear plans to increase its
debt ratio to 60 percent. The change will not affect sales or total assets; however, it will reduce the
firm’s profit margin to 11 percent. By how much will the change in K9 WebbWear’s debt ratio affect
its ROE? (LG3-6)
3-37 DuPont Analysis You are considering investing in Dakota’s Security Services. You have been able to

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locate the following information on the firm: Total assets are $32 million, accounts receivable are $4.4
million, ACP is 25 days, net income is $4.66 million, and debt-to-equity is 1.2 times. All sales are on
credit. Dakota’s is considering loosening its credit policy such that ACP will increase to 30 days. The
change is expected to increase credit sales by 5 percent. Any change in accounts receivable will be
offset with a change in debt. No other balance sheet changes are expected. Dakota’s profit margin will
remain unchanged. How will this change in accounts receivable policy affect Dakota’s net income,
total asset turnover, equity multiplier, ROA, and ROE? (LG3-6)
3-38 Internal Growth Rate Last year, Marly Brown, Inc., reported an ROE of 20 percent. The firm’s debt-
to-equity was 1.50 times, sales were $20 million, the capital intensity was 1.25 times, and dividends
paid to common stockholders were $1,000,000. The firm has no preferred stock outstanding. This
year, Marly Brown plans to decrease its debt-to-equity ratio to 1.20 times. The change will not affect
sales, total assets, or dividends paid; however, it will reduce the firm’s profit margin to 9.85 percent.
Use the DuPont equation to determine how the change in Marly Brown’s debt ratio will affect its
internal growth rate. (LG3-6)
3-39 Sustainable Growth Rate You are considering investing in Annie’s Eatery. You have been able to
locate the following information on the firm: Total assets are $40 million, accounts receivable are $6.0
million, ACP is 30 days, net income is $4.75 million, debt-to-equity is 1.5 times, and dividend
payout ratio is 45 percent. All sales are on credit. Annie’s is considering loosening its credit
policy such that ACP will increase to 35 days. The change is expected to increase credit sales by 5
percent. Any change in accounts receivable will be offset with a change in debt. No other balance
sheet changes are expected. Annie’s profit margin and dividend payout ratio will remain unchanged.
Use the DuPont equation to determine how this change in accounts receivable policy will affect
Annie’s sustainable growth rate. (LG3-6)

Notes
CHAPTER 3
1 To see this remember the balance sheet identity is Assets (A) = Debt (D) + Equity (E). Dividing each side of this equation by assets, we
get A/A = D/A + E/A. Rearranging this equation, D/A = A/A − E/A = 1 − E/A = 1 − [1/(A/E)]. Also, D/A = (A − E)/A = 1/[A/(A − E)] = 1/[(A
− E + E)/(A − E)] = 1/[(E/(A − E) + (A − E)/(A − E)] = 1/[E/D + 1] = 1/[1/(D/E) + 1]. Dividing each side of the balance sheet identity
equation by equity, we get A/E = D/E + E/E, or A/E = D/E + 1. Also, rearranging this equation, D/E = A/E − 1.
2 The fixed-charge and cash coverage ratios can be tailored to a particular firm’s situation, depending on what really constitutes fixed
charges that must be paid. One version of it follows: (EBIT + Lease payments)/[Interest + Lease payments + Sinking fund/(1 − t)],
where t is the firm’s marginal tax rate. Here, it is assumed that sinking fund payments must be made. They are adjusted by the division
of (1 − t) into a before-tax cash outflow so they can be added to other before-tax cash outflows.

Part Three

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page 89

I
chapter four
time value of money 1:
analyzing single cash flows
©liseykina/Shutterstock
n business and personal life, cash flows of different types are paid and received in the future. Your
company can contract to build and ship its product to a foreign buyer for a $10 million single payment in
two years. You may have a car loan and a $300 per month level payment over the next four years. It
may be that you will pay a series of uneven tuition payments over the next couple of years as tuition
changes. Whether the future entails single, level, or uneven cash flows, we need a method for comparing
them when paid at different points in time.
Both this chapter and the next illustrate time value of money (TVM) calculations, which we will use
throughout the rest of this book. We hope you will see what powerful tools they are for making financial
decisions. Whether you’re managing the financial or other functional area of a business or making
decisions in your personal life, being able to make TVM calculations will help you make financially sound
decisions.

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This background will also allow you to understand why CEOs, CFOs, and other professionals make
the decisions that they do. Together, this chapter and the next will present all aspects of TVM. Since
some students find this topic intimidating, we split the topic into two chapters as a way of providing more
examples and practice opportunities. As you see the examples and work the practice problems, we
believe that you will find that TVM is not difficult.
Factors to consider when making time value of money decisions include
Size of the cash flows.
Time between the cash flows.
Rate of return we can earn.
LEARNING GOALS
LG4-1 Create a cash flow time line.
LG4-2 Compute the future value of money.
LG4-3 Show how the power of compound interest increases wealth.
LG4-4 Calculate the present value of a payment made in the future.
LG4-5 Move cash flows from one year to another.
LG4-6 Apply the Rule of 72.
LG4-7 Compute the rate of return realized on selling an investment.
LG4-8 Calculate the number of years needed to grow an investment.

viewpoints
business APPLICATION
As the production manager of Head Phone Gear, Inc., you have received an offer from the supplier who provides the wires used in
headsets. Due to poor planning, the supplier has an excess amount of wire and is willing to sell $500,000 worth for only $450,000.
You already have one year’s supply on hand. It would cost you $2,000 to store the wire until Head Phone Gear needs it next year.
What implied interest rate would you be earning if you purchased and stored the wire? Should you make the purchase? (See the
solution at the end of the book.)
The title of this chapter refers to the time value of money. But why might money change values, and
why does it depend on time? The term “time value of money” really refers to the difference in buying
power for a dollar over time. Consider that $100 can buy you an assortment of food and drinks today. Will
you be able to buy those same items in five years with the same $100? Probably not. Inflation might
cause these items to cost $120. If so, in terms of buying “stuff,” the dollar would have lost value over the
five years. If you don’t need to spend your money today, putting it in your mattress will only cause it to
lose value over time. Instead, there are banks that would like to use your money and pay you back later,
with interest. This interest is your compensation to offset the money’s decline in value. Each dollar will be
worth less in the future, but you’ll get more dollars. So you’ll be able to buy the same items as before.
The basic idea behind the time value of money is that $1 today is worth more than $1 promised next
year. But how much more? Is $1 today worth $1.05 next year? $1.08? $1.12? The answer varies
depending on current interest rates. This chapter describes the time value of money concept and provides
the tools needed to analyze single cash flows at different points in time.■
4.1 • ORGANIZING CASH FLOWS LG4-1
Managing cash flow timing is one of the most important tasks in successfully operating a business. A helpful tool
for organizing our analysis is the time line, which shows the magnitude of cash flows at different points in time, such

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as monthly, quarterly, semiannually, or yearly. Cash we receive is called an inflow, and we denote it with a positive
number. Cash that leaves us, such as a payment or contribution to a deposit, is an outflow designated with a negative
number.
time line A graphical representation showing the size and timing of cash flows through time.
inflow Cash received, often from income or sale of an investment.
outflow Cash payment, often a cost or the price of an investment or deposit.
The following time line illustrates a $100 deposit you made at a bank that pays 5 percent interest. In one year, the
$100 has become $105. Given that interest rate, having $100 now (in year 0) has the same value as having $105 in
one year.
Here’s a simple example: Suppose you allowed the bank to rent your $100 for a year at a cost of 5 percent, or $5.
This cost is known as the interest rate.
interest rate The cost of borrowing money denoted as a percent.

personal APPLICATION
Payday lending has become a multibillion-dollar industry across the United States in just a few years. It provides people with short-
term loans and gets its name from the fact that the loan is to be paid back at the borrower’s next payday. Anthony is short a few
hundred dollars and his next paycheck is two weeks away. For a $300 loan, Anthony must pay a $50 “fee” in advance and repay the
$300 loan in two weeks. What implied interest rate would Anthony pay for this two-week period? Is this a good deal? (See the
solution at the end of the book.)
But what if Anthony can’t pay the loan back on time?
Interest rates will affect you throughout your life, both in business and in your personal life. Companies borrow
money to build factories and expand into new locations and markets. They expect the future revenues generated by
these activities to more than cover the interest payments and repay the loan. People borrow money on credit cards
and obtain loans for cars and home mortgages. They expect their purchases to give them the satisfaction in the future
that compensates them for the interest payments charged on the loan. Understanding the dynamics between interest
rates and cash inflows and outflows over time is key to financial success. The best place to start learning these
concepts lies in understanding how money grows over time.
4.2 • FUTURE VALUE LG4-2
The $105 one-time cash flow that your bank credits to your account in one year is known as a future value (FV) of
$100 in one year at a 5 percent annual interest rate. If interest rates were higher than 5 percent, then the future value
of your $100 would also be higher. If you left your money in the bank for more than one year, then its future value
would continue to grow over time. Let’s see why.
future value (FV) The value of an investment after one or more periods.

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time out!
4-1 Why is a dollar worth more today than a dollar received one year from now?
4-2 Drawing on your past classes in accounting, explain why time lines must show one negative cash flow and one positive
cash flow.
4-3 Set up a time line, given a 6 percent interest rate, with a cash inflow of $200 today and a cash outflow of $212 in one year.
Single-Period Future Value
Computing the future value of a sum of money one year from today is straightforward: Add the interest earned to
today’s cash flow. In this case
We computed the $5 interest figure by multiplying the interest rate by today’s cash flow ($100 × 5%). Note that in
equations, interest rates appear in decimal format. So we use 0.05 for 5 percent:
Note that this is the same as
We need the 1 in the parentheses to recapture the original deposit and the 0.05 is for the interest earned. We can
generalize this computation to any amount of today’s cash flow. In the general form of the future value equation, we
call cash today present value, or PV. We compute the future value one year from now, called FV1, using the interest
rate, i:
present value (PV) The amount a future cash flow is worth today.
(4-1)

▼ TABLE 4.1 Higher Interest Rates and Cash Flows Lead to Higher Future Values
A B C D
1 Higher Interest Rates Lead to Higher Future Values
2 Today’s Cash Flow Interest Rate Interest Earned Next Year’s Future Value
3 $100.00 5% $5.00 $105.00
4 $100.00 6% $6.00 $106.00
5 $15,000.00 5% $750.00 $15,750.00
6 $15,000.00 6% $900.00 $15,900.00
7
8 Higher Cash Flows Today Lead to Higher Future Values
9 Today’s Cash Flow Interest Rate Interest Earned Next Year’s Future Value

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10 $500.00 7.50% $37.50 $537.50
11 $750.00 7.50% $56.25 $806.25
Notice that this is the same equation we used to figure the future value of your $100. We’ve simply made it generic
so we can use it over and over again. The 1 subscript means that we are calculating for only one period—in this
case, one year. If interest rates were 6 percent instead of 5 percent per year, for instance, we could use equation 4-1
to find that the future value of $100 in one year is $106 [= $100 × (1 + 0.06)].
Of course, the higher the interest rate, the larger the future value will be. Table 4.1 shows the interest earned and
future value for a sample of different cash flows and interest rates. Notice from the first two lines of the table that,
while the difference in interest earned between 5 percent and 6 percent ($1) doesn’t seem like much on a $100
deposit, the difference on a $15,000 deposit (the following two lines) is substantial ($150).
Compounding and Future Value LG4-3
After depositing $100 for one year, you must decide whether to take the $105 or leave the money at the bank for
another year to earn another 5 percent (or whatever interest rate the bank currently pays). In the second year at the
bank, the deposit earns 5 percent on the $105 value, which is $5.25 (= $105 × 0.05). Importantly, you get more than
the $5 earned the first year, which would be a simple total of $110. The extra 25 cents earned in the second year is
interest on interest that was earned in the first year. We call this process of earning interest both on the original
deposit and on the earlier interest payments compounding.
compounding The process of adding interest earned every period on both the original investment and the reinvested earnings.
So, let’s illustrate a $100 deposit made for two years at 5 percent
LG4-1
The question mark denotes the amount we want to solve for. As with all TVM problems, we simply have to identify
what element we’re solving for; in this case, we’re looking for the FV. To compute the two-year compounded future
value, simply use the 1-year equation (4-1) twice.
So the future value of $100 deposited today at 5 percent interest is $110.25 in period 2. You can see that this
represents $10 of interest payments generated from the original $100 ($5 each year) and $0.25 of interest earned in
the second year on previously earned interest payments. The $5 of interest earned every year on the original deposit
is called simple interest. Any amount of interest earned above the $5 in any given year comes from
compounding. Over time, the new interest payments earned from compounding can become substantial.
The multiyear form of equation (4-1) is the future value in year N, shown as:
simple interest Interest earned only on the original deposit.
(4-2)
We can solve the two-year deposit problem more directly using equation 4-2 as $110.25 = $100 × (1.05)2. Here,
solving for FV in the equation requires solving for only one unknown. In fact, all TVM equations that you will
encounter only require figuring out what is unknown in the situation and solving for that one unknown factor.
We can easily adapt equation 4-2 to many different future value problems. What is the future value in 30 years of
that $100 earning 5 percent per year? Using equation 4-2, we see that the future value is $100 × (1.05)30 = $432.19.



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The money has increased substantially! You have made a profit of $332.19 over and above your original $100. Of
this profit, only $150 (= $5 × 30 years) came from simple interest earned on the original deposit. The rest, $182.19
(= $332.19 − $150), is from the compounding effect of earning interest on previously earned interest.
Remember that the difference between earning 5 percent and 6 percent in interest on the $100 was only $1 the first
year. So what is the future value difference after 15 years? Is it $15? No, as Figure 4.1 shows, the difference in
future value substantially increases over time. The difference is $31.76 in year 15 and $142.15 in year 30.
The Power of Compounding LG4-3 Compound interest is indeed a powerful tool for building wealth.
Albert Einstein, the German-born American physicist who developed the special and general theories of relativity
and won the Nobel Prize for Physics in 1921, is supposed to have said, “The most powerful force in the universe is
compound interest.”1 Figure 4.2 illustrates this point. It shows the original $100 deposited, the cumulative interest
earned on that deposit, and the cumulative interest-on-interest earned. By the 27th year, the money from the interest-
on-interest exceeds the interest earned on the original deposit. By the 40th year, interest-on-interest contributes more
than double the interest on the deposit. The longer money can earn interest, the greater the compounding effect.
FIGURE 4-1 The Future Value of $100
Small differences in interest rates can really add up over time!

FIGURE 4-2 Interest Earned on Prior Interest at a 5 Percent Rate

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The money from interest-on-interest will eventually exceed the interest from the original deposit.
Earning higher interest rates on the investment for additional time periods magnifies compounding power. Consider
the future value of $100 deposited at different interest rates and over different time periods as shown in Table 4.2.
The future value of $100 earning 5 percent per year for five years is $127.63, for a gain of $27.63. Would you
double your gain by simply investing that same $100 at double the interest rate, 10 percent? No, because
compounding changes the nature of the investment so that your money grows exponentially, not in a simple linear
relationship. The future value of $100 in five years at 10 percent is $161.05. The $61.05 gain is more than double
the gain of $27.63 earned at 5 percent. Tripling the interest rate to 15 percent shows a gain of $101.14 that is nearly
quadruple the gain earned at 5 percent.
The same effect occurs when we increase the time. When the deposit earns 10 percent per year for five years, the
gain is $61.05. When we double the amount of time to 10 years, the gain more than doubles to $159.37. If we double
the time again to 20 years, the gain increases not to just $318.74 (= $159.37 × 2) but to $572.75. At 10 percent for
30 years, the gain on $100 is a whopping $1,644.94. Interest rates and time are both important factors in
compounding! These relationships are illustrated in Figure 4.3.
▼ TABLE 4.2 Compounding Builds Wealth Over Time
A B C D E
1 Future Value of $100 Deposited at 5%, 10%, and 15% Interest Rates
2
3 Future Value
4 Interest Rate Earned 5 years 10 years 20 years 30 years
5 5% $127.63 $162.89 $265.33 $432.19
6 10% $161.05 $259.37 $672.75 $1,744.94
7 15% $201.14 $404.56 $1,636.65 $6,621.18
8
9 =FV(A7, 5, 0, −100) =FV(A6, 30, 0, −100)

▼FIGURE 4-3 The Impact of Time and the Magnitude of the Interest Rate
Future value of $100 deposited at 5%, 10%, and 15% interest rates: The future value differences between compounding interest rates
expand exponentially over time.
EXAMPLE
4-1 Graduation Celebration Loan LG4-3
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
Dominic is a fourth-year business student who wants to go on a graduation
celebration/vacation in Mexico but he has no money to pay for the trip. After
the vacation, Dominic will start his career. His job will require moving to a new
town and buying professional clothes. He asked his parents to lend him
$1,500, which he figures he will be able to pay back in three years. His
parents agree to lend him the money, but they will charge 7 percent interest
per year. What amount will Dominic need to pay back? How much interest will
he pay? How much of what he pays is interest-on-interest?
SOLUTION:
Dominic will have to pay:
Of the $1,837.56 he owes his parents, $337.56 (= $1,837.56 − $1,500) is
interest. We can illustrate this time-value problem in the following time line.
Compare this compound interest with simple interest. Simple interest would
be 7 percent of $1,500 (which is $105) per year. The three-year cost would

http://mhhe.com/CornettM4e

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then be $315 (= 3 × $105). The difference between the compound interest of
$337.56 and the total simple interest of $315 is the interest-on-interest of
$22.56.
Similar to Problems 4-3, 4-4, 4-5, 4-6, 4-21, 4-22, 4-33, 4-34, Self-Test
Problem 1

Compounding at Different Interest Rates Over Time LG4-4
We already know that the $100 deposit will grow to $105 at the end of the first year. This $105 will then earn 6
percent in the second year and have a value of $111.30 (= $105 × 1.06). If we put the two steps together into one
equation, the solution appears as $111.30 = $100 × 1.05 × 1.06. From this you should not be surprised that a general
equation for future value of multiple interest rates is
(4-3)
Note that the future value equation 4-2 is a special case of the more general equation 4-3. If the interest rate every
period is the same, we can write equation 4-3 as equation 4-2.
time out!
4-4 How does compounding help build wealth (or increase debt) over time?
4-5 Why does doubling the interest rate or time quickly cause more than a doubling of the future value?
EXAMPLE 4-2
Celebration Loan with Payback
Incentive LG4-3
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Reexamine the loan Dominic was seeking from his parents in the
previous example. His parents want to give him an incentive to pay off
the loan as quickly as possible. They structure the loan so they charge
7 percent interest the first year and increase the rate 1 percent each
year until the loan is paid. How much will Dominic owe if he waits three
years to pay off the loan? Say that in the third year he considers
whether to pay off the loan or wait one more year. How much more will
he pay if he waits one more year?
SOLUTION:

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For a payment in the third year, Dominic will pay interest of 7 percent
the first year, 8 percent the second year, and 9 percent the third year.
He will have to pay
The cash flow time line is
Even worse, if he waits until the fourth year, he will pay one year of
interest at 10 percent. The total payment will be
Because of both the escalating interest rate and the compounding
effect, Dominic must make timely and increasing payments the longer
he delays in paying off the loan. Deciding in the third year to put off the
payment an extra year would cost him an additional $188.94 (=
$2,078.35 − $1,889.41).
Similar to Problems 4-7, 4-8

Math Coach
Using a Financial Calculator
Financial, or business, calculators are programmed to perform the time value of money equations we develop in this chapter and the
next. The two most common types of inexpensive financial calculators that can perform such functions are the Hewlett-Packard 10B II
Business Calculator and the Texas Instruments BA II (Plus or Professional). Among many useful financial shortcuts these calculators
have five specific financial buttons. The relevant financial buttons for time value of money (TVM) calculations are listed below. The HP
10B II calculator buttons look like this:

1. N (for the number of periods),
2. I/YR (for the interest rate),
3. PV (for present value),
4. PMT (for a constant payment every period), and
5. FV (for future value).
Notice that the TI BA II Plus financial calculator buttons appear to be very similar:
To get to the TVM menu, select APPLICATIONS and then choose FINANCE, and finally 1 TVM SOLVER on the previous screens.
A common, more sophisticated and expensive calculator is the TI-83. This calculator has a menu system that includes the financial
functions as shown:
Setting up Your Calculator
These calculators come from the factory with specific settings. You will find it useful to change two of them. The first is to set the
number of digits shown after the decimal point on the calculator display. The factory setting is for two digits. However, consider a
problem in which we use a 5.6 percent interest rate. The decimal version of this percentage is 0.056, which a two-digit display would
round to 0.06. It’s less worrisome to set the calculator to display the number of digits necessary to show the right number; this is called
a floating point display. To set a floating point display for the HP calculator, press the color button, then the DISP button, and finally the
decimal (.) button. To set the display for a floating point decimal on the TI calculator, push the 2ND button, followed by the FORMAT
button, followed by the 9 button, and finally the ENTER button.
The second change you’ll want to make is to set the number of times the calculator compounds each period. The settings may be
preset to 12 times per period. Reset this to one time per period. To change the HP calculator to compound once per period, push the 1
button, then the color button, and finally the P/YR button. On the TI calculator, simply push the 2ND button, the P/Y button, the number
one, and the ENTER button. These new settings will remain in the calculator until you either change them or remove the calculator’s
batteries.
Using Your Calculator

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The calculators compute time-value problems in similar ways. Enter the cash flows into the time-value buttons (PV, PMT, and FV)
consistent with the way they are shown in a time line. In other words, cash inflows should be positive and cash outflows negative. Thus,
PV and FV cash flows are nearly always opposite in sign. Enter interest rates (I) in the percentage form, not the decimal form. Also
enter the number of periods in the problem (N).
Consider our earlier example of the $100 deposit for two years earning a 5 percent interest rate.
1. To set the number of years, press 2 and then the N button.
2. To set the interest rate, press 5 and then the I button. (Note that interest rates are in percentage format for using a financial
calculator and in decimal format for using the equations.)
3. To enter the current cash flow: press 100, then make it negative by pressing the +/− button, then press the PV
button.
4. We won’t use the PMT button, so enter 0 and then the PMT button.
5. To solve for future value, press the compute button (CPT) [for the TI] and then the FV button [press the FV button only for the
HP].
6. Solution: the display should show FV = 110.25
Note that the answer is positive, consistent with an inflow and the time line diagram. These values remain in the TVM registers even
after the calculator is turned off. So when you start a new problem, you should clear out old values first. For the HP calculator, clear the
registers by pressing the shift/orange key before pressing C. You can clear the BAII Plus calculator using 2ND and CLR TVM.
You’ll notice that throughout this book we use the equations in the main text to solve time value of money problems. We provide the
calculator solutions in the margins.
4.3 • PRESENT VALUE LG4-4
We asked earlier what happens when you deposit $100 cash in the bank to earn 5 percent interest for one year—the
bank pays you a $105 future value. However, we could have asked the question in reverse. That is, if the bank will
pay $105 in one year and interest rates are 5 percent, how much would you be willing to deposit now, to receive that
payment in a year? Here, we start with a future value and must find the present value—a different kind of
calculation called discounting.

How much would you be willing to deposit now to receive a certain payment in a year?
©Ryan McVay/Getty Images
Discounting
While the process of a present value growing over time into the future is called compounding, the process of
figuring out how much an amount that you expect to receive in the future is worth today is discounting. Just as
compounding significantly increases the present value into the future, discounting significantly decreases the value
of a future amount to the present. Since discounting is the reverse of compounding, we can rearrange equation 4-1 to
solve for the present value of a cash flow received one year in the future.
(4-4)
discounting The process of finding present value by reducing future values using the discount, or interest, rate.
Suppose the bank is going to pay $105 in one year and interest rates are 5 percent. Then the present value of the
payment is $105/1.05 = $100. Present values are always smaller than future values (as long as interest rates are
greater than zero!), and the difference between what an investment is worth today and what it’s worth when you’re
supposed to redeem it gets larger as the interest rate increases. Likewise, if the amount of time until the expected
payment date increases, the difference will also increase in value.
Discounting Over Multiple Periods Discounting over multiple periods is the reverse process of compounding
over multiple periods. Knowing this, we can find the general equation for present value by rearranging the terms in
equation 4-2 to form:
(4-5)

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The interest rate, i, which we use to calculate present value, is often referred to as the discount rate. How much is a
$100 payment to be received in the future worth today? Of course, it depends on how far into the future you expect
to receive the payment and the discount rate used. If you receive a $100 cash flow in five years, then its present
value is $78.35, discounted at 5 percent:
discount rate The interest rate used to discount future cash flow(s) to the present.
The time line looks like this:
LG4-1
If the discount rate rises to 10 percent, the present value of our $100 to be paid to us in five years is only $62.09
today. At a 15 percent interest rate, the present value declines to less than half the future cash flow: $49.72. Higher
interest rates discount future cash flows more quickly and dramatically. You can see this principle illustrated in
Figure 4.4.
Moving right from point A in Figure 4.4, notice that if interest rates are 0 percent, the present value will equal the
future value. Also note from the curved lines that when the discount rate is greater than zero, the discounting to
present value is not linear through time. The higher the discount rate, the more quickly the cash flow value falls. If
the discount rate is 10 percent, a $100 cash flow that you would receive in 25 years is worth less than $10 today, as
shown at point B in the figure. With a 15 percent discount rate, the $100 payment to be received in 33 years, at point
C, is worth less than $1 today.
the Math Coach on…


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“When using a financial calculator, be sure to either clear
the time value of money buttons or enter a zero for the
factors that you won’t use to solve the problem.„
FIGURE 4-4 Present Value of a $100 Cash Flow Made in the Future
The higher the discount rate, the more quickly the cash flow value falls.

EXAMPLE 4-3
Buy Now and Don’t Pay for Two
Years LG4-4
For interactive versions
of this example, log in
to Connect or go to
Suppose that a marketing manager for a retail furniture company
proposes a sale. Customers can buy now but don’t have to pay for their
furniture purchases for two years. From a time value of money
perspective, selling furniture at full price with payment in two years is
equivalent to selling furniture at a sale, or discounted, price with
immediate payment. If interest rates are 7.5 percent per year, what is
the equivalent sale price of a $1,000 sleeper-sofa when the customer
takes the full two years to pay for it?
SOLUTION:

mhhe.com/CornettM4e. The time line for this problem is:
Using equation 4-5, the present value computation is
In this case, the marketing proposal for delaying payment for two years
is equivalent to selling the $1,000 sleeper-sofa for a sale price of
$865.33, or a 13.5 percent discount. When stores promote such sales,
they often believe that customers will not be able to pay the full amount
at the end of the two years and then must pay high interest rate
charges and late fees. Customers who do pay on time are getting a
good deal.
Similar to Problems 4-9, 4-10, 4-11, 4-12, Self-Test Problem 2
Discounting with Multiple Rates LG4-4 We can also discount a future cash flow at different interest rates
per period. We find the general form of the equation for present value with multiple discount rates by rearranging
equation 4-3:
Present value with different discount rates = Future cash flow ÷ Each period’s discounting
(4-6)
LG4-1
Suppose that we expect interest rates to increase over the next few years, from 7 percent this year, to 8 percent next
year, to 8.5 percent in the third year. In this environment, how would we work out the present value of a future
$2,500 cash flow in year 3? The time line for this problem is
time out!
4-6 How are interest rates in the economy related to the way people value future cash payments?
4-7 Explain how discounting is the reverse of compounding.
Using equation 4-6 shows that the present value is $1,993.90:

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4.4 • USING PRESENT VALUE AND FUTURE VALUE LG4-5
Moving Cash Flows
As managers analyze investment projects, debt management, and cash flows, they frequently find it useful to move
cash flows to different points in time. While you may be planning to keep money deposited in the bank for three
years when you will buy a car, life often has a way of altering plans. What type of car might you purchase if the
money earns interest for only two years, or for four years? How is a corporate financial forecast affected if the firm
needs to remodel a factory two years sooner than planned? Moving cash flows around in time is important to
businesses and individuals alike for sound financial planning and decision making.
LG4-1
Moving cash flows from one point in time to another requires us to use both present value and future value
equations. Specifically, we use the present value equation for moving cash flows to an earlier point in time, and the
future value cash flows for moving cash flows to a later point in time. For example, what’s the value in year 2 of a
$200 cash flow to be received in three years, when interest rates are 6 percent? This problem requires moving the
$200 payment in the third year to a value in the second year, as shown in the time line:
Since the cash flow is to be moved one year earlier in time, we use the present value equation:
When interest rates are 6 percent, a $188.68 payment in year 2 equates to a $200 payment in year 3.
What about moving the $200 cash flow to year 5? Since this requires moving the cash flow later in time by two
years, we use the future value equation. In this case, the equivalent of $200 in the third year is a fifth-year payment
of:
Table 4.3 illustrates how we might move several cash flows. At an 8 percent interest rate, a $1,000 cash flow due in

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year 5 compounded to year 10 equals $1,469.33. We could also discount that same $1,000 cash flow to a value of
$793.83 in year 2. At an 8 percent interest rate, the three cash flows ($793.83 in year 2, $1,000 in year 5, and
$1,469.33 in year 10) become equivalent. Table 4.3 illustrates the movement of other cash flows given different
interest rates and time periods.
Moving cash flows from one year to another creates an easy way to compare or combine two cash flows. Would you
rather receive $150 in year 2 or $160 in year 2? Since both cash flows occur in the same year, the comparison is
straightforward. But we can’t directly add or compare cash flows in different years until we consider their time
value. We can compare cash flows in different years by moving one cash flow to the same time as the other using
the present value or future value equations. Once you have the value of each cash flow in the same year, you can
directly compare or combine them.
Rule of 72 LG4-6 Albert Einstein is also credited with popularizing compound interest by introducing a
simple mathematical approximation for the number of years required to double an investment. It’s called the Rule of
72.
Rule of 72 An approximation for the number of years needed for an investment to double in value.

▼ TABLE 4.3 Equivalent Cash Flows in Time
When Interest
Rates Are
A Cash Flow
of In Year
Can be
Moved to
Year With Equation
Equivalent Cash
Flow
Moving Later versus Moving Earlier
8% $1,000 5 10
FV10 = PV5 × (1 + i )
5 =
$1,000 × (1.08)5 =
$1,469.33
8 1,000 5 2
PV2 = FV5 / (1 + i)
3 =
$1,000 / (1.08)3 =
793.83
Moving Earlier
10 500 9 8
PV8 = FV9 / (1 + i )
1 =
$500 / (1.10)1 =
454.55
10 500 9 0
PV0 = FV9 / (1 + i)
9 =
$500 / (1.10)9 =
212.05
Moving Later
12 100 4 20
FV20 = PV4 × (1 + i )
16 =
$100 × (1.12)16 =
613.04
12 100 4 30
FV30 = PV4 × (1 + i
)26 = $100 ×
(1.12)26 =
1,904.01

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(4-7)
The Rule of 72 illustrates the power of compound interest. How many years will it take to double money deposited
at 6 percent per year? Using the Rule of 72, we find the answer is 12 years (= 72/6). A higher interest rate causes
faster increases in future value. A 9 percent interest rate allows money to double in just eight years (= 72/9).
Remember that this rule provides only a mathematical approximation. It’s more accurate with lower interest rates.
After all, with a 72 percent interest rate, the rule predicts that it will take one year to double the money (= 72/72).
However, we know that it actually takes a 100 percent rate to double money in one year.
We can also use the Rule of 72 to approximate the interest rate needed to double an investment in a specific amount
of time. What rate do we need to double an investment in five years? Rearranging equation 4-7 shows that the rate
needed is 14.4 percent (= 72/5) per year.
time out!
4-8 In Example 4-4, could Timber, Inc., have performed its analysis by moving the $175,000 to year 2 and comparing? Would
the firm then have made the same decision?
4-9 At what interest rate (and number of years) does the Rule of 72 become too inaccurate to use?
EXAMPLE 4-4 Pay Damages or Appeal? LG4-5
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Timber, Inc., lost a lawsuit in a business dispute. The judge ordered the
company to pay the plaintiff $175,000 in one year. Timber’s attorney
advises Timber to appeal the ruling. If so, Timber will likely lose again
and will still have to pay the $175,000. But by appealing, Timber moves
the $175,000 payment to year 2, along with the attorney’s fee of
$20,000 for the extra work. The interest rate is 7 percent. What
decision should Timber make?
SOLUTION:
Timber executives must decide whether to pay $175,000 in one year or
$195,000 in two years. To compare the two choices more directly,
move the payment in year 2 to year 1 and then compare it to $175,000.
Timber should choose to make the smaller payment. The computation
is
The value in year 1 of a year 2 payment of $195,000 is $182,242.99,
which is clearly more than the $175,000 year 1 payment. So Timber
should not appeal and should pay the plaintiff $175,000 in one year
(and may want to look for another attorney).
Similar to Problems 4-23, 4-24, 4-25, 4-26, 4-27, 4-28, 4-41

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finance at work //: investments
TVM Caveat Emptor
©Trevor Lush/Blend Images LLC
Not making your payments on time can get very expensive. Reconsider the furniture selling experience in Example 4-3. The store has
given customers the opportunity to buy the sleeper-sofa today and not pay the $1,000 price for two years. But what happens if you forget
to pay on time? Indeed, many people do forget. Others simply haven’t saved $1,000 and can’t make the payment. The fine print in these
deals provides the penalties for late payment. For example, the late clause might require a 10 percent annually compounded interest
rate to apply to any late payment—retroactive to the sale date. Thus, being one day late with the payment will automatically incur an
interest charge for the entire two years of $210 (= $1,000 × 1.12 − $1,000), which is in addition to the original $1,000 still owed, of
course.
The impact of making late payments can also show up later when you apply for credit cards, auto loans, and other credit. Credit
rating agencies gather information on us from companies, banks, and landlords to grade our payment history. If you consistently make
late payments on your apartment, credit card, or electric bill, these agencies will give you a poor grade. The higher your grade, called a
credit score, the more likely you are to be able to get a loan and pay a lower interest rate on that loan. People with lower credit scores
may not be able to borrow money and when they can, they will pay higher interest rates on their credit cards and auto loans. Paying a
higher interest rate can really cost you a lot of money. Remember the future value differences between interest rates illustrated in Table
4.2 and Figure 4.3. Those people who have really bad credit scores can’t get loans from banks and merchants and have to rely on
payday lending places that charge enormously high rates, as highlighted in this chapter’s Personal Application Viewpoint.
Making a late payment might not seem like a big deal at the time, but it can really cost you!
Want to know more?
Key Words to Search for Updates: housing bubble, subprime lending, mortgage-backed securities, AIG, Countrywide Financial
4.5 • COMPUTING INTEREST RATES LG4-7
Time value of money calculations come in handy when we know two cash flows and need to find the interest rate.
The investment industry often uses this analysis. Solving for the interest rate, or rate of return,2 can answer questions
like, “If you bought a gold coin for $350 three years ago and sell it now for $475, what rate of return have you
earned?” The time line for this problem looks like this:

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LG4-1
In general, computing interest rates is easiest with a financial calculator. To compute the answer using the time-
value equations, consider how the cash flows fit into the future value equation 4-2:

the Math Coach on…
“When using a financial calculator to compute an interest rate between two cash
flows, you must enter one cash flow as a negative number. This is because you
must inform the calculator which payments are cash inflows and which are cash
outflows. If you input all the cash flows as the same sign, the calculator will show
an error when asked to compute the interest rate.„
Rearranging gives
To solve for the interest rate, i, take the third root of both sides of the equation. To do this, take 1.357 to the 1/3
power using the yx button on your calculator.3 Doing this leads to
If you buy a gold coin for $350 and sell it three years later for $475, you earn a 10.7 percent return per year.
LG4-6
Time is an important factor in computing the return that you’re earning per year. Turning a $100 investment into

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$200 is a 100 percent return. If your investments earn this much in two years, then they earned a 41.42 percent rate
of return per year [$100 × (1.4142)2 = $200]. Table 4.4 shows the annual interest rate earned for doubling an
investment over various time periods. Notice how compounding complicates the solution: It’s not as simple as just
dividing by the number of years. Getting a 100 percent return in two years means earning 41.42 percent per year, not
50 percent per year. Table 4.4 also shows the Rule of 72 interest rate estimate.
▼ TABLE 4.4 Interest Rate per Year to Double an Investment

Return Asymmetries
Suppose you bought a gold coin for $700 last year and now the market will pay you only $350. Clearly, the
investment earned a negative rate of return. Use a financial calculator or a time-value equation to verify that this is a
return of −50 percent. You lost half your money! So, in order to break even and get back to $700, you need to earn a
positive 50 percent, right? Wrong. Note that to get from $350 to $700, your money needs to double! You need a 100
percent return to make up for a 50 percent decline. Similarly, you need a gain of 33.33 percent to make up for a 25
percent decline. If your investment declines by 10 percent, you’ll need an 11.11 percent gain to offset the loss. In
general, only a higher positive return can offset any given negative return.
time out!
4-10 Say you double your money in three years. Explain why the rate of return is NOT 33.3 percent per year.
4-11 Show that you must earn a 25 percent return to offset a 20 percent loss.
4.6 • SOLVING FOR TIME LG4-8
Sometimes you may need to determine the time period needed to accumulate a specific amount of money. If you
know the starting cash flow, the interest rate, and the future cash flow (the amount you will need), you can solve the
time value equations for the number of years that you will need to accumulate that money. Just as with solving for
different interest rates, solving for the number of periods is complicated and requires using natural logarithms.4
Many people prefer to use a financial calculator to solve for the number of periods.

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When interest rates are 9 percent, how long will it take for a $5,000 investment to double? Finding the solution with
a financial calculator entails entering
I = 9
PV = −5,000
PMT = 0
FV = 10,000
The answer is 8.04 years, or eight years and two weeks. The Rule of 72 closely approximates the answer, which
predicts eight years (= 72/9).
time out!
4-12 In Example 4-5, how long will it take your company to double its sales?
4-13 In what other areas of business can these time-value concepts be used?
EXAMPLE 4-5 Growth in Staffing Needs LG4-8
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Say that you are the sales manager of a company that produces
software for human resource departments. You are planning your
staffing needs, which depend on the volume of sales over time. Your
company currently sells $350 million of merchandise per year and has
grown 7 percent per year in the past. If this growth rate continues, how
long will it be before the firm reaches $500 million in sales? How long
before it reaches $600 million?
SOLUTION:
You could set up the following time line to illustrate the problem:
As shown in the margin, $350 million of sales growing at 7 percent per
year will reach $500 million in five years and three months. To reach
$600 million will take just two weeks short of eight years.
Similar to Problems 4-31, 4-32, Self-Test Problem 4

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page 107
the Math Coach on…
Simple TVM Spreadsheet Functions
Common spreadsheet programs include time value of money functions. The functions are
Compute a future value = FV(rate,nper,pmt,pv,type)
Compute a present value = PV(rate,nper,pmt,fv,type)
Compute the number of periods = NPER(rate,pmt,pv,fv,type)
Compute an interest rate = RATE(nper,pmt,pv,fv,type)
Compute a repeating payment = PMT(rate,nper,pv,fv,type)
The five input/outputs (FV, PV, NPER, RATE, PMT) work similarly to the five TVM buttons on a business calculator. The type input
defaults to 0 for normal situations, but can be set to 1 for computing annuity due problems (see Chapter 5). Different spreadsheet
programs might have slightly different notations for these five functions.
Consider the future value problem of Example 4-1. The spreadsheet solution is the same as the TVM calculator solution. Note that
since the PV is listed as a positive number, the FV output is a negative number.
The inputs to the function can be directed to other cells, like the rate, nper, and pv in the this illustration. Or the input can be the actual
number, like pmt and type.
This spreadsheet solves for the interest rate in the preceding example in the text. Just like using the TVM calculator, the PV and FV
must be of opposite signs to avoid getting an error message.
See this textbook’s online student center to watch instructional videos on using spreadsheets. Also note that the solution for all the
examples in the book are illustrated using spreadsheets in videos that are available in Connect.

Get Online
©JGI/Jamie Grill/Blend Images LLC.
Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow.
Which cash flows should be negative and which positive? Why? (LG4-1)
2. How are the present value and future value related? (LG4-2)
3. Would you prefer to have an investment earning 5 percent for 40 years or an investment earning 10 percent for
20 years? Explain. (LG4-3)
4. How are present values affected by changes in interest rates? (LG4-4)
5. What do you think about the following statement? “I am going to receive $100 two years from now and $200
three years from now, so I am getting a $300 future value.” How could the two cash flows be compared or
combined? (LG4-5)
6. Show how the Rule of 72 can be used to approximate the number of years to quadruple an investment. (LG4-6)
7. Without making any computations, indicate which of each pair has a higher interest rate: (LG4-7)
a. $100 doubles to $200 in five years or seven years.
b. $500 increases in four years to $750 or to $800.
c. $300 increases to $450 in two years or increases to $500 in three years.

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8. A $1,000 investment has doubled to $2,000 in eight years because of a 9 percent rate of return. How much
longer will it take for the investment to reach $4,000 if it continues to earn a 9 percent rate? (LG4-8)

Problems
BASIC PROBLEMS
4-1 Time Line Show the time line for a $500 cash inflow today, a $605 cash outflow in year 2, and a 10
percent interest rate. (LG4-1)
4-2 Time Line Show the time line for a $400 cash outflow today, a $518 cash inflow in year 3, and a 9
percent interest rate. (LG4-1)
4-3 One Year Future Value What is the future value of $500 deposited for one year earning an 8 percent
interest rate annually? (LG4-2)
4-4 One Year Future Value What is the future value of $400 deposited for one year earning an interest rate
of 9 percent per year? (LG4-2)
4-5 Multiyear Future Value How much would be in your savings account in 11 years after depositing $150
today if the bank pays 8 percent per year? (LG4-3)
4-6 Multiyear Future Value Compute the value in 25 years of a $1,000 deposit earning 10 percent per year.
(LG4-3)
4-7 Compounding with Different Interest Rates A deposit of $350 earns the following interest rates:
a. 8 percent in the first year.
b. 6 percent in the second year.
c. 5.5 percent in the third year.
What would be the third year future value? (LG4-3)
4-8 Compounding with Different Interest Rates A deposit of $750 earns interest rates of 9 percent in the
first year and 12 percent in the second year. What would be the second year future value? (LG4-3)
4-9 Discounting One Year What is the present value of a $350 payment in one year when the discount rate is
10 percent? (LG4-4)
4-10 Discounting One Year What is the present value of a $200 payment in one year when the discount
rate is 7 percent? (LG4-4)
4-11 Present Value What is the present value of a $1,500 payment made in nine years when the discount
rate is 8 percent? (LG4-4)
4-12 Present Value Compute the present value of an $850 payment made in 10 years when the discount
rate is 12 percent. (LG4-4)
4-13 Present Value with Different Discount Rates Compute the present value of $1,000 paid in three
years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8
percent in the third year. (LG4-4)
4-14 Present Value with Different Discount Rates Compute the present value of $5,000 paid in two
years using the following discount rates: 8 percent in the first year and 7 percent in the second year.
(LG4-4)
4-15 Rule of 72 Approximately how many years are needed to double a $100 investment when
interest rates are 7 percent per year? (LG4-6)
4-16 Rule of 72 Approximately how many years are needed to double a $500 investment when interest
rates are 10 percent per year? (LG4-6)
4-17 Rule of 72 Approximately what interest rate is needed to double an investment over five years? (LG4-
6)
4-18 Rule of 72 Approximately what interest rate is earned when an investment doubles over 12 years?
(LG4-6)
4-19 Rates over One Year Determine the interest rate earned on a $1,400 deposit when $1,800 is paid
back in one year. (LG4-7)

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4-20 Rates over One Year Determine the interest rate earned on a $2,300 deposit when $2,900 is paid
back in one year. (LG4-7)
INTERMEDIATE PROBLEMS
4-21 Interest-on-Interest Consider a $2,000 deposit earning 8 percent interest per year for five years.
What is the future value, and how much total interest is earned on the original deposit versus how
much is interest earned on interest? (LG4-3)
4-22 Interest-on-Interest Consider a $5,000 deposit earning 10 percent interest per year for 10 years.
What is the future value, how much total interest is earned on the original deposit, and how much is
interest earned on interest? (LG4-3)
4-23 Comparing Cash Flows What would be more valuable, receiving $500 today or receiving $625 in
three years if interest rates are 7 percent? Why? (LG4-5)
4-24 Comparing Cash Flows Which cash flow would you rather pay, $425 today or $500 in two years if
interest rates are 10 percent? Why? (LG4-5)
4-25 Moving Cash Flows What is the value in year 3 of a $700 cash flow made in year 6 if interest rates
are 10 percent? (LG4-5)
4-26 Moving Cash Flows What is the value in year 4 of a $1,000 cash flow made in year 6 if interest rates
are 8 percent? (LG4-5)
4-27 Moving Cash Flows What is the value in year 10 of a $1,000 cash flow made in year 3 if interest
rates are 9 percent? (LG4-5)
4-28 Moving Cash Flows What is the value in year 15 of a $250 cash flow made in year 3 if interest rates
are 11 percent? (LG4-5)
4-29 Solving for Rates What annual rate of return is earned on a $1,000 investment when it grows to
$1,800 in six years? (LG4-7)
4-30 Solving for Rates What annual rate of return is earned on a $5,000 investment when it grows to
$9,500 in five years? (LG4-7)
4-31 Solving for Time How many years (and months) will it take $2 million to grow to $5 million with an
annual interest rate of 7 percent? (LG4-8)
4-32 Solving for Time How long will it take $2,000 to reach $5,000 when it grows at 10 percent per year?
(LG4-8)
ADVANCED PROBLEMS
4-33 Future Value At age 30 you invest $1,000 that earns 8 percent each year. At age 40 you invest
$1,000 that earns 12 percent per year. In which case would you have more money at age 60?
(LG4-2)
4-34 Future Value At age 25 you invest $1,500 that earns 8 percent each year. At age 40 you invest
$1,500 that earns 11 percent per year. In which case would you have more money at age 65? (LG4-2)
4-35 Solving for Rates You invested $2,000 in the stock market one year ago. Today, the investment is
valued at $1,500. What return did you earn? What return would you need to get next year to break
even overall? (LG4-7)
4-36 Solving for Rates You invested $3,000 in the stock market one year ago. Today, the investment is
valued at $3,750. What return did you earn? What return would you suffer next year for your
investment to be valued at the original $3,000? (LG4-7)
4-37 Solving for Rates What annual rate of return is earned on a $4,000 investment made in year 2 when
it grows to $6,500 by the end of year 7? (LG4-7)
4-38 Solving for Rates What annual rate of return is implied on a $2,500 loan taken next year when
$3,500 must be repaid in year 4? (LG4-7)
4-39 General TVM Ten years ago, Hailey invested $2,000 and locked in a 9 percent annual interest rate
for 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in a 10
percent interest rate. How much money should he invest now in order to have the same amount of
money in 20 years as Hailey? (LG4-2, LG4-4)

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4-40 General TVM Ten years ago, Hailey invested $3,000 and locked in an 8 percent annual interest rate
for 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in a 10
percent interest rate. How much money should he invest now in order to have the same amount of
money in 20 years as Hailey? (LG4-2, LG4-4)
4-41 Moving Cash Flows You are scheduled to receive a $500 cash flow in one year, a $1,000 cash flow
in two years, and pay an $800 payment in three years. If interest rates are 10 percent per year, what is
the combined present value of these cash flows? (LG4-5)
4-42 Spreadsheet Problem Oil prices have increased a great deal in the last decade. The following table
shows the average oil price for each year since 1949. Many companies use oil products as a resource
in their own business operations (like airline firms and manufacturers of plastic products). Managers
of these firms will keep a close watch on how rising oil prices will impact their costs. The interest rate
in the PV/FV equations can also be interpreted as a growth rate in sales, costs, profits, and so on (see
Example 4-5).
a. Using the 1949 oil price and the 1969 oil price, compute the annual growth rate in oil prices during
those 20 years.
b. Compute the annual growth rate between 1969 and 1989 and between 1989 and 2015.
c. Given the price of oil in 2015 and your computed growth rate between 1989 and 2015, compute the
future price of oil in 2018 and 2025.

Average Oil Prices
Year Per Barrel Year Per Barrel Year Per Barrel
1949 $2.54 1971 $ 3.39 1993 $14.25
1950 $2.51 1972 $ 3.39 1994 $13.19
1951 $2.53 1973 $ 3.89 1995 $14.62
1952 $2.53 1974 $ 6.87 1996 $18.46
1953 $2.68 1975 $ 7.67 1997 $17.23
1954 $2.78 1976 $ 8.19 1998 $10.87
1955 $2.77 1977 $ 8.57 1999 $15.56
1956 $2.79 1978 $ 9.00 2000 $26.72
1957 $3.09 1979 $12.64 2001 $21.84
1958 $3.01 1980 $21.59 2002 $22.51
1959 $2.90 1981 $31.77 2003 $27.54
1960 $2.88 1982 $28.52 2004 $38.93
1961 $2.89 1983 $26.19 2005 $46.47
1962 $2.90 1984 $25.88 2006 $58.30
1963 $2.89 1985 $24.09 2007 $64.67
1964 $2.88 1986 $12.51 2008 $91.48
1965 $2.86 1987 $15.40 2009 $53.48
1966 $2.88 1988 $12.58 2010 $71.21
1967 $2.92 1989 $15.86 2011 $87.04
1968 $2.94 1990 $20.03 2012 $93.02
1969 $3.09 1991 $16.54 2013 $97.91

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1970 $ 3.18 1992 $15.99 2014 $93.26
2015 $48.79
4-43 Spreadsheet Problem Consider that you are the marketing manager of a firm. You need to have
approximately one additional salesperson for every $10 million in sales. You currently have $50
million in sales and have five employees handling the sales accounts. In order to plan ahead, you want
to get an idea of when you may need to hire more salespeople. Build a table that shows the sales for
each of the next 10 years for sales growth of 5%, 10%, 15%, and 20% (see Example 4-5).
Comment on when new sales staff should be hired for each growth rate.
A B C D E F G H I J K L
1 Growth Rate Today Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10
2 5% $50 $52.50
3 10% $50 $55.00
4 15% $50 $57.50
5 20% $50 $60.00

Notes
CHAPTER 4
1 No one seems to know exactly what he said, when he said it, or to whom. Similar statements commonly attributed to Einstein are: (1)
compound interest is the greatest wonder of the universe, (2) compound interest is the ninth wonder of the world, and (3) it is the
greatest mathematical discovery of all time. If he did not say any of these things, he (or someone else) should have!
2 The terms interest rate and rate of return are referring to the same thing. However, it is a common convention to refer to interest rate
when you are the one paying the cash flows and refer to rate of return when you are the one receiving the cash flows.
3 The general equation for computing the interest rate is
4 The equation for solving for the number of periods is

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page 115

W
Chapter five
time value of money 2:
analyzing annuity cash flows
©Stuart Monk/Shutterstock
e explained basic time value computations in the previous chapter. Those TVM equations covered
moving a single cash flow from one point in time to another. While this circumstance does
describe some problems that businesses and individuals face, most debt and investment
applications of time value of money feature multiple cash flows. In fact, most situations require many
equal payments over time. Since these situations require a bit more complicated analysis, this chapter
continues the TVM topic for applications that require many equal payments over time. For example, car
loans and home mortgage loans require the borrower to make the same monthly payment for many
months or years. People save for the future through monthly contributions to their pension portfolios.
People in retirement must convert their savings into monthly income. Companies also make regular
payments. Johnson & Johnson (ticker: JNJ) will pay level semiannual interest payments through 2033 on
money it borrowed. The Boeing Company (ticker: BA) paid a $0.42 per share quarterly dividend to
stockholders for three straight years until 2012, when it switched to a $0.44 dividend. These examples

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require payments (and compounding) over different time intervals (monthly for car loans and
semiannually for company debt). How are we to value these payments into common or comparable
terms? In this chapter, we illustrate how to value multiple cash flows over time, including equal and
uneven payments, and how to incorporate different compounding frequencies.
LEARNING GOALS
LG5-1 Compound multiple cash flows to the future.
LG5-2 Compute the future value of frequent, level cash flows.
LG5-3 Discount multiple cash flows to the present.
LG5-4 Compute the present value of an annuity.
LG5-5 Figure cash flows and present value of a perpetuity.
LG5-6 Adjust values for beginning-of-period annuity payments.
LG5-7 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.
LG5-8 Compute the interest rate of annuity payments.
LG5-9 Compute payments and amortization schedules for car and mortgage loans.
LG5-10 Calculate the number of payments on a loan.

viewpoints
business APPLICATION
Walkabout Music, Inc., issued $20 million in debt 10 years ago to finance its factory construction. The debt allows Walkabout to make
interest-only payments at a 7 percent coupon rate, paid semiannually for 30 years. Debt issued today would carry only 6 percent
interest. The company’s CFO is considering whether or not to issue new debt (for 20 years) to pay off the old debt. To pay off the old
debt early, Walkabout would have to pay a special “call premium” totaling $1.4 million to its debt holders. To issue new debt, the firm
would have to pay investment bankers a fee of $1.2 million. Should the CFO replace the old debt with new debt? (See the solution at
the end of the book.)
5.1 • FUTURE VALUE OF MULTIPLE CASH FLOWS LG5-1
Chapter 4 illustrated how to take single payments and compound them into the future. To save enough money for a
down payment on a house or for retirement, people typically make many contributions over time to their savings
accounts. We can add the future value of each contribution together to see what the total will be worth at some
future point in time—such as age 65 for retirement or in two years for a down payment on a house.
Finding the Future Value of Several Cash Flows
Consider the following contributions to a savings account over time. You make a $100 deposit today, followed by a
$125 deposit next year, and a $150 deposit at the end of the second year. If interest rates are 7 percent, what’s the
future value of your deposits at the end of the third year? The time line for this problem is illustrated as
Note that the first deposit will compound for three years. That is, the future value in year 3 of a cash flow in year 0
will compound 3 v(= 3 − 0) times. The deposit at the end of the first year will compound twice (= 3 − 1). In general,
a deposit in year m will compound N−m times for a future value in year N. We can find the total amount at the end
of three years by computing the future value of each deposit and then adding them together. Using the future value
equation from Chapter 4, the future value of today’s deposit is $100 ×  (1 + 0.07) 3 = $122.50. Similarly, the future

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value of the next two deposits are $125 ×  (1 + 0.07) 2 = $143.11 and $150 ×  (1 + 0.07) 1 = $160.50, respectively.
Putting these three individual future value equations together would yield

personal APPLICATION
Say that you obtained a mortgage for $150,000 three years ago when you purchased your home. You’ve been paying monthly
payments on the 30-year mortgage with a fixed 8 percent interest rate and have $145,920.10 of principal left to pay. Recently, your
mortgage broker called to mention that interest rates on new mortgages have declined to 7 percent. He suggested that you could save
money every month if you refinanced your mortgage. You could find a 27-year mortgage at the new interest rate for a $1,000 fee.
Should you refinance your mortgage? (See the solution at the end of the book.)
But what if you want to move in the next few years? Is it still a good idea?
The general equation for computing the future value of multiple and varying cash flows (or payments) is
(5-1)

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In this equation, the letters m, n, and p denote when the cash flows occur in time, so N − m etc. represent the length
of time that the respective cash flow will get to earn compound interest. Each deposit can be different from the
others.
EXAMPLE 5-1 Saving for a Car LG5-1
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Say that, as a freshman in college, you will be working as a house
painter for each of the next three summers. You intend to set aside
some money from each summer’s paycheck to buy a car for your
senior year. If you can deposit $2,000 at the end of the first summer,
$2,500 at the end of the second summer, and $3,000 at the end of the
last summer, how much money will you have to buy a car at the end of
the last summer if interest rates are 5 percent?
SOLUTION:
The time line for the forecast is
The first cash flow, which occurs at the end of the first year, will
compound for two years. The second cash flow will be invested for only
one year. The last contribution will not have any time to grow before the
purchase of the car. Using equation 5-1, the solution is
You will have $7,830 in cash to purchase a car for your senior year.
Similar to Problems 5-1, 5-2, 5-17, 5-18, 5-43, 5-44

Future Value of Level Cash Flows LG5-2
Now suppose that each cash flow is the same and occurs every year. Level sets of frequent cash flows are common
in finance—we call them annuities. The first cash flow of an annuity occurs at the end of the first year (or other time
period) and continues every year to the last year. We derive the equation for the future value of an annuity from the
general equation for future value of multiple cash flows, equation 5-1. Since each cash flow is the same, and the
cash flows are every period, the equation appears as
annuity A stream of level and frequent cash flows paid at the end of each time period—often referred to as an ordinary annuity.

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The term FVA is used to denote that this is the future value of an annuity. Factoring out the common level cash flow,
PMT, we can summarize and reduce the equation as
(5-2)
Suppose that $100 deposits are made at the end of each year for five years. If interest rates are 8 percent per year, the
future value of this annuity stream is computed using equation 5-2 as
We can show these deposits and future value on a time line as
Five deposits of $100 each were made. So, the $586.66 future value represents $86.66 of interest paid. As with
almost any TVM problem, the length of time of the annuity and the interest rate for compounding are very important
factors in accumulating wealth within the annuity. Consider the examples in Table 5.1. A $50 deposit made every
year for 20 years will grow to $1,839.28 with a 6 percent interest rate. Doubling the annual deposits to $100 also
doubles the future value to $3,678.56. However, making $100 deposits for twice the amount of time, 40 years, more
than quadruples the future value to $15,476.20! Longer time periods lead to more total compounding and much
more wealth. Interest rates also have this effect. Doubling the interest rate from 6 to 12 percent on the 40-year
annuity results in nearly a five-fold increase in the future value to $76,709.14. Think about it: Depositing only $100
per year (about 25 lattes per year) can generate some serious money over time. See Figure 5.1. How much would
$2,000 annual deposits generate?
▼ TABLE 5.1 Magnitude of Periodic Payments, Number of Years Invested, and Interest Rate on FV of Annuity

FIGURE 5-1 Future Value of a $100 Annuity at 6 Percent

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Longer time periods lead to more total compounding and much more wealth.
the Math Coach on…
Annuities and the Financial Calculator
“In the previous chapter, the level payment button (PMT) in the financial calculator was always set to zero
because no constant payments were made every period. We use the PMT button to input the annuity amount.
For calculators, the present value is of the opposite sign (positive versus negative) from the future value. This
is also the case with annuities. The level cash flow will be of the opposite sign as the future value, as the time
line on page 118 shows.
You would use the financial calculator to solve the problem of depositing $100 for five years via the following
inputs: N = 5, I = 8, PV = 0, PMT = –100. In this case, the input for present value is zero because no deposit is
made today. The result of computing the future value is 586.66.„
Future Value of Multiple Annuities
At times, multiple annuities can occur in both business and personal life. For example, you may find that you can
increase the amount of money you save each year because of a promotion or a new and better job. As an illustration,
reconsider the annual $100 deposits made for five years at 8 percent per year. This time, the deposit can be increased
to $150 for the fourth and fifth years. How can we use the annuity equation to compute the future value when we
have two levels of cash flows? In this case, the cash flow can be categorized as two annuities. The first annuity is a
$100 cash flow for five years. The second annuity is a $50 cash flow for two years. We demonstrate this as

the Math Coach on…
Solving Multiple Annuities
“The trick to solving multiple annuity problems is to disentangle cash flows into groups of level payments
ending in the future value year that we’ve designated.„
To determine the future value of these two annuities, compute the future value of each one separately, and then
simply add them together. The future value of the $100 annuity is the same as computed before, $586.66. The future
value of the $50 annuity, using the TVM equation for the future value of a cash stream, is
EXAMPLE 5-2
Saving in the Company Pension
Plan LG5-2
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
You started your first job after graduating from college. Your company
offers a retirement plan for which the company contributes 50 percent
of what you contribute each year. So, if you contribute $3,000 per year
from your salary, the company adds another $1,500. You get to decide
how to invest the total annual contribution from several portfolio
choices that the plan administrator provides. Suppose that you pick a
mixture of stocks and bonds that is expected to earn 7 percent per
year. If you plan to retire in 40 years, how big will you expect that
retirement account to be? If you could earn 8 percent per year, how
much money would be available?
SOLUTION:
Every year, you and your employer will set aside a total of $4,500 for
your retirement. Using equation 5-2 shows that the future value of this
annuity is
Note that you can build a substantial amount of wealth ($898,358)

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through your pension plan at work. If you can earn just 1 percent more
each year, 8 percent total, you could be a millionaire!
Similar to Problems 5-3, 5-4, Self-Test Problem 1

finance at work //: personal
Who Will Save for Their Future?
©Chris Ryan/Age Fotostock
Though it seems way too early for you to think about planning for your “golden years,” financially wise people realize that it’s never too
early to start. Unfortunately, most people save little for their retirement years. Twenty-nine percent of households age 55 and older have
no pension or retirement savings. About 23 percent have no savings, but do have a pension. Of the 48 percent that have retirement
savings, the median amount is $109,000. How far does that get you? Using a 6 percent investment return, $109,000 can generate a
monthly income of only $653.51 for 30 years, at which time it is used up. That is less than $8,000 per year! The average Social Security
monthly benefit is just over $1,318 per month, or about $15,816 per year. Few people will have the lifestyle they wanted in their
retirement years. However, that doesn’t have to be true for you if you start saving early!
This chapter illustrates that much higher amounts of wealth can be accumulated if you start early. One easy way to do this is through
a retirement plan at work. Most company and government employers offer their employees defined contribution plans. (The corporate
version is called a 401(k) plan; a nonbusiness plan is usually referred to as a 403(b) plan—both named after the legislation that created
the plans.) These plans place all of the responsibility on employees to provide for their retirement. Employees contribute from their own
paychecks and decide how to invest. Employees’ decisions about how much to contribute and how early to start contributing have a
dramatic impact on retirement wealth.
Consider employees who earn $50,000 annually for 40 years and then retire. Note that if the employees contribute for 40 years, they
must start by age 25 or so—starting early is vitally important! Contributing 5 percent of their salaries ($2,500) to the 401(k) plan every
year and having it earn a 4 percent return will generate $237,564 for retirement. A 10 percent contribution ($5,000) would create
$475,128 for retirement. Finally, investment decisions that yield an 8 percent return would yield $1.3 million with a 10 percent
contribution. This is quite a range of retirement wealth generated from just three important decisions each employee must make—how
much to contribute, how to invest the funds, and when to start! Unfortunately, too many people make poor decisions. Their first mistake
is to start making 401(k) contributions too late to allow the funds to generate significant compounding.
Saving and investing money through a defined contribution plan is a good way to build wealth for retirement. But you must follow
these rules: Start early, save much, and don’t touch!
Want to know more?
Key Words to Search for Updates: Employee Benefit Research Institute (go to www.ebri.org), retirement income

http://www.ebri.org

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Source: “Retirement Security: Most Households Approaching Retirement Have Low Savings,” Government Accountability Office, GAO-
15-419, May 12, 2015. http://www.gao.gov/products/GAO-15-419.
So, the future value of both of the annuities is $690.66 (= $586.66 + $104). In the same way, we could easily
compute the future value if the last two cash flows are $50 lower ($50 each), instead of $50 higher ($150 each). To
solve this alternative version, we would simply subtract the $104 future value instead of adding it.

EXAMPLE 5-3
Growing Retirement
Contributions LG5-2
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
In the previous example, you are investing a total of $4,500 per year for
40 years in your employer’s retirement program. You believe that with
raises and promotions, you will eventually be able to contribute more
money each year. Consider that halfway through your career, you are
able to increase your investment in the retirement program to $6,000
per year (your contribution plus the company match). What would be
the future value of your retirement wealth from this program if
investments are compounded at 7 percent?
SOLUTION:
You can compute the future value using two annuities. The first annuity
is one with payments of $4,500 that lasts 40 years. The second is a
$1,500 (= $6,000 – $4,500) annuity that lasts only 20 years. We
already computed the future value of the first annuity in the previous
example: $898,358. The future value of the second annuity is
So, your retirement wealth from this program would be $959,851 (=
$898,358 + $61,493).
Similar to Problems 5-19, 5-20, Self-Test Problem 1
time out!
5-1 Describe how compounding affects the future value computation of an annuity.
5-2 Reconsider your original retirement plan example to invest $4,500 per year for 40 years. Now consider the result if you don’t
contribute anything for four years (years 19 to 22) while your child goes to college. How many annuity equations will you
need to find the future value of your 401(k) in this situation?

http://www.gao.gov/products/GAO-15-419

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5.2 • PRESENT VALUE OF MULTIPLE CASH FLOWS LG5-3
The future value concept is very useful to understand how to build wealth for the future. The present value concept
will help you most particularly for personal applications such as evaluating loans (like car and mortgage loans) and
business applications (like determining the value of business opportunities).
Finding the Present Value of Several Cash Flows
Consider the cash flows that we showed at the very beginning of the chapter: You deposit $100 today, followed by a
$125 deposit next year, and a $150 deposit at the end of the second year. In the previous situation, we sought the
future value when interest rates are 7 percent. Instead of future value, we compute the present value of thesethree
cash flows. The time line for this problem appears as
The first cash flow is already in year zero, so its value will not change. We will discount the second cash flow one
year and the third cash flow two years. Using the present value equation from the previous chapter, the present value
of today’s payment is simply $100 ÷ (1 + 0.07)0 = $100. Similarly, the present value of the next two cash flows are
$125 ÷ (1 + 0.07)1 = $116.82 and $150 ÷ (1 + 0.07)2 = $131.02, respectively. Therefore, the present value of these
cash flows is $347.84 (= $100 + $116.82 + $131.02).
Putting these three individual present value equations together would yield
The general equation for discounting multiple and varying cash flows is
(5-3)
In this equation, the letters m, n, and p denote when the cash flows occur in time. Each deposit can differ from the
others in terms of size and timing.

Present Value of Level Cash Flows LG5-4
You will find that this present value of an annuity concept will have many business and personal applications
throughout your life. Most loans are set up so that the amount borrowed (the present value) is repaid through level
payments made every period (the annuity). Lenders will examine borrowers’ budgets and determine how much each
borrower can afford as a payment. The maximum loan offered will be the present value of that annuity payment. The
equation for the present value of an annuity can be derived from the general equation for the present value of
multiple cash flows, equation 5-3. Since each cash flow is the same, and the borrower pays the cash flows every
period, the present value of an annuity, PVA, can be written as
(5-4)
Suppose that someone makes $100 payments at the end of each year for five years. If interest rates are 8 percent per
year, the present value of this annuity stream is computed using equation 5-4 as

The time line for these payments and present value appears as
Notice that although five payments of $100 each were made, $500 total, the present value is only $399.27. As we’ve
noted previously, the span of time over which the borrower pays the annuity and the interest rate for discounting
strongly affect present value computations. When you borrow money from the bank, the bank views the amount it
lends as the present value of the annuity it receives over time from the borrower. Consider the examples in Table
5.2.
A $50 deposit made every year for 20 years is discounted to $573.50 with a 6 percent discount rate. Doubling the
annual cash flow to $100 also doubles the present value to $1,146.99. But extending the time period does not impact
the present value as much as you might expect. Making $100 payments for twice the amount of time—40 years—
does not double the present value. As you can see in Table 5.2, the present value increases less than 50 percent to
only $1,504.63! If the discount rate increases from 6 percent to 12 percent on the 40-year annuity, the present value
will shrink to $824.38.
The present value of a cash flow made far into the future is not very valuable today, as Figure 5.2 illustrates. Thats
why doubling the number of years in the table from 20 to 40 only increased the present value by approximately 30
percent. Notice how the present value of $100 annuity payments declines for the cash flows made later in time,
especially at higher discount rates. The $100 cash flow in year 20 is worth less than $15 today if we use a 10 percent
discount rate; they’re worth more than double, at nearly $38 today, if we use a discount rate of 5 percent. The figure
also shows how quickly present value declines with a higher discount rate relative to a lower rate. As we showed
above, the present values of the annuities in the figure are the sums of the present values shown. Since the present
values for the 10 percent discount rate are smaller, the present value of an annuity is smaller as interest rates rise.

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page 125

▼ TABLE 5.2 Magnitude of the Annuity, Number of Years Invested, and Interest Rate on PV
Present Value of Multiple Annuities
Just as we can combine annuities to solve various future value problems, we can also combine annuities to solve
some present value problems with changing cash flows. Consider David Price’s Major League Baseball contract
signed in 2015 with the Boston Red Sox. This was the largest contract for a pitcher ever. It was reported as having a
$217 million value. The contract was structured so that the Red Sox paid Price $30 million per year in 2016 through
2018, $31 million in 2019, and $32 million per year in 2020 through 2022.1 However, we know that future cash
flows have lower present values. So, using a 5 percent discount rate, what is the present value of Prices contract?
FIGURE 5-2 Present Value of Each Annuity Cash Flow

the Math Coach on…
Using a Financial Calculator—Part 2
The five TVM buttons/functions in financial calculators have been fine, so far, for the types of TVM problems we’ve been solving.
Sometimes we had to use them two or three times for a single problem, but that was usually because we needed an intermediate
calculation to input into another TVM equation.
Luckily, most financial calculators also have built-in worksheets specifically designed for computing TVM in problems with multiple
nonconstant cash flows.
To make calculator worksheets as flexible as possible, they are usually divided into two parts: one for input, which we’ll refer to as the
CF (cash flow) worksheet, and one or more for showing the calculator solutions. We’ll go over the conventions concerning the CF
worksheet here, and we’ll discuss the output solutions in Chapter 13.
The CF worksheet is usually designed to handle inputting sets of multiple cash flows as quickly as possible. As a result, it normally
consists of two sets of variables or cells—one for the cash flows and one to hold a set of frequency counts for the cash flows, so that
we can tell it we have seven $1,500 cash flows in a row instead of having to enter $1,500 seven times.
Using the frequency counts to reduce the number of inputs is handy, but you must take care. Frequency counts are only good for
embedded annuities of identical cash flows. You have to ensure that you don’t mistake another kind of cash flow for an annuity.
Also, using frequency counts will usually affect the way that the calculator counts time periods. As an example, let’s talk about how we
would put the set of cash flows shown here into a CF worksheet:
To designate which particular value we’ll place into each particular cash flow cell in this worksheet, we’ll note the value and the cell
identifier, such as CF0, CF1, and so forth. We’ll do the same for the frequency cells, using F1, F2, etc., to identify which CF cell the
frequency cell goes with. (Note that, in most calculators, CF0 is treated as a unique value with an unalterable frequency of 1; we’re
going to make the same assumption here so you’ll never see a listing for F0.) For this sample time line, our inputs would be
−$800 [CF0]
$150 [CF1] 1 [F1]
$200 [CF2] 1 [F2]
$  0 [CF3] 1 [F3]
$150 [CF4] 3 [F4]
$ 75 [CF5] 2 [F5]

To compute the present value of these cash flows, use the NPV calculator function. The NPV function computes the present value of all
the future cash flows and then adds the year 0 cash flow. Then, on the NPV worksheet, you would simply need to enter the interest rate
and solve for the NPV:
10% [I]
[CPT] [NPV] = −$144.61
Note a few important things about this example:
1. We had to manually enter a value of $0 for CF3. If we hadn’t, the calculator wouldn’t have known about it and would have
implicitly assumed that CF4 came one period after CF2.
2. Once we use a frequency cell for one cash flow, all numbering on any subsequent cash flows that we enter into the calculator is
going to be messed up, at least from our point of view. For instance, the first $75 isn’t what we would call “CF5,” is it? We’d call it
“CF7” because it comes at time period 7; but calculators usually treat CF5 as “the fifth set of cash flows,” so we’ll just have to try
to do the same to be consistent.
3. If we really don’t need to use frequency cells, we will usually just leave them out of the guidance instructions in this chapter to
save space.

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The reported value for many sports contracts may be misleading in present value terms.
©Akihiro Sugimoto/age fotostock

We begin by showing the salary cash flows with the time line
First create a $32 million, seven-year annuity. Here are the associated cash flows:

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Now create a –$1 million, four-year annuity:
Notice that creating the –$1 million annuity also resulted in the third annuity of –$1 million for three years. This
time line shows three annuities. If you add the cash flows in any year, the sum is Price’s salary for that year. Now
we can find the present value of each annuity using equation 5-4 three times.
Adding the value of the three annuities reveals that the present value of Price’s salary was $178.89 million
(= $185.16m – $3.55m – $2.72m). So, the present value of Price’s contract turns out to be quite
considerable, but it is not the $217 million contract value advertised!
EXAMPLE 5-4 Value of Payments LG5-4
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Your firm needs to buy additional physical therapy equipment that costs
$20,000. The equipment manufacturer will give you the equipment now
if you will pay $6,000 per year for the next four years. If your firm can
borrow money at a 9 percent interest rate, should you pay the
manufacturer the $20,000 now or accept the four-year annuity offer of
$6,000?
SOLUTION:
We can find the cost of the four-year, $6,000 annuity in present value
terms using equation 5-4:

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The cost of paying for the equipment over time is $19,438.32. This is
less, in present value terms, than paying $20,000 cash. The firm should
take the annuity payment plan.
Similar to Problems 5-7, 5-8, Self-Test Problem 2
Perpetuity—A Special Annuity LG5-5
A perpetuity is a special type of annuity with a stream of level cash flows that are paid forever. These arrangements
are called perpetuities because payments are perpetual. Assets that offer investors perpetual payments are preferred
stocks and British 2½% Consolidated Stock, a debt referred to as consols.
perpetuity An annuity with cash flows that continue forever.
consols Investment assets structured as perpetuities.
The value of an investment like this is the present value of all future annuity payments. As the cash flow continues
indefinitely, we can’t use equation 5-4. Luckily, mathematicians have figured out that when the number of periods,
N, in equation 5-4 goes to infinity, the equation reduces to a very simple one:
(5-5)
For example, the present value of an annual $100 perpetuity discounted at 10 percent is $1,000 (= $100 ÷ 0.10).
Compare this to the present value of a $100 annuity of 40 years as shown in Table 5.2. The 40-year annuity’s value
is $977.91. You’ll see that extending the payments from 40 years to an infinite number of years adds only $22.09 (=
$1,000 − $977.91) of value. This demonstrates once again how little value today is placed on cash flows paid many
years into the future.

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5.3 • ORDINARY ANNUITIES VERSUS ANNUITIES DUE LG5-
6
So far, we’ve assumed that every cash flow comes in at the end of every period. But in many instances, cash flows
come in at the beginning of each period. An annuity in which the cash flows occur at the beginning of each period is
called an annuity due.
annuity due An annuity in which cash flows are paid at the beginning of each time period.
Consider the five-year $100 annuity due. The cash flow in the beginning of year 1 looks like it’s actually a cash flow
today. Annuity due moved the cash flow from the end of the year to the beginning, which looks like the end of the
previous year.
Note that these five annuity-due cash flows are essentially the same as a payment today and a four-year ordinary
annuity.
time out!
5-3 How important is the magnitude of the discount rate in present value computations? Do significantly higher interest rates
lead to significantly higher present values?
5-4 Reconsider the physical therapy equipment example. If interest rates are only 7 percent, should you pay the up-front fee or
the annuity?
Future Value of an Annuity Due So, how do we calculate the future value of the five-year annuity due shown in
the time line? The first cash flow of an ordinary five-year annuity can compound for four years. The last cash flow
does not compound at all. From the time line, you can see that the first cash flow of the annuity due essentially
occurs in year zero, or today. So the first cash flow compounds for five years. The last cash flow of an annuity due
compounds one year. The main difference between an annuity due and an ordinary annuity is that all the cash flows
of the annuity due compound one more year than the ordinary annuity. The future value of the annuity due will
simply be the future value of the ordinary annuity multiplied by (1 + i):
(5-6)
Earlier in the chapter, the future value of this ordinary annuity was shown to be $586.66. Therefore, the future value
of the annuity due is $633.59 (= $586.66 × 1.08).

finance at work //: behavioral
Take Your Lottery Winnings Now or Later?

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©McGraw-Hill Education
On January 13, 2016, three lottery tickets co-won a record Powerball jackpot of $1.5 billion. So each ticket won $500 million. The
winners had two choices for payment: They could take a much-discounted lump sum cash payment immediately or take 30 annuity
payments (one immediately and then one every year for 29 years, which is a 30-year annuity due). The annuity payment would be
$16.67 million (= $500 million ÷ 30) for 30 years. The alternative immediate lump sum was $309.97 million before taxes. One way to
decide between the two alternatives would be to use the time value of money concepts. The winners might have computed the present
value of the annuity and compared it to the lump sum cash payment.
At the time, long-term interest rates were 3.9 percent. The present value of the annuity offered was $303.11 million per winning ticket.
(Compute this yourself.) Notice that winning $500 million does not deliver $500 million of value! If the decision was made from this
perspective, the group should choose to take the lump sum because it has more value than the annuity alternative, and that is what the
three winners did. In fact, most winners do. Financial advisors tend to recommend that lottery winners take the lump sum because they
believe that the money can earn a higher return than the 3.9 percent interest rate. Of course, you pay income taxes too. The 39.6%
federal tax rate brings the lump sum payment down to $187.2 million.
Good reasons arise for taking the annuity, however. To earn the higher return on the lump sum, the advisor (and the group of
owners) would have to take risks. In addition, most of the lump sum would have to be invested. But most people who choose the lump
sum end up spending much of it in the first couple of years. Stories abound about lottery winners who declare bankruptcy a few years
after receiving their money. Choosing the annuity helps instill financial discipline, since the winners can’t waste money today that they
won’t receive for years.
Want to know more?
Key Words to Search for Updates: Powerball winners (go to www.powerball.com)
Source: Riley, Charles, Sara Sidner, and Tina Burnside, “We Have Powerball Winners!,” CNN Money, January 13, 2016,
http://money.cnn.com/2016/01/13/news/powerball-winner-lottery.
Present Value of an Annuity Due What is a five-year annuity due, shown previously, worth today? Remember
that we discount the first cash flow of an ordinary five-year annuity one year. We discount the last cash flow for the
full five years. But since the first cash flow of the annuity due is already paid today, we don’t discount it at all. We
discount the last cash flow of an annuity due only four years. Indeed, we discount all the cash flows of the annuity
due one year less than we would discount the ordinary annuity. Therefore, the present value of the annuity due is
simply the present value of the ordinary annuity multiplied by (1 + i):
(5-7)

the Math Coach on…
Setting Financial Calculators for Annuity Due

http://www.powerball.com

http://money.cnn.com/2016/01/13/news/powerball-winner-lottery/

“Financial calculators can be set for beginning-of-period payments. Once set, you compute future and
present values of annuities due just as you would the ordinary annuity. To set the HP calculator, press the
color button followed by the BEG/END button. To set the TI calculator for an annuity due, push the 2ND
button, followed by the BGN button, followed by the 2ND button again, followed by the SET button, and
followed by the 2ND button a third time, finally the QUIT button. To set the HP and TI calculators back to end-
of-period cash flows, repeat these procedures.„
Earlier in the chapter, we discovered that the present value of this ordinary annuity was $399.27. So the present
value of the annuity due is $431.21 (= $399.27 × 1.08).
Interestingly, we make the same adjustment, (1 + i), to both the ordinary annuity present value and future value to
compute the annuity due value.
5.4 • COMPOUNDING FREQUENCY LG5-7
So far, all of our examples and illustrations have used annual payments and annual compounding or discounting
periods. But many situations that use cash flow time-value-of-money analysis require more frequent or less frequent
time periods than simple yearly entries. Bonds make semiannual interest payments; stocks pay quarterly dividends.
Most consumer loans require monthly payments. Monthly payments require monthly compounding. In this section,
we’ll discuss the implications of compounding more than once a year.
time out!
5-5 In what situations might you need to use annuity due analysis instead of an ordinary annuity analysis?
5-6 Reconsider your retirement plan earlier in this chapter. What would your retirement wealth grow to be if you started
contributing today?
Effect of Compounding Frequency
Consider a $100 deposit made today with a 12 percent annual interest rate. What’s the future value of this deposit in
one year? Equation 4-2 from the previous chapter shows that the answer is $112. What would happen if the bank
compounded the interest every six months instead of at the end of the year? Halfway through the year, the bank
would compute that the deposit has grown 6 percent (half the annual 12 percent rate) to $106. At the end of the year,
the bank would compute another 6 percent interest payment. However, this 6 percent is earned on $106, not the
original $100 deposit. The end-of-year value is therefore $112.36 (= $106 × 1.06). By compounding twice per year
instead of just once, the future value is $0.36 higher. Though this amount may seem negligible, you might be
surprised to see how quickly the difference becomes significant.

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Instead of compounding annually or semiannually, what might happen if compounding were quarterly? Since each
year contains four quarters, the interest rate per quarter would be 3 percent (= 12 percent ÷ 4 quarters). The future
value in one year, compounded quarterly, is $112.55 (= $100 × 1.034). Again, the compounding frequency increased
and so did the future value. Table 5.3 shows the effect of various compounding frequencies. We’d like to draw your
attention to two important points in the table. First, the higher the compound frequency, the higher the future value
will be. Second, the relative increase in value from increasing compounding frequency seems to diminish with
increasing frequencies. For example, increasing frequency from annual to semiannual increased the future value by
36 cents. However, increasing frequency from daily to hourly compounding increases the future value by only 0.1
cent.2

▼ TABLE 5.3 Future Value in One Year and Compounding Frequency of $100 at 12 percent
A B C D
1 Frequency Period Interest Rate Future Value Equation Future Value
2 Annual 12% $100 × 1.121
$ 112.00
3 Semiannual 6 $100 × 1.062
112.36
4 Quarterly 3 $100 × 1.034
112.55
5 Monthly 1 $100 × 1.0112
112.68
6 Daily 0.032877 $100 × 1.00032877365
112.748
7 Hourly 0.00136986 $100 × 1.00001369868760
112.749
The higher the compound frequency, the higher the future value will be.
When we work with annuity cash flows, the compound frequency used is the same as the timing of the cash flows.
When annuity cash flows are paid monthly, then interest is also compounded monthly, as seen in Examples 5-5 and
5-6.
EARs and APRs If you borrowed $100 at a 12 percent interest rate, you would expect to pay $112 in one year. If
the loan compounded monthly, then you would owe $112.68 at the end of the year, as Table 5.3 shows. So a 12
percent loan compounded monthly means that you really pay more than 12 percent. In fact, you would pay 12.68
percent. In this example, the 12 percent rate is called the annual percentage rate (APR). The 12.68 percent is called the
effective annual rate (EAR)—a more accurate measurement of what you will actually pay.
annual percentage rate (APR) The interest rate per period times the number of periods in a year.
effective annual rate (EAR) The interest rate per period times the number of periods in a year.
Lenders are legally required to show potential borrowers the APR on any loan offered. While the difference in APR
and EAR is not that large in this example, it’s interesting that the law requires only the less accurate (and lower) one
to be shown. Since the EAR is a more accurate measure of what you will pay, it’s useful to know how to convert a
stated APR to an EAR. Equation 5-8 shows this conversion with a compounding frequency of m times per year:
(5-8)
Table 5.4 shows various EAR conversions. If compounding occurs annually, you will see that the EAR and the APR
will be the same. If compounding happens more than once a year, then the EAR will be higher than the APR. The
table also demonstrates that the compound frequency effect grows substantially for higher interest rates or longer
term loans. Compounded quarterly, the EAR is hardly different at all from a 5 percent APR: 5.09 percent versus 5

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percent. The difference is larger when the APR is 12 percent. Compounded quarterly, the EAR is higher at 12.55
percent.
the Math Coach on…
Annuity Computations in Spreadsheets
“The TVM functions in a spreadsheet handle annuity payments similar to financial calculators. The
spreadsheet Math Coach in Chapter 4 shows the functions. The functions have an annuity input.
The example illustrated earlier in this chapter asks for the FV of annual $100 deposits earning 8 percent. The
spreadsheet solution is the same as the equation and calculator solutions. If you want the FV of an annuity
due, just change the type from 0 to 1.
See this textbook’s online student center to watch instructional videos on using spreadsheets.„

EXAMPLE 5-5 Car Loan Debt LG5-4
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Now you would like to buy a car. You have reviewed your budget and
determined that you can afford to pay $500 per month as a car
payment. How much can you borrow if interest rates are 9 percent and
you pay the loan over four years? How much could you borrow if you
agree to pay for six years instead?
SOLUTION:
The loan amount is the present value of the 48-month, $500 annuity.
Note that the loan term will be 48 (= 4 × 12) months and the interest
rate is 0.75 (= 9 ÷ 12) percent. Using equation 5-4, you discover that
you can borrow up to $20,092 to buy a car:
If you are willing to borrow money for six years instead of four, the
small change to the equation results in your ability to borrow $27,738.
Although this would allow you to buy a more expensive car, it would

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also require two more years of $500 payments (an additional $12,000
of payments!).
Similar to Problems 5-25, 5-26, Self-Test Problem 4
EXAMPLE 5-6
Making Monthly Pension
Contributions LG5-7
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Reexamine your original plan to contribute to your company retirement
plan. Instead of a total contribution of $4,500 per year for 40 years, you
are able to contribute monthly. Given your expected 7 percent per year
investment return, how much money can you expect in your retirement
account?
SOLUTION:
Now your total monthly contribution will be $375 (= $4,500 ÷ 12), which
will continue for 480 months and earn a 0.58333 (= 7 ÷ 12) percent
monthly return. The results of equation 5-2 show that the future value
of this annuity is
When you made contributions annually, the future value was $898,358
(Example 5-2). By changing to monthly contributions, your retirement
nest egg increased by nearly $86,000 to $984,305!
Similar to Problems 5-51, 5-52, Self-Test Problem 3

the Math Coach on…
Common Mistakes
“As you figure present and future values of annuity cash flows, check that all terms are consistent: the
number of payments, interest rate, and payment size all need to use common terms. If your payments are
monthly, then the number of payments must reflect the number of months; the interest rate must be stated as
a per-month rate, and the payment register must reflect that monthly payment.„
time out!
5-7 Why is EAR a more accurate measure of the rate actually paid than APR?

http://mhhe.com/CornettM4e

5-8 What would have a smaller present value: a future sum discounted annually or one discounted monthly?
▼ TABLE 5.4 The EAR Is Higher than the APR
A B C D
1 APR Compounding Periods Equation = EAR
2 Varying the Compounding Periods
3 5%  1     (1 + 0.05/1)1 − 1 5.00% 
4 5 4     (1 + 0.05/4)4 − 1 5.09
5 5 12     (1 + 0.05/12)12 − 1 5.12
6 Varying APR and Compounding Periods
7 9 4     (1 + 0.09/4)4 − 1 9.31
8 9 12     (1 + 0.09/12)12 − 1 9.38
9 12 4     (1 + 0.12/4)4 − 1 12.55
10 12 12     (1 + 0.12/12)12 − 1 12.68
Note: This compound frequency effect grows substantially for higher interest rates or longer term loans.
EXAMPLE 5-7
Evaluating Credit Card
Offers LG5-7
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
As a college student, you probably receive many credit card offers in
the mail. Consider these two offers. The first card charges a 16 percent
APR. An examination of the footnotes reveals that this card compounds
monthly. The second credit card charges 15.5 percent APR and
compounds weekly. Which card has a lower effective annual rate?
SOLUTION:
Compute the EAR of each card to compare them in common (and
realistic) terms. The first card has an EAR of
The EAR of the second card is
You should pick the second credit card because it has a lower effective
annual rate. But note also that you will always be better off if you pay

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your credit card balance whenever the bill comes due.
Similar to Problems 5-15, 5-16, Self-Test Problem 3

5.5 • ANNUITY LOANS LG5-8
In this chapter, we’ve focused on computing the future and present value of annuities. But in many situations, these
values are already known and what we really need to compare are the payments or implied interest rate—usually,
the highest interest rate offered.
the Math Coach on…
Common Mistakes
“As we noted in Chapter 4, when computing the interest rate, make sure that the present value and the
annuity payments are of different signs (positive versus negative). Otherwise, the calculator will show an error.

What Is the Interest Rate?
Many business and personal applications already state the cost of an investment, as well as the annuity cash flows
and time period. We need, then, to solve for the implied interest rate of this investment. Unfortunately, we have no
general, easy equation to solve for the interest rate. Even financial calculators use an iterating process, which causes
them to “think” a little longer before displaying the estimated interest rate result.
Consider the plight of a manager of a small doctor’s office who has the opportunity to buy a piece of imaging
equipment for $100,000. The equipment will allow the office to generate $25,000 in profits for six years, at which
time the equipment will be worn out and without value in the United States. What rate of return does this purchase
offer the doctor’s office? The time line for this problem appears as
For the financial calculator solution, input N = 6, PV = –100000, PMT = 25000, and FV = 0. The interest rate result
is then 12.98 percent. So, if this is a high enough return relative to other uses of the $100,000, the doctor’s office
should seriously consider purchasing the imaging machine.
EXAMPLE 5-8
Computing Interest Rate
Needed LG5-8
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
After saving diligently throughout your entire career, you and your
spouse are finally ready to retire with a nest egg of $800,000. You need
to invest this money in a mix of stocks and bonds that will allow you to
withdraw $6,000 per month for 30 years. What interest rate do you

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need to earn?
SOLUTION:
Use a financial calculator and input N = 360, PV = –800000, PMT =
6000, and FV = 0. The interest rate result is 0.6860 percent. But
remember, since the periods and payments are in months, the interest
rate is too. It is customary to report this as an APR: 8.23 percent (=
0.6860 percent × 12). However, the EAR more accurately reflects the
true interest rate, 8.55 percent (= 1.0068612 – 1). In order for your
money to last for 30 years while funding a $6,000 per month income,
you must earn at least an 8.23 APR per year return.
If you have uneven cash flows, use the calculator CF worksheet and
then solve with the IRR function.
Similar to Problems 5-33, 5-34, 5-35, 5-36

Finding Payments on an Amortized Loan LG5-9
©Phillip Spears/Getty Images
Many consumers and small business owners already know how much money they want to borrow and the level of
current interest rates. Usually, they need to translate this information into the actual payments to determine if they
can really afford the purchase. A loan structured for annuity payments that completely pay off the debt is called an
amortized loan. To compute the annuity cash flow of an amortized loan, rearrange the present value of an annuity
formula, equation 5-4, to solve for the payment:
amortized loan A loan in which the borrower pays interest and principal over time.

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(5-9)
Most car loans require monthly payments for three to five years. Assume that you need a $10,000 loan to buy a car.
The loan is for four years and interest rates are 9 percent per year APR. To implement equation 5-9, use an interest
rate of 0.75 percent (= 9 percent/12) and 48 periods (= 4 × 12) as
So, when interest rates are 9 percent, it takes monthly payments of $248.85 to pay off a $10,000 loan in four years.
Interest rate levels and loan length strongly affect how large your payments will be. Table 5.5 shows the monthly
payments needed to pay off a mortgage debt at various interest rates and lengths of time. (Try computing the
payments yourself!) Note that as the interest rate declines, the monthly payment also declines. This is why people
rush to refinance their mortgages after interest rates fall. A decline of 1 or 2 percent can save a homeowner hundreds
of dollars every month. You will also see from the table that paying off a mortgage in only 15 years requires larger
payments, but generally saves thousands in interest.
Amortized Loan Schedules When you pay a car loan or home mortgage, you will often find it useful to know
how much of the debt, or loan principal, you still owe. For example, consider a case wherein you bought a car two
years ago using a four-year loan. In order to sell the car now, the loan balance will have to be paid off.
Being able to compute this principal balance may influence your chances of selling the car.
loan principal The balance yet to be paid on a loan.
▼ TABLE 5.5 Monthly Payments on a $225,000 Loan

An interest-only loan allows the borrower to make payments that consist totally of interest payments, so none of the
debt is reduced. A $10,000 interest-only loan with a 9 percent APR paid monthly will cost $75 per month (=
$10,000 × 0.09 ÷ 12). Amortizing this loan over four years requires monthly payments of $248.85 (see earlier car
loan problem). The difference in the first month’s payment on the two loans is $173.85 (= $248.85 – $75) and
represents the amount of the regular amortized loan’s payment that goes to reducing the principal balance. So after
the first month’s payment, the amortized loan’s balance has fallen to $9,826.15, while the interest-only loan still has
a balance of $10,000.
In the second month, the interest incurred on the regular amortized loan is $73.70 (= $9,826.15 × 0.09 ÷ 12), so the
$248.85 second-month payment represents principal payment of $175.15. These numbers are shown in the
amortization schedule of Table 5.6. The table will show you that the early payments on a car loan go mostly to paying
the interest rather than reducing the principal. That interest component declines over time, and then the principal
balance declines.
amortization schedule A table detailing the periodic loan payment, interest payment, and debt balance over the life of the loan.
The amortization schedule shows that if you wish to sell the car after two years, you will have to pay the loan
company a car loan (principal) debt of $5,447.13. Of course, if you had an interest-only loan, you would still owe
the full principal of $10,000 after two years. Amortization schedules are also useful for determining other things,
like the total amount of interest that you will pay over the life of the loan. In this case, if you take a regular loan in
which you pay both principal and interest, you pay $10,000 in principal and nearly $1,945 in interest during the four
years of the loan. The interest component is an even larger component of longer-term loans, like 30-year mortgages.
Depending on the interest rate charged, the first payment in a mortgage consists of 75 percent to 95 percent interest.
The home mortgage principal balance falls very slowly in the first years of the loan.
▼ TABLE 5.6 Amortization Schedule over Four Years (9 percent APR)

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EXAMPLE 5-9
Monthly Mortgage
Payments LG5-9
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Say that you have your heart set on purchasing a beautiful, old Tudor-
style house for $250,000. A mortgage broker says that you can qualify
for a mortgage for 80 percent (or $200,000) of the price. If you get a
15-year mortgage, the interest rate will be 6.1 percent APR. A 30-year
mortgage costs 6.4 percent. One of the factors that will help you decide
which mortgage to take is the magnitude of the monthly payments.
What will they be?3
SOLUTION:
To pay off the mortgage in only 15 years, the payments would have to
be larger than for the 30-year mortgage. The higher payment will be
eased somewhat because the interest rate is lower on the 15-year
mortgage. The interest rate would be i = 0.061 ÷ 12 = 0.0050833, or
0.50833% per month. The payment for the 15-year mortgage is

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The payment for the 30-year mortgage would be
So, the payments on the 15-year mortgage are nearly $450 more each
month than the 30-year mortgage payments. You must decide whether
the cost of paying the extra $450 each month is worth it to own the
house with no debt 15 years sooner. The decision would depend on
your financial budget and the strength of your desire to be debt free.
Similar to Problems 5-39, 5-40, Self-Test Problems 1 and 4
We construct amortization schedules by showing the loan’s principal balance at the beginning of the month. This is
the same as the balance at the end of the previous month (except for the very first payment). Then we compute the
interest owed on that balance for the month. After paying that interest, what’s left of the monthly payment reduces
the loan balance for the next month. Because of these repetitive computations, spreadsheets make amortization
schedules easy to construct.
time out!
5-9 How might credit card companies keep their cardholders in debt for a long time? What payment do the credit card
companies expect your friend to make so that he never pays down the debt?
5-10 Can you find the interest rate if you know the annuity payments and a future value? Under what circumstances might you
want to solve this kind of problem? Which equation would you use?
Compute the Time Period You might also find it useful to know how long it will take to pay off a loan with
specific annuity payments. To find the number of periods, you can solve equation 5-9 for N—the number of
payments—but the equation becomes quite complicated.4 Many people just use a financial calculator or spreadsheet.
We can check to see if the $248.85 monthly payment would indeed pay off the $10,000, 9 percent car loan in four
years. Finding the solution with a financial calculator entails entering I = 0.75, PV = 10000, PMT = –248.85, and FV
= 0. The answer is 48 months.
Add-On Interest One method of calculating payments of a loan that is popular in payday lending is called add-on
interest. This method computes the amount of the interest payable at the beginning of the loan, which is then added
to the principal of the loan. This total is then divided into the number of payments to be made. Consider a loan of
$1,000 to be paid with 9 percent add-on interest and repaid in six monthly payments.
add-on interest A calculation of the amount of interest determined at the beginning of the loan and then added to the principal.

the Math Coach on…

Using the AMORT Function in TVM Calculators
“TVM calculators have preprogrammed functions to compute the amount of principal paid part way through a
mortgage. For example, if you took out a 30-year, $200,000 mortgage at a 6 percent APR, how much principal
have you paid after five years? How much do you still owe? How much interest have you paid?
To answer these questions, first enter the mortgage information to compute the monthly payments. Then use
the AMORT function. This example uses the Texas Instruments BA II + as an example. The Hewlett-Packard
and other TVM calculators have similar functions. The AMORT function allows you to compute the loan
balance at any time during the mortgage period. It also computes the amount of principal and interest that has
been paid during any time period. To answer the questions above
1. Press 2nd AMORT and P1 = 1 appears. (This refers to the first payment of the mortgage.)
2. Press the down arrow ↓, P2 = appears. (This refers to the last payment made.)
3. The question refers to 5 years of payments, which is 60 months. Enter 60 and press ENTER.
The calculator has now computed the loan balance after the 60th payment and the amount of principal and
interest that have been paid between the 1st and the 60th payments.
4. Press the down arrow ↓, displayed is BAL = 186,108.71, which is the loan balance.
5. Press the down arrow ↓, displayed is PRN = 13,891.29, which is the principal paid in the first five years.
6. Press the down arrow ↓, displayed is INT = –58,054.78, which is the interest paid in the first five years.
Note that in the beginning of a mortgage, far more interest is paid than principal.„
The total interest for this loan is computed as 9 percent of $1,000 for six months, or $45 (= 0.09 × $1,000 × ½). This
is added to the principal for a total of $1,045. Each of the six monthly payments is then $1,045 ÷ 6 = $174.17. Be
alert that the add-on interest method seriously understates the real interest rate that is being paid! If you borrow
$1,000 and repay a $174.17 monthly annuity for six months, the monthly interest rate is 1.27 percent. This is a 15.27
percent APR (= 1.27% × 12) and a 16.39 percent EAR (= 1.012712 − 1)—both much higher than the advertised 9
percent interest rate of this loan.
EXAMPLE 5-
10
Time to Pay Off a Credit Card
Balance LG5-10
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Through poor financial management, your friend has racked up $5,000
in debt on his credit card. The card charges a 19 percent APR and
compounds monthly. His latest bill shows that he must pay a minimum
of $150 this month. At this rate, how long will it take your friend to pay
off his credit card debt?

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SOLUTION:
Using the financial calculator, input I = 1.58333 (= 19/12), PV = 5000,
PMT = –150, FV = 0. The answer is 48 months, or 4 years. If the friend
pays the minimum payment, then it will be a long time before he will be
out of debt. The credit card company is very content to continue to earn
the high return for many years—essentially, the interest on the loan
and a very small portion of the principal. Your friend should pay more
than the minimum charge to reduce his debt quicker.
Similar to Problems 5-41, 5-42, Self-Test Problem 4

Get Online
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Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. How can you add a cash flow in year 2 and a cash flow in year 4? In year 7? (LG5-1)
2. People can become millionaires in their retirement years quite easily if they start saving early in employer

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401(k) or 403(b) programs (or even if their employers don’t offer such programs). Demonstrate the growth of a
$250 monthly contribution for 40 years earning 9 percent APR. (LG5-2)
3. When you discount multiple cash flows, how does the future period that a cash flow is paid affect its present
value and its contribution to the value of all the cash flows? (LG5-3)
4. How can you use the present value of an annuity concept to determine the price of a house you can afford?
(LG5-4)
5. Since perpetuity payments continue forever, how can a present value be computed? Why isn’t the present value
infinite? (LG5-5)
6. Explain why you use the same adjustment factor, (1 + i), when you adjust annuity due payments for both future
value and present value. (LG5-6)
7. Use the idea of compound interest to explain why EAR is larger than APR. (LG5-7)
8. Would you rather pay $10,000 for a five-year, $2,500 annuity or a 10-year, $1,250 annuity? Why? (LG5-8)
9. The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in
reducing taxes than in the later years? (LG5-9)
10. How can you use the concepts illustrated in computing the number of payments in an annuity to figure how to
pay off a credit card balance? How does the magnitude of the payment impact the number of months? (LG5-10)

Problems
BASIC PROBLEMS
5-1 Future Value Compute the future value in year 9 of a $2,000 deposit in year 1 and another $1,500 deposit
at the end of year 3 using a 10 percent interest rate. (LG5-1)
5-2 Future Value Compute the future value in year 7 of a $2,000 deposit in year 1 and another $2,500 deposit
at the end of year 4 using an 8 percent interest rate. (LG5-1)
5-3 Future Value of an Annuity What is the future value of a $900 annuity payment over five years if interest
rates are 8 percent? (LG5-2)
5-4 Future Value of an Annuity What is the future value of a $700 annuity payment over six years if interest
rates are 10 percent? (LG5-2)
5-5 Present Value Compute the present value of a $2,000 deposit in year 1 and another $1,500 deposit at the
end of year 3 if interest rates are 10 percent. (LG5-3)
5-6 Present Value Compute the present value of a $2,000 deposit in year 1 and another $2,500 deposit at the
end of year 4 using an 8 percent interest rate. (LG5-3)
5-7 Present Value of an Annuity What’s the present value of a $900 annuity payment over five years if
interest rates are 8 percent? (LG5-4)
5-8 Present Value of an Annuity What’s the present value of a $700 annuity payment over six years if
interest rates are 10 percent? (LG5-4)
5-9 Present Value of a Perpetuity What’s the present value, when interest rates are 7.5 percent, of a $50
payment made every year forever? (LG5-5)
5-10 Present Value of a Perpetuity What’s the present value, when interest rates are 8.5 percent, of a $75
payment made every year forever? (LG5-5)
5-11 Present Value of an Annuity Due If the present value of an ordinary, seven-year annuity is $6,500
and interest rates are 7.5 percent, what’s the present value of the same annuity due? (LG5-6)
5-12 Present Value of an Annuity Due If the present value of an ordinary, six-year annuity is $8,500 and
interest rates are 9.5 percent, what’s the present value of the same annuity due? (LG5-6)
5-13 Future Value of an Annuity Due If the future value of an ordinary, seven-year annuity is $6,500 and
interest rates are 7.5 percent, what is the future value of the same annuity due? (LG5-6)

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5-14 Future Value of an Annuity Due If the future value of an ordinary, six-year annuity is $8,500 and
interest rates are 9.5 percent, what’s the future value of the same annuity due? (LG5-6)
5-15 Effective Annual Rate A loan is offered with monthly payments and a 10 percent APR. What’s the
loan’s effective annual rate (EAR)? (LG5-7)
5-16 Effective Annual Rate A loan is offered with monthly payments and a 13 percent APR. What’s the
loan’s effective annual rate (EAR)? (LG5-7)
INTERMEDIATE PROBLEMS
5-17 Future Value Given a 4 percent interest rate, compute the year 6 future value of deposits made in
years 1, 2, 3, and 4 of $1,100, $1,200, $1,200, and $1,500. (LG5-1)
5-18 Future Value Given a 5 percent interest rate, compute the year 6 future value of deposits made in
years 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. (LG5-1)
5-19 Future Value of Multiple Annuities Assume that you contribute $200 per month to a retirement plan
for 20 years. Then you are able to increase the contribution to $300 per month for another 30 years.
Given a 7 percent interest rate, what is the value of your retirement plan after the 50 years? (LG5-2)
5-20 Future Value of Multiple Annuities Assume that you contribute $150 per month to a
retirement plan for 15 years. Then you are able to increase the contribution to $350 per month
for the next 25 years. Given an 8 percent interest rate, what is the value of your retirement plan after
the 40 years? (LG5-2)
5-21 Present Value Given a 6 percent interest rate, compute the present value of payments made in years 1,
2, 3, and 4 of $1,000, $1,200, $1,200, and $1,500. (LG5-3)
5-22 Present Value Given a 7 percent interest rate, compute the present value of payments made in years 1,
2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. (LG5-3)
5-23 Present Value of Multiple Annuities A small business owner visits her bank to ask for a loan. The
owner states that she can repay a loan at $1,000 per month for the next three years and then $2,000 per
month for two years after that. If the bank is charging customers 7.5 percent APR, how much would it
be willing to lend the business owner? (LG5-4)
5-24 Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. The
owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per
month for two years after that. If the bank is charging customers 8.5 percent APR, how much would it
be willing to lend the business owner? (LG5-4)
5-25 Present Value You are looking to buy a car. You can afford $450 in monthly payments for four years.
In addition to the loan, you can make a $1,000 down payment. If interest rates are 5 percent APR,
what price of car can you afford? (LG5-4)
5-26 Present Value You are looking to buy a car. You can afford $650 in monthly payments for five years.
In addition to the loan, you can make a $750 down payment. If interest rates are 8 percent APR, what
price of car can you afford? (LG5-4)
5-27 Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 7.5 percent.
How much would its value change if interest rates increased to 9 percent? Did the value increase or
decrease? (LG5-5)
5-28 Present Value of a Perpetuity A perpetuity pays $50 per year and interest rates are 9 percent. How
much would its value change if interest rates decreased to 7.5 percent? Did the value increase or
decrease? (LG5-5)
5-29 Future and Present Value of an Annuity Due If you start making $50 monthly contributions today
and continue them for five years, what’s their future value if the compounding rate is 10 percent APR?
What is the present value of this annuity? (LG5-6)
5-30 Future and Present Value of an Annuity Due If you start making $75 monthly contributions today
and continue them for four years, what is their future value if the compounding rate is 12 percent
APR? What is the present value of this annuity? (LG5-6)
5-31 Compound Frequency Payday loans are very short-term loans that charge very high interest rates.
You can borrow $225 today and repay $300 in two weeks. What is the compounded annual rate
implied by this 33.33 percent rate charged for only two weeks? (LG5-7)

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5-32 Compound Frequency Payday loans are very short-term loans that charge very high interest rates.
You can borrow $500 today and repay $590 in two weeks. What is the compounded annual rate
implied by this 18 percent rate charged for only two weeks? (LG5-7)
5-33 Annuity Interest Rate What’s the interest rate of a six-year, annual $5,000 annuity with present value
of $20,000? (LG5-8)
5-34 Annuity Interest Rate What’s the interest rate of a seven-year, annual $4,000 annuity with present
value of $20,000? (LG5-8)
5-35 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a
$1,000 per month contribution to grow to $75,000 in six years? (LG5-8)
5-36 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a $600 per
month contribution to grow to $45,000 in six years? (LG5-8)
5-37 Add-On Interest Payments To borrow $500, you are offered an add-on interest loan at 8 percent.
Two loan payments are to be made, one at six months and the other at the end of the year. Compute
the two equal payments. (LG5-8)
5-38 Add-On Interest Payments To borrow $800, you are offered an add-on interest loan at 7 percent.
Three loan payments are to be made, one at four months, another at eight months, and the last one at
the end of the year. Compute the three equal payments. (LG5-8)
5-39 Loan Payments You wish to buy a $25,000 car. The dealer offers you a four-year loan with a 9
percent APR. What are the monthly payments? How would the payment differ if you paid interest
only? What would the consequences of such a decision be? (LG5-9)
5-40 Loan Payments You wish to buy a $10,000 dining room set. The furniture store offers you a three-
year loan with an 11 percent APR. What are the monthly payments? How would the payment differ if
you paid interest only? What would the consequences of such a decision be? (LG5-9)
5-41 Number of Annuity Payments Joey realizes that he has charged too much on his credit card and has
racked up $5,000 in debt. If he can pay $150 each month and the card charges 17 percent APR
(compounded monthly), how long will it take him to pay off the debt? (LG5-10)
5-42 Number of Annuity Payments Phoebe realizes that she has charged too much on her credit card and
has racked up $6,000 in debt. If she can pay $200 each month and the card charges 18 percent APR
(compounded monthly), how long will it take her to pay off the debt? (LG5-10)
ADVANCED PROBLEMS
5-43 Future Value Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,000
and $2,000 are made in years 1 and 3, respectively, and a withdrawal of $700 is made in year 4. (LG5-
10)
5-44 Future Value Given a 9 percent interest rate, compute the year 6 future value if deposits of $1,500
and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $600 is made in year 5. (LG5-
1)
5-45 EAR of Add-On Interest Loan To borrow $2,000, you are offered an add-on interest loan at 10
percent with 12 monthly payments. First compute the 12 equal payments and then compute the EAR
of the loan. (LG5-7, LG5-8)
5-46 EAR of Add-On Interest Loan To borrow $700, you are offered an add-on interest loan at 9 percent
with 12 monthly payments. First compute the 12 equal payments and then compute the EAR of the
loan. (LG5-7, LG5-8)
5-47 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $500
cash back on the purchase or a 3 percent APR, four-year loan. The price of the car is $15,000 and you
could obtain a four-year loan from your credit union, at 6 percent APR. Which deal is cheaper? (LG5-
4, LG5-9)
5-48 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $1,000
cash back on the purchase, or a 2 percent APR, five-year loan. The price of the car is $20,000 and you
could obtain a five-year loan from your credit union, at 7 percent APR. Which deal is cheaper? (LG5-
4, LG5-9)
5-49 Amortization Schedule Create the amortization schedule for a loan of $15,000, paid monthly

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over three years using a 9 percent APR. (LG5-9)
5-50 Amortization Schedule Create the amortization schedule for a loan of $5,000, paid monthly over two
years using an 8 percent APR. (LG5-9)
5-51 Investing for Retirement Monica has decided that she wants to build enough retirement wealth that,
if invested at 8 percent per year, will provide her with $3,500 of monthly income for 20 years. To date,
she has saved nothing, but she still has 30 years until she retires. How much money does she need to
contribute per month to reach her goal? (LG5-4, LG5-9)
5-52 Investing for Retirement Ross has decided that he wants to build enough retirement wealth that, if
invested at 7 percent per year, will provide him with $3,000 of monthly income for 30 years. To date,
he has saved nothing, but he still has 20 years until he retires. How much money does he need to
contribute per month to reach his goal? (LG5-4, LG5-9)
5-53 Loan Balance Rachel purchased a $15,000 car three years ago using an 8 percent, four-year loan. She
has decided that she would sell the car now, if she could get a price that would pay off the balance of
her loan. What is the minimum price Rachel would need to receive for her car? (LG5-9)
5-54 Loan Balance Hank purchased a $20,000 car two years ago using a 9 percent, five-year loan. He has
decided that he would sell the car now, if he could get a price that would pay off the balance of his
loan. What’s the minimum price Hank would need to receive for his car? (LG5-9)
5-55 Teaser Rate Mortgage A mortgage broker is offering a $183,900 30-year mortgage with a teaser rate.
In the first two years of the mortgage, the borrower makes monthly payments on only a 4 percent APR
interest rate. After the second year, the mortgage interest rate charged increases to 7 percent APR.
What are the monthly payments in the first two years? What are the monthly payments after the
second year? (LG5-9)
5-56 Teaser Rate Mortgage A mortgage broker is offering a $279,000 30-year mortgage with a teaser rate.
In the first two years of the mortgage, the borrower makes monthly payments on only a 4.5 percent
APR interest rate. After the second year, the mortgage interest rate charged increases to 7.5 percent
APR. What are the monthly payments in the first two years? What are the monthly payments after the
second year? (LG5-9)
5-57 Spreadsheet Problem Consider a person who begins contributing to a retirement plan at age 25 and
contributes for 40 years until retirement at age 65. For the first 10 years, she contributes $3,000 per
year. She increases the contribution rate to $5,000 per year in years 11 through 20. This is followed by
increases to $10,000 per year in years 21 through 30 and to $15,000 per year for the last 10 years. This
money earns a 9 percent return. First compute the value of the retirement plan when she turns age 65.
Then compute the annual payment she would receive over the next 40 years if the wealth was
converted to an annuity payment at 8 percent. (LG5-2, LG5-9)
5-58 Spreadsheet Problem When paying off a home mortgage, extra principle payments can have a
dramatic impact on the time needed to pay off the mortgage. (LG5-9)
a. Create an amortization schedule for a $200,000, three-year mortgage, with a 6% APR.
b. After the fifth year, add an extra $100 to each monthly payment. When is the loan paid off?

Combined Chapter 4 and Chapter 5 Problems
4&5-1 Future Value Consider that you are 35 years old and have just changed to a new job. You have
$80,000 in the retirement plan from your former employer. You can roll that money into the
retirement plan of the new employer. You will also contribute $3,600 each year into your new
employer’s plan. If the rolled-over money and the new contributions both earn a 7 percent return,
how much should you expect to have when you retire in 30 years?
4&5-2 Future Value Consider that you are 45 years old and have just changed to a new job. You have
$150,000 in the retirement plan from your former employer. You can roll that money into the
retirement plan of the new employer. You will also contribute $7,200 each year into your new

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employer’s plan. If the rolled-over money and the new contributions both earn an 8 percent
return, how much should you expect to have when you retire in 20 years?
4&5-3 Future Value and Number of Annuity Payments Your client has been given a trust fund
valued at $1 million. He cannot access the money until he turns 65 years old, which is in 25
years. At that time, he can withdraw $25,000 per month. If the trust fund is invested at a 5.5
percent rate, how many months will it last your client once he starts to withdraw the money?
4&5-4 Future Value and Number of Annuity Payments Your client has been given a trust fund
valued at $1.5 million. She cannot access the money until she turns 65 years old, which is in 15
years. At that time, she can withdraw $20,000 per month. If the trust fund is invested at a 5
percent rate, how many months will it last your client once she starts to withdraw the money?
4&5-5 Present Value and Annuity Payments A local furniture store is advertising a deal in which you
buy a $3,000 dining room set and do not need to pay for two years (no interest cost is incurred).
How much money would you have to deposit now in a savings account earning 5 percent APR,
compounded monthly, to pay the $3,000 bill in two years? Alternatively, how much would you
have to deposit in the savings account each month to be able to pay the bill?
4&5-6 Present Value and Annuity Payments A local furniture store is advertising a deal in which you
buy a $5,000 living room set with three years before you need to make any payments (no interest
cost is incurred). How much money would you have to deposit now in a savings account earning
4 percent APR, compounded monthly, to pay the $5,000 bill in three years? Alternatively, how
much would you have to deposit in the savings account each month to be able to pay the bill?
4&5-7 House Appreciation and Mortgage Payments Say that you purchase a house for $200,000 by
getting a mortgage for $180,000 and paying a $20,000 down payment. If you get a 30-year
mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan
balance be in 10 years? If the house appreciates at 3 percent per year, what will be the value of
the house in 10 years? How much of this value is your equity?
4&5-8 House Appreciation and Mortgage Payments Say that you purchase a house for $150,000 by
getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year
mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan
balance be in five years? If the house appreciates at 4 percent per year, what will be the value of
the house in five years? How much of this value is your equity?
4&5-9 Construction Loan You have secured a loan from your bank for two years to build your home.
The terms of the loan are that you will borrow $200,000 now and an additional $100,000 in
one year. Interest of 10 percent APR will be charged on the balance monthly. Since no
payments will be made during the two-year loan, the balance will grow at the 10 percent
compounded rate. At the end of the two years, the balance will be converted to a traditional 30-
year mortgage at a 6 percent interest rate. What will you be paying as monthly mortgage
payments (principal and interest only)?
4&5-10 Construction Loan You have secured a loan from your bank for two years to build your home.
The terms of the loan are that you will borrow $100,000 now and an additional $50,000 in one
year. Interest of 9 percent APR will be charged on the balance monthly. Since no payments will
be made during the two-year loan, the balance will grow. At the end of the two years, the balance
will be converted to a traditional 15-year mortgage at a 7 percent interest rate. What will you pay
as monthly mortgage payments (principal and interest only)?

Notes
CHAPTER 5
1. The contract actually contains some complications like incentives to play well and salary deferral. We ignore those complicating factors
here.
2. It is also possible to continuously compound. The future value of a continuously compounded deposit is , where e
has a value of 2.7183.
3. Most homeowners are actually most interested in their total payment, which will include hazard insurance for the home and property
taxes. Such payments are referred to as PITI—principal, interest, taxes, and insurance. For simplicity, we use only PI payments here—
principal and interest.

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4. The equation for solving for the number of periods in an annuity is:

Part Four

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chapter six
understanding financial
markets and institutions
©Steve Allen/Stockbyte/Getty Images

H
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ow do funds flow throughout the economy? How do financial markets operate and relate to one
another? As an individual investor or a financial manager you need to know. Your future decision-
making skills depend on it. Investors’ funds flow through financial markets such as the New York
Stock Exchange and mortgage markets. Financial institutions—commercial banks (e.g., Bank of
America), investment banks (e.g., Morgan Stanley), and mutual funds (e.g., Fidelity)—act as
intermediaries to channel funds from individual savers or investors through financial markets. This chapter
looks at the nature and operations of financial markets and discusses the financial institutions (FIs) that
participate in those markets. Bonds, stocks, and other securities that trade in the markets are covered in
Chapters 7 and 8.
In this chapter we also examine how significant changes in the way financial institutions deliver
services played a major role in forming the severe financial crisis that began in late 2008. We examine
some of the crisis’s underlying causes, review some of the major events that occurred during that time,
and discuss some resulting regulatory and industry changes that are in effect today in Appendix 6A,
available in Connect or at mhhe.com/Cornett4e.
LEARNING GOALS
LG6-1 Differentiate between primary and secondary markets and between money and capital markets.
LG6-2 List the types of securities traded in money and capital markets.
LG6-3 Identify different types of financial institutions and the services that each provides.
LG6-4 Know the main suppliers and demanders of loanable funds.
LG6-5 Understand how equilibrium interest rates are determined.
LG6-6 Analyze specific factors that influence interest rates.
LG6-7 Offer different theories that explain the shape of the term structure of interest rates.
LG6-8 Demonstrate how forward interest rates derive from the term structure of interest rates.

viewpoints
business APPLICATION
DPH Corporation needs to issue new bonds either this year or in two years. DPH Corp. is a profitable firm, but if the U.S. economy
were to experience a downturn, the company would see a big drop in sales over the next two years as its products are very sensitive
to changes in the overall economy. DPH Corp. currently has $10 million in public debt outstanding, but its bonds are not actively
traded. What questions must DPH Corp. consider as its managers decide whether to issue bonds today or in two years? How can
DPH Corp. get these bonds to potential buyers and thus raise the needed capital? (See the solution at the end of the book.)
6.1 • FINANCIAL MARKETS LG6-1
Financial markets exist to manage the flow of funds from investors to borrowers as well as from one investor to
another. We generally differentiate financial markets by their primary financial instruments’ characteristics (such as
bond maturities) or the market’s location. Specifically, we can distinguish markets along two major dimensions:
financial markets The arenas through which funds flow.
1. Primary versus secondary markets.
2. Money versus capital markets.
Primary Markets versus Secondary Markets
Primary Markets Primary markets provide a forum in which demanders of funds (e.g., corporations such as IBM or

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government entities such as the U.S. Treasury) raise funds by issuing new financial instruments, such as stocks and
bonds. Corporations or government entities continually have new projects or expanded production needs, but do not
have sufficient internally generated funds (such as retained earnings) to support their capital needs. Thus,
corporations and governments issue securities in external primary markets to raise additional funds. These entities
sell the new financial instrument issues to initial fund suppliers (e.g., households) in exchange for the funds (money)
that the issuer requires.
primary markets Markets in which corporations raise funds through new issues of securities.
In the United States, financial institutions called investment banks arrange most primary market transactions for
businesses. Some of the best-known examples of U.S. investment banks include Morgan Stanley, Goldman Sachs,
or Merrill Lynch (owned by Bank of America, a commercial bank). These firms intermediate between issuing parties
(fund demanders) and investors (fund suppliers). Investment banks provide fund demanders with a number of
services, including advising the company or government agency about the securities issue (such as an appropriate
offer price and number of securities to issue) and attracting initial public purchasers of the customer’s securities
offerings. Firms that need funds are seldom expert at raising capital themselves, so they avert risk and lower their
costs by turning to experts at investment banks to issue their primary market securities.
investment banks Banks that help companies and governments raise capital.
commercial bank Depository institutions whose major assets are loans and whose major liabilities are deposits.
The initial (or primary market) sale of securities occurs either through a public offering or as a private placement to
a small group of investors. An investment bank serves as a security underwriter in a public offering. In a private
placement, the security issuer engages the group of buyers (usually fewer than 10) to purchase the whole issue.
Buyers are typically financial institutions. To protect smaller individual investors against a lack of disclosure,
publicly traded securities must be registered with the Securities and Exchange Commission (SEC). Private
placements, on the other hand, can be unregistered and resold to large, financially sophisticated investors only.
Large investors supposedly possess the resources and expertise to analyze a security’s risk. Privately placed bonds
and stocks traditionally have been among the most illiquid securities in the securities markets; only the very largest
financial institutions or institutional investors are able or willing to buy and hold them in the absence of an active
secondary market. Issuers of privately placed securities tend to be less well known (e.g., medium-sized
municipalities and corporations). Because of this lack of information and its associated higher risk, returns paid to
holders of privately placed securities tend to be higher than those on publicly placed securities issues.

personal APPLICATION
John Adams wants to invest in one of two corporate bonds issued by separate firms. One bond yields 8.00 percent with a 10-year
maturity; the other offers a 10.00 percent yield and a 9-year maturity. The second bond seems to be the better deal if one only looks
at the interest rate. Is it necessarily the bond in which John should invest? Once he decides which bond represents the better
investment, how can John go about buying the bond? (See the solution at the end of the book.)
Should John consider bonds from other countries?
Figure 6.1 illustrates a time line for the primary market exchange of funds for a new issue of corporate bonds or
equity. We will further discuss how companies, the U.S. Treasury, and government agencies that market primary
government securities, such as Ginnie Mae and Freddie Mac, go about selling primary market securities in Chapter
8. Throughout this text, we focus on government securities from the buyer’s, rather than the seller’s, point of view.
You can find in-depth discussions of government securities from the seller’s point of view in a public finance text.
Primary market financial instruments include stock issues from firms initially going public (e.g., allowing their
equity shares to be publicly traded on stock markets for the first time). We usually refer to these first-time issues as

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initial public offerings (IPOs). For example, on June 16, 2015, Fitbit announced a $732 million IPO of its common
stock. Fitbit used several investment banks, including Morgan Stanley, Deutsche Bank, and Bank of
America Merrill Lynch, to underwrite the company’s stock. Publicly traded firms may issue additional
bonds or stocks as primary market securities. For example, on February 25, 2015, American Tower Group
announced that it would sell an additional 23.5 million shares of common stock (at $97.00 per share) underwritten
by investment banks such as Goldman Sachs, Bank of America Merrill Lynch, Barclays, Citigroup and J.P. Morgan.
The funds were used to finance the acquisition of Verizon. If the acquisition of Verizon was not completed,
American Tower expected to use the net proceeds from the offering for general corporate purposes.
initial public offerings (IPOs)  A first-time issue of stock by a private firm going public (e.g., allowing its equity, some of which was held
privately by managers and venture capital investors, to be publicly traded in stock markets for the first time).
FIGURE 6.1 Primary Market Transfer of Funds
Secondary Markets Once firms issue financial instruments in primary markets, these same stocks and bonds are
then traded—that is, bought and resold—in secondary markets. The New York Stock Exchange (NYSE) and the
NASDAQ are two well-known examples of secondary markets for trading stocks (see Chapters 7 and 8). In addition
to stocks and bonds, secondary markets also exist for financial instruments backed by mortgages and other assets,
foreign exchange, and futures and options (i.e., derivative securities, discussed later in the chapter).
secondary markets Markets that trade financial instruments once they are issued.
Buyers find sellers of secondary market securities in economic agents that need funds (fund demanders). Secondary
markets provide a centralized marketplace where economic agents know that they can buy or sell most securities
quickly and efficiently. Secondary markets, therefore, save economic agents the search costs of finding buyers or
sellers on their own. Figure 6.2 illustrates a secondary market transfer of funds. Secondary market buyers often use
securities brokers such as Charles Schwab or other brokerage firms to act as intermediaries as they exchange funds
for securities (see Chapter 8). An important note: The firm that originally issued the stock or bond is not involved in
secondary market transactions in any way—no money accrues to the company itself when its stock trades in a
secondary market.
Secondary markets offer benefits to both investors (fund suppliers) and issuers (fund demanders). Investors gain
liquidity and diversification benefits (see Chapter 10). Although corporate security issuers are not directly involved
in secondary market transactions, issuers do gain information about their securities’ current market value. Publicly
traded firms can thus observe how investors perceive their corporate value and their corporate decisions by tracking
their firms’ securities’ secondary market prices. Such price information allows issuers to evaluate how well they are
using internal funds as well as the funds generated from previously issued stocks and bonds and provides indications
about how well any subsequent bond or stock offerings might be received—and at what price.
FIGURE 6.2 Secondary Market Transfer of Funds


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Secondary market trading volume can be quite large. Trading volume is defined as the number of shares of a security
that are simultaneously bought and sold during a given period. Each seller and each buyer actually contract with the
exchange’s clearinghouse, which then matches sell and buy orders for each transaction. The clearinghouse is a
company whose stock trades on the exchange, and the clearinghouse runs on a for-profit basis.
trading volume The number of shares of a security that are simultaneously bought and sold during a period.
FIGURE 6.3 Money versus Capital Market Maturities
The exchange and the clearinghouse can process many transactions in a single day. For example, on October 28,
1997, NYSE trading volume exceeded 1 billion shares for the first time ever. On October 10, 2008 (at the
height of the financial crisis), NYSE trading volume topped 7.3 billion shares, the highest level to date. In
contrast, during the mid-1980s, a NYSE trading day during which 250 million shares traded was considered a high-
volume day.
Money Markets versus Capital Markets
We noted that financial markets are differentiated in part by the maturity dates of the instruments traded. This
distinction becomes important when we differentiate money markets from capital markets. Both of these markets
deal in debt securities (capital markets also deal in equity securities); the question becomes one of when the
securities come due.
Money Markets Money markets feature debt securities or instruments with maturities of one year or less (see Figure
6.3). In money markets, agents with excess short-term funds can lend (or supply) to economic agents who need (or
demand) short-term funds. The suppliers of funds buy money market instruments and the demanders of funds sell
money market instruments. Because money market instruments trade for only short periods of time, fluctuations in
secondary-market prices are usually quite small. With less volatility, money market securities are thus less risky
than longer-term instruments. In the United States, many money market securities do not trade in a specific location;
rather, transactions occur via telephones, wire transfers, and computer trading. Thus, most U.S. money markets are
said to be over-the-counter (OTC) markets.
money markets Markets that trade debt securities or instruments with maturities of less than one year.
over-the-counter market Markets that do not operate in a specific fixed location—rather, transactions occur via telephones, wire
transfers, and computer trading.


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Money Market Instruments LG6-2 Corporations and government entities issue a variety of money market
securities to obtain short-term funds. These securities include
Treasury bills.
Federal funds and repurchase agreements.
Commercial paper.
Negotiable certificates of deposit.
Banker’s acceptances.
Table 6.1 lists and defines each money market security. Figure 6.4 graphically depicts the proportion of U.S. money
market instruments outstanding across three decades. Notice that, in 2016, federal funds and repurchase agreements
commanded the highest dollar value of all money market instruments, followed by negotiable CDs, Treasury bills,
and commercial paper.
Capital Markets Capital markets are markets in which parties trade equity (stocks) and debt (bonds) instruments
that mature in more than one year (see Figure 6.3). Given their longer maturities, capital market instruments are
subject to wider price fluctuations than are money market instruments (see the term structure discussion below and
in Chapter 7).
capital markets Markets that trade debt (bonds) and equity (stock) instruments with maturities of more than one year.
▼ TABLE 6.1 Money Market Instruments
Treasury bills: Short-term U.S. government obligations.
Federal funds: Short-term funds transferred between financial institutions, usually for no more than one day.
Repurchase agreements (repos): Agreements involving security sales by one party to another, with the promise to reverse the
transaction at a specified date and price, usually at a discounted price.
Commercial paper: Short-term unsecured promissory notes that companies issue to raise short-term cash (sometimes called
Paper).
Negotiable certificates of deposit: Bank-issued time deposits that specify an interest rate and maturity date and are negotiable
—that is, traded on an exchange. Their face value is usually at least $100,000.
Banker acceptances (BAs): Bank-guaranteed time drafts payable to a vendor of goods.

FIGURE 6.4 Money Market Instruments Outstanding


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Here we see how the percentage of each money market instrument traded changes across three decades.
Source: Federal Reserve Board, “Financial Accounts of the United States,” Statistical Releases, Washington, DC, various issues.
www.federalreserve.gov
Capital Market Instruments Capital market securities include
U.S. Treasury notes and bonds.
U.S. government agency bonds.
State and local government bonds.
Mortgages and mortgage-backed securities.
Corporate bonds.
Corporate stocks.
Table 6.2 lists and defines each capital market security. Figure 6.5 graphically depicts U.S. capital market
instruments outstanding over several decades. Note that corporate stocks (equities) represent the largest capital
market instrument, followed by mortgages and mortgage-backed securities and then corporate bonds. The relative
size of capital markets depends on two factors: the number of securities issued and their market prices. The 1990s
saw consistently rising bull markets; hence the sharp increase in equities’ dollar value outstanding. Stock values fell
in the early 2000s as the U.S. economy experienced a downturn—partly because of 9/11 and partly because interest
rates began to rise—and stock prices fell. Stock prices in most sectors subsequently recovered and, by 2007, even
surpassed their 1999 levels. Stock prices fell precipitously during the financial crisis of 2008 and 2009. As of mid-
March 2009, the Dow Jones Industrial Average (DJIA) had fallen in value 53.8 percent in less than 1½ year’s time.
This was greater than the decline during the market crash of 1937 and 1938, when it fell 49 percent. However, stock
prices recovered along with the economy in the last half of 2009 and first half of 2010, rising 71.1 percent between
March 2009 and April 2010. However, it took until March 5, 2013, for the DJIA to surpass its pre-crisis high of
14,164.53, closing at 14,253.77 for the day.
▼ TABLE 6.2 Capital Market Instruments
Treasury notes and bonds: U.S. Treasury long-term obligations issued to finance the national debt and pay for other federal
government expenditures.
U.S. government agency bonds: Long-term debt securities collateralized by a pool of assets and insured by agencies of the
U.S. government.
State and local government bonds: Debt securities issued by state and local (e.g., county, city, school) governments, usually
to cover capital (long-term) improvements.
Mortgages: Long-term loans issued to individuals or businesses to purchase homes, pieces of land, or other real property.
Mortgage-backed securities: Long-term debt securities that offer expected principal and interest payments as collateral. These
securities, made up of many mortgages, are gathered into a pool and are thus “backed” by promised principal and interest cash
flows.
Corporate bonds: Long-term debt securities issued by corporations.
Corporate stocks: Long-term equity securities issued by public corporations; stock shares represent fundamental corporate
ownership claims.

FIGURE 6.5 Capital Market Instruments Outstanding

http://www.federalreserve.gov

Source: Federal Reserve Board, “Financial Accounts of the United States,” Statistical Releases, Washington, DC, various issues.
www.federalreserve.gov
Other Markets
Foreign Exchange Markets Today, most U.S.-based companies operate globally. Competent financial
managers understand how events and movements in financial markets in other countries can potentially affect their
own companies’ profitability and performance. For example, in 2015, IBM experienced a drop in revenue of 9
percent due to foreign exchange trends. Coca-Cola, which gets the majority of its sales from outside the United
States, also saw revenues decrease by approximately 6 percent as the U.S. dollar strengthened relative to foreign
currencies.
©Jack Star/PhotoLink/Getty Images
Foreign exchange markets trade currencies for immediate (also called “spot”) or some future stated delivery. When a
U.S. corporation sells securities or goods overseas, the resulting cash flows denominated in a foreign currency

http://www.federalreserve.gov

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expose the firm to foreign exchange risk. This risk arises from the unknown value at which foreign currency cash
flows can be converted into U.S. dollars. Foreign currency exchange rates vary day to day with worldwide demand
and supply of foreign currency and U.S. dollars. Investors who deal in foreign-denominated securities face the same
risk.
foreign exchange risk Risk arising from the unknown value at which foreign currency cash flows can be converted into U.S. dollars.
foreign exchange markets Markets in which foreign currency is traded for immediate or future delivery.
The actual number of U.S. dollars that a firm receives on a foreign investment depends on the exchange rate
between the U.S. dollar and the foreign currency just as much as it does on the investment’s performance. Firms will
have to convert the foreign currency into U.S. dollars at the prevailing exchange rate. If the foreign currency
depreciates (falls in value) relative to the U.S. dollar (say from 0.1679 dollar per unit of foreign currency to
0.1550 dollar per unit of foreign currency) over the investment period (i.e., the period between when a
foreign investment is made and the time it comes to fruition), the dollar value of cash flows received will fall. If the
foreign currency appreciates, or rises in value, relative to the U.S. dollar, the dollar value of cash flows received
from the foreign investment will increase.
Foreign currency exchange rates are variable. They vary day to day with demand for and supply of foreign currency
and with demand for and supply of dollars worldwide. Central governments sometimes intervene in foreign
exchange markets directly—such as China’s valuing of the yuan at artificially high rates relative to the dollar.
Governments also affect foreign exchange rates indirectly by altering prevailing interest rates within their own
countries. You will learn more about foreign exchange markets in Chapter 19.
Derivative Securities Markets A derivative security is a financial security (such as a futures contract, option
contract, or mortgage-backed security) with a value that is linked to another, underlying security, such as a stock
traded in capital markets or British pounds traded in foreign exchange (forex) markets. Derivative securities
generally involve an agreement between two parties to exchange a standard quantity of an asset or cash flow at a
predetermined price and at a specified date in the future. As the value of the underlying security changes, the value
of the derivative security changes.
derivative security A security formalizing an agreement between two parties to exchange a standard quantity of an asset at a
predetermined price on a specified date in the future.
While derivative security contracts, especially for physical commodities like corn or gold, have existed for centuries,
derivative securities markets grew increasingly popular in the 1970s, 1980s, and 1990s as traders, firms, and
academics figured out how to spread risk for more and more underlying commodities and securities by using
derivative contracts. Derivative contracts generally feature a high degree of leverage; that is, the investor only has to
put up a very small portion of the underlying commodity or security’s value to affect or control the underlying
commodity or security.
Derivative securities traders can be either users of derivative contracts (for hedging and other purposes) or dealers
(such as banks) that act as counterparties in customer trades for fees. An example of hedging involves commodities
such as corn, wheat, or soybeans. For example, suppose you run a flour mill and will need to buy either soft wheat
(Chicago) or hard red winter wheat (Kansas City) in the future. If you are concerned that the price of wheat will rise,
you might lock in a price today to meet your needs six months from now by buying wheat futures on a commodities
exchange. If you are correct and wheat prices rise over the six months, you may purchase the wheat by closing out
your futures positions, buying the wheat at the futures price rather than the higher market price. Likewise, if you
know that you will be delivering a large shipment to, say, Europe, in three months, you might take an offsetting
position in euro futures contracts to lock in the exchange rate between the dollar and the euro as it stands today—
and (you hope) eliminate foreign exchange risk from the transaction.
Derivative securities markets are the newest—and potentially the riskiest—of the financial security markets. Losses
associated with off-balance-sheet mortgage-backed securities created and held by FIs were at the very heart of the
financial crisis. Signs of significant problems in the U.S. economy first appeared in late 2006 and early 2007 when
home prices plummeted and defaults began to affect the mortgage lending industry as a whole, as well as other parts
of the economy noticeably. Mortgage delinquencies, particularly on subprime mortgages, surged in the last quarter
of 2006 through 2008 as homeowners who had stretched themselves to buy or refinance a home in the early 2000s
fell behind on their loan payments. As mortgage borrowers defaulted, the financial institutions that held their


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mortgages and credit derivative securities (in the form of mortgage-backed securities) started announcing huge
losses on them. These losses reached $700 billion worldwide by early 2009. The situation resulted in the failure,
acquisition, or bailout of some of the largest FIs and a near meltdown of the world’s financial and economic
systems. More recently, as the nearby Finance at Work box highlights, JPMorgan Chase experienced huge losses
from positions in the derivative securities markets.
time out!
6-1 How do primary and secondary markets differ?
6-2 What are foreign exchange markets?
6-3 What are derivativeas securities?

6.2 • FINANCIAL INSTITUTIONS LG6-3
Financial institutions (e.g., banks, thrifts, insurance companies, mutual funds) perform vital functions to securities
markets of all sorts. They channel funds from those with surplus funds (suppliers of funds) to those with shortages
of funds (demanders of funds). In other words, FIs operate financial markets. FIs allow financial markets to function
by providing the least costly and most efficient way to channel funds to and from these markets. FIs play a second
crucial role by spreading risk among market participants. This risk-spreading function is vital to entrepreneurial
efforts, for few firms or individuals could afford the risk of launching an expensive new product or process by
themselves. Individual investors take on pieces of the risk by buying shares in risky enterprises. Investors then
mitigate their own risks by diversifying their holdings into appropriate portfolios, which we cover in Chapters 9 and
10. Table 6.3 lists and summarizes the various types of FIs.
financial institutions Institutions that perform the essential function of channeling funds from those with surplus funds to those with
shortages of funds.
To understand just how important FIs are to the efficient operation of financial markets, imagine a simple world in
which FIs did not exist. In such a world, suppliers of funds (e.g., households), generating excess savings by
consuming less than they earn, would have a basic choice. They could either hold cash as an asset or invest that cash
in the securities issued by users of funds (e.g., corporations, governments, or retail borrowers). In general,
demanders (users) of funds issue financial claims (e.g., equity and debt securities) to finance the gap between their
investment expenditures and their internally generated savings, such as retained earnings. As shown in Figure 6.6, in
a world without financial institutions, we would have direct transfers of funds from fund suppliers to fund users. In
return, financial claims would flow directly from fund users to fund suppliers.
direct transfer The process used when a corporation sells its stock or debt directly to investors without going through a financial
institution.
FIGURE 6.6 Flow of Funds in a World without FIs

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▼ TABLE 6.3 Types of Financial Institutions
Commercial banks: Depository institutions whose major assets are loans and whose major liabilities are deposits. Commercial
bank loans cover a broader range, including consumer, commercial, and real estate loans, than do loans from other depository
institutions. Because they are larger and more likely to have access to public securities markets, commercial bank liabilities
generally include more nondeposit sources of funds than do those of other depository institutions.
Thrifts: Depository institutions including savings associations, savings banks, and credit unions. Thrifts generally perform
services similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans or
consumer loans. Credit unions operate on a not-for-profit basis for particular groups of individuals, such as a labor union or a
particular company’s employees.
Insurance companies: Protect individuals and corporations (policyholders) from financially adverse events. Life insurance
companies provide protection in the event of untimely death or illness, and help in planning retirement. Property casualty
insurance protects against personal injury and liability due to accidents, theft, fire, and so on.
Securities firms and investment banks: Underwrite securities and engage in related activities such as securities brokerage,
securities trading, and making markets in which securities trade.
Finance companies: Make loans to both individuals and businesses. Unlike depository institutions, finance companies do not
accept deposits, but instead rely on short- and long-term debt for funding, and many of their loans are collateralized with some
kind of durable good, such as washer/dryers, furniture, carpets, and the like.
Mutual funds: Pool many individuals’ and companies’ financial resources and invest those resources in diversified asset
portfolios.
Pension funds: Offer savings plans through which fund participants accumulate savings during their working years. Participants
then withdraw their pension resources (which have presumably earned additional returns in the interim) during their retirement
years. Funds originally invested in and accumulated in a pension fund are exempt from current taxation. Participants pay taxes
on distributions taken after age 55, when their tax brackets are (presumably) lower.
In this economy without FIs, the amount of funds flowing between fund suppliers and fund users through financial
markets would likely be quite low for several reasons:
Once they have lent money in exchange for financial claims, fund suppliers would need to continually monitor the use of their funds. Fund
suppliers must ensure that fund users neither steal the funds outright nor waste the funds on projects that have low or negative returns,
since either theft or waste would lower fund suppliers’ chances of being repaid and/or earning a positive return on their
investments (such as through the receipt of dividends or interest). Monitoring against theft, misuse, or underuse of their funds
would cost any given fund supplier a lot of time and effort, and of course each fund supplier, regardless of the dollar value of the
investment, would have to carry out the same costly and time-consuming process. Further, many investors do not have the financial
training to understand the necessary business information to assess whether a securities issuer is making the best use of their funds. In
fact, so many investment opportunities are available to fund suppliers, that even those trained in financial analysis rarely have the time to
monitor how their funds are used in all of their investments. The resulting lack of monitoring increases the risk of directly investing in
financial claims. Given these challenges, fund suppliers would likely prefer to delegate the task of monitoring fund borrowers to ensure
good performance to others.
Many financial claims feature a long-term commitment (e.g., mortgages, corporate stock, and bonds) for fund suppliers, but suppliers may
not wish to hold these instruments directly. Specifically, given the choice between holding cash or long-term securities, fund suppliers may
choose to hold cash for its liquidity. This is especially true if the suppliers plan to use their savings to finance consumption expenditures
before their creditors expect to repay them. Fund suppliers may also fear that they will not find anyone to purchase their financial claim and
free up their funds. When financial markets are not very developed, or deep, in terms of the number of active buyers and sellers in the
market, such liquidity concerns arise.
liquidity The ease with which an asset can be converted into cash.
Even though real-world financial markets provide some liquidity services by allowing fund suppliers to trade financial securities among
themselves, fund suppliers face price risk when they buy securities—fund suppliers may not get their principal back, let alone any return
on their investment. The price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE)
or NASDAQ may well differ from the price they initially paid for the security. The investment community as a whole may change the
security’s valuation between the time the fund supplier bought it and the time the fund supplier sold it. Also, dealers, acting as
intermediaries between buyers and sellers, charge transaction costs for completing a trade. So even if an investor bought a security and
then sold it the next day, the investor would likely lose money from transaction and other costs.
price risk The risk that an asset’s sale price will be lower than its purchase price.
Unique Economic Functions Performed by Financial Institutions
Because of (1) monitoring costs, (2) liquidity costs, and (3) price risk, most average investors may well view direct
investment in financial claims and markets as an unattractive proposition and, as fund suppliers, they will likely
prefer to hold cash. As a result, financial market activity (and therefore savings and investment) would likely remain
quite low. However, the financial system has developed an alternative, indirect way for investors (or fund suppliers)
to channel funds to users of funds: Financial intermediaries indirectly transfer funds to ultimate fund users. Because of


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monitoring, liquidity risk, and price risk costs, fund suppliers often prefer to hold financial intermediaries’ financial
claims rather than those directly issued by the ultimate fund users. Consider Figure 6.7, which more closely
represents the way that funds flow in the U.S. financial system than does Figure 6.6. Notice how financial
institutions stand—or intermediate—between fund suppliers and fund users. That is, FIs channel funds from
ultimate suppliers to ultimate fund users. Fund suppliers and users use these FIs to channel funds because of
financial intermediaries’ unique ability to measure and manage risk, and thus reduce monitoring costs, liquidity
costs, and price risk.
indirect transfer A transfer of funds between suppliers and users of funds through a financial institution.
FIGURE 6.7 Flow of Funds in a World with FIs
Financial institutions stand between fund suppliers and users.

finance at work //: markets
JP Morgan’s $2 Billion Blunder
©Monica and Michael Sweet/Getty Images
JP Morgan Chase & Co. is reeling after a huge trading bet backfired and left the bank with at least $2 billion in losses from the bad trade.
This may be the end of chief executive James Dimon’s run as the so-called “King of Wall Street.” The bank’s Chief Investment Office
(CIO), responsible for managing the New York company’s risk, placed a series of risky bets and trades. In an article published last
month, The Wall Street Journal reported that “large positions taken in that office by a trader nicknamed ‘the London whale’ had roiled a
sector of the debt markets. The bank, betting on a continued economic recovery with a complex web of trades tied to the values of
corporate bonds, was hit hard when prices moved against it starting last month, causing losses in many of its derivatives positions. The
losses occurred while J.P. Morgan tried to scale back that trade.”
In April of 2012, The Wall Street Journal reported that investors and hedge funds were trying to take advantage of trades made by
Chase’s London whale, Bruno Iksil, who worked out of the CIO, by making bets in the market on credit default swaps (CDSs). The CIO
group previously had stopgaps in place to protect and prevent the company from significant losses during periods of downturn in the
economy. However, the Journal reports that earlier in 2012, “it began reducing that position, [taking] a bullish stance on the financial
health of certain companies and selling protection that would compensate buyers if those companies defaulted on debts. Mr. Iksil was a
heavy seller of CDS contracts tied to a basket, or index, of companies.” In April of 2012, these protection costs began to go up, which

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further contributed to the bank’s losses.
According to JP Morgan Chase company filings, Mr. Iksil’s group had approximately $350 billion in investment securities, about 15%
of the bank’s total assets, on December 31, 2011. Mr. Dimon said the bank has an extensive review under way of what went wrong.
“These were grievous mistakes, they were self-inflicted, we were accountable and we happened to violate our own standards and
principles by how we want to operate the company. This is not how we want to run a business.”
Mr. Dimon held a conference call with investors and analysts on May 10, stating, “In hindsight, the . . . strategy was flawed, complex,
poorly reviewed, poorly executed, and poorly monitored. The portfolio has proven to be riskier, more volatile and less effective . . . than
we thought.” Dimon resolves, “We will learn from it, we will fix it, we will move on, hopefully in the end, it will make us a better company.”
Though JP Morgan Chase came through the financial crisis better off than many other financial institutions, this trading loss certainly
tarnishes their reputation. Mr. Dimon reports that the loss is “slightly more than $2 billion” in the second quarter of this year.
Want to know more?
Key Words to Search for Updates: JPMorgan, London whale, derivative trading losses
Sources: Fitzpatrick, Dan, Gregory Zuckerman, and Liz Rappaport, “J.P. Morgan’s $2 Billion Blunder,” The Wall Street Journal Online,
May 11, 2012. JP Morgan Chase & Co. Business Update Call, May 10, 2012.
Monitoring Costs As we noted above, a fund supplier who directly invests in a fund user’s financial claims faces
a high cost of comprehensively monitoring the fund user’s actions in a timely way. One solution to this problem is
that a large number of small investors can group their funds together by holding claims issued by an FI. In turn, the
FI will invest in direct financial claims that fund users issue. Financial institutions’ aggregation of funds from fund
suppliers resolves a number of problems:
First, large FIs now have much greater incentive to collect information and monitor the ultimate fund user’s actions, because the FI has far
more at stake than any small individual fund supplier would have.
Second, the FI performs the necessary monitoring function via its own internal experts. In an economic sense, fund suppliers appoint the
FI as a delegated monitor to act on their behalf. For example, full-service securities firms such as Bank of America Merrill Lynch carry out
investment research on new issues and make investment recommendations for their retail clients (investors), while
commercial banks collect deposits from fund suppliers and lend these funds to ultimate users, such as corporations. An
important part of these FIs’ functions is their ability and incentive to monitor ultimate fund users.
delegated monitor An economic agent appointed to act on behalf of smaller investors in collecting information and/or investing funds on
their behalf.
Liquidity and Price Risk In addition to providing more and better information about fund users’ activities,
financial intermediaries provide additional liquidity to fund suppliers, acting as asset transformers as follows: FIs
purchase the financial claims that fund users issue—primary securities such as mortgages, bonds, and stocks—and
finance these purchases by selling financial claims to household investors and other fund suppliers as deposits,
insurance policies, or other secondary securities. The secondary securities—packages or pools of primary claims—
that FIs collect and then issue are often more liquid than are the primary securities themselves. For example, banks
and thrift institutions (e.g., savings associations) offer draft deposit accounts with fixed principal values and (often)
guaranteed interest rates. Fund suppliers can generally access the funds in those accounts on demand. Money market
mutual funds issue shares to household savers that allow the savers to maintain almost fixed principal amounts while
earning somewhat higher interest rates than on bank deposits. Further, savers can also withdraw these funds on
demand whenever the saver writes a check on the account. Even life insurance companies allow policyholders to
borrow against their company-held policy balances with very short notice.
asset transformer Service provided by financial institutions in which financial claims issued by an FI are more attractive to investors
than are the claims directly issued by corporations.
secondary securities Packages or pools of primary claims.
The Shift Away from Risk Measurement and Management and the Financial Crisis Certainly, a major
event that changed and reshaped the financial services industry was the financial crisis of the late 2000s. As FIs
adjusted to regulatory changes brought about in the 1980s and 1990s, one result was a dramatic increase in systemic
risk of the financial system, caused in large part by a shift in the banking model from that of “originate and hold” to
“originate to distribute.” In the traditional model, banks take short-term deposits and other sources of funds and use
them to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus
have an incentive to screen and monitor borrower activities even after a loan is made. However, the traditional
banking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these


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risk exposures and generate improved return-risk trade-offs, banks have shifted to an underwriting model in which
they originate or warehouse loans, and then quickly sell them. Figure 6.8 shows the growth in bank loan secondary
market trading from 1991 through 2015. Note the huge growth in bank loan trading even during the financial crisis
of 2008 and 2009. When loans trade, the secondary market produces information that can substitute for the
information and monitoring of banks. Further, banks may have lower incentives to collect information and monitor
borrowers if they sell loans rather than keep them as part of the bank’s portfolio of assets. Indeed, most large banks
are organized as financial service holding companies to facilitate these new activities.
More recently activities of shadow banks, nonfinancial service firms that perform banking services, have facilitated
the change from the “originate and hold” model of commercial banking to the “originate and distribute” banking
model. Participants in the shadow banking system include structured investment vehicles (SIVs), special purpose
vehicles (SPVs), asset-backed commercial paper (ABCP) conduits, limited-purpose finance companies, money
market mutual funds (MMMFs), and credit hedge funds. In the shadow banking system, savers place their funds
with money market mutual and similar funds, which invest these funds in the liabilities of other shadow banks.
Borrowers get loans and leases from shadow banks such as finance companies rather than from banks. Like the
traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net
borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or
shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit
intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps
involving many nonbank, unregulated financial service firms.

FIGURE 6.8 Bank Loan Secondary Market Trading
Bank loan sales have increased dramatically over the last 20 years.
These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet and
to other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity,
and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowers
to whom they originate loans. Thus, FIs’ role as specialists in risk measurement and management is reduced.
The economy relies on financial institutions to act as specialists in risk measurement and management. The

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importance of this was demonstrated during the global financial crisis. When FIs failed to perform their critical risk
measurement and management functions, a crisis of confidence that disrupted financial markets ensued. The result
was a worldwide breakdown in credit markets, as well as an enhanced level of equity market volatility.
time out!
6-4 List the major types of financial institutions.
6-5 What three main issues would deter fund suppliers from directly purchasing securities?
6-6 What events resulted in banks’ shift from the traditional banking model of “originate and hold” to a model of “originate and
distribute”?
6.3 • INTEREST RATES AND THE LOANABLE FUNDS
THEORY LG6-3
We often speak of “the interest rate” as if only one rate applies to all financial situations or transactions. In fact, we
can list tens or hundreds of interest rates that are appropriate in various conditions or situations within the U.S.
economy on any particular day. Let’s explore a bit how the financial sector sets these rates and how the rates relate
to one another. We actually observe nominal interest rates in financial markets—these are the rates most often quoted
by financial news services. As we will see in Chapters 7 and 8, nominal interest rates (or, simply, interest rates)
directly affect most tradable securities’ value or price. Since any change in nominal interest rates has such profound
effects on security prices, financial managers and individual investors spend a lot of time and effort trying to identify
factors that may influence future interest rate levels.
nominal interest rates The interest rates actually observed in financial markets.
Of course, interest rate changes influence investment performance and trigger buy or sell decisions for individual
investors, businesses, and governmental units alike. For example, in 2008 and 2009, the Federal Reserve,
in an effort to address the severe financial crisis, unexpectedly announced that it would drop its target fed
funds rate to a range between 0 and 0.25 percent and lowered its discount window rate to 0.5 percent, the lowest
level since the 1940s. These rates remained at historically low levels until December 2015 when the Federal Reserve
raised the fed funds rate to a range of 0.25 to 0.5 percent and the discount window rate to 1 percent. This was the
first interest rate increase since 2006.
Figure 6.9 illustrates the movement of the following key U.S. interest rates over the past 44 years:
The prime commercial loan rate.
The three-month T-bill rate.
The home mortgage rate.
The high-grade corporate bond rate.
Figure 6.9 shows how interest rates vary over time. For example, the prime rate hit highs of over 20 percent in the
early 1980s, yet fell as low as 4.75 percent in the early 1970s. The prime rate stayed below 10 percent throughout
much of the 1990s, fell back further to 4.00 percent in the early 2000s, then rose to as high as 8.25 percent in the
mid-2000s. During the financial crisis of 2008 and 2009, the Fed took aggressive actions to stimulate the
economy, including dropping interest rates to historic lows. As a result, the prime rate fell to 3.25 percent
and stayed there until December 2015.
FIGURE 6.9 Key U.S. Interest Rates, 1972–2016

Loan rates tend to move together over time.
Source: Federal Reserve Board, website, various dates. www.federalreserve.gov
Interest rates play a major part in the determination of the value of financial instruments. For example, in September
2015 the Federal Reserve unexpectedly announced that it would not raise interest rates. The financial markets
reacted significantly: The Dow Jones Industrial Average declined almost 300 points, 1.75 percent in value; the
interest rate on Treasury securities decreased (i.e., the yield on 10-year T-notes decreased 0.123 percent); gold prices
increased 1.6 percent; and the U.S. dollar strengthened against foreign currencies. Given the impact a change in
interest rates has on security values, financial institution and other firm managers spend much time and effort trying
to identify factors that determine the level of interest rates at any moment in time, as well as what causes interest rate
movements over time.
One model that is commonly used to explain interest rates and interest rate movements is the loanable funds theory.
The loanable funds theory views the level of interest rates as resulting from factors that affect the supply of and
demand for loanable funds. It categorizes financial market participants—consumers, businesses, governments, and
foreign participants—as net suppliers or demanders of funds.
loanable funds theory A theory of interest rate determination that views equilibrium interest rates in financial markets as a result of the
supply of and demand for loanable funds.
Supply of Loanable Funds LG6-4
The supply of loanable funds is a term commonly used to describe funds provided to the financial markets by net
suppliers of funds. In general, the quantity of loanable funds supplied increases as interest rates rise. Figure 6.10
illustrates the supply curve for loanable funds. Other factors held constant, more funds are supplied as interest rates
increase (the reward for supplying funds is higher). Table 6.4 presents data on the supply of loanable funds from the
various groups of market participants from U.S. flow of funds data as of 2015.

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The household sector (consumer sector) is the largest supplier of loanable funds in the United States—$70.27 trillion
in 2015. Households supply funds when they have excess income or want to reallocate their asset portfolio holdings.
For example, during times of high economic growth, households may replace part of their cash holdings with
earning assets (i.e., by supplying loanable funds in exchange for holding securities). As the total health of a
consumer increases, the total supply of loanable funds from that consumer will also generally increase.
Households determine their supply of loanable funds not only on the basis of the general level of interest
rates and their total wealth, but also on the risk of securities investments. The greater the perceived risk of securities
investments, the less households are willing to invest at each interest rate. Further, the supply of loanable funds from
households also depends on their immediate spending needs. For example, near-term educational or medical
expenditures will reduce the supply of funds from a given household.
FIGURE 6.10 Supply of and Demand for Loanable Funds
The demand and supply of loanable funds varies with interest rates.
▼ TABLE 6.4 Funds Supplied and Demanded by Various Groups (in trillions of dollars)
Funds Supplied
Funds
Demanded
Net Funds Supplied (Funds
Supplied − Funds Demanded)
Households $70.27 $23.95 $46.32   
Business—nonfinancial 22.30 58.15 −35.85   
Business—financial 53.69 81.68 −27.99   
Government units 26.61 18.43 8.18   
Foreign participants 23.26 13.92 9.34   
Source: Federal Reserve Board, “Flow of Fund Accounts,” December 2015, www.federalreserve.gov
Higher interest rates will also result in higher supplies of funds from the U.S. business sector ($22.3 trillion from
nonfinancial business and $53.69 trillion from financial business in 2015), which often has excess cash, or working
capital, that it can invest for short periods of time in financial assets. In addition to the interest rates on these
investments, the expected risk on financial securities and their businesses’ future investment needs will affect their
overall supply of funds.
Loanable funds are also supplied by some governments ($26.61 trillion in 2015). For example, some governments
(e.g., municipalities) temporarily generate more cash inflows (e.g., through local taxes) than they have budgeted to
spend. These funds can be loaned out to financial market fund users until needed. During the recent financial crisis,
the federal government significantly increased the funds it supplied to businesses and consumers as it attempted to
rescue the U.S. economy from a deep economic recession (see Appendix 6A online in Connect or at
mhhe.com/Cornett4e).
Finally, foreign investors increasingly view U.S. financial markets as alternatives to their domestic financial markets
($23.26 trillion of funds were supplied to the U.S. financial markets in 2015). When interest rates are higher on U.S.
financial securities than they are on comparable securities in their home countries, foreign investors increase their

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supply of funds to U.S. markets. Indeed the high savings rates of foreign households (such as Japanese households)
has resulted in foreign market participants being major suppliers of funds to U.S. financial markets in recent years.
Similar to domestic suppliers of loanable funds, foreigners assess not only the interest rate offered on financial
securities, but also their total wealth, the risk on the security, and their future expenditure needs. Additionally,
foreign investors alter their investment decisions as financial conditions in their home countries change relative to
the U.S. economy and the exchange rate of their country’s currency changes vis-à-vis the U.S. dollar (see Chapter
19). For example, during the recent financial crisis, investors worldwide, searching for a safe haven for their funds,
invested huge amounts of funds in U.S. Treasury securities. The amount of money invested in Treasury bills was so
large that the yield on the three-month Treasury bill went below zero for the first time ever; investors were
essentially paying the U.S. government to borrow money.
Demand for Loanable Funds
The demand for loanable funds is a term used to describe the total net demand for funds by fund users. In general,
the quantity of loanable funds demanded is higher as interest rates fall. Figure 6.10 also illustrates the demand curve
for loanable funds. Other factors held constant, more funds are demanded as interest rates decrease (the cost of
borrowing funds is lower).
Households (although they are net suppliers of funds) also borrow funds in financial markets ($23.95 trillion in
2015). The demand for loanable funds by households reflects the demand for financing purchases of homes (with
mortgage loans), durable goods (e.g., car loans, appliance loans), and nondurable goods (e.g., education loans,
medical loans). Additional nonprice conditions and requirements (discussed below) also affect a household’s
demand for loanable funds at every level of interest rates.
Businesses demand funds to finance investments in long-term (fixed) assets (e.g., plant and equipment) and for
short-term working capital needs (e.g., inventory and accounts receivable) usually by issuing debt and other
financial instruments ($58.15 trillion for nonfinancial businesses and $81.68 trillion for financial businesses in
2015). When interest rates are high (i.e., the cost of loanable funds is high), businesses prefer to finance
investments with internally generated funds (e.g., retained earnings) rather than through borrowed funds.
Further, the greater the number of profitable projects available to businesses, or the better the overall economic
conditions, the greater the demand for loanable funds.
Governments also borrow heavily in the markets for loanable funds ($18.43 trillion in 2015). For example, state and
local governments often issue debt instruments to finance temporary imbalances between operating revenues (e.g.,
taxes) and budgeted expenditures (e.g., road improvements, school construction). Higher interest rates can cause
state and local governments to postpone borrowings and thus capital expenditures. Similar to households and
businesses, governments’ demand for funds varies with general economic conditions. The federal government is
also a large borrower partly to finance current budget deficits (expenditures greater than taxes) and partly to finance
past deficits. The cumulative sum of past deficits is called the national debt, which in the United States in 2015
stood at a record $18.94 trillion. Thus, the national debt and especially the interest payments on the national debt
have to be financed in large part by additional government borrowing.
Finally, foreign participants (households, businesses, and governments) also borrow in U.S. financial markets
($13.92 trillion in 2015). Foreign borrowers look for the cheapest source of dollar funds globally. Most foreign
borrowing in U.S. financial markets comes from the business sector. In addition to interest costs, foreign borrowers
consider nonprice terms on loanable funds as well as economic conditions in their home country and the general
attractiveness of the U.S. dollar relative to their domestic currency (e.g., the euro or the yen).
Equilibrium Interest Rate LG6-5
The aggregate supply of loanable funds is the sum of the quantity supplied by the separate fund-supplying sectors
(e.g., households, businesses, governments, foreign agents) discussed above. Similarly, the aggregate demand for
loanable funds is the sum of the quantity demanded by the separate fund-demanding sectors. As illustrated in Figure
6.11, the aggregate quantity of funds supplied is positively related to interest rates, while the aggregate quantity of
funds demanded is inversely related to interest rates. As long as competitive forces are allowed to operate freely in a
financial system, the interest rate that equates the aggregate quantity of loanable funds supplied with the aggregate
quantity of loanable funds demanded for a financial security, Q*, is the equilibrium interest rate for that security, i*,
point E in Figure 6.11. For example, whenever the rate of interest is set higher than the equilibrium rate, such as iH,
the financial system has a surplus of loanable funds. As a result, some suppliers of funds will lower the interest rate

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at which they are willing to lend and the demanders of funds will absorb the loanable funds surplus. In contrast,
when the rate of interest is lower than the equilibrium interest rate, such as iL, there is a shortage of loanable funds in
the financial system. Some borrowers will be unable to obtain the funds they need at current rates. As a result,
interest rates will increase, causing more suppliers of loanable funds to enter the market and some demanders of
funds to leave the market. These competitive forces will cause the quantity of funds supplied to increase and the
quantity of funds demanded to decrease until a shortage of funds no longer exists.
Factors That Cause the Supply and Demand Curves for Loanable Funds to Shift
While we have alluded to the fundamental factors that cause the supply and demand curves for loanable funds to
shift, in this section we formally summarize these factors. We then examine how shifts in the supply and demand
curves for loanable funds determine the equilibrium interest rate on a specific financial instrument. A shift in the
supply or demand curve occurs when the quantity of a financial security supplied or demanded changes at every
given interest rate in response to a change in another factor besides the interest rate. In either case, a
change in the supply or demand curve for loanable funds causes interest rates to move. Table 6.5 recaps
the factors that affect the supply and demand for loanable funds discussed in this section, their impact on the supply
and demand for loanable funds for a specific security, and the impact on the market clearing (or equilibrium) interest
rates holding all other factors constant.
FIGURE 6.11 Determination of Equilibrium Interest Rates
Interest rates always move toward the equilibrium.
Supply of Funds We have already described the positive relation between interest rates and the supply of
loanable funds along the loanable funds supply curve. Factors that cause the supply curve of loanable funds to shift,
at any given interest rate, include the wealth of fund suppliers, the risk of the financial security, future spending
needs, monetary policy objectives, and economic conditions.
Wealth As the total wealth of financial market participants (households, businesses, etc.) increases, the absolute
dollar value available for investment purposes increases. Accordingly, at every interest rate, the supply of loanable
funds increases, or the supply curve shifts down and to the right. For example, as the U.S. economy grew in the
early 2010s, total wealth of U.S. investors increased as well. Consequently, the supply of funds available for
investing (e.g., in stock and bond markets) increased at every available interest rate. We show this shift (increase) in
the supply curve in Figure 6.12(a) as a move from SS to SS”. The shift in the supply curve creates a disequilibrium
between demand and supply. To eliminate the imbalance or disequilibrium in this financial market, the equilibrium
interest rate falls, from i* to i*”, which is associated with an increase in the quantity of funds loaned between fund
suppliers and fund demanders, from Q* to Q*”. Conversely, as the total wealth of financial market
participants decreases, the absolute dollar value available for investment purposes decreases. Accordingly,


at every interest rate, the supply of loanable funds decreases, or the supply curve shifts up and to the left. The
decrease in the supply of funds due to a decrease in the total wealth of market participants results in an increase in
the equilibrium interest rate and a decrease in the equilibrium quantity of funds loaned (traded).
▼ TABLE 6.5 Factors That Affect the Supply of and Demand for Loanable Funds for a Financial Security
Panel A: The Supply of Funds
Factor Impact on Supply of Funds
Impact on Equilibrium Interest
Rate*
Interest rate Movement along supply
curve
Direct
Total wealth Shift supply curve Inverse
Risk of financial security Shift supply curve Direct
Near-term spending needs Shift supply curve Direct
Monetary expansion Shift supply curve Inverse
Economic conditions Shift supply curve Inverse
Panel B: The Demand for Funds
Factor Impact on Supply of Funds
Impact on Equilibrium Interest
Rate
Interest rate Movement along demand
curve
Direct
Utility derived from asset purchased with
borrowed funds
Shift demand curve Direct
Restrictiveness of nonprice conditions Shift demand curve Inverse
Economic conditions Shift demand curve Direct
A “direct” impact on equilibrium interest rates means that as the “factor” increases (decreases), the equilibrium interest rate increases
(decreases). An “inverse” impact means that as the factor increases (decreases), the equilibrium interest rate decreases (increases).
Risk As the risk of a financial security decreases (e.g., the probability that the issuer of the security will default on
promised repayments of the funds borrowed), it becomes more attractive to suppliers of funds. At every interest rate,
the supply of loanable funds increases, or the supply curve shifts down and to the right, from SS to SS” in Figure
6.12(a). Holding all other factors constant, the increase in the supply of funds, due to a decrease in the risk of the
financial security, results in a decrease in the equilibrium interest rate, from i* to i*”, and an increase in the
equilibrium quantity of funds traded, from Q* to Q*”.
Conversely, as the risk of a financial security increases, it becomes less attractive to suppliers of funds. Accordingly,
at every interest rate, the supply of loanable funds decreases, or the supply curve shifts up and to the left. Holding all
other factors constant, the decrease in the supply of funds due to an increase in the financial security’s risk results in
an increase in the equilibrium interest rate and a decrease in the equilibrium quantity of funds loaned (or traded).
FIGURE 6.12 The Effect on Interest Rates from a Shift in the Supply Curve of or a Demand Curve for Loanable Funds

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Changes in the supply of and demand for loanable funds have varying effects.
Near-Term Spending Needs When financial market participants have few near-term spending needs, the absolute
dollar value of funds available to invest increases. For example, when a family’s son or daughter moves out of the
family home to live on his or her own, current spending needs of the family decrease and the supply of available
funds (for investing) increases. At every interest rate, the supply of loanable funds increases, or the supply curve
shifts down and to the right. The financial market, holding all other factors constant, reacts to this increased supply
of funds by decreasing the equilibrium interest rate and increasing the equilibrium quantity of funds traded.
Conversely, when financial market participants have increased near-term spending needs, the absolute
dollar value of funds available to invest decreases. At every interest rate, the supply of loanable funds
decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in the
financial market that results in an increase in the equilibrium interest rate and a decrease in the equilibrium quantity
of funds loaned (or traded).
Monetary Expansion One method used by the Federal Reserve to implement monetary policy is to alter the
availability of funds, the growth in the money supply, and thus the rate of economic expansion of the economy.
When monetary policy objectives are to allow the economy to expand (as was the case in the late 2000s, during the
financial crisis, and in the early 2010s), the Federal Reserve increases the supply of funds available in the financial
markets. At every interest rate, the supply of loanable funds increases, the supply curve shifts down and to the right,
and the equilibrium interest rate falls, while the equilibrium quantity of funds traded increases.

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Conversely, when monetary policy objectives are to restrict the rate of economic expansion (and thus inflation), the
Federal Reserve decreases the supply of funds available in the financial markets. At every interest rate, the supply of
loanable funds decreases, the supply curve shifts up and to the left, and the equilibrium interest rate rises, while the
equilibrium quantity of funds loaned or traded decreases.
Economic Conditions Finally, as the underlying economic conditions themselves (e.g., the inflation rate,
unemployment rate, economic growth) improve in a country relative to other countries, the flow of funds to that
country increases. This reflects the lower risk (country or sovereign risk) that the country, in the guise of its
government, will default on its obligation to repay funds borrowed. For example, the severe economic crisis in
Greece in the early 2010s resulted in a decrease in the supply of funds to that country. An increased inflow of
foreign funds to U.S. financial markets increases the supply of loanable funds at every interest rate, and the supply
curve shifts down and to the right. Accordingly, the equilibrium interest rate falls, and the equilibrium quantity of
funds loaned or traded increases.
Conversely, when economic conditions in foreign countries improve, domestic and foreign investors take their funds
out of domestic financial markets (e.g., the United States) and invest abroad. Thus, the supply of funds available in
the financial markets decreases and the equilibrium interest rate rises, while the equilibrium quantity of funds traded
decreases.
Demand for Funds We explained above that the quantity of loanable funds demanded is negatively related to
interest rates. Factors that cause the demand curve for loanable funds to shift include the utility derived from assets
purchased with borrowed funds, the restrictiveness of nonprice conditions on borrowing, and economic conditions.
Utility Derived from Assets Purchased with Borrowed Funds As the utility (i.e., satisfaction or pleasure) derived
from an asset purchased with borrowed funds increases, the willingness of market participants (households,
businesses, etc.) to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interest
rate, the demand for loanable funds increases, or the demand curve shifts up and to the right. For example, suppose a
change in jobs takes an individual from Arizona to Minnesota. The individual currently has a convertible
automobile. Given the move to Minnesota, the individual’s utility from the convertible decreases, while it would
increase for a car with heated seats. Thus, with a potential increased utility from the purchase of a new car, the
individual’s demand for funds in the form of an auto loan increases. We show this shift (increase) in the demand
curve in Figure 6.12(b) as a move from DD to DD”. The shift in the demand curve creates a disequilibrium in this
financial market. Holding all other factors constant, the increase in the demand for funds due to an increase in the
utility from the purchased asset results in an increase in the equilibrium interest rate, from i* to i*”, and an increase
in the equilibrium quantity of funds traded, from Q* to Q*”.
Conversely, as the utility derived from an asset purchased with borrowed funds decreases, the willingness of market
participants (households, businesses, etc.) to borrow decreases and the absolute dollar amount borrowed decreases.
Accordingly, at every interest rate, the demand for loanable funds decreases, or the demand curve shifts down and to
the left. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forces
adjust, and holding all other factors constant, the decrease in the demand for funds due to a decrease in the utility
from the purchased asset results in a decrease in the equilibrium interest rate and a decrease in the equilibrium
quantity of funds loaned or traded.
Restrictiveness of Nonprice Conditions on Borrowed Funds As the nonprice restrictions put on borrowers as a
condition of borrowing decrease, the willingness of market participants to borrow increases and the absolute dollar
value borrowed increases. Such nonprice conditions may include fees or collateral. The lack of such restrictions
makes the loan more desirable to the user of funds. Accordingly, at every interest rate, the demand for
loanable funds increases, or the demand curve shifts up and to the right, from DD to DD”. As competitive
forces adjust, and holding all other factors constant, the increase in the demand for funds due to a decrease in the
restrictive conditions on the borrowed funds results in an increase in the equilibrium interest rate, from i* to i*”, and
an increase in the equilibrium quantity of funds traded, from Q* to Q*”. Conversely, as the nonprice restrictions put
on borrowers as a condition of borrowing increase, market participants’ willingness to borrow decreases, and the
absolute dollar value borrowed decreases. Accordingly, the demand curve shifts down and to the left. The shift in
the demand curve results in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of
funds traded.
Economic Conditions When the domestic economy experiences a period of growth, such as that in the United
States in the mid-2000s and early 2010s, market participants are willing to borrow more heavily. For example, state

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and local governments are more likely to repair and improve decaying infrastructure when the local economy is
strong. Accordingly, the demand curve for funds shifts up and to the right. Holding all other factors constant, the
increase in the demand for funds due to economic growth results in an increase in the equilibrium interest rate and
an increase in the equilibrium quantity of funds traded. Conversely, when domestic economic growth is stagnant,
market participants reduce their demand for funds. Accordingly, the demand curve shifts down and to the left,
resulting in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded.
Movement of Interest Rates over Time
As discussed in the previous section of this chapter, the loanable funds theory of interest rates is based on the supply
of and demand for loanable funds as functions of interest rates. The equilibrium interest rate (point E in Figure 6.12)
is only a temporary equilibrium. Changes in underlying factors that determine the demand and supply of loanable
funds can cause continuous shifts in the supply and/or demand curves for loanable funds. Market forces will react to
the resulting disequilibrium with factors that influence a change in the equilibrium interest rate and quantity of funds
traded in that market. Refer again to Figure 6.12(a), which shows the effects of an increase in the supply curve for
loanable funds, from SS to SS” (and the resulting decrease in the equilibrium interest rate, from i* to i*”), while
Figure 6.12(b) shows the effects of an increase in the demand curve for loanable funds, from DD to DD” (and the
resulting increase in the equilibrium interest rate, from i* to i*”).
time out!
6-7 Who are the main suppliers and demanders of loanable funds?
6-8 What happens to the equilibrium interest rate when the demand for (supply of) loanable funds increases?
6-9 How do supply and demand together determine interest rates?
6.4 • FACTORS THAT INFLUENCE INTEREST RATES FOR
INDIVIDUAL SECURITIES LG6-6
So far we have looked at the general determination of equilibrium (nominal) interest rates for financial securities in
the context of the loanable demand and supply theory of the flow of funds. In this section, we examine the specific
factors that affect differences in interest rates across the range of real-world financial markets (i.e., differences
among interest rates on individual securities, given the underlying level of interest rates determined by the demand
and supply of loanable funds). These factors include
Inflation.
The real risk-free rate.
Default risk.
Liquidity risk.
Special provisions regarding the use of funds raised by a particular security issuer.
The security’s term to maturity.
We will discuss each of these factors after summarizing them in Table 6.6.
Inflation
The first factor that influences interest rates is the economy-wide actual or expected inflation rate. Specifically, the
higher the level of actual or expected inflation, the higher will be the level of interest rates. We define inflation of the
general price index of goods and services (or the inflation premium, IP) as the (percentage) increase in the price of a
standardized basket of goods and services over a given period of time. The U.S. Department of Commerce measures
inflation using indexes such as the consumer price index (CPI) and the producer price index (PPI). For example, the
annual inflation rate using the CPI index between years t and t + 1 would be equal to
inflation The continual increase in the price level of a basket of goods and services.

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(6-1)
The positive relationship between interest rates and inflation rates is fairly intuitive: When inflation raises the
general price level, investors who buy financial assets must earn a higher interest rate (or inflation premium) to
compensate for continuing to hold the investment. Holding on to their investments means that they incur higher
costs of forgoing consumption of real goods and services today, only to have to buy these same goods and services
at higher prices in the future. In other words, the higher the rate of inflation, the more expensive the same basket of
goods and services will be in the future.
Real Risk-Free Rate
A real risk-free rate is the rate that a risk-free security would pay if no inflation were expected over its holding period
(e.g., a year). As such, it measures only society’s relative time preference for consuming today rather than
tomorrow. The higher society’s preference to consume today (i.e., the higher its time value of money or rate of time
preference), the higher the real risk-free rate (RFR) will be.
real risk-free rate The interest rate that would exist on a risk-free security if no inflation were expected.
▼ TABLE 6.6 Factors Affecting Nominal Interest Rates
Inflation: A continual increase in the price level of a basket of goods and services throughout the economy as a whole.
Real risk-free rate: Risk-free rate adjusted for inflation; generally lower than nominal risk-free rates at any particular time.
Default risk: Risk that a security issuer will miss an interest or principal payment or continue to miss such payments.
Liquidity risk: Risk that a security cannot be sold at a price relatively close to its value with low transaction costs on short notice.
Special provisions: Provisions (e.g., taxability, convertibility, and callability) that impact a security holder beneficially or
adversely and as such are reflected in the interest rates on securities that contain such provisions.
Time to maturity: Length of time until a security is repaid; used in debt securities as the date upon which the security holders get
their principal back.
Fisher Effect Economists often refer to the relationship among real risk-free rates (RFR), expected inflation
(expected IP), and nominal risk-free rates (i), described previously, as the Fisher effect, named for Irving Fisher,
who identified these economic relationships early last century. The Fisher effect theorizes that nominal risk-free
rates that we observe in financial markets (e.g., the one-year Treasury bill rate) must compensate investors
for
Any inflation-related reduction in purchasing power lost on funds lent or principal due.
An additional premium above the expected rate of inflation for forgoing present consumption (which reflects the real risk-free rate issue
discussed previously).
(6-2)
Thus, the nominal risk-free rate will equal the real risk-free rate only when market participants expect inflation to be
zero: Expected IP = 0. Similarly, the nominal risk-free rate will equal the expected inflation rate only when the real
risk-free rate is zero. We can rearrange the nominal risk-free rate equation to show what determines the real interest
rate:1
(6-3)
It needs to be noted that the expected inflation rate is difficult to estimate accurately, so the real risk-free rate can be
difficult to measure accurately. Investors’ expectations are not always realized either.
The one-year T-bill rate in 2015 was 0.32 percent, while the CPI for the year was 0.50 percent, which implies a real
risk-free rate of –0.18 percent—that is, the real risk-free rate was actually negative. Thus, the real value of
investments actually decreased in that year.

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Figure 6.13 shows the nominal risk-free rate (one-year T-bill rate) versus the change in the CPI from 1962 through
2015. Note that generally the T-bill rate is greater than the CPI, that is, the real risk-free rate earned on securities is
positive. It is during periods of economic slowdowns that the T-bill rate is less than the CPI; that is, real risk-free
rates are negative.
Default or Credit Risk
Default risk is the risk that a security issuer may fail to make its promised interest and principal payments to its
bondholders (or its dividend in the case of preferred stockholders). The higher the default risk, the higher the interest
rate that security buyers will demand to compensate them for this default (or credit) risk relative to default-risk-free
U.S. Treasury securities. Since the U.S. government has taxation powers and can print currency, the risk of its
defaulting on debt payments is practically zero. But some borrowers, such as corporations or individuals, have less
predictable cash flows (and no powers to tax anyone to raise funds immediately). So investors must charge issuers
other than the U.S. government a premium for any perceived probability of default and the cost of potentially
recovering the amount loaned built into their regular interest rate premium. The difference between a quoted interest
rate on a security (security j) and a Treasury security with similar maturity, liquidity, tax, and other features is called
a default or credit risk premium (DRPj). That is
default risk The risk that a security issuer will default on that security by being late on or missing an interest or principal payment.
(6-4)
where ijt = Interest rate on a security issued by a non−Treasury issuer (issuer j) of maturity m at time t.
iTt = Interest rate on a security issued by the U.S. Treasury of maturity m at time t.
Various rating agencies, including Moody’s and Standard & Poor’s, evaluate and categorize the potential default
risk on many corporate bonds, some state and municipal bonds, and some stocks. We cover these ratings in more
detail in Chapter 8. For example, in 2015, the 10-year Treasury rate was 2.14 percent. Moody’s Aaa-rated and Baa-
rated corporate debt carried interest rates of 3.89 percent and 5.00 percent, respectively. Thus, the average default
risk premiums on the Aaa-rated and Baa-rated corporate debt were
Figure 6.14 presents these risk premiums for the stated creditworthiness categories of bonds from 1977 through
2015. Notice from this figure and Figure 6.13 that default risk premiums tend to increase when the economy is
contracting and decrease when the economy is expanding. For example, from 2007 to 2008, real risk-free rates (T-
bills—CPI in Figure 6.13) increased from 0.43 percent to 1.73 percent. Over the same period, default risk premiums
on Aaa-rated bonds increased from 1.39 percent to 1.97 percent. Baa-rated bonds showed a default risk premium
increase from 2.55 percent to 3.78 percent.

EXAMPLE 6-1
Calculating Real Risk-Free
Rates LG6-6
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
One-year Treasury bill rates in 2007 averaged 4.53 percent and
inflation (measured by the consumer price index) for the year was 4.10
percent. If investors had expected the same inflation rate as that
actually realized, calculate the real risk-free rate for 2007 according to

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the Fisher effect.
SOLUTION:
4.53% − 4.10% = 0.43%
Similar to Problems 6-1, 6-2, Self-Test Problem 1
Liquidity Risk
A highly liquid asset can be sold at a predictable price with low transaction costs. That is, the holder can convert the
asset at its fair market value on short notice. The interest rate on a security reflects its relative liquidity, with highly
liquid assets carrying the lowest interest rates (all other characteristics remaining the same). Likewise, if a security is
illiquid, investors add a liquidity risk premium (LRP) to the interest rate on the security. In the United States,
most government securities sell in liquid markets, as do large corporations’ stocks and bonds. Securities
issued by smaller companies trade in relatively less liquid markets.
liquidity risk The risk that a security cannot be sold at a predictable price with low transaction costs on short notice.
FIGURE 6.13 Nominal Interest Rates versus Inflation
Notice the difference between the nominal risk-free rate and the change in CPI over the last several decades.
Source: Federal Reserve Board and U.S. Department of Labor websites, various dates. www.federalreserve.gov and www.dol.gov.
A different type of liquidity risk premium may also exist if investors dislike long-term securities because their prices
(present values, as discussed below and in Chapters 4 and 7) react more to interest rate changes than short-term
securities do. In this case, a higher liquidity risk premium may be added to a security with a longer maturity because
of its greater exposure to price risk (loss of capital value) on the longer-term security as interest rates change.
Special Provisions or Covenants
Sometimes a security’s issuing party attaches special provisions or covenants to the security issued. Such provisions
affect the interest rates on these securities relative to securities without such provisions attached to them. Some of
these special provisions include the security’s taxability, convertibility, and callability. For example, investors pay
no federal taxes on interest payments received from municipal securities. So a municipal bondholder may demand a

http://www.federalreserve.gov

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lower interest rate than that demanded on a comparable taxable bond—such as a Treasury bond (which is taxable at
the federal level but not at the state or local levels) or a corporate bond (the interest on which is taxable at the state,
local, and federal levels).
Another special covenant is convertibility: A convertible bond offers the holder the opportunity to exchange the
bond for another type of the issuer’s securities—usually preferred or common stock—at a preset price (see Chapter
7). This conversion option can be valuable to purchasers, so convertible security buyers require lower interest rates
than a comparable nonconvertible security holder would require (all else equal). In general, special provisions that
benefit security holders (e.g., tax-free status and convertibility) bring with them lower interest rates, and special
provisions that benefit security issuers (e.g., callability, by which an issuer has the option to retire, or call, the
security prior to maturity at a preset price) require higher interest rates to encourage purchase.
Term to Maturity
Interest rates also change—sometimes daily—because of a bond’s term to maturity. Financial professionals refer to
this daily or even hourly changeability in interest rates as the term structure of interest rates, or the yield curve. The
shape of the yield curve derives directly from time value of money principles. The term structure of interest rates
compares interest rates on debt securities based on their time to maturity, assuming that all other characteristics (i.e.,
default risk, liquidity risk) are equal. Interest rates change as the maturity of a debt security changes; in general, the
longer the term to maturity, the higher the required interest rate buyers will demand. This addition to the required
interest rate is the maturity premium (MP). The MP, which is the difference between the required yield on long-
versus short-term securities of the same characteristics except maturity, can be positive, negative, or zero.
term structure of interest rates A comparison of market yields on securities, assuming all characteristics except maturity are the same.
FIGURE 6.14 Default Risk Premiums on Corporate Bonds
Source: Federal Reserve Board website, various dates. www.federalreserve.gov

FIGURE 6.15 Common Shares for Yield Curves on Treasury Securities

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Three common yield curve shapes are (a) upward sloping, (b) downward sloping, and (c) a flat slope.
Source: U.S. Treasury, Office of Debt Management, Daily Treasury Yield Curves, various dates. www.ustreas.gov

http://www.ustreas.gov

EXAMPLE 6-2 Determinants of Interest Rates for
Individual Securities LG6-6
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Morningstar Corp.’s eight-year bonds are currently yielding a return of
6.85 percent. The expected inflation premium is 1.15 percent annually
and the real risk-free rate is expected to be 2.25 percent annually over
the next eight years. The default risk premium on Morningstar’s bonds
is 1.35 percent. The maturity risk premium is 0.50 percent on two-year
securities and increases by 0.05 percent for each additional year to
maturity. Calculate the liquidity risk premium on Morningstar’s eight-
year bonds.
SOLUTION:
Similar to Problems 6-3, 6-4, Self-Test Problem 2
The financial industry most often reports and analyzes the yield curve for U.S. Treasury securities. The yield curve
for U.S. Treasury securities has taken many shapes over the years, but the three most common shapes appear in
Figure 6.15. In graph (a), the yield curve on January 15, 2016, yields rise steadily with maturity when the yield
curve slopes upward. This is the most common yield curve. On average, the MP is positive, as you might expect.
Graph (b) shows an inverted, or downward-sloping, yield curve, reported on November 24, 2000, in which yields
decline as maturity increases. Inverted yield curves do not generally last very long. In this case, the yield curve
inverted as the U.S. Treasury began retiring long-term (30-year) bonds as the country began to pay off the national
debt. Finally, graph (c) shows a flat yield curve, reported on June 4, 2007, when the yield to maturity is virtually
unaffected by the term to maturity.
Putting together the factors that affect interest rates in different markets, we can use the following general equation
to note the influence of the factors that functionally impact the fair interest rate—the rate necessary to compensate
investors for all security risks—(ij
*) on an individual (jth) financial security.
(6-5)
where
IP = Inflation premium.
RFR = Real risk-free rate.
DRPj = Default risk premium on the jth security.
LRPj = Liquidity risk premium on the jth security.
SCPj = Special covenant premium on the jth security.
MPj = Maturity premium on the jth security.
The first two factors, IP and RFR, are common to all financial securities, while the other factors can uniquely
influence the price of a single security.
time out!

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page 174
6-10 What is the difference between nominal and real risk-free rates?
6-11 What does “the term structure of interest rates” mean?
6-12 What shape does the term structure usually take? Why?

6.5 • THEORIES EXPLAINING THE SHAPE OF THE TERM
STRUCTURE OF INTEREST RATES2 LG6-7
We just explained the necessity of a maturity premium, the relationship between a security’s interest rate and its
remaining term to maturity. We can illustrate these issues by showing that the term structure of interest rates can
take a number of different shapes. As you might expect, economists and financial theorists with various viewpoints
differ among themselves in theorizing why the yield curve takes different shapes. Explanations for the yield curve’s
shape fall predominantly into three categories:
1. The unbiased expectations theory.
2. The liquidity premium theory.
3. The market segmentation theory.
Look again at Figure 6.15 (a), which presents the Treasury yield curve as of January 15, 2016. We see that the yield
curve on this date reflected the normal upward-sloping relationship between yield and maturity. Now let’s turn to
explanations for this shape based on the three predominant theories noted above.
Unbiased Expectations Theory
According to the unbiased expectations theory of the term structure of interest rates, at any given point in time, the
yield curve reflects the market’s current expectations of future short-term rates. As illustrated in Figure 6.16, the
intuition behind the unbiased expectations theory is this: If investors have a four-year investment horizon, they could
either buy current four-year bonds and earn the current (or spot) yield on a four-year bond (1R4, if held to maturity)
each year, or they could invest in four successive one-year bonds [of which they know only the current one-year
spot rate (1R1)]. But investors also expect what the unknown future one-year rates [E(2r1), E(3r1), and E(4r1)] will
be. Note that each interest rate term has two subscripts, e.g., 1R4. The first subscript indicates the period in which the
security is bought, so that 1 represents the purchase of a security in period 1. The second subscript indicates the
maturity on the security. Thus, 4 represents the purchase of a security with a four-year life. Similarly, E(3r1) is the
expected return on a security with a one-year life purchased in period 3.
According to the unbiased expectations theory, the return for holding a four-year bond to maturity should equal the
expected return for investing in four successive one-year bonds (as long as the market is in equilibrium). If this
equality does not hold, an arbitrage opportunity exists. That is, if investors could earn more on the one-year bond
investments, they could short (or sell) the four-year bond, use the proceeds to buy the four successive one-year
bonds, and earn a guaranteed profit over the four-year investment horizon. So, according to the unbiased
expectations theory, if the market expects future one-year rates to rise each successive year into the future,
then the yield curve will slope upward. Specifically, the current four-year T-bond rate or return will exceed the
three-year bond rate, which will exceed the two-year bond rate, and so on. Similarly, if the market expects future
one-year rates to remain constant each successive year into the future, then the four-year bond rate will equal the
three-year bond rate. That is, the term structure of interest rates will remain constant (flat) over the relevant time
period. Specifically, the unbiased expectation theory states that current long-term interest rates are geometric
averages of current and expected future short-term interest rates. The mathematical equation representing this
relationship is
(6-6)
therefore


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(6-7)
where 1RN = Actual N-period rate today (i.e., the first day of year 1).
N = Term to maturity.
1R1 = Actual 1-year rate today.
E(ir1) = Expected 1-year rates for years 2, 3, 4, . . ., N in the future.
Notice that uppercase interest rate terms, 1Rt, are the actual current interest rates on securities purchased today with a
maturity of t years. Lowercase interest rate terms, tr1, represent estimates of future one-year interest rates starting t
years into the future.
FIGURE 6.16 Unbiased Expectations Theory of the Term Structure of Interest Rates
Return from buying four 1-year maturity bonds versus buying one 4-year maturity bond.

the Math Coach on…
“When putting interest rates into the equation, enter them in decimal format, not percentage format.
Correct: (1 + 0.0294)
Not correct: (1 +2.94)„
EXAMPLE 6-3 Calculating Yield Curves LG6-7
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Suppose that the current one-year rate (one-year spot rate) and
expected one-year T-bond rates over the following three years (i.e.,
years 2, 3, and 4, respectively) are as follows:
1R1 = 2.94%, E(1r1) = 4%, E(3r1) = 4.74%, E(4r1) = 5.10%
Construct a yield curve using the unbiased expectations theory.
SOLUTION:
Using the unbiased expectations theory, current (or today’s) rates for
one-, two-, three-, and four-year maturity Treasury securities should be

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and the current yield to maturity curve will be upward sloping as shown:
This upward-sloping yield curve reflects the market’s expectation of
persistently rising one-year (short-term) interest rates over the future
horizon.3
Similar to Problems 6-5, 6-6, 6-7, 6-8, Self-Test Problem 3
Liquidity Premium Theory
The second popular explanation—the liquidity premium theory of the term structure of interest rates—builds on the
unbiased expectations theory. The liquidity premium idea is as follows: Investors will hold long-term maturities
only if these securities with longer term maturities are offered at a premium to compensate for future uncertainty in
the security’s value. Of course, uncertainty or risk increases with an asset’s maturity. This theory is thus consistent
with our discussions of market risk and liquidity risk, above. Specifically, in a world of uncertainty, short-term
securities provide greater marketability (due to their more active secondary markets) and have less price risk than
long-term securities do. As a result (due to smaller price fluctuations for a given change in interest rates), investors
will prefer to hold shorter-term securities because this kind of paper can be converted into cash with little market
risk. Said another way, investors face little risk of a capital loss, that is, a fall in the price of the security below its
original purchase price. So, investors must be offered a liquidity premium to buy longer-term securities that carry
higher capital loss risk. This difference in market and liquidity risk can be directly related to the fact that longer-term
securities are more sensitive to interest rate changes in the market than are shorter-term securities—Chapter 7
discusses bond interest rate sensitivity and the link to a bond’s maturity. Because longer maturities on securities
mean greater market and liquidity risk, the liquidity premium increases as maturity increases.
The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected
short-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security’s
maturity (this is the extension of the liquidity premium added to the unbiased expectations theory). Figure 6.17
illustrates the differences in the shape of the yield curve under the unbiased expectations theory versus the liquidity
premium theory. For example, according to the liquidity premium theory, an upward-sloping yield curve may reflect
investors’ expectations that future short-term rates will be flat, but because liquidity premiums increase with
maturity, the yield curve will nevertheless slope upward. Indeed, an upward-sloping yield curve may reflect
expectations that future interest rates will rise, be flat, or even fall as long as the liquidity premium increases with
maturity fast enough to produce an upward-sloping yield curve. The liquidity premium theory can be


page 177
mathematically represented as
(6-8)
where Lt = Liquidity premium for a period t and L2 < L3 < LN. FIGURE 6.17 Yield Curve Using the Unbiased Expectation Theory (UET) versus the Liquidity Premium Theory (LPT) Notice the differences in the shape of the yield curve under the UET and the LPT. Let’s compare the yield curves in Examples 6-3 (using the unbiased expectations theory) and 6-4. Notice that the liquidity premium in year 2 (L2 = 0.10%) produces a 0.05 (= 3.52% − 3.47%) percent premium on the yield to maturity on a two-year T-note, the liquidity premium for year 3 (L3 = 0.20%) produces a 0.10 (= 3.99% − 3.89%) percent premium on the yield to maturity on the three-year T-note, and the liquidity premium for year 4 (L4 = 0.30%) produces a 0.15 (= 4.34% − 4.19%) percent premium on the yield to maturity on the four-year T-note. Market Segmentation Theory The market segmentation theory does not build on the unbiased expectations theory or the liquidity premium theory, but rather argues that individual investors and FIs have specific maturity preferences, and convincing them to hold securities with maturities other than their most preferred requires a higher interest rate (maturity premium). The main thrust of the market segmentation theory is that investors do not consider securities with different maturities as perfect substitutes. Rather, individual investors and FIs have distinctly preferred investment horizons dictated by the dates when their liabilities will come due. For example, banks might prefer to hold relatively short-term U.S. Treasury bonds because their deposit liabilities also tend to be short-term—recall that bank customers can access their funds on demand. Insurance companies, on the other hand, may prefer to hold long-term U.S. Treasury bonds because life insurance contracts usually expose insurance firms to long-term liabilities. Accordingly, distinct supply and demand conditions within a particular maturity segment—such as the short end and long end of the bond market page 178 —determine interest rates under the market segmentation theory. EXAMPLE 6-4 Calculating Yield Curves Using the Liquidity Premium Theory LG6-7 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bond rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: In addition, investors charge a liquidity premium on longer-term securities such that Using the liquidity premium theory, construct the yield curve. SOLUTION: Using the liquidity premium theory, current rates for one-, two-, three-, and four-year maturity Treasury securities should be and the current yield to maturity curve will be upward sloping as shown: Similar to Problems 6-9, 6-10, Self-Test Problem 3 http://mhhe.com/CornettM4e ▼ page 179 The market segmentation theory assumes that investors and borrowers generally do not want to shift from one maturity sector to another without adequate compensation—that is, an interest rate premium. Figure 6.18 demonstrates how changes in supply for short- versus long-term bond market segments result in changing shapes of the yield to maturity curve. Specifically, as shown in Figure 6.18, the higher the demand for securities is, the higher the yield on those securities.4 Further, as the supply of securities decreases in the short-term market and increases in the long-term market, the slope of the yield curve becomes steeper. If the supply of short-term securities had increased while the supply of long-term securities had decreased, the yield curve would have a flatter slope and might even have sloped downward. Indeed, the U.S. Treasury’s large-scale repurchase of long-term Treasury bonds (i.e., reductions in supply) in early 2000 has been viewed as the major cause of the inverted yield curve that appeared in February 2000. FIGURE 6.18 Market Segmentation and Determination of the Slope of the Yield Curve The higher the demand for securities, the higher the yield on those securities. time out! 6-13 What three theories explain the shape of the yield curve? 6-14 Explain how arbitrage plays a role in the unbiased expectations explanation of the shape of the yield curve. 6.6 • FORECASTING INTEREST RATES5 LG6-8 We noted in the time value of money (TVM) chapters (Chapters 4 and 5) that as interest rates change, so do the values of financial securities. Accordingly, both individual investors and public corporations want to be able to predict or forecast interest rates if they wish to trade profitably. For example, if interest rates rise, the value of investment portfolios of individuals and corporations will fall, resulting in a loss of wealth. So, interest rate forecasts are extremely important for the financial wealth of both public corporations and individuals. Recall our discussion of the unbiased expectations theory in the previous section of this chapter. That theory page 180 indicated that the market’s expectation of future short-term interest rates determines the shape of the yield curve. For example, an upward-sloping yield curve implies that the market expects future short-term interest rates to rise. So, we can use the unbiased expectations theory to forecast (short-term) interest rates in the future (i.e., forward one- year interest rates). A forward rate is an expected, or implied, rate on a short-term security that will originate at some point in the future. Using the equations in the unbiased expectations theory, we can directly derive the market’s expectation of forward rates from existing or actual rates on spot market securities. forward rate An expected rate (quoted today) on a security that originates at some point in the future. To find an implied forward rate on a one-year security to be issued one year from today, we can rewrite the unbiased expectations theory equation as follows: (6-9) EXAMPLE 6-5 Estimating Forward Rates LG6-8 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. In the mid-2010s, the existing or current (spot) one-, two-, three-, and four-year zero coupon Treasury security rates were as follows: 1R1 = 0.70%, 1R2 = 0.87%, 1R3 = 1.04%, 1R4 = 1.34% Using the unbiased expectations theory, calculate one-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4. SOLUTION: Similar to Problems 6-15, 6-16, Self-Test Problem 4 where 2 f1 = expected one-year rate for year 2, or the implied forward one-year rate for next year. Saying that 2 f1 is the expected one-year rate for year 2 is the same as saying that, once we isolate the 2 f1 term, the equation will give us the market’s estimate of the expected one-year rate for year 2. Solving for 2 f1 we get (6-10) In general, we can find the forward rate for any year, N, into the future using the following generalized equation derived from the unbiased expectations theory: (6-11) time out! http://mhhe.com/CornettM4e page 181 6-15 What is a forward rate? 6-16 How can we obtain an implied forward rate from current short- and long-term interest rates? 6-17 Why is it useful to calculate forward rates? Get Online ©JGI/Jamie Grill/Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. Classify the following transactions as taking place in the primary or secondary markets (LG6-1): a. IBM issues $200 million of new common stock. b. The New Company issues $50 million of common stock in an IPO. c. IBM sells $5 million of GM preferred stock out of its marketable securities portfolio. d. The Magellan Fund buys $100 million of previously issued IBM bonds. e. Prudential Insurance Co. sells $10 million of GM common stock. 2. Classify the following financial instruments as money market securities or capital market securities (LG6-2): page 182 a. Federal funds b. Common stock c. Corporate bonds d. Mortgages e. Negotiable certificates of deposit f. U.S. Treasury bills g. U.S. Treasury notes h. U.S. Treasury bonds i. State and government bonds 3. What are the different types of financial institutions? Include a description of the main services offered by each. (LG6-3) 4. How would economic transactions between suppliers of funds (e.g., households) and users of funds (e.g., corporations) occur in a world without FIs? (LG6-3) 5. Why would a world limited to the direct transfer of funds from suppliers of funds to users of funds likely result in quite low levels of fund flows? (LG6-3) 6. How do FIs reduce monitoring costs associated with the flow of funds from fund suppliers to fund users? (LG6- 3) 7. How do FIs alleviate the problem of liquidity risk faced by investors wishing to invest in securities of corporations? (LG6-3) 8. Who are the suppliers of loanable funds? (LG6-4) 9. Who are the demanders of loanable funds? (LG6-4) 10. What factors cause the supply of funds curve to shift? (LG6-5) 11. What factors cause the demand for funds curve to shift? (LG6-5) 12. What are six factors that determine the nominal interest rate on a security? (LG6-6) 13. What should happen to a security’s equilibrium interest rate as the security’s liquidity risk increases? (LG6-6) 14. Discuss and compare the three explanations for the shape of the yield curve. (LG6-7) 15. Are the unbiased expectations and liquidity premium theories explanations for the shape of the yield curve completely independent theories? Explain why or why not. (LG6-7) 16. What is a forward interest rate? (LG6-8) 17. If we observe a one-year Treasury security rate that is higher than the two-year Treasury security rate, what can we infer about the one-year rate expected one year from now? (LG6-8) Problems BASIC PROBLEMS 6-1 Determinants of Interest Rates for Individual Securities A particular security’s default risk premium is 2 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.50 percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security’s equilibrium rate of return. (LG6-6) 6-2 Determinants of Interest Rates for Individual Securities You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that one-year T-bills are currently earning 1.25 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds: Real risk-free rate = 0.75% Default risk premium = 1.15% page 183 Liquidity risk premium = 0.50% Maturity risk premium = 1.75% a. What is the inflation premium? (LG6-6) b. What is the fair interest rate on Moore Corporation 30-year bonds? (LG6-6) 6-3 Determinants of Interest Rates for Individual Securities Dakota Corporation 15-year bonds have an equilibrium rate of return of 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.50 percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the bond’s default risk premium. (LG6-6) 6-4 Determinants of Interest Rates for Individual Securities A two-year Treasury security currently earns 1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and the inflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the two- year Treasury security. (LG6-6) 6-5 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. (LG6-7) 6-6 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. (LG6-7) 6-7 Unbiased Expectations Theory One-year Treasury bills currently earn 1.45 percent. You expect that one year from now, one-year Treasury bill rates will increase to 1.65 percent. If the unbiased expectations theory is correct, what should the current rate be on two-year Treasury securities? (LG6-7) 6-8 Unbiased Expectations Theory One-year Treasury bills currently earn 2.15 percent. You expect that one year from now, one-year Treasury bill rates will increase to 2.65 percent and that two years from now, one- year Treasury bill rates will increase to 3.05 percent. If the unbiased expectations theory is correct, what should the current rate be on three-year Treasury securities? (LG6-7) 6-9 Liquidity Premium Theory One-year Treasury bills currently earn 3.45 percent. You expect that one year from now, one-year Treasury bill rates will increase to 3.65 percent. The liquidity premium on two-year securities is 0.05 percent. If the liquidity premium theory is correct, what should the current rate be on two- year Treasury securities? (LG6-7) 6-10 Liquidity Premium Theory One-year Treasury bills currently earn 2.25 percent. You expect that one year from now, one-year Treasury bill rates will increase to 2.45 percent and that two years from now, one-year Treasury bill rates will increase to 2.95 percent. The liquidity premium on two-year securities is 0.05 percent and on three-year securities is 0.15 percent. If the liquidity premium theory is correct, what should the current rate be on three-year Treasury securities? (LG6-7) 6-11 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6- page 184 7) 6-12 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6- 7) INTERMEDIATE PROBLEMS 6-13 Determinants of Interest Rates for Individual Securities Tom and Sue’s Flowers, Inc.’s, 15-year bonds are currently yielding a return of 8.25 percent. The expected inflation premium is 2.25 percent annually and the real risk-free rate is expected to be 3.50 percent annually over the next 15 years. The default risk premium on Tom and Sue’s Flowers’ bonds is 0.80 percent. The maturity risk premium is 0.75 percent on five-year securities and increases by 0.04 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sue’s Flowers, lnc.’s, 15-year bonds. (LG6-6) 6-14 Determinants of Interest Rates for Individual Securities NikkiG’s Corporation’s 10-year bonds are currently yielding a return of 6.05 percent. The expected inflation premium is 1.00 percent annually and the real risk-free rate is expected to be 2.10 percent annually over the next 10 years. The liquidity risk premium on NikkiG’s bonds is 0.25 percent. The maturity risk premium is 0.10 percent on two- year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on NikkiG’s 10-year bonds. (LG6-6) 6-15 Unbiased Expectations Theory Suppose we observe the following rates: 1R1 = 8%, 1R2 = 10%. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(2r1)? (LG6-7) 6-16 Unbiased Expectations Theory The Wall Street Journal reports that the rate on four-year Treasury securities is 1.60 percent and the rate on five-year Treasury securities is 2.15 percent. According to the unbiased expectations theories, what does the market expect the one-year Treasury rate to be four years from today, E(5r1)? (LG6-7) 6-17 Liquidity Premium Theory The Wall Street Journal reports that the rate on three-year Treasury securities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-year interest rate expected in three years is, E(4r1), is 6.10 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the four-year Treasury security, L4? (LG6-7) 6-18 Liquidity Premium Theory Suppose we observe the following rates: 1R1 = 0.75%, 1R2 = 1.20%, and E(2r1) = 0.907%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2? (LG6-7) 6-19 Forecasting Interest Rates You note the following yield curve in The Wall Street Journal. According to the unbiased expectations theory, what is the one-year forward rate for the period beginning one year from today, 2f1? (LG6-8)  Maturity Yield One day 2.00% One year 5.50 Two years 6.50 page 185 page 186 Three years 9.00 6-20 Forecasting Interest Rates On March 11, 20XX, the existing or current (spot) one-, two-, three-, and four-year zero coupon Treasury security rates were as follows: Using the unbiased expectations theory, calculate the one-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4 as of March 11, 20XX. (LG6-8) ADVANCED PROBLEMS 6-21 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 7.25 percent, on 20-year Treasury bonds is 7.85 percent, and on a 20-year corporate bond issued by MHM Corp. is 8.75 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on a 10-year corporate bond issued by MHM Corp. are the same as those on the 20-year corporate bond, calculate the current rate on MHM Corp.’s 10-year corporate bond. (LG6-6) 6-22 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 8-year Treasury bonds is 5.85 percent, the rate on 15-year Treasury bonds is 6.25 percent, and the rate on a 15-year corporate bond issued by MHM Corp. is 7.35 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on an 8-year corporate bond issued by MHM Corp. are the same as those on the 15-year corporate bond, calculate the current rate on MHM Corp.’s 8-year corporate bond. (LG6-6) 6-23 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 5-year Treasury bonds is 1.85 percent and on 10-year Treasury bonds is 3.35 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 5-year Treasury bond purchased five years from today, E(5r5). (LG6-6) 6-24 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 2.25 percent and the rate on 20-year Treasury bonds is 4.50 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 10-year Treasury bond purchased 10 years from today, E(10r10). (LG6-6) 6-25 Unbiased Expectations Theory Suppose we observe the three-year Treasury security rate (1R3) to be 8 percent, the expected one-year rate next year— E(2r1)—to be 4 percent, and the expected one-year rate the following year—E(3r1)—to be 6 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate, 1R1? (LG6-7) 6-26 Unbiased Expectations Theory The Wall Street Journal reports that the rate on three-year Treasury securities is 1.20 percent and the rate on five-year Treasury securities is 2.15 percent. According to the unbiased expectations theory, what does the market expect the two-year Treasury rate to be three years from today, E(3r2)? (LG6-7) 6-27 Forecasting Interest Rates Assume the current interest rate on a one-year Treasury bond (1R1) is 4.50 percent, the current rate on a two-year Treasury bond (1R2) is 5.25 percent, and the current rate on a three-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year forward rate expected on Treasury bills during year 3, 3f1? (LG6-8) 6-28 Forecasting Interest Rates A recent edition of The Wall Street Journal reported interest rates of 1.25 percent, 1.60 percent, 1.98 percent, and 2.25 percent for three-, four-, five-, and six-year Treasury security yields, respectively. According to the unbiased expectation theory of the term structure of interest rates, what are the expected one-year forward rates for years 4, 5, and 6? (LG6-8) page 187 chapter six appendix 6A: The Financial Crisis: The Failure of Financial Institution Specialness In the late 2000s, the United States—and indeed the world—experienced the worst financial crisis since the Great Depression of the 1930s. As of mid-March 2009, in less than a year and a half, the Dow Jones Industrial Average (DJIA) had fallen in value 53.8 percent, compared to 49 percent in the market crash of 1937 and 1938. Home foreclosures reached record highs in late 2008 and continued to rise through 2009. One in 45 households (2.8 million properties) were in default on their home mortgage in 2009. The investment banking industry saw the failure (or acquisition) of all but two of its major firms (Goldman Sachs and Morgan Stanley), and these two firms converted to commercial bank holding companies. AIG, one of the largest insurance companies in the U.S., survived only because of a federal government bailout. Commercial banking giant Citigroup required a massive government guarantee against losses and an injection of cash to prevent failure. The three major U.S. automakers faced bankruptcy without federal money. Even after having received government loans, Chrysler declared Chapter 11 bankruptcy in May 2009, while General Motors followed suit a month later. As of October 2009, the U.S. unemployment rate was over 10 percent, the highest level since 1983. This financial crisis had huge effects on financial institutions and the way they do business today and will do business in the future. In the chapter, we explored the root causes of and changes brought about by the financial crisis as they apply to specific areas of risk measurement and management within FIs. In this appendix, we review the major events leading up to and throughout the financial crisis so we can see the full economywide impact and implications for the future. The Beginning of the Collapse Signs of significant problems in the U.S. economy first arose in late 2006 and the first half of 2007 when home prices plummeted and mortgage delinquencies began to mount. Mortgage defaults by subprime borrowers surged in the last quarter of 2006 through 2008 as homeowners, who a half decade earlier had stretched themselves financially to buy a home or refinance a mortgage, fell behind on their loan payments. Foreclosure filings jumped 93 percent in July 2007 over July 2006. Between August 2007 and October 2008, an additional 936,439 homes were lost to foreclosure. As the mortgage defaults continued, financial institutions that held these mortgages (and mortgage- backed securities) started announcing huge losses on them. These securitized loans, particularly securitized subprime mortgage loans, led to the huge financial losses that quite possibly were the root cause of the weakness of the U.S. economy during this time. Losses from the falling value of subprime mortgages and securities backed by these mortgages reached over $400 billion worldwide through 2007. In 2007, Citigroup, Merrill Lynch, and Morgan Stanley lost a combined $40 billion due mainly to bad mortgage loans. Bank of America took a $3 billion dollar loss for bad loans in just the fourth quarter of 2007, while Wachovia lost $1.2 billion. UBS took a loss of $10 billion, Morgan Stanley lost $9.4 billion, Merrill Lynch lost $5 billion, and Lehman Brothers took a loss of $52 million, all because of losses on investments in subprime mortgages or assets backed by subprime mortgages. Even mortgage-backed security insurers felt the losses. In February 2008, MBIA Inc.—one of the largest insurers of mortgage-backed securities credit risk—reported a $2 billion loss for the fourth quarter of 2007, due mainly to declines in values of mortgage-backed securities it insured. Early on, some large financial institutions were unable to survive the mortgage crisis. For example, Countrywide Financial, the country’s largest mortgage issuer, nearly failed in the summer of 2007 due to subprime mortgage defaults. In an effort to add liquidity, Countrywide drew down its entire $11.5 billion line of credit with other financial institutions. Such an enormous and sudden drawdown sent Countrywide’s shares down from $24.46 to $21.29 (and down 50 percent for the year) and the DJIA down 2.83 percent on fears of an increasing degradation of the mortgage markets and potential contagion to other financial markets. Only a $2 billion equity investment by Bank of America in 2007 and then an acquisition offer in 2008 kept this financial institution alive. Another early casualty of the financial crisis was IndyMac Bank, the ninth-largest mortgage lender in the country in 2007, which was seized by the FDIC in July 2008. At that time, IndyMac had more than $32 billion in assets, making it one of the largest savings institutions in the U.S. In late 2007 and early 2008, with mounting defaults on its mortgages, page 188 IndyMac was desperate for more capital, but it could not find investors willing to put new funds into what appeared to be a failing institution. So in the summer of 2008, despite FDIC insurance coverage, depositors withdrew a total of $1.3 billion, and the FDIC stepped in to rescue the institution. At a cost to the FDIC of between $8.5 billion and $9.4 billion, IndyMac represented the largest depository institution failure in more than 20 years. The Failure of Bear Stearns In the early 2000s, investment banks and securities firms were major purchasers of mortgages and mortgage-backed securities. Packaging loans as securities allowed them to increase their business. It followed that as mortgage defaults increased in the mid-2000s, investment banks were particularly hard hit with huge losses on the mortgages and securities backing them. A prime example of the losses incurred is that of Bear Stearns, at one time the fifth largest investment bank in the United States. In the summer of 2007, two Bear Stearns funds suffered heavy losses on investments in the subprime mortgage market. The two funds filed for bankruptcy in the fall of 2007. Bear Stearns’s market value was hurt badly from these losses. The losses became so great that in March 2008 JPMorgan Chase and the Federal Reserve stepped in to rescue the bank before it failed or was sold piecemeal to various financial institutions. JPMorgan Chase purchased Bear Stearns for $236 million, or $2 per share. Three days prior to the purchase, Bear Stearns’s stock was selling for $30 per share, and it was selling for $170 less than a year earlier. Along with brokering the sale of Bear Stearns to JPMorgan Chase, in the spring of 2008, the Federal Reserve Bank (the Fed) took a series of unprecedented steps. First, for the first time the Fed lent directly to Wall Street investment banks through the Primary Dealer Credit Facility (PDCF). In the first three days, securities firms borrowed an average of $31.3 billion per day from the Fed. Second, the Fed cut interest rates sharply, including one cut on a Sunday night in March 2008. The widening regulatory arm of the Fed came amid criticism aimed at the SEC (U.S. Securities and Exchange Commission, traditionally the main regulator of investment banks) and its oversight of Bears Stearns before its collapse. The Fed was now acting as a lender to various financial institutions beyond depository institutions. The Crisis Hits September 2008 marked a crucial turning point in the financial crisis. On September 8, the U.S. government seized Fannie Mae and Freddie Mac, taking direct responsibility for these two government-sponsored agencies. These agencies provided funding for about three-quarters of new home mortgages written in the United States and were deeply involved in the market that securitizes subprime mortgages. The two firms recorded approximately $9 billion in losses in the last half of 2007 related to the market for subprime mortgage-backed securities. With the seizure, the two companies were put under a conservatorship. (Today they continue to operate with management under the control of their previous regulator, the Federal Housing Finance Agency.) On Monday, September 15, Lehman Brothers (the 158-year-old investment bank) filed for bankruptcy. Merrill Lynch, rather than face bankruptcy, allowed a sale to Bank of America. AIG (one of the world’s largest insurance companies) met with federal regulators to raise desperately needed cash. Washington Mutual (the largest savings institution in the U.S.) sought a buyer to save it from failing. A sense of foreboding gripped Wall Street. As news spread that Lehman Brothers would not survive, FIs moved to disentangle trades made with Lehman. The Dow fell more than 500 points, the largest drop in over seven years (see Figure 6A.1). By Wednesday, September 17, tension had mounted around the world. Stock markets saw huge swings in value as investors tried to sort out who might survive (markets throughout Europe were forced to suspend trading as stock prices plunged). Money market mutual fund withdrawals skyrocketed: fund investors pulled out a record $144.5 billion through Wednesday (redemptions during the week of September 8 totaled just $7.1 billion) as investors worried about the safety of even these safest investments. Money market mutual funds participated heavily in the $1.7 trillion commercial paper market, which provided a bulk of the short-term funds to corporations. As investors pulled their money from these funds, the commercial paper market shrank by $52.1 billion for the week (through Wednesday). Without these funds available to meet short-term expenses, factories faced the real possibility of shutting down and laying off employees. Likewise, without these short-term funds, banks faced the inability to fund short-term lending units (such as credit card units). As these events unfolded, financial markets froze, and banks stopped lending to each other at anything but exorbitantly high rates. Banks rely on each other for cash to meet their daily needs. Interest rates on interbank borrowing are generally low because of the confidence that the financial institutions will pay each other back. However, in mid-September, the overnight London Interbank Offered Rate (a benchmark rate that reflects the rate at ▼ ▼ page 189 which banks lend to one another) more than doubled (see Figure 6A.2). Confidence had broken down in August of 2007 and had not been completely restored. Without funding, banks became reluctant to lend at all and credit markets froze further. FIGURE 6A-1 The Dow Jones Industrial Average, October 2007–January 2010 FIGURE 6A-2  Overnight London Interbank Offered Rate (Libor in USD), 2001–2010 In mid-September 2008, the overnight London Interbank Offered Rate had more than doubled. The Rescue Plan Begins With a financial crisis evident, on Thursday, September 18, the Federal Reserve and central banks around the world page 190 invested $180 billion in global financial markets in an attempt to unfreeze credit markets. U.S. Treasury Secretary Henry Paulson met with Congressional leaders to devise a plan to get bad mortgage loans and mortgage-backed securities off balance sheets of financial institutions. After two weeks of debate (and one failed vote for passage), a $700 billion rescue plan was passed and signed into law by President George W. Bush on October 3, 2008. The bill established the Troubled Asset Relief Program (or TARP), which gave the U.S. Treasury funds to buy “toxic” mortgages and other securities from financial institutions. The federal government was mandated to take an equity stake and executive compensation was limited in the companies that took part in the TARP program. The bill also called for the administration to develop a plan to ease the wave of home foreclosures by modifying loans acquired by the government and increased FDIC deposit insurance to $250,000 from $100,000. The Crisis Spreads Worldwide As the U.S. government debated the rescue plan, the financial crisis continued to spread worldwide. During the last week of September and first week of October 2008, the German government guaranteed all consumer bank deposits and arranged a bailout of Hypo Real Estate, the country’s second largest commercial property lender. The United Kingdom nationalized mortgage lender Bradford & Bingley (the country’s eighth largest mortgage lender) and raised deposit guarantees from $62,220 to $88,890 per account. Ireland guaranteed deposits and debt of its six major financial institutions. Iceland rescued its third largest bank with an $860 million purchase of 75 percent of the bank’s stock, a few days later it seized the country’s entire banking system. Central governments of The Netherlands, Belgium, and Luxembourg together agreed to inject $16.37 billion into Fortis NY (Europe’s first ever cross-border financial services company) to keep it afloat. However, five days later this deal fell apart and the bank was split up. The central bank in India stepped in to stop a run on the country’s second largest bank, ICICI Bank, by promising to pump in cash. Central banks in Asia injected cash into their banking systems as banks’ reluctance to lend to each other, and a run on Bank of East Asia Ltd. led the Hong Kong Monetary Authority to inject liquidity into its banking system. South Korean authorities offered loans and debt guarantees to help small and midsize businesses with short- term funding. All of these actions were a result of the spread of the U.S. financial market crisis to world financial markets. After the Rescue Plan In the two months after the TARP rescue plan was enacted in the United States, the financial crisis deepened as the world feared that the initial attempts to rescue the world’s financial system would not be sufficient. Worldwide, stock market values plunged. By mid-October the Dow had dropped 24.7 percent in less than a month, the Shanghai Composite had dropped 30.4 percent, and the various markets in Europe fell between 20 and 30 percent. By mid- November, the Dow fell to a 5½-year low and the S&P 500 index erased its gains from the previous 10 years. Third- quarter GDP in the United States declined to −2.7 percent. Indeed, some measures of economic activity found the United States entered a recession as early as December 2007. The United Kingdom and Germany also saw growth decline by 0.5 percent in the third quarter of 2008. Countries across the world saw companies scrambling for credit and cutting their growth plans. Additionally, consumers worldwide reduced their spending as the value of their investments shrank. Even China’s booming economy slowed faster than had been predicted, from 10.1 percent in the second quarter of 2008 to 9.0 percent in the third quarter. This was the first time since 2002 that China’s growth was below 10 percent and dimmed hopes that Chinese demand could help keep world economies going. In late October, the global crisis hit the Persian Gulf as Kuwait’s central bank intervened to rescue Gulf Bank, the first bank rescue in the oil-rich gulf. Until this time, the area had been relatively immune to the world financial crisis. However, plummeting oil prices (which had dropped over 50 percent between July and October) left the area’s economies suddenly vulnerable. Between January and November 2008, 22 U.S. banks failed, up from 3 in all of 2007. The FDIC reported that it added 54 banks to its list of troubled institutions in the third quarter, a 46 percent increase over the second quarter. Additions to the list reflected the escalating problems in the banking industry. However, it should be noted that the 171 banks on the FDIC’s problem list represented only about 2 percent of the nearly 8,500 FDIC-insured institutions. Still, the increase from 117 troubled banks in the second quarter was the largest seen since late 1995. In what came to be known as the “too big to fail” category, commercial banking giant Citigroup required a massive government guarantee against losses (up to $306 billion) and a $20 billion injection of cash to prevent failure. By the middle of November it became apparent that the rescue plan enacted in early October actually would not be page 191 page 192 sufficient. Even more distressed financial and nonfinancial companies and consumers called for assistance. Among the largest companies in need of a bailout were the Big Three automobile manufacturers (General Motors, Ford, and Chrysler). The leaders of these companies painted a grim picture of their financial position during two days of Congressional hearings, warning that the collapse of the auto industry could lead to the loss of 3 million jobs nationwide. Both General Motors and Chrysler said they could collapse in weeks. However, automakers ran into resistance from House lawmakers, who chastised the executives for fighting tougher fuel-efficiency standards in the past and questioned their use of private jets while at the same time seeking government handouts. Fearing that the Big Three would take any bailout money and continue the same “stupid” decisions they had been making for 25 years, the U.S. Senate canceled plans for a vote on a bill to take $25 billion in new auto industry loans out of the $700 billion TARP rescue fund. Lawmakers gave the three automakers until mid-December to come back with substantial business plans outlining what they would do with any federal funds that might be lent and how they would restructure and improve the efficiency in their respective companies. After more days of testimony in mid- December, the U.S. Senate again failed to vote on a bailout for the automakers. General Motors and Chrysler stated that they did not have sufficient funds to continue operations through the end of December. Then on December 19, 2008, President Bush announced that $13.4 billion in federal loans would be made immediately available to General Motors and Chrysler. By the end of December, nearly $7 trillion of loans or commitments had been made (Table 6A.1 outlines the major commitments, loans, and investments made by the U.S. government through 2009). The U.S. Treasury had used the first $362 billion of TARP money: $250 billion of the $700 billion bailout money to inject capital into banks ($125 billion of which went to the nine largest banks), another $40 billion to further stabilize insurer AIG, $25 billion to stabilize Citigroup, $20 billion to Bank of America, $20 billion used by the Fed to stabilize other lending institutions, and $24.9 billion lent to the auto industry. Note that the Treasury had dropped the original plans to use TARP bailout money to buy troubled mortgage assets from financial institutions, stating that it was no longer the most effective way to restart credit markets. Rather, plans were to take equity stakes in financial institutions. ▼ TABLE 6A.1 Federal Government Rescue Efforts through December 2009 Program Committed Invested Description TARP $700.0billion $356.2 billion Financial rescue plan aimed at restoring liquidity to financial markets AIG 70.0b 69.8b Auto industry financing 80.1b 77.6b Capital Purchase Program 218.0b 204.7b Public–Private Investment Program 100.0b 26.7b Targeted investments to Citigroup and Bank of America 52.5b 45.0b Amount repaid $118.5 billion Federal Reserve Rescue Efforts $6.4trillion $1.5 trillion Financial rescue plan aimed at restoring liquidity to financial markets Asset-backed commercial paper money market mutual fund liquidity facility Unlimited $0.0 Bear Stearns bailout 29.0b 26.3b Commercial paper funding facility 1.8t 14.3b Foreign exchange dollar swaps Unlimited 29.1b GSE (Fannie Mae and Freddie Mac) debt purchases 200.0b 149.7b GSE mortgage-backed securities purchases 1.2t 775.6b Term asset-backed securities loan facility 1.0t 43.8b U.S government bond purchase 300.0b 295.3b Federal Stimulus Programs $1.2trillion $577.8 billion Programs designed to save or create jobs Economic Stimulus Act 168.0b 168.0b Student loan guarantees 195.0b 32.6b American Recovery and Reinvestment Act 787.2b 358.2b American International Group $182.0billion $127.4 billion Bailout to help AIG through restructuring, get rid of toxic assets Asset purchases 52.0b 38.6b Bridge loan 25.0b 44.0b TARP investment 70.0b 44.8b FDIC Bank Takeovers $45.4billion $45.4 billion Cost to FDIC to fund deposit losses on bank failures 2008 failures 17.6b 17.6b 2009 failures 27.8b 27.8b Other Financial Initiatives $1.7trillion $366.4 billion Other programs designed to rescue the financial sector NCUA bailout of U.S. Central Credit Union 57.0b 57.0b Temporary Liquidity Guarantee Program 1.5t 308.4b Other Housing Initiatives $745.0billion $130.6 billion Other programs intended to rescue the housing market and prevent home foreclosures Fannie Mae and Freddie Mac bailout 400.0b 110.6b FHA housing rescue 320.b 20.0b Overall Total $11.0trillion $3.0 trillion Some Bright Spots While the economy remained in crisis, some positive developments occurred between September and December 2008. Oil, which rose to over $142 per barrel in July, had dropped to below $40 in late 2008. As a result, gas prices, which rose to over $4.00 per gallon in the summer of 2008, had fallen to a national average of $1.65 in December. Led by a federal government push, many banks moved to restructure delinquent mortgage loans rather than foreclose. Fannie Mae and Freddie Mac suspended foreclosures on 16,000 homes over the 2008 holiday period while they evaluated whether the borrowers would qualify for the new loan modification programs. Fannie and Freddie’s modification plan allowed mortgage restructuring, rather than foreclosure, for homeowners whose mortgages were held by one of the two companies, were at least three months behind on their payments, and whose mortgage payments were no more than 38 percent of the homeowner’s pretax monthly income. The Federal Reserve’s attempt to stabilize the housing market resulted in a drop in long-term mortgage rates (30-year fixed-rate mortgage rates dipped to below 5.0 percent in late November). In a historic move, on December 17, 2008, the Fed unexpectedly announced that it would drop its target Fed funds rate to a range between 0 and 0.25 percent and lower its discount window rate to 0.5 percent, the lowest level since the 1940s (see Figure 6A.3). Along with this announcement, the Fed announced that it would continue to use all its available tools to promote economic growth and preserve price stability. This was followed by interest rate cuts in many other countries including Japan and the United Kingdom, as well as Hong Kong and the European Central Bank. The Crisis Continues in 2009 Despite the many efforts of regulators to stem the tide of the growing recession, the U.S. and world economies ▼ page 193 deteriorated further at the start of 2009. The DJIA and the S&P 500 Index had their worst January ever, falling 8.84 percent and 8.57 percent, respectively. Unemployment in January hit 7.6 percent, the highest level since September 1992. Also in January, employers cut 589,000 jobs, the highest monthly job losses in over 34 years. Since December 2007 (as the recession began) the U.S. economy lost 3.6 million jobs, half of which were lost in the period November 2008 through January 2009. Gross domestic product growth was announced, showing a drop of 5.4 percent in the fourth quarter of 2008. New vehicle sales in the United States fell 37 percent in January, the industry’s worst month since 1982 and the worst January since 1963. For the first time ever, more vehicles were sold in China than in the United States. Worldwide, central governments tried to grapple with the building recession. The United Kingdom, Belgium, Canada, Italy, and Ireland were just a few of the countries to pass an economic stimulus plan and/or bank bailout plan. The Bank of England lowered its target interest rate to a record low of 1 percent, hoping to help the British economy out of a recession. The Bank of Canada, Bank of Japan, and Swiss National Bank also lowered their main interest rate to 1 percent or below. The U.S. Stimulus Plan With the U.S. economy deteriorating at its swiftest rate in history, President Obama made good on his pre-election promise to have an economic stimulus plan approved and enacted shortly after his election. The House passed its version of an $819 billion stimulus package on January 28, 2009. The Senate passed an $827 billion version of a stimulus plan on February 10, 2009. After more debate and compromise, both arms of Congress agreed on and passed the economic stimulus plan, called the American Recovery and Reinvestment Act, on February 13, 2009. The plan devoted $308.3 billion to appropriations spending, including $120 billion on infrastructure and science and more than $30 billion on energy-related infrastructure projects. Another $267 billion went for direct spending, including increased unemployment benefits and food stamps. Finally, $212 billion was set aside for tax breaks for individuals and businesses (Table 6A.2 lists some of the major items in the stimulus plan). FIGURE 6A-3 Federal Funds Rate and Discount Window Rate, January 1971–January 2010 page 194 On December 17, 2008, the Fed dropped the target Fed funds rate to a range between 0 and 0.25 percent and the discount window rate to 0.5 percent. Stabilizing the Financial System In addition to the overall economic stimulus plan, the Obama administration, including Treasury Secretary Geithner, announced a separate plan that focused on the stabilization of the financial system. Early 2009 saw a plunge in the DJIA (falling to a low of 6,547.05 on March 9, 2009) and, particularly, the market values of financial institutions. Banks, including Citigroup, Bank of America, and JPMorgan Chase, traded at less than their book values as investors had little confidence in the value of their assets. Through February 13, 2009, 13 U.S. banks had already failed in 2009, while 25 had failed in all of 2008 (the highest annual total since 1993). The plan, announced on February 10, 2009, involved a number of initiatives, including Injecting capital into banks. Offering federal insurance to banks against losses on bad assets. Buying distressed mortgages from banks. Helping homeowners avoid foreclosure. Giving the FDIC power to help troubled financial firms other than depository institutions. ▼ TABLE 6A.2 The $787 Billion Stimulus Program as Passed by the U.S. Congress, February 13, 2009 $116.1b Tax cuts and credits to low- and middle-income workers 69.8b Middle income taxpayers to get an exemption from the alternative minimum tax 87.0b Medicaid provisions 27.0b Jobless benefits extension to a total of 20 weeks on top of regular unemployment compensation 17.2b Increase in student aid page 195 40.6b Aid to states 30.0b Modernization of electric grid and energy efficiency 19.0b Payments to hospitals and physicians who computerize medical record systems 29.0b Road and bridge infrastructure construction and modernization 18.0b Grants and loans for water infrastructure, flood prevention, and environmental cleanup 17.2b Increases in student aid The plan also proposed expanding the Fed’s Term Asset-Backed Securities Loan Facility (TALF). The TALF combined capital provided by the TARP with funding from the Federal Reserve in order to promote lending by increasing investor demand for securitized loans. The TALF significantly expanded the availability and reduced the cost of term financing for investors in derivative securities. The goal of TALF was to stimulate demand for these securities and thereby allow originators of securitized loans to lower the cost and increase the availability of credit to consumers and businesses. The Fed’s TALF program initially provided financing for investors to purchase securities backed by consumer loans. The Treasury wanted to expand this beyond consumer loans. For homeowners, the banking plan called for the creation of national standards for loan modifications and for the use of tax dollars to give mortgage companies an incentive to modify mortgage loans. Further, along with the expanded TALF program, the Treasury, working with the Federal Reserve, FDIC, and private investors, created the Public–Private Investment Fund (PPIF) to acquire real estate–related off-balance-sheet assets. By selling to PPIF, financial institutions could reduce balance sheet risk, support new lending, and help improve overall market functioning. Finally, in late February 2009, the Obama administration announced that it would conduct a “stress test” of the 19 largest U.S. banks. This instrument would measure the ability of these banks to withstand a protracted economic slump, with an unemployment rate above 10 percent and home prices dropping another 25 percent. Results of the stress test showed that 10 of the 19 banks needed to raise a total of $74.6 billion in capital. Within a month of the May 7, 2009, release of the results, the banks had raised $149.45 billion of capital. The Economy Begins to Recover Throughout the spring of 2009, the federal government continued to take actions to combat the stagnant economy. These included actions such as passage (in May 2009) of the Job Creation through Entrepreneurship Act to help small businesses access capital and credit markets. The Cash for Clunkers Program (in June 2009) to stimulate automobile sales was wildly popular. By the summer and fall of 2009 the economy slowly began to recover. Pending home sales and residential construction both posted significant increases in September. September marked the eighth consecutive monthly increase in pending home sales, which was the longest such streak since 1991, when this data began to be tracked. Home sales rose at an annual rate of 6.1 percent in September (21.2 percent ahead of their September 2008 level). Meanwhile, the Commerce Department reported that residential construction spending increased at a 3.9 percent annual rate in September. It was the third consecutive monthly increase in residential construction. The National Association of Realtors announced that the number of signed contracts increased for the ninth consecutive month to the biggest year-over-year gain in the history of the index—31.8 percent higher than September 2008. These signs of life in the construction industry were an indication that the first-time Homebuyer Tax Credit, put in place as part of the American Recovery and Reinvestment Act, was working. Indeed, in November 2009, President Obama signed into law an expanded Homebuyer Tax Credit that extended the tax credit of up to $8,000 for qualified first-time home buyers and $6,500 for repeat home buyers purchasing a principal residence. Third-quarter 2009 GDP increased by 2.2 percent and fourth-quarter GDP rose 5.7 percent. This increase was the first since the second quarter of 2008. The increases were the result of consumer spending, which increased significantly. Spending on new cars and trucks was a big contributor (adding 1.45 percent to the third-quarter change), reflecting the federal Cash for Clunkers program in effect in July and August. The increase in GDP in the fourth quarter primarily reflected increases in private inventory investment, exports, and personal consumption expenditures. Automobile output continued to do well, adding 0.61 percent to the fourth-quarter change in GDP. With the positive economic news, on October 14, 2009, the DJIA reached 10,000 for the first time in a year. Still, unemployment lagged, exceeding 10 percent in October 2009. But this rate was short-lived, as the unemployment rate dropped below 10 percent in November 2009 and job losses began to decline sharply, with only 11,000 American jobs lost in November 2009, compared to 741,000 jobs lost in December 2008. There were 140 failures of banks in 2009, with assets totaling $170.9 billion. The five largest bank failures were BankUnited ($12.5 billion in assets), Colonial Bank ($25 billion in assets), Guaranty Bank ($13 billion in assets), page 196 United Commercial Bank ($11.2 billion in assets), and AmTrust Bank ($12 billion in assets). The cost to the FDIC for resolving these failures was $27.5 billion. Compare this with statistics for 2008, when there were 25 bank failures with assets totaling $373.6 billion. In December 2009, the Obama Administration announced that the long-term cost of the Troubled Asset Relief Program would be at least $200 billion less than previously projected, which would help bring down the projected federal budget deficit. Throughout 2010 and into 2012, the economy was still fragile and had certainly not recovered from the extreme financial crisis, but it was stabilizing. Finally, in July 2010, the U.S. Congress passed, and President Obama signed, the 2010 Wall Street Reform and Consumer Protection Act which sought to prevent a repeat of the market meltdown. Touted as the most extensive proposal for the overhaul of financial rules since the Great Depression, this bill proposed a sweeping overhaul of the nation’s financial system and the rules that govern it. The bill called for the Federal Reserve to receive new oversight powers and to impose conditions designed to discourage any type of financial institution from getting too big. The proposals put the Federal Reserve in charge of monitoring the country’s biggest financial firms—those considered critical to the health of the system as a whole. Those firms would also face new, stiffer requirements on how much capital and liquidity they keep in reserve. The proposed overhaul also provided unprecedented powers to the Fed to step into any financial institution—such as insurance giant AIG (whose main regulators include the New York State Department of Insurance and the Office of Thrift Supervision)—that is facing imminent collapse, in order to force an orderly bankruptcy that would protect the wider economy. More specifically, the bill set forth reforms to meet five key objectives: 1. Promote robust supervision and regulation of financial firms by establishing (i) a new Financial Services Oversight Council of financial regulators (chaired by Treasury and including the heads of the principal federal financial regulators as members) to identify emerging systemic risks and improve interagency cooperation; (ii) a new authority for the Federal Reserve to supervise all firms that could pose a threat to financial stability, even those that do not own banks; (iii) stronger capital and other prudential standards for all financial firms, and even higher standards for large, interconnected firms; (iv) a new National Bank Supervisor to supervise all federally chartered banks; (v) elimination of the federal thrift charter for thrifts not dedicated to mortgage lending and other loopholes that allowed some depository institutions to avoid bank holding company regulation by the Federal Reserve; and (vi) the registration of advisers of hedge funds and other private pools of capital with the SEC. 2. Establish comprehensive supervision of financial markets by establishing (i) the regulation of securitization markets, including new requirements for market transparency, stronger regulation of credit rating agencies, and a requirement that issuers and originators retain a financial interest in securitized loans; (ii) comprehensive regulation of all over-the-counter derivatives; and (iii) new authority for the Federal Reserve to oversee payment, clearing, and settlement systems. 3. Protect consumers and investors from financial abuse by establishing (i) a new Consumer Financial Protection Agency to protect consumers across the financial sector from unfair, deceptive, and abusive practices; (ii) stronger regulations to improve the transparency, fairness, and appropriateness of consumer and investor products and services; and (iii) a level playing field and higher standards for providers of consumer financial products and services, whether or not they are part of a bank. 4. Provide the government with the tools it needs to manage financial crises by establishing (i) a new regime to resolve nonbank financial institutions whose failure could have serious systemic effects and (ii) revisions to the Federal Reserve’s emergency lending authority to improve accountability. 5. Raise international regulatory standards and improve international cooperation by establishing international reforms to support our efforts in the United States, including strengthening the capital framework, improving oversight of global financial markets, coordinating supervision of internationally active firms, and enhancing crisis management tools. Notes CHAPTER 6 1 Often the Fisher effect formula is written as (1 + i ) = (1 + IP ) × (1 + RFR ), which, when solved for i, becomes: i = Expected IP + RFR + (Expected IP × RFR), where Expected IP × RFR is the inflation premium for the loss of purchasing power on the promised nominal interest rate payments due to inflation. For small values of Expected IP and RFR this term is negligible. The approximation formula page 197 used here assumes these values are small. 2 This section, which contains more technical details, may be included or dropped from the chapter reading, depending on the rigor of the course. 3 That is, E (4 r 1) > E (3 r 1) > E (2 r 1) > 1 R 1 .
4 In general, the price and yield on a bond are inversely related. Thus, as the price of a bond falls (become cheaper), the demand for the
bond will rise. This is the same as saying that as the yield on a bond rises, it becomes cheaper and the demand for it increases. See
Chapter 7.
5 This section, which contains more technical details, may be included in or dropped from the chapter reading depending on the rigor of
the course.

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page 199

chapter seven
Valuing
Bonds
©DNY59/Getty Images

H
page 200
ow important are bonds and the bond market to a capitalist economy? Those unfamiliar with the
financial markets may have the impression that the stock market dominates capital markets in the
United States and in other countries. Stock market performance appears constantly on 24-hour TV
news channels and on the evening news. By contrast, we seldom hear any mention of the bond market.
While bonds may not generate the same excitement that stocks do, they are an even more important
capital source for companies, governments, and other organizations. The bond market is actually larger
than the stock market. At the end of 2015, the U.S. bond market represented roughly $39.6 trillion in
outstanding debt obligations. At the same time, the market value of all common stock issues was worth
just over half of the value of the bond market, at roughly $21.0 trillion.
Bonds also trade in great volume and frequency. During 2015, the total average daily trading in all
types of U.S. bonds reached over $730 billion. Investors are often attracted to the stock market because it
offers the potential for high investor returns—but great risks come with that high potential return. While
some bonds offer safer and more stable returns than stocks, other bonds also offer high potential rewards
and, consequently, higher risk.
In this chapter, we will explore bond characteristics and their price dynamics. You will see that bond
pricing uses many time value of money principles that we’ve used in the preceding chapters. ■
LEARNING GOALS
LG7-1 Describe bond characteristics.
LG7-2 Identify various bond issuers and their motivation for issuing debt.
LG7-3 Read and interpret bond quotes.
LG7-4 Compute bond prices using present value concepts.
LG7-5 Explain the relationship between bond prices and interest rates.
LG7-6 Compute bond yields.
LG7-7 Find bond ratings and assess credit risk’s effects on bond yields.
LG7-8 Assess bond market performance.

viewpoints
business APPLICATION
You are the chief financial officer (CFO) for Beach Sand Resorts. The firm needs $150 million of new capital to renovate a hotel
property. As you discuss the firm’s plans with a credit rating agency, you learn that if 15-year bonds are used to raise this capital, the
bonds will be rated BB and will have to offer a 7 percent return. How many bonds will you have to issue to raise the necessary
capital? What semiannual interest payments will Beach Sand have to make? (See the solution at the end of the book.)
7.1 • BOND MARKET OVERVIEW LG7-1
Bond Characteristics
Bonds are debt obligation securities that corporations, the federal government or its agencies, or states and local
governments issue to fund various projects or operations. All of these organizations periodically need to raise capital
for various reasons, which was formally discussed in Chapter 6. Bonds are also known as fixed-income securities
because bondholders (investors) know both how much they will receive in interest payments and when their
principal will be returned. From the bond issuer’s point of view, the bond is a loan that requires regular interest
payments and an eventual repayment of the borrowed principal. Investors—often pension funds, banks, and mutual
funds—buy bonds to earn investment returns. Most bonds follow a relatively standard structure. A legal contract
called the indenture agreement outlines the precise terms between the issuer and the bondholders. Any bond’s main

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characteristics include:
bond Publicly traded form of debt.
fixed-income securities Any securities that make fixed payments.
principal Face amount, or par value, of debt.
indenture agreement Legal contract describing the bond characteristics and the bondholder and issuer rights.
The date the principal will be repaid (the maturity date).
maturity date The calendar date on which the bond principal comes due.
The par value, or face value, of each bond, which is the principal loan amount that the borrower must repay.
par value Amount of debt borrowed to be repaid; face value.
The coupon (interest) rate.
A description of any property to be pledged as collateral.
Steps that the bondholder can take in the event that the issuer fails to pay the interest or principal.
Table 7.1 describes par value and other bond characteristics. Most bonds have a par value of $1,000. This is the
amount of principal the issuer has promised to repay. Bonds have fixed lives. The bond’s life ends when the issuer
repays the par value to the buyer on the bond’s maturity date. Although a bond will mature on a specific calendar
date, the bond is usually referenced by its time to maturity, that is, 2 years, 5 years, 20 years, and so on. In fact, the
market groups bonds together by their time to maturity and classifies them as short-term bonds, medium-term bonds,
or long-term bonds, regardless of issuer. Long-term bonds carry 20 or 30 years to maturity. Of course, over time, the
30-year bond becomes a 20-year bond, 10-year bond, and eventually matures. But other time periods to maturity do
exist. For example, in 2011, the railroad company Norfolk Southern Corp. issued $400 million of bonds with 100
years to maturity. The bonds have a coupon (interest) rate of 6 percent and mature in 2111.
time to maturity The length of time (in years) until the bond matures and the issuer repays the par value.

personal APPLICATION
You would like to invest in bonds. Your broker suggests two different bonds. The first, issued by Trust Media, will mature in 2023. Its
price is quoted at 96.21 and it pays a 5.7 percent coupon. The second bond suggested, issued by Abalon, Inc., also matures in 2023.
This bond’s price is 101.94 and pays a 5.375 percent coupon. To help you decide between the bonds, you want to know how much
money it will cost to buy 10 bonds, what interest payments you will receive, and what return the bonds offer if purchased today. Also,
you want to understand the differences between what the two bonds imply about their risk. (See the solution at the end of the
book.)
How do you even purchase a bond in the first place?
When interest rates economywide fall several percentage points (which often takes several years), homeowners
everywhere seek to refinance their home mortgages. They want to make lower interest payments (and sometimes
want to pay down their mortgage principal) every month. Corporations that have outstanding bond debt will also
want to refinance those bonds. Sometimes the indenture contract (the legal contract between a bond issuer and
bondholders) allows companies to do so; sometimes the indenture prohibits refinancing. Bonds that can be
refinanced have a call feature, which means that the issuer can “call” the bonds back and repay the principal before
the maturity date. To compensate the bondholders for getting the bond called, the issuer pays the principal and a call
premium. The most common call premium is one year’s worth of interest payments. In some indentures, the call
premium declines over time.
call An issuer redeeming the bond before the scheduled maturity date.

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call premium The amount in addition to the par value paid by the issuer when calling a bond.
The bond’s coupon rate determines the dollar amount of interest paid to bondholders. The coupon rate appears on the
bond and is listed as a percentage of the par value. So a 5 percent coupon rate means that the issuer will pay 5
percent of $1,000, or $50, in interest every year, usually divided into two equal semiannual payments. So a
5 percent coupon bond will pay $25 every six months. Companies set the coupon rate as the prevailing
market interest rate at the time of bond issue. The name coupon is a holdover from the past, when bonds were
actually issued with a coupon book. Every six months a bondholder would tear out a coupon and mail it to the
issuer, who would then make the interest payment. These are sometimes referred to as bearer bonds (often a feature
of spy or mystery movies), because whoever held the coupon book could receive the payments. Nowadays, issuers
register bond owners and automatically wire interest payments to the owner’s bank or brokerage account.
Nevertheless, the term coupon persists today.
coupon rate The annual amount of interest paid expressed as a percentage of the bond’s par value.
▼ TABLE 7.1 Typical Bond Features
Characteristic Description Common Values
Par value The amount of the loan to be repaid. This is often referred to as the
principal of the bond.
$ 1,000
Time to maturity The number of years left until the maturity date. 1 year to 30 years
Call
The opportunity for the issuer to repay the principal before the maturity
date, usually because interest rates have fallen or issuer’s
circumstances have changed. When calling a bond, the issuer
commonly pays the principal and one year of interest payments.
Many bonds are not callable. For
those that are, a common feature is
that the bond can be called any time
after 10 years of issuance.
Coupon rate
The interest rate used to compute the bond’s interest payment each
year. Listed as a percentage of par value, the actual payments usually
are paid twice per year.
2 to 10 percent
Bond price The bond’s market price reported as a percentage of par value. 80 to 120 percent of par value
the Math Coach on…
Percent-to-Decimal Conversions
“When discussing interest rates or using them in calculator or spreadsheet time value of money functions,
the value should be in percent (%) form, like 2.5%, 7%, and 11%. When using interest rates in formulas, the
value needs to be in decimal form, like 0.025, 0.07, and 0.11.
To convert between the two forms of representing an interest rate, use

At original issue, bonds typically sell at par value, unless interest rates are very volatile. Bondholders recoup the par
value on the bond’s maturity date. However, at all times in between these two dates, bonds might trade among
investors in the secondary bond market. The bond’s price as it trades in the secondary market will not likely be the
par value. Bonds trade for higher and lower prices than their par values. We’ll thoroughly demonstrate the reasons
for bond pricing in a later section of this chapter. Bond prices are quoted in terms of percent of par value rather than
in dollar terms. Sources of trading information list a bond that traded at $1,150 as 115, and a bond that traded for
$870 as 87.
bond price Current price that the bond sells for in the bond market.


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Bond Issuers LG7-2
For many years, bonds were considered stodgy, overly conservative investments. Not anymore! The fixed-income
industry has seen tremendous innovation in the past couple of decades. The financial industry has created and issued
many new types of bonds and fixed-income securities, some with odd-sounding acronyms, like TIGRs, CATS,
COUGRs, and PINEs, all of which are securities based on U.S. Treasuries. Even with all the innovation, the
traditional three main bond issuers remain: U.S. Treasury bonds, corporate bonds, and municipal bonds. Figure 7.1
shows the amount of money that these bond issuers have raised each year.
EXAMPLE 7-1 Bond Characteristics LG7-1
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Consider a bond issued 10 years ago with an at-issue time to maturity
of 30 years. The bond’s coupon rate is 8 percent and it currently trades
in the bond market for 109. Assuming a par value of $1,000, what is the
bond’s current time to maturity, semiannual interest payment, and bond
price in dollars?
SOLUTION:
Time to maturity = 30 years − 10 years = 20 years
Annual payment = 0.08 × $1,000 = $80, so semiannual payment is $40
Bond price = 1.09 × 1,000 = $1,090
Similar to Problems 7-1, 7-2, 7-3, 7-4, Self-Test Problem 1

FIGURE 7-1 Amount of Capital Raised Yearly from Bonds Issued by Local and Federal Government and Corporations

http://mhhe.com/CornettM4e

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Local or municipal governments, the U.S. Treasury, and corporations have issued many new types of bonds and fixed-income securities over
the past two decades.
Source: Securities Industry and Financial Markets Association.
Treasury Bonds Treasury bonds carry the “full-faith-and-credit” backing of the U.S. government and investors
have long considered them among the safest fixed-income investments in the world. The federal government sells
Treasury securities through public auctions to finance the federal deficit. When the deficit is large, more bonds come
to auction. In addition, the Federal Reserve System (the Fed) uses Treasury securities to implement monetary policy.
Technically, Treasury securities issued with 1 to 10 years until maturity are Treasury notes. Securities issued with 10
to 30 years until maturity are Treasury bonds. Figure 7.1 shows that the number of new Treasuries being offered
actually declined in the late 1990s as the federal budget deficit declined. However, this reversed in 2002 and then
dramatically accelerated in 2009 after the global financial crisis and during the years of the Fed’s quantitative easing
programs.
Corporate Bonds Corporations raise capital to finance investments in inventory, plant and equipment, research
and development, and general business expansion. As managers decide how to raise capital, corporations can issue
debt, equity (stocks), or a mixture of both. The driving force behind a corporation’s financing strategy is the desire
to minimize its total capital costs. Through much of the 1990s, corporations tended to issue equity (stocks) to raise
capital. Beginning in 1998 and through 2015, corporations switched to raising capital by issuing bonds to take
advantage of low interest rates and issued $17.1 trillion in new bonds. You can see this rise in capital reflected in
Figure 7.1.
Municipal Bonds State and local governments borrow money to build, repair, or improve streets, highways,
hospitals, schools, sewer systems, and so on. The interest and principal on these municipal bonds are repaid in two
ways. Projects that benefit the entire community, such as courthouses, schools, and municipal office buildings, are
typically funded by general obligation bonds and repaid using tax revenues. Projects that benefit only certain groups
of people, such as toll roads and airports, are typically funded by revenue bonds and repaid from user fees. Interest
payments paid to municipal bondholders are not taxed at the federal level, or by the state for which the bond is
issued.
Other Bonds and Bond-Based Securities
Treasury Inflation-Protected Securities (TIPS) have proved one of the most successful recent innovations in the bond
market. The U.S. Treasury began issuing this new type of Treasury bond, which is indexed to inflation, in 1997.
TIPS have fixed coupon rates like traditional Treasuries. The new aspect is that the federal government adjusts the
par value of the TIPS bond for inflation. Specifically, it increases at the rate of inflation (measured by the consumer
price index, CPI). As the bond’s par value changes over time, interest payments also change. At maturity, investors
receive an inflation-adjusted principal amount. If inflation has been high, investors will expect that the adjusted
principal amount will be substantially higher than the original $1,000. Consider a 10-year TIPS issued on January
15, 2009, that pays a 2⅛ percent coupon. The reference CPI for these bonds is 214.69971. Four years later (on
January 15, 2013) the reference CPI was 230.22100. So the par value of the TIPS in early 2013 was $1,072.29 (=
$1,000 × 230.22100 ÷ 214.69971). Therefore, the 2⅛ percent coupon (paid semiannually) would be $11.39 =
(0.02125 × $1,072.29 ÷ 2). A TIPS total return comes from both the interest payments and the inflation adjustment
to the par value.
Treasury Inflation-Protected Securities TIPS are U.S. government bonds where the par value changes with inflation.
U.S. government agency securities are debt securities issued to provide low-cost financing for desirable private-
sector activities such as home ownership, education, and farming. Fannie Mae, Freddie Mac, Student Loan
Marketing Association (Sallie Mae), Federal Farm Credit System, Federal Home Loan Banks, and the Small
Business Administration, among others, issue these agency bonds to support particular sectors of the economy.
Agency securities do not carry the federal government’s full-faith-and-credit guarantee, but the government has
never let one of its agencies fail. Because investors believe that the federal government will continue in this
watchdog role, agency bonds are thought to be very safe and may provide a slightly higher return than Treasury
securities do.
agency bonds Bonds issued by U.S. government agencies.

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EXAMPLE 7-2 TIPS Payments LG7-2
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
A TIPS bond was issued on July 15, 2006, that pays a 2½ percent
coupon. The reference CPI at issue was 201.95. The reference CPI for
the following interest payments were
January 2009 214.70
July 2009 213.52
January 2010 216.25
Given these numbers, what is the par value and interest payment of the
TIPS on the three interest-payment dates? What is the total return from
January 2009 to January 2010?
SOLUTION:
Compute the TIPS index ratio for each period as current CPI divided by
the at-issue CPI: The par value for January 2009 is $1,000 × 214.70 ÷
201.95 = $1,063.13, so the interest payment is 0.025 × $1,063.13 ÷ 2 =
$13.29. The answers for the next two dates are:
July 2009 Par value = $1,057.29 Interest payment = $13.22
January 2010 Par value = $1,070.81 Interest payment = $13.39
The capital gain between January 2009 and January 2010 is $1,070.81
− $1,063.13 = $7.68. Adding the two interest payments together results
in $26.61 (= $13.22 + $13.39). Thus, the total return is 3.23% = ($7.68
+ $26.61 )/$ 1,063.13.
Similar to Problems 7-7, 7-8, 7-19, 7-20, 7-33, 7-34

finance at work //: personal finance
Buy Treasuries Direct!

http://mhhe.com/CornettM4e

©Comstock Images/Jupiter Images
Treasury bonds are U.S. government-issued debt securities that investors trade on secondary markets. The government also issues
nonmarketable debt, called “savings bonds,” directly to investors. The common EE savings bonds, introduced in 1980, do not pay
regular interest payments. Instead, interest accrues and adds to the bond’s value. After a one-year holding period, they can be
redeemed at many banks or credit unions. You can also purchase savings bonds and other Treasury securities (bills, notes, bonds, and
TIPS) electronically through the U.S. Treasury’s website, treasurydirect.gov. You can set up an account in minutes and buy savings
bonds with cash from your bank account. You can also redeem your bonds and transfer the proceeds back to your bank account. Bonds
can be purchased 24 hours a day, 7 days a week at no cost.
When bondholders redeem savings bonds, they receive the original value paid plus the accrued interest. Paper bonds sell at half of
the face value; if investors hold them for the full 30 years, they receive the par value. Investors buy electronic bonds at face value and
earn interest in addition to the par value. Unlike other bonds, savers need not report income from these interest payments to the IRS
until they actually redeem the bonds. So savings bonds count as tax-deferred investments.
About one in six Americans owns savings bonds. Savings bonds are used for a variety of purposes, such as personal savings
instruments or gifts from grandparents to grandchildren. After the September 11, 2001, terrorist attacks, many Americans wanted to
show support for the government. In December 2001, banks selling government EE savings bonds began printing “Patriot bond” on
them. So EE savings bonds are now often called Patriot Bonds.
Want to know more?
Key Words to Search for Updates: TreasuryDirect (go to www.treasurydirect.gov)
U.S. government agencies invented one popular type of debt security: mortgage-backed securities (MBSs). Fannie Mae
and Freddie Mac offer subsidies or mortgage guarantees for people who wouldn’t otherwise qualify for mortgages,
especially first-time homeowners. Fannie Mae started out as a government-owned enterprise in 1938 and became a
publicly held corporation in 1968. Freddie Mac was chartered as a publicly held corporation at its inception in 1970.
Since 2008, both have been in government conservatorship and run by the Federal Housing Finance Agency. To
increase the amount of money available (liquidity) for the home mortgage market, Fannie Mae and Freddie Mac
purchase home mortgages from banks, credit unions, and other lenders. They combine the mortgages into diversified
portfolios of such loans and then issue mortgage-backed securities, which represent a share in the mortgage debt, to
investors. As homeowners pay off or refinance the underlying portfolio of mortgage loans, MBS investors receive
interest and principal payments. After selling mortgages to Fannie Mae or Freddie Mac, mortgage lenders have
“new” cash to provide more mortgage loans. This process worked well for decades until the late 2000s, when
subprime mortgages were given to people who couldn’t afford them. As you know, defaults on these loans were the
underpinnings of the financial crisis.
mortgage-backed securities Securities that represent a claim against the cash flows from a pool of mortgage loans.
We could apply the same concept to any type of loan; indeed, the financial markets have already invented many
such pooled-debt securities. Typical examples include credit card debt, auto loans, home equity loans, and
equipment leases. Like mortgage-backed securities, investors receive interest and principal from asset-backed

http://www.treasurydirect.gov

page 206securities as borrowers pay off their consumer loans. The asset-backed securities market is one of the
fastest-growing areas in the financial services sector.
asset-backed securities Debt securities whose payments originate from other loans, such as credit card debt, auto loans, and home
equity loans.
On the bond’s maturity date, the bondholder receives the par value, which is typically $1,000. However, some
corporate bonds give the bondholder a choice between the par value and a specified number of shares of stock. This
type of bond is referred to as a convertible bond because it can be converted to company stock. The number of shares
of stock for which the bond can be converted is specified when the bond is originally issued. Thus, the bondholder
will want to receive the shares when the stock price has risen since bond issuance, and they will want the $1,000
when the stock has declined in value. Although the bondholder can convert to the stock shares anytime, investors
tend to wait until the maturity date when the interest payments from the bond exceed the dividends that would be
paid from the stock shares.
convertible bond A debt security that can be converted to shares of stock or another type of security.
finance at work //: markets
Mortgage-Backed Securities and Financial Crisis
©Andy Dean Photography/Alamy
In the old days, a bank with $100,000 to lend would fund a mortgage and charge a fee for originating the loan. The bank would then
collect interest on the loan over time. In the past few decades, the process changed to where that bank could sell that mortgage to
investment banks and get the $100,000 back. The bank could then originate another mortgage and collect another fee. Bank revenue
transitioned from interest earnings to fee earnings. This worked pretty well for several decades because the bank made more profits and
more money was funneled into the community for home buyers. It is the securitization of debt that makes this possible. Financial
institutions like Fannie Mae and investment banks bought up these mortgages, pooled them, and issued bonds against them (called
mortgage-backed securities, or MBSs) to sell to investors. In effect, buyers of the MBSs are the actual lenders of the mortgage and
banks simply earned fees for servicing the loans.
Note that this lending model gives banks and mortgage brokers the incentive to initiate as many mortgage loans as they can resell to
maximize fee income. Then in 2000 to early 2004, the Federal Reserve kept adjusting interest rates on federal funds downward and kept
them low. This both made home ownership more affordable, sparking a housing bubble, and drove investors to look for bonds that paid
higher yields. Consequently, many loans were granted to individuals with poor creditworthiness (subprime borrowers). These subprime
borrowers were charged higher interest rates. When these subprime mortgages were packed into the pool of mortgages, the MBSs
offered higher yields. Thus, there was a high demand from investors for these MBSs, which fostered more poor credit quality loan
originations.
Then from July 2004 to July 2006, the Federal Reserve started increasing interest rates. This placed some downward pressure on
housing prices because it made homes less affordable. At the same time, most subprime mortgages originating from 2005 and 2006
were written on adjustable rates, and those interest rates adjusted upward too, making the payments too high for many borrowers. The
subprime borrowers soon began to fall behind on their monthly payments leading to foreclosures and additional downward pressure on
housing prices. The devaluation of housing prices eroded the home equity of homeowners and led to further foreclosures and further
price decreases. The MBSs also devalued quickly.
Who owned MBSs? It turns out that the owners of these securities were financial firms, such as investment banks, commercial

page 207
banks, insurance companies, mutual funds, and pension funds all over the world. Their weakened financial strength led to bank failures,
bailouts, and a global credit crisis.
Want to know more?
Key Words to Search for Updates: subprime, MBS, financial crisis
Further Reading: John W. Schoen, “7 years on from crisis, $150 billion in bank fines and penalties,” CNBC, April 30, 2015.
http://www.cnbc.com/2015/04/30/7-years-on-from-crisis-150-billion-in-bank-fines-and-penalties.html

Reading Bond Quotes LG7-3
To those familiar with bond terminology, bond quotes provide all of the information needed to make informed
investment decisions. The volume of Treasury securities traded each day is substantial. Treasury bonds and notes
average more than a half billion dollars in trading daily. Investors exhibit much less enthusiasm for corporate or
municipal bonds, perhaps because the markets for each particular bond or bonds with the same maturity, coupon
rate, and credit ratings are much thinner and, therefore, less liquid. Most bond quote tables report only a small
fraction of the outstanding bonds on any given day. Bond quotes and data can be found in The Wall Street Journal
and online at places like Yahoo! Finance (finance.yahoo.com). Table 7.2 shows three bond quote examples.
A typical listing for Treasury bonds appears first. Here, this Treasury bond pays bondholders a coupon of 2.750
percent. On a $1,000 par value bond, this interest income would be $27.50 annually, paid as $13.750 every six
months per bond. The bond will mature in February of 2018—since this is fairly soon, the bond is considered a
short-term bond. Both the bid and the ask quotes for the bond appear, expressed as percentages of the bond’s par
value of $1,000. The bid price is the price at which investors can sell the bond. A bid of 104.0156 means that an
investor could sell for $1,040.156. Investors can buy this bond at the ask price of 104.0313, or $1,040.313. Since the
price is higher than the par value of the bond, the bond is selling at a premium to par because its coupon rate is
higher than current rates. Thus, investors call this kind of security a premium bond.
premium bond A bond selling for greater than its par value.
Notice that the ask price is higher than the bid price. The difference is known as the bid-ask spread. Investors buy at
the higher price and sell at the lower price. The bid-ask spread is thus the cost of actively trading bonds. Investors
buy and sell with a bond dealer. Since the bond dealer takes the opposite side of the transaction, the dealer buys at
the low price and sells at the higher price. The bid-ask spread is part of the dealer’s compensation for taking on risk.
An investor who bought this bond and held it to maturity would experience a $40.31 (= $1,040.31 − $1,000) capital
loss (−3.87 percent = −$40.31/$1,040.31]). The bond lost 0.0234 percent of its value during the day’s trading—a
change of −$0.23 for a $1,000 par value bond. Last, the bond is offering investors who purchase it at the ask price
and hold it to maturity a 0.771 percent annual return.
Corporate bond quotes provide similar information. The table shows the quote for a Boeing bond that offers
bondholders a coupon of 2.60 percent, or $13.00 semiannually (= $1,000 × 0.026 ÷ 2). The bond would be
considered a mid-term bond (usually five years to maturity), since it matures in the year 2025. Corporate bonds are
also quoted in percentage of par value. The price quote of 98.400 indicates that the last trade occurred at a price of
$984.00 per bond. Since the bond is selling for a price lower than its $1,000 par value, it’s called a discount bond. An
investor who bought this bond would reap a $16.00 (= $1,000 − $984.00) capital gain if the bond were held to
maturity. The Boeing bond represents an annual return of 2.79 percent for the investor who purchases the bond at
$984.00.
discount bond A bond selling for lower than its par value.
▼ TABLE 7.2 Bond Quote Examples
Treasury Securities

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COUPON RATE MO/YR BID ASKED CHG ASK YLD
2.750 Feb 18 104.0156 104.0313 −0.0234 0.771
Corporate Bond
COMPANY COUPON MATURITY LAST PRICE YIELD
Boeing Co 2.60 October 2025 98.400 2.79
Municipal Bond
ISSUE COUPON MATURITY PRICE BID YLD
NYC Muni Wtr Fin Auth 4.500 06-15-37 97.570 4.66

Companies set a bond’s coupon rate when they originally issue the bond. A number of factors determine that coupon
rate:
The amount of uncertainty about whether the company will be able to make all the payments.
The term of the loan.
The level of interest rates in the overall economy at the time.
Bonds from different companies carry different coupon rates because some, or all, of these determining factors
differ. Even a single company that has raised capital through bond issues many times may carry very different
coupon rates on its various issues, because the bond issues would be offered in different years when the overall
economic condition and interest rates differ.
Table 7.2 also shows a quote for a municipal bond issued by the New York City Municipal Water Finance
Authority. This city government agency has raised capital by issuing municipal bonds to build reservoir facilities to
provide water to New York City. The bond pays a 4.500 percent coupon, and since it matures in 2037, it’s
considered a long-term bond. According to Table 7.2, the bond is trading at a price just below par value—97.57
percent. Most municipal bonds, unlike other bonds, feature a $5,000 face value rather than the typical par value of
$1,000. So, the 97.57 percent price quote represents a dollar amount of $4,878.50 (= 0.9757 × $5,000). The
low rate of return relative to Treasury bonds with similar maturities also has an explanation. Municipal
bondholders do not have to pay federal income taxes on the interest payments that they receive from those securities.
We explore this (sometimes) substantial advantage further in a later section of this chapter.
EXAMPLE
7-3 Bond Quotes LG7-3
For interactive
versions of this
example, log in to
Connect or go to
mhhe.com/CornettM4e.
You note the following bond quotes and wish to determine each bond’s price, term, and interest
payments.
Treasury Securities
MATURITY
RATE MO/YR BID ASKED CHG
9.00 Nov 20 137.5938 137.6250 −0.1563
Corporate Bond

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COMPANY COUPON MATURITY
LAST
PRICE
LAST
YIELD
Kohls Corp 7.375 Oct 15,
2023
110.01 4.991
Municipal Bond
ISSUE COUPON MATURITY PRICE
YLD TO
MAT
Florida St
Aquis &
Bridge
Constr
5.00 July 1,
2025
106.78 4.458
SOLUTION:
The Treasury bond matures in November of 2020 and pays 9 percent interest. Investors receive cash
interest payment of $45 (= 0.09 × $1,000 ÷ 2) semiannually. Since the bond matures in less than 10
years but more than 1 year, we would consider it a mid-term bond. Since no “n” appears next to the
maturity date, we can also tell that the security was issued as a bond that would mature in 30 years.
Investors could sell this bond for $1,375.94 (= 137.594 × $1,000) and buy it for $1,376.25 (= 1.37625
× $1,000). The price fell on this particular day by $1.56 (= −0.001 5625 × $1,000). The dealer earned
$0.31 (× $1,376.25 − $1,375.94) on each trade of these premium bonds.
The Kohls corporate bond pays a semiannual interest payment of $36.88 (= 0.07375 × $1,000 ÷ 2)
and its price is $1,100.10 (= 1.1001 × $1,000). This premium bond’s 7.375 percent rate is likely well
above market rates, which is why an investor would be willing to pay a premium for it.
The state of Florida issued the muni bond to fund bridge construction. With a $5,000 par value, the
interest payments are $125 (= 0.05 × $5,000 ÷ 2) every six months. The bonds are priced at
$5,339.00 (= 1.0678 × $5,000).
Similar to Problems 7-9, 7-10, Self-Test Problem 1
time out!
7-1 Describe the different reasons that the U.S. government, local governments, and corporations would issue bonds.
7-2 What is the following bond’s price and what dollar amount will the bond pay for its semiannual interest payment?
COMPANY COUPON MATURITY PRICE YIELD
Home Depot Inc. 5.40 Mar 1, 2020 100.06 5.391

7.2 • BOND VALUATION LG7-4
Present Value of Bond Cash Flows
Any bond’s value computation directly applies time value of money concepts. Bondholders know the interest
payments that they are scheduled to receive and the repayment of the par value at maturity. The current price of a
bond is, therefore, the present value of these future cash flows discounted at the prevailing market interest rate. The
prevailing market interest rate will depend on the bond’s term to maturity, credit quality, and tax status.
The simplest type of bond for time value of money calculations is a zero coupon bond. As you might guess from its
name, a zero coupon bond makes no interest payments. Instead, the bond pays only the par value payment at its
maturity date. So a zero coupon bond sells at a substantial discount from its par value. For example, a bond with a
par value of $1,000, maturing in 20 years, and priced to yield 6 percent, might be purchased for about $306.56. At
the end of 20 years, the bond investor will receive $1,000. The difference between $1,000 and $306.56 (which is
$693.44) represents the interest income received over the 20 years based upon the discount rate of 6 percent. The
time line for this zero coupon bond valuation appears as
zero coupon bond A bond that does not make interest payments but generally sells at a deep discount and then pays the par value at
the maturity date.
We compute the zero’s price by finding the present value of the $1,000 cash flow received in 20 years. However, to
be consistent with regular coupon-paying bonds, zero coupon bonds are priced using semiannual compounding. So
the formula and calculator valuation would use 40 semiannual periods at a 3 percent interest rate rather than 20
periods at 6 percent. Using the present value equation of Chapter 4 results in
So the zero coupon bond’s price is indeed a steep discount to its par value. This makes sense because investors
would only buy a security that pays $1,000 in many years for a price that is much lower to make enough profit to
make up for the forgone semiannual interest payments. For comparison’s sake, instead of the 20-year zero, consider
a 20-year bond with a 7 percent coupon. So this 20-year maturity bond pays $35 in interest payments every six
months. We can think of these interest payments as an annuity stream. If the market discount rate is 6 percent
annually, the time line appears as

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The time line shows the 40 semiannual payments (with the accompanying semiannual interest rate at 3 percent) of
$35 and the par value payment at the bond’s maturity. Think through this: When bonds pay semiannual
payments, the discount rate must be a semiannual rate. Thus, the 6 percent annual rate becomes a 3 percent
semiannual rate. So we then compute the price of this bond by adding the present value of the interest payment
annuity cash flow to the present value of the future par value. A combination of the present value equations for the
annuity cash flows and the value of the par redemption appear in the bond valuation equation 7-1:
(7-1)
where PMT is the interest payment, N is the number of periods until maturity, and i is the market interest rate per
period on securities with the same bond characteristics. If this bond paid interest annually, then these variables
would take yearly period values. Since this bond pays semiannually, PMT, N, and i are all denoted in semiannual
periods. The price of this coupon bond should be
Of the $1,115.57 bond price, most of the value comes from the semiannual $35 coupon payments ($809.017) and
not the value from the future par value payment ($306.557).
Because equation 7-1 is quite complex, we usually compute bond prices using a financial calculator or computer
program. An investor would compute the bond value using a financial calculator by entering N = 40, I = 3, PMT =
35, FV = 1000, and computing the present value (PV). The calculator solution is $1,115.57.1

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EXAMPLE 7-4 Consider a 15-year bond that has a 5.5 percent coupon, paidsemiannually. If the current market interest rate is 6.5 percent, and the
bond is priced at $940, should you buy this bond?
For interactive versions
of this example, log in
to Connect or go to
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SOLUTION:
Compute the value of the bond using equation 7-1. Use semiannual
compounding (N = 2 × 15 = 30, i = 6.5 ÷ 2 = 3.25, and PMT = 0.055 ×
$1,000 ÷ 2 = $27.50) as
So this bond’s value is $905.09, which is less than the $940 price. The
bond is overvalued in the market and you should not buy it.
Similar to Problems 7-21, 7-22, 7-23, 7-24, Self-Test Problem 1

the Math Coach on…
Bond Pricing and Periods
“Since most bonds have semiannual interest payments, we must use semiannual periods to discount the
cash flows. Most errors in computing a bond price occur in the adjustment for semiannual periods. The errors
happen whether you are using either the bond pricing equation or a financial calculator. To convert to
semiannual periods, be sure to adjust the three variables: number of periods, interest rate, and payments.
The number of years needs to be multiplied by 2 for the number of semiannual periods. The interest rate
should be divided by 2 for a six-month rate. Divide the annual coupon payment by 2 for the six-month
payment. Remember to adjust all three inputs for the semiannual periods.
A coupon-paying bond’s price should hover reasonably around the par value of the bond. For a $1,000 par
value bond, we could expect a price in the range of $700 to $1,300. If you compute a price outside this range,
check to see whether you made the semiannual period adjustments correctly.„
Bond Prices and Interest Rate Risk LG7-5
At the time of purchase, the bond’s interest payments and par value expected at maturity are fixed and known. Over
time, economywide interest rates change, but the bond’s coupon rate remains fixed. A rise in prevailing interest rates
(also called increasing the discount rate) reduces all bonds’ values. If interest rates fall, all bonds will enjoy rising
values. Consider that when interest rates rise, newly issued bonds offer to pay higher interest rates than the rates
offered on existing bonds. So to sell an existing bond with its lower coupon rate, its market price must fall so that
the buyer can expect a profit similar to that offered by newly issued bonds. Similarly, when prevailing interest rates
fall, market prices for outstanding bonds rise to bring the offered return on older bonds with higher coupon rates into
line with new issues. So market interest rates and bond prices are inversely related. That is, they move in opposite
directions.
Figure 7.2 demonstrates how the price of a 30-year Treasury bond may change over time. The 7.47 percent coupon

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exactly matched prevailing interest rates when the bond was issued in 1986. Consequently, the bond sells for its par
value of $1,000. Shortly thereafter, interest rates quickly rose to over 9 percent. As interest rates rose, bond prices
had to decline. Then in 1988, interest rates started a prolonged descent to lows not seen for decades. Note that while
a bond is issued at $1,000 and returns $1,000 at maturity, its price can vary a great deal in between. Bond investors
must be aware that bond prices fluctuate on a day-to-day basis as interest rates fluctuate. Note that since the bond
will only pay $1,000 when it matures, the price must converge to $1,000 at the end. The determinants of market
interest rate levels and changes are discussed in Chapter 6. Bondholders can incur large capital gains or capital
losses.
The fact that, as prevailing interest rates change, the prices of existing bonds will change has a specific name in the
financial industry—interest rate risk. Interest rate risk means that during periods when interest rates change
substantially (and quickly), bondholders experience distinct gains and losses in their bond inventories. But interest
rate risk does not affect all bonds exactly the same. Very short-term bonds experience little or no fluctuation in their
prices, and thus expose the bondholder to little interest rate risk. Long-term bondholders experience substantial
interest rate risk. Table 7.3 illustrates the impact of interest rate risk on bonds with different coupons and times to
maturity.
interest rate risk The chance of a capital loss due to interest rate fluctuations.
The first four rows show the prices and price changes for 30-year bonds with different coupon rates. Notice that the
bonds with higher coupon rates also have higher prices. Bondholders as a rule find it more valuable to receive the
large annuity payments. Also notice that a 1 percent increase in interest rates from 6 percent to 7 percent causes
bond prices to fall. Bondholders with higher coupon bonds are not affected as much by interest rate increases
because they can take the large coupon payments and reinvest those cash flows in new bonds that offer higher
returns.

FIGURE 7-2 A Demonstration of the Price and Market Interest Rate over Time of a 30-Year Treasury Bond Issued in 1986 with a Coupon
of 7.47 Percent
As interest rates rise, bond prices fall. Here you can see great variance in the economy over 30 years. Long-term bondholders experience
substantial interest rate risk.
Source: Yahoo! Finance, finance.yahoo.com.
▼ TABLE 7.3 Interest Rate Risk

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The price decline is greater for bonds with lower coupons because of reinvestment rate risk. When interest rates
increase, bondholders’ cash flows—both periodic payments and final payoff at maturity—are discounted at a higher
rate, decreasing a bond’s value. Because the cash flows from low-coupon bonds are smaller, the holder of such
bonds will have less money available from interest payments to buy the new, higher coupon bonds. Thus
bondholders of lower coupon bonds have their capital tied up in assets that are not making them as much money.
They face a bad dilemma: They can sell their lower coupon bonds and take a greater capital loss, using the (smaller)
proceeds to buy new bonds with higher coupon rates. Or they can continue to receive the small income payments
and hold their lower coupon bonds to maturity to avoid locking in the capital loss. Either way, they lose money
relative to those bondholders with higher coupon rates. You can see this illustrated in the 30-year bonds shown in
Table 7.3. Reinvestment rates tend to help partially offset changing discount rates for higher coupon paying bonds.
reinvestment rate risk The chance that future interest payments will have to be reinvested at a lower interest rate.

EXAMPLE 7-5
Capital Gains in the Bond
Market LG7-5
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Say that you anticipate falling long-term interest rates from 6 percent to
5.5 percent during the next year. If this occurs, what will be the total
return for a 20-year, 6.5 percent coupon bond through the interest rate
decline?
SOLUTION:
To determine the total return, compute the capital gain or loss and the
interest paid over the year. The capital gain or loss is determined from
the change in price. The current bond price is

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The price in one year would be
So, the capital gain is $59.18 (= $1,116.97 − $1,057.79). The interest
payment during the year is $65 (= 0.065 × $1,000). If interest rates fall
to 5.5 percent, then this bond should provide a total return of $124.18,
which would be an 11.74 percent return (= $124.18 ÷ $1,057.79). Of
course, this is only an anticipated interest rate change and it may not
occur.
Similar to Problems 7-25, 7-26, 7-35, 7-36, Self-Test Problem 5
Another factor that influences the amount of reinvestment risk bondholders face is their bonds’ time to maturity. The
last four bonds in the table all have a 5 percent coupon but have different times to maturity. Note that when interest
rates increase, the bond prices of longer-term bonds decline more than shorter-term bonds. This shows that bonds
with longer maturities and lower coupons have the highest interest rate risk. Short-term bonds with high coupons
have the lowest interest rate risk. High interest rate risk bonds experience considerable price declines when interest
rates are rising. However, these bonds also experience dramatic capital gains when interest rates are falling. While a
1 percent change in market interest rates is not commonly seen on a daily or monthly basis, such a change is not
unusual over the course of several months or a year.
time out!
7-3 Show the time line and compute the present value for an 8.5 percent coupon bond (paid semiannually) with 12 years left
to maturity and a market interest rate of 7.5 percent.
7-4 Describe the relationship between interest rate changes and bond prices.
7.3 • BOND YIELDS LG7-6
Current Yield
Although we speak about “the prevailing interest rate,” bond relationships reflect many interest rates (also called
yields). Some rates are difficult to calculate but accurately reflect the return the bond is offering. Others, like the
current yield, are easy to compute but only approximate the bond’s true return. A bond’s current yield is defined as
the bond’s annual coupon rate divided by the bond’s current market price. Current yield measures the rate
of return a bondholder would earn annually from the coupon interest payments alone if the bond were
purchased at a stated price. Current yield does not measure the total expected return because it does not account for
any capital gains or losses that will occur from purchasing the bond at a discount or premium to par.
current yield Return from interest payments; computed as the annual interest payment divided by the current bond price.
Yield to Maturity
Yield to maturity is a more meaningful equation for investors than the simple current yield calculation. The yield to

maturity calculation tells bond investors the total rate of return that they might expect if the bond were bought at a
particular price and held to maturity. While the yield to maturity calculation provides more information than the
current yield calculation, it’s also more difficult to compute, because we must compute the bond’s cash flows’
internal rate of return. This calculation seeks to equate the bond’s current market price with the value of all
anticipated future interest and par value payments. In other words, it is the discount rate that equates the present
value of all future cash flows with the current price of the bond. To calculate yield to maturity, investors must solve
for the interest rate, i, in equation 7-2, or solve for i in
yield to maturity The total return the bond offers if purchased at the current price and held to maturity.
(7-2)
Investors commonly compute the yield to maturity using financial calculators. For example, consider a 7 percent
coupon bond (paid semiannually) with eight years to maturity and a current price of $1,150. The return that the bond
offers investors, the yield to maturity, is computed as N = 16, PV = −1150, PMT = 35, and FV = 1000. Computing
the interest rate (i) gives us 2.363 percent. We must remember, however, that 2.363 percent is only the return for six
months because the bond pays semiannually. Yield to maturity always means an annual return. So, this bond’s yield
to maturity is 4.73 percent (2 × 2.363 percent).
Notice the link between a bond’s yield to maturity and the prevailing market interest rates used to determine a
bond’s price as we discussed in the previous section. We use the market interest rate to compute the bond’s value.
We use the actual bond price to compute its yield to maturity. If the bond is correctly priced at its economic value,
then the market interest rate will equal the yield to maturity. Thus, the relationship that we previously identified
between bond prices and market interest rates applies to yields as well. This shows the inverse relationship between
bond prices and bond yields. As a bond’s price falls, its yield to maturity increases and a rising bond price
accompanies a falling yield. Look back at Figure 7.2 and you will see this relationship clearly.
EXAMPLE 7-6
Computing Current Yield and
Yield to Maturity LG7-6
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
You have identified a 3.5 percent Treasury bond with four years left to
maturity and a quoted price of 96.281. Calculate the bond’s current
yield and yield to maturity.
SOLUTION:
(1) First, identify that the bond’s price is $962.81 (= 96.281% × $1,000 =
0.96281 × $1,000).
(2) The annual $35 in interest payments is paid in two $17.50 semiannual
payments. Therefore, the current yield of the bond is 3.64 percent (=
$35 ÷ $962.81).
(3) The yield to maturity is computed using equation 7-2 and the financial
calculator as N = 8, PV = −962.81, PMT = 17.50, and FV = 1,000.
Computing the interest rate (/) results in 2.263 percent and multiplying
by 2 gives the yield to maturity of 4.53 percent.
(4) Note that the current yield is less than the yield to maturity because it
does not account for the capital gain to be earned if held to maturity.
Similar to Problems 7-13, 7-14, 7-27, 7-28, Self-Test Problem 2

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the Math Coach on…
Bond Yields and Financial Calculators
“People computing a bond’s yield to maturity make three common mistakes. To avoid the first mistake,
ensure that the bond price (PV) is a different sign than the interest and par value cash flows (PMT and FV).
The second mistake: People forget to make the number of periods (N) and the per-period interest payment
(PMT) consistent. Both should be in semiannual terms if the coupon payment is paid semiannually. Last,
many people forget to multiply the resulting calculator interest rate (I) output by 2 to convert the semiannual
rate back to an annual rate.„
Yield to Call
The yield to maturity computation assumes that the bondholder will hold the bond to its maturity. But remember that
some bonds have call provisions that allow the issuers to repay the bondholder’s par value prior to its scheduled
maturity. Issuers often call bonds after large drops in market interest rates. In such cases, issuers commonly pay
bondholders the bond’s par value plus one year of interest payments. The reasons behind early bond redemptions are
obvious. When interest rates fall, issuers can sell new bonds at lower interest rates. Companies want to refinance
their debt—just as homeowners do—to reduce their interest payments.
Issuers gain important advantages with call provisions because they allow refinancing opportunities. Of course, the
same provisions are disadvantages for bond investors. When bonds are called, investors receive the par value and
call premium, but then investors must seek equally profitable bonds to buy with the proceeds. You will recall that
investors can face reinvestment risk—the available bonds aren’t as profitable because interest rates have declined.
Bonds are called away at the worst time for investors. In addition, bond prices will rise as market interest rates fall,
which could provide issuers opportunities to sell the bonds at a profit. But the price increases will be limited by the
fact that the bond will likely be called early. As partial compensation, bond investors receive the call price, which is
the par value of the bond plus the call premium (typically one year of interest payments). The possibility that bonds
can be called early dampens their upside price potential. We can even compute the price of a bond that’s likely to be
called from the equation
(7-3)
In this case, N is the number of periods until the bond can be called and i is the prevailing market rate. The
prevailing market interest rate will probably differ from the rate for a noncallable bond. The previous section
demonstrated via the yield curve that bonds with different maturities have different yields. A bond that matures in 20
years, but is likely to be called in 5 years, will carry a yield appropriate for a five-year bond.
Now, reconsider the 20-year bond with a 7 percent coupon that we discussed previously. If the bond can be called in
five years with a call price of $1,070, the appropriate discount rate happens to be 5.75 percent annually at
that time (instead of the 6 percent in the original problem). This time line would be

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The changes in this time line are only 10 semiannual payments of $35 (rather than 40 such semiannual payments), a
2.875 percent semiannual discount rate, and the call price payment of $1,070. The price of this callable bond would
be
the Math Coach on…
Spreadsheets and Bond Pricing
“Common spreadsheet programs have functions that can compute the price or yield to maturity of a bond.
The functions are
Compute a bond price = PRICE(settlement,maturity,rate,yld,redemption,frequency,basis)
Compute a yield to maturity = YIELD(settlement,maturity,rate,pr,redemption,frequency,basis)
Settlement is the bond’s settlement date. This is the purchase date of the bond; typically it is today. Maturity is
the bond’s maturity date. Rate is the bond’s annual coupon rate. Pr is the bond’s price per $100 face value.
Note that the par value of a bond is typically $1,000, so an adjustment is needed for this input. Redemption is
the bond’s redemption value per $100 face value. Frequency is the number of coupon payments per year. For
semiannual, frequency = 2. Basis is the type of day count basis to use.
Consider the bond valuation problem of Example 7-4. The spreadsheet solution is the same as the TVM
calculator solution and the pricing equation.
Also consider the yield to maturity problem in Example 7-6. This spreadsheet solves for the yield to maturity.
See this textbook’s online student center to watch instructional videos on using spreadsheets. Also note that
the solutions for all the examples in the book are illustrated using spreadsheets in videos that are also
available on the textbook website.„

In this example, the callable bond would be priced at $1,106.38, which is slightly lower than an identical bond that

was not callable, priced at $1,115.57.
If a bond is likely to be called, then the yield to maturity calculation does not give investors a good estimate of their
return. Bondholders can use instead a yield to call calculation, which differs from the yield to maturity only in that its
calculation assumes that the investor will receive the par value and call premium at the earliest call date. For
example, reconsider the 7 percent coupon bond (paid semiannually) with eight years to maturity, which we
examined previously. The current bond price is $1,130 (which is slightly lower than the yield to maturity bond price
of $1,150). If the bond can be called in three years at a specific call price of the par value plus one annual coupon,
then what is the yield to call? The yield to call is computed as N = 6, PV = −1130, PMT = 35, and FV = 1070. The
resulting interest rate (i) is 2.26 percent. The yield to call for this bond is thus 4.52 percent (= 2 × 2.26%).
yield to call The total return that the bond offers if purchased at the current price and held until the bond is called.
Municipal Bonds and Yield
Municipal bonds (munis) seem to offer low yields to maturity compared to the return that corporate bonds and
Treasury securities offer. Munis offer lower rates because the interest income they generate for investors is tax-
exempt—at least at the federal level.2 Specifically, income from municipal bonds is not subject to taxation by the
federal government or the state government where the bonds are issued. As a result, municipal bond investors
willingly accept lower yields than those they can obtain from taxable bonds. Generally speaking, investors compare
the after-tax interest income earned on taxable bonds against the return earned on municipal bonds. For example,
suppose an investor in the 35 percent marginal income tax bracket has $100,000 to invest in either corporate or
municipal bonds. The $100,000 investment would earn a taxable $7,000 annually from 7 percent corporate bonds or
$5,000 from tax-exempt 5 percent municipal bonds. After taxes, the corporate bond leaves the investor with $4,550
[=(1 − 0.35) × $7,000]. Obviously, this is less than the tax-free income of $5,000 generated by the muni bond.
A common way to compare yields from muni bonds versus those from taxable bonds is to convert the yield to
maturity of the muni to a taxable equivalent yield, as shown in equation 7-4.
(7-4)
taxable equivalent yield Modification of a municipal bond’s yield to maturity used to compare muni bond yields to taxable bond yields.
EXAMPLE 7-7
Which Bond Has a Better After-
Tax Yield? LG7-6
For interactive versions
of this example, log in
to Connect or go to
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Imagine a time when you have a high income, placing you in the 31
percent marginal tax bracket. You are interested in investing some
money in a bond issue and have three alternatives. The first is a
corporate bond with a 6.4 percent yield to maturity. The second bond is
a Treasury that offers a 5.7 percent yield. The third choice is a
municipal bond priced at a yield to maturity of 4.0 percent. Which bond
gives you the highest after-tax yield?
SOLUTION:
The Treasury and corporate bonds are both taxable, so we can
compare them directly with each other. The yield of 6.4 percent on the
corporate is clearly higher than the 5.7 percent yield offered by the
Treasury bond. To include a comparison with the nontaxable municipal
bond, compute its equivalent taxable yield as in equation 7-4:

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The municipal bond’s equivalent taxable yield of 5.80 percent is higher
than the Treasury but lower than the corporate bond.
Similar to Problems 7-15, 7-16, 7-31, 7-32, 7-37, 7-38, Self-Test
Problem 3

For high-income investors (in the 35 percent marginal tax bracket) a 5 percent muni bond has an equivalent taxable
yield of 7.69 percent = 0.05 ÷ (1 − 0.35)]. The 5 percent muni is more attractive for this investor than a 7 percent
corporate bond. However, for an investor with lower income (in the 28 percent marginal tax bracket) the equivalent
taxable yield is only 6.94 percent. The corporate bond provides more after-tax profit than the muni for this investor.
It’s easy to see why muni bonds are popular among high-income investors (those with substantial marginal tax
rates).
Summarizing Yields
In this section, we have presented several different types of interest rates, or yields, associated with bonds. See a
summary in Table 7.4. Many of these yields relate to one another. Consider the bonds and associated yields reported
in Table 7.5. Treasury bonds (1) to (3) show how coupon rates, current yield, and yield to maturity relate. When a
bond trades at its par value (usually $1,000), then the coupon rate, current yield, and yield to maturity are all the
same. When that bond is priced at a premium (bond 2), then both the current yield and the yield to maturity will be
lower than the coupon rate. They are both higher than the coupon rate when the bond trades at a discount. Notice
that yield to maturity is higher than current yield for discount bonds, and that yield to maturity is lower than current
yield for premium bonds. In other words, the current yield always lies between the coupon rate and the yield to
maturity. Both the current yield and the yield to maturity move in the opposite direction to the bond’s price.
Bonds (4) to (6) are callable corporate bonds. Recall that all the yields (current yield, yield to maturity, and yield to
call) are identical when the bond trades at par value. When interest rates fall and bond prices increase, as with bond
(5), the issuing corporation has a strong incentive to call the bond after five years, as allowed in the indenture
agreement. So investors should base their purchase decisions on the yield to call. When interest rates increase, bond
prices decline (as bond (6) shows). In this case, investors could compute the yield to call (as shown), but the
information isn’t useful because the company will not likely call the bond while interest rates are high.

▼ TABLE 7.4 Summary of Interest Rates
Interest
Rate Purpose Description
Coupon
rate
Compute
bond cash
interest
payments
The coupon rate is reported as a bond characteristic. It is reported as a percentage
and is multiplied by the par value of the bond to determine the annual cash interest
payment. The coupon rate will not change through the life of the bond.
Current
yield
Quick
assessment
of the interest
rate a bond is
offering
Computed as the annual interest payment divided by the current price of the bond. It
measures the return to be expected from just the interest payments if the bond was
purchased at the current price. Since the bond price may change daily, the current
yield will change daily.
Yield to
maturity
Accurate
measurement
of the interest
rate a bond is
offering
The return offered by the bond if purchased at the current price. This return includes
both the expected income and capital gain/loss if held to the maturity date. The yield
to maturity will change daily as the bond price changes.
Interest rate

Yield to
call
obtained if the
bond is called
Same as the yield to maturity except that it is assumed that the bond will be called at
the earliest date it can be called.
Taxable
equivalent
yield
Comparison
of nontaxable
bond yields to
taxable bond
yields
Investors must pay taxes on most types of bonds. However, municipal bonds are tax
free. To compare the muni’s nontaxable yield to maturity to that of taxable bonds,
divide the yield by one minus the investor’s marginal tax rate.
Market
interest
rate
Comparison
of prices of all
bonds
The interest rate determined by the bond prices of actual trades between buyers and
sellers. The market interest rate will be different for bonds of different times to
maturity and different levels of risk.
Total
return
Determine
realized
performance
of an
investment
Realized return that includes both income and capital gain/loss profits.
▼ TABLE 7.5 Price, Coupon, and Yield Relationships of a 10-Year Bond
Call price = Par value + One year’s interest
The last three bonds shown in the table are municipal bonds. Recall that these bonds typically offer lower yields
because the income from munis is tax exempt. It is easier to compare municipal bonds with Treasuries and corporate
bonds if you compute the municipal bond’s taxable equivalent yield first. Here, we use a marginal tax rate of 35
percent in the calculation. The last column of the table shows that the taxable equivalent yield of the municipal
bonds is really quite competitive with corporate bond yields. Any investor with income taxed at the 35 percent
marginal tax bracket would prefer the municipal bond over the corporate bond if the muni’s taxable equivalent yield
is higher than the yield to maturity (or yield to call) of the corporate bond.
The table also shows that Treasury securities offer lower yields than corporate bonds with similar terms to maturity.
The difference (or spread) between Treasury and corporate yields gives rise to a discussion of bond credit risk,
which follows.
time out!
7-5 Calculate the yield to maturity for a zero coupon bond with a price of $525 and 10 years left to maturity.
7-6 Which is higher for a discount bond, the yield to maturity or the coupon rate? Why?
7.4 • CREDIT RISK LG7-7

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Bond Ratings
Will a bond issuer make the promised interest and par value payments over the next 10, 20, or even 30 years? Credit
quality risk is the chance that the bond issuer will not be able to make timely payments. To assess this risk,
independent bond rating agencies, such as Moody’s and Standard & Poor’s, monitor corporate, U.S. agency, or
municipal developments during the bond’s lifetime and report their findings as a grade or rating. The U.S.
government issues the highest credit quality debt, though that consensus has recently come into doubt as the U.S.
debt and budget deficit have ballooned.
credit quality risk The chance that the issuer will not make timely interest payments or even default.
bond rating A grade of credit quality as reported by credit rating agencies.
The primary “big three” bond credit rating agencies in the United States include Moody’s Investors Service,
Standard & Poor’s Corporation, and Fitch IBCA Inc. Each of these credit analysis firms assigns similar ratings
based on detailed analyses of issuers’ financial condition, general economic and credit market conditions, and the
economic value of any underlying collateral. The Standard & Poor’s ratings are shown in Table 7.6. Their
highest credit quality rating is AAA. Bonds rated AAA, AA, A, or BBB are considered investment grade
bonds. The issuers of these securities have the highest chance of making all interest and par value payments
promised in the indenture agreement.
investment grade High credit quality corporate bonds.
▼ TABLE 7.6 Standard & Poor’s Bond Credit Ratings
Credit Risk
Credit
Rating Description
Investment Grade
Highest
quality
AAA The obligor’s (issuer’s) capacity to meet its financial commitment on the obligation is
extremely strong.
High
quality
AA The obligor’s capacity to meet its financial commitment on the obligation is very strong.
Upper
medium
grade
A
The obligor’s capacity to meet its financial commitment on the obligation is still strong,
though somewhat susceptible to the adverse effects of changes in circumstances and
economic conditions.
Medium
grade BBB
The obligor exhibits adequate protection. However, adverse economic conditions or
changing circumstances are more likely to lead to a weakened capacity to meet its financial
commitment.
Below Investment Grade
Somewhat
speculative BB
Faces major ongoing uncertainties or exposure to adverse business, financial, or economic
conditions which could lead to the obligor’s inadequate capacity to meet its financial
commitment.
Speculative B Adverse business, financial, or economic conditions will likely impair the obligor’s capacity or
willingness to meet its financial commitment.
Highly
speculative
CCC Currently vulnerable to nonpayment, and is dependent upon favorable business, financial,
and economic conditions for the obligor to meet its financial commitment.
Most
speculative
CC Currently highly vulnerable to nonpayment.
Imminent
default
C Bankruptcy petition has been filed or similar action taken, but payments on this obligation
are being continued.
Default D Obligations are in default or the filing of a bankruptcy petition has occurred and payments
are jeopardized.
Source: Standard & Poor’s.
The investment community considers bonds rated BB and below to be below-investment grade bonds, and some
investors, such as pension funds or other fiduciaries, cannot purchase these securities for their portfolios. These

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bonds are considered to be speculative because they carry a significant risk that the issuer will not make current or
future payments. Speculative bonds are sometimes called junk bonds because of this risk. In order to attract buyers,
issuers sell these bonds at a considerable discount from par and a high associated yield to maturity. Agencies often
enhance ratings from “AA” to “CCC” with the addition of a plus (+) or minus (−) sign to show relative standing
within the major rating categories. For example, the Greek government saw its bonds upgraded from CCC+ to B−
by Standard & Poor’s on January 22, 2016. The next week, Standard and Poor’s downgraded Dutch Shell Plc from
AA− to A+. These rating changes impact not only the current prices of these bonds, but also the interest rate Greece
and Royal Dutch Shell would have to pay if they issued new bonds.
junk bonds Low credit quality corporate bonds, also called speculative bonds or high-yield bonds.
Standard & Poor’s signals that it’s considering a rating change by placing an individual bond, or all of a given
issuer’s bonds, on CreditWatch (S&P). Rating agencies make their ratings information available to the public
through their ratings information desks. In addition to published reports, ratings are made available in many public
libraries and over the Internet.
Credit rating agencies conduct general economic analyses of companies’ business and analyze firms’ specific
financial situations. A single company may carry several outstanding bond issues. If these issues feature
fundamental differences, then they may have different credit level risks. For example, unsecured corporate bonds, or
debentures, are backed only by the reputation and financial stability of the corporation. A senior bond has a priority
claim over junior (more recently issued) securities in the event of default or bankruptcy. So, senior bonds
carry less credit risk than junior bonds. Some bonds are secured with collateral. When you buy a car using
a loan, the car is collateral for that loan. If you don’t make the loan payments, the bank will repossess the car.
Companies can also offer collateral when issuing bonds. When a firm uses collateral such as real estate or factory
equipment, the bonds are called mortgage bonds or equipment trust certificates, respectively. Bonds issued with no
collateral generally carry higher credit risk.
unsecured corporate bonds Corporate debt not secured by collateral such as land, buildings, or equipment.
debentures Unsecured bonds.
senior bonds Older bonds that carry a higher claim to the issuer’s assets.
mortgage bonds Bonds secured with real estate as collateral.
equipment trust certificates Bonds secured with factory and equipment as collateral.
Credit Risk and Yield
Investors will only purchase higher risk bonds if those securities offer higher returns. Therefore, issuers price bonds
with high credit risk to offer high yields to maturity. So another common name for junk bonds is high-yield bonds.
Differences in credit risk are a prime source of differences in yields between government and various corporate
bonds. Figure 7.3 shows the historical average annual yields for long-term Treasury bonds and corporate bonds with
credit ratings of Aaa and Baa since 1980. Riskier low-quality bonds always offer a higher yield than the higher
quality bonds. However, the yield spread between high- and low-quality bonds varies substantially over time. The
yield difference between Baa bonds and Treasuries was as high as 3.7 percent and 3.3 percent in 1982 and 2003,
respectively. The spread has been as narrow as 1.3 percent and 1.4 percent in 1994 and 2006, respectively.
high-yield bonds Bonds with low credit quality that offer a high yield to maturity, also called junk bonds.
How do some corporations’ debt obligations become junk bonds? Some companies that aren’t economically sound
or those that use a high degree of financial leverage issue junk bonds. In other cases, financially strong companies
issue investment grade bonds and then, over time, begin to have trouble. Eventually a company’s bonds can be
downgraded to junk status. For example, General Motors (GM) bonds were considered of the highest quality from
the 1950s through the 1980s and much of the 1990s. On May 9, 2005, Standard & Poor’s downgraded GM bonds to
junk status. Junk bonds that were originally issued at investment grade status are called fallen angels. GM eventually
filed for bankruptcy protection in June 2009. By 2016, its credit rating was at the lowest end of investment grade
(BBB−).
FIGURE 7-3 Yield to Maturity on Long-Term Bonds of Different Credit Risk, 1980–2015

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Looking at the historical yields for long-term Treasury and corporate bonds, notice how the yield spread between high- and low-quality bonds
varies substantially over time.

finance at work //: markets
A Greek Tragedy: Debt Crisis
©Max Shen/Getty Images
Greece joined the European monetary union in 2000, which means the euro replaced drachmas as the national currency. The euro was
a much stronger currency than the drachma because it was backed by the economic prosperity of the whole European Union. Hence,
the Greek government was able to borrow from foreign investors at much lower interest rates. This contributed to the ensuing economic
boom and expansion of government spending in Greece.
The Greek government has long been operating on high budget deficits and borrowing. But the problems really began in the Fall of
2009 when the new elected government found that it had inherited a financial burden that was much larger than previously reported. The
budget deficit was revised to be larger than 13 percent of the size of the economy. The revelation of these huge government deficits and
debts cast enormous doubt on the ability of the Greek government to pay its debts.
This increase in risk was reflected on December 8, 2009, by the downgrade to BBB (lowest in the Euro Zone) of the Sovereign bond
of Greece by the Fitch credit rating firm. Standard & Poor’s and Moody’s both downgraded Greece Sovereigns to junk bond status in
May and June of 2010. As a consequence, Greece found that it was difficult to borrow more money and had to offer lenders yields of as
much as 12 percent and a financial crisis developed.
In order to restore investor confidence, the Greek government has pledged to an austerity plan that cuts spending and reduces the
budget deficit. However, the success of the plans has been undermined by strong domestic opposition as illustrated by strikes and even

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riots. As a temporary solution, the European Union and the International Monetary Fund together offered a large loan package to help
out Greece. This calmed the bond market and Greek bond yields fell, but they are still high. Unfortunately, the severe economic
depression in Greece has caused further problems with its ability to pay its debt. In 2011 and 2012, Greece enacted several bond
restructurings which mandated changes in the terms. They are considered selective bond defaults. In June of 2015, Greece became the
first developed country to miss an International Monetary Fund loan repayment.
Want to know more?
Key Words to Search for Updates: Greek bonds, Greek debt crisis
time out!
7-7 Explain why a change in a bond’s credit rating will cause its price to change.
7-8 One company has issued two bond classes. One issue is a mortgage bond and the other is a debenture. Which issue will
have a higher bond rating and which will offer a higher yield?
Bonds that experience credit-rating downgrades must offer a higher yield. As all the future cash flows are fixed, the
bond price must fall to create a higher yield to maturity. Alternatively, bonds that are upgraded experience price
increases and yield decreases. Bond upgrades often occur during strong economic periods because corporate issuers
tend to perform better financially at these times. In a weak economy, high-yield bonds lose their luster because the
default risk rises. More credit downgrades occur during economic recessions. In general, any event that impacts the
likelihood of a firm paying back the interest payments and principle it owes will impact its credit risk. Credit risk is
a determinant of the discount rate. The discount rate is also influenced by macroeconomic factors, like decisions by
the Federal Reserve Board. A change in the discount rate directly changes the value of the bond. Therefore,
company performance, strength of the economy, and monetary policy all affect bond values.
7.5 • BOND MARKETS LG7-8
The majority of trading volume in the bond market occurs in a decentralized, over-the-counter market. Most trades
occur between bond dealers and large institutions (like mutual funds, pension funds, and insurance companies).
Dealers bid for bonds that investors seek to sell and offer bonds from their own inventory when investors
want to buy. This is especially true for the very active Treasury securities market. However, a small
number of corporate bonds are listed on centralized exchanges.
FIGURE 7-4 Most Active Investment Grade Bonds, February 5, 2016
This is an example of the most actively traded investment bonds for a given day.
Source: The New York Times, http://markets.on.nytimes.com/research/markets/bonds/bonds.asp

http://markets.on.nytimes.com/research/markets/bonds/bonds.asp


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The NYSE operates the largest centralized U.S. bond market. The majority of bond volume at the NYSE is in
corporate debt. The most actively traded investment grade bonds for the day are shown in Figure 7.4. Even the most
active corporate bonds experience relatively low trading volume. Note that some of the bonds traded are short-term,
like Anadarko Pete Corp and JPMorgan Chase & Co. Other bonds have many years to maturity, like the Anheuser-
busch Inbev bond that matures in February 2046. Most of the ones shown are premium bonds (price greater than par
value), while one is a discount bond.
Following the Bond Market
The entire bond market encompasses a wide variety of securities with varying credit quality from different issuers.
Large differences also arise among bonds in terms of their characteristics such as term to maturity and size of the
coupon. The biggest factor associated with changes in bond prices is changes in interest rates. So, one common way
to describe the direction of bond prices is simply to report the change in interest rates, since we know that interest
rate changes will affect all bonds the same way. The interest rate referenced is the yield to maturity and daily yield
change for the 10-year Treasury. Knowing how this interest rate changed today gives bond investors a good idea of
the general price movement of all types of bonds.
Bond indexes track specific segments of the bond market. Various securities firms, such as Barclays Capital or
Merrill Lynch, maintain these indexes that capture bond price and yield changes in particular segments. You can
find information about major bond indexes on the Internet and in publications like The Wall Street Journal (both in
print and online). Figure 7.5 shows indexes that track bonds by type of issuer (federal government, corporation, local
government, etc.) and time to maturity (short, intermediate, and long).
time out!
7-9 Why can we use various interest rates to describe the performance of the entire bond market?
7-10 What bond segments are measured by which bond indexes?

FIGURE 7-5 Major Bond Indexes as Reported in The Wall Street Journal and on the Internet, February 5, 2016

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Here are indexes that track bonds by type of issuer (federal government, corporation, local government, etc.) and time to maturity (short,
intermediate, and long).
Source: The Wall Street Journal Online. Tracking Bond Benchmarks web page.

Get Online
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Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. What does a call provision allow issuers to do, and why would they do it? (LG7-1)
2. List the differences between the new TIPS and traditional Treasury bonds. (LG7-2)
3. Explain how mortgage-backed securities work. (LG7-2)
4. Provide the definitions of a discount bond and a premium bond. Give examples. (LG7-3)
5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero
coupon bond. (LG7-4)
6. All else equal, which bond’s price is more affected by a change in interest rates, a short-term bond or a longer-
term bond? Why? (LG7-5)
7. All else equal, which bond’s price is more affected by a change in interest rates, a bond with a large coupon or
a small coupon? Why? (LG7-5)?
8. Explain how a bond’s interest rate can change over time even if interest rates in the economy do not change.
(LG7-5)
9. Compare and contrast the advantages and disadvantages of the current yield computation versus yield to
maturity calculations. (LG7-6)

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10. What is the yield to call and why is it important to a bond investor? (LG7-6)
11. What is the purpose of computing the equivalent taxable yield of a municipal bond? (LG7-6)
12. Explain why high-income and wealthy people are more likely to buy a municipal bond than a corporate bond.
(LG7-6)
13. Why does a Treasury bond offer a lower yield than a corporate bond with the same time to maturity?
Could a corporate bond with a different time to maturity offer a lower yield? Explain. (LG7-7)
14. Describe the difference between a bond issued as a high-yield bond and one that has become a “fallen angel.”
(LG7-7)
15. What is the difference in the trading volume between Treasury bonds and corporate bonds? Give examples
and/or evidence. (LG7-8)

Problems
BASIC PROBLEMS
7-1 Interest Payments Determine the interest payment for the following three bonds: 3½ percent coupon
corporate bond (paid semiannually), 4.25 percent coupon Treasury note, and a corporate zero coupon bond
maturing in 10 years. (Assume a $1,000 par value.) (LG7-1)
7-2 Interest Payments Determine the interest payment for the following three bonds: 4½ percent coupon
corporate bond (paid semiannually), 5.15 percent coupon Treasury note, and a corporate zero coupon bond
maturing in 15 years. (Assume a $1,000 par value.) (LG7-1)
7-3 Time to Maturity A bond issued by Ford on May 15, 1997, is scheduled to mature on May 15, 2097. If
today is November 16, 2014, what is this bond’s time to maturity? (LG7-1)
7-4 Time to Maturity A bond issued by IBM on December 1, 1996, is scheduled to mature on December 1,
2096. If today is December 2, 2015, what is this bond’s time to maturity? (LG7-1)
7-5 Call Premium A 6 percent corporate coupon bond is callable in five years for a call premium of one year
of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer
calls the bond? (LG7-1)
7-6 Call Premium A 5.5 percent corporate coupon bond is callable in 10 years for a call premium of one year
of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer
calls the bond? (LG7-1)
7-7 TIPS Interest and Par Value A 2¾ percent TIPS has an original reference CPI of 185.4. If the current
CPI is 210.7, what is the current interest payment and par value of the TIPS? (LG7-2)
7-8 TIPS Interest and Par Value A 3⅛ percent TIPS has an original reference CPI of 180.5. If the current
CPI is 206.8, what is the current interest payment and par value of the TIPS? (LG7-2)
7-9 Bond Quotes Consider the following three bond quotes: a Treasury note quoted at 97.844, a corporate
bond quoted at 103.25, and a municipal bond quoted at 101.90. If the Treasury and corporate bonds have a
par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three
bonds in dollars? (LG7-3)
7-10 Bond Quotes Consider the following three bond quotes: a Treasury bond quoted at 106.438, a
corporate bond quoted at 96.55, and a municipal bond quoted at 100.95. If the Treasury and corporate
bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price
of these three bonds in dollars? (LG7-3)
7-11 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 20 years if the
market interest rate is 3.8 percent. (LG7-4)

7-12 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 15 years if the
market interest rate is 5.75 percent. (LG7-4)
7-13 Current Yield What’s the current yield of a 3.8 percent coupon corporate bond quoted at a price of
102.08? (LG7-6)

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7-14 Current Yield What’s the current yield of a 5.2 percent coupon corporate bond quoted at a price of
96.78? (LG7-6)
7-15 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to
maturity of 3.5 percent for an investor in the 33 percent marginal tax bracket? (LG7-6)
7-16 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to
maturity of 2.9 percent for an investor in the 28 percent marginal tax bracket? (LG7-6)
7-17 Credit Risk and Yield Rank from highest credit risk to lowest risk the following bonds, with the
same time to maturity, by their yield to maturity: Treasury bond with yield of 5.55 percent, IBM bond
with yield of 7.49 percent, Trump Casino bond with yield of 8.76 percent, and Banc One bond with a
yield of 5.99 percent. (LG7-7)
7-18 Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk all
with the same time to maturity, by their yield to maturity: Treasury bond with yield of 4.65 percent,
United Airlines bond with yield of 9.07 percent, Bank of America bond with a yield of 6.25 percent,
and Hewlett-Packard bond with yield of 6.78 percent. (LG7-7)
INTERMEDIATE PROBLEMS
7-19 TIPS Capital Return Consider a 3.5 percent TIPS with an issue CPI reference of 185.6. At the
beginning of this year, the CPI was 193.5 and was at 199.6 at the end of the year. What was the capital
gain of the TIPS in dollars and in percentage terms? (LG7-2)
7-20 TIPS Capital Return Consider a 2.25 percent TIPS with an issue CPI reference of 187.2. At the
beginning of this year, the CPI was 197.1 and was at 203.8 at the end of the year. What was the capital
gain of the TIPS in dollars and in percentage terms? (LG7-2)
7-21 Compute Bond Price Compute the price of a 3.8 percent coupon bond with 15 years left to maturity
and a market interest rate of 6.8 percent. (Assume interest payments are semiannual.) Is this a discount
or premium bond? (LG7-4)
7-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with 10 years left to maturity
and a market interest rate of 7.0 percent. (Assume interest payments are semiannual.) Is this a discount
or premium bond? (LG7-4)
7-23 Compute Bond Price Calculate the price of a 5.2 percent coupon bond with 18 years left to maturity
and a market interest rate of 4.6 percent. (Assume interest payments are semiannual.) Is this a discount
or premium bond? (LG7-4)
7-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 22 years left to maturity
and a market interest rate of 6.5 percent. (Assume interest payments are semiannual.) Is this a discount
or premium bond? (LG7-4)
7-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with 10 years left to maturity is
priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will
be 5.8 percent. What is the change in price the bond will experience in dollars? (LG7-5)
7-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to maturity is
priced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield to maturity will
be 6.8 percent. What is the change in price the bond will experience in dollars? (LG7-5)

7-27 Yield to Maturity A 5.65 percent coupon bond with 18 years left to maturity is offered for sale at
$1,035.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.)
(LG7-6)
7-28 Yield to Maturity A 4.30 percent coupon bond with 14 years left to maturity is offered for sale at
$943.22. What yield to maturity is the bond offering? (Assume interest payments are semiannual.)
(LG7-6)
7-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in 6 years. The
call premium is one year of coupon payments. It is offered for sale at $1,135.25. What is the yield to
call of the bond? (Assume interest payments are semiannual.) (LG7-6)
7-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in 4 years. The
call premium is one year of coupon payments. It is offered for sale at $1,075.50. What is the yield to

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call of the bond? (Assume interest payments are semiannual.) (LG7-6)
7-31 Comparing Bond Yields A client in the 39 percent marginal tax bracket is comparing a municipal
bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45
percent yield. Which bond will give the client more profit after taxes? (LG7-6)
7-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is comparing a municipal
bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45
percent yield. Which bond will give the client more profit after taxes? (LG7-6)
ADVANCED PROBLEMS
7-33 TIPS Total Return Reconsider the 3.5 percent TIPS discussed in problem 7-19. It was issued with
CPI reference of 185.6. The bond is purchased at the beginning of the year (after the interest payment),
when the CPI was 193.5. For the interest payment in the middle of the year, the CPI was 195.1. Now,
at the end of the year, the CPI is 199.6 and the interest payment has been made. What is the total
return of the TIPS in dollars and in percentage terms for the year? (LG7-2)
7-34 TIPS Total Return Reconsider the 2.25 percent TIPS discussed in problem 7-20. It was issued with
CPI reference of 187.2. The bond is purchased at the beginning of the year (after the interest payment),
when the CPI was 197.1. For the interest payment in the middle of the year, the CPI was 200.1. Now,
at the end of the year, the CPI is 203.8 and the interest payment has been made. What is the total
return of the TIPS in dollars and in percentage terms for the year? (LG7-2)
7-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to maturity is
priced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield to maturity will
be 6.0 percent. If this occurs, what would be the total return of the bond in dollars and percent? (LG7-
5)
7-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to maturity is
priced to offer a 6.25 percent yield to maturity. You believe that in one year, the yield to maturity will
be 7.0 percent. If this occurs, what would be the total return of the bond in dollars and percentage
terms? (LG7-5)
7-37 Yields of a Bond A 2.50 percent coupon municipal bond has 12 years left to maturity and has a price
quote of 98.45. The bond can be called in four years. The call premium is one year of coupon
payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield
(for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest payments
are semiannual and a par value of $5,000.) (LG7-6)
7-38 Yields of a Bond A 3.85 percent coupon municipal bond has 18 years left to maturity and has a price
quote of 103.20. The bond can be called in eight years. The call premium is one year of coupon
payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield
(for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest payments
are semiannual and a par value of $5,000.) (LG7-6)

7-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It
has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has recently gotten into
some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount
rate will be 8.5 percent. What will be the change in the bond’s price in dollars and percentage terms?
(Assume interest payments are semiannual.) (LG7-7)
7-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has 10 years left to maturity.
It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has recently become
more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate
discount rate will be 7.1 percent. What will be the change in the bond’s price in dollars and percentage
terms? (Assume interest payments are semiannual.) (LG7-7)
7-41 Spreadsheet Problem Say that in June of this year, a company issued bonds that are scheduled to
mature three years from now in June. The coupon rate is 5.75 percent and is semiannually. The bond
issue was rated AAA.
a. Build a spreadsheet that shows how much money the firm pays for each interest rate payment and
when those payments will occur if the bond issue sells 50,000 bonds.

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b. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30 percent.
Show the interest payments with this rating. Explain why bond ratings are important to firms issuing
capital debt.
c. Consider that interest rates in the economy increased in the first half of this year. If the firm would
have issued the bonds in January of this year, then the coupon rate would have only been 5.40
percent. How much extra money per year is the firm paying because it issued the bonds in June
instead of January?
7-42 Spreadsheet Problem You have a portfolio of three bonds. The long bond will mature in 19 years
and has a 5.5% coupon rate. The midterm bond matures in 9 years and has a 6.6% coupon rate. The
short bond matures in only 2 years and has a 4% coupon rate.
a. Construct a spreadsheet that shows the value of these three bonds and the portfolio when the
discount rate is 5%. The spreadsheet can look something like this:
b. Illustrate what happens when the discount rate increases by 0.5%. What do you notice about the
changes in price between the three bonds?
c. Show the bond prices when the discount rate decreases by 0.5% from the discount rate in part a.
What do you notice about the price change between parts b and c?
A B C D E
1 Now Change to
2 Interest rate = 5.00% 5.50%
3 Bonds Bond Price Now Price After Change Change in $ Change in %
4 Long bond
5 Midterm bond
6 Short bond
7 Total = $0.00 $0.00

Notes
CHAPTER 7
1. In order to focus on the valuation concepts, we present these examples with the full six months until the bond’s next interest payment.
However, bonds can be sold anytime between interest payments. When this occurs, we simply add the interest accrued since the last
payment to the price.
2. States have differing rules about whether they tax the income from a particular municipal bond—they will generally tax income from
munis issued out of state. Further, capital gains arising from municipal bond sales may be taxed, and the income from municipal bonds
must be added to overall income when determining the Alternative Minimum Tax consesquences.

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chapter eight
Valuing
Stocks
©Benny Marty/Shutterstock

B
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usinesses need capital to start up operations, expand product lines and services, and serve new
markets. In the last chapter, we discussed debt, which is one source of financial capital upon which
businesses can draw. Their other source of capital is called equity, or business ownership. Public
corporations share business ownership and raise money by issuing stocks to investors. When the
company sells this form of equity ownership to raise money, it gives up some ownership—and thus some
control—over the business. Investors buy stock to receive the benefits of business ownership. Most
citizens do not have the time or expertise to operate their own businesses. Buying stock allows them to
participate in the profits of economic activities. Access to equity capital has allowed entrepreneurs like Bill
Gates of Microsoft and Larry Page of Google to take their companies public so that their businesses can
become large corporations. Both the company founders and the new owners (stock investors) have
amassed much wealth over the years under this arrangement. One very important reason that investors
are willing to buy company stock as an investment is that they know that they can sell the stock
during any trading day. Investors buy and sell stocks among themselves in stock markets. Well-
functioning stock markets are critical to any capitalistic economy. In this chapter, we’ll discuss stock
market operations and stock valuation.■
LEARNING GOALS
LG8-1 Understand the rights and returns that come with common stock ownership.
LG8-2 Know how stock exchanges function.
LG8-3 Track the wider stock market with stock indexes and differentiate among the kinds of information each index provides.
LG8-4 Know the terminology of stock trading.
LG8-5 Compute stock values using dividend discount and constant-growth models.
LG8-6 Calculate the stock value of a variable-growth-rate company.
LG8-7 Assess relative stock values using the P/E ratio model.
viewpoints
business APPLICATION
As CEO of your firm, Dawa Tech, which makes computer components, you have been able to grow its dividends by 8 percent per
year to a recent $2 per share. You expect this growth to continue. As a result, the stock price has risen to $65 and has a P/E ratio of
16.25.
Tomorrow, you are scheduled to meet with some stockholders and financial analysts. To prepare for the meeting, you should know
what return the shareholders seem to expect and estimate where the Dawa stock price may be in three years. How will you go about
preparing for this meeting? (See the solution at the end of the book.)
8.1 • COMMON STOCK LG8-1
Equity securities (stocks) represent ownership shares in a corporation. Common stock offers buyers the potential for
current income from dividends and capital appreciation from any stock price increases. Over time, some corporate
profits are reinvested in the firm, which increases the value of each shareholder’s stake in the business. At any point
in time, the market value of a firm’s common stock depends on many factors, including
common stock An ownership stake in a corporation.
The company’s profitability.
Growth prospects for the future.
Current market interest rates.
Conditions in the overall stock market.
Over periods of 30 to 40 years, stocks have offered investors the best opportunities to increase wealth. Since stocks

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are also susceptible to price declines and stock price fluctuations can be very volatile over short periods of time,
stock investing requires a longer-term outlook.
Virtually any business firm that is organized as a corporation (see Chapter 1) may choose to issue publicly traded
stock. Common stockholders vote to elect the board of directors; they also vote on various other proposals requested
by other shareholders or the management team. As owners of the firm, common stockholders are considered to be
residual claimants. This means that common stockholders have the right to claim any cash flows or value after all
other claimants have received what they are owed. As a company earns cash flows, it must pay suppliers,
employees, expenses, taxes, and debt interest payments. Stockholders claim the leftover (or residual) cash flow.
These profits can be used to reinvest in the firm to foster growth, pay dividends to shareholders, or a combination of
the two.
residual claimants Ownership of cash flows and value after other claimants are paid.
Stocks of growing firms are valuable. Stocks in firms that pay dividends to shareholders are also valuable. Stocks
issued by firms that have greater amounts of residual cash flow are more valuable. The value is reflected in the stock
price. Therefore, stock price values arise from the company’s underlying business success. Many different investors
and analysts may estimate a stock’s fundamental value based upon some outlook or theory. But the actual
stock price is determined on stock exchanges when investors seek to trade with one another. Let’s discuss
this trading process and then explore how stocks are valued.
personal APPLICATION
You are impressed with the news and entertainment firm CBC Newscorp. The per-share dividends have increased from $1.25 per
year three years ago to the recent $1.68 annual dividend. Then you discover that 15 analysts are following the firm and that their
mean growth estimate for the future is 10.1 percent. Now you want to know if the current selling price of $54 seems like a good deal if
the appropriate required return for the stock is 13.5 percent. (See the solution at the end of the book.)
Who are these “analysts,” and where can you find their opinions?
8.2 • STOCK MARKETS LG8-2
In general, people will invest significant amounts of their wealth in stocks only if they know that they can convert
their shares into cash at any time. Stock exchanges provide this liquidity, allowing buyers and sellers the means to
transact stock trades with each other. This liquidity gives many people the confidence to invest in the first place and
makes stocks (as well as bonds) attractive investments relative to less-liquid assets like real estate or fine collectibles
—which can be difficult to sell quickly at full value.
The most well-known stock exchange in the world is the New York Stock Exchange (NYSE). The New York Stock
Exchange, located in New York City on the corner of Wall Street and Broad Street, is the largest U.S. stock
exchange as measured by the value of companies listed and the dollar value of trading activity. The NYSE is the
largest equities marketplace in the world and is home to approximately 2,800 companies (many with multiple
securities listed). While other exchanges may boast more companies listed, the largest companies in the world tend
to list in New York. The holding company that owns the NYSE, Intercontinental Exchange, also operates Euronext,
a Europe-based electronic exchange market. For decades, the American Stock Exchange, located just down the
street, competed with the NYSE. However, in 2008, the NYSE acquired this exchange. Now, smaller companies
trade at this location, which is referred to as AMEX.
New York Stock Exchange (NYSE) Large and prestigious stock exchange with a trading floor.


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The NYSE trades millions upon millions of stock shares in a given day.
©Tetra Images/Getty Images
Much of the stock buying and selling at the NYSE occurs at 17 stations, called trading posts, on the trading floor.
Each post is staffed by a designated market maker (formerly known as specialists), who oversees the orderly trading
of the specific stocks assigned to that post. Brokers, located around the perimeter of the floor, act as agents for those
buying and selling stocks. Brokers execute orders by matching buy and sell orders. Once the buy and sell orders
match, the transaction is completed and the trade appears on trading screens viewed by people all over the world.
trading posts Trading location on the floor of a stock exchange.
brokers Floor traders who execute orders for others and themselves.

Consider this scenario. You decide to buy shares of McDonald’s stock because of new menu items and other
initiatives. You place a buy order for 100 shares with your broker—either with a simple phone call or through an
online brokerage service. The broker then sends the order to the NYSE electronically to the trading post assigned for
McDonald’s stock. At the trading post, the specialist makes sure the transaction is executed in a fair and orderly
manner. Your buy order competes with other orders at the point of sale for the best price and an on-floor broker
executes your purchase. You will receive a trade confirmation from your broker describing the trade and noting the
exact amount you owe for the 100 shares of McDonald’s plus any applicable commissions. The NYSE reports the
transaction and it appears within seconds on displays across the country and around the world. Note that buy and sell
orders are electronically routed from all over the world to the NYSE, which then routes trade results back. Since
most of the trade orders are already in electronic form, why not electronically match buy and sell orders and bypass
any human intervention in floor trading? Indeed, the NYSE has joined many other exchanges in becoming
increasingly electronic. Some floor market-maker firms can see a time when no human intervention will be a part of
floor trading at the NYSE.
The NYSE will trade millions of McDonald’s stock shares in a given day. A stock quote for McDonald’s stock,
ticker symbol MCD, is shown in Figure 8.1. On February 10, 2016, more than 5.7 million McDonald’s shares traded.
The stock closed at $117.54 per share, which was $0.53 higher than the closing price of the previous day. At this
price, McDonald’s stock is currently closer to its 52-week high of $124.83 than to its 52-week low of $87.50.
ticker symbol Unique code for a company consisting of one to five letters.
FIGURE 8-1 Read a Stock Quote, February 10, 2016, Yahoo! Finance

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If you know what to look for, reading a stock quote is not as complicated as it first may appear.
Source: Yahoo! Finance.
To list its stock on the NYSE, a company must meet minimum requirements for its
Total number of stockholders.
Level of trading volume.
Corporate earnings.
Firm size.
The exchange also charges an initial list fee and an annual fee. Listing standards and fees are higher for the NYSE
than for other stock exchanges, so many firms cannot (or choose not to) list their stocks there.
Another popular stock trading system is the NASDAQ Stock Market, an electronic stock market without a physical
trading floor. Today, NASDAQ features many of the big-name high-tech companies investors have come to know,
like Apple Computer (ticker: AAPL), Intel (ticker: INTC), Microsoft (ticker: MSFT), and Qualcomm (ticker:
QCOM). Many newer high-tech companies like Google (ticker: GOOG), Netflix (ticker: NFLX), and Adobe
Systems Inc. (ticker: ADBE), are also listed on NASDAQ. In 2007, NASDAQ purchased OMX, which owned seven
Nordic and Baltic stock exchanges, and became NASDAQ OMX. NASDAQ ranks second, behind the NYSE,
among the world’s equity markets in terms of total dollar volume. NASDAQ lists approximately 3,100 domestic and
foreign companies.
NASDAQ Stock Market Large electronic stock exchange.
Instead of having a trading floor, NASDAQ uses a vast electronic trading system that executes trades via computer
rather than in person. Instead of one designated market maker overseeing the process for an individual stock on a
trading floor, Nasdaq’s system uses multiple market makers, or dealers. Market makers use their own stock inventory
and capital to compete with other dealers to buy and sell the stocks they represent. When an investor places an order
through a stockbroker for a NASDAQ-listed stock, the electronic system routes the order and the investor buys
shares from the dealer offering the best (lowest) price. Typical NASDAQ stocks support 10 market makers actively
competing with one another for investor trades.
market makers Dealers and specialists who oversee an orderly trading process.
dealers NASDAQ market makers who use their own capital to trade with investors

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time out!
8-1 What are three primary stock exchanges in the United States and where are they located? For which of the exchanges does
physical location matter? Why?
8-2 Describe differences in trading procedures on the NYSE versus the NASDAQ. Which do you think is most fair to investors?
Why?
Table 8.1 shows trading activity on the three main stock exchanges for one day in February 2016. Note that all three
exchanges traded more than 1 billion shares during the day.
The business of providing platforms or forums for investors and speculators to trade stocks and other financial assets
has been changing rapidly. Many exchanges that previously used physical floor trading systems with specialists and
open outcry to establish stock prices are shifting to electronic systems with no trading floors. Long-standing,
traditional exchanges are also merging with other domestic and international exchanges to create fewer, but larger,
forums that focus not just on U.S. securities but on many more internationally focused financial assets. The wider
range of represented securities allows traders new opportunities to explore trading relationships among securities
traded across the world. This worldwide trading will establish economically sound prices and additional financial
stability around the world.
▼ TABLE 8.1 Trading on the NYSE, NASDAQ, and AMEX, February 10, 2016
NYSE AMEX NASDAQ
Advancing issues 1,624 (52%) 744 (53%) 1,269 (48%)
Declining issues 1,426 (46%) 607 (44%) 1,298 (49%)
Unchanged issues    78 (2%)  42 (3%)    94 (4%)
New highs 44 20 6
New lows 156 67 201
Total volume 4,428,773,681 1,042,526,864 2,388,659,663
Source: Yahoo! Finance.

Tracking the Stock Market LG8-3
With thousands of stocks trading every minute, many stock prices rise while others fall. Table 8.1 also shows that,
throughout the trading day, 1,624 stocks increased in price on the NYSE while 1,426 stocks decreased in price.
While the AMEX also experienced more stocks with increases in price than declines, the NASDAQ saw more
declines. In addition to the number of stocks advancing and declining, the table also shows the number of stocks that
hit new 52-week price highs (44 listed on the NYSE) and new lows (156 on the NYSE) on that day. So, was this a
good day or a bad day in the stock market?
To say anything about the general direction of the stock market, stock indexes are useful. Dozens of stock indexes are
designed to track the overall market; many more track different market segments. The three most recognized indexes
are the Dow Jones Industrial Average (DJIA), the Standard & Poor’s 500 Index (S&P 500), and the NASDAQ Composite Index.
stock index Index of market prices of a particular group of stocks. The index is used to measure those stocks’ performance.
Dow Jones Industrial Average (DJIA) A popular index of 30 large, industry-leading firms.
Standard & Poor’s 500 Index (S&P 500) A stock index of 500 large companies.
NASDAQ Composite Index A technology-firm weighted index of stocks listed on the NASDAQ Stock Exchange.

Charles H. Dow invented the first stock average in 1884. At the turn of the 20th century, railroads were the first
major corporations. So he began with 11 stocks, mostly railroads. Dow created a price average by simply adding up
11 stock prices and dividing by the number 11. Two years later, Dow began tracking a 12-stock industrial average.
This industrial average would eventually evolve into the modern DJIA, which is a price average of 30 large,
industry-leading stocks that together represent roughly 30 percent of the total stock value of all U.S. equities. DJIA
level changes describe how the largest companies that participate in the stock market performed over a given period.
The DJIA was at 15,914.74, a change of −99.64 (or −0.62 percent), on the day illustrated in Table 8.1.
The Standard & Poor’s Corp. introduced its 500-stock index in 1957. Standard & Poor’s chooses companies to
include in the S&P 500 Index to represent the 10 sectors of
the economy:
1. Financial
2. Information technology
3. Health care
4. Industrials
5. Consumer discretionary
6. Consumer staples
7. Energy
8. Telecom services
9. Utilities
10. Materials
S&P uses market capitalization (a measure of company size using stock price times shares outstanding), not just stock
prices, of the largest 500 U.S. firms to compute the index. These 500 firms represent roughly 80 percent of the
overall stock market capitalization (number of shares times share price). Although the DJIA is a long-time favorite
with the media and individual investors, the S&P 500 is much preferred in the investment industry because of its
broader representation of the market as a whole. S&P 500 performance provides a standard against which most U.S.
money managers and pension plan sponsors can compare their investment performance. During trading on February
10, 2016, the S&P 500 lost 0.35 (-0.02 percent) to close at 1,851.86.
market capitalization The size of the firm measured as the current stock price multiplied by the number of shares outstanding.

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Investors consider the NASDAQ to be a reflection of the tech sector’s general performance.
©TongRo Image Stock/Alamy
The NASDAQ Composite Index measures the market capitalization of all common stocks listed on the NASDAQ
stock exchange. Since the NASDAQ lists so many large, technology-oriented companies, many investors and
analysts consider this index to reflect the tech sector performance more than that of the overall stock
market. The NASDAQ Composite gained 14.83 to 4,283.59 on February 10, 2016, a gain of 0.35 percent.
It was a bit of an unusual trading day because the DJIA was down, the S&P 500 was flat, and the NASDAQ was up.
Figure 8.2 shows the levels of all these stock indexes since 1980. The DJIA (maroon line) level appears on the left-
hand axis. Both the S&P 500 (green line) and the NASDAQ Composite (orange line) run from the right-hand axis.
The rapid price appreciation for NASDAQ stocks during the late 1990s—the tech boom years—is unprecedented for
such a large and widely followed market index. The NASDAQ Composite soared from 817 in March 1995 to peak
on March 10, 2000, at 5,048.62, for a 518 percent total return in only five years—a 43.9 percent annual rate of
share-price appreciation for NASDAQ stocks. The NASDAQ index performed much better than did the DJIA (19.0
percent per year) or the S&P 500 (22.7 percent per year). The NASDAQ “price bubble” set the stage for one of the
most dramatic stock price declines in history: The NASDAQ Composite Index plunged to 1,114.11 on October 9,
2002, losing 78 percent of its value. The other index values also fell during this period, albeit not as sharply. Note
that the DJIA didn’t climb back to its 2000 high until March 2006. The S&P 500 Index finally recovered in May
2007. The NASDAQ Composite did not exceed its 2000 high until April 22, 2015. The stock market has been very
volatile during the past two decades.
time out!
8-3 Discuss why the day’s market return may be different when measured by the DJIA, S&P 500 Index, and NASDAQ
Composite taken separately.
8-4 Why might the “market bubble” phenomenon appear more dramatic because it occurred in the NASDAQ Composite rather
than by the DJIA or S&P 500 Index?


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8-5 If you followed the market regularly, to which index would you give the most credence? Why?
The figure also shows the stock market reaction to the financial crisis that began in 2008. There were sharp declines
in all three indexes. After closing at a new high of 14,093.08 on October 12, 2007, the DJIA then fell to close at only
6,547.05 on March 9, 2009. The DJIA fully recovered in early 2013 and closed above 15,000 for the first time on
May 7, 2013, and above 18,000 on February 13, 2015. This massive stock market rise coincides with the
quantitative easing programs implemented by the U.S.
Federal Reserve.
FIGURE 8-2 Stock Market Index Levels since 1980
This graph comparing the DJIA, S&P 500, and NASDAQ Composite indexes gives you a picture of their magnitude, as well as their patterns.

Trading Stocks LG8-4
People who wish to buy and sell stocks need to open stock brokerage accounts. Traditional, full-service stockbrokers
(e.g., Morgan Stanley Smith Barney, Merrill Lynch, UBS, Edward Jones) provide clients with research and advice
in addition to executing trades. Their clients pay for this research and advice: Commission fees for these services
may run well over $100 per trade. Discount brokerage firms (e.g., Charles Schwab, E-trade, Scottrade, TD
Ameritrade) charge a much lower commission, $5 to $30 per trade, but do not provide the additional services.
Investors at discount brokerages usually place trades through the brokerage’s Internet sites.
finance at work //: behavioral
Investor Psychology
To us today, it may seem ludicrous that in the years 1634 to 1636, the people of Holland were in the midst of “Tulip Mania,” and the price
for a single rare tulip bulb approached the equivalent of $35,000. Then the bubble burst and tulip prices quickly plunged to less than the
equivalent of $1. We may call those people who invested in a $35,000 tulip bulb irrational or even “crazy.”
But this type of story seems to repeat itself throughout history. Investors paid extremely high prices for the new computer stocks in
the 1960s, the “nifty fifty” companies in the 1970s, Japanese stocks during the 1980s, and Internet stocks during the late 1990s. The
mania for stocks like Iomega drove its price from an equivalent of $1 per share in January of 1995 to over $75 in just 16 months. When
the bubble burst, the price fell hard. Many years later, in 2008, the company was purchased by EMC Corporation for dollars per share.

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But that’s just one company. A portfolio full of Internet stocks experienced a similar price mania followed by a severe fall. Investors
created a stock index (TheStreet.com Internet Index) designed to track Internet stocks in late 1998, but by that time, part-time investors
and veterans alike were already well into the craze. The Internet index started at 250, quickly rose to 1,270 by March of 2000, and
subsequently fell to a low of 63 in October of 2002. Of course, the tech stock bubble was followed by the real estate bubble. In
retrospect, irrational bubble-like prices are not confined to tulips and the 17th century in Holland.
Seemingly irrational behavior may not occur only during highly emotional periods of a price bubble. Recently, a growing recognition
has arisen that “normal” investors often behave in a way that might not be described as fully rational. Investors, being human, are
subject to cognitive biases and emotions. Studies of investor behavior have discovered that investors commonly succumb to
psychological biases and
Source: USDA Natural Resources Conservation Service
Trade too much.
Sell winners too soon.
Refuse to realize losses.
Become overconfident—especially when trading online.
Seek stocks that have already increased in price—perhaps up to their full potential price.
Consider and react to what’s happening with each stock in isolation, rather than remembering the purpose for forming an overall
portfolio.
Investors who succeed in the long run are those who learn to avoid these psychological biases.
Want to know more?
Key Words to Search for Updates: irrational exuberance, price bubble, mania
Buy and sell orders go through the brokerage firm to a market maker (a dealer or a specialist) at a stock exchange.
The quoted bid is the highest price at which the market maker offers to pay for the stock. Investors have little choice
but to accept this selling price, because regardless of the broker used, the market maker offers the only place to sell
the stock. The quoted ask price is the lowest price at which a market maker will sell a stock—so investors
buy at the ask price. The difference between the bid and the ask price may be only $0.01 for high-volume
stocks and can be as high as $0.20 for less-often traded companies. The spread between the bid and the ask price is a
cost to the investor and a profit for the market maker. This profit compensates the market maker for providing a
market and liquidity for that stock.
bid The quoted price investors are likely to receive when they sell stock.
ask The quoted price investors are likely to pay when they buy stock.
Investors can place a buy or sell market order. A market order to buy stock will be filled immediately at the current
ask price when routed to the stock exchange. A sell market order will be filled at the current bid price. The
advantage of a market order is that it executes immediately at the best available price. The disadvantage of a market
order is that the investor does not know in advance what that fill price will be. Investors can name their own prices
by using limit orders, in which investors specify the price at which they are willing to execute the buy or sell order.
With a buy limit order, a trade is executed if the ask quote is at or below the price target. For a sell limit order, a

http://www.TheStreet.com

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trade is executed if the bid quote moves through the specified price. If the current quote does not meet the price cited
in the limit order, the trade is not executed. The advantage of a limit order is that the investor makes the trade at the
desired price; the disadvantage is that the trade might not be executed at all.
market order A stock buy or sell order to be immediately executed at the current market price.
limit order A stock buy or sell order at a specific price. It will only be executed if the market price meets the specified price.
Consider a quote of McDonald’s stock with a bid price of $117.00 and an ask price of $117.05. An investor placing
a market buy order would purchase the stock at $117.05. A market sell order would execute as the price rises
through $117.00. Note that an investor who simultaneously bought and sold 100 shares would pay $11,705 and
receive $11,700—losing $5. An investor who places a buy limit order at $116.75 will only purchase the shares if the
ask price falls to $117.75 or lower. If the ask does not fall, the order will not execute. Bid and ask prices tell
investors at what prices the stock can currently be traded in general. But being able to buy at the ask price does not
guarantee that the stock should be valued at that price. We’ll discuss various ways to arrive at reasonable per-share
stock values in the next section.
time out!
8-6 Explain how the difference in the bid and ask prices might be considered a hidden cost to the investor.
8-7 The bid and ask prices for Amazon.com are $37.79 and $37.85. If these quotes occur when a trade order is made, at what
price would a market buy order execute? Would a limit sell order execute with a target price of $37.75?
8.3 • BASIC STOCK VALUATION LG8-5
Cash Flows
In the previous chapter, we showed how we value bonds by finding the present value of the future interest payments
and the future par value. Stock valuation uses the same concept of finding the present value of future dividends and
the future selling price. But of course uncertainty about both price appreciation and future dividend payment streams
complicate stock valuation. Consider the simple case of valuing a stock to be held for one year shown in the time
line.
The value of such a stock today, P0, is the present value of the dividend to be received in the first year, D1, plus the
present value of the expected sales price in one year, P1. The interest rate used to discount the cash flows is shown
as i. Using the present value equation from Chapter 4 results in
(8-1)
Whenever investors deal with future stock prices and future dividend payments, they must use expected values, not
certain ones. Companies rarely decrease their dividends; most companies’ dividends either remain constant
or slowly grow. Examining a firm’s dividend history over the past few years will give clues to that
company’s future dividend policy. For example, The Coca-Cola Company (ticker: KO) paid a $0.155 per share
dividend for each quarter in 2006. The firm then raised the quarterly dividend to $0.17 for each quarterly dividend in
2007. The company paid quarterly dividends in 2008, 2009, 2010, 2011, and 2012 of $0.19, $0.205, $0.22, $0.235,
and $0.255, respectively. For 2013 through 2015, Coca-Cola raised its quarterly dividend 2.5 cents every year. So

http://www.Amazon.com

the quarterly dividend was $0.33 in 2015, for an annual dividend of $1.32. This dividend growth seems fairly stable
and predictable.
Coca-Cola increased its dividend by 3 cents per year over a five-year span.
©McGraw-Hill Education/Jill Braaten, photographer
Stock prices, though, show much more volatility than dividend histories do. We face much uncertainty in trying to
predict stock prices in the short term. Using a longer holding period to estimate stock value reduces some, but by no
means all, of the uncertainty. A 2-year holding period appears like this:
The present value of the cash flows in years 1 and 2 is today’s stock value:
(8-2)
Notice that the divisor for the second term on the right-hand side of equation 8-2 is raised to the second power. This
reflects the two years over which those cash flows must be discounted. You can do this analysis over any holding
period. For a holding period of n years, the value of a stock is measured by the present value of dividends over the n

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years, and the eventual sale price, Pn.
(8-3)
This formula incorporates both dividend income and capital appreciation or capital loss. It fully includes both major
components of the investor’s total return from investment.
McDonald’s pays an annual dividend instead of quarterly dividends.
©McGraw-Hill Education/John Flournoy, photographer
As is often the case in finance, implementing equation 8-3 presents problems for some firms in practical terms.
What will the future dividends of the firm be? What will the stock price be in 3, 5, or 10 years? While it seems that
the dividend growth of Coca-Cola will be constant, consider the actual dividends and stock price of McDonald’s
Corp. since 2000 shown in Figure 8.3.
McDonald’s paid an annual dividend from 2000 to 2007. Some increases were small, like the $0.01 increase from
2000 to 2001 and again to 2002. Other increases were quite large, like the $0.50 increase between 2006 and 2007.
Then McDonald’s changed to the more common quarterly dividend in 2008. Since the change to quarterly
payments, McDonald’s dividend growth has been more stable and predictable through 2015. The figure also shows
that McDonald’s stock price has been very volatile. The price fell from a split adjusted $25 in 2000 to
$9.50 in 2003 and then steadily climbed to $45 in 2007. The stock went sideways during the financial
crisis and then shot up to $88 in late 2011. The stock again went mostly sideways from 2012 to 2014 and then shot
up again in 2015. An investor in 2000 would have had a very difficult time accurately forecasting these future
dividends and stock prices. Indeed, short-term stock price changes seem almost random. Stock valuation can really
only be viewed from a long-term perspective. Because predicting future dividends is uncertain at best, it’s better to
project valuation as a likely range of prices under reasonable assumptions rather than as a single price. After all, this
computed price is an estimate of the firm’s intrinsic value. This intrinsic value may differ from the stock price
trading in the market. This possibility is discussed as a market efficiency topic in Chapter 10.
EXAMPLE
8-1 Valuing Coca-Cola Stock LG8-5
For interactive

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versions of this
example, log in
to Connect or go to
mhhe.com/CornettM4e.
In February 2016, you are valuing Coca-Cola stock to compare its value to its
market price. The current market price is $43.01. Given the history of Coca-
Cola’s dividends, you believe that the company will pay total dividends in
2016 of $1.42 (= 4 ×$0.355). Your analysis indicates that the total dividends in
2017 and 2018 will be $1.54 and $1.66, respectively. In addition, you believe
that the price of Coca-Cola stock at the end of 2015 will be $54.10 per share.
If the appropriate discount rate is 11.0 percent, what is the value of Coca-Cola
stock?
SOLUTION:
To organize your data, you first create the following timeline:
Using equation 8-3, you compute the stock value as
Since your analysis shows that Coca-Cola’s stock should be valued at $43.30
while it’s selling for only $43.01, the stock appears to be slightly undervalued.
You believe that this might be a good time to buy some Coca-Cola stock.
Similar to Problems 8-15, 8-16, 8-27, 8-28, Self-Test Problem 1
Dividend Discount Models
We can extend the discounted cash flow approach in equation 8-3 for an infinite stream of dividends, n→∞, and no
final future selling price. If stockholders receive all future cash flows as future dividends, the stock’s value to the
investor is the present value of all these future dividends. In other words, embedded in any stock price is the value of
all future dividends. We can demonstrate this value as
(8-4)
This equation shows the general case of the dividend discount model. The dividend discount model provides
a useful theoretical basis because it illustrates the importance of dividends as a fundamental stock price
determinant.
dividend discount model A valuation approach based on future dividend income.
FIGURE 8-3 Dividends and Stock Price of McDonald’s since 2000

http://www.mhhe.com/CornettM4e

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Dividends rarely decline, but stock prices often do!
But, again, finance professionals find it difficult to apply the dividend discount model because it requires that they
estimate an infinite number of future dividends. To use the model in practice, analysts make simplifying
assumptions to make the model workable. One common assumption: The firm has a constant dividend growth rate,
g. If this is the case, next year’s dividend is simply this year’s dividend that grew one year at the growth rate, that is,
D1 = D0 × (1 + g). In fact, we can express each dividend as a function of D0 and we can rewrite equation 8-4 as
(8-5)
So, with this version of the model, we need not forecast an infinite string of dividends; D0 and g take care of that.
However, we must still compute an infinite sum of numbers. Luckily, mathematicians know equations like these;
they are known as power series. This power series can be simplified to the constant-growth model, and it assumes that
the growth rate is smaller than the discount rate (i.e., for g < i): constant-growth model A valuation method based on constantly growing dividends. Stock value = Next year’s dividend ÷ (Discount rate − Growth rate) (8-6) If g ≥ i, then the denominator would be zero or negative. Economically and mathematically, this is a nonsensical result. In the short run, a firm can grow very quickly. In the long run, no company can grow faster than the overall economic growth rate forever. You may hear the constant-growth model referred to as the Gordon growth model, after financial economist Myron J. Gordon. EXAMPLE Constant Growth and Coca-Cola 8-2 Stock LG8-3 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Assume that you are valuing Coca-Cola stock again. This time you are using the constant growth model, assuming a discount rate of 11.0 percent. SOLUTION: You have a choice of three growth rates to use. The implied projected dividend growth rate is 7.94 percent. Past dividend growth has been 7.63 percent and analysts forecast an 8.95 percent growth. Compute the stock value using all three growth rates. Using a dividend growth rate of 7.94 percent and equation 8-6, the stock value is $47.27: Using a dividend growth rate of 8.95 percent, the stock value is $71.22: Using a dividend growth rate of 7.63 percent, the stock value is $42.80: Notice how a small change in the growth rate has a large impact on the stock value in this model. At a current price of $43.01 per share, Coca-Cola could be considered undervalued or overvalued depending on the growth rate used. Similar to Problems 8-19, 8-20, 8-29, 8-30, 8-31, 8-32, Self-Test Problem 2 Investors use several methods to estimate a firm’s growth rate for this model. They can project the dividend trend into the future and determine the implied growth rate, compute the past growth rate, or even consider a financial analyst’s growth rate predictions. Consider Coca-Cola’s dividend behavior. If the 2015 dividend was $1.34 and the projected dividends will grow to $1.66 in 2018, the implied projected dividend growth rate is therefore 7.94 percent (N = 3, PV = −1.34, PMT = 0, FV = 1.66, CPT I = 7.94) annually. The growth rate in dividend changes from 2008 to 2012 was 7.63 percent (N = 4, PV = −0.76, PMT = 0, FV = 1.02, CPT I = 7.63) per year. You can find analyst forecasts many places online. The Yahoo! Finance web page for Coca-Cola has an Analyst Estimates link, which shows the average analysts’ forecast for the firm’s growth in the next five years at 8.95 percent. Preferred Stock A special case of the constant-growth model occurs when the dividend does not grow but is the same every year. This zero-growth rate case describes a preferred stock. The term preferred comes from the fact that this type of stock takes preference over common stock in bankruptcy proceedings. Preferred stockholders have a higher priority for receiving proceeds from bankruptcy proceedings than do common stockholders. Preferred stock is largely owned by other companies, rather than by individual investors, because its dividends are mostly nontaxable income (70 percent of the income is exempt from taxes) to other corporations. Preferred stockholders do not have voting rights http://www.mhhe.com/CornettM4e page 246 like common stockholders, though, which prevents one company from controlling another through preferred stock ownership. preferred stock A hybrid security that has characteristics of both long-term debt and common stock. An interesting characteristic of preferred stock is that it pays a constant dividend. Because the dividend does not change, the preferred stock can be valued using the constant-growth-rate model with a zero growth rate expressed as P = D/i. What would Coca-Cola’s stock be worth if its dividend stayed at $1.34 and never grew? Using the same 11.0 percent discount rate, the stock would be valued at $12.18 (= $1.34 ÷ 0.110). Given Coca- Cola’s current stock price of $43.01, over 71.6 percent [= ($43.01 − $12.18)/$43.01] of its stock value comes from the expectation that Coca-Cola’s dividend will grow. In other words, investors highly value a growing firm. Most companies issue only common stock, but nearly 1,000 preferred stock issues still exist. Table 8.2 compares the common stock and preferred stock for 10 firms. Many of the preferred stocks come from the finance, energy, and real estate sectors. Notice that the dividend yield for preferred stock is higher than for the common stock, because preferred stock investors should expect a return from dividend payments only. Common stockholders will also expect a return from capital appreciation over time. Common stocks also trade much more frequently than preferred stocks do. dividend yield Last four quarters of dividend income expressed as a percentage of the current stock price. the Math Coach on… Using the Constant-Growth-Rate Model “The distinction between the recent year’s dividends, D0, and next year’s dividends, D1, can be confusing in the constant growth-rate model. The model’s equation presents two different numerators. If you are given information about dividends last year or just paid, use the D0(1 + g) version of the equation. If you have information about expected dividends or next year’s dividend, use the D1 version of the equation.„ The zero-growth-rate version of the constant-growth valuation model shows that, since dividends are fixed, a preferred stock’s price changes because of changes in the discount rate, i. When interest rates throughout the economy change, the discount rate also changes. Preferred stock prices thus tend to act like bond prices. When interest rates rise, preferred stock prices fall. When interest rates decline, preferred stock prices rise. Preferred stock is usually categorized with bonds in the fixed-income security group because it acts so much like debt securities, even though a preferred stock represents equity ownership, like common stock. Expected Return Stock valuation models require a discount rate, i, in order to compute the present value of the future cash flows. The discount rate used should reflect the investment risk level. Higher risk investments should be evaluated using higher interest rates. For example, the previous chapter on bonds demonstrated that higher risk bonds, such as junk bonds, offer higher rates of return. Similarly, investors demand higher returns from higher risk stocks than they do from lower risk stocks. We discuss stock risk measurement and appropriate expected returns in the next section of this book. ▼ TABLE 8.2 Common and Preferred Stock, February 12, 2016 page 247 COMMON STOCK PREFERRED STOCK Company Ticker Price Annual Dividend (Yield%) Volume Ticker Price Annual Dividend (Yield%) Volume Alcoa Inc. AA $ 7.69 $0.12(1.2) 26,021,380 AAPRB $26.74 $2.69(8.1) 49,122 El Du Pont de Nemours & Co. DD $ 58.48 $1.72(2.6) 5,397,520 DDPRA $79.75 $3.50(4.5) Ford Motor Co. F $ 11.55 $0.60(4.3) 28,080,850 FPRA $25.55 $1.88(7.3) 97,959 National Healthcare NHC $ 61.29 $1.54(2.5) 23,484 NHCA $15.52 $0.80(5.1) PG&E Corp. PCG $ 55.21 $1.82(3.4) 2,877,339 PCG.PRA $30.57 $0.75(2.6) 3,247 Public Storage Inc. PSA $233.61 $6.50(2.6) 1,040,665 PSAPRW $24.74 $1.30(5.7) 51,329 Source: New York Stock Exchange (www.nyse.com). finance at work //: investments Financial Analysts’ Predictions and Opinions ©bunhill/Getty Images Financial analysts examine a firm’s business and financial success and assess long-term prospects and management effectiveness. They combine this microeconomic analysis with a macroeconomic view of the conditions of the economy, financial markets, and industry outlooks. Their evaluation results in earnings predictions, stock price targets, and opinions about whether investors should buy the stock. Such recommendations can help investors decide whether to buy, hold, or sell the stock. Analysts hired by brokerage firms and investment banks are called sell-side analysts because their firms make money by selling stocks and bonds. These analysts publicize their predictions and opinions publicly and in company “tip sheets” that are passed along to clients. Keep in mind that sell-side analysts often have incentives to be optimistic. Pension funds and mutual funds often hire analysts to give fund managers private opinions about securities. These analysts are referred to as buy-side analysts because they are hired by investment firms looking for advice on what stocks to buy for their portfolios. Because this is private, little buy-side research is made public. Consider the 26 sell-side analysts’ predictions reported for Coca-Cola on the Yahoo! Finance website. The average five-year share price growth prediction from these analysts is 8.95 percent. This is lower than the growth prediction for the industry (12.96 percent) and sector (12.79 percent). Last, analysts give opinions on whether investors should buy, sell, or hold Coca-Cola stock. Recommendations come in five levels: Strong Buy, Buy, Hold, Underperform, and Sell. Of the 26 analysts, 4 recommend a Strong Buy, 9 recommend a Buy, and 10 recommend a Hold. Note that even though the analysts predict lower than average growth for the industry and sector, and that the analysts provide meager price targets, only three of the analysts recommend an Underperform and none a Sell. This optimism in analysts’ opinions is common. Knowledgeable investors know that a “hold” recommendation is as negative as most public or sell-side http://www.nyse.com page 248 analysts get, and therefore a “hold” may actually represent a signal to sell. Want to know more? Key Words to Search for Updates: analyst opinion, financial analyst bias However, one method for determining what return stock investors require from a stock is to use the constant- growth-rate model. If the current stock price fairly reflects its value, then the discount rate, i, in equation 8-6 should be the expected return for the stock. Solving for this expected return results in equation 8-7: (8-7) Note that the expected return comes again from two sources: dividend yield and expected appreciation of the stock price, or capital gain. For example, consider that Coca-Cola’s dividend in 2016, D1, is expected to be $1.42 per share. At a current price of $43.01, Coca-Cola offers a dividend yield of 3.30 percent (= $1.42 ÷ $43.01). Since analysts believe that the firm’s stock price will grow at 8.95% percent in the future, investors expect a total return of 12.25 percent (= 3.30% + 8.95%). Dividend yield can represent a substantial portion of the profits for an investor. Many people get too enamored of high growth stocks that do not pay dividends and therefore miss out on an important source of stable returns. growth stocks Companies expected to have above-average rates of growth in revenue, earnings, and/or dividends. time out! 8-8 Explain how valuable a firm’s (and therefore its stock’s) growth is. Demonstrate this with growth and no-growth examples. 8-9 What proportion of the 12.25 percent of Coca-Cola’s expected return above comes from dividend yield? Corporate managers conduct an important application of the expected return concept to determine the return that their shareholders expect of them. We will discuss this application in detail in Part Six: Capital Budgeting. 8.4 • ADDITIONAL VALUATION METHODS LG8-6 Variable-Growth Techniques Some companies grow at such a high rate that we cannot use the constant-growth-rate model to forecast their value. High growth rates might be sustainable for several years, but cannot continue forever. Consider what happens to a high-growth firm. Other companies will surely notice the market potential for high-growth rates and will enter those product markets to compete with the high-growth firm. The competition will soon drive down the growth rates for all companies in that product market. Companies that experience unusually high-growth tend to see that growth become only average in the future unless they possess some kind of entry barrier such as a patent or government regulation due to economies of scale. Remember that the constant-growth-rate model does not work for companies where g > i. And of course, we do not
really expect the growth rate for these fast-growing firms to remain constant. To value these firms, we must use a
variable-growth-rate technique. The variable-growth-rate method combines the present-value cash flow from equation
8-3 and the constant-growth-rate model from equation 8-6.
variable growth rate A valuation technique used when a firm’s current growth rate is expected to change some time in the future.

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First, the investor chooses two different growth rates for two stages of the analysis. The first and higher growth rate,
g1, is the current growth rate, which we expect to last only a few years. A few years from now, we expect the firm to
grow at a slower but more sustainable rate of growth, g2. Figure 8.4 shows the cash flow time line when the first
growth rate applies for the first n years, followed by the second growth rate, which applies forever.
When we analyze a variable-growth-rate stock like the one in the figure, we know the recent dividend, D0, and the
two expected growth rates. Therefore, we can calculate each of the dividends shown in general terms (i.e., D1). For
example, the dividend in the first year (D1) is the year zero dividend that grows at g1, specifically D1 = D0 × (1 +
g1). The dividend then grows at g1 again for the second year dividend, D2 = D0 × (1 + g1)
2. The dividend continues
to grow through the first stage to year n at Dn = D0 × (1 + g1)
n. Figure 8.5 shows the first-stage dividends.
At this point, the company starts to move into stage 2 at the more modest growth rate, g2, and the dividends reflect
that slower growth rate. So Dn+1 is the dividend Dn that grew at the rate g2, or Dn+1 = D0 × (1 + g1)
n × (1 + g2).
Similarly, the dividend in year n + 2 is Dn+2 = D0 × (1 + g1)
n × (1 + g2)
2. We can now substitute the known
dividends as presented in Figure 8.5 into Figure 8.6.
Once we have calculated all of the dividends, we can begin finding the value of the variable-growth stock by
focusing on Stage 2 of the problem. Assume that the dividends in Stage 2 are growing at a modest rate, g2, forever.
As long as g2 < i, Stage 2 can use the constant-growth model, equation 8-6. Remember that the constant-growth model, P0 = D1/(i − g), replaces all future dividends with one value in the previous period. In previous applications, the growth began in year 1, so the value used for all future dividends came from the year 0 dividend. In this case, the change in the dividend rate occurs in year n + 1, so we will use the value from year n. So, using the constant-growth model, we can replace all the cash flows in Stage 2 with one value from year n, as The cash flows from Figure 8.6 now appear as shown in Figure 8.7. FIGURE 8-4 Variable Dividend Growth Divide into two stages at the first year of the new growth rate. FIGURE 8-5 Stage 1 Dividends Calculate the dividends in the first stage. ▼ ▼ page 250 FIGURE 8-6 Details of the Variable Growth Dividends Compute the dividends in the second stage. By replacing all the Stage 2 cash flows that continued indefinitely with one terminal price in year n, we reduce the problem to a fixed number of cash flows. The value of this variable-growth stock is finally computed as the present value of these cash flows, as solved with equation 8-3. Substituting the cash flows shown in Figure 8.7 into equation 8-3 gives us the general formula for finding the value of a variable-growth stock: General two-stage growth valuation model: (8-8) The practical application of the variable-growth valuation technique requires the investor to decide how long the current high-growth rate will last before declining to a more stable rate. FIGURE 8-7 New Stage 1 of the Variable Growth Dividend Technique Replace all of the dividends to infinity with the price (terminal value) in year n. Stage 2 disappears. The constant-growth-rate model is most useful for large, mature companies that grow in a stable manner. The variable-growth-rate model works well for dividend-paying companies that have an unusually fast rate of growth in the near future but are expected to enter a more stable growth rate environment soon. But there are still many firms that do not fit these two descriptions of firm growth. For example, many firms pay no dividends. To value firms with no dividends, replace the dividends in the models with cash flows. When you do this, you are valuing the entire firm, not just the stock value, because cash flows go to both stockholders and debt holders. In the case where a firm has low or even negative cash flows, the valuation techniques in the next section can be employed. page 251 time out! 8-10 Explain how the variable-growth-rate technique could be used for a firm whose dividend is not expected to grow for three years and then will grow at 5 percent indefinitely. 8-11 Set up and solve the McDonald’s valuation problem assuming that the first stage growth will last only two years. EXAMPLE 8-3 Variable Growth and Stock Value LG8-6 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. The dividend has grown from $1.00 per share on November 13, 2009, to $2.80 during 2015. This represents an annual growth rate of 18.7 percent (N = 6, PV = −1.00, PMT = 0, FV = 2.80, CPT I = 18.7). You think this growth rate will continue for three years and then fall to the long-term growth rate of 9.29 percent predicted by analysts. You assume a 13 percent discount rate. SOLUTION: Figure 8.3 shows a $2.80 (= 4 × $0.70) per share recent annual dividend. Modify equation 8-8 for a Stage 1 length of three years and then substitute i = 0.13, g1 = 0.187, g2 = 0.0929, and D0 = $2.80. The valuation equation and solution becomes Given these parameters, the company’s stock is worth nearly $105 per share. Similar to Problems 8-33, 8-34, Self-Test Problem 3 http://www.mhhe.com/CornettM4e page 252 ▼ The P/E Model LG8-7 The valuation models that we’ve presented thus far help investors attempt to compute a stock’s fundamental value based upon its cash flows to the investor. Another common approach is to assess a stock’s relative value. This approach compares one company’s stock valuation to other firms’ stock values to evaluate whether your target company’s stock is appropriately priced. The price of a stock taken in isolation doesn’t give us a good measure of how expensive it is. Let’s use an analogy: At the grocery store, we are less concerned with the total price of a bag of sugar than we are with the price per pound. Similarly, the price of the stock matters less than its price per one dollar of earnings. relative value A stock’s priceyness measured relative to other stocks. Consider one company that earned $5 per share in profits for the year. Its stock sells for $100. Another company earned $2 per share and its stock price is $50 per share. At first glance, the first stock appears to be more expensive because its price is a high $100 compared to the lower $50 price of the second stock. However, the first company generated higher per-share profits than did the second company. Buying the first stock means that you purchase $5 in earnings. The $100 stock price implies a cost of $20 for every $1 in earnings (= $100 ÷ $5) generated. The $50 price of the second stock implies a cost of $25 for every $1 in earnings (= $50 ÷ $2). So in this regard, the second company becomes more expensive. The price-earnings (P/E) ratio represents the most common valuation yardstick in the investment industry; it allows investors to quickly compare the cost of earnings. The P/E ratio is simply the current price of the stock divided by the last four quarters of earnings per share: (8-9) price-earnings (P/E) ratio Current stock price divided by four quarters of earnings per share. More accurately, this figure is the trailing P/E ratio and it is often denoted as P/E0, where the 0 subscript denotes the past (or trailing) earnings. trailing P/E ratio The P/E ratio computed using the past four quarters of earnings per share. Figure 8.8 shows two companies’ trailing P/E ratios: Coca-Cola and McDonald’s, as well as the Dow Jones Industrial Average’s trailing P/E ratio over a 16-year period. The P/E ratio for the DJIA changes slowly and mostly stays in the 18 to 27 range until the recent drop to 15. Historically, the DJIA’s P/E ratio has fallen as low as single digits and climbed to over 30. The figure also shows that the P/E ratio for McDonald’s has varied more than has the index’s P/E ratio. The P/E ratio for Coca-Cola has experienced wild changes—as high as 63 and as low as 18. Figure 8.8 shows that investors valued Coca-Cola more than McDonald’s in the late 1990s, but valued them nearly the same by the beginning of 2008. FIGURE 8-8 Historical P/E Ratio of the DJIA, Coca-Cola, and McDonald’s P/E ratios of large, successful companies can vary considerably over time. Here, you see that investors valued Coca-Cola over McDonald’s for much of the period, but there were periods when McDonald’s was valued higher. Source: Dow Jones and Company. Variations in P/E ratios between popular companies can be quite large. For example, in February of 2016, the P/E ratio for Alphabet (the parent company of Google) was 28.7, while the ratio for Boeing Company was only 14.6. Alphabet stock is much more expensive than Boeing. But this does not mean that Boeing stock is a better deal than Alphabet stock. Investors are willing to pay much more in relative terms for Alphabet because they expect Alphabet will grow much faster than Boeing. Indeed, analysts predict an annual growth rate of 16.7 percent per year for Alphabet over the next five years, while they expect a growth rate of only 11.9 percent for Boeing. Remember that Example 8-2 shows how small changes in growth can result in large stock value changes. The large difference in expected growth between Alphabet and Boeing causes a large difference in their relative value. We can more directly see the impact that growth can have on the P/E ratio by modifying the constant-growth model. Begin with the model, P0 = D1 ÷ (i − g). Dividing both sides by the firm’s earnings results in P0/E0 = (D1/E0) ÷ (i − g). Note that the dividend payout ratio of the firm (D/E), the discount rate (i), and the growth rate (g), taken together, determine the P/E ratio. All else held equal, larger growth rates will lead to larger P/E ratios. Also, firms that have higher payout ratios will have higher P/E ratios. Of course, if a firm pays out a high portion of its earnings as dividends, then it may not have the cash to fund high growth. Thus, high dividend payout firms tend not to be priced the same as high growth firms. The value of a stock, and thus its price, relates directly to its future success. Note that valuation models use estimates of future dividends and growth rates. Because of this focus on the future, many people prefer to use a P/E ratio that also looks forward rather than trailing. A forward P/E ratio uses analyst estimates of the earnings in the next 12 months instead of the past 12 months and can be denoted as P/E. The forward P/E ratio has the advantage over the trailing P/E ratio in that it incorporates investors’ expectations of the firm’s upcoming profits. A disadvantage is that expected earnings are harder to estimate and thus less accurate than past earnings. The media uses the trailing P/E ratio, while financial managers and investors use the forward P/E ratio more. forward P/E ratio The P/E ratio computed using the estimated next four quarters of earnings per share. page 253 Investors consider Home Depot an appropriately priced stock. Knowledgeable investors who use the P/E ratio as a relative measure of value compare it to the firm’s expected growth rate. Table 8.3 shows the forward P/E ratio and analysts’ expected growth rates for the 30 Dow Jones Industrial Average firms. Investors consider companies with high P/E ratios and high growth rates to be appropriately priced. Companies with low P/E ratios and low growth also seem to be appropriately priced. Investors should be concerned about firms with high P/E ratios and only single-digit growth rates. As such, Procter & Gamble, Coca-Cola, McDonald’s, and Chevron, among others, may be too expensive for their expected growth rates. Many investors like to buy growth stocks. They seek companies with high growth rates. But growth stock investors are also concerned about paying too much for a stock. While examining growth stocks, they can use the P/E ratio to assess how expensive the stock is. On the other hand, investors consider companies with low P/E ratios and high expected growth to be undervalued, and they are often referred to as value stocks. Apple and Boeing would qualify as value stocks. Many investors like to buy value stocks because they feel they are getting a bargain price for a stable company. value stocks Companies considered to be temporarily undervalued. ▼ TABLE 8.3 P/E Ratios and Analyst Growth Estimates of DJIA Firms, February 12, 2016 A B C D E 1 Ticker Company Name Stock Price Forward P/E Ratio Next 5 Year’s Growth (%) 2 HD Home Depot $116.32 18.88 14.39 3 PG Procter & Gamble 80.99 20.00 6.95 4 KO Coca-Cola Company 43.11 20.83 8.95 page 254 5 MCD McDonald’s Corporation 117.93 19.56 9.50 6 VZ Verizon Communication 50.11 12.31 4.51 7 DIS Walt Disney 91.15 14.68 11.85 8 MMM 3M Company 153.96 17.26 8.10 9 JNJ Johnson & Johnson 101.82 14.76 5.32 10 AAPL Apple, Inc. 93.99 9.39 11.93 11 UTX United Technologies 85.95 12.24 9.07 12 GE General Electric 28.26 15.96 7.97 13 WMT Walmart Stores 66.18 15.87 0.87 14 AXP American Express 52.66 9.37 8.10 15 PFE Pfizer 29.36 11.65 5.44 16 MRK Merck & Company 49.03 12.87 4.24 17 XOM Exxon Mobil 81.03 18.58 26.40 18 IBM International Business Machines 121.04 8.55 7.25 19 TRV The Travelers Company 107.49 10.79 2.94 20 DD E.I. du Pont de Nemours 58.40 16.88 9.00 21 BA Boeing Company 108.63 11.53 11.92 22 NKE Nike, Inc. 56.42 22.84 12.62 23 CSCO Cisco Systems 25.11 10.51 8.24 24 INTC Intel Corporation 28.64 10.77 10.00 25 CAT Caterpillar 63.15 17.21 0.43 26 CVX Chevron Corporation 85.43 18.18 −23.86 27 UNH UnitedHealth Group 111.82 12.74 14.03 28 MSFT Microsoft Corporation 50.50 16.45 9.51 29 GS Goldman Sachs Group 146.13 7.54 4.31 30 JPM JPMorgan Chase 57.49 8.59 7.89 31 V Visa, Inc. 70.42 21.67 16.62 Source: Yahoo! Finance Screener. There are some cases when a P/E ratio is not useful for relative valuation. For example, sometimes, a firm will lose money. That is, the earnings are negative. In other cases, a firm will take a large “write-off” that will temporarily suppress earnings. In these cases, the P/E ratio would be negative or temporarily large. Therefore, other common relative value techniques are to utilize cash flow (CF) or book value (B) instead of earnings. The P/CF ratio is useful when firms take accounting write-offs that temporarily and dramatically impact earnings. The P/B ratio is useful in all cases but is particularly useful when a firm loses money and has negative cash flows. The book value of a firm is a very stable measure of accounting value, and it is therefore useful when earnings are volatile. EXAMPLE 8-4 The P/E Ratio Model for Caterpillar LG8-7 page 255 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Look at Table 8.3 and notice that the P/E ratio for Caterpillar seems high at 17.21 relative to the growth (0.43 percent) that analysts expect. Caterpillar earned $3.50 per share and paid a $3.08 dividend last year. You decide to explore this apparent anomaly and figure out what Caterpillar’s stock price might reach in five years. SOLUTION: Compute the expected future price in five years under two different scenarios. The first assumption is that Caterpillar’s P/E ratio will be the same in five years as it is today. But since this P/E ratio seems a bit high, the second scenario allows for a decline in the P/E ratio to 13. Under these two scenarios, the future price estimates are Note that if the P/E ratio decreases from 17.21 to 13 in five years, the future price could be much lower than analysts expect without the change. Similar to Problems 8-25, 8-26, 8-35, 8-36 time out! 8-12 Consider two firms with the same P/E ratio. Explain how one could be described as expensive compared to the other. 8-13 Compute the stock price for Goldman Sachs in five years if you expect the P/E ratio to decline to 6 and the earnings per share is $18.58. Estimating Future Stock Prices We can often find it useful to estimate a stock’s future price. Consider equation 8-3’s cash flow discount valuation model. The model requires estimates of future dividends and a future price. How can investors estimate this future price? They can use the P/E ratio model for this purpose. Upon reflection, you will see that multiplying the P/E ratio by earnings results in a stock price. So, in order to estimate a future price, simply multiply the expected P/E ratio by the expected earnings. This concept is captured in the following equation: Future price = Future P / E ratio × Future earnings per share (8-10) As the formula shows, we can use assumptions about the earnings growth rate to estimate earnings in year n. Many investors believe the firm’s P/E ratio in year n is best estimated using today’s P/E ratio. However, if today’s P/E ratio seems unusual compared with similar firms or even compared with a stock index, then adjustments might be wise. http://www.mhhe.com/CornettM4e http://www.mhhe.com/CornettM4e Get Online ©JGI/Jamie Grill/Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. As owners, what rights and advantages do shareholders obtain? (LG8-1) 2. Describe how being a residual claimant can be very valuable. (LG8-1) 3. Obtain a current quote of McDonald’s (MCD) from the Internet. Describe what has changed since the quote in Figure 8.1. (LG8-2) 4. Get the trading statistics for the three main U.S. stock exchanges. Compare the trading activity to that of Table 8.1. (LG8-2) 5. Why might the Standard & Poor’s 500 Index be a better measure of stock market performance than the Dow Jones Industrial Average? Why is the DJIA more popular than the S&P 500? (LG8-3) 6. Explain how it is possible for the DJIA to increase one day while the NASDAQ Composite decreases during the same day. (LG8-3) 7. Which is higher, the ask quote or the bid quote? Why? (LG8-4) 8. Illustrate through examples how trading commission costs impact an investor’s return. (LG8-4) 9. Describe the difference in the timing of trade execution and the certainty of trade price between market orders and limit orders. (LG8-4) page 256 page 257 10. What are the differences between common stock and preferred stock? (LG8-5) 11. How important is growth to a stock’s value? Illustrate with examples. (LG8-5) 12. Under what conditions would the constant-growth model not be appropriate? (LG8-5) 13. The expected return derived from the constant-growth-rate model relies on dividend yield and capital gain. Where do these two parts of the return come from? (LG8-5) 14. Describe, in words, how to use the variable-growth-rate technique to value a stock. (LG8-6) 15. Can the variable-growth-rate model be used to value a firm that has a negative growth rate in Stage 1 and a stable and positive growth in Stage 2? Explain. (LG8-6) 16. Explain why using the P/E relative value approach may be useful for companies that do not pay dividends. (LG8-7) 17. How is a firm’s changing P/E ratio reflected in the stock price? Give examples. (LG8-7) 18. Differentiate the characteristics of growth stocks and value stocks. (LG8-7) 19. What’s the relationship between the P/E ratio and a firm’s growth rate? (LG8-7) 20. Describe the process for using the P/E ratio to estimate a future stock price. (LG8-7) Problems BASIC PROBLEMS 8-1 Stock Index Performance On March 5, 2013, the Dow Jones Industrial Average set a new high. The index closed at 14,253.77, which was up 125.95 that day. What was the return (in percent) of the stock market that day? (LG8-3) 8-2 Stock Index Performance On March 9, 2009, the Dow Jones Industrial Average reached a new low. The index closed at 6,547.05, which was down 79.89 that day. What was the return (in percent) of the stock market that day? (LG8-3) 8-3 Buying Stock with Commissions Your discount brokerage firm charges $7.95 per stock trade. How much money do you need to buy 200 shares of Pfizer, Inc. (PFE), which trades at $31.40? (LG8-4) 8-4 Buying Stock with Commissions Your discount brokerage firm charges $9.50 per stock trade. How much money do you need to buy 300 shares of Time Warner, Inc. (TWX), which trades at $22.62? (LG8- 4) 8-5 Selling Stock with Commissions Your full-service brokerage firm charges $140 per stock trade. How much money do you receive after selling 200 shares of Nokia Corporation (NOK), which trades at $20.13? (LG8-4) 8-6 Selling Stock with Commissions Your full-service brokerage firm charges $135 per stock trade. How much money do you receive after selling 250 shares of International Business Machines (IBM), which trades at $96.17? (LG8-4) 8-7 Buying Stock with a Market Order You would like to buy shares of Sirius Satellite Radio (SIRI). The current ask and bid quotes are $3.96 and $3.93, respectively. You place a market buy order for 500 shares that executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4) 8-8 Buying Stock with a Market Order You would like to buy shares of Coldwater Creek, Inc. (CWTR). The current ask and bid quotes are $20.70 and $20.66, respectively. You place a market buy order for 200 shares that executes at these quoted prices. How much money did it cost to buy these shares? (LG8-4) 8-9 Selling Stock with a Limit Order You would like to sell 200 shares of Xenith Bankshares, Inc. (XBKS). The current ask and bid quotes are $4.66 and $4.62, respectively. You place a limit sell order at $4.65. If the trade executes, how much money do you receive from the buyer? (LG8-4) 8-10 Selling Stock with a Limit Order You would like to sell 100 shares of Echo Global Logistics, Inc. (ECHO). The current ask and bid quotes are $15.33 and $15.28, respectively. You place a limit sell order at $15.31. If the trade executes, how much money do you receive from the buyer? (LG8-4) page 258 8-11 Value of a Preferred Stock A preferred stock from Duquesne Light Company (DQUPRA) pays $3.55 in annual dividends. If the required return on the preferred stock is 6.7 percent, what’s the value of the stock? (LG8-5) 8-12 Value of a Preferred Stock A preferred stock from Hecla Mining Co. (HLPRB) pays $3.50 in annual dividends. If the required return on the preferred stock is 6.8 percent, what is the value of the stock? (LG8- 5) 8-13 P/E Ratio and Stock Price Ultra Petroleum (UPL) has earnings per share of $1.56 and a P/E ratio of 32.48. What’s the stock price? (LG8-7) 8-14 P/E Ratio and Stock Price JPMorgan Chase Co. (JPM) has earnings per share of $3.53 and a P/E ratio of 13.81. What is the price of the stock? (LG8-7) INTERMEDIATE PROBLEMS 8-15 Value of Dividends and Future Price A firm is expected to pay a dividend of $1.35 next year and $1.50 the following year. Financial analysts believe the stock will be at their price target of $68 in two years. Compute the value of this stock with a required return of 10 percent. (LG8-5) 8-16 Value of Dividends and Future Price A firm is expected to pay a dividend of $2.05 next year and $2.35 the following year. Financial analysts believe the stock will be at their price target of $110 in two years. Compute the value of this stock with a required return of 12 percent. (LG8-5) 8-17 Dividend Growth Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate? (LG8-5) 8-18 Dividend Growth Annual dividends of Generic Electrical grew from $0.66 in 2012 to $1.03 in 2017. What was the annual growth rate? (LG8-5) 8-19 Value a Constant Growth Stock Financial analysts forecast Safeco Corp.’s (SAF) growth rate for the future to be 8 percent. Safeco’s recent dividend was $0.88. What is the value of Safeco stock when the required return is 12 percent? (LG8-5) 8-20 Value a Constant Growth Stock Financial analysts forecast Limited Brands (LTD) growth rate for the future to be 12.5 percent. LTD’s recent dividend was $0.60. What is the value of Limited Brands stock when the required return is 14.5 percent? (LG8-5) 8-21 Expected Return Ecolap Inc. (ECL) recently paid a $0.46 dividend. The dividend is expected to grow at a 14.5 percent rate. At a current stock price of $44.12, what is the return shareholders are expecting? (LG8-5) 8-22 Expected Return Paychex Inc. (PAYX) recently paid an $0.84 dividend. The dividend is expected to grow at a 15 percent rate. At a current stock price of $40.11, what is the return shareholders are expecting? (LG8-5) 8-23 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.20 per share in three years. This dividend will grow at 11 percent indefinitely. Using a 12 percent discount rate, compute the value of this stock. (LG8-6) 8-24 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.25 per share in two years. This dividend will grow at 10 percent indefinitely. Using an 11.5 percent discount rate, compute the value of this stock. (LG8-6) 8-25 P/E Ratio Model and Future Price Kellogg Co. (K) recently earned a profit of $2.52 earnings per share and has a P/E ratio of 13.5. The dividend has been growing at a 5 percent rate over the past few years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio declined to 12 in five years? (LG8-7) 8-26 P/E Ratio Model and Future Price New York Times Co. (NYT) recently earned a profit of $1.21 per share and has a P/E ratio of 19.59. The dividend has been growing at a 7.25 percent rate over the past six years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to 22 in five years? (LG8-7) ADVANCED PROBLEMS 8-27 Value of Future Cash Flows A firm recently paid a $0.45 annual dividend. The dividend is expected page 259 to increase by 10 percent in each of the next four years. In the fourth year, the stock price is expected to be $80. If the required return for this stock is 13.5 percent, what is its value? (LG8-5) 8-28 Value of Future Cash Flows A firm recently paid a $0.60 annual dividend. The dividend is expected to increase by 12 percent in each of the next four years. In the fourth year, the stock price is expected to be $110. If the required return for this stock is 14.5 percent, what is its value? (LG8-5) 8-29 Constant Growth Stock Valuation Waller Co. paid a $0.137 dividend per share in 2000, which grew to $0.55 in 2012. This growth is expected to continue. What is the value of this stock at the beginning of 2013 when the required return is 13.7 percent? (LG8-5) 8-30 Constant Growth Stock Valuation Campbell Supper Co. paid a $0.632 dividend per share in 2013, which grew to $0.76 in 2016. This growth is expected to continue. What is the value of this stock at the beginning of 2017 when the required return is 8.7 percent? (LG8-5) 8-31 Changes in Growth and Stock Valuation Consider a firm that had been priced using a 10 percent growth rate and a 12 percent required return. The firm recently paid a $1.20 dividend. The firm just announced that because of a new joint venture, it will likely grow at a 10.5 percent rate. How much should the stock price change (in dollars and percentage)? (LG8-5) 8-32 Changes in Growth and Stock Valuation Consider a firm that had been priced using an 11.5 percent growth rate and a 13.5 percent required return. The firm recently paid a $1.50 dividend. The firm has just announced that because of a new joint venture, it will likely grow at a 12 percent rate. How much should the stock price change (in dollars and percentage)? (LG8-5) 8-33 Variable Growth A fast-growing firm recently paid a dividend of $0.35 per share. The dividend is expected to increase at a 20 percent rate for the next three years. Afterwards, a more stable 12 percent growth rate can be assumed. If a 13 percent discount rate is appropriate for this stock, what is its value? (LG8-6) 8-34 Variable Growth A fast-growing firm recently paid a dividend of $0.40 per share. The dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 11 percent growth rate can be assumed. If a 12.5 percent discount rate is appropriate for this stock, what is its value? (LG8-6) 8-35 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per share and dividend per share are $2.50 and $1.30, respectively. Both are expected to grow at 8 percent. However, the firm’s current P/E ratio of 22 seems high for this growth rate. The P/E ratio is expected to fall to 18 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using a 10 percent required rate. (LG8-5, LG8-7) 8-36 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per share and dividend per share are $2.75 and $1.60, respectively. Both are expected to grow at 9 percent. However, the firm’s current P/E ratio of 23 seems high for this growth rate. The P/E ratio is expected to fall to 19 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 11 percent required rate. (LG8-5, LG8-7) 8-37 Spreadsheet Problem Spreadsheets are especially useful for computing stock value under different assumptions. Consider a firm that is expected to pay the following dividends: Year 1 2 3 4 5 6 $1.20 $1.20 $1.50 $1.50 $1.75 $1.90 and grow at 5% thereafter a. Using an 11 percent discount rate, what would be the value of this stock? b. What is the value of the stock using a 10 percent discount rate? A 12 percent discount rate? c. What would the value be using a 6 percent growth rate after year 6 instead of the 5 percent rate using each of these three discount rates? d. What do you conclude about stock valuation and its assumptions? 8-38 Spreadsheet Problem Design a spreadsheet similar to the one below to compute the value of a variable growth rate firm over a five-year horizon. a. What is the value of the stock if the current dividend is $1.30, the first stage growth is 18 percent, the second stage growth is 9 percent, and the discount rate is 11 percent? b. What is the value of the stock if the current dividend is $1.30, the first stage growth is 2 percent, the second stage growth is 8 percent, and the discount rate is 9.5 percent? c. What is the value of the stock if the current dividend is $2.50, the first stage growth is 15 percent, the second stage growth is 7 percent, and the discount rate is 10 percent? A B C D E F 1 Inputs 2 Current dividend = 3 First-stage growth = 4 Second-stage growth = 5 Discount rate = 6 7 Year 1 2 3 4 5 8 Projected dividend 9 Terminal price = 10 Present value = Part Five page 260 page 261 chapter nine characterizing risk and return ©Brand X/JupiterImages Y page 262 ou can invest your money very safely by opening a savings account at a bank or by buying Treasury bills. So why would you invest your money in risky stocks and bonds if you can take advantage of low-risk opportunities? The answer: Very low risk investments also provide a very low return. Investors take on higher risk investments in expectation of earning higher returns. Likewise, businesses also take on risky capital investments only if they expect to earn higher returns that at least cover their costs, including investors’ required return. Both investor and business sentiments create a positive relationship between risk and expected return. Of course, taking risk means that you get no guarantee that you will recoup your investment. In the short run, higher risk investments often significantly underperform lower risk investments. In addition, not all forms of risk are rewarded. In this chapter, you’ll see how the risk-return relationship fundamentally affects finance theory. We focus on using historical information to characterize past returns and risks. We show how you can diversify to eliminate some risk and expect the highest return possible for your desired risk level. In Chapter 10, we’ll turn to estimating the risks and returns you should expect in the future. ■ LEARNING GOALS LG9-1 Compute an investment’s dollar and percentage return. LG9-2 Find information about the historical returns and volatility for the stock, bond, and cash markets. LG9-3 Measure and evaluate the total risk of an investment using several methods. LG9-4 Recognize the risk-return relationship and its implications. LG9-5 Plan investments that take advantage of diversification and its impact on total risk. LG9-6 Find efficient and optimal portfolios. LG9-7 Compute a portfolio’s return. viewpoints business APPLICATION Managers from the production and marketing departments have proposed some risky new business projects for your firm. These new ideas appear to be riskier than the firm’s current business operations. You know that diversifying the firm’s product offerings could reduce the firm’s overall risk. However, you are concerned that taking on these new projects will make the firm’s stock too risky. How can you determine whether these project ideas would make the firm’s stock riskier or less risky? (See the solution at the end of the book.) 9.1 • HISTORICAL RETURNS LG9-1 Let’s begin our discussion of risk and return by characterizing the concept of return. First, we need a method for calculating returns. After computing a return, investors need to assess whether it was a good, average, or bad investment return. Examining returns from the past gives us a general idea of what we might expect to see in the future. We should think in terms of return for the long run because a return for any one year can be quite different from the average returns from the past couple of decades. Computing Returns How much have you earned on each of your investments? Two ways to determine this are to compute the actual dollar return or compute the dollar return as a percentage of the money invested. Dollar Return The dollar return earned includes any capital gain (or loss) that occurred as well as any income that you received over the period. Equation 9-1 illustrates the dollar return calculation: page 263 (9-1) dollar return The amount of profit or loss from an investment denoted in dollars. For example, say you held 50 shares of Alphabet (GOOG), the parent company of Google. The stock price had a market price of $526.40 per share at the end of 2014. Alphabet paid no dividends during 2015. At the end of 2015, Alphabet’s stock price was $758.88. For the whole of 2015, you earned a capital gain of ($758.88 − $526.40) × 50 shares, or $11,624. In Alphabet’s case, the stock price increased, so you experienced a capital gain. On the other hand, the toy and game producer Mattel, Inc. (MAT) started the year at $30.95 per share, paid $1.52 in dividends, and ended 2015 at $27.17. If you owned 200 shares of Mattel, you would have experienced a capital loss of −$756 (= [$27.17 − $30.95] × 200 shares). This loss would have been partially offset by the $304 of dividends received. However, the total dollar return would still have been −$452 (= −$756 + $304). Stock prices can fluctuate substantially and cause large positive or negative dollar returns. personal APPLICATION Suppose an investor owns a portfolio invested 100 percent in long-term Treasury bonds because the owner prefers low risk. The investor has avoided owning stocks because of their high volatility. The investor’s stockbroker claims that putting 10 percent of the portfolio in stocks would actually reduce total risk and increase the portfolio’s expected return. The investor knows that stocks are riskier than bonds. How can adding the risky stocks to the bond portfolio reduce the risk level? (See the solution at the end of the book.) Is there such a thing as a high-reward, zero-risk investment? Does your dollar return depend on whether you continue to hold the Alphabet and Mattel stock or sell it? No. In general, finance deals with market values. Alphabet stock was worth $758.88 at the end of 2015 regardless of whether you held the stock or sold it. If you sell it, then we refer to your gains as “realized” gains. If you continue to hold the stock, the gains are “unrealized” gains. Percentage Return We usually find it more useful to characterize investment earnings as percentage returns so that we can easily compare one investment’s return to other alternatives’ returns. We calculate percentage return by dividing the dollar return by the investment’s value at the beginning of the time period. (9-2) Because it’s standardized, we can use percentage returns for almost any type of investment. We can use beginning and ending values for stock positions, bond prices, real estate values, and so on. Investment income may be stock dividends, bond interest payments, or other receipts. The percentage return for holding the Mattel stock during calendar year 2015 was −7.3 percent, computed as The return for the Alphabet position during the same period was a whopping 44.16 percent: page 264 Both firms belong to the S&P 500 Index, which earned 1.38 percent in 2015. Are one-year returns typical for expectations in the long run? We look to average returns to examine performance over time. The arithmetic average return provides an estimate for how the investment has performed over longer periods of time. The formula for the average return is (9-3) where the return for each subperiod is summed up and divided by the number of subperiods. You can state the returns in either percentage or decimal format. percentage return The dollar return characterized as a percentage of money invested. average returns A measure summarizing the past performance of an investment. EXAMPLE 9-1 Computing Returns LG9-1 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. You are evaluating a stock’s short-term performance. On August 16, 2010, technology firm 3PAR saw its stock price surge on news of a takeover battle between Dell and Hewlett-Packard. 3PAR stock had closed the previous trading day at $9.65 and was up to $18.00 by the end of the day. 3PAR had ended 2009 at $11.85 and does not pay a dividend. What is the dollar return and percentage return of 300 shares of 3PAR for the day and year to date? SOLUTION: For the day, realize that no income is paid. Therefore, the dollar return is $2,505 = 300 × ($18.00 − $9.65) + 0 and the percent return is 86.53% = $2,505 ÷ (300 × $9.65). The year to date (YTD) return also does not include dividend income. So the dollar YTD return is $1,845 = 300 × ($18.00 − $11.85). The 3PAR YTD percentage return is Hewlett-Packard eventually won the bidding war and purchased 3PAR for $33 per share! Similar to Problems 9-1, 9-2, 9-3, 9-4, Self-Test Problem 1 Alphabet has only been a public company for a relatively brief period, so it will not have a long history of returns. Thus, Table 9.1 shows the annual returns for Mattel and office supply store Staples, Inc., from 1991 to 2015. First, notice that over time, the returns are quite varied for both firms. The stock return for Mattel has ranged from a low of −52.4 percent in 1999 to a high of 82.6 percent in 1991. Staples’ stock return varied between −45.7 percent (2015) to 171.6 percent (1991). Also note that the returns appear unpredictable or random. Sometimes a large http://mhhe.com/CornettM4e negative return is followed by another bad year, like Mattel’s returns in 2007 and 2008. Other times, a poor year is followed by a very good year, like 2008 and 2009 for Staples. The table also reports average annual returns for Mattel and Staples of 14.8 percent and 19.4 percent, respectively. Over the years, the annual returns for these stocks have been quite different from their average returns. ▼ TABLE 9.1 Annual and Average Returns for Mattel and Staples, 1991 to 2015 A B C D E F 1 Mattel Staples Mattel Staples 2 1991 82.6% 171.6% 2004 5.4% 24.0% 3 1992 33.0% 14.9% 2005 −12.6% 9.5% 4 1993 6.9% 13.5% 2006 52.1% 9.4% 5 1994 15.5% 30.0% 2007 −10.5% −5.9% 6 1995 59.8% 46.3% 2008 −28.5% −32.5% 7 1996 10.5% 24.9% 2009 44.3% 49.5% 8 1997 46.6% 32.9% 2010 24.0% −3.3% 9 1998 −43.0% 136.4% 2011 35.6% −32.7% 10 1999 −52.4% −16.8% 2012 25.9% −4.6% 11 2000 47.4% −30.5% 2013 34.3% 0.8% 12 2001 28.8% 10.0% 2014 −32.1% 34.5% 13 2002 5.5% −5.8% 2015 −5.2% −45.7% 14 2003 −3.5% 55.0% 15 Average = 14.8% 19.4% Note the range of returns. Few annual returns are close to the average return. Source: Yahoo! Finance. page 265 Mattel’s stock returns have ranged from -52.4 percent to 82.6 percent. ©McGraw-Hill Education/Mark Steinmetz, photographer The average returns shown in this chapter are more precisely called arithmetic average returns. These average returns are appropriate for statistical analysis. However, they do not accurately illustrate the historical performance of a stock or portfolio. To see this, consider the $100 stock that earned a 50 percent return one year (to $150) and then earned a −50 percent return the next year (to $75). The arithmetic average return is therefore (50% + −50%) ÷ 2 = 0%. Do you believe the average return was zero percent per year? If you started with a $100 stock and ended with a $75 stock, did you earn zero percent? No, you lost money. A measure of that performance should illustrate a negative return. The accurate measure to be used in performance analysis is called the geometric mean return, or the mean return computed by finding the equivalent return that is compounded for N periods. In this example, the mean return is [(1 + 0.50) × (1 + −0.50)]1/2 − 1 = −0.134, or −13.4 percent. Given the loss of $25 over two years, this −13.4 percent per year mean return seems more reasonable than the zero percent average return. The general formula for the geometric mean return is (9-4) geometric mean return The mean return computed by finding the equivalent return that is compounded for N periods. Performance of Asset Classes LG9-2 During any given year, the stock market may perform better than the bond market, or it may perform worse. Over longer time periods, how do stocks, bonds, or cash securities perform? Historically, stocks have performed better than either bonds or cash. Table 9.2 shows the average returns for these three asset classes over the period 1950 to 2015, as well as over various subperiods. Over the entire period, stocks (as measured by the S&P 500 Index) earned an average 12.6 percent return per year. This is nearly double the 6.6 percent return earned by long-term Treasury bonds. Cash securities, measured by U.S. Treasury bills, earned an average 4.4 percent return. ▼ TABLE 9.2 Annual and Average Returns for Stocks, Bonds, and T-Bills, 1950 to 2015 A B C D E 1 Stocks Long-Term Treasury Bonds T-Bills 2 1950 to 2015 Average 12.6% 6.6% 4.4% page 266 3 1950 to 1959 Average 20.9% 0.0% 2.0% 4 1960 to 1969 Average 8.7% 1.6% 4.0% 5 1970 to 1979 Average 7.5% 5.7% 6.3% 6 1980 to 1989 Average 18.2% 13.5% 8.9% 7 1990 to 1999 Average 19.0% 9.5% 4.9% 8 2000 to 2009 Average 0.9% 8.0% 2.7% 9 2010 Annual Return 15.1% 9.4% 0.01% 10 2011 Annual Return 2.1% 29.9% 0.02% 11 2012 Annual Return 16.0% 3.6% 0.02% 12 2013 Annual Return 32.4% −12.7% 0.07% 13 2014 Annual Return 13.7% 25.1% 0.05% 14 2015 Annual Return 1.4% −1.2% 0.21% 15 2010 to 2015 Average 13.4% 9.0% 0.06% Returns have been very different among decades. The table also shows each asset class’s average return for each decade since 1950. The best decade for the stock market was the 1950s, when stocks earned an average 20.9 percent per year. The 1990s ran a close second with a 19 percent per year return. The best decade for the bond market was the 1980s, when it earned an average 13.5 percent per year return due to capital gains as interest rates fell. Stocks have outperformed bonds in every decade since 1950 except the recent 2000s. Notice that the average return in the stock and bond markets has not been negative during any decade since 1950. But average stock returns do not really paint a very accurate picture of annual returns. Individual annual returns can vary strongly and be quite negative in any particular year. Indeed, this annual variability defines risk. The stock market return in 2008 was particularly poor because of the financial crisis. However, not all stocks fell the same amount. Notice that Mattel and Staples declined by only 28.5 and 32.5 percent while the stock market in general declined 35.5 percent. Financial company stocks fell the most during the crisis. time out! 9-1 How important were dividend payments to the total returns that Mattel and Staples offered investors? 9-2 Using the average returns shown in Table 9.2, compute how much a $10,000 investment made in each asset class at the beginning of each decade would become at the end of each decade. 9.2 • HISTORICAL RISKS LG9-3 page 267 page 268 When you purchase a U.S. Treasury bill, you know exactly what your dollar and percentage return are going to be. Many people find comfort in the certainty from this safe investment. On the other hand, when you purchase a stock, you do not know what your return is going to be—either in the short term or in the long run. This uncertainty is precisely what makes stock investing risky. It’s useful to evaluate this uncertainty quantitatively so that we can compare risk among different stocks and asset classes. Computing Volatility Financial theory suggests that investors should look at an investment’s historical returns to assess how much uncertainty to expect in the future. If you see high variability in historical returns, you should expect a high degree of future uncertainty. Table 9.2 shows that between 2010 and 2015, the stock market experienced a range of 1.4 percent return in 2015 to a 32.4 percent return in 2013. Bonds also experienced variability: −12.7 percent return in 2013 to 29.9 percent return in 2011. Examining the range of historical returns provides just one way to express the return volatility that we can expect. In practical terms, the finance industry uses a statistical return volatility measure known as the standard deviation of percentage returns. We calculate standard deviation as the square root of the variance, and this figure represents the security’s or portfolio’s total risk. We’ll discuss other risk measurements in the next chapter. standard deviation A measure of past return volatility, or risk, of an investment. total risk The volatility of an investment, which includes current portions of firm-specific risk and market risk. Our process of computing standard deviation starts with the average return over the period. The average annual return for the stock market since 1950 is 12.6 percent. How much can the return in any given year deviate from this average? We compute the actual annual deviation by subtracting the return each year from this average return: Return(1950) − Average return; Return(1951) − Average return; Return(1952) − Average return, and so on. Note that many of these deviations will be negative (from a lower-than-average return that year) and others will be positive (from a higher-than-average return). If we computed the average of these return deviations, our result would be zero. Large positive deviations cancel out large negative deviations and hide the variability. To really see the size of the variations without the distractions that come with including a positive or negative sign, we square each deviation before adding them up. Dividing by the number of returns in the sample minus one provides the return variance.1 The square root of the return variance is the standard deviation: (9-5) Note that this equation provides an estimate of the true population standard deviation using a specific historical sample. A large standard deviation indicates greater return volatility—or high risk. Table 9.3 shows the standard deviations of Mattel stock returns over 25 years. The Deviation column shows the annual return minus Mattel’s average return of 14.8 percent. The last column squares each deviation. Then we sum up these squared deviations and divide the result by the number of observations less one (24) to compute the return variance. If we want to use a measure that makes sense in the real world (how would you interpret a squared percentage, anyway?), we take the square root of the variance to get the standard deviation. Mattel’s standard deviation of returns during this sample period comes to 33.4 percent. In comparison, the standard deviation of Staples stock returns for this same period is 48.7 percent. Since Staples’ standard deviation is higher, its stock features more total risk than Mattel’s stock does. ▼ TABLE 9.3 Computation of Mattel Stock Return Standard Deviation Investors use standard deviation as a measure of risk; the higher the standard deviation, the riskier the asset. Source: Yahoo! Finance. EXAMPLE 9-2 Risk and Return LG9-1, LG9-3 page 269 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Find the average return and risk (as measured by standard deviation) for Mattel since 2006. Table 9.3 shows the annual returns for years 2006 to 2015. SOLUTION: First, compute the average annual return for the period. Using equation 9-3 Mattel has averaged a 14.0 percent return per year since 2006. To compute the risk, use the standard deviation equation 9-5. First, find the deviations of return for each year: Year 2006 2007 2008 2009 2010 2011 2012 2013 2014 52.1% −14.0% −10.5% −14.0% −28.5% −14.0% 44.3% −14.0% 24.0% −14.0% 35.6% −14.0% 25.9% −14.0% 34.3% −14.0% −32.1% −14.0% Square those deviations: Year 2006 2007 2008 2009 2010 2011 2012 2013 (52.1% −14.0%)2 (−10.5% −14.0%)2 (−28.5% −14.0%)2 (44.3% −14.0%)2 (24.0% −14.0%)2 (35.6% −14.0%)2 (25.9% −14.0%)2 (34.3% −14.0%) Then add them up, divide by n − 1, and take the square root: Mattel stock has averaged a 14.0 percent return with a standard deviation of 30.5 percent since 2006. Similar to Problems 9-15, 9-16, 9-17, 9-18, 9-33, 9-34, Self-Test Problem 2 Although analysts and investors use a stock return’s standard deviation as an important and common measure of risk, it’s laborious to compute by hand. Most people use a spreadsheet or statistical software to calculate stock return standard deviations. Risk of Asset Classes LG9-2 http://mhhe.com/CornettM4e Because RadioShack’s standard deviation is higher, it’s stock features more total risk. ©Juice Images/Getty Images We report the standard deviations of return for stocks, bonds, and T-bills in Table 9.4 for 1950 to 2015 and for each decade since 1950. Over the entire sample, the stock market returns’ standard deviation is 17.3 percent. As we would expect, stock market volatility is higher than bond market volatility (11.1 percent) or for T-bills (3.0 percent). These volatility estimates are consistent with our previously stated position that the stock market carries more risk than the bond or cash markets do. Every decade since 1950 has seen a lot of stock market volatility. The bond market has experienced the most volatility since the 1980s as interest rates varied dramatically. ▼ TABLE 9.4 Annual Standard Deviation of Returns for Stocks, Bonds, and T-Bills, 1950 to 2015 Stocks Long-Term Treasury Bonds T-Bills 1950 to 2015 17.3% 11.1% 3.0% 1950 to 1959 19.8 4.9 0.8 1960 to 1969 14.4 6.2 1.3 1970 to 1979 19.2 6.8 1.8 1980 to 1989 12.7 15.1  2.6 1990 to 1999 14.2 12.8  1.2 2000 to 2009 20.4 10.3  1.9 2010 to 2015 11.3 16.1  0.1 Some decades experience higher risk than others in each asset class. You will recall from Chapter 7 that since any bond’s par value and coupon rate are fixed, bond prices must fluctuate to adjust for changes in interest rates. Bond prices respond inversely to interest rate changes: As interest rates rise, bond prices fall, and if interest rates fall, bond prices rise. T-bill returns have experienced very low volatility over each decade. Indeed, T-bills are commonly considered to be one of the only risk-free assets. Higher-risk investments offer higher returns over time. But short-term fluctuations in the value of higher risk investments can be substantial. The stock market is risky—while it has offered a good annual return of 12.6 percent, that return comes with volatility of 17.3 percent standard deviation. Many investors may intellectually understand that this high risk means that they may receive very poor returns in the short term. Investors really felt the full force of this risk when the stock market declined three years in a row (2000 to 2002). Some investors even decided that this was too much risk for them and they sold out of the stock market before the 2003 rally. Other investors got out of the stock market after it plunged to lows in March 2009. Market volatility can cause investors to make emotionally based decisions— selling at low prices. The stock market returns’ standard deviations that appear in Table 9.4 are all considerably lower than the standard deviations of Mattel and of Staples stocks (33.4 percent and 48.7 percent, respectively). In this case, we measure page 270 stock market return and standard deviation using the S&P 500 Index. Mattel and Staples are both included in the S&P 500 Index. Why do these two large firms have measures of total risk—standard deviations—that are at least twice as large as the standard deviations on the stock market returns? Are Mattel and Staples just two of the most risky firms in the Index? Actually, no. The differences in standard deviations between these individual companies and the entire market have much more to do with diversification. Owning 500 companies, such as all of those included in the S&P 500 Index, generates much less risk than owning just one company. This phenomenon appears in the standard deviation measure. We’ll discuss the effects of diversification in detail later in this chapter. Risk versus Return LG9-4 Investors can buy very safe T-bills. Or they can take some risk to seek higher returns. How much extra return can you expect for taking more risk? This is known as the trade-off between risk and return. The coefficient of variation (CoV) is a common relative measure of this risk-vs-reward relationship. The equation for the coefficient of variation is simply the standard deviation divided by average return. It is interpreted as the amount of risk (measured by volatility) per unit of return: (9-6) As an investor, you would want to receive a very high return (the denominator in the equation) with a very low risk (the numerator). So, a smaller CoV indicates a better risk-reward relationship. Since the average return and standard deviation for Mattel stock are 14.8 percent and 33.4 percent, its CoV is 2.26 (= 33.4 ÷ 14.8). This is better than Staples’ CoV of 2.51 (= 48.7 ÷ 19.4). For all asset classes for the period 1950 to 2015, the stock market earned a higher return than bonds and was also riskier. But which one had a better risk-return relationship? The CoV for common stock is 1.37 (= 17.3 ÷ 12.6). For Treasury bonds, the coefficient of variation is 1.68 (= 11.1 ÷ 6.6). Even though stocks are riskier than bonds, they involve a somewhat better risk-reward trade-off. coefficient of variation A measure of risk to reward (standard deviation divided by average return) earned by an investment over a specific period of time. EXAMPLE 9-3 Risk versus Return LG9-4 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. You are interested in the risk-return relationship of stocks in each decade since 1950. Obtain the average returns and risks in Table 9.2 and Table 9.4. SOLUTION: Using the coefficient of variation, the average returns, and standard deviation of return, compute the following risk-return relationships: Note that over short time periods, the stock risk-return relationship varies significantly. http://mhhe.com/CornettM4e page 271 Similar to Problems 9-7, 9-8, 9-19, 9-20, 9-33, and 9-34, Self-Test Problem 3 time out! 9-3 What volatility measure can we use to evaluate and compare risk among different investment alternatives? 9-4 Explain why the coefficients of variation for Mattel and Staples are so much higher than the CoV for the stock market as a whole. 9.3 • FORMING PORTFOLIOS LG9-5 As we noted previously, Mattel and Staples stocks’ risk as measured by their standard deviations appear quite high compared to the standard deviation of the S&P 500 Index. This is by no means a coincidence. Combining stocks into portfolios can reduce many sources of stock risk. Diversification reduces risk. The S&P 500 Index, for example, tracks 500 companies, which allows for a great deal of diversification. Diversifying to Reduce Risk Think about a stock’s total risk as having two components. The first component includes risks that are both specific to that company and common to other companies in the same industry. We call this risk firm-specific risk. The stock’s other risk component is general risk that all firms—and all individuals, for that matter—face based upon economic strength both domestically and globally. We call this type of risk market risk. These risks appear in the equation (9-7) Standard deviations measure total risk. Individual stocks are subject to many firm-specific risks. We can reduce firm-specific risk by combining stocks into a portfolio. Since we can reduce firm-specific risk by diversifying, this risk is sometimes referred to as diversifiable risk. If Staples announces lower-than-expected profits, its stock price will decline. However, since this news is specific to Staples, the news should not affect Mattel stock’s price. On the other hand, if the government announces a change in unemployment, both stocks’ prices will change to some degree. Macroeconomic events represent market risks because such events—unemployment claims, interest rate changes, national budget deficits or surpluses—affect all companies. portfolio A combination of investment assets held by an investor. diversification The process of putting money in different types of investments for the purpose of reducing the overall risk of the portfolio. firm-specific risk The portion of total risk that is attributable to firm or industry factors. Firm-specific risk can be reduced through diversification. market risk The portion of total risk that is attributable to over-all economic factors. diversifiable risk Another term for firm-specific risk. Diversification reduces risk. ©Dimitri Vervitsiotis/Getty Images Suppose that you own only Mattel stock and have earned the annual returns shown in Table 9.5. Then someone suggests that you add Staples to your Mattel stock to form a two-stock portfolio. Both Mattel and Staples stocks carry a lot of total risk. But look at the risk and return characteristics of a portfolio consisting of 50 percent Staples stock and 50 percent Mattel stock. You start with Mattel stock, which provided an average return of 14.8 percent with a risk of 33.4 percent. The Staples stock you are adding has more risk than Mattel. The two-stock portfolio earns an average 17.1 percent return with a standard deviation of only 32.1 percent. You added a high-risk stock to a high-risk stock and you ended up with a portfolio with lower risk and a higher return! This is a hallmark of most portfolios, which pool market risk but often provide offsetting, reduced firm-specific risks overall. ▼ TABLE 9.5 Combining Stocks Can Greatly Reduce Risk The risk-reducing power of diversification! Note that the risk of the portfolio is lower than the risk of the two stocks individually. Source: Yahoo! Finance. Next, add IBM stock to your Mattel and Staples stock portfolio. Figure 9.1 shows that the total risk of this three- stock portfolio declines to 25.7 percent. Note that adding Newmont Mining, Disney, and General Electric also reduces the total risk of the stock portfolio. As you add more stocks, the firm-specific risk portion of the total portfolio risk declines. The total risk falls rapidly as we add the first few stocks. Diversification’s power to reduce page 272 ▼ page 273 firm-specific risk weakens for the later stocks added to the portfolio, because we have already eliminated much of the firm-specific risk. We could continue to add stocks until the portfolio comprises all S&P 500 Index firms, in which case the standard deviation of the portfolio would be 17.3 percent. At this point, virtually all of the firm-specific risk has been purged and the portfolio carries only market risk, which is sometimes called nondiversifiable risk. nondiversifiable risk Another term for market risk. FIGURE 9.1 Adding Stocks to a Portfolio Reduces Risk The total portfolio risk is greatly reduced by adding the first few stocks to a portfolio. finance at work //: personal Investor Diversification Problems Experts have examined investor behavior using detailed datasets of stock brokerage accounts, employee pension plans, and the Survey of Consumer Finances. Studies have identified many investor behaviors that are inconsistent with the principle of full diversification: Many households own relatively few individual stocks—they held a median number of two stocks until 2001, when it rose to three. Of course, many households own equity indirectly, through mutual funds or retirement accounts, and these indirect holdings tend to be much better diversified. Ten to 15 percent of households with between $100,000 and $1 million in financial asset wealth own no stocks (neither directly nor indirectly through funds). Investors seem to prefer securities of local firms. Many geographic regions feature companies that are heavily concentrated in few industries. Thus, a local preference could reduce diversification opportunities. Many employees hold mostly their employers’ stocks (more than 50 percent of employee holdings), particularly within their 401(k) retirement savings accounts. Holding a lot of a single stock creates a “portfolio” with high total risk. Finance professionals and the investment industry have established diversification concepts for many decades and can help investors maximize their returns with appropriate risk levels. But many investors do not consult professionals; they fail to diversify and thus take unnecessary diversifiable risk. ▼ page 274 Ten to fifteen percent of households with between $100,00 and $1 million in financial asset wealth own no stocks. ©Photodisc/Punchstock Want to know more? Key Words to Search for Updates: diversification, pension plan choices, asset allocation Sources: Dimmock, Stephen G., Roy Kouwenberg, Olivia S. Mitchell, and Kim Peijnenburg, “Ambiguity Aversion and Household Portfolio Choice Puzzles: Empirical Evidence,” Journal of Financial Economics; in press (2016); and Hans-Martin Von Gaudecker, “How Does Household Portfolio Diversification Vary with Financial Literacy and Financial Advice?,” Journal of Finance 70 (2015): 489–507. Modern Portfolio Theory LG9-6 The concept that diversification reduces risk was formalized in the early 1950s by Harry Markowitz, who eventually won the Nobel Prize in Economics for his work. Markowitz’s modern portfolio theory shows how risk reduction occurs when securities are combined. The theory also describes how to combine stocks to achieve the lowest total risk possible for a given expected return. Or, said differently, it describes how to achieve the highest expected return for the desired risk level. The combination of securities that achieves the highest expected return for a person’s desired level of risk is called the investor’s optimal portfolio. In our Mattel and Staples portfolio example, we allocated 50 percent of the portfolio to Mattel and 50 percent to Staples. Is this the best allocation for the portfolio? Consider the different allocations shown in Figure 9.2 for the two stocks. The graph shows the expected return (computed as average return) and risk (computed as standard deviation) of various portfolios. It would be terrific if you could find a portfolio located in the upper left-hand corner. That is, investors would like a high expected return with low risk. One large dot shows the risk-return point for owning only Mattel. The other large dot shows owning only Staples. The smaller diamonds show 10/90, 25/75, 40/60, 50/50, 60/40, 75/25, and 90/10 allocations of Mattel/Staples stocks. FIGURE 9.2 Risk and Return Ramifications of Portfolio Allocations to Mattel and Staples page 275 ▼ Investors only value the portfolios at the top of the graph because they offer the same risk as the lower portfolios but with higher expected return! While all these portfolios are possible, not all are desirable. For example, the portfolio of 75 percent Mattel and 25 percent Staples is not desirable. Other portfolios provide both higher return and lower risk. We say that one portfolio dominates the other if it has higher expected return for the same (or less) risk, or the same (or higher) expected return with lower risk. The dominating portfolios appear higher and to the left in the figure. One such portfolio consists of 25 percent Mattel stock and 75 percent Staples stock. The 50/50 portfolio (circled in the figure) is also better than the 75/25 portfolio. Portfolios with the highest return possible for each risk level are called efficient portfolios. Notice that if you drew a line connecting the dots, the figure would appear like the end of a bullet. The portfolios on the top of the bullet dominate the portfolios on the bottom; the top portfolio dots show the efficient portfolios for these two stocks. modern portfolio theory A concept and procedure for combining securities into a portfolio to minimize risk. optimal portfolio The best portfolio of securities for the investor’s level of risk aversion. efficient portfolios The set of portfolios that have the maximum expected return for each level of risk. Figure 9.3 shows efficient portfolios for combining the four stocks: Staples, Mattel, IBM, and Newmont Mining. We used this portfolio to demonstrate how diversification reduces risk in Figure 9.1. These portfolios appear as diamonds in the figure with each diamond representing a different allocation of the four stocks. The single square represents the portfolio that consists of 25 percent in each of the four stocks. Notice that other, efficient portfolios dominate this portfolio. FIGURE 9.3 Efficient Portfolios from Four Stocks page 276 ▼ The efficient portfolios dominate all of the individual stocks. If we showed all efficient portfolios, they would appear as a line that connects the upper side of the bullet shape. If we added all available securities to the graph, then all of the efficient portfolios of those securities form the efficient frontier. Efficient frontier portfolios dominate all other possible stock portfolios. The shape of the efficient frontier implies that diminishing returns apply to risk-taking in the investment world. To gain ever-higher expected rates of return, investors must be willing to take on ever-increasing amounts of risk. The optimal portfolio for you is one on the efficient frontier that reflects the amount of risk that you’re willing to take. Clearly, optimal portfolio choice depends on individual risk preferences. Highly risk-averse investors will select low-risk portfolios on the efficient frontier, while more adventuresome investors will select higher-risk portfolios. Any choice may be appropriate, given differences in individual risk preferences. Investors can further diversify by adding foreign stocks and commodities to their portfolio. For example, a U.S. investor can lower total risk by adding stocks from emerging market countries and gold. efficient frontier The combination of all efficient portfolios. How Does Diversification Work? LG9-5 Will combining any two stocks greatly reduce total risk as much as combining Staples and Mattel did? The answer is no. If two stocks are subject to exactly the same kinds of events such that their returns always behave the same way over time, then we have no need to own both stocks—simply pick the one that performs better. Diversification comes when two stocks are subject to different kinds of events such that their returns differ over time. Consider the illustration in Figure 9.4. You own Stock A in Panel A of the figure. The stock features risk, as demonstrated by its price volatility over time. You would like to reduce the risk by combining your position in Stock A with an equal position in Stock B. In this case, the alternative stock, Stock B, moves the same way over time as Stock A does. When Stock A goes up, so does Stock B. They also decline together. A portfolio of both stocks is illustrated. Notice how the portfolio has the same volatility of Stocks A and B separately. Combining these two stocks did not reduce volatility, or total risk. FIGURE 9.4 Efficient Portfolios from Four Stocks page 277 Combining stocks that move together over time does not offer much risk reduction. Combining stocks that do not move together provides a lot of risk reduction. Correlation shows that some stocks move together and some do not. Now consider Stock C, shown in Panel B. Stock C has the same volatility as Stock A, but its price moves in different directions than does the price of Stock A. When Stock A’s price increases, Stock C’s price increases sometimes and decreases sometimes. As shown, a portfolio of Stock A and Stock C features much lower volatility than either Stock A or Stock C alone. Combining Stocks A and C reduces risk because their price movements often counteract one another. In short, combining stocks with similar characteristics does not provide much diversification and thus risk reduction. Combining stocks with many differences does provide diversification and thus lowers risk. The ways that stocks co-move over time determines how much diversification and thus risk reduction we can achieve by combining them. So what we need is some measure of co-movement to help investors form diversified portfolios. That measure, called correlation, is denoted by the Greek letter ρ (rho). Correlation is a statistical measure with some very useful characteristics that makes it easy to interpret. Its value is bounded between −1 and +1. A correlation value of +1 means that returns from two different securities move perfectly in sync. They change lock- step up and down together. A value of −1 means that returns from two securities are perfectly inversely correlated— they move exactly opposite. A value of 0 means that the movements of the two returns over time are unrelated to one another. Investors seeking diversification look for stocks where the returns have low or negative correlations with each other. page 278 correlation A measurement of the co-movement between two variables that ranges between −1 and +1. What return correlations are common between stocks? Panel A of Table 9.6 shows the correlations between many companies. One high correlation shown is the 0.690 correlation between Citigroup and the Bank of New York. This shouldn’t be surprising, because these are two similar firms in the same industry. Combining these two stocks wouldn’t reduce risk very much in a portfolio. The largest negative correlation is the correlation of −0.212 between Newmont Mining and the Bank of New York. These firms practice in very different industries and provide large risk reduction possibilities. Note that the correlation between Staples and Mattel is 0.198. This low correlation gives us an answer to the question of why total risk (in the form of standard deviations) fell so much when we combined the two stocks relative to their individual standard deviations as shown in Figure 9.2. Most of the correlations in Table 9.6 are positive. Because most stocks are positively correlated, we typically add many stocks together to fully eliminate all the firm-specific risk in the portfolio, as we showed in Figure 9.1. ▼ TABLE 9.6 Correlation between Various Stocks and Asset Classes PANEL A: COMPANY ANNUAL RETURNS, 1991 TO 2015 Staples Mattel IBM Newmont Mining Disney General Electric Citigroup Staples 1 Mattel 0.198 1 IBM 0.314 −0.029 1 Newmont Mining −0.036 −0.117 −0.087 1 Disney 0.163 0.440 0.076 −0.171 1 General Electric 0.380 0.134 0.396 −0.038 0.517 1 Citigroup 0.297 0.328 0.056 0.139 0.414 0.773 1 Bank of New York 0.584 0.459 0.045 −0.212 0.606 0.671 0.690 PANEL B: ASSET CLASS ANNUAL RETURNS,1950 TO 2015 Stocks Long-Term Treasury Bonds T-Bills Stocks 1 Long-term Treasury bonds −0.035 1 T-bills −0.063 0.137 1 LG9-2 Panel B of Table 9.6 shows correlations between stocks, bonds, and T-bills. At −0.035, the correlation between stocks and bonds is small. The small correlation allows for the possibility of good risk reduction by adding bonds to a stock portfolio. Therefore, a well-diversified portfolio will contain both stocks and bonds. finance at work //: markets International Opportunities for Diversification The U.S. stock market represents nearly 47 percent of all stock value worldwide. Japanese and U.K. stock markets represent 11 percent and 8 percent of the worldwide stock market value, respectively. Many investment and diversification opportunities present themselves internationally! However, most people allocate very little or none of their portfolios to international securities. If worldwide opportunities can create greater diversification, then those who don’t invest in international stocks miss out on an important opportunity to reduce risk in their portfolios. MSCI Barra is the leading provider of global stock market indexes. Some MSCI Barra indexes follow individual countries. In addition, MSCI Barra compiles composite indexes for groups of companies in developed markets, emerging markets, frontier markets, and by geographic regions. Investment managers use the MSCI World Index, the MSCI EAFE (Europe, Australasia, Far East) Index, and the MSCI Emerging Markets Index as premier benchmarks to measure global stock market performance. The following table shows the average annual returns and standard deviations for the U.S. stock market, Treasury bonds, and the page 279 MSCI EAFE and MSCI Emerging Markets indexes for the period 1988 to 2015. Note that both the EAFE and the Emerging Markets indexes feature higher risk than the S&P 500 Index. The Emerging Markets return has been high, but the EAFE return has been low compared to the U.S. stock and bond markets. S&P 500 Bonds EAFE Emerging Markets Average 11.7%  9.2%  5.6% 13.3% Std. Deviation 17.6 11.9 19.4 33.7 The correlations among these markets appear as follows: S&P 500 Bonds EAFE Emerging Markets S&P 500  1 Bonds −0.15  1 EAFE  0.74 −0.41 1 Emerging Markets  0.48 −0.31 0.73 1 The correlation between the S&P 500 Index and the MSCI EAFE is 0.74 and between the Emerging Markets is 0.48. These correlations indicate that diversification might work. Even better diversification appears to be possible between the U.S. Treasury Bond Market and the EAFE and Emerging Markets indexes—look at the negative correlations! Source: www.msci.com. Want to know more? Key Words to Search for Updates: international diversification, global asset allocation Portfolio Return LG9-7 A portfolio’s return calculation is straightforward. A portfolio’s return comes directly from the returns of the portfolio securities and the proportion of the portfolio invested in each security. For example, General Electric stock earned −1.9 percent. The Newmont Mining earned 17.3 percent over the same period. If you had invested a quarter of your money in General Electric stock and three quarters of it in Newmont Mining stock, then your portfolio return would be the Math Coach on… “When computing portfolio returns, use the decimal format for the portfolio weights and the percentage format for the security returns. The result of equation 9-8 will then be in percentage format.„ To calculate the return on a three-stock portfolio, you will need the proportion of each stock in the portfolio and each stock’s return. We typically call these proportions weights, signified by w. So, a portfolio with n securities will have a return of (9-8) http://www.msci.com page 280 where the sum of the weights, w, must equal one. The portfolio’s rate of return is a simple weighted sum of the returns of each stock in the portfolio. Investors choose portfolio weights by determining how much of each stock they want in their portfolios. Ideally, investors will choose weights for their portfolios located on the efficient frontier (shown in Figure 9.3). EXAMPLE 9-4 Computing Portfolio Returns LG9-7 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. At the beginning of the year, you owned $5,000 of Disney stock, $10,000 of Bank of New York stock, and $15,000 of IBM stock. During the year, Disney, Bank of New York, and IBM returned −4.8 percent, 19.4 percent, and 12.8 percent, respectively. What is your portfolio’s return? SOLUTION: First determine your portfolio weights. The three stocks make up a $30,000 portfolio. Disney makes up a 16.67 percent (= $5,000 ÷ $30,000) portion of the portfolio. Bank of New York stock makes up a 33.33 percent (=$10,000 ÷ $30,000) portion, and IBM a 50.0 percent (=$15,000 ÷ $30,000) portion. The portfolio return can now be computed as Similar to Problems 9-11, 9-12, 9-13, 9-14, 9-23, 9-24, 9-25, 9-26, 9- 29, 9-30, 9-31, 9-32, Self-Test Problem 1 time out! 9-5 Describe characteristics of companies that would be good to combine into a portfolio. 9-6 Explain why one portfolio made up of the same companies (but not in the same proportions) as another portfolio can be undesirable in comparison. 9-7 Combining which two companies in Table 9.6 would reduce risk the most? Combining which two would create the least diversification? Get Online http://mhhe.com/CornettM4e page 281 ©JGI/Jamie Grill/Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. Why is the percentage return a more useful measure than the dollar return? (LG9-1) 2. Characterize the historical return, risk, and risk-return relationship of the stock, bond, and cash markets. (LG9- 2) 3. How do we define risk in this chapter and how do we measure it? (LG9-3) 4. What are the two components of total risk? Which component is part of the risk-return relationship? Why? (LG9-3) 5. What’s the source of firm-specific risk? What’s the source of market risk? (LG9-3) 6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why? (LG9-3) 7. Can a company change its total risk level over time? How? (LG9-3) 8. What does the coefficient of variation measure? Why is a lower value better for the investor? (LG9-4) 9. You receive an investment newsletter advertisement in the mail. The letter claims that you should invest in a stock that has doubled the return of the S&P 500 Index over the last three months. It also claims that this stock is a surefire safe bet for the future. Explain how these two claims are inconsistent with finance theory. (LG9-4) 10. What does diversification do to the risk and return characteristics of a portfolio? (LG9-5) 11. Describe the diversification potential of two assets with a −0.8 correlation. What’s the potential if the correlation is +0.8? (LG9-5) 12. You are a risk-averse investor with a low-risk portfolio of bonds. How is it possible that adding some page 282 stocks (which are riskier than bonds) to the portfolio can lower the total risk of the portfolio? (LG9-5) 13. You own only two stocks in your portfolio but want to add more. When you add a third stock, the total risk of your portfolio declines. When you add a tenth stock to the portfolio, the total risk declines. Adding which stock, the third or the tenth, likely reduced the total risk more? Why? (LG9-5) 14. Many employees believe that their employer’s stock is less likely to lose half of its value than a well-diversified portfolio of stocks. Explain why this belief is erroneous. (LG9-5) 15. Explain what we mean when we say that one portfolio dominates another portfolio. (LG9-6) 16. Explain what the efficient frontier is and why it is important to investors. (LG9-6) 17. If an investor’s desired risk level changes over time, should the investor change the composition of his or her portfolio? How? (LG9-6) 18. Say you own 200 shares of Mattel and 100 shares of Staples. Would your portfolio return be different if you instead owned 100 shares of Mattel and 200 shares of Staples? Why? (LG9-7) Problems BASIC PROBLEMS 9-1 Investment Return FedEx Corp. stock ended the previous year at $103.39 per share. It paid a $0.35 per share dividend last year. It ended last year at $106.69. If you owned 200 shares of FedEx, what was your dollar return and percent return? (LG9-1) 9-2 Investment Return Sprint Nextel Corp. stock ended the previous year at $23.36 per share. It paid a $2.37 per share dividend last year. It ended last year at $18.89. If you owned 500 shares of Sprint, what was your dollar return and percent return? (LG9-1) 9-3 Investment Return A corporate bond that you own at the beginning of the year is worth $975. During the year, it pays $35 in interest payments and ends the year valued at $965. What was your dollar return and percent return? (LG9-1) 9-4 Investment Return A Treasury bond that you own at the beginning of the year is worth $1,055. During the year, it pays $35 in interest payments and ends the year valued at $1,065. What was your dollar return and percent return? (LG9-1) 9-5 Total Risk Rank the following three stocks by their level of total risk, highest to lowest. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. (LG9-3) 9-6 Total Risk Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has an average return of 12 percent and standard deviation of 32 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. (LG9-3) 9-7 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. (LG9-4) 9-8 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Night Ryder has an average return of 13 percent and standard deviation of 29 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. (LG9-4) 9-9 Dominant Portfolios Determine which one of these three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Blue has an expected return of 12 percent and risk of 18 percent. The expected return and risk of portfolio Yellow are 15 percent and 17 percent, and for the Purple portfolio are 14 percent and 21 percent. (LG9-6) 9-10 Dominant Portfolios Determine which one of the three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Green has an expected return of 15 page 283 percent and risk of 21 percent. The expected return and risk of portfolio Red are 13 percent and 17 percent, and for the Orange portfolio are 13 percent and 16 percent. (LG9-6) 9-11 Portfolio Weights An investor owns $6,000 of Adobe Systems stock, $5,000 of Dow Chemical, and $5,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7) 9-12 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of Dow Chemical, and $7,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7) 9-13 Portfolio Return Year-to-date, Oracle had earned a –1.34 percent return. During the same time period, Valero Energy earned 7.96 percent and McDonald’s earned 0.88 percent. If you have a portfolio made up of 30 percent Oracle, 25 percent Valero Energy, and 45 percent McDonald’s, what is your portfolio return? (LG9-7) 9-14 Portfolio Return Year-to-date, Yum Brands had earned a 3.80 percent return. During the same time period, Raytheon earned 4.26 percent and Coca-Cola earned −0.46 percent. If you have a portfolio made up of 30 percent Yum Brands, 30 percent Raytheon, and 40 percent Coca-Cola, what is your portfolio return? (LG9-7)? INTERMEDIATE PROBLEMS 9-15 Average Return The past five monthly returns for Kohls are 4.11 percent, 3.62 percent, −1.68 percent, 9.25 percent, and −2.56 percent. What is the average monthly return? (LG9-1) 9-16 Average Return The past five monthly returns for PG&E are −3.17 percent, 3.88 percent, 3.77 percent, 6.47 percent, and 3.58 percent. What is the average monthly return? (LG9-1) 9-17 Standard Deviation Compute the standard deviation of Kohls’ monthly returns shown in problem 9- 15. (LG9-3) 9-18 Standard Deviation Compute the standard deviation of PG&E’s monthly returns shown in problem 9-16. (LG9-3) 9-19 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.2 and 9.4) during each decade since 1950. (LG9-2, LG9-4) 9-20 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9.2 and 9.4) during each decade since 1950. (LG9-2, LG9-4) 9-21 Diversifying Consider the characteristics of the following three stocks: The correlation between Thumb Devices and Air Comfort is −0.12. The correlation between Thumb Devices and Sport Garb is −0.21. The correlation between Air Comfort and Sport Garb is 0.77. If you can pick only two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5) Expected Return Standard Deviation Thumb Devices 13% 23% Air Comfort 10  19  Sport Garb 10  17  9-22 Diversifying Consider the characteristics of the following three stocks: The correlation between Pic Image and Tax Help is 0.88. The correlation between Pic Image and Warm Wear is −0.21. The correlation between Tax Help and Warm Wear is −0.19. If you can pick only two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5) Expected Return Standard Deviation Pic Image 11% 19% Tax Help 9  19  Warm Wear 14  25  9-23 Portfolio Weights If you own 200 shares of Alaska Air at $42.88, 350 shares of Best Buy at $51.32, and 250 shares of Ford Motor at $8.51, what are the portfolio weights of each stock? (LG9-7) page 284 9-24 Portfolio Weights If you own 400 shares of Xerox at $17.34, 500 shares of Qwest at $8.15, and 350 shares of Liz Claiborne at $44.73, what are the portfolio weights of each stock? (LG9-7) 9-25 Portfolio Return At the beginning of the month, you owned $5,500 of General Dynamics, $7,500 of Starbucks, and $8,000 of Nike. The monthly returns for General Dynamics, Starbucks, and Nike were 7.44 percent, −1.36 percent, and −0.54 percent. What is your portfolio return? (LG9-7) 9-26 Portfolio Return At the beginning of the month, you owned $6,000 of News Corp, $5,000 of First Data, and $8,500 of Whirlpool. The monthly returns for News Corp, First Data, and Whirlpool were 8.24 percent, −2.59 percent, and 10.13 percent. What’s your portfolio return? (LG9-7) ADVANCED PROBLEMS 9-27 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks, 40 percent long- term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. (LG9-2, LG9-5) 9-28 Asset Allocation You have a portfolio with an asset allocation of 35 percent stocks, 55 percent long- term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. (LG9-2, LG9-5) 9-29 Portfolio Weights You have $15,000 to invest. You want to purchase shares of Alaska Air at $42.88, Best Buy at $51.32, and Ford Motor at $8.51. How many shares of each company should you purchase so that your portfolio consists of 30 percent Alaska Air, 40 percent Best Buy, and 30 percent Ford Motor? Report only whole stock shares. (LG9-7) 9-30 Portfolio Weights You have $20,000 to invest. You want to purchase shares of Xerox at $17.34, Qwest at $8.15, and Liz Claiborne at $44.73. How many shares of each company should you purchase so that your portfolio consists of 25 percent Xerox, 40 percent Qwest, and 35 percent Liz Claiborne? Report only whole stock shares. (LG9-7) 9-31 Portfolio Return The following table shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return? (LG9-7) Company Shares Beginning of Year Price Dividend Per Share End of Year Price US Bank 300 $43.50 $2.06 $43.43 PepsiCo 200 59.08 1.16 62.55 JDS Uniphase 500 18.88 16.66 Duke Energy 250 27.45 1.26 33.21 9-32 Portfolio Return The following table shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return? (LG9-7) Company Shares Beginning of Year Price Dividend Per Share End of Year Price Johnson Controls 350 $72.91 $1.17 $85.92 Medtronic 200 57.57 0.41 53.51 Direct TV 500 24.94 24.39 Qualcomm 250 43.08 0.45 38.92 9-33 Risk, Return, and Their Relationship Consider the following annual returns of Estee Lauder and page 285 Lowe’s Companies: Compute each stock’s average return, standard deviation, and coefficient of variation. Which stock appears better? Why? (LG9-3, LG9-4) Estee Lauder Lowe’s Companies Year 1 23.4% −6.0% Year 2 −26.0  16.1  Year 3 17.6  4.2  Year 4 49.9  48.0  Year 5 −16.8  −19.0  9-34 Risk, Return, and Their Relationship Consider the following annual returns of Molson Coors and International Paper: Compute each stock’s average return, standard deviation, and coefficient of variation. Which stock appears better? Why? (LG9-3, LG9-4) Molson Coors International Paper Year 1 16.3% 4.5% Year 2 −9.7  −17.5   Year 3 36.5  −0.2  Year 4 −6.9  26.6  Year 5 16.2  −11.1  9-35 Spreadsheet Problem Following are the monthly returns for March 2011 to February 2016 of three international stock indices: All Ordinaries of Australia, Nikkei 225 of Japan, and FTSE 100 of England. a. Compute and compare each index’s monthly average return and standard deviation. b. Compute the correlation between (1) All Ordinaries and Nikkei 225,(2) All Ordinaries and FTSE 100, and (3) Nikkei 225 and FTSE 100, and compare them. c. Form a portfolio consisting of one-third of each of the indexes and show the portfolio return each year, and the portfolio’s return and standard deviation. page 286 9-36 Spreadsheet Problem a. Create a spreadsheet like the one shown below. The spreadsheet should use the returns for assets A and B to form a portfolio return using the weights for each asset shown in cells E1 and E2. The average portfolio return and standard deviation should compute at the bottom of the column of portfolio returns. When you change the weights, the portfolio returns, average, and standard deviation should recalculate. page 287 b. Use the Solver function to find the weights that provide the highest return for a standard deviation of 6 percent, 7.5 percent, 9 percent, 10.5 percent, 12 percent, and 13.5 percent. Report the weights and the return for each of these portfolio standard deviations. The Solver function is found in the Data tab. (You may have to enable the function through the File tab, then Options, then Add-ins.) The solver image illustrates the maximizing of the average return for the specific constraints. The constraints are that the weights must be between 0 and 1, inclusive, and must sum to 1. Lastly, set the standard deviation constraint to the desired level. Notes CHAPTER 9 1. We use the denominator of N – 1 to compute a sample’s standard deviation, which is the most common for finance applications. We would divide the standard deviation of a population simply by N. page 288 page 289 I chapter ten estimating risk and return ©Ingram Publishing s it possible for investors to know the exact risk they have to take? In Chapters 9 and 10, we explore methods to find the return that individual or institutional investors require to make a particular investment attractive. In the previous chapter, we established a positive relationship between risk and return using historical data. Risk and return play an undeniable role as investors seek the best return for the least risk. But until there’s some way to forecast the future, financial managers and investors must make investment decisions armed only with their expectations about future risk and return. We need an exact specification that shows directly the amount of reward required for investors to take the level of risk in a given firm’s stock or portfolio of securities. In this chapter we will also see how investors get the information they need to make risk-reward decisions. Investors need to know how much risk they have to take to confidently expect a 10 percent return. Managers also want to know what return shareholders require so that they can decide how to meet those expectations. In Chapter 11, we’ll explore how managers conduct financial analysis to find the shareholders’ required return. If we want to specify the exact risk–return relationship, we need to develop a better measure of risk for individuals and institutional investors. As we saw in Chapter 9, any firm’s total risk is specific to that particular firm. But the market doesn’t reward firm-specific risk because investors can easily diversify away any single firm’s specific risks by owning other offsetting firms’ stocks to create a portfolio subject only to market or undiversifiable risk. So, we need to find just the market risk portion of page 291 page 290 total risk for investors. The theory to find the market risk portion of stock ownership extends modern portfolio theory. Our search to find market risk will lead us to the capital asset pricing model (CAPM), which utilizes a measure of market risk called beta. CAPM’s risk–return specification provides us a powerful tool to make better investment decisions. LEARNING GOALS LG10-1 Compute forward-looking expected return and risk. LG10-2 Understand risk premiums. LG10-3 Know and apply the capital asset pricing model (CAPM). LG10-4 Calculate and apply beta, a measure of market risk. LG10-5 Differentiate the levels of market efficiency and their implications. LG10-6 Calculate and explain investors’ required return and risk. LG10-7 Use the constant-growth model to compute required return. viewpoints business APPLICATION Consider that you work in the finance department of a large corporation. Your team is analyzing several new projects the firm can pursue. To complete the analysis, the team needs to know what return stockholders require from the firm. You are to estimate this required return. Shareholders’ expected return will depend on your company’s risk level. What information do you need to gather and how might you compute this return? (See the solution at the end of the book.) Corporate finance managers and investment professionals commonly use the beta measure. But like any theory, CAPM has its limitations. We’ll discuss the CAPM’s limitations and concerns about beta and propose an alternate required return measure. Whether beta or any other risk–return specification is useful relies in part on whether a stock’s price represents a fair estimate of the true company value. Stock price validity and reliability—their general correctness— are vitally important both to investors and corporate managers. 10.1 • EXPECTED RETURNS LG10-1 In the previous chapter, we characterized risk and return in historical terms. We defined a stock’s return as the actual profit realized while holding the stock or the average return over a longer period. We described risk simply as the standard deviation of those returns—a term already familiar to you from your statistics classes. So, we did a good job describing the risk and return that the stock experienced in the past. But do those risk and return figures hold into the future? Firms can quite possibly change their stocks’ risk level by substantially changing their business. If a firm takes on riskier new projects over time, or changes the nature of its business, the firm itself will become riskier. Similarly, firms can reduce their risk level—and hence, their stock’s riskiness—by choosing low-risk new projects. Both investors and firms find expected return, a forward-looking return calculation that includes risk measures, very useful to estimate future stock performance. Expected Return and Risk We can attribute a company’s business success over a year partly to its management talent, strategies, and other firm-specific activities, but overall economic conditions will also affect a firm’s level of success or failure. Consider a steel manufacturer—Nucor Corp. The steel business closely follows economic trends. In a good economy, demand for steel is strong as builders and manufacturers step up building and production. During economic recessions, demand for steel falls off quickly. So, if we want to assess Nucor’s probabilities for success next year, we know that we must look partly at Nucor’s managerial ability and partly at the economic outlook. personal APPLICATION You have just started your first job in the corporate world and need to make some retirement plan decisions. The company’s 401(k) retirement plan offers three investment choices: a stock portfolio with a beta of 1, a bond portfolio with a beta of 0.18, and a money market account. For your allocation, you decide to contribute $200 per month to the stock portfolio, $100 to the bond portfolio, and $50 to the money market account. If the expected return to the market portfolio is 11 percent, what risk level are you taking in your retirement portfolio and what return should you expect over the long run? (See the solution at the end of the book.) Investing mainly in my own company’s stock is safer, right? Maybe not . . . Unfortunately, we cannot accurately predict what the economy will be like next year. Predicting economic activity is like predicting the weather—forecasts give the probability of rain or sunshine. Economists cannot say for sure whether the economy will be good or bad next year. Instead, they may forecast a 70 percent chance that the economy will be good and a 30 percent chance of a recession. Similarly, analysts might say that given Nucor’s managerial talent, if the economy is good, Nucor will perform well and the stock will increase 20 percent. If the economy goes into a recession, then Nucor’s stock will fall 10 percent. So what return do you expect from Nucor? The return still depends on the state of the economy. A company’s success depends partly on management talent, strategies, and other activities. ©Robert Nicholas/AGE Fotostock This leads us directly to a key concept: expected return. We compute expected return by multiplying each possible return by the probability, p, of that return occurring. We then sum them (recall that all probabilities must add to one). Let’s place Nucor in an economy with only two states: good and recession. In this scenario, Nucor’s expected return would be 11 percent [= (0.7 × 20%) + (0.3 × −10%)]. Of course, nothing is quite that simple. Economists seldom predict simple two-state views of the economy as in the previous example. Rather, economists give much more detailed forecasts (such as three states: red-hot economy, average expansion, and recession). So our general equation for a stock’s expected return with S different conditions of the economy is (10-1) page 292 The result of this expected return calculation has some interesting properties. First, the expected return figure expresses what the average return would be over time if the probabilistic states of the economy occur as predicted. For example, the 70/30 probability distribution for good/recession economic states suggests that the economy will be good in 7 of the next 10 years, earning Nucor shareholders a 20 percent return in each of those years. Shareholders would lose 10 percent in each of the three recession years. So the average return over those 10 years would be 11 percent, the same as the expected return. The second interesting property: The expected return itself will not likely occur during any one year. Remember that Nucor will earn either a return of 20 percent or −10 percent. Yet its expected return is 11 percent, a value that it cannot earn because we have no economic condition for which the return is 11 percent. Again, this illustration seems extreme because we used only two economic states. Any real economic forecast would instead include a probability distribution of many potential economic conditions. probability The likelihood of occurrence. expected return The average of the possible returns weighted by the likelihood of those returns occurring. probability distribution The set of probabilities for all possible occurrences. We can also characterize risk via this expected return figure. The expected return procedure shows potential return possibilities, but we don’t know which one will actually occur, so we face uncertainty. In the last chapter, we measured risk using the standard deviation of returns over time. We can use the same principle to measure risk for expected returns. What range of different expected returns will Nucor exhibit from the expected return of 11 percent? In our two-state description of the economy, the deviation could be either 9 percent (= 20% − 11%) or −21 percent (= −10% − 11%). We compute the standard deviation of expected returns the same way we did for historical returns. We square the deviations, then multiply by the probability of that deviation occurring, and then sum them all up. So Nucor’s return variance is 189.0 As a final step, we take the square root of our result to put the figure back into sensible terms. The standard deviation for Nucor is 13.75 percent (= ). The general equation for the standard deviation of S different economic states is (10-2) the Math Coach on… Expected Return and Standard Deviation “When you compute expected return and standard deviation, you’ll find it helpful to use the decimal format for the probability of the economic state and percentages to state the return in each state.„ Risk Premiums LG10-2 Throughout the book, we have mentioned the positive relationship between expected return and risk. Consider this key question: You have a riskless investment available to you. The short-term government debt security, the T-bill, page 293 offers you a low return with no risk. Why would you invest in anything risky, when you could simply buy T-bills? The answer, of course, is that some investors want a higher return and are willing to take some risk to raise their returns. Investors who take on a little risk should expect a slightly higher return than the T-bill rate. People who take on higher risk levels should expect higher returns. Indeed, it’s only logical that investors require this extra return to willingly take the added risk. The expected return of an investment is often expressed in two parts, a risk-free return and a risky contribution. The return investors require for the risk level they take is called the required return: (10-3) required return The level of total return needed to be compensated for the risk taken. It is made up of a risk-free rate and a risk premium. The risk-free rate is typically considered the return on U.S. government bonds and bills and equals the real interest rate and the expected inflation premium that we discussed in Chapter 6. The risk premium is the reward investors require for taking risk. How large are the rewards for taking risk? As we discussed in the previous chapter, the market doesn’t reward all risks. The firm-specific portion of total risk for any stock can be diversified away, and since the investor takes on such risk out of ignorance or by mistake, an efficient market will not reward anyone for taking on this “superfluous” risk. So as we examine historical risk premiums, we do so with a diversified portfolio that contains no firm-specific risk. risk premium The portion of the required return that represents the reward for taking risk. EXAMPLE 10- 1 Expected Return and Risk LG10-1 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Bailey has a probability distribution for four possible states of the economy, as shown below. She has also calculated the return that Motor Music stock would earn in each state. Given this information, what’s Motor Music’s expected return and risk? Economic State Probability Return Fast growth 0.15 25% Slow growth 0.60 15 Recession 0.20 −5 Depression 0.05 −20 SOLUTION: Bailey can compute the expected return using equation 10-1: http://mhhe.com/CornettM4e page 294 Then Bailey can compute the expected return by computing the standard deviation using equation 10-2: The expected return and standard deviation are 10.75 percent and 11.76 percent, respectively. We could also show these equations in a table, such as Similar to Problems 10-1, 10-2, 10-17, 10-18, 10-23, 10-24, Self-Test Problem 1 ▼ TABLE 10.1 The Realized Average Annual Risk Premium for Stocks 1950 to 2015 1950 to 1959 1960 to 1969 1970 to 1979 1980 to 1989 1990 to 1999 2000 to 2009 2010 to 2015 Risk premium 8.2% 18.8% 4.7% 1.2% 9.3% 14.1% −1.8% 13.4% Realized risk premiums were very different in each decade. The recent decade even had a negative risk premium! Source: S&P 500 Index and T-bill rate data. Table 10.1 shows the average annual return on the S&P 500 Index minus the T-bill rate for different time periods. The remainder after we subtract the T-bill rate is the risk premium; in this case, it’s the market risk premium—the reward for taking general (unsystematic) stock market risk. Since 1950, the average market risk premium has been 8.3 percent per year. Over the long run, this is the reward for taking stock market risk. The actual, realized risk premium during particular decades has varied. The average risk premium has been as high as 18.8 percent for the 1950s and as low as −1.8 percent during the 2000s. The performance in the 2000s is unusual; the stock market return has been so poor that it has not beaten the risk-free rate. Investors require a risk premium for taking on market risk. But taking that risk also means that they will periodically experience poor returns. time out! 10-1 Describe the similarities between computing average return and expected return. Also, describe the similarities between expected return risk and historical risk. 10-2 Why would people take risks by investing their hard-earned money? 10.2 • MARKET RISK LG10-3 ▼ How much risk should you take to achieve the return you want over time? In the previous chapter, we demonstrated that individual stocks and different portfolios exhibit different levels of total risk. Recall that the rewards for carrying risk apply only to the market risk (or undiversifiable) portion of total risk. But how do investors know how much of the 33.4 percent standard deviation of returns for Mattel Inc. is firm-specific risk and how much of that deviation is market risk? The answer to this important question will determine how much of a risk premium investors should require for Mattel. The attempt to specify an equation that relates a stock’s required return to an appropriate risk premium is known as asset pricing. The Market Portfolio The best-known asset pricing equation is the capital asset pricing model, typically referred to as CAPM. Though many theorists formulated theories that, in the end, supported the CAPM’s effectiveness, credit for the model goes to William Sharpe and John Lintner. Sharpe eventually won a Nobel Prize for his work in 1990. (Lintner died in 1983, and Nobel Prizes are not awarded posthumously.) Today, both investors and corporate finance professionals use CAPM widely. In developing the CAPM, Lintner and Sharpe sought to emphasize the individual investor’s best strategy to maximize returns for a given amount of market risk. CAPM starts with modern portfolio theory. Remember from the previous chapter that when you combine securities into a portfolio, you can find a set of portfolios that dominate all others. The best combinations possible use all the risky securities available (but not the risk-free asset) to create efficient frontier portfolios, which would lie along a curved line in risk/return space, as shown in Figure 10.1, panel A. These portfolios represent combinations of various risky securities that give the highest expected return for each potential level of risk (i.e., they lie the furthest “up and to-the-left” that we can achieve when considering all possible combinations of the available risky securities). FIGURE 10.1 Maximizing Expected Return page 295 In MPT, investors want to be on the efficient frontier (Panel A) because it gives them the highest expected return for each level of risk. However, after adding a riskless asset (Panel B), investors can then get portfolios on the straight line (shown), which offers a higher expected return for each level of risk than the efficient frontier. The idea of a risk premium in equation 10-3 implies a risk-free investment, like T-bills. Panel B shows where the risk-free asset would appear on the capital market line (CML). The risk-free asset must lie on the y-axis precisely because it carries no risk. Now we draw a line from the risk-free security to a point tangent to the efficient frontier. The CML relationship appears as a line because investments show a direct risk–reward relationship. You may recall from your economics classes that only one tangency point will be possible between this kind of curve and a straight line. The spot where the tangency occurs is called the market portfolio, which has a special significance. The market portfolio represents ownership in all traded assets in the economy, so this portfolio provides maximum diversification. You can locate your optimal portfolio on this line by owning various combinations of the risk-free security and the market portfolio. If most of your money is invested in the market portfolio, then you will have a portfolio on the line that lies just to the left of the market portfolio dot in the graph. If you own just a little of the market portfolio and hold mostly risk-free securities, then your portfolio will lie on the line near the risk- free security dot. For your investments to lie on the line to the right of the market portfolio, you would have to invest all your money in the market portfolio, then borrow more money at the risk-free rate and invest these additional funds in the market portfolio. Borrowing money to invest is known as using financial leverage. Using financial leverage increases the overall risk of the portfolio, which is illustrated in this figure as a higher standard deviation. page 296 market risk premium The return on the market portfolio minus the risk-free rate. Risk premiums for specific firms are based on the market risk premium. asset pricing The process of directly specifying the relationship between required return and risk. capital asset pricing model (CAPM) An asset pricing theory based on a beta, a measure of market risk. capital market line (CML) The line on a graph of return and risk (standard deviation) from the risk-free rate through the market portfolio. market portfolio In theory, the market portfolio is the combination of securities that places the portfolio on the efficient frontier and on a line tangent from the risk-free rate. In practice, the S&P 500 Index is used to proxy for the market portfolio. financial leverage The extent to which debt securities are used by a firm. Notice that if you had a portfolio on the efficient frontier (labeled “old portfolio”), you could do better. Instead of owning the old portfolio, you can put some of your money in the market portfolio and some in the risk-free security to obtain the “new portfolio.” See how the new portfolio dominates that old one? It carries the same risk level, but offers a higher return. In fact, notice that the line drawn between the risk-free investment and the market portfolio dominates all of the efficient frontier portfolios (except the market portfolio itself). All portfolio allocations between the risk-free security and the market portfolio constitute the capital market line. All investors should want to locate their portfolios on the CML, rather than the efficient frontier. Portfolios on the CML offer the highest expected return for any level of desired risk, which the investor controls by deciding how much of the market portfolio and how much of the risk-free asset to hold. Risk-averse investors can put more of their money in T-bills and less into the market portfolio. Investors willing to take on higher risk for larger returns can put more of their money in the market portfolio. Beta, a Measure of Market Risk LG10-4 The CML demonstrates that the market portfolio is crucial. Indeed, its return less the risk-free rate represents the expected average market risk premium. The market portfolio features no firm-specific risk; all such risk is diversified away. So the market portfolio carries only market risk. Thus the market portfolio’s risk factor allows us to compute a measure of firm-specific risk for any individual stock or portfolio. We can now examine the question posed at the beginning of this section: “How much of Mattel’s total risk is attributable to market risk?” The standard deviation of returns includes all of Mattel stock’s risk—it quantifies how much the stock price rises and falls. The market risk portion will rise and fall along with the market portfolio. If we subtract the market risk portion from the total risk measure, we’re left with firm-specific risk. This part of risk rises and falls in ways unrelated to market changes. Remember that portfolio theory describes a measure—correlation—that measures how two stocks move together through time. Instead of measuring how any two stocks or portfolios move together, we now want to know how a stock or portfolio moves relative to market portfolio movements. This measure is known as beta ( β). Beta measures the comovement between a stock and the market portfolio. beta (β) A measure of the sensitivity of a stock or portfolio to market risk. If Mattel’s total risk level is measured by its standard deviation, σMattel, then we can find the portion of this risk that is attributable to the market in general by multiplying Mattel’s total risk by its correlation with the market portfolio, σMattel × ρMattel, Market. The beta computation is scaled so that the market portfolio itself has a beta of one. The scaling is done by dividing by standard deviation of the market portfolio: σMattel × ρMattel, Market ÷ σMarket. 1 Stocks with betas larger than one are considered riskier than the market portfolio, while betas of less then one indicate lower risk. Mattel has a beta of 0.65, meaning that Mattel has low sensitivity to market risk. When the market portfolio moves, you can expect Mattel stock to move in the same direction. Technically, you should expect Mattel’s realized risk premium to be 35 percent less than the realized market risk premium. Table 10.2 shows the beta for each of the 30 companies in the Dow Jones Industrial Average. Investors consider many of these companies high risk, like Du Pont (β = 2.01) and Disney (1.56). These firms’ stocks carry high market risk because the demand for their products is very sensitive to the overall economy’s strength. Investors consider other companies safe bets with low risk, like Walmart (0.19), Verizon (0.47), and McDonald’s (0.56). Many lower-beta firms sell consumer goods that we consider the necessities of life, which we will buy whether the economy is in recession or expansion. The demand for these products is price inelastic and not sensitive to economic conditions. Some companies have nearly the same risk as the market portfolio, like Pfizer (1.02), Microsoft (1.02), ▼ and Intel (1.02). ▼ TABLE 10.2 Dow Jones Industrial Average Stock Betas Company Beta Company Beta 3M Company 1.08 Intel 1.02 American Express 1.21 Johnson & Johnson 0.89 Apple 1.35 JPMorgan Chase 1.20 Boeing 1.36 McDonald’s 0.56 Caterpillar 1.09 Merck 0.75 Cisco Systems 1.18 Microsoft 1.02 Chevron 1.17 Nike 0.63 Coca-Cola 0.77 Pfizer 1.02 Disney 1.56 Procter & Gamble 0.66 Du Pont de Nemours 2.01 Travelers 1.22 Exxon Mobil 0.92 United Technologies 1.18 General Electric 1.22 UnitedHealth Group 0.62 Goldman Sachs 1.35 Verizon Communications 0.47 Home Depot 0.96 Visa 1.06 IBM 0.66 Walmart Stores 0.19 Source: Yahoo! Finance, March 2, 2016. The Security Market Line LG10-3 Beta indicates the market risk that each stock represents to investors. So the higher the beta, the higher the risk premium investors will demand to undertake that security’s market risk. Since beta sums up precisely what investors want to know about risk, we often replace the standard deviation risk measure shown in Figure 10.1 with beta. Figure 10.2 shows required return versus beta risk. We call the line in this figure the security market line (SML), which illustrates how required return relates to risk at any particular time, all else held equal. The SML also shows the market portfolio’s risk premium or any stock’s risk premium. FIGURE 10.2 The Security Market Line Uses Beta as the Risk Measure General Electric has higher risk than the overall stock market, so it should require a higher return. security market line Similar to the capital market line except risk is characterized by beta instead of standard deviation. When a stock like General Electric carries a beta greater than one, then its risk premium must be larger than the market risk premium. A stock like Johnson & Johnson carries a lower beta than does the overall market; therefore Johnson & Johnson would offer a lower risk premium to investors. We can use the SML to show the relationship between risk and return for any stock or portfolio. To precisely quantify this relationship, we need the equation for the SML. The equation of any line can be defined as y = b + mx, where b is the intercept and m is the slope. In this case, the y-axis is required return and the x-axis is beta. The intercept is Rf. You may remember that the slope is the “rise over run” between two points on the line. The rise between the risk-free security and the market portfolio is RM − Rf and the run is 1−0. Substituting into the line equation results in the CAPM: (10-4) So, we have determined a way to estimate any stock’s required return once we have determined its beta. Consider this: We expect the market portfolio to earn 12 percent and T-bill yields are 5 percent. Then General Electric’s required return, with a β = 1.22, is 5% + 1.22 × (12%−5%) = 13.54 percent. Table 10.3 shows the 30 Dow Jones Industrial Average stocks’ required return, using these same market and risk-free rate assumptions. Higher-risk companies have higher betas, and thus require higher returns. ▼ TABLE 10.3 Required Returns for DJIA Stocks Company Required Return Company Required Return 3M Company 12.56% Intel 12.14% American Express 13.47  Johnson & Johnson 11.23  Apple 14.45  JPMorgan Chase 13.40  Boeing 14.52  McDonald’s 8.92  page 297 page 298 Caterpillar 12.63  Merck 10.25  Cisco Systems 13.26  Microsoft 12.14  Chevron 13.19  Nike 9.41  Coca-Cola 10.39  Pfizer 12.14  Disney 15.92  Proctor & Gamble 9.62  Du Pont de Nemours 19.07  Travelers 13.54  Exxon Mobil 11.44  United Technologies 13.26  General Electric 13.54  UnitedHealth Group 9.34  Goldman Sachs 14.45  Verizon Communications 8.29  Home Depot 11.72  Visa 12.42  IBM 9.62  Walmart Stores 6.33  Higher beta stocks require higher expected returns. Assumptions: market return = 12% and risk-free rate = 5%. Source: Yahoo! Finance, March 2, 2016. Portfolio Beta As you might expect, a stock portfolio’s beta is the weighted average of the portfolio stocks’ betas.The portfolio beta equation resembles equation 9-7, which gives the return of a portfolio: (10-5) portfolio beta The combination of the individual company betas in an investor’s portfolio. EXAMPLE 10- 2 CAPM and Under- or Overvalued Stock LG10-3 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Say that you are a corporate CFO. You know that the risk-free rate is currently 4.5 percent and you expect the market to earn 11 percent this year. Through your own analysis of the firm, you think it will earn a 13.5 percent return this year. If the beta of the company is 1.2, should you consider the firm undervalued or overvalued? SOLUTION: You can compute shareholders’ required return with CAPM as 4.5% + 1.2 × (11% − 4.5%) = 12.3%. Since you think the firm will actually earn more than this required return, the firm appears to be currently undervalued. That is, its price must rise more then predicted by CAPM to obtain the return you estimated in your original analysis. http://mhhe.com/CornettM4e page 299 Similar to Problems 10-7, 10-8, 10-19, 10-20, Self-Test Problem 3 With this equation, you can easily determine whether adding a particular stock to the portfolio will increase or decrease the portfolio’s total market risk. If you add a stock with a higher beta than the existing portfolio, then the new portfolio will carry higher market risk than the old one did. Although we can find the effects on total portfolio risk of adding particular stocks using beta, the same is not necessarily true if we use standard deviations as our risk measure. The new stock, however risky, might have low correlations with the other stocks in the portfolio— offsetting (negative) correlations would reduce total risk. Finding Beta LG10-4 The CAPM is an elegant explanation that relates the return you should require for taking on various levels of market risk. Although CAPM provides many practical applications, you need a company’s beta to use those applications. Where or how can you obtain a beta? You have two ways. First, given the returns of the company and the market portfolio, you can compute the beta yourself. Second, you can find the beta that others have computed through financial information data providers. Many financial outlets publish company betas. Websites that provide company betas for free include MSN Money and Yahoo! Finance, to name just a couple. For example, in March 2016, the beta these websites listed for Disney were: MSN Money (1.41) and Yahoo! Finance (1.56). Note that these reported betas have some differences. To know why differences might arise, consider how you would go about gathering information and computing beta yourself. EXAMPLE 10- 3 Portfolio Beta LG10-4 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. You have a portfolio consisting of 20 percent Boeing stock (β = 1.04), 40 percent Hewlett- Packard stock (β = 1.54), and 40 percent McDonald’s stock (β = 0.34). How much market risk does the portfolio have? SOLUTION: Compute a beta for the portfolio. Using equation 10-5, the portfolio beta is 0.2 × 1.04 + 0.4 × 1.54 + 0.4 × 0.34 = 0.96. Note that this portfolio carries 4 percent less market risk than the general market does. Similar to Problems 10-11, 10-12, 10-21, 10-22, 10-27, 10-28, Self-Test Problem 2 To compute your own beta, first obtain historical returns for the company of interest and of the market portfolio. Then run a regression of the company return as the dependent variable and the market portfolio return as the independent variable. The resulting market portfolio return coefficient is beta. Many important questions may come to mind. First, what do you use as the market portfolio? People typically use a major stock index like the S&P 500 Index to proxy for the market portfolio. Second, what time frame should you use? You can use daily, weekly, monthly, or even annual returns. Using monthly returns is the most common. How long a time series is needed? As you will recall, statistical estimates become more reliable and valid as more data are used. But you will have to weigh those statistical advantages against the fact that companies change their business enterprises and thus their risk levels over time. Using data from too long ago reflects risks that may no longer apply. Generally speaking, using time series data of three to five years is common. Whatever decisions you make to address these questions, be consistent by making the same decisions for all the company betas you compute. Table 10.4 shows the spreadsheet of a stock’s beta calculation. In this case, monthly returns from five years are used for the stock return and a market index. The SLOPE() function of the spreadsheet directly computes the regression coefficient of http://mhhe.com/CornettM4e page 300 interest. The beta estimation using the spreadsheet function is 0.83. ▼ TABLE 10.4 Compute Beta Using a Spreadsheet The spreadsheet function SLOPE() finds the statistical relationship between a stock’s return and the market return. Considering these monthly returns for a stock and a market index, the beta of this stock is 0.83. finance at work //: markets Are Stocks Really Good or Bad? One of the basic financial theories tells us how we should view the relationship between risk and expected returns. In a nutshell, risk and expected return are positively related. A high-risk investment needs to have a high expected return, or no one would want to buy that investment. With this lack of demand, the investment’s price would drop until it offers new buyers a high expected return for the future. The higher return is the reward for taking the extra risk. Similarly, low-risk investments offer low expected returns. To quantify risk, the finance industry tends to use two measures; volatility of returns and beta. The volatility, measured by variance or standard deviation, tells us how much a return can deviate from the average return. Beta tells us how much market risk an investment has. These measures are very useful in assessing the risk of an investment or portfolio and what return premium should be expected for taking risk. However, people do not naturally think of risk within this financial theory framework. First, investors care less about how an investment’s return deviates from expectations and more about how the return may be lower than expected. In other words, a higher return than expected is not considered risky, only a lower return, or even, gulp, a loss, is viewed as risk. Also, real people do not think in terms of the high risk/return versus the low risk/return scale. Instead, people think in terms of better or worse. For example, three financial economists ran an experiment in which they asked high net worth individuals for either their expected return predictions or their risk assessment (both on a 0 to 10 scale) of over 200 of the Fortune 500 companies. When they compiled all the responses, they found the relationship in the figure shown below. Notice anything odd? This shows that firms with low risk are expected to earn a high return. People act as if expected return and risk are negatively related! This is the opposite of financial theory. Instead of evaluating firms within the framework that high expected return goes with high risk and low return goes with low risk, people seem to think in terms of good versus bad stocks. What are the characteristics of a “good” stock? Characteristics that seem good are high expected return and low risk. When an investor feels a stock is good, then it is attributed with high return and low risk. When an investor feels the stock is bad, then it is attributed with low return and high risk. Psychologists call this perception or belief an “affect.” page 301 Unfortunately, thinking about risk and return from the affect framework causes investors to misunderstand the underlying dynamics of actual expected return and risk. Thus, they may make poor decisions regarding risk and return. Want to know more? Key Words to Search for Updates: affect, measuring investment risk, risk and behavioral finance Source: Statman, Meir, Kenneth L. Fisher, and Deniz Anginer, “Affect in a Behavioral Asset-Pricing Model,” Financial Analysts Journal, March/April 2008, Figure 3: Relationship between Expected Return Scores and Risk Scores. Concerns about Beta Consider the estimation choices just mentioned. Say you estimate a firm’s beta using monthly data for five years and the Dow Jones Industrial Average return as the market portfolio. Suppose that the result is a beta of 1.3. Then you try again using weekly returns for three years and the return from the S&P 500 Index as the market portfolio’s yield, resulting in a beta of 0.9. These estimates are quite different and would create a large variation in required return if you plugged them into the CAPM. So, which is the more accurate estimate? Unfortunately, we may not be able to determine which is most representative, or “true.” In general, you may estimate a little different beta using different market portfolio proxies, different return intervals (like monthly returns versus annual returns), and different time periods. Problem 10-31 at the end of this chapter explores these differences. In addition to these estimation problems, a company can change its risk level, and thus its beta, by changing the way it operates within its business, by expanding into new businesses, and/or by changing its debt load. So even if beta is an accurate measure of what the firm’s risk level was in the past, does it apply to the future? Beta’s applicability will depend on the firm’s future plans. Both financial managers and investors share these concerns about beta. In the end, beta’s usefulness depends on its reliability. Unfortunately, beta’s empirical record is not as good as we would like. We should expect that companies with high betas yield higher returns than companies with low betas. On average, though, this does not turn out to be the case. A company’s beta does not appear to predict its future return very well. Since characterizing the risk–return relationship is so important, finance researchers have introduced other asset pricing models. One promising model adds more risk factors to the predictive relationship other than just market risk. Firm size and book-to-market ratio have had some success predicting returns, so new models often include factors derived from these characteristics along with beta as a measure of market risk. time out! 10-3 Explain why portfolios that lie on the capital market line offer better risk–return trade-offs than those that lie on the efficient frontier. 10-4 Examine the betas in Table 10.2. Which seem about right to you and which seem to indicate too much or too little risk for that firm? page 302 10.3 • CAPITAL MARKET EFFICIENCY LG10-5 The risk and return relationship rests on an underlying assumption that stock prices are generally “correct”—they are not predictably too high or too low. Imagine having a system that identified undervalued stocks with low risks (i.e., relatively high returns with a low beta). Because those stocks are undervalued, they will earn you a high return, on average, as their stock prices rise to their correct value. Note that the CAPM’s risk-return relationship would be incorrect. You would be consistently getting high returns with low risk. On the other hand, if you consistently picked overvalued stocks, you wouldn’t be earning enough return to compensate you for the risks you are taking. Investors move their money to the best alternatives by selling overvalued stocks and buying undervalued stocks. This causes the prices of the overvalued stocks to drop and the prices of the undervalued stocks to rise until both stocks’ returns stand more in line with their riskiness. Thus, the risk–return relationship relies on the idea that prices are generally accurate. What conditions are necessary for an efficient market? Efficient, or perfectly competitive, markets feature Many buyers and sellers. No prohibitively high barriers to entry. Free and readily available information available to all participants. Low trading or transaction costs. Are these conditions met for the U.S. stock market? Certainly millions of stock investors trade every day, buying and selling securities. With discount brokers and online traders, the costs to trade are fairly minimal and present no real barriers to enter the market. Information is increasingly accessible from many sources and trading philosophies, and commission costs and bid–ask spreads have steadily declined. With millions of the larger companies’ shares (say the S&P 500) of stock trading every day, the U.S. stock exchanges appear to meet efficiency conditions. But other segments of the market, like those exchanges that trade in penny stocks, feature very thin trading. The prices of these very small companies’ stock may not be fair and these equities may be manipulated in fraudulent scams. In the 1970s and 1980s, penny stock king Meyer Blinder and his firm Blinder-Robinson was known as “blind ’em and rob ’em” as they practiced penny stock price manipulation to rob many small investors of their entire investments in these small markets. These days, penny stock price manipulation is typically conducted through e-mail and Web posting scams. efficient market A securities market in which prices fully reflect available information on each security. penny stocks The stocks of small companies that are priced below $1 per share. Efficient Market Hypothesis Our concept of market efficiency provides a good framework for understanding how stock prices change over time. This theory is described in the efficient market hypothesis (EMH), which states that security prices fully reflect all available information. At any point in time, the price for any stock or bond reflects the collective wisdom of market participants about the company’s future prospects. Security prices change as new information becomes available. Since we cannot predict whether new information about a company will be good news or bad news, we cannot predict whether its stock price will go up or go down. This makes short-term stock-price movements unpredictable. But in the longer run, stock prices will adjust to their proper level as market participants gather and digest all available information. The EMH brings us to the question of what type of information is embedded within current stock prices. Segmenting information into three categories leads to the three basic levels of market efficiency, described as: 1. Weak-form efficiency—current prices reflect all information derived from trading. This stock market information generally includes current and past stock prices and trading volume. 2. Semistrong-form efficiency—current prices reflect all public information. This includes all information that has already been revealed to the public, like financial statements, news, analyst opinions, and so on. 3. Strong-form efficiency—current prices reflect all information. In addition to public information, prices reflect the privately held information that has not yet been released to the public, but may be known to some people, like managers, accountants, auditors, and so on. page 303 ▼ efficient market hypothesis (EMH) A theory that describes what types of information are reflected in current stock prices. public information The set of information that has been publicly released. Public information includes data on past stock prices and volume, financial statements, corporate news, analyst opinions, etc. privately held information The set of information that has not been released to the public but is known by few individuals, likely company insiders. Each of the EMH’s three forms rests on different assumptions regarding the extent of information that is incorporated into stock prices at any point in time. A fourth possibility—that markets may not be efficient and prices may not reflect all the information known about a company—also arises. The weak-form efficiency level involves the lowest information hurdle, stating that stock prices reflect all past price and trading volume activity. If true, this level of efficiency would have important ramifications. A segment of the investment industry uses price and volume charts to make investment timing decisions. Technical analysis has a large following and its own vocabulary of patterns and trends (resistance, support, breakout, momentum, etc.). If the market is at least weak-form efficient, then prices already reflect this information and these activities would not result in useful predictions about future price changes, and thus would be a waste of time. Indeed, the people who make the most money from price charting services are the people who sell the services, not the investors who buy and use those services. The semistrong-form efficiency level assumes that stock prices include all public information. Notice that past stock prices and volumes are publicly available information, so this level includes the weak form as a subset. Important investment implications arise if markets are efficient to public information. Many investors conduct security analysis in which they obtain financial data and other public information to assess whether a company’s stock is undervalued or overvalued. But in a semistrong-form efficient market, stock prices already reflect this information and are thus “correct.” Using only public information, you would not be able to determine whether a stock is misvalued because that information is already reflected in the price. If prices reflect all public information, then those prices will react as traders hear new (or private) information. Consider a company that announces surprisingly good quarterly profits. Traders and investors will have factored the old profit expectations into the stock price. As they incorporate the new information, the stock price will quickly rise to a new and accurate price as shown in the solid black line in Figure 10.3. Note that the stock price was $35 before the announcement and $40 immediately following. If you tried to buy the stock after hearing the news, then you would have bought at $40 and not received any benefit of the good quarterly profit news. On the other hand, if the market is not semistrong-form efficient, then the price might react quickly, but not accurately. The dashed red line shows a reaction in a non-semistrong efficient market where the price continues to drift up well after the announcement. This gradual drift to the “correct” price indicates that the market initially underreacted to the news. In this case, you could have bought the stock after the announcement and still earned a profit. The dashed blue line shows an overreaction to the firm’s better-than-expected profits announcement. If markets either consistently underreact or consistently overreact to announcements that would change stock prices (earnings, stock split, dividend, etc.), then we would believe that the market is not semistrong efficient. FIGURE 10-3 Potential Price Reaction to a Good News Announcement Stock prices react quickly to news, but do they react accurately? The strong-form market efficiency level presents the highest hurdle to test market reaction to information. The strong-form level includes information considered by the weak-form, the semistrong-form, as well as privately known information. People within firms, like CEOs and CFOs, know information that has not yet been released to the public. They may trade on this privately held, or insider, information and their trading may cause stock prices to change as it reflects that private information. In this way, stock prices could reflect even privately known information. Note that the firm managers, accountants, and auditors know several days in advance that a firm has earned unexpectedly high quarterly profits. If the stock price already incorporated this closely held private knowledge, then the big price reaction shown in Figure 10.3 would not occur. So, is the stock market efficient? If it is, at what level? This has been a hotly debated topic for decades and continues to be. It is not likely that the market is strong-form efficient. Since insider trading is punished, insider information must be valuable. However, much evidence suggests that the market could be weak-form or semistrong-form efficient. Of course, we also have evidence that the market is not efficient at any of the three levels. We will explore this more in the following section. Behavioral Finance The argument for the market being efficient works as follows: Many individual and professional investors constantly look for mispriced stocks. If they find a stock that is undervalued, they will buy it and drive up its price until it’s correctly priced. Likewise, investors would sell an overpriced stock, driving down its price until it’s correctly valued. With so many investors looking for market “mistakes,” it’s unlikely that any mispriced stock opportunities will be left in the market. page 304 The technology sector fell victim to a stock market bubble in 2000. ©Ingram Publishing/SuperStock The argument against the market being efficient is equally convincing. The market comprises many people transacting with one another. When someone makes trading decisions influenced by emotion or psychological bias, those decisions may not seem rational. When many people fall under such influences, their trading decisions may actually drive stock prices away from the correct price as emotion carries the traders away from rationality. For example, many people believe that investors were “irrationally exuberant” about technology stocks in the late 1990s —and that their buying excitement drove prices to an artificially high level. In 2000, the excitement wore off and tech stock prices plummeted. Whenever a set of stock prices go unnaturally high and subsequently crash down, the market experiences what we call a stock market bubble. In the past couple of decades, finance researchers have studied behavioral finance and found that people often behave in ways that are very likely “irrational.” At times, investors appear to be too optimistic, as though they are looking through rose-colored glasses. At other times they appear to be too pessimistic. Common investment decisions aren’t necessarily optimal ones, which flies in the face of the economist’s expectation of rational economic actors. Perhaps, then, capital markets don’t represent perfectly competitive or efficient markets if buyers and sellers do not always make rational choices. It may take many biased investors to move a stock’s price enough that it would be considered a pricing mistake. However, the important decisions in a company are typically made by just one CEO or a management team. Thus, their biases can have a direct impact on decisions involving hundreds of millions, or even billions of dollars. In other words, the contribution of behavioral finance to economic decision making is likely to be even more important in corporate behavior than market behavior. For example, consider the psychological concept of overconfidence. One of the most pervasive biases, overconfidence describes a tendency for people to overestimate the accuracy of their knowledge and underestimate the risks of a decision. These problems can adversely affect important decisions of investment (i.e., acquiring other firms) and financing (i.e., issuing new stock or bonds). stock market bubble Investor enthusiasm causes an inflated bull market that drives prices too high, ending in a dramatic collapse in prices. behavioral finance The study of the cognitive processes and biases associated with making financial and economic decisions. overconfidence Overconfidence is used to describe three psychological observations. First, people are miscalibrated on understanding the precision of their knowledge. Second, people have a tendency to underestimate risks, and third, people tend to believe that they are better than average at tasks they are familiar with. time out! 10-5 Can the market be semistrong-form efficient but not weak-form efficient? Explain. 10-6 If the market usually overreacts to bad news announcements, what would your return be like if you bought after you heard the bad news? 10.4 • IMPLICATIONS FOR FINANCIAL MANAGERS LG10-6 Financial managers must understand the crucial relationship between risk and return for several reasons. First, while the relationship between risk and return is demonstrated here using the capital markets, it equally applies to many business decisions. A firm’s product mix, marketing campaign combination, and research and development programs all entail risk and potential rewards. Being able to understand and characterize these decisions within a risk and return framework can help managers make better decisions. In addition, managers must understand what return their stockholders require at various times of firm operations. After all, a firm must receive enough revenue from its variously risky activities to pay its business and debt costs and reward the owners (the stockholders). Managers must thus include the return to shareholders when they analyze new business opportunities. Firms and capital markets also interact directly. For example, a good understanding of market efficiency helps managers understand how their stock prices will react to different types of decisions (like dividend changes) and page 305 news announcements (like unexpectedly high or low profitability). In fact, many managers own company stock and are thus compensated through programs that rely on the stock price, like restricted stock and executive stock options. Companies also periodically issue (sell) additional shares of stock to raise more capital, and these sales depend upon market efficiency assumptions. The firm would not want to sell additional shares if the stock price is too low (i.e., undervalued). They would want to sell more shares at any time that they thought their shares are overvalued. Other times, firms repurchase (buy back) shares of stock. The firm might want to do this if its shares were undervalued, but not if its shares were overvalued. Of course, valuation is not an issue if security markets are efficient. restricted stock A special type of stock that is not transferable from the current holder to others until specific conditions are satisfied. executive stock options Special rights given to corporate executives to buy a specific number of shares of the company stock at a fixed price during a specific period of time. Using the Constant-Growth Model for Required Return LG10-7 For decades, financial managers have used the CAPM to compute shareholders’ required return. Given recent concerns about beta’s limitations, many see the CAPM as a less useful model for calculating appropriate returns. Some have turned instead to another model useful for computing required return—the constant-growth model discussed in Chapter 8. We can arrange the terms of that model as (10-6) finance at work //: markets Bubble Trouble Many professionals criticize the EMH because the overall market sometimes seems too high or too low. A very dramatic example of the market level being artificially high is the market bubble. During a market bubble, the market quickly inflates on rampant speculation and subsequently crashes. Investors who buy near the peak of the bubble risk losing nearly all their investment. One of the United States’ earliest stock market bubbles was the bubble and crash of 1929. Note from the figure that the DJIA started in 1927 at around 160. By October 1929, the DJIA had reached nearly 400 and then crashed. By mid-1932, the DJIA had fallen to the 40s. The sustained fall coincided with an economic depression. Panel A of the figure also shows a price bubble in gold. The price of gold was $230 per ounce in January 1979. The late 1970s and early 1980s saw double-digit inflation throughout the economy, and many investors felt that gold represented a safe and inflation-proof investment. Just one year later, the price had skyrocketed to $870. It then fell below $300 in less than two and a half years. Could gold be in another bubble? In late 2008, gold’s price was $750; it shot to $1,500 in late 2011. See the spectacular tech bubble during the 1990s? The NASDAQ 100, which started in 1985 at 250, soared to a peak of 4,816.35 on March 24, 2000. It then fell to less than 1,000 in two and a half years. The rise and fall of the NASDAQ 100 seems much more pronounced than the Japanese stock bubble of the 1980s. From a January 2, 1985, start at 11,543, the Nikkei 225 soared to a closing high of 38,916 on December 29, 1989. The bubble then burst and the Japanese stock market plummeted. The Nikkei has yet to fully recover, trading today at around the 16,500 level. EMH critics do not believe that the entire stock market, or a substantial segment of it, can be correctly valued before, during, or after a bubble. It certainly appears to be overvalued during the time the bubble is inflating. Want to know more? Key Words to Search for Updates: stock bubble, irrational exuberance page 306 Of course, this model assumes that the stock is efficiently priced. This model holds an advantage in that it uses current firm data (dividend, D1, and price, P0) and a simple forward estimate (growth, g) to assess what investors currently expect the stock to return, i. For example, Table 10.2 shows McDonald’s beta as 0.56. Using this beta, Table 10.3 shows that shareholders require only 8.92 percent return to hold McDonald’s stock, given its low risk profile. You may find it hard to believe that McDonald’s owners (the shareholders) expect such a low return from one of the world’s most profitable firms. So perhaps this is a case in which the CAPM result isn’t very useful. Applying the constant-growth model looks something like this: McDonald’s is expected to pay a $3.56 dividend this year and the stock price currently stands at $117 per share. Financial analysts believe McDonald’s will grow at 9.50 percent per year for the next five years. The constant growth rate model suggests that McDonald’s shareholders expect a 12.54 percent return [= ($3.56 ÷ $117) + 0.095]. So, which required return seems more likely, the 8.92 percent computed from CAPM or the 12.54 percent suggested by the constant-growth model? It is likely that McDonald’s investors are expecting closer to the 13 percent return than the 9 percent estimate. Financial managers need an estimate of their shareholders’ required return in order to make appropriate decisions about their companies’ future growth. Good financial managers will compute shareholders’ required return using as many methods as they can to determine the most realistic value possible. EXAMPLE 10- 4 Required Return LG10-7 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Consider that the required returns for 3M, Home Depot, and Hewlett- Packard are 12.56 percent, 12.07 percent, and 15.78 percent, respectively. These expectations may seem quite far apart, considering that all three firms are in the DJIA and are leaders in their market sectors. Use the following information to compute the constant-growth model estimate of the required return: Expected Dividend Current Price Analyst Growth Estimate 3M Company $2.54 $105.70 10.4% Home Depot 1.56  70.10 14.5  Hewlett- 0.53  22.00 0.25  http://mhhe.com/CornettM4e page 307 Hewlett- Packard 0.53  22.00 0.25  SOLUTION: You can now use equation 10-6 to find each company’s required return as The 3M estimates using CAPM and the constant-growth rate model are similar. The constant-growth rate model estimate is more than 4 percent higher than the CAPM estimate for Home Depot, but far lower for Hewlett-Packard. Similar to Problems 10-15, 10-16, 10-29, 10-30, Self-Test Problem 3 time out! 10-7 Why is the shareholders’ required return important to corporate managers? Get Online page 308 ©JGI/ Jamie Grill/ Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. Consider an asset that provides the same return no matter what economic state occurs. What would be the standard deviation (or risk) of this asset? Explain. (LG10-1) 2. Why is expected return considered “forward-looking”? What are the challenges for practitioners to utilize expected return? (LG10-1) 3. In 2000, the S&P 500 Index earned −9.1 percent while the T-bill yield was 5.9 percent. Does this mean the market risk premium was negative? Explain. (LG10-2) 4. How might the magnitude of the market risk premium impact people’s desire to buy stocks? (LG10-2) 5. Describe how adding a risk-free security to modern portfolio theory allows investors to do better than the efficient frontier. (LG10-3) 6. Show on a graph like Figure 10.2 where a stock with a beta of 1.3 would be located on the security market line. Then show where that stock would be located if it is undervalued. (LG10-3) 7. Consider that you have three stocks in your portfolio and wish to add a fourth. You want to know if the fourth stock will make the portfolio riskier or less risky. Compare and contrast how this would be assessed using standard deviation versus market risk (beta) as the measure of risk. (LG10-3) 8. Describe how different allocations between the risk-free security and the market portfolio can achieve any level of market risk desired. Give examples of a portfolio from a person who is very risk averse and a portfolio for someone who is not so averse to taking risk. (LG10-3) 9. Cisco Systems has a beta of 1.25. Does this mean that you should expect Cisco to earn a return 25 percent page 309 higher than the S&P 500 Index return? Explain. (LG10-4) 10. Note from Table 10.2 that some technology-oriented firms (Apple) in the Dow Jones Industrial Average have high market risk while others (Intel and Verizon) have low market risk. How do you explain this? (LG10-4) 11. Find a beta estimate from three different sources for General Electric (GE). Compare these three values. Why might they be different? (LG10-4) 12. If you were to compute beta yourself, what choices would you make regarding the market portfolio, the holding period for the returns (daily, weekly, etc.), and the number of returns? Justify your choices. (LG10-4) 13. Explain how the concept of a positive risk–return relationship breaks down if you can systematically find stocks that are overvalued and undervalued. (LG10-5) 14. Determine what level of market efficiency each event is consistent with the following: (LG10-5) a. Immediately after an earnings announcement the stock price jumps and then stays at the new level. b. The CEO buys 50,000 shares of his company and the stock price does not change. c. The stock price immediately jumps when a stock split is announced, but then retraces half of the gain over the next day. d. An investor analyzes company quarterly and annual balance sheets and income statements looking for undervalued stocks. The investor earns about the same return as the S&P 500 Index. 15. Why do most investment scams conducted over the Internet and e-mail involve penny stocks instead of S&P 500 Index stocks? (LG10-5) 16. Describe a stock market bubble. Can a bubble occur in a single stock? (LG10-5) 17. If stock prices are not strong-form efficient, what might be the price reaction to a firm announcing a stock buyback? Explain. (LG10-6) 18. Compare and contrast the assumptions that need to be made to compute a required return using CAPM and the constant-growth model. (LG10-7) 19. How should you handle a case where required return computations from CAPM and the constant-growth model are very different? (LG10-7) Problems BASIC PROBLEMS 10-1 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: (LG10-1) Economic State Probability Return Fast growth 0.3 40% Slow growth 0.4 10  Recession 0.3 −25  10-2 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: (LG10-1) Economic State Probability Return Fast growth 0.2 35% Slow growth 0.6 10  Recession 0.2 −30  10-3 Required Return If the risk-free rate is 3 percent and the risk premium is 5 percent, what is the required page 310 return? (LG10-2) 10-4 Required Return If the risk-free rate is 4 percent and the risk premium is 6 percent, what is the required return? (LG10-2) 10-5 Risk Premium The average annual return on the S&P 500 Index from 1986 to 1995 was 15.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years? (LG10-2) 10-6 Risk Premium The average annual return on the S&P 500 Index from 1996 to 2005 was 10.8 percent. The average annual T-bill yield during the same period was 3.6 percent. What was the market risk premium during these 10 years? (LG10-2) 10-7 CAPM Required Return Hastings Entertainment has a beta of 0.65. If the market return is expected to be 11 percent and the risk-free rate is 4 percent, what is Hastings’ required return? (LG10-3) 10-8 CAPM Required Return Nanometrics, Inc., has a beta of 3.15. If the market return is expected to be 10 percent and the risk-free rate is 3.5 percent, what is Nanometrics’ required return? (LG10-3) 10-9 Company Risk Premium Netflix, Inc., has a beta of 3.61. If the market return is expected to be 13 percent and the risk-free rate is 3 percent, what is Netflix’s risk premium? (LG10-3) 10-10 Company Risk Premium Paycheck, Inc., has a beta of 0.94. If the market return is expected to be 11 percent and the risk-free rate is 3 percent, what is Paycheck’s risk premium? (LG10-3) 10-11 Portfolio Beta You have a portfolio with a beta of 1.35. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 5 percent in a stock with a beta of 0.78? (LG10-3) 10-12 Portfolio Beta You have a portfolio with a beta of 1.1. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 15 percent in a stock with a beta of 0.5? (LG10-3) 10-13 Stock Market Bubble The NASDAQ stock market bubble peaked at 4,816 in 2000. Two and a half years later it had fallen to 1,000. What was the percentage decline? (LG10-5) 10-14 Stock Market Bubble The Japanese stock market bubble peaked at 38,916 in 1989. Two and a half years later it had fallen to 15,900. What was the percentage decline? (LG10-5) 10-15 Required Return Paccar’s current stock price is $48.20 and it is likely to pay a $0.80 dividend next year. Since analysts estimate Paccar will have an 8.8 percent growth rate, what is its required return? (LG10-7) 10-16 Required Return Universal Forest’s current stock price is $57.50 and it is likely to pay a $0.26 dividend next year. Since analysts estimate Universal Forest will have a 9.5 percent growth rate, what is its required return? (LG10-7) INTERMEDIATE PROBLEMS 10-17 Expected Return Risk For the same economic state probability distribution in problem 10-1, determine the standard deviation of the expected return. (LG10-1) Economic State Probability Return Fast growth 0.3 40% Slow growth 0.4 10  Recession 0.3 −25  10-18 Expected Return Risk For the same economic state probability distribution in problem 10-2, determine the standard deviation of the expected return. (LG10-1) Economic State Probability Return Fast growth 0.2 35% page 311 Slow growth 0.6 10  Recession 0.2 −30  10-19 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.5, the expected return on the market is 12 percent, and the risk-free rate is 4 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued. (LG10-3) 10-20 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.2, the expected return on the market is 11 percent, and the risk-free rate is 5 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued. (LG10-3) 10-21 Portfolio Beta You own $10,000 of Olympic Steel stock that has a beta of 2.2. You also own $7,000 of Rent-a-Center (beta = 1.5) and $8,000 of Lincoln Educational (beta = 0.5). What is the beta of your portfolio? (LG10-3) 10-22 Portfolio Beta You own $7,000 of Human Genome stock that has a beta of 3.5. You also own $8,000 of Frozen Food Express (beta = 1.6) and $10,000 of Molecular Devices (beta = 0.4). What is the beta of your portfolio? (LG10-3) ADVANCED PROBLEMS 10-23 Expected Return and Risk Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: (LG10-1) Economic State Probability Return Fast growth 0.30 60% Slow growth 0.50 13  Recession 0.15 −15  Depression 0.05 −45  10-24 Expected Return and Risk Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: (LG10-1) Economic State Probability Return Fast growth 0.25 50% Slow growth 0.55 11  Recession 0.15 −15  Depression 0.05 −50  10-25 Risk Premiums You own $10,000 of Denny’s Corp. stock that has a beta of 2.9. You also own $15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7). Assume that the market return will be 11.5 percent and the risk-free rate is 4.5 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? (LG10-3) 10-26 Risk Premiums You own $15,000 of Opsware, Inc., stock that has a beta of 3.8. You also own $10,000 of Lowe’s Companies (beta = 1.6) and $10,000 of New York Times (beta = 0.8). Assume that the market return will be 12 percent and the risk-free rate is 6 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? (LG10- 3) 10-27 Portfolio Beta and Required Return You hold the positions in the following table. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio? (LG10-3) page 312 Price Shares Beta Amazon.com $40.80 100 3.8 Family Dollar Stores 30.10 150 1.2 McKesson Corp. 57.40 75 0.4 Schering-Plough Corp. 23.80 200 0.5 10-28 Portfolio Beta and Required Return You hold the positions in the following table. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio? (LG10-3) Price Shares Beta Advanced Micro Devices $ 14.70 300 4.2 FedEx Corp. 120.00 50 1.1 Microsoft 28.90 100 0.7 Sara Lee Corp. 17.25 150 0.5 10-29 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant-growth model. Compare and discuss the results. Assume that the market portfolio will earn 12 percent and the risk-free rate is 3.5 percent. (LG10-3, LG10-7) Price Upcoming Dividend Growth Beta US Bancorp $36.55 $1.60 10.0% 1.8 Praxair  64.75  1.12 11.0  2.4 Eastman Kodak  24.95  1.00 4.5  0.5 10-30 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant-growth model. Compare and discuss the results. Assume that the market portfolio will earn 11 percent and the risk-free rate is 4 percent. (LG10-3, LG10-7) Price Upcoming Dividend Growth Beta Estee Lauder $47.40 $0.60 11.7% 0.75 Kimco Realty  52.10  1.54 8.0  1.3  Nordstrom  5.25  0.50 14.6  2.2  10-31 Spreadsheet Problem As discussed in the text, beta estimates for one firm will vary depending on various factors such as the time over which the estimation is conducted, the market portfolio proxy, and the return intervals. You will demonstrate this variation using returns for Microsoft. a. Using all 45 monthly returns for Microsoft and the two stock market indexes, compute Microsoft’s beta using the S&P 500 Index as the market proxy. Then compute the beta using the NASDAQ index as the market portfolio proxy. Compare the two beta estimates. b. Now estimate the beta using only the most recent 30 monthly returns and the S&P 500 Index. Compare the beta estimate to the estimate in part (a) when using the S&P 500 Index and all 45 monthly returns. c. Estimate Microsoft’s beta using the following quarterly returns. Compare the estimate to the ones from parts (a) and (b). page 313 10-32 Spreadsheet Problem Build a spreadsheet that automatically computes the expected market return and risk for different assumptions about the state of the economy. a. First, create a spreadsheet like the one shown below and compute the expected return and standard deviation. b. Compute the expected return and risk for the following two scenarios: Notes CHAPTER 10 1. A mathematically equivalent equation for beta is , where cov() is the covariance between the stock and market portfolio returns, and var() is the variance of the market portfolio. Part Six page 314 page 315 I chapter eleven Calculating the cost of capital ©Photodisc/Getty Images n the previous two chapters, we discussed investors’ required return given a particular risk profile. In this chapter, we examine the question from the firm’s point of view: How much must the firm pay to finance its operations and expansions using debt and equity sources? Firms use a combination of debt and equity sources to fund their operations, projects, and any expansions they may undertake. In Chapter 14, we’ll explore the factors that managers consider as they choose the optimal capital structure mix. For now, we’ll assume that management has chosen the optimal mix for us, and that it’s our job to implement it. LG11-1 As we’ve seen in previous chapters, investors face different kinds of risks associated with debt, preferred stock, and equity. As a result, their required rates of return for each debt or equity source differ as well. So, as the firm uses a combination of different financing sources, we must calculate the investors’ average required rate of return to use as the cost of capital for evaluating decisions about investing the firm’s capital. Since firms seldom use equal amounts of debt and equity capital sources, we will need to calculate this as a weighted average, with weights based on the proportion of debt and equity capital used. As we’ll see, we can measure such a weighted-average cost of capital (WACC) in a variety of situations and page 316 for a number of purposes. For example, if we’re interested in determining the average rate of return that the firm must earn from existing operations when we don’t expect the firm’s capital structure to change, we can calculate the WACC using the firm’s current capital structure and existing component costs; however, if we’re trying to determine the average rate of return that we would need to earn from a new project in order for it to add value to the firm, we would want to use the project’s proposed capital structure and its component costs. weighted-average cost of capital (WACC) The weighted-average after-tax cost of the capital used by a firm, with weights set equal to the relative percentage of each type of capital used. component costs The individual costs of each type of capital—bonds, preferred stock, and common stock. LEARNING GOALS LG11-1 Understand the relationship of cost of capital to the investor’s required return. LG11-2 Use the weighted-average cost of capital (WACC) formula to calculate a project’s cost of capital. LG11-3 Explain how the firm chooses among estimating costs of equity, preferred stock, and debt. LG11-4 Calculate the weights used for WACC projections. LG11-5 Identify which elements of WACC are used to calculate a project-specific WACC. LG11-6 Evaluate trade-offs between a firmwide WACC and a divisional cost of capital approach. LG11-7 Distinguish subjective and objective approaches to divisional cost of capital. LG11-8 Demonstrate how to adjust the WACC to reflect flotation costs. viewpoints business APPLICATION MP3 Devices, Inc., is about to launch a new project to create and market a combination MP3 player-video projector. MP3 Devices currently uses a particular mixture of debt, common stock, and preferred shares in its capital structure, but the firm is thinking of using the launch of the new project as an opportunity to change that capital structure. The new project will be funded with 40 percent debt, 10 percent preferred stock, and 50 percent common stock. MP3 Devices currently has 10 million shares of common stock outstanding, selling at $18.75 per share, and expects to pay an annual dividend of $1.35 one year from now, after which future dividends are expected to grow at a constant 6 percent rate. MP3’s debt consists of 20- year, 10 percent annual coupon bonds with a face value of $150 million and a market value of $165 million, and the company’s capital mix also includes 100,000 shares of 10 percent preferred stock selling at par. If MP3 Devices faces a marginal tax rate of 34 percent, what weighted average cost of capital should it use as it evaluates this project? (See the solution at the end of the book.) One important point about the component costs to be used in the firm’s computation of the average required rate of return is that dividends paid to either common or preferred stockholders are not tax deductible, but interest paid to debt holders is. Therefore, paying a certain rate of return to stockholders costs the firm that same rate, but paying the same interest rate to debt holders actually costs the firm less than the rate paid. The reason is that, since interest on debt is tax deductible, paying rate iD to debt holders is, for all intents and purposes, subsidized by the government: If the firm hadn’t paid out that interest rate to the debt holders, it would have had to have paid out taxes to the government on the money it used to pay the interest. So, effectively, the firm’s effective after-tax interest cost will be equal to the interest rate paid on debt multiplied by one minus the firm’s relevant tax rate. For example, if a firm pays a 10 percent coupon on $1 million in debt while it is subject to a 35 percent tax rate, then each coupon payment will be equal to 0.10 × $1,000,000 = $100,000, but that $100,000 in interest, being tax deductible, will reduce the firm’s tax bill by 0.35 × $100,000 = $35,000. So paying $100,000 in interest saves the firm $35,000 in taxes, making the effective after-tax cost of debt equal to $100,000 − $35,000 = $65,000 and the effective after-tax interest rate equal to 10% × (1 − 0.35) = 6.5%. page 317 ■ 11.1 • THE WACC FORMULA LG11-2 The average cost per dollar of capital raised is called the weighted-average cost of capital (WACC). We calculate WACC using equation 11-1: (11-1) personal APPLICATION Mackenzie is currently finishing up her bachelor’s degree and is considering going back to grad school for a master’s degree. She currently has $17,125 in student loans carrying an 8 percent interest rate from her bachelor’s degree and estimates that she will need to take out an additional $29,000 in student loans (at the same interest rate) to make it through the master’s program she’d like to attend. The IRS allows taxpayers with student loans to deduct the interest on those loans, but only up to a maximum amount of $2,500 per year. Assuming that Mackenzie will face a marginal personal tax rate of 25 percent when she graduates, what will be the average after-tax interest rate that she will be paying on the student loans immediately after she graduates with her master’s? (See the solution at the end of the book.) How else can Mackenzie finance her graduate degree? What will happen to her after-tax interest rate? where Notice that we use weights based on market values rather than book values because market values reflect investors’ assessment of what they would be willing to pay for the various types of securities, while book values would reflect what was paid for such securities at varying times in the past. Since we’re interested in coming up with the cost of capital for new investments in the firm or its projects, using market values here makes more sense. Calculating the Component Cost of Equity LG11-3 page 318 We could calculate iE using the capital asset pricing model, as discussed in Chapter 10: (11-2) Or, we can assume that the equity in question is a constant-growth stock such as the ones we modeled in Chapter 8. Under this assumption, we can solve the constant-growth model for iE: (11-3) Which way is better? Well, theoretically, both should give us the same answer, but depending on the situation, some pragmatic reasons may dictate your choice. 1. In situations where you do not have sufficient historic observations to estimate β (i.e., when the stock is fairly new), or when you suspect that the past level of the stock’s systematic (or market) risk might not be a good indicator of the future risk, you do not want to use the CAPM. Using calculated historic systematic risk when it is not a good estimate of βE, estimated future systematic risk, will not work too well. 2. In situations where you can expect constant dividend growth, the constant-growth model is appropriate. But although you can try to adjust the model for stocks without constant dividend growth, doing so may introduce potentially sizable errors, so it is not the best choice for stocks that increase their dividends irregularly. EXAMPLE 11- 1 Cost of Equity LG11-2 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. ADK Industries’ common shares sell for $32.75 per share. ADK expects to set its next annual dividend at $1.54 per share. If ADK expects future dividends to grow by 6 percent per year, indefinitely, the current risk-free rate is 3 percent, the expected return on the market is 9 percent, and the stock has a beta of 1.3, what should be firm’s cost of equity? SOLUTION: The cost of equity using the CAPM will be The cost of equity using the constant-growth model will be Similar to Problems 11-1, 11-2 Overall, we should expect that the CAPM approach to estimating iE will apply more accurately in most cases. However, if you do encounter a situation in which the constant-growth model applies, then you can certainly use it. http://mhhe.com/CornettM4e page 319 If we are really fortunate and happen to have enough information to use both approaches, then we should probably use both, taking an average of the resulting estimates of iE. 1 Calculating the Component Cost of Preferred Stock As we discussed in Chapter 8, preferred stock represents a special case of the constant-growth model, wherein g equals zero. So we can estimate preferred stocks’ component cost using a simplified version of equation 11-3: (11-4) Calculating the Component Cost of Debt Because of the tax deductibility of debt for the firm, computing the component cost of debt actually has two parts. We must estimate the before-tax cost of debt, iD, and then adjust this figure to convert it to the after-tax rate of return, iD × (1 − TC). To estimate iD, we need to solve for the yield to maturity (YTM) on the firm’s existing debt (11-5) EXAMPLE 11- 2 Cost of Preferred Stock LG11-3 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that ADK also has one million shares of 7 percent preferred stock outstanding, trading at $72 per share. What is ADK’s component cost for preferred equity? SOLUTION: The cost of the preferred stock will equal Similar to Problems 11-7, 11-8 Solve for the interest rate that makes the price equal to the sum of the present values of the coupons and the face value of the bond, as discussed in Chapter 7. Intuitively, by using the price on the firm’s existing debt in equation 11-5, we are calculating the rate of return expected by investors currently buying the firm’s existing bonds. As discussed later when we cover how to calculate project-specific WACCs, the fact that all of the firms’ bonds get their interest paid out of all the firm’s cash flows before any of the firm’s shareholders get anything implies that this expected rate of return on existing firm debt should also be a good proxy for the rate of return that potential investors would demand on any new debt issued by the firm, as well. http://mhhe.com/CornettM4e page 320 Finally, if we think of the YTM as the rate that bond investors expect to get for investing in the bond, then we need to adjust it for the tax deductibility of debt interest to convert this to a measure of how much it actually costs the firm to pay that YTM. We do so by multiplying the YTM by (1 − TC). Choosing Tax Rates The interest paid on debt is tax deductible, but the benefit to each dollar of interest will vary based on the marginal tax rate that the firm would have had to have paid on that dollar if it was not paid out as interest. Therefore, the appropriate, overall average marginal tax rate to be used in the WACC will be the weighted average of the marginal tax rates that would have been paid on the taxable income shielded by the interest deduction, where the weights will be equal to the proportion of the taxable income that would have been taxed at each marginal rate. the Math Coach on… Preferred Stock Dividends “The assumed par value of preferred stock is $100. So, a 7 percent preferred stock pays $7 a year in dividends.„ For example, if a firm had earnings before interest and taxes (EBIT) of $400,000, taxable interest deductions of $100,000, and faced the corporate tax schedule shown in Table 11.1, then the $100,000 in taxable interest deductions would reduce the firm’s taxable income from $400,000 to $400,000 − $100,000 = $300,000, meaning that the taxes saved by the interest deduction would have been from dollars that would have been taxed in the fourth (i.e., $100,001 to $335,000) and fifth ($335,001 to $10,000,000) rows (or “brackets”) in Table 11.1. So the appropriate tax rate to use in the WACC would be a weighted average of the marginal tax rates from the fourth (i.e., 39%) and fifth (34%) tax brackets, where the weights would be determined by how much of the $100,000 in taxable interest deductions would have been taxed at 39 percent and how much would have been taxed at 34 percent if the $100,000 had not been paid out as interest: ▼ TABLE 11.1 Corporate Tax Rates Taxable Income Tax Rate $    0 − $  50,000 15% 50,001 − 75,000 25  75,001 − 100,000 34  100,001 − 335,000 39  335,001 − 10,000,000 34  10,000,001 − 15,000,000 35  15,000,001 − 18,333,333 38  18,333,334 + 35  EXAMPLE 11- 3 Cost of Debt LG11-3 page 321 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. ADK has 30,000 20-year, 8 percent annual coupon bonds outstanding. If the bonds currently sell for 97.5 percent of par and the firm pays an average tax rate of 35.92 percent, what will be the before-tax and after- tax component cost for debt? SOLUTION: The before-tax cost of debt will be the solution to which will equal 8.26 percent. Multiplying this by one minus the tax rate will yield the after-tax cost of debt: 0.0826 × (1 − 0.3592) = 0.0529, or 5.29%. Similar to Problems 11-3, 11-4 EXAMPLE 11- 4 Tax Rate LG11-3 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that ADK expects EBIT to be approximately $20 million per year for the foreseeable future. Given the 30,000 20-year, 8 percent annual coupon bonds discussed in the previous example, what would the appropriate tax rate be for use in the calculation of the debt component of ADK’s WACC? SOLUTION: The interest payments on the bonds would total 30,000 × $1,000 × 0.08 = $2,400,000 per year, resulting in earnings before tax (EBT) of $20,000,000 − $2,400,000 = $17,600,000. As taxable income falls from $20,000,000 to $17,600,000 after the firm pays the interest on the bonds, $1,666,667, or 69.44 percent, of the $2,400,000 reduction would fall in the highest 35 percent bracket, while the remaining $733,333, or 30.56 percent ($733,333/$2,400,000), would occur in the 38 percent tax bracket, making the weighted average applicable tax rate equal to Similar to Problems 11-5, 11-6 Calculating the Weights LG11-4 http://mhhe.com/CornettM4e http://mhhe.com/CornettM4e page 322 Calculating the weights to be used in the WACC formula is mathematically very simple: We just calculate the percentages of the funding that come from equity, preferred stock, and debt, respectively. Sounds easy, right? Well, the tricky part to this lies in determining what we mean by “the funding”: If we are calculating WACC for a firm, then “the funding” encompasses all the capital in the firm, and E, P, and D will be determined by computing the total market value of the firm’s common stock, preferred stock, and debt, respectively. However, if we are computing WACC for a project, then “the funding” will only include the financing for that project, and E, P, and D will be equal to the amount of each used in the financing of that project.2 EXAMPLE 11- 5 Capital Structure Weights and WACC LG11-4 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Let us continue the previous examples. Suppose that ADK has issued 3 million shares of common stock, 1 million shares of preferred stock, and the previously mentioned 30,000 bonds outstanding. What will ADK’s WACC be, considering ADK as a firm? SOLUTION: Using the securities’ prices given in previous examples, ADK’s equity, preferred stock, and debt will have the following total market values: Equity: 3m × $32.75 = $98.25m Preferred stock: 1m × $72 = $72m Debt: 30,000 × $975 = $29.25m The total combined market value for all three capital sources is $199.5 million. The applicable weights for each capital source will therefore be Tying this all together with the answers from the previous examples, ADK will have a WACC of Similar to Problems 11-9 to 11-14, 11-21, 11-22, Self-Test Problem 1 http://mhhe.com/CornettM4e http://mhhe.com/CornettM4e page 323 If you think about this for a second, you will realize that this means that projects can wind up having different WACCs than their firm. That is not just OK, it is also exactly right because, as we will see in a later chapter, the firm is like a diversified portfolio of different projects, all with different risks and returns. And one of the things that can contribute to the risk of a project is the choice of how much common stock, preferred stock, and debt is used to finance it. time out! 11-1 Explain why we multiply the component cost of debt by the marginal tax rate, TD, but don’t do so for the component costs of equity or preferred stock. 11-2 How would we compute iD if a company had multiple bond issues outstanding? 11.2 • FIRM WACC VERSUS PROJECT WACC LG11-5 So far, we have been defining the WACC as a weighted-average cost across the firm’s different financing sources. If we think of the firm as a portfolio of different projects and products, we see that the WACC will be a weighted- average cost of capital across the items in that portfolio, too. This way it represents the cost of capital for the “typical” project that the firm is currently undertaking. However, firms grow by taking on new projects. So now the question is: Can managers use our firm-wide WACC, calculated previously, to evaluate the firm’s newly proposed projects? The answer is: It depends. If a new project is similar enough to existing projects, then yes, managers can use the firm’s WACC as the new project’s cost of capital. But say that your firm is contemplating undertaking a significantly different project—one far different from any project that the firm is already engaged in. What then? Then we cannot expect the firm’s overall WACC to appropriately measure the new project’s cost of capital. Let your intuition work on this for a second: If the new project is riskier than the firm’s existing projects, then it should be “charged” a higher cost of capital; if it’s safer, then the firm should assign the new project a lower cost of capital. That seems only fair, right? Consider a U.S. firm—let’s call it GassUp—that currently owns a chain of gas stations. Firm management is considering a new project: opening up a series of gourmet coffee shops inside their existing gas stations. Given the demand for upscale coffee in the United States, as well as the historically volatile oil markets, it’s probably difficult to say exactly whether the coffee shops will be more or less risky than gas stations. We can probably say, though, that the two enterprises will face different risks. For example, one could argue that at least a certain amount of gas is a necessity, while gourmet coffee is more of a luxury good, so it makes sense that the two “parts” of the new, expanded product line for GassUp will perform differently in boom or bust periods. Likewise, what if the coffee shops are located within the busiest and most stable gas stations—say the ones that lie along freeways? Then the firm faces remodeling existing buildings, rather than starting from scratch, and can pick and choose to put gourmet coffee facilities in the gas stations that have the volume to support them, which likely means that the risks of adding the facilities for gourmet coffee to those stations will be lower than building new facilities from scratch. So, this means that GassUp probably should not use the same WACC for the new line of gourmet coffee expansions to its gas stations as it does for the gas stations themselves; that is, the WACC for the new expansion projects should not be equal to the WACC of the firm as it currently exists. ©Ingram Publishing/Superstock Even if GassUp’s coffee venture fails, the firm’s creditors would likely still collect payments from gas station operations. ©Tetra Images/Alamy However, does this mean that all the components of WACC for each new gourmet coffee expansion should be different for every store? Well, not exactly. As we’ll discuss, some inputs to WACC should be project-specific, but others should be consistent with the firmwide values used in calculating a firmwide WACC. page 324 Project Cost Numbers to Take from the Firm It is tempting to argue that all component inputs for a project-specific WACC should be based on the specific project attributes, but if we created all project-specific numbers, what fundamental issue related to bonds and preferred stock would we be ignoring? That both bonds and preferred stocks create claims on the firm, not on any particular group of projects within that firm. Furthermore, debt claims are superior to those of common stockholders. So if the new project does significantly increase the firm’s overall risk, the increased risk will be borne disproportionately by common stockholders. Debt holders and preferred stockholders will likely face minimal impact on the risk and return that their investments give them, no matter what new project the firm undertakes—even if those claimants own bonds or preferred shares that the firm issued to fund the new project. For example, suppose GassUp decides to build entirely separate facilities for its coffee shops, which it will name “Bottoms Up.” Furthermore, suppose GassUp partially finances its expansion into coffee shops with debt, and that the project turns out to be more like “Bottoms Down”—far less successful than the firm had hoped. Though this would be an unfortunate turn of events for GassUp’s common shareholders, the firm’s creditors and preferred shareholders would likely still collect their usual interest and dividend payments from GassUp’s gross revenues from gas station operations. Creditors understand that their repayment probably comes from continuing operations and take current cash flows into account when a firm comes seeking funds. For example, if a small firm approaches a bank for a loan to finance an expansion, the bank will normally spend more time analyzing current cash flows to determine the probability that they will recoup their loan than it will analyzing the potential new cash flows from the proposed expansion. Note that this situation holds true only as long as the new projects represent fairly small investments compared to ongoing operations. As new projects become large relative to ongoing cash-flow producing activities, creditors will have to examine the likelihood of being repaid from the new projects much more closely. New projects, however great their potential, inherently carry more risk than do established current operations. Changes in the proportion of new projects relative to ongoing operations will thus translate into increased risk for the creditor, who will ask for a higher rate of return to offset the risk. Since most firms tend to grow incrementally, we will assume (unless otherwise indicated) that we’re examining situations in which the number of new projects is small relative to ongoing operations. We can therefore also assume that using the firm’s existing, pre-project component costs of debt and preferred stock to calculate WACC is appropriate. Project Cost Numbers to Find Elsewhere: The Pure-Play Approach Since we have decided not to adjust the firmwide costs of debt or preferred stock for the risk of a project, where should we account for the new project risk brought to the firm overall? As with several other questions associated with risk-and profit-sharing that we’ll discuss in Chapter 16, the answer lies with equity. The firm’s risk changes when it takes on a project that is noticeably different from its existing lines of business. Debt holders and preferred stockholders will not bear much of this change in risk; rather, when it takes on a new project, the firm instead creates risk for its common stockholders that is disproportionately large compared to the amount of stockholder capital used to finance the project. In response to such a change in the firm’s risk profile, stockholders adjust their required rate of return to adjust for the new risk level. Absent any alteration to the firm’s capital structure,3 changes in the firm’s risk profile are due to differences in the firm’s business risks based on the mix of the new and existing product lines. The stock’s beta reflects those differences in each product line. Obviously, no proposed new project will have a history of previous returns. Without such data, neither analysts nor investors can calculate a project-specific beta. So what data can we use? To the extent that we can find other firms engaged in the proposed new line of business, we can use their betas as proxies to estimate the project’s risk. Ideally, the other firms would be engaged only in the proposed new line of business; such monothemed firms are usually referred to as pure plays, with this term also in turn being applied to this approach to estimating a project’s beta. An average of n such proxy betas will give us a fairly accurate estimate of what the new project’s beta will be.4 page 325 where (11-6) business risk The risk of a project arising from the line of business it is in; the variability of a firm’s or division’s cash flows. proxy beta The beta (a measure of the riskiness) of a firm in a similar line of business as a proposed new project. This average will be an estimate, in the strictest statistical sense of the word. You might recall from your statistics classes that we will need to be careful to get as large a sample as possible if we want to get as much statistical power for our estimate as possible. Ideally, we would like to find at least three or four companies from which to draw proxy betas, called pure-play proxies, to ensure that we have a large enough sample size to safely make meaningful inferences. In reality, however, two proxies (or even one) might represent a suitable sample if their business line resembles the proposed new project closely enough. In particular, we may want to use betas from industry front-runners, and rely less on betas of any firms that the company really doesn’t want to emulate. EXAMPLE 11- 6 Calculation of Project WACC LG11-5 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that Evita’s Subs, a local shipyard, is considering opening up a chain of sandwich shops. Evita’s capital structure currently consists of 2 million outstanding shares of common stock, selling for $83 per share, and a $50 million bond issue, selling at 103 percent of par. Evita’s stock has a beta of 0.72, the expected market risk premium is 7 percent, and the current risk-free rate is 4.5 percent. The bonds pay a 9 percent annual coupon and mature in 20 years. The current operations of the firm produce EBIT of $100 million per year, and the new sandwich operations would add only an expected $12 million per year to that. Also, suppose that Evita’s management has done some research on the sandwich shop industry, and discovered that such firms have an average beta of 1.23. If the new project will be funded with 50 percent debt and 50 percent equity, what should be the WACC for this new project? SOLUTION: First, note that Evita’s currently doesn’t have any outstanding preferred stock and doesn’t plan on using any to finance the new project, so that makes our job a little simpler. Also note that, though we are given enough information to calculate the firm’s current capital structure weights and component cost of equity, we won’t need those figures, as this new project’s capital structure differs from the firm’s existing structure. We already know the capital structure weights for the new project (50 percent debt and 50 percent equity), so we just need to calculate the appropriate component costs. For equity, the appropriate cost will be based upon the average risk of sandwich shops: http://mhhe.com/CornettM4e page 326 Since the new sandwich project appears to be small relative to the firm’s existing line of business, we will assume that the new bondholders will expect to be repaid out of cash flows to the existing shipyards, and the YTM on the new bonds issued to finance this project will be the same as the YTM on the existing bonds: which gives us an iD of 8.68 percent. Finally, the current EBIT already puts the firm in the top 35 percent tax bracket, so the additional EBIT generated by the project will also be taxed at this same marginal 35 percent tax rate. Therefore, the WACC of the new project will be Similar to Problems 11-16 to 11-21, Self-Test Problem 2 What shall we do if we cannot find any pure-play proxies? Well, in that case, we may want to use firms that, while not solely in the same business as the proposed project’s venture, have a sizable proportion of revenues from that line. We may then be able to “back out” the impact of their other lines of business from their firm’s beta to leave us with a good enough estimate of what the new project’s beta might be. Be sure to use weights based on the project’s sources of capital, and not necessarily the firm’s capital structure. If the new project is going to use more or less debt than the firm’s existing projects do, then the risk- and reward- sharing are going to vary across the different types of capital (as discussed in Chapter 16), and we will want to recognize this in our WACC computation. Finally, we need to consider the appropriate corporate tax rate to use in calculating the WACC for a project. That marginal corporate tax rate will be the average marginal tax rate to which the project’s cash flows will be subject. Assume a firm with $400,000 of EBIT from current operations is considering a new project that will increase EBIT by $200,000. Since this $200,000 increase will keep the firm’s marginal tax in the fifth bracket of Table 11.1, the appropriate tax rate to compute the project’s WACC will simply be 34 percent. To summarize, the component costs and weights to compute a project-specific WACC should be as shown in equation 11-7, with the source of each part indicated by the appropriate subscript: (11-7) page 327 ▼ time out! 11-3 For computing a project WACC, why do we take some component costs from the firm but compute others that are specific for the project being considered? 11-4 It is usually much easier to find proxy firms that are engaged in multiple lines of business than it is to find pure-play proxies. Explain how such firms can be used to estimate the beta for a new project. 11.3 • DIVISIONAL WACC LG11-6 Do firms calculate risk-appropriate WACC for every new project they consider? While this would be ideal, pragmatically it just is not always feasible. In large corporations, managers evaluate dozens or even hundreds of proposed new projects each year. The costs in terms of time and effort of estimating project-specific WACCs individually for each project are simply prohibitive. Instead, large firms often take a middle-of-the-road approach that can achieve many of the results of using project-specific WACC calculations with much less time and resources. The key to this approach is to calculate divisional WACCs for each product line of the company based on that line’s, but not each individual product’s, risk profile. divisional WACC An estimated WACC computed using some sort of proxy for the average equity risk of the projects in a particular division. Pros and Cons of a Divisional WACC As with most choices in life as well as finance, there are pros and cons to using the divisional WACC approach. Let’s first consider the disadvantage of using a firm’s WACC to evaluate new, risk-heterogeneous projects. To make things simple, let’s assume that we are looking at a firm that uses only equity finance, so that WACC is simply equal to iE, and let’s further assume that all the proposed new projects are in the same product line as each other and as the firm’s existing projects, so that the divisional WACC would be equal to the firm’s existing WACC. Take a look at Figure 11.1. Similar to our discussion of the security market line in Chapter 10, required rates of return for projects with varying degrees of risk would lie along the sloped line shown in the figure. We could then evaluate projects with various degrees of risk based on the relationship between their expected rate of return and the required rate of return for that risk level. Turning to Figure 11.2, you can see that using risk-appropriate WACCs, projects A and B would be accepted, since their expected rates of return would be higher than their respective required rates of return. Projects C and D would be rejected because our simple scheme shows that these projects are not expected to return enough to cover market-required returns, given the projects’ riskiness. FIGURE 11.1 Risk-Appropriate WACCs ▼ ▼ In an all-equity firm, WACC is theoretically equal to iE for each proposed project, which will increase as the risk (i.e., β ) of the project increases. FIGURE 11.2 Sample Projects versus Risk-Sensitive WACC Projects A and B have expected returns greater than their risk-appropriate WACCs. Projects C and D have expected returns less than their risk-appropriate WACCs. However, using a firmwide WACC would result in a comparison of the project’s expected rates of return to a single, flat, firmwide cost of capital as Figure 11.3 shows. Using a simple firmwide WACC to evaluate new projects would give an unfair advantage to projects that present more risk than the firm’s average beta. Using a firmwide WACC would also work against projects that involved less risk than the firm’s average beta. Looking at the same sample projects as before, we see that Project A would now be rejected, while Project C would be accepted. FIGURE 11.3 Sample Project versus Firmwide WACC ▼ page 328 ▼ If we were to mistakenly compare projects bearing different risks to this single firmwide WACC, we would conclude that projects A and D have expected rates of return less than the firmwide WACC and Projects B and C have expected returns greater than the firmwide WACC. Using a firmwide WACC in this way, as an inappropriate benchmark for projects of differing risk from the firm’s current operations, will result in quite a few incorrect decisions. In fact, the use of a firmwide WACC to evaluate any projects with risk-return coordinates lying in the two shaded triangles shown in Figure 11.4 will result in an incorrect accept/reject decision. FIGURE 11.4 Incorrect Decisions Caused by Inappropriate Use of Firmwide WACC The gold-shaded triangle on the lower left contains projects such as Project A, which is incorrectly rejected by a firm. It has risk less than the average risk of the firm. Its expected rate of return is greater than its correctly calculated risk-appropriate WACC but less than an inappropriately calculated firmwide WACC. The pink-shaded triangle on the upper right contains projects such as Project C, which is incorrectly accepted by a firm. It has risk greater than the average risk of the firm. Its expected rate of return is less than a correctly calculated risk-appropriate WACC but greater than an inappropriately calculated firmwide WACC. Computing a few“risk aware” divisional WACCs instead of just one“risk insensitive” firmwide WACC can greatly reduce the number of projects that get incorrectly accepted or rejected this way. To do so, we divide the firm’s existing projects into divisions, where the different divisions proxy for systematically different average project risk levels. Calculating WACCs for each division separately, as Figure 11.5 shows, greatly reduces the problem of basing decisions on inaccurate results from using firmwide WACC for all projects. FIGURE 11.5 Divisional WACCs ▼ ▼ Instead of calculating a single firmwide WACC based on the average risk of all projects in the firm, assume that the firm calculates division- specific WACCs based on the average risk of the projects in each respective division. Using divisional WACCs like this will not eliminate problems of incorrect acceptance and incorrect rejection, but it will greatly reduce their frequency. Instead of making errors corresponding to the two large triangular areas indicated in Figure 11.4, we will instead have six smaller areas of error shown in Figure 11.6. More acceptance/rejection regions will result in fewer errors. FIGURE 11.6 Divisional WACC Errors Total incorrect acceptances/rejections turn out to be less when divisional WACCs are used. For example, let’s consider our four sample projects from before. Suppose that, instead of assigning the proposed new projects to the same firmwide division we had previously assumed, the firm divides its operations into “low- risk,” “mid-risk,” and “high-risk” product lines and decides that, based on their associated products and risk profiles, Project A should be assigned to the “low-risk” division, Project D to the “mid-risk” division, and Projects B and C to the “high-risk” division. If we were to now evaluate them using divisional WACCs as shown in Figure 11.7, we would correctly accept both projects A and B and correctly reject projects C and D. FIGURE 11.7 Example Decisions Using Divisional WACCs page 329 Projects A and B here are correctly accepted, while projects C and D are correctly rejected. Subjective versus Objective Approaches LG11-7 We can form divisional WACCs subjectively by simply considering the project’s risk relative to the firm’s existing lines of business and then, if the project is riskier (safer) than the firm average, adjust the firm WACC upward (downward) to account for our subjective opinion of project riskiness. The biggest disadvantage to this approach is that the adjustments are pretty much picked out of thin air and created just for the project at hand. For example, consider the sample subjective divisional WACCs in Table 11.2. Both the project assignments to the divisions and then the WACC adjustments for the very low risk, low risk, high risk, and very high risk are fairly arbitrary. ▼ TABLE 11.2 Subjective Divisional WACCs Risk Level Discount Rate Very low risk Firm WACC − 5% Low risk Firm WACC − 2% Same risk as firm Firm WACC High risk Firm WACC + 3% Very high risk Firm WACC + 7% EXAMPLE 11- 7 Divisional Costs of Capital LG11- 7 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Assume that BF, Inc., an all-equity firm, has a firmwide WACC of 10 percent, and that the firm is broken into three divisions: Textiles, Accessories, and Miscellaneous. The average Textiles project has a beta of 0.7; the average Accessories project has a beta of 1.3; and the average Miscellaneous project has a beta of 1.1. The firm is currently considering the projects shown in the table below. The current approach is to use the firm’s WACC to evaluate all projects, but management sees the wisdom in adopting a subjective divisional cost of capital approach. Firm management is thus considering a divisional cost of capital scheme in which they will use the firm’s WACC for Miscellaneous projects, the firm’s WACC minus 1 http://mhhe.com/CornettM4e percent for Textiles projects, and the firm’s WACC plus 3 percent for Accessories projects. The current expected return to the market is 12 percent, and the current risk-free rate is 5.75 percent. For this group of projects, how much better would their accept/reject decisions be if they used this approach rather than if they continued to use the firm’s WACC to evaluate all projects? Would switching to an objective divisional cost of capital approach, where the WACC for each division is based on that division’s average beta, improve their accept/reject criteria any further? Project Division Expected iE Beta A βAccessories 17.00% 1.3 B βAccessories 15.00  1.2 C βMiscellaneous 13.00  1.3 D βMiscellaneous 11.00  0.7 E βTextiles 9.00  0.8 F βTextiles 7.00  0.5 SOLUTION: Determine the required rates of return for each project assuming that the firm uses the firmwide WACC and adds the subjective adjustments to construct divisional WACCs. The objective computation of divisional WACCs using each division’s average beta and the iE computed using each project’s specific beta is indicated in the table on the next page. In each case, project acceptances appear in blue print, and project rejections appear in red print. Using the “Specific iE” yields the“correct” accept/reject decision; that is, these accept/reject decisions would be generated exactly the same if the firm had the time and resources to compute the iE on a project-by- project basis. In this particular situation, using the firm WACC as a benchmark for all the projects would result in projects E and F being rejected, since they both will return expected rates less than the firm’s 10 percent required rate of return. By comparison to the results using the Specific iE, both of these rejections are appropriate. We would prefer that the accept/reject criteria took account of risk; that is, both page 330 projects would be rejected because their expected returns (9 percent and 7 percent, respectively) are less than the required returns (10.75 and 8.88 percent, respectively) based on their specific levels of project risk rather than assuming that both projects carry the same risk as the firm’s overall risk. However, using the firm’s WACC incorrectly accepts project C. Using the subjectively adjusted approach to calculating iE results in required rates of return of 13 percent for Accessories projects, 10 percent for Miscellaneous projects, and 9 percent for Textiles projects. The associated accept/reject decisions actually incorrectly accepts projects C and E, making the subjectively adjusted WACC approach worse (in this specific example) than simply using the firmwide WACC. Finally, using the objective approach to constructing divisional costs of capital, along with the three divisions’ average betas given above, results in required rates of return for the three divisions of As these solutions show, using these divisional costs of capital figures as required rates of return for each project results in correct rejections of projects E and F, but also results in an incorrect rejection of project D and an incorrect acceptance of project C relative to computing iE on a project-by-project basis. Overall, using either the objective or subjective approaches to calculating divisional costs of capital will not be as precise as using project-specific WACCs: We will wind up incorrectly accepting and/or rejecting some projects. Making incorrect decisions on some of our project choices may be worth it if the projects in question aren’t large enough for project-specific calculations to be cost-effective. Similar to Problems 11-25 to 11-28 An objective approach would be to compute the average beta per division, use these figures in the CAPM formula to calculate iE for each division, and then, in turn, use divisional estimates of iE to construct divisional WACCs. Though the objective approach would usually be more precise, resulting in fewer incorrect accept/reject decisions, the subjective approach is more frequently used because it is easier to implement. time out! 11-5 Divisions of a corporation are not usually formed based explicitly on differences in risk between the projects in different divisions. Rather, they are normally formed along product-type or geographic differences. Explain how this division scheme may still result in divisions that do differ among themselves by average risk. Also explain why calculating divisional WACCs in such a situation will still improve decision making over simply using a firmwide WACC for project acceptance or rejection. page 331 11-6 Explain why, in Example 11-7, using objectively computed divisional WACCs still resulted in an incorrect accept/reject decision for project D. 11.4 • FLOTATION COSTS LG11-8 We know that firms use varied sources of funding. Until now, our calculations have been assuming that we were using retained earnings to fund projects. What if a firm funds a project by issuing externally generated new capital— additional stock, bonds, and so on? Then the firm has to pay the costs of printing the new stock or bond certificates, commissions to the underwriters helping the firm to sell the stocks and bonds, government registration fees, and other associated costs. So to figure project WACCs, we must integrate these flotation costs into our component costs as well. flotation costs Fees paid by firms to investment banks for issuing new securities. We can approach the commission costs in two basic ways. We can either increase the project’s WACC to incorporate the flotation costs’ impact as a percentage of WACC, or we can leave the WACC alone and adjust the project’s initial investment upward to reflect the “true” cost of the project. Both approaches have advantages and disadvantages. The first approach tends to understate the component cost of new equity, and the latter approach violates the separation principle of capital budgeting, which states that the calculations of cash flows should remain independent of financing. We will discuss the separation principle and the second approach in the next chapter. separation principle Theory maintaining that the sources and uses of capital should be decided upon independently. Adjusting the WACC The first approach to adjusting for flotation costs is to adjust the issue price of new securities by subtracting flotation cost, F, to reflect the net security price. Then use this net price to calculate the component cost of capital. For equity, this approach is most commonly applied to the constant-growth model: (11-8) If we instead want to apply this approach to the cost of equity obtained from the CAPM formula, we would adjust it upward by an equivalent amount. EXAMPLE 11- 8 Flotation-Adjusted Cost of Equity LG11-8 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that, as in Example 11-1, ADK Industries’ common shares are selling for $32.75 per share, and the company expects to set its next annual dividend at $1.54 per share. All future dividends are expected to grow by 6 percent per year indefinitely. In addition, let us suppose that ADK faces a flotation cost of 20 percent on new equity issues. Calculate the flotation-adjusted cost of equity. SOLUTION: Twenty percent of $32.75 will be $6.55, so the flotation-adjusted cost of equity will be http://mhhe.com/CornettM4e page 332 Notice that the result is 1.18 percent above the non-flotation-adjusted cost of equity, 10.70 percent, computed using the constant-growth model in Example 11-1. If we instead wanted to use the CAPM estimate, we would take the non-flotation-adjusted CAPM estimate from the same example, 10.80 percent, and add the same differential of 1.18 percent to it to get the flotation-adjusted value: The adjustments for the component costs of preferred stock and debt will be similar: (11-9) (11-10) Similar to Problems 11-23, 11-24 time out! 11-7 Why should we expect the flotation costs for debt to be significantly lower than those for equity? 11-8 Explain how we should go about computing the WACC for a project that uses both retained earnings and a new equity issue. Get Online page 333 ©JGI/Jamie Grill/Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. How would you handle calculating the cost of capital if a firm were planning to issue two different classes of common stock? (LG11-1) 2. Expressing WACC in terms of iE, iP, and iD, what is the theoretical minimum for the WACC? (LG11-2) 3. Under what situations would you want to use the CAPM approach for estimating the component cost of equity? The constant-growth model? (LG11-3) 4. Could you calculate the component cost of equity for a stock with nonconstant expected growth rates in dividends if you didn’t have the information necessary to compute the component cost using the CAPM? Why or why not? (LG11-3) 5. Why do we use market-based weights instead of book-value-based weights when computing the WACC? (LG11-4) 6. Suppose your firm wanted to expand into a new line of business quickly, and that management anticipated that the new line of business would constitute over 80 percent of your firm’s operations within three years. If the expansion was going to be financed partially with debt, would it still make sense to use the firm’s existing cost of debt, or should you compute a new rate of return for debt based on the new line of business? (LG11-5) 7. Explain why the divisional cost of capital approach may cause problems if new projects are assigned to the wrong division. (LG11-6) 8. When will the subjective approach to forming divisional WACCs be better than using the firmwide WACC to evaluate all projects? (LG11-7) page 334 9. Suppose a new project was going to be financed partially with retained earnings. What flotation costs should you use for retained earnings? (LG11-8) Problems BASIC PROBLEMS 11-1 Cost of Equity Diddy Corp. stock has a beta of 1.2, the current risk-free rate is 5 percent, and the expected return on the market is 13.5 percent. What is Diddy’s cost of equity? (LG11-3) 11-2 Cost of Equity JaiLai Cos. stock has a beta of 0.9, the current risk-free rate is 6.2 percent, and the expected return on the market is 12 percent. What is JaiLai’s cost of equity? (LG11-3) 11-3 Cost of Debt Oberon, Inc., has a $20 million (face value) 10-year bond issue selling for 97 percent of par that pays an annual coupon of 8.25 percent. What would be Oberon’s before-tax component cost of debt? (LG11-3) 11-4 Cost of Debt KatyDid Clothes has a $150 million (face value) 30-year bond issue selling for 104 percent of par that carries a coupon rate of 11 percent, paid semiannually. What would be Katydid’s before-tax component cost of debt? (LG11-3) 11-5 Tax Rate Suppose that LilyMac Photography expects EBIT to be approximately $200,000 per year for the foreseeable future, and that it has 1,000 10-year, 9 percent annual coupon bonds outstanding. What would the appropriate tax rate be for use in the calculation of the debt component of LilyMac’s WACC? (LG11-3) 11-6 Tax Rate PDQ, Inc., expects EBIT to be approximately $11 million per year for the foreseeable future, and that it has 25,000 20-year, 8 percent annual coupon bonds outstanding. What would the appropriate tax rate be for use in the calculation of the debt component of PDQ’s WACC? (LG11-3) 11-7 Cost of Preferred Stock ILK has preferred stock selling for 97 percent of par that pays an 8 percent annual coupon. What would be ILK’s component cost of preferred stock? (LG11-3) 11-8 Cost of Preferred Stock Marme, Inc., has preferred stock selling for 96 percent of par that pays an 11 percent annual coupon. What would be Marme’s component cost of preferred stock? (LG11-3) 11-9 Weight of Equity FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what would be the weight used for equity in the computation of FarCry’s WACC? (LG11-4) 11-10 Weight of Equity OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5,000 bonds. If the common shares are selling for $17 per share, the preferred shares are selling for $26 per share, and the bonds are selling for 108 percent of par, what would be the weight used for equity in the computation of OMG’s WACC? (LG11-4) 11-11 Weight of Debt FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what weight should you use for debt in the computation of FarCry’s WACC? (LG11-4) 11-12 Weight of Debt OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $26 per share, and the bonds are selling for 108 percent of par, what weight should you use for debt in the computation of OMG’s WACC? (LG11-4) 11-13 Weight of Preferred Stock FarCry Industries, a maker of telecommunications equipment, has 2 million shares of common stock outstanding, 1 million shares of preferred stock outstanding, and 10,000 bonds. If the common shares sell for $27 per share, the preferred shares sell for $14.50 per share, and the bonds sell for 98 percent of par, what weight should you use for preferred stock in the computation of FarCry’s WACC? (LG11-4) 11-14 Weight of Preferred Stock OMG Inc. has 4 million shares of common stock outstanding, 3 million shares of preferred stock outstanding, and 5,000 bonds. If the common shares sell for $17 per share, page 335 the preferred shares sell for $16 per share, and the bonds sell for 108 percent of par, what weight should you use for preferred stock in the computation of OMG’s WACC? (LG11-4) INTERMEDIATE PROBLEMS 11-15 WACC Suppose that TapDance, Inc.’s, capital structure features 65 percent equity, 35 percent debt, and that its before-tax cost of debt is 8 percent, while its cost of equity is 13 percent. If the appropriate weighted average tax rate is 34 percent, what will be TapDance’s WACC? (LG11-2) 11-16 WACC Suppose that JB Cos. has a capital structure of 78 percent equity, 22 percent debt, and that its before-tax cost of debt is 11 percent while its cost of equity is 15 percent. If the appropriate weighted- average tax rate is 25 percent, what will be JB’s WACC? (LG11-2) 11-17 WACC Suppose that B2B, Inc., has a capital structure of 37 percent equity, 17 percent preferred stock, and 46 percent debt. If the before-tax component costs of equity, preferred stock, and debt are 14.5 percent, 11 percent, and 9.5 percent, respectively, what is B2B’s WACC if the firm faces an average tax rate of 30 percent? (LG11-2) 11-18 WACC Suppose that MNINK Industries’ capital structure features 63 percent equity, 7 percent preferred stock, and 30 percent debt. If the before-tax component costs of equity, preferred stock, and debt are 11.60 percent, 9.5 percent, and 9 percent, respectively, what is MNINK’s WACC if the firm faces an average tax rate of 34 percent? (LG11-2) 11-19 WACC TAFKAP Industries has 3 million shares of stock outstanding selling at $17 per share, and an issue of $20 million in 7.5 percent annual coupon bonds with a maturity of 15 years, selling at 106 percent of par. If TAFKAP’s weighted-average tax rate is 34 percent and its cost of equity is 14.5 percent, what is TAFKAP’s WACC? (LG11-3) 11-20 WACC Johnny Cake Ltd. has 10 million shares of stock outstanding selling at $23 per share and an issue of $50 million in 9 percent annual coupon bonds with a maturity of 17 years, selling at 93.5 percent of par. If Johnny Cake’s weighted-average tax rate is 34 percent, its next dividend is expected to be $3 per share, and all future dividends are expected to grow at 6 percent per year, indefinitely, what is its WACC? (LG11-3) 11-21 WACC Weights BetterPie Industries has 3 million shares of common stock outstanding, 2 million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $47 per share, the preferred shares are selling for $24.50 per share, and the bonds are selling for 99 percent of par, what would be the weights used in the calculation of BetterPie’s WACC? (LG11-4) 11-22 WACC Weights WhackAmOle has 2 million shares of common stock outstanding, 1.5 million shares of preferred stock outstanding, and 50,000 bonds. If the common shares are selling for $63 per share, the preferred shares are selling for $52 per share, and the bonds are selling for 103 percent of par, what would be the weights used in the calculation of WhackAmOle’s WACC? (LG11- 4) 11-23 Flotation Cost Suppose that Brown-Murphies’ common shares sell for $19.50 per share, that the firm is expected to set their next annual dividend at $0.57 per share, and that all future dividends are expected to grow by 4 percent per year, indefinitely. If Brown-Murphies faces a flotation cost of 13 percent on new equity issues, what will be the flotation-adjusted cost of equity? (LG11-8) ADVANCED PROBLEMS 11-24 Flotation Cost A firm is considering a project that will generate perpetual after-tax cash flows of $15,000 per year beginning next year. The project has the same risk as the firm’s overall operations and must be financed externally. Equity flotation costs 14 percent and debt issues cost 4 percent on an after-tax basis. The firm’s D/E ratio is 0.8. What is the most the firm can pay for the project and still earn its required return? (LG11-2) 11-25 Firmwide versus Project-Specific WACCs An all-equity firm is considering the projects shown below. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly rejected? (LG11-6) Project Expected Return Beta page 336 page 337 A 8.0% 0.5 B 19.0  1.2 C 13.0  1.4 D 17.0  1.6 11-26 Firmwide versus Project-Specific WACCs An all-equity firm is considering the projects shown below. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly accepted? (LG11-6) Project Expected Return Beta A 8.0% 0.5 B 19.0  1.2 C 13.0  1.4 D 17.0  1.6 11-27 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has four divisions, A through D, with average betas for each division of 0.6, 1.0, 1.3, and 1.6, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk- free rate of 7 percent) is 13 percent and the after-tax yield on the company’s bonds is 8 percent, what will the WACCs be for each division? (LG11-7) 11-28 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has four divisions, A through D, with average betas for each division of 0.9, 1.1, 1.3, and 1.5, respectively. If all current and future projects will be financed with 25 percent debt and 75 percent equity, and if the current cost of equity (based on an average firm beta of 1.2 and a current risk-free rate of 4 percent) is 12 percent and the after-tax yield on the company’s bonds is 9 percent, what will the WACCs be for each division? (LG11-7) Notes CHAPTER 11 1. Think of taking such an average as being intuitively the same as diversifying our “portfolio” of data across the two different estimation techniques, thereby reducing the average amount of estimation error. Taking this average is intuitively the same as diversifying your portfolio of data across two different estimation techniques. These options allow you to reduce your average amount of estimation error. 2. We’ll discuss more about calculating WACC for a project later in the chapter. 3. In reality, new projects are often financed with different proportions of equity, debt, and preferred stock than were used to fund the firm’s existing operations. As we will discuss in Chapter 16, such a change in capital structure will result in a change in financial risk with increased leverage magnifying β. 4. As we will also discuss in Chapter 16, we will be able to take a straight average of the proxy firm’s betas as the estimate of our beta only if the capital structures of all the proxies are identical to each other and to that of our proposed new project. If not, we will need to adjust the proxies’ estimated betas for differences in capital structures before averaging them. Then we will need to readjust the average beta for our project’s capital structure before using the estimate. page 338 page 339 T chapter twelve estimating cash flows on capital budgeting projects ©Stockbyte/Getty Images o evaluate capital budgeting projects, we have to estimate how much cash outflow each project will need and how much cash inflow it will generate, as well as exactly when such outflows and inflows will occur. Estimating these cash flows isn’t difficult, but it is complicated, as there are lots of little details to keep track of. Accordingly, as you look through this chapter’s examples, questions, and problems, you’ll notice that these types of problems involve a lot more information than those you’ve seen elsewhere in the text, such as The particular new product or service’s costs and revenues. The likely impact that the new service or product will have on the firm’s existing products’ costs and revenues. The impact of using existing assets or employees already employed elsewhere in the firm. How to handle charges such as the research and development costs incurred to develop the new product. One of the keys to this chapter will be making sure that we have a systematic approach to handling and arranging details. In the next few sections, we’re going to construct a process which, if we follow it faithfully, will guide us in considering factors such as those listed. LEARNING GOALS page 340 LG12-1 Explain why we use pro forma statements to analyze project cash flows. LG12-2 Identify which cash flows we can incrementally apply to a project and which ones we cannot. LG12-3 Calculate a project’s expected cash flows using the free cash flow approach. LG12-4 Explain how accelerated depreciation affects project cash flows. LG12-5 Calculate free cash flows for replacement equipment. LG12-6 Calculate cash flows associated with cost-cutting proposals. LG12-7 Demonstrate the EAC approach to choosing among alternative cash streams for recurring projects. LG12-8 Adjust initial project investments to account for flotation costs. viewpoints business APPLICATION Suppose that McDonald’s is considering introducing the McTurkey Dinner (MTD). The company anticipates that the MTD will have unit sales, prices, and cost figures as shown in the following table for the next five years, after which the firm will retire the MTD. Introducing the MTD will require $7 million in new assets, which will fall into the MACRS five-year class life. McDonald’s expects the necessary assets to be worth $2 million in market value at the end of the project life. In addition, the company expects that NWC requirements at the beginning of each year will be approximately 13 percent of the projected sales throughout the coming year and fixed costs will be $2 million per year. McDonald’s uses an 11 percent cost of capital for similar projects and is subject to a 35 percent marginal tax rate. What will be this project’s expected cash flows? (See the solution at the end of the book.) McTurkey Dinner Projections Year Estimated Unit Sales Estimated Selling Price per Unit Estimated Variable Cost per Unit 1  400,000 $7.00 $3.35 2 1,000,000  7.21  3.52 3 1,000,000  7.43  3.70 4 1,000,000  7.65  3.89 5  500,000  7.88  4.08 LG12-1 The exact process that we’re going to use is more formally referred to as pro forma analysis, which estimates expected future cash flows of a project using only the necessary parts of the balance sheet and income statements; if a part of either financial statement doesn’t change because of the new project, we’ll ignore it. This approach will allow us to focus on the question, “What will be this project’s impact on the firm’s total cash flows if we go forward?” ■ pro forma analysis Process of estimating expected future cash flows of a project using only the relevant parts of the balance sheet and income statements. 12.1 • SAMPLE PROJECT DESCRIPTION LG12-1 Let’s suppose that we are working for a game development company, First Strike Software (FSS). FSS is considering leasing a new plant in Gatlinburg, Tennessee, which it will use to produce copies of its new console game “FinProf,” a role-playing game where the player battles aliens invading a local college’s finance department. FSS will price this game at $39.99, and the firm estimates sales for each of the next three years as shown in Table 12.1. Given buyers’ rapidly changing tastes in console games, FSS does not expect to be able to sell any more copies after year 3. page 341 ▼ TABLE 12.1 Sample Project Projected Unit Sales Year Unit Sales 1 15,000 2 27,000 3  5,000 Variable costs per game are low ($4.25), and FSS expects fixed costs to total $150,000 per year, including rent. Start-up costs include $75,000 for the purchase of a software-duplicating machine, plus an additional $2,000 in shipping and installation costs. For our first stab at analyzing this project, we will assume that the duplicating machine will be straight-line depreciated to an estimated ending salvage value of $5,000 over the life of the project. However, due to the rapidly declining market for such machines (many of FSS’s competitors are switching to download-only games), we are also estimating that we’ll only be able to sell the machine for $2,000 after we’re done using it. salvage value The estimated amount for tax purposes that a company will receive when it disposes of an asset at the end of the asset’s usable life. personal APPLICATION Achmed contemplates going back to school part time to get an MBA. He anticipates that it would take him four years to get his MBA, and the program would cost $15,000 per year in books and tuition (payable at the beginning of each year). He also thinks that he would need to get a new laptop (which he was going to buy anyway as a portable gaming system) for $2,500 when he starts the program, and he just paid $250 to take the GMAT. After graduation, Achmed anticipates that he will be able to earn approximately $10,000 more per year with the MBA, and he thinks he’ll work for about another 20 years after getting the MBA. What total cash flows should Achmed consider in his decision? (See the solution at the end of the book.) Thinking about an MBA? What returns can you expect from the investment? FinProf is an updated version of an older game sold by FSS, MktProf. FSS intends to keep selling MktProf but anticipates that FinProf will decrease sales of MktProf by 2,000 units per year throughout the life of the new game. MktProf sells for $19.99 and has variable costs of $3.50 per unit. The decrease in MktProf sales will not affect either NWC or fixed assets. Development costs totaled $150,000 throughout the creation of the game, and First Strike estimates its NWC requirements at the beginning of each year will be approximately 10 percent of the projected sales during the coming year. First Strike is in the 34 percent tax bracket and uses a discount rate of 15 percent on projects with risk profiles such as this. The relevant question: Should FSS put FinProf into production or not? 12.2 • GUIDING PRINCIPLES FOR CASH FLOW ESTIMATION LG12-2 When we calculate a project’s expected cash flows, we must ensure that we cover all incremental cash flows; that is, the cash flow changes that we would expect throughout the entire firm, for both this project and for everything else the firm is already doing, because of the new project coming on board. Some incremental cash flow effects are fairly obvious. For example, suppose a firm has to buy a new asset to support a new project but would not be buying the asset if the project were not adopted. Clearly, the cash associated with buying the asset is due to the project, and we should therefore count it when we calculate the cash flows associated with that project. But we can hardly expect all incremental cash flows to be so obvious. Other incremental cash flows, as discussed in the following sections, are more subtle, and we’ll have to watch for them very carefully. incremental cash flows Cash flows directly attributable to the adoption of a new project. page 342 Opportunity Costs As you likely remember from your microeconomics classes, an opportunity cost exists whenever a firm has to choose how to allocate scarce resources. If those resources go into project A, the firm must forgo using them in any other way. Those forgone choices represent lost opportunities, and we have to account for them when calculating cash flows attributable to project A. For example, suppose that FSS already owned the piece of software-duplicating machinery discussed previously. If the machinery was already being fully utilized by another project within the company, then obviously switching it over to the FinProf game would require that other project to find another source of software duplication. Therefore, to be fair, the FinProf project should be charged for the use of the machinery. Even if the machinery was not currently being used in any other projects, it could still possibly have an opportunity cost associated with using it in the FinProf project. If FSS could potentially sell the machinery on the open market for $75,000, the company would have to give up receiving that $75,000 in order to use the piece of machinery for the FinProf game. In the end, it would not really matter whether the firm had to buy the asset from outside sources or not; either way, the project will be tying up $75,000 worth of capital, and it should be charged for doing so. The underlying concept behind charging the project for the opportunity cost of using an asset also applies to expenses other than those associated with capital assets such as machinery: Overall, we should charge any new project for any assets used by that project as well as any wages and benefits paid to employees working on it. Even if the firm was already employing those people prior to starting work on the new project, they are no longer available to work on any existing projects; and if the firm did not have any new projects, it could have laid those employees off, saving their wages and benefits. In the FSS project, wages and benefits to employees would constitute part of the variable costs we were quoted earlier. Just as with the software-duplicating machinery, whether these employees were previously working for FSS on another project would be irrelevant; if FSS is going to use these employees on this project, the project should be charged for them. Sunk Costs If a firm has already paid an expense in the past or is obligated to pay one in the future (i.e., there’s no way out of paying it), regardless of whether a particular project is undertaken, that expense is a sunk cost. A firm should never count sunk costs in project cash flows. Intuitively, if you have to pay the expense regardless of your decision concerning the project, it doesn’t meet the definition of being “incremental.” opportunity cost The dollar cost or forgone opportunity of using an asset already owned by the firm, or a person already employed by the firm, in a new project. sunk cost A cost that has already been incurred and cannot be recovered. For example, we are told that FSS incurred $150,000 in development costs as they developed the game. Development costs would presumably include items such as the salaries of the game’s programmers, market research costs, and so forth. Since we are not told otherwise, we can sensibly assume that this money is gone, and that FSS will never recoup the money, even if it decides not to go ahead with publishing the game. Thus those costs are sunk, and FSS should not even consider them as part of its decision about whether to move forward with putting the FinProf game into production. Substitutionary and Complementary Effects If a new product or service will either reduce or increase sales, costs, or necessary assets for other, already existing products or services, then those changes to the cash flows of the other projects are incremental to the new project and should rightfully be included in the new project’s cash flows. For example, consider how FSS’s FinProf game may affect the existing MktProf game. The gross sales and variable cost figures for the new game might be as shown in Table 12.2. page 343 ▼ TABLE 12.2 Gross Sales and Variable Costs for FinProf Year Sales Variable Costs 1 15,000 × $39.99 = $599,850 15,000 × $4.25 = $63,750 2 27,000 × $39.99 = $1,079,730 27,000 × $4.25 = $114,750 3 5,000 × $39.99 = $199,950 5,000 × $ 4.25 = $21,250 However, FSS also expects the MktProf game to lose yearly sales of 2,000 × $19.99 = $39,980 when the FinProf game starts selling. Partially offsetting this, the decrease in sales of MktProf will also result in a decrease in yearly variable costs for MktProf of 2,000 × $3.50 = $7,000 in savings (i.e., forgone costs) per year. So the net incremental sales and variable cost figures for the project will be as shown in Table 12.3. ▼ TABLE 12.3 Net Incremental and Variable Costs for FinProf Year Sales Variable Costs 1 $599,850 − $39,980 = $559,870 $63,750 − $7,000 = $56,750 2 $1,079,730 − $39,980 = $1,039,750 $114,750 − $7,000 = $107,750 3 $199,950 − $39,980 = $159,970 $21,250 − $7,000 = $14,250 As we see, we have to reduce FinProf’s sales each year by the $39,980 reduction in MktProf sales attributable to the Finprof game existing, but we also get to reduce FinProf’s costs by $7,000 each year due to the cost savings of not having to make so many copies of MktProf. Technically speaking, we are seeing a reduction in both sales and variable costs because FinProf is a partial substitute for MktProf. If the new game had been a complement (i.e., if we had sold more of the MktProf game due to the rollout of FinProf), then both sales and variable costs of the existing product would have increased instead. Stock Dividends and Bond Interest One final, important note concerning incremental project cash flows: We will never count any financing costs, including dividends paid on stock or interest paid on debt, as expenses of the project. The costs of capital are already included as component costs in the weighted-average cost of capital (WACC) that we will be using to discount these cash flows in the next chapter. If we were to include them in the cash flow figures as well, we would be double- counting them. substitute and complement Effects that arise from a new product or service either decreasing or increasing sales, respectively, of the firm’s existing products and services. financing costs Interest paid to debt holders or dividends paid to stockholders. time out! 12-1 Suppose that your manager will be devoting half of her time to a new project, with the other half devoted to currently existing projects. How would you reflect this in your calculation of the incremental cash flows of the project? 12-2 Could a new product have both substitutionary and complementary effects on existing products? 12.3 • TOTAL PROJECT CASH FLOW LG12-3 In Chapter 2, we discussed the concept of free cash flow (FCF), which we defined as (12-1) page 344 In this chapter, we are going to use this variable again as a measure of the total amount of available cash flow from a project. However, we will observe two important differences from how we used it in Chapter 2. First, since we will be considering potential projects rather than a particular firm’s actual, historic activities, the FCF numbers we calculate will be, frankly, guesses—informed guesses, surely, but still guesses. Since we will be “calculating” guesses, we will introduce possible estimation error into our capital budgeting decision statistics, but we will hold off on discussing that until the next chapter. Second, we will now calculate FCF on potential projects individually, rather than across the firm as a whole as we did in Chapter 2. In some ways, calculating FCF on individual projects will make our job much easier, since we don’t have to worry about estimating an entire set of balance sheets for the firm. Instead, we will only have to be concerned with the limited subset of pro forma statements necessary to keep track of the assets, expense categories, and so on, that a new project will affect. Unfortunately, the elements of that limited set will vary from situation to situation, and the hard part will be identifying which parts of the balance sheets are necessary and which are not. Calculating Depreciation Expected depreciation on equipment used during the life of the project will affect both the operating cash flows and the change in gross fixed assets that will occur at the end of the project when we sell or abandon them, so let’s start our organizing there. For First Strike’s proposed FinProf project, the firm will depreciate capital assets such as the software- duplicating machine using the straight-line method to an ending book value of $5,000. To calculate the annual depreciation amount, First Strike will first need to compute the machinery’s depreciable basis. According to the Internal Revenue Service’s (IRS) Publication 946, the depreciable basis for real property is the sum of: Its cost. Amounts paid for items such as sales tax. Freight charges. Installation and testing fees. depreciable basis An asset’s cost plus the amounts you paid for items such as sales tax, freight charges, and installation and testing fees. We aren’t told anything about sales tax on the machinery, so the depreciable basis for the new project’s software- duplicating machine will be the $75,000 purchase price plus the $2,000 shipping and installation cost, for a total depreciable basis of $77,000. Under straight-line depreciation, the annual depreciation for each year will be equal to the depreciable basis minus the projected ending book value, all over the number of years in the life of the asset: (12-2) We’ll discuss later in the chapter why this depreciation assumption is far too simple, and why other, more complicated depreciation methods can be much more advantageous to the company. For now, though, this straight- line depreciation approach will suffice for our initial go at calculating the project’s cash flows. Calculating Operating Cash Flow We defined operating cash flow (OCF) in Chapter 2 as EBIT (1 − Tax rate) + Depreciation. We will still calculate OCF as being mathematically equal to EBIT (1 − Tax rate) + Depreciation. But remember that we will be constructing the FCF components ourselves instead of taking them off an income statement that someone else has already produced. So we will usually find it most helpful to conduct this calculation by using what we will call a “quasi-income statement” that leaves out some components that don’t matter for project cash flows, such as interest deductions. (Note that the process of leaving out any interest deduction is exactly in line with our discussion of not counting interest on debt as an expense of the project, but the resulting financial statement would not make an page 345 accountant happy). The depreciable basis for real property includes freight charges. ©Steve Boyko/Shutterstock Such a statement is shown in Table 12.4 for First Strike’s proposed project. The primary benefit of calculating OCF this way instead of as an algebraic formula is that with this format, we have space to expand subcalculations, such as the impact of FinProf being a partial substitute for the MktProf product. ▼ TABLE 12.4 Calculation of OCF Before we move on, notice that not only is EBIT negative in year 3 of OCF calculations, but we also assume that this negative EBIT, in turn, generates a “negative tax bill” (i.e., a tax credit, when we subtract the negative tax amount of −$9,615 from the negative EBIT). How, and when, can we get away with making this assumption? Well, the rule for handling negative EBIT is that when calculating the cash flows for a single project for a firm, we assume that any loss by this project in a particular period can be applied against assumed before-tax profits made by the rest of the firm in that period. So, while our project is expected to have a loss of $28,280 before taxes during year 3, the assumed ability of the firm to use that loss to shelter $28,280 in before-tax profits elsewhere in the firm means that the incremental after-tax net income for this project during year 3 is expected to be −$28,280 − (−$9,615) = −$18,665. This is still negative, but less negative than the EBIT because of this tax- sheltering effect. What would we do if we expected a negative EBIT during a particular year and this was the only project the firm was undertaking, or if this project was so big that a negative EBIT would overshadow any potential profits elsewhere in the firm? Long story short, we would not get to take the tax credit during that year . . . but we will leave the discussion of just exactly when we would get to take it to a more advanced text. page 346 Calculating Changes in Gross Fixed Assets Gross fixed assets will change in almost every project at both the beginning (when assets are usually purchased) and at the end (when assets are usually sold). First Strike’s proposed project is no exception. Calculating the change in gross fixed assets at the beginning of the project is fairly straightforward—it will simply equal the asset’s depreciable basis. So, for FSS’s project, we will increase gross fixed assets by $77,000 at time zero. At the end of a project, the change in gross fixed assets is a little more complicated, because whenever a firm sells any asset, it has to consider the tax consequences of that sale. The IRS treats any sale of assets for more than depreciated book value as a taxable gain and any sale for less than book value as a taxable loss. In either event, we can calculate the after-tax cash flow (ATCF) from the sale of an asset using the following formula, where TC is the same appropriate corporate tax rate discussed in the previous chapter. (12-3) Since the machinery for FSS’s project will be depreciated down to $5,000 but is expected to sell for only $2,000, the ATCF for that asset’s sale will equal EXAMPLE 12- 1 ATCF for an Asset Sold at a Gain LG12-3 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that a firm facing a marginal tax rate of 25 percent sells an asset for $4,000 when its depreciated book value is $2,000. What will be the ATCF from the sale of this asset? SOLUTION: The ATCF will equal Similar to Problems 12-1, 12-8 Although it may be a little difficult to wrap your brain around the idea of reducing the $5,000 we were “supposed to get” (at least, according to the IRS) from the sale of the machinery at the end of the project by only 66 percent of the shortfall from that amount we actually expect to happen (i.e., $5,000 − $2,000 = $3,000), that’s exactly what we’re doing. “Losing” $3,000 of the $5,000 expected book value when we sell the machinery will let us hide $3,000 in revenues elsewhere from the tax man, so we get credit for shielding $3,000 from our 34 percent tax rate loss (i.e., $3,000 × 34% = $1,020) in addition to estimating that we’ll be able to sell the machinery for $2,000 cash. If this really is making your brain hurt, just realize that, as long as you faithfully and precisely apply the formula for ATCF, it will give you the net cash flow from the sale of the asset. In particular, note that this formula would work equally well on an asset sold at a gain. Calculating Changes in Net Working Capital http://mhhe.com/CornettM4e page 347 We can make several different assumptions concerning the NWC level necessary to support a project. The most straightforward of these would be to simply assume that we add NWC at the beginning of the project and subtract it at the end. This assumption would be valid if the project is expected to have steady sales throughout its life, or if variations in NWC do not affect the project much. FSS’s proposed project, however, features a more typical product life cycle. Its unit sales will follow an approximate bell-shaped curve, starting out low at the beginning, peaking in the middle of the project, and then dropping off again at the end. When sales are timed in this way, FSS needs to give a little more thought to exactly when the firm needs to set aside net working capital to support high sales volumes and when it can reduce NWC as sales drop off. The assumption that First Strike’s NWC at any particular time will be a function of the next year’s sales might seem odd at first glance. But a little thought about how we measure balance sheet numbers (such as NWC) and income statement items (such as sales) will show that, really, this assumption makes a lot of sense. Since income statements (and our quasi-income statement discussed previously) measure what happens during a period, the sales show up on the statement at the end of the year, even though they actually start accumulating at the beginning of the year. The balance sheet “snapshots,” on the other hand, capture how much capital sits in NWC accounts at a particular point in time. So, for example, the sales figures from our quasi-income statement for year 1 that are used in the OCF calculation for year 1 must be supported when they start occurring, which would be at the start of year 1. But remember, timelines are funny things: The start of year 1 is actually year 0, so we have to plan to have the NWC shown on the year 0 balance sheet reflect capital earmarked for NWC that will be supporting year 1 sales. Of course, this same line of reasoning can be generalized for all other time periods, too: Any sales figure that appears in a time N OCF calculation needs NWC support at the beginning of year N, which is actually time N − 1. So NWC at time N − 1 should vary with time N sales. Therefore, the assumption that First Strike’s NWC at any particular time will be a function of the next year’s sales isn’t as crazy as we first thought. Also, note that it is just the changes in the level of NWC, not the levels themselves, that will affect our cash flows. To explain why, we need to throw a little more intuition into the pot here. First, we have to admit that we do not really care about the changes in NWC, either, at least not for their own sake; instead, what we are actually measuring is the investment in capital necessary to make those changes happen. (And that’s why there is a negative sign in front of NWC in our formula for free cash flow: It costs us money to make NWC bigger, and vice versa). First Strike’s NWC at any time will be a function of next year’s sales. ©Brand X Pictures/Getty Images Second, we need to think a little about exactly what we are measuring when we talk about using NWC to support sales. Since NWC equals current assets minus current liabilities, it’s probably easier to think of it as being composed of cash, accounts receivable, and inventory, net of current liabilities. Do these types of assets get used up? Sure, when cash is used to make change, or when someone pays off an account receivable, or when we sell finished goods out of inventory, the respective asset account will go down. But those accounts go down because we are bringing in money, and some of that money can be used to “restock the shelves,” so to speak; that is, when someone buys one of our products out of inventory, we assume that part of the purchase price goes toward replenishing the inventory we just sold, and when someone pays off an account receivable, we assume that allows us to turn around and lend that money to someone else and so forth. The basic point here is that cash, once invested in NWC, pretty much replenishes itself until we manually take it back out. So when we are looking at the levels of NWC throughout the life of a project, it is the changes in those levels that we have to finance, not the levels themselves. Once we put a million dollars into inventory, it sort of stays page 348 page 349 there because of this idea of replenishment, even when we sell some of the inventory. And if we are keeping track of the amount of money that we have to invest in inventory or some other type of NWC account, we will find investment necessary only when we need to grow NWC by adding to that million dollars (or when we decide to take some of it back out). So, we can use the given information for the First Strike project to compute the NWC necessary to support sales throughout the project’s life, and then in turn use NWC levels to compute the necessary changes in NWC, as shown in Table 12.5. Notice that the NWC level at each time is simply 10 percent of the following year’s sales figures from Table 12.4. ▼ TABLE 12.5 Change in NWC This method for computing changes in NWC levels has several appealing features: The changes in NWC at the beginning of a project will always equal the level at time 0, as NWC will be going from a presumed zero level before the project starts up to that new, non-zero level. Allowing NWC to vary as a percentage of coming sales like this allows FSS to add NWC during periods when it expects sales to increase (e.g., years 0 and 1 in this example) and to decrease NWC when it expects sales to fall off (e.g., years 2 and 3 in this example). NWC levels fall off the last two years of this project precisely because FSS expects sales to fall off and is adjusting NWC to compensate. Finally, one especially nice feature of this approach is that it will always automatically bring NWC back down to a zero level when the project ends. Since sales in the year after the project ends are always zero, 10 percent of zero will also be zero. This corresponds to what we would expect to see in the real world: when a project ends, the firm sells off inventory, collects from customers, pays off accounts receivable, and so forth. Bringing It All Together Using the numbers that we calculated for OCF, change in gross fixed assets, and change in NWC, First Strike’s expected total cash flows from the new project would be as shown in Table 12.6. ▼ TABLE 12.6 Total Cash Flows Note, in particular, that correct use of the after-tax cash flow from selling the machinery at the end of the project requires that we change the cash flows’ sign to negative when we enter it for year 3. Why? Because the ATCF formula shown in equation 12-3 does a little too much work for us. It computes cash flow effects of selling the asset, while the formula we are using for FCF wants us to enter the change in fixed assets. Or, to put it another way, cash flow at the end of the project should go up because fixed assets decrease. We subtract that decrease in our FCF = OCF − (ΔFA + ΔNWC) calculation, which has the effect of “subtracting a minus.” Eventually, then, we increase the final year’s FCF above that which we would have generated by just combining OCF with the cash freed up from decreasing NWC. time out! 12-3 Explain why an increase in NWC is treated as a cash outflow rather than as an inflow. 12-4 Will OCF typically be larger or smaller than net income? Why? page 350 12.4 • ACCELERATED DEPRECIATION AND THE HALF- YEAR CONVENTION LG12-4 Our FCF calculation in the previous section was complete, but we used a rather simplistic assumption concerning depreciation in the calculations. In reality, the IRS requires that depreciation must be calculated using the half-year convention, which basically says that all property placed in service during a given period is assumed to be placed in service at the midpoint of that period.1 By implication, three years of asset life, such as the machinery in the First Strike example, will extend over four calendar years of the firm, starting a half-year before the project starts and ending a half-year after it ends. Just to make things a little more confusing, the IRS names an asset’s class life in its depreciation tables according to how long the asset will live, not according to how many of the firm’s calendar years the depreciation will stretch across. For example, Table 12.7 shows an excerpt from the IRS depreciation table for straight-line depreciation using the half-year convention. ▼ TABLE 12.7 Excerpt of Straight-Line Depreciation Table with Half-Year Convention class life The number of years of assumed usage for an asset to be used in the calculation of depreciation. Note that assets falling in, for example, the three-year class life (denoted by the column headings along the top) get depreciation taken during the first four calendar years after purchase, with the percentage figures in the relevant column denoting how much of the asset’s depreciable basis may be deducted in each respective firm calendar year. For example, an asset with a depreciable basis of $100,000 falling into the three-year class life would be depreciated $100,000 × 0.1667 = $16,670 during the first calendar year the firm owned it, $33,330 during the second and third years of ownership, and another $16,670 during the fourth year of ownership. The IRS provides guidance on which categories various assets fall into, so it’s usually pretty easy to figure out which column to use. For this text, we will assume that we are always told which column to use. Note that the IRS’s interpretation of the half-year convention is not as direct as simply taking one-half of the first year’s depreciation and moving it to the end of the asset’s life. For example, the column for 3.5-year depreciation shows that such an asset would have 14.29 percent of its value depreciated during the first year and 28.57 percent during each of the second, third, and fourth years. So, rather than using a formula to compute the depreciation percentage, it’s preferable to look the percentages up from the appropriate IRS table. A copy of the entire table for straight-line depreciation using the half-year convention appears as Appendix 12A at the end of this chapter. MACRS Depreciation Calculation Though the IRS allows firms to use the straight-line method with the half-year convention to depreciate assets, most businesses probably benefit from using some form of accelerated depreciation. Accelerated depreciation allows firms to expense more of an asset’s cost earlier in the asset’s life. An example of this is the double-declining-balance (DDB or 200 percent declining balance) depreciation method, under which the depreciation rate is double that used in the straight-line method. To make all of this completely confusing, the IRS also uses the half-year convention with DDB depreciation and tends to switch back and forth between DDB and SL depreciation methods in the same table, depending upon which method is more advantageous to the taxpayer. For example, MACRS (modified accelerated cost recovery system) depreciation tables use DDB for 3- to 10-year property, the 150 percent declining balance method for 15- to 20-year property, and straight-line depreciation whenever it becomes more advantageous to the taxpayer. But for real estate, MACRS uses straight-line depreciation and the mid-month convention for all asset classes. This all can be more than enough to make you want to cry, but the good news is that the applicable depreciation percentages are provided for you in the MACRS depreciation tables compiled by the IRS. We have provided this for you in Appendix 12A. An excerpt of the DDB section of the MACRS table appears as Table 12.8. MACRS is generally the depreciation method of choice for firms since it provides the most advantageous method of depreciation. ▼ TABLE 12.8 DDB Depreciation with Half-Year Convention Normal Recovery Period Year 3 5 7 10 1 33.33% 20.00% 14.29% 10.00% 2 44.45  32.00  24.49  18.00  3 14.81  19.20  17.49  14.40  4 7.41  11.52  12.49  11.52  5 0.00  11.52  8.93  9.22  6 0.00  5.76  8.92  7.37  7 0.00  0.00  8.93  6.55  8 0.00  0.00  4.46  6.55  9 0.00  0.00  0.00  6.56  10 0.00  0.00  0.00  6.55  11 0.00  0.00  0.00  3.28  12 0.00  0.00  0.00  0.00  13 0.00  0.00  0.00  0.00  14 0.00  0.00  0.00  0.00  15 0.00  0.00  0.00  0.00  16 0.00  0.00  0.00  0.00  17 0.00  0.00  0.00  0.00  18 0.00  0.00  0.00  0.00  19 0.00  0.00  0.00  0.00  20 0.00  0.00  0.00  0.00  21 0.00  0.00  0.00  0.00  page 351 Section 179 Deductions In certain circumstances, we can accelerate asset expensing even further by expensing assets immediately in the year of purchase rather than having to depreciate them over time. The IRS allows most businesses to immediately expense up to $500,000 of property placed in service each year under what is referred to as a Section 179 deduction. The Section179 deduction is obviously targeted at helping small businesses, so it places an annual limit on the amount of deductible property. If the cost of qualifying Section 179 property you put into service in a single tax year exceeds the current statutory base of $2 million (as of the 2015 tax year), then you cannot take the full deduction. The maximum deduction is also limited to the annual taxable income from the active conduct of the business. Section 179 deduction A deduction targeted at small businesses that allows them to immediately expense asset purchases up to a certain limit rather than depreciating them over the assets’ useful lives. For example, consider a manufacturer who completely re-equips his facility in 2015, at a cost of $2.1 million. This is $100,000 more than allowed, so he must reduce his eligible deductible limit to $400,000, which is the current $500,000 expensing limit minus the $100,000 excess over the current statutory base limit. To take this deduction, the firm must have at least $400,000 of taxable income for the year. A company that spent $2.5 million (= $2 million + $500,000) or more on qualifying Section 179 property would not be able to take the deduction at all, regardless of its taxable income. Property that does not qualify for a Section 179 deduction can be depreciated using MACRS. Property eligible for a Section 179 deduction includes Machinery and equipment. Furniture and fixtures. Most storage facilities. Single-purpose agricultural or horticultural structures. Off-the-shelf computer software. Certain qualified real property (limited to $250,000 of the $500,000 expensing limit). Ineligible property includes Buildings and their structural components (unless specifically qualified). Income-producing property (investment or rental property). Property held by an estate or trust. Property acquired by gift or inheritance. Property used in a passive activity. Property purchased from related parties. Property used outside of the United States. Like many IRS deductions, there are several terms and conditions that apply, so be sure to get all the facts if you intend to use this method of depreciation. page 352 Machinery is eligible for a Section 179 deduction. ©Brand X Pictures/Getty Images Impact of Accelerated Depreciation So, let’s return to our FSS example and FinProf. Remember that our initial, simplistic view of depreciation had us taking $24,000 per year in depreciation for each of the three years of the project’s life. If the software reproduction machinery fell into the three-year life class, we could instead have taken the following depreciation amounts by using either the straight-line or DDB approaches, as shown in Table 12.9. ▼ TABLE 12.9 FSS’s Yearly Depreciation and Ending Book Values under Alternative Depreciation Year 1 Year 2 Year 3 Ending BV Straight- line $77,000 − 16.67% = $12,835.90 $77,000 − 33.33% = $25,664.10 $77,000 − 33.33% = $25,664.10 $12,835.90 DDB $77,000 − 33.33% = $25,664.10 $77,000 − 44.45% = $34,226.50 $77,000 − 14.81% = $11,403.70 $5,705.70 If First Strike could take advantage of the Section 179 deduction that would probably be the most advantageous way to deduct the cost of the new machinery—it could deduct the entire $77,000 in year 1. If FSS could not use a Section 179 deduction, the DDB depreciation available under MACRS would result in the next quickest recovery of the tax breaks associated with the machinery purchase. And why is it better to depreciate the cost of an asset as quickly as possible? Well, taking the depreciation over a longer time span doesn’t get you more dollars of depreciation tax shield; it just stretches the same total amount of dollars over that longer time span. So, think about it in the context of time value of money: The present value of $X of total income tax shield will be highest when we get the $X as soon as possible. time out! 12-5 Explain why, under MACRS, “five-year” depreciation is actually spread over six years, six-year depreciation spreads into seven years, and so forth. 12-6 If the IRS wanted to encourage businesses to invest in certain types of assets, would it put them into shorter or longer MACRS life-class categories? 12.5 • “SPECIAL” CASES AREN’T REALLY THAT SPECIAL LG12-5 As long as we are consistent in using incremental FCF to calculate total project cash flows, we can handle many project types that are habitually viewed as “special” cases requiring extraordinary treatment with some relatively simple revisions to the methods we used for valuing First Strike’s proposed new project. EXAMPLE 12- 2 Replacement Problem LG12-5 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that Just-in-Time Donuts is considering replacing one of its existing ovens. The original oven cost $100,000 when purchased five years ago and has been depreciated by $9,000 per year since then. Just-in-Time thinks that it can sell the old machine for $65,000 if it sells today, and for $10,000 by waiting another five years until the oven’s anticipated life is over. Just-in-Time is considering replacing this oven with a new one, which costs $150,000, partly because the new oven will save $50,000 in costs per year relative to the old oven. The new oven will be subject to three-year class life DDB depreciation under MACRS, with an anticipated useful life of five years. At the end of the five years, Just-in-Time will abandon the oven as worthless. If Just-in- Time faces a marginal tax rate of 35 percent, what will be the total project cash flows if it replaces the oven? SOLUTION: If Just-in-Time sells the old oven today for $65,000 when it has a remaining book value of $55,000 ($100,000 purchase price − 5 years of $9,000 per year depreciation), then the ATCF from its sale will equal In return for selling the old oven today, however, Just-in-Time will have to forgo both the yearly depreciation that the company would have received for it over the next five years and the $10,000 that it could get for selling it at the end of the five years. We must reflect both of these factors in our calculation of incremental FCFs so that we are reckoning http://mhhe.com/CornettM4e page 353 the true costs of the project. In addition, switching from the old oven to the new one would apparently alter neither sales nor NWC requirements across the five-year life of the new oven (see table on the previous page). We usually think that a positive value for ΔFA is associated with the purchase of FA. But note that in this circumstance, the $10,000 for the forgone sale of the old oven at time 5 is not an investment in fixed assets, but rather the opportunity cost of not getting to sell the old oven at that time. Similar to Problem 12-13 EXAMPLE 12- 3 Cost-Cutting Problem LG12-6 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Your company is considering a new computer system that will initially cost $1 million. It will save your firm $300,000 a year in inventory and receivables management costs. The system is expected to last for five years and will be depreciated using three-year MACRS. The firm expects that the system will have a salvage value of $50,000 at the end of year 5. This purchase does not affect net working capital; the marginal tax rate is 34 percent, and the required return is 8 percent. What will be the total project cash flows if this cost-cutting proposal is implemented? SOLUTION: Since the new computer falls into the three-year MACRS category, it will be fully depreciated when the project ends five years from now. As a result, the ATCF from the sale of the computer will be http://mhhe.com/CornettM4e page 354And the FCFs for the cost-cutting proposal will be equal to Similar to Problçem 12- 9 time out! 12-7 Explain why, in Example 12-2, the investment in operating capital in the last year of the project was positive instead of negative. 12-8 Would it ever be possible to have a project that generated net positive cash flows across all years of a project’s life just by buying and depreciating assets? 12.6 • CHOOSING BETWEEN ALTERNATIVE ASSETS WITH DIFFERING LIVES: EAC LG12-7 One type of problem that also deserves special mention involves situations where we’re asked to choose between two different assets that can be used for the same purpose. Such a problem does not usually require the computation of incremental FCF, but instead will require you to take the two alternatives sets of incremental cash flows associated with the two assets and restructure them so that they can be compared to each other. For example, suppose a company has decided to go ahead with a project but needs to choose between two alternative assets, where Both assets will result in the same sales. Both assets may have different costs and recurring expenses. Assets will last different lengths of time. When the chosen asset wears out, it will be replaced with an identical machine. In such a situation, the firm cannot really compare one iteration of each machine to the other, since they last different lengths of time. The key here is to use the fact that, since the firm will replace each machine with another page 355 identical machine when it wears out, it is really being asked to choose between two sets of infinite, but systematically varying, cash flows. To handle such a situation, we need to “smooth out” the variation in each set of cash flows so that each becomes a perpetuity. Then the company can choose between the two machines based on which will generate the highest present value of cash flows. Since the decision will involve only a subset of a project’s cash flows—the purchase of one of a choice of assets— that present value will probably be negative. If the firm were to look at all the benefits deriving from the choice of which asset to use, including expected sales and so forth, the present value of all cash flows would need to be positive for the entire project to be attractive. We will discuss this in much greater depth in the next chapter when we cover the net present value (NPV) rule for capital budgeting decisions. The basic concept behind the EAC approach is to use TVM to turn each iteration of each project into an annuity. Once we have done that, then we can think of the stream of iterations of doing that project again and again as a stream of annuities, all with equal payments—or, to put it another way, as a perpetuity. To compute and use the EACs of two or more alternative assets 1. Find the sum of the present values of the cash flows (the net present value, or NPV, which we will cover in great detail in the next chapter) for one iteration of A and one iteration of B. 2. Treat each sum as the present value of an annuity with life equal to the life of the respective asset, and solve for each asset’s EAC (i.e., payment). 3. Choose the asset with the highest (i.e., least negative) EAC. It may seem that we have just done exactly what we said we should not do: compare the cash flows from one machine A to those from one machine B. In fact, the comparison we just did is actually much broader than that, though it will take a little explanation to see. EXAMPLE 12-4 EAC Approach LG12-7 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Suppose that your company has won a bid for a new project—painting highway signs for the local highway department. Based on past experience, you are pretty sure that your company will have the contract for the foreseeable future, and now you have to decide whether to use machine A or machine B to paint the signs: Machine A costs $20,000, lasts five years, and will generate annual after-tax net expenses of $2,500. Machine B costs $12,000, lasts three years, and will have after-tax net expenses of $3,500 per year. Assume that, in either case, each machine will simply be junked at the end of its useful life, and the firm faces a cost of capital of 12 percent. Which machine should you choose? SOLUTION: One iteration of each machine will consist of the sets of cash flows shown below: Year 0 1 2 3 4 5 Machine A CFs − $20,000 − $2,500 − $2,500 − $2,500 − $2,500 − $2,500 Machine B CFs −12,000 −3,500 −3,500 −3,500 http://mhhe.com/CornettM4e page 356 ▼ The sum of the present values of machine A’s cash flows will be Treating this as the present value of a five-period annuity, setting i to 12 percent, and solving for payment will yield a payment of −$8,048, which is machine A’s EAC. The sum of the present values of machine B’s cash flows will be Treating this as the present value of a 3-period annuity, setting i to 12 percent, and solving for payment will yield a payment of −$8,496, which is machine B’s EAC. Since machine A’s EAC is less negative than machine B’s, your firm should choose machine A. Similar to Problems 12-3 to 12-5, Self-Test Problem 3 Visualize the cash flows to the infinitely repeated purchases of machine B (chosen simply because it has a short life, so it will be easier to see multiple iterations on a time line in the following discussion) as shown in Figure 12.1. FIGURE 12.1 Cash Flows of Repeated Purchases of Machine B Notice that, after the initial purchase of the first machine B, the cash flows exhibit a systematic cycle: −$3,500 for two years, followed by −$15,500 for one year (when the next machine B is purchased), repeating this way forever. This systematic cycle, which we don’t have a formula for valuing, makes it necessary to convert these cash flows into a perpetuity, which we can value. When we computed the NPV of one iteration of machine B, we basically “squished” that machine’s cash flows down to a single lump sum at one point in time (i.e., the purchase point for that particular machine), and when we ▼ page 357 treated that as the present value of an annuity and solved for the payments we were effectively taking that same value and spreading it evenly across the life of the first machine B. Furthermore, since subsequent machine B purchases will be identical to this first one, we can visualize doing the exact same thing to every machine B’s cash flow. Turning each machine B’s cash flow into an annuity in this manner has the net effect of turning all the machine B’s cash flows into a perpetuity, as shown in Figure 12.2. FIGURE 12.2 Converted Cash Flows of Repeated Purchases of Machine B In the process, we also turn the repeated purchase of machine A into a perpetuity. We could calculate the present values of these two perpetuities and then compare them, which is what we’re really interested in doing: But do we really need to? No. The relationship between these two present values of the respective perpetuities is really the same as the relationship between their payment amounts2—each machine’s respective EAC. time out! 12-9 Explain how the EAC approach turns uneven cash flows for infinitely repeated asset purchases into perpetuities. 12-10 What if two alternative assets lasted the same length of time: Would the EAC approach still work? 12.7 • FLOTATION COSTS REVISITED LG12-8 In the previous chapter, we talked about how to take flotation costs into account by adjusting the WACC upwards, incorporating flotation costs directly into the issue prices of the securities used to fund projects. Another way that we can account for flotation costs is to adjust the project’s initial cash flow so that it will reflect the flotation costs of raising capital for the project as well as the necessary investment in assets. In this approach, we will 1. Compute the weighted-average flotation cost, fA, using the firm’s target capital weights (because the firm will issue securities in these percentages over the long term): (12-4) where fE, fP, and fD are the percentage flotation costs for new equity, preferred stock, and debt, respectively. 2. Compute the flotation-adjusted initial investment, CF0, using (12-5) EXAMPLE 12-5 Adjusting CF0 for Flotation Cost LG12-8 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Your company is considering a project that will cost $1 million. The project will generate after-tax cash flows of $375,000 per year for five years. The WACC is 15 percent and the firm’s target D/A ratio is 0.375. The flotation cost for equity is 5 percent, the flotation cost for debt is 3 percent, and your firm does not plan on issuing any preferred stock within its capital structure. If your firm follows the practice of incorporating flotation costs into the project’s initial investment, what will the flotation-adjusted cash flows for this project be? SOLUTION: Since the D/A is 0.375, the E/A ratio will be equal to 1 − 0.375 = 0.625, and the weighted-average flotation cost for the firm will be Using this, the adjusted CF0 for the project will be So the flotation-adjusted cash flows for the project will be Year 0 1 2 3 Cash Flow − $1,044,386 $375,000 $375,000 $375,000 As we discussed in the previous chapter, this approach to adjusting for flotation costs violates the spirit of the separation principle of capital budgeting, which states that the calculations of cash flows should remain independent of the choice of financing. On the other hand, the approach we used in the last chapter, increasing the project’s WACC to incorporate the flotation costs’ impact, tends to understate the component cost of new equity. So, which approach is better? Well, even though most practitioners have historically taken the approach of adjusting the WACC upward, it is intuitively a little “distasteful”; it burdens the capital raised to finance a project with a higher required rate of return from then on, even though those flotation costs are actually a one-time thing. So, ideally, we would handle flotation costs as we’ve done in this chapter, by adjusting the project’s initial cash flow to account for them. Pragmatically, however, it is not unusual for firms to use either approach based on what they find the most intuitively appealing. time out! http://mhhe.com/CornettM4e page 358 12-11 How would you compute the equity flotation cost if a firm were going to use a mixture of retained earnings and new equity to finance a project? 12-12 Why do we divide the initial cash flow by (1 − fA) instead of multiplying it by (1 + fA)? Get Online ©JGI/Jamie Grill/Blend Images LLC. Log in to your Connect course for study materials including self-test problems with solutions, answers to the Time Out quizzes, guided example videos, and more. Your Turn… Questions 1. How is the pro forma statement we used in this chapter for computing OCF different from an accountant’s income statement? (LG12-1) 2. Suppose you paid your old college finance professor to evaluate a project for you. If you would pay him regardless of your decision concerning whether to proceed with the project, should his fee for evaluating the project be included in the project’s incremental cash flows? (LG12-2) 3. Why does a decrease in NWC result in a cash inflow to the firm? (LG12-3) 4. Everything else held constant, would you rather depreciate a project with straight-line depreciation or with DDB? (LG12-3) page 359 page 360 5. Everything else held constant, would you rather depreciate a project with DDB depreciation or deduct it under a Section 179 deduction? (LG12-4) 6. In a replacement problem, would we ever see changes in NWC? (LG12-5) 7. In a replacement problem, will incremental net depreciation always be less than the gross depreciation on the new piece of equipment? (LG12-5) 8. In a cost-cutting proposal, what might cause you to sometimes have negative EBIT? (LG12-6) 9. How many TVM formulas do you use every time you calculate EAC for a project? (LG12-7) 10. Will an increase in flotation costs increase or decrease the initial cash flow for a project? (LG12-8) Problems BASIC PROBLEMS 12-1 After-Tax Cash Flow from Sale of Assets Suppose you sell a fixed asset for $109,000 when its book value is $129,000. If your company’s marginal tax rate is 39 percent, what will be the effect on cash flows of this sale (i.e., what will be the after-tax cash flow of this sale)? (LG12-3) 12-2 PV of Depreciation Tax Benefits Your company is considering a new project that will require $1 million of new equipment at the start of the project. The equipment will have a depreciable life of 10 years and will be depreciated to a book value of $150,000 using straight-line depreciation. The cost of capital is 13 percent, and the firm’s tax rate is 34 percent. Estimate the present value of the tax benefits from depreciation. (LG12-4) 12-3 EAC Approach You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $14,000 to purchase and which will have OCF of −$1,200 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $20,000 to purchase and which will have OCF of −$650 annually throughout that vehicle’s expected four-year life. Both cars will be worthless at the end of their life. If you intend to replace whichever type of car you choose with the same thing when its life runs out, again and again out into the foreseeable future, and if your business has a cost of capital of 12 percent, which one should you choose? (LG12-7) 12-4 EAC Approach You are evaluating two different cookie-baking ovens. The Pillsbury 707 costs $57,000, has a five-year life, and has an annual OCF (after tax) of −$10,000 per year. The Keebler CookieMunster costs $90,000, has a seven-year life, and has an annual OCF (after tax) of −$8,000 per year. If your discount rate is 12 percent, what is each machine’s EAC? (LG12-8) 12-5 EAC Approach You are considering the purchase of one of two machines used in your manufacturing plant. Machine A has a life of two years, costs $80 initially, and then $125 per year in maintenance costs. Machine B costs $150 initially, has a life of three years, and requires $100 in annual maintenance costs. Either machine must be replaced at the end of its life with an equivalent machine. Which is the better machine for the firm? The discount rate is 12 percent and the tax rate is zero. (LG12-8) INTERMEDIATE PROBLEMS 12-6 Project Cash Flows KADS, Inc., has spent $400,000 on research to develop a new computer game. The firm is planning to spend $200,000 on a machine to produce the new game. Shipping and installation costs of the machine will be capitalized and depreciated; they total $50,000. The machine has an expected life of three years, a $75,000 estimated resale value, and falls under the MACRS seven-year class life. Revenue from the new game is expected to be $600,000 per year, with costs of $250,000 per year. The firm has a tax rate of 35 percent, an opportunity cost of capital of 15 percent, and it expects net working capital to increase by $100,000 at the beginning of the project. What will the cash flows for this project be? (LG12- 3) 12-7 Depreciation Tax Shield Your firm needs a computerized machine tool lathe that costs $50,000 and requires $12,000 in maintenance for each year of its three-year life. After three years, this machine will be replaced. The machine falls into the MACRS three-year class life category. Assume a tax rate of 35 percent and a discount rate of 12 percent. Calculate the depreciation tax shield for this project in page 361 year 3. (LG12-4) 12-8 After-Tax Cash Flow from Sale of Assets If the lathe in the previous problem can be sold for $5,000 at the end of year 3, what is the after-tax salvage value? (LG12-4) 12-9 Project Cash Flows You have been asked by the president of your company to evaluate the proposed acquisition of a new special-purpose truck for $60,000. The truck falls into the MACRS three-year class, and it will be sold after three years for $20,000. Use of the truck will require an increase in NWC (spare parts inventory) of $2,000. The truck will have no effect on revenues, but it is expected to save the firm $20,000 per year in before-tax operating costs, mainly labor. The firm’s marginal tax rate is 40 percent. What will the cash flows for this project be? (LG12-6) ADVANCED PROBLEMS 12-10 Change in NWC You are evaluating a project for The Tiff-any golf club, guaranteed to correct that nasty slice. You estimate the sales price of The Tiff-any to be $400 per unit and sales volume to be 1,000 units in year 1; 1,500 units in year 2; and 1,325 units in year 3. The project has a three-year life. Variable costs amount to $225 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $165,000 in assets, which will be depreciated straight-line to zero over the three- year project life. The actual market value of these assets at the end of year 3 is expected to be $35,000. NWC requirements at the beginning of each year will be approximately 20 percent of the projected sales during the coming year. The tax rate is 34 percent and the required return on the project is 10 percent. What change in NWC occurs at the end of year 1? (LG12-3) 12-11 Operating Cash Flow Continuing the previous problem, what is the operating cash flow for the project in year 2? (LG12-3) 12-12 Project Cash Flows Your highly successful software company is considering adding a new software title to your list. If you add the new product, it will use the full capacity of your disk duplicating machines that you had planned on using for your flagship product, “Battlin’ Bobby.” You had previously planned on using the unused capacity to start selling “BB” on the west coast in two years. Eventually, you would have had to purchase additional duplicating machines 10 years from today, but since your new product will use up the extra capacity, this will require moving this purchase up to 2 years from today. If the new machines will cost $100,000 and will be depreciated straight-line over a five-year period to a zero salvage value, your marginal tax rate is 32 percent, and your cost of capital is 12 percent, what is the opportunity cost associated with using the unused capacity for the new product? (LG12-3) 12-13 Project Cash Flows You are evaluating a project for The Ultimate recreational tennis racket, guaranteed to correct that wimpy backhand. You estimate the sales price of The Ultimate to be $400 per unit and sales volume to be 1,000 units in year 1; 1,250 units in year 2; and 1,325 units in year 3. The project has a three-year life. Variable costs amount to $225 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $165,000 in assets, which will be depreciated straight-line to zero over the three-year project life. The actual market value of these assets at the end of year 3 is expected to be $35,000. NWC requirements at the beginning of each year will be approximately 20 percent of the projected sales during the coming year. The tax rate is 34 percent and the required return on the project is 10 percent. What will the cash flows for this project be? (LG12-3) 12-14 Project Cash Flows Mom’s Cookies, Inc., is considering the purchase of a new cookie oven. The original cost of the old oven was $30,000; it is now five years old, and it has a current market value of $13,333.33. The old oven is being depreciated over a 10-year life toward a zero estimated salvage value on a straight-line basis, resulting in a current book value of $15,000 and an annual depreciation expense of $3,000. The old oven can be used for six more years but has no market value after its depreciable life is over. Management is contemplating the purchase of a new oven whose cost is $25,000 and whose estimated salvage value is zero. Expected before-tax cash savings from the new oven are $4,000 a year over its full MACRS depreciable life. Depreciation is computed using MACRS over a five-year life, and the cost of capital is 10 percent. Assume a 40 percent tax rate. What will the cash flows for this project be? (LG12-5) 12-15 Project Cash Flows Your company is contemplating replacing its current fleet of delivery vehicles with Nissan NV vans. You will be replacing five fully-depreciated vans, which you think you can sell for $3,000 each and which you could probably use for another two years if you chose not to replace page 362 them. The NV vans will cost $29,850 each in the configuration you want them and can be depreciated using MACRS over a five-year life. Expected yearly before-tax cash savings due to acquiring the new vans amounts to about $3,700 each. If your cost of capital is 8 percent and your firm faces a 34 percent tax rate, what will the cash flows for this project be? (LG12-5) Notes CHAPTER 12 1. There are also midmonth and midquarter conventions, which apply in special circumstances. Please refer to IRS Publication 946 for details. 2. Because the two perpetuities have the same interest rate and the same periodicity (i.e., length between payments), the only possible source of difference in their present values would be the respective payment amounts. page 363 chapter twelve appendix 12A MACRS Depreciation Tables ▼ MACRS DEPRECIATION ▼ SL DEPRECIATION page 364 ▼ SL DEPRECIATION page 365 page 366 ▼ SL DEPRECIATION page 367 page 368 page 369 O chapter thirteen weighing net present value and other capital budgeting criteria ©Stockbyte/Getty Images nce you have calculated the cost of capital for a project and estimated its cash flows, deciding whether to invest in that project basically boils down to asking the question “Is the project worth more or less than it costs?” To answer this question, we will, not surprisingly, turn once again to the time value of money (TVM) formulas we used to value stocks, bonds, loans, and other marketable page 370 securities in Chapters 7 and 8. But first, a caveat: Though the mechanics of using the TVM formulas will be the same, the intuition underlying our analysis of investment criteria will be very different in this chapter. And this shift in intuition will be signaled by a seemingly minor thing. You will recall that when we used the pricing equations for marketable securities such as stocks, bonds, and other instruments, they all had “=” signs. In this chapter, we’re going to see that most capital budgeting decision rules that we will encounter will have “>” or “<” signs. Even though it seems like a small thing, this switch from an assumption of equality in all our previous TVM equations to one of inequality in those used in this chapter reflects a dramatic shift in both the investment environment we are operating in and in our assessment of what types of returns are possible in that environment. This difference arises because the marketable securities valued in all the previous chapters are financial assets that trade in competitive financial markets, while the capital budgeting projects that we consider in this chapter usually involve investment in real assets (such as land, machinery, and so forth), which typically trade in much less competitive markets. In this context, “less competitive” basically means that we will be operating in an environment where these real assets associated with a project will convey at least some monopoly power (and the associated monopolistic revenues) to us if we undertake the project. LEARNING GOALS LG13-1 Analyze the logic underlying capital budgeting decision techniques. LG13-2 Calculate and use the payback (PB) and discounted payback (DPB) methods for valuing capital investment opportunities. LG13-3 Calculate and use the net present value (NPV) method for evaluating capital investment opportunities. LG13-4 Calculate and use the internal rate of return (IRR) and the modified internal rate of return (MIRR) methods for evaluating capital investment opportunities. LG13-5 Use NPV profiles to reconcile sources of conflict between NPV and IRR methods. LG13-6 Compute and use the profitability index (PI). viewpoints business APPLICATION ADK Industries, a startup firm in the online social networking industry, has run into capacity constraints with their Internet bandwidth provider. ADK management is considering building their own dedicated Web server farm at a cost of $5 million. In return, the firm expects that the increased bandwidth will generate higher demand for its services, resulting in increased cash flows of $1.2 million in the first year, $1.6 million in the second year, $2.3 million in the third year, and $2.8 million in the fourth year, for a total of $7.9 million over the next four years. At that point, the firm will scrap the server farm as obsolete. If ADK estimates that its target rate of return on such projects is 14 percent, should ADK go ahead with the project? (See the solution at the end of the book.) To see this difference, consider two situations: In one, an investor is deciding whether to buy a share of stock in a company that only has one class of common stock, while in the other, a restaurant chain is deciding whether to purchase a particular corner lot as a location for one of their restaurants. The stock purchase decision will focus on the cash flows expected to be received back from the stock, but which particular share of stock is purchased won’t really matter; all shares of stock will get the same cash flows and, as long as the stock markets are reasonably efficient, you’ll pay about the same price and commission regardless of which particular share of stock you buy. The restaurant purchase decision, though, will be different from the stock purchase decision on a couple of levels. First, real estate markets are nowhere near as efficient as stock markets, so the fees paid in the form of commissions, closing costs, etc., will represent a far higher percentage of the purchase price of the restaurant than the commission rate on the stock purchase does. Even more important, though, is that, if the restaurant chain does buy a particular piece of land, no one else can buy that exact piece of land. So their asset will be unique, and no one else will be able to perfectly compete with a page 371 page 372 restaurant built there. Oh, their competitors might try to build on plots of land that are as close as possible (there’s a reason that you will often see competing restaurant chains clustered on corner lots around the same intersection, or across the road from each other), but, if this particular lot has the best traffic flow potential. . . you get the picture. In sum, uses of TVM equations in previous chapters were dealing with assets trading in financial markets where “what you get is what you pay for,” that is, where the present value of the expected future cash flows should just equal what you have to pay for it, taking into account the risks associated with those cash flows, as well as the going rate for compensating the purchaser for bearing those risks. In this chapter, we’re going to be using TVM to value real assets, a situation where it is possible to expect to earn returns above and beyond those necessary to compensate us for the associated risks (a situation sometimes referred to as earning economic profits). In other words, the name of the game in this chapter is to always look for projects that are worth more than they cost, even after we take risks in to account. ■ personal APPLICATION Letitia Tyler is considering some improvements to her house. The work will take six months to complete, and the contractor has asked for payments of $5,000 at the start, $5,000 after three months, and another $10,000 upon completion. Letitia plans to sell the house in approximately three years and estimates that the work will increase the selling price of her house by approximately $30,000 from its current estimated market price of $124,000. If she must borrow money to pay for the improvements from the bank at an APR (based upon monthly compounding) of 9 percent, should she have the improvements done? (See the solution at the end of the book.) How do interest rates impact Letitia’s decision? What does that have to do with the economy? 13.1 • THE SET OF CAPITAL BUDGETING TECHNIQUES LG13-1 So, now we are going to apply what we have learned in the preceding two chapters about the cost of capital and cash flows that result from capital budgeting decisions to choose the projects that most deserve to be funded using the firm’s scarce capital—that is, to determine which projects promise the best expected returns to the company. Commonly used capital budgeting techniques for doing this include NPV (net present value). IRR (internal rate of return). PB (payback). DPB (discounted payback). MIRR (modified internal rate of return). PI (profitability index). As we discuss each of these techniques in this chapter, you will find that, while the net present value (NPV) technique is the preferred one for most project evaluations, in some cases using one of the other decision rules, either in lieu of NPV or in conjunction with it, makes sense. For example, a company or person faced with a time constraint to repay the initial capital for a project may be more worried about a project’s payback (PB) statistic, while a firm facing capital constraints might prefer to use one of the interest-rate-based decision statistics, such as the profitability index (PI), to prioritize its project choices. Choosing a capital budgeting technique or techniques to use is affected by five subchoices: 1. The statistical format you choose. 2. The benchmark you compare it to. 3. Whether you compute it with TVM. 4. Whether non-normal cash flows are a factor. 5. What other projects you may or may not have to decide among. page 373 Table 13.1 details the implicit subchoices associated with each of the capital budgeting techniques. ▼ TABLE 13.1 Capital Budgeting Technique Attributes 13.2 • THE CHOICE OF DECISION STATISTIC FORMAT LG13-1 Managers tend to focus on three general measurement units for financial decisions: currency, time, and rate of return. Of these three types, rate-based statistics can potentially be the trickiest to use. Computing these statistics usually involves summarizing the relationship between cash inflows and cash outflows across the project’s lifetime through the use of a ratio. Any time we use a ratio to create a summary statistic like this, some (crucial) information is lost along the way. In particular, although rate-based decision statistics tell us the rate of return per dollar invested, they don’t reflect the amount of the investment on which that return is based. To see why this can be a problem, particularly when choosing between two or more projects, ask yourself this question: Would you rather earn a 10 percent rate of return on $100 or a 9 percent rate of return on $1,000? While “10 percent” sounds better than “9 percent,” the discrepancy in terms of the amounts invested is important, as there is usually an either explicit or implied restriction on what can/must be done with the difference in amounts. For example, suppose that this question was clarified for you as, “Would you rather earn a 10 percent rate of return on $100 or a 9 percent rate of return on $1,000, assuming that if you chose to invest $100 at 10 percent, the other $990 (i.e., $1,000 – $100) could not be invested in anything?” As this clarification allows you to refine your choice to one between a $10 return on $1,000 or a $90 return on $1,000, you would logically choose the one offering $90, or 9 percent on the whole $1,000. ©Image Source/Alamy P. Ughetto/PhotoAlto imageshop/Punchstock Among currency, time and rate of return, managers usually prefer rate-based statistics. Despite this tendency to focus on the return per dollar invested while ignoring the number of dollars in question, rate-based decision statistics are actually very popular. Perhaps because many managers are so often asked to choose between projects or investments of roughly equal size (where the problem we discussed above doesn’t exist, or at least isn’t as big of an issue), they often fall into the habit of using expected rates of return as “shorthand” for the expected dollars of return involved. They also appreciate the ease of being able to easily compare an expected “earned” rate of return generated by one of these rate-based capital budgeting rules with the “borrowing” rates that potential lenders and the capital markets are quoting to them. But, as we’ve seen above, sometimes using a rate- based decision rule can create problems when choosing between different-sized projects, or when money raised on the capital markets comes in different-sized “chunks” than the amounts required for the projects we’re investing in. Likewise, time-based decision statistics, such as the payback (PB) statistic discussed later in this chapter, are often attractive to managers, particularly when they’ve raised the money for a project by taking out a fixed-term loan or by issuing a nonperpetual bond: If you have to pay back the money you’ve borrowed within a certain number of years, it seems logical to invest that money in projects that will pay back their initial investments before the term of the loan or bond. However, similar to our previous discussion of why looking just at different rates of return can be misleading if dollars invested aren’t considered, using time of repayment in this manner without considering other factors such as dollars involved or rates of return earned/paid can also lead to making counterproductive decisions. For example, what if you are going to raise money for your firm through a 10-year bond issue, and therefore decide to constrain yourself to projects that will pay back any money invested in them within those 10 years? Well, then you might ignore an excellent, extremely high rate of return project that takes, say, 11 years to achieve completion. Even though, if the project does as well as you think it will, you’ll probably be able to easily obtain some form of “bridge” financing that would allow you to borrow the money at time 10 to pay back the bondholders and then repay that borrowing at time 11. 13.3 • PROCESSING CAPITAL BUDGETING page 374 DECISIONS LG13-1 For all of our decision techniques, we need to identify how to calculate a decision statistic, decide on an appropriate benchmark for comparing the calculated statistic, and define what relationship between the two will dictate project acceptance or rejection. When we consider one project at a time, or when we examine each of a group of independent projects, capital budgeting techniques involve two-step decision processes: 1. Compute the statistic. 2. Compare the computed statistic with the benchmark to decide whether to accept or reject the project. However, when we deal with mutually exclusive projects, we will need to add a new step in the middle of the process: 1. Compute the statistic for each project. 2. Have a “runoff” between the mutually exclusive projects, choosing the one with the best statistic. 3. Compare the computed statistic from the runoff winner with the benchmark to decide whether to accept or reject. As we will see, the presence of this runoff step for mutually exclusive projects, as well as its placement, will create problems when we use decision statistics that either ignore or summarize critical information in the first step. 13.4 • PAYBACK AND DISCOUNTED PAYBACK LG13-1 Both the payback and discounted payback rules carry great emotional appeal: If we assume that we are borrowing money to finance a new project, both techniques answer slightly different versions of the question, “How long is it going to take us to recoup our costs?” So it would seem that these techniques use the same reasoning that banks and other lenders employ when they examine a potential borrower’s finances to determine the probability of repayment. While at first this seems like a fairly simple question, it can actually lead to some rather sophisticated insight concerning a project’s potential. For example, a project that lasts seven years but is slated to repay its initial investment within the first two years is obviously a stronger candidate than a project that also repays in two years but is slated to last only three years: The first project will be “in the black” (i.e., having repaid the initial investment and earning money above and beyond that; from the standard accounting practice of using black ink, as opposed to red ink, to denote positive values) for the last five years, while the second project will be in the black for only one year. However, earning money above and beyond the project investment is only part of the picture and using it as the sole decision criterion involves an implicit assumption that the two projects are expected to have the same yearly cash flows once payback is achieved. Payback Statistic LG13-2 The payback (PB) statistic remains very popular because it is easy to compute. All we have to do is keep a running subtotal of the cumulative sum of the cash flows up to the point that this sum exactly offsets the initial investment. That is, PB is determined by using this formula: payback (PB) A capital budgeting technique that generates decision rules and associated metrics for choosing projects based on how quickly they return their initial investment. (13-1) Notice that this computation demands a couple of strong assumptions: 1. The concept of payback rests on the assumption that cash flows are normal, with all outflows occurring at the beginning of the project’s life, so that we can think of the PB statistic as a type of recovery period for that initial investment. This implies that payback would be meaningless for a set of non-normal cash flows. If, for example, a project required an infusion of cash after it started, such as the cash outflows shown at times 1 and 2 in Example 13-5 (later in the chapter), we could not calculate a payback statistic. 2. Note that PB will not be very likely to occur in an exact, round number of periods, so we will need to make another assumption concerning how cash inflows occur during the course of a year. The usual approach to handling this condition is to assume that cash flows arrive smoothly throughout each period, allowing us to count out the months and days to estimate the exact payback statistic. page 375 normal cash flows A set of cash flows with all outflows occurring at the beginning of the set. Payback Benchmark The payback method shows an additional weakness in that its benchmark must be exogenously specified: In other words, it is not always the same value, nor is it determined by the required rate of return or any other input variable. Ideally, the maximum allowable PB for a project should be set based on some relevant external constraint, such as the number of periods until capital providers need their money back, or the time available until a project would violate a bond issue’s protective covenants. As you might suspect, in real life managers often indicate the maximum allowable payback—that is, set the exogenous specification—arbitrarily. Let us assume that we have been told that the maximum allowable payback for this project is three years. With this decision rule, we want to accept projects that show a calculated statistic less than the benchmark of three years: (13-2) Discounted Payback Statistic Yet another problem that arises when we use the payback technique is that it does not recognize or incorporate the time value of money. To compensate for this exclusion, we often calculate the discounted payback (DPB) statistic instead, using the following formula: discounted payback (DPB) A capital budgeting method that generates decision rules and associated metrics that choose projects based on how quickly they return their initial investment plus interest. (13-3) Notice that all we are doing here is summing the present values of the cash flows until we get a cumulative sum of zero, instead of summing the cash flows themselves as we did for the PB statistic. Other than that, we follow all the steps in the computation of DPB just as we did for the PB statistic. EXAMPLE 13-1 Payback Calculation LG13-2 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Consider the sample project with the cash flows shown in Table 13.2. Should this project be accepted based on payback if the maximum allowable payback period is three years? ▼ TABLE 13.2 Discounted Payback Calculation: Present Values of Cash Flows Year: 0 1 2 3 4 5 Cash flow – $10,000 $2,500 $3,500 $5,000 $4,000 $2,000 Cumulative cash flow –10,000 –7,500 –4,000 1,000 http://mhhe.com/CornettM4e. page 376 SOLUTION: To calculate this project’s payback, we would first calculate the cumulative cash flows until they went from negative to positive. From this first step, we know that payback occurs somewhere between periods 2 and 3. To determine the exact statistic, we note that if the magnitude of the last negative cumulative cash flow represents how much cash flow we need during year 3 to achieve payback, then the marginal cash flow for year 3 represents how much we will get over the course of the entire third year. By linear interpolation, our exact statistic is therefore where we start (year 2) plus what we need (the absolute value of the last negative cumulative cash flow, –$4,000) over what we are going to get during that year: Since our calculated payback is 2.8 years and the maximum allowable payback period is three years, we should accept the project based on the payback rule. Similar to Problems 13-5, 13-6, 13-17, 13-23, Self-Test Problem 1 EXAMPLE 13- 2 Discounted Payback Calculation LG13-2 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Consider the same project from Example 13-1. To calculate this project’s discounted payback, we would first need to calculate the PV of each cash flow separately. Assuming a 12 percent interest rate, we would calculate these values as shown in Table 13.3. ▼ TABLE 13.3 Discounted Payback Calculation: Present Values of Cash Flows http://mhhe.com/CornettM4e. In Table 13.4 we calculate the cumulative present value of the cash flows until they switch from negative to positive: ▼ TABLE 13.4 Discounted Payback Calculation on Sample Project with Normal Cash Flows SOLUTION: As before, we can stop once the cumulative values go from negative to positive. In this case, linear interpolation will give us a DPB statistic of Since our calculated DPB is 3.56 years and the maximum allowable amount is 3.5 years, we should reject the project. Similar to Problems 13-7, 13-8, 13-18, 13-24, Self-Test Problem 1 the Math Coach on… Payback and Discounted Payback Using Financial Calculators and Spreadsheet Programs “Most financial calculators and spreadsheet programs (with the notable exception of Texas Instrument’s BA II Plus Professional) will not compute PB or DPB for you. Instead, you have to go through the process of cumulating cash flows or the PV of cash flows noted in Examples 13-1, 13-2, and 13-3.„ Discounted Payback Benchmark We may be tempted to assume that we should simply use the same maximum allowable payback benchmark for page 377 DPB that we used for PB. If we did so, then we would obviously have to reject this project, since its calculated DPB is 3.56 years (Example 13-2) versus a stated maximum allowable time of only three years. However, we should be very cautious about applying the same benchmark to DPB that we did to PB. To see why, recall that payback calculations only make sense when applied to normal cash flows, so we would assume that we will be dealing with normal cash flows here. But think about which cash flows are affected when we switch from calculating payback to discounted payback: Only the ones in the future will fall to lower values, because the present value of the time 0 cash flow will always be the same as its nominal value. And if the future cash flows are all positive and the initial cash flow is negative, then it is only the positive cash flows that will be affected by switching to cumulative present value for DPB. EXAMPLE 13- 3 Payback Calculation for Alternative Project LG13-2 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Consider once again the sample project shown in Table 13.2. As we calculated in Example 13-1, that project has a PB statistic of 2.8 years. Now, compare that project to the one shown in Table 13.5: ▼ TABLE 13.5 Payback Calculation on Alternative Sample Project with Normal Cash Flows SOLUTION: This project would have a slightly higher PB statistic of 3.0. Given that it still achieves payback in exactly the maximum allowable three years, it should be highly favored over the first project due to the large positive cash flows that will accrue in the later years. But managers who ignore this aspect of the PB rule and who focus only on the PB statistics of these two projects will likely incorrectly choose the first project due to its lower PB statistic. Note that NPV will not suffer from this problem. Since the NPV statistic takes all of a project’s cash flows into account, there aren’t “remaining” cash flows to get left out of the statistic as there are with PB and DPB. Similar to Problems 13-5, 13-6, 13-17, 13-23 In other words, we would expect the calculated DPB statistic to always be larger than the “regular” PB statistic because DPB incorporates the interest you must pay until you reach the benchmark. Said another way, DPB will always take longer to achieve payback if you are “chipping away” at the same-sized initial cash outflow with the present values of a bunch of positive cash inflows rather than their simple nominal values. Therefore, it probably is not fair to hold the DPB statistic up to the same benchmark we use for the PB statistic. What benchmark should we use? Well, as with PB, management will set the DPB maximum allowable payback exogenously and, once again, often arbitrarily. Let us assume that we are told that senior management has set the maximum allowable payback for DPB as 3.5 years. http://mhhe.com/CornettM4e. page 378 (13-4) Payback and Discounted Payback Strengths and Weaknesses LG13-1 A common criticism of PB is that it does not account for the time value of money. The use of PV formulas in computing DPB compensates for TVM, but DPB is not intended to really replace PB, but rather to complement it, providing additional information to analyze capital budgeting decisions. For example, if we consider a typical, normal payback statistic based on a set of cash flows as a loan problem in which the company borrows the money for the initial investment and then pays it off over time, then the PB statistic will intuitively equal the amount of time necessary to repay just principal on the loan, and the DPB statistic will indicate the time necessary to repay principal plus interest. But, as discussed above, there is no way to impose a correspondingly logical relationship between the benchmarks used with each of these statistics due to their exogeneously specified nature. Both PB and DPB have another, potentially even more serious, flaw. Both decision statistics completely ignore any cash flows that accrue after the project reaches its respective payback benchmark. Ignoring this vital information can have serious implications when managers choose between two mutually exclusive projects that have very similar paybacks but very different cash flows after payback is achieved. time out! 13-1  Which should we expect to be larger: a project’s payback statistic, or its discounted payback statistic? 13-2  If the discount rate is increased, will a project’s discounted payback period increase or decrease? 13.5 • NET PRESENT VALUE LG13-1 At its heart, net present value (NPV) represents the “purest” of capital budgeting rules, measuring exactly the value we are interested in: the amount of wealth increase we expect from accepting a project. As we cover in more detail below, the NPV method measures this expected wealth increase by computing the difference between the present values of a project’s cash inflows and outflows. Since this calculation includes the necessary capital expenditures and other startup costs of the project as cash outflows, a positive value indicates that the project is desirable—that it more than covers all of the necessary resource costs to do the project. net present value (NPV) A technique that generates a decision rule and associated metric for choosing projects based on the total discounted value of their cash flows. NPV Statistic LG13-3 We actually already know how to calculate the NPV statistic. In fact, we used a very similar approach in developing bond and stock pricing equations. The NPV statistic is simply the sum of all the cash flows’ present values: (13-5) page 379 the Math Coach on… Financial Calculators versus Spreadsheet Programs “While financial calculators expect to be told CF0 when being asked to compute NPV, the NPV functions in spreadsheet programs such as Microsoft Excel usually don’t want to be told CF0. Instead, they expect you to handle the inclusion of CF0 in the calculation of the NPV statistic outside the NPV function. For example, if you wanted to find the NPV of the cash flows in Example 13-4 using Excel, the function would look like “ = NPV(.12,2500,3500,5000,4000,2000) – 10000”.„ NPV Benchmark NPV analysis includes all of the cash flows—both inflows and outflows. This inclusion implies that any required investment in the project is already factored in, so any NPV greater than zero represents value above and beyond that investment. Accordingly, the NPV decision rule is the Math Coach on… Using a Financial Calculator–Part 2 (Revisited) The TVM worksheet present in most financial calculators has been fine, so far, for the types of TVM problems we’ve been solving. Sometimes we had to use the worksheet two or three times for a single problem, but that was usually because we needed an intermediate calculation to input into another TVM equation. In this chapter, we will generally be using simpler TVM equations (i.e., PV and FV), but we’ll find ourselves having to use them repeatedly, making only small variations in inputs over and over again within the same problem. We’re also going to run up against the problem of cash flow inconsistencies in most projects. If you thought the cash flows of stocks jumped around a lot, wait until you see what project cash flows do! If we stick with the TVM worksheet, these inconsistent cash flows will be a problem for us. If we want to solve for a “common” i or N value, the TVM worksheet won’t let us enter multiple cash flows unless we’re solving an annuity problem. (The one notable exception to this has been when we used the TVM worksheet to simultaneously solve the annuity/lump sum problems that arise with bonds. If you recall, those problems require agreement between the inputs to the annuity and the lump sum problems. This kind of agreement is highly unlikely to occur in other circumstances.) Remember that most financial calculators also have built-in worksheets specifically designed for computing NPV in problems with multiple nonconstant cash flows. In many cases, they will also calculate most of the other decision rule statistics that we’re going to be discussing. page 380 Here is what we already know: To make calculator worksheets as flexible as possible, they are usually divided into two parts—one for input, which we’ll refer to as the CF (cash flow) worksheet, and one or more for calculating decision statistics. We’ll go over the conventions concerning the CF worksheet here. The CF worksheet is usually designed to handle inputting sets of multiple cash flows as quickly as possible. As a result, it normally consists of two sets of variables or cells—one for the cash flows and one to hold a set of frequency counts for the cash flows, so that we can tell it we have seven $1,500 cash flows in a row instead of having to enter $1,500 seven times. Using the frequency counts to reduce the number of inputs is handy, but you must take care. Frequency counts are only good for embedded annuities of identical cash flows. You have to ensure that you don’t mistake another kind of cash flow for an annuity. Also, using frequency counts will usually affect the way that the calculator counts time periods. As an example, let’s talk about how we would put the set of cash flows shown here into a CF worksheet: To designate which particular value we’ll place into each particular cash flow cell in this worksheet, we’ll note the value and the cell identifier, such as CF0, CF1, and so forth. We’ll do the same for the frequency cells, using F1, F2, etc., to identify which CF cell the frequency cell goes with. (Note that in most calculators, CF0 is treated as a unique value with an unalterable frequency of 1; we’re going to make the same assumption here so you’ll never see a listing for F0.) For this sample timeline, our inputs would be Then, on the NPV worksheet, you would simply need to enter the interest rate and solve for the NPV: Note a few important things about this example: 1. We had to manually enter a value of $0 for CF3: If we hadn’t, the calculator wouldn’t have known about it and would have implicitly assumed that CF4 came one period after CF2. 2. Once we use a frequency cell for one cash flow, all numbering on any subsequent cash flows that we enter into the calculator is going to be messed up, at least from our point of view. For instance, the first $75 isn’t what we would call “CF5,” is it? We’d call it “CF7” because it comes at time period 7; but calculators usually treat CF5 as “the fifth set of cash flows,” so we’ll just have to try to do the same to be consistent. 3. If we really don’t need to use frequency cells, we will usually just leave them out of the guidance instructions in this chapter to save space. (13-6) NPV Strengths and Weaknesses One strength of the NPV rule is that the statistic is not a ratio as with the rate-based decision statistics. It works equally well for independent projects and for choosing among mutually exclusive projects. In the latter case, the mutually exclusive project with the highest NPV should add the most wealth to the firm, and so management should accept it over any competing projects. Unfortunately, this ability to choose among projects stems from exactly what gives it its greatest weakness—the format of the statistic. Since the NPV statistic is a dollar figure, it accurately reflects the net effect of any differences in timing or scale of two projects’ expected cash flows. It thus allows comparisons of two projects’ NPV statistics to fully incorporate those differences. However, this same currency format often results in confusion for uninformed decision makers: Managers not completely familiar with how the NPV statistic works often insist on comparing the NPV to the cost of the project, not understanding that the cost is already incorporated into the NPV. page 381 EXAMPLE 13-4 NPV for a Normal Set of Cash Flows LG13-2 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. A company is evaluating a project with a set of normal cash flows using a risk-appropriate discount rate of 12 percent as shown in Table 13.6. Compute the NPV to determine whether the company should undertake the project. ▼ TABLE 13.6 Sample Project with Normal Cash Flows Year: 0 1 2 3 4 Cash flow – $10,000 $2,500 $3,500 $5,000 $4,000 SOLUTION: The NPV statistic for this project will be The NPV decision will be to accept the project. When you first start calculating NPV, it is easy to miss its deeper meaning. A relatively small NPV, such as the $2,258.15 figure in this example, raises the question of whether $2,258.15 is “worth it,” in this sense: Will the project cover the opportunity cost of using the $10,000 of necessary capital? The point, of course, is that the $2,258.15 is above and beyond the recovery of that opportunity cost, so, it. Similar to Problems 13-1, 13-2, 13-21, 13-27, Self-Test Problem 1 EXAMPLE 13-5 NPV for a Non-Normal Set of Cash Flows  For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Note that the NPV rule works equally well with non-normal cash flows, such as those for the project shown in Table 13.7. Compute the NPV for this project to determine whether it should be accepted. Use a 12 percent discount rate. ▼ TABLE 13.7 Sample Project with Normal Cash Flows Year: 0 1 2 3 4 http://mhhe.com/CornettM4e. http://mhhe.com/CornettM4e. page 382 Cash flow $5,000 – $10,000 – $3,000 $5,000 $4,000 SOLUTION: The NPV statistic will be Based on this NPV, the project should be accepted. Similar to Problems 13-3, 13-4 13.6 • INTERNAL RATE OF RETURN AND MODIFIED INTERNAL RATE OF RETURN LG13-1 The internal rate of return (IRR) technique is, by far, the most popular rate-based capital budgeting technique. The main reason for its popularity is that, if you are considering a project with normal cash flows that is independent of other projects, the IRR statistic will give exactly the same accept/reject decision as the NPV rule does. This is due to the fact that NPV and IRR are very closely related. NPV is the sum of the present values of the cash flows at a particular interest rate (usually the firm’s cost of capital), whereas IRR is the interest rate that will cause the NPV to be equal to zero. (13-7) internal rate of return (IRR) A capital budgeting technique that generates decision rules and associated metrics for choosing projects based on the implicit expected geometric average of a project’s rate of return. As long as the cash flows of a project are normal, the NPV calculated in the equation on the left will be greater than zero if and only if the IRR calculated in the equation on the right is greater than i. time out! 13-3  Why is a project’s cost not an appropriate benchmark for its NPV? 13-4  Assuming that it is fairly priced, what should be the NPV of a purchase decision on a corporate bond? However, IRR runs into a lot of problems if project cash flows are not normal or if you are using this statistic to decide among mutually exclusive projects. As we will show, we can correct for the non-normal cash flows, but all of the rate-based decision statistics will exhibit the problem of choosing between multiple projects that we discussed above. Internal Rate of Return Statistic LG13-4 To solve for the IRR statistic, we simply solve the NPV formula for the interest rate that will make NPV equal zero: page 383 (13-8) Unfortunately, we cannot solve directly for the interest rate that will set NPV equal to zero. We either have to use trial-and-error to determine the appropriate rate, or we have to rely on a calculator or computer, both of which use much the same approach. Internal Rate of Return Benchmark Once we calculate the IRR, we must then compare the decision statistic to the relevant cost of capital for the project —the average rate of return necessary to pay back the project’s capital providers, given the risk that the project represents: (13-9) At this point, you may find yourself getting a little confused about which rate is the interest rate. The IRR statistic will equal the expected rate of return, which incorporates risk (as probabilities). We will compare that expected rate of return to the cost of capital, which is often called the required rate of return. Up until this chapter, we have been using all of these phrases interchangeably for “the” interest rate. We have been able to get away with doing so to this point because stocks, bonds, and all other types of financial assets trade in relatively liquid, competitive financial markets. In liquid markets, the rate of return you expect to earn is pretty much equal to the rate of return you require for taking on that particular security’s risk. In such an environment, it makes sense to assume that we are not going to be able to earn any “extra” return or economic profit above and beyond what is appropriate for the amount of risk we are bearing. EXAMPLE 13- 6 IRR Calculation LG13-4 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Looking once again at our sample set of normal cash flows from Table 13.6, IRR will be the solution to Similar to Problems 13-9, 13-10, 13-19, 13-25, Self-Test Problem 1 Remember, though, that in this chapter, we are no longer talking about financial assets, but real assets such as land, factories with inventories, and production lines. These types of assets do not generally trade in perfectly competitive markets. Instead, they trade in quite illiquid markets in which an individual or a firm can gain at least some amount of market or monopoly power by virtue of technological, legal, or marketing expertise. http://mhhe.com/CornettM4e We noted this difference at the beginning of this chapter when we differentiated between formulas for financial assets such as stocks and bonds and the equations we are using in this chapter to value projects. The formulas we used to value stocks and bonds use “=” signs because those assets trade in nearly perfectly competitive markets, where what you get is (approximately, at least) equal to what you paid for it. Here, on the other hand, we examine situations in which companies seek to choose projects that are worth more than what they pay for them—leaving room for economic profit. That is why all of these capital budgeting rules use “>” and “<” signs. So, when we deal with physical asset projects, we have to expect that two different rates of return will arise. The best way to think of these two rates is as the expected rate of return (IRR), and the required rate of return (i). We only want to invest in projects where the rate we expect to get (IRR) is larger than the rate investors require (i) based on the project’s expected return, including risk.1 Real assets like production lines don’t trade in perfectly competitive markets. ©Digital Vision/Getty Images Problems with Internal Rate of Return LG13-5 As we mentioned previously, IRR will give the same accept/reject decision as NPV if two conditions hold true: 1. The project has normal cash flows. 2. We are evaluating the project independently of other projects—that is, we are not considering mutually exclusive projects. To see the problems that arise if these conditions do not hold, we will make use of a tool called the NPV profile. This is simply a graph of a project’s NPV as a function of possible capital costs. The NPV profile for our sample project with normal cash flows from Table 13.6 appears as Figure 13.1. ▼ page 384 NPV profile A graph of a project’s NPV as a function of the cost of capital. As you can see, the NPV profile for this normal set of cash flows slopes downward. As we noted previously concerning the relationship between the PB and DPB statistics, increasing values of i with a normal set of cash flows affect the present value of positive cash flows, but not that of negative cash flows. All sets of normal cash flows will therefore share this general, downward-sloping shape. Note that IRR appears on this graph as the intersection of the NPV profile with the x-axis (horizontal)—the intersection will represent the interest rate where NPV equals exactly zero. With normal cash flows such as these, the constant downward slope of the NPV profile dictates that only one such intersection will exist for each project. time out! 13-5 Is it possible for the NPV profile of a finite set of normal cash flows to never cross the x-axis? 13-6 Suppose a normal set of cash flows has an IRR equal to zero. Would NPV accept or reject such a project? IRR and NPV Profiles with Non-Normal Cash Flows But let us revisit what happens to the NPV profile if cash flows are not normal. The NPV profile will not necessarily slope continually downward and thus may cross over the x-axis at more than one interest rate. In this case we may find more than one valid IRR for which NPV equals zero. An example of such an NPV profile, constructed from the cash flows in Table 13.7, appears in Figure 13.2. In this instance, the project shows two valid IRRs: one at 23.62 percent and another at 88.62 percent. Which of these two should we use as “the” statistic? Well, it depends on what the firm pays as the actual cost of capital. If the firm pays 12 percent for capital, then using either of these two IRR values would generate a correct “accept” decision, as the project does have a positive NPV at i = 12 percent. But what if the firm paid a relatively high cost of capital, for example, 30 percent? Then the IRR rule would have us accept the project if we used the higher value (88.62 percent) as the project’s statistic but reject it if we used the lower IRR (23.62 percent). Of course, since the project generates a negative NPV if i is 30 percent, we would actually want to reject the project. FIGURE 13-1 NPV Profile for Sample Normal Cash Flows ▼ This graph presents our sample project’s NPV profile, using the normal cash flows listed in Table 13.6. Using the IRR technique requires a bit more complicated analysis if we come across more than one valid IRR like this. Perhaps the best thing to do in such a situation is to simply use a decision statistic other than IRR on projects with non-normal cash flows. If you (or, more likely, upper management) insist on using IRR with non-normal cash flows, you are going to need to use some trial and error to find all the possible IRRs. It will help to know how many there might possibly be. According to the Rule of Signs,2 we can end up with no more different positive IRRs than the number of sign changes in the cash flows—that is, inflows to outflows or outflows to inflows. Since our non-normal cash flow set shows two sign changes (one change from positive to negative and one change from negative to positive), we know that the two IRRs we have found constitute the entire possible set. FIGURE 13-2 NPV Profile for Sample Non-Normal Cash Flows page 385 Notice how the graph shows two valid IRRs. Which one should you use? Luckily we can solve IRR’s problems associated with non-normal cash flows by using the modified internal rate of return (MIRR), which also accounts for another problem associated with IRR, that of an unrealistic reinvestment rate assumption. Differing Reinvestment Rate Assumptions of NPV and IRR In addition to the problems associated with non-normal cash flows and handling mutually exclusive projects discussed above, IRR also has a different assumption than NPV concerning what we do with the cash inflows once we get them back. IRR assumes that any cash inflows will be reinvested in another project with the same earning power as the first project, while NPV assumes that cash inflows will be reinvested at the cost of capital, i. Which assumption is more reasonable? NPV’s is, because one way to effectively “earn” the cost of capital is to pay back your capital investors, and all companies have this option. On the other hand, IRR’s assumption seems a little far-fetched: If we assume that this project beat out a bunch of other projects at step 2 of the decision process, it must have had the highest possible IRR among all the alternatives, right? But now that the cash flows are rolling in, we find another project with the same “highest” possible rate of return? Seems like a little too much to expect, doesn’t it? Modified Internal Rate of Return Statistic LG13-4 The name modified internal rate of return is a little misleading. We are going to calculate IRR the same way we did before, but we are going to modify the set of cash flows to account for the cost of capital before we calculate IRR. We first use the cost of capital to “move” all the negative cash flows to the initial project start date (i.e., time 0) and all the positive cash inflows to the project termination date—and only then will we use the regular steps to calculate IRR. modified internal rate of return (MIRR) A capital budgeting method that converts a project’s cash flows using a more consistent reinvestment rate prior to applying the IRR decision rule. the Math Coach on… MIRR Using Financial Calculators and Spreadsheet Programs “Notice that we have assumed that both the positive and negative cash flows get moved using the same interest rate. In many situations, practitioners want to move the negative cash flows using one interest rate and the positive cash flows using another. Because of this, both spreadsheet programs and more advanced financial calculators allow for the use of two interest rates in exactly that way. For now, if you are using a calculator or spreadsheet program that requires two interest rates, just use the cost of capital for both rates.„ IRRs, MIRRs, and NPV Profiles with Mutually Exclusive Projects LG13-5 Even if we use the MIRR method for a project with non-normal cash flows, we can still run into problems if we’re trying to use it to choose between mutually exclusive projects. page 386 Two (or more) projects are mutually exclusive if management can accept one, the other, or neither, but not both, projects. As we will discuss, if we compare two mutually exclusive projects using a rate-based decision statistic, problems can arise if the projects’ cash flows exhibit differences in scale or timing (i.e., the size of the initial investment in each project). Over time, a “large” project that earns a slightly lower rate of return may be a better choice for the firm than a “small” project that earns a higher rate, but we will see that the rate-based decision techniques do not do well in choosing between these types of alternative projects. mutually exclusive projects Groups or pairs of projects where you can accept one but not all. What makes two or more projects mutually exclusive? Generally, mutually exclusive projects either share a common asset or target a common market, but the firm can only spare resources for one of them, or the market may only accept one product. Consider the prototypical example of mutually exclusive projects: A landowner owns two plots of land on either side of a river that people want to cross, and she is considering either building a bridge or operating a ferry for that purpose. EXAMPLE 13-7 MIRR Calculation LG13-4 For interactive versions of this example, log in to Connect or go to mhhe.com/CornettM4e. Turning once again to the sample non-normal project cash flows in Table 13.7, and assuming that the firm still faces a cost of capital of 12 percent, we convert the cash flows as shown in Table 13.8. ▼ TABLE 13.8 MIRR Cash Flow Adjustments for Sample Project with Non-Normal Cash Flows SOLUTION: Finding the PV of just the negative cash flows and finding the FV of just the positive cash flows gives us the following set of modified cash flows: Year: 0 1 2 3 4 5 http://mhhe.com/CornettM4e. page 387 Cash flow – $11,320.15 $21,563.71 With this new set of modified cash flows, the MIRR is Since our MIRR decision statistic exceeds the 12 percent cost of capital, we would accept the project under the MIRR method, which uses the same benchmark as the IRR rule. Notice that, regardless of how many possible IRRs a project may have, it will only ever have one possible MIRR. When you take a bunch of cash flows and convert them into two cash flows, one negative and one positive, you will only ever see one change in sign. Similar to Problems 13-11, 13-12, 13-20, 13-26, Self-Test Problem 1 First, let us assume there is enough land on each lot to provide space for bridge footings or for pier pilings, but not for both. In this case, the two plots of land represent assets that the two projects cannot share, which is the first factor making the bridge and the ferry mutually exclusive projects. Second, even if the land provided enough room to build both ferry landing piers and bridge footings, it stands to reason that no one would take the ferry if they could simply drive across the bridge—so the two projects’ inability to share a potential target market provides a second reason why the projects are mutually exclusive. ©Stockbyte/Getty Images To see the problems associated with choosing between two mutually exclusive projects using a rate-based decision statistic, let us suppose that we face a choice between two mutually exclusive projects with the cash flows shown in Table 13.9. ▼ TABLE 13.9 Sample Mutually Exclusive Projects Calculating the NPVs for these two projects across a range of possible rates as shown in Table 13.10 will yield the page 388 NPV profiles shown in Figure 13.3. As you can see approximately (and calculate precisely), A’s IRR equals 32.88 percent and B’s equals 40.59 percent. You will also notice that the two NPV profiles cross each other in the first quadrant, and that intersection is exactly what is going to cause problems for us as we try to apply an IRR decision rule. To see why, recall our discussion of the three-step decision process necessary for mutually exclusive projects, and go through that process for both NPV and IRR using a couple of not-so-arbitrary interest rates. ▼ TABLE 13.10 NPV Profiles First, let us suppose that the project would be subject to a 30 percent cost of capital. In that case, as per Table 13.11, the NPV for project A would be $29.47 and the NPV for project B would be $68.88. This means that project B would win the runoff. Since its NPV is greater than zero, the NPV decision rule would have us also accept project B. Likewise, if we were using IRR in the same situation, project B’s IRR of 40.59 percent would win the runoff over project A’s IRR of 32.88 percent. But since 40.59 percent is greater than the 30 percent cost of capital, IRR would also have us accept project B. These results appear in Table 13.11. Now let’s see what happens if the cost of capital is, say, 10 percent. In that case, as per Table 13.10, the NPV for project A would be $312.91 and the NPV for project B would be $276.63. This means that project A would now win the runoff and, ultimately, would be accepted under the NPV statistic as well. However, if we were using IRR in the same situation, project B’s IRR of 40.59 percent would still win the runoff over project A’s IRR of 32.88 percent, and since 40.59 percent is greater than the 30 percent cost of capital, IRR would continue to have us accept project B. These results are summarized in Table 13.12. Why is IRR still choosing project B, despite the 30 percent cost of capital? Well, IRR’s refusal to “change its mind”3 arises from a combination of how we calculate the statistic and how we use it in the three-step decision process. Think about it this way: The NPV statistic includes the cost of capital in its calculation, so when we get to the runoff, NPV is able to make an interest-rate-cognizant decision. IRR does not incorporate the cost of capital in calculating its statistic. Therefore, when it reaches step 2 it will always be comparing the same two IRRs for two particular projects, no matter what the cost of capital is. interest-rate cognizant A decision-making process that includes the cost of capital calculation. The implication here is that for any interest rate to the right of where the two NPV profiles cross, NPV and IRR will make the same accept/reject decision. For rates to the left of the crossover point, NPV will choose the right project but IRR will choose the wrong project. So, since it is sort of important, how do we calculate the rate at which the two NPV profiles cross? Well, we mathematically manipulate each NPV profile until one comes as close to the x- ▼ axis as possible, and then figure out the rate at which they cross each other as the IRR of the other project. FIGURE 13-3 NPV Profiles for Sample Mutually Exclusive Projects Notice how the two profiles cross each other in the first quadrant. How will this intersection affect how we apply an IRR decision? It sounds complicated, but it really is not. All we have to do is subtract one project’s cash flows from those of the other, period by period, to get a new set of cash flows that show the differences between the original two projects’ cash flows, and then find the IRR of these differences. The values for the cash flows of “A – B,” the calculated values for the NPV profile of these differences, and the resulting translated NPV profiles appear in Table 13.13, Table 13.14, and Figure 13.4. Note that A’ will be equal to “A – B,” while B’ will be the new, translated, x-axis. ▼ TABLE 13.11 Decision Process for Projects A and B at i = 30% NPV 1. Compute the statistic for each project. 2. Have a runoff between the mutually exclusive projects, choosing the one with the best statistic. 3. Compare the computed statistic for the winner of the runoff to the benchmark to decide whether to accept or reject. NPVA = $29.47 NPVB = $68.88 NPVB >
NPVA
NPVB > 0
IRR
1. Compute the statistic for each project.
2. Have a runoff between the mutually exclusive projects, choosing the one with the best statistic.
3. Compare the computed statistic for the winner of the runoff to the benchmark to decide whether to
accept or reject.
IRRA =
32.88%
IRRB =
40.59%
IRRB >
IRRA
IRRB > 30%
The crossover rate will be equal to the IRR of the “A − B” cash flows:

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So now, IRR will give us the correct answer for these two projects if i is greater than 18.56 percent, and will choose
exactly the wrong project if i is less than 18.56 percent.

▼ TABLE 13.12 Decision Process for Projects A and B at i = 10%
NPV
1. Compute the statistic for each project.
2. Have a runoff between the mutually exclusive projects, choosing the one with the best statistic.
3. Compare the computed statistic for the winner of the runoff to the benchmark to decide whether to
accept or reject.
NPVA =
$312.91
NPVB =
$276.63
NPVA >
NPVB
NPVA > 0
IRR
1. Compute the statistic for each project.
2. Have a runoff between the mutually exclusive projects, choosing the one with the best statistic.
3. Compare the computed statistic for the winner of the runoff to the benchmark to decide whether to
accept or reject.
IRRA =
32.88%
IRRB =
40.59%
IRRB > IRRA
IRRB > 10%
▼ TABLE 13.13 Difference in Cash Flows—Sample Mutually Exclusive Projects
Year: 0 1 2 3 4 5
Project A cash flows –$800 $600 $500 $ 40 $ 0 $200
Project B cash flows –400 250 200 250 50 100
A − B –400 350 300 210 –50 100
▼ TABLE 13.14 NPV Profile, A − B
i NPV, A − B
 0% $ 90.00
2 77.98
4 66.67
6 55.99
8 45.88
10 36.28
12 27.15
14 18.45
16 10.13
18 2.17

20 –5.45
22 –12.77
24 –19.81
26 –26.59
28 –33.12
30 –39.41
32 –45.49
34 –51.37
36 –57.06
38 –62.56
40 –67.89
You may have noticed that the set of “A – B” cash flows is not normal. How, then, can we feel comfortable using
IRR to calculate the crossover rate given that we have previously decided not to use IRR with non-normal cash
flows? Well, this is a special case: We knew that the two original projects’ cash flows were normal. So we
intuitively understood that their NPV profiles, while not exactly straight lines, at least sloped downward continually.
So, if two “almost straight” lines do cross, they are probably only going to cross once. That is, we expect only one
solution to the IRR problem for the “A – B” differences in cash flows.
Also notice that we have to worry about IRR giving incorrect decisions only if the NPV profiles cross in the so-
called first quadrant of the graph. If they cross outside this quadrant at a rate higher than both projects’ IRRs, then
we do not have to worry about problems with IRR choosing the wrong project. Any cost of capital high enough for
IRR to reject the project at the third step of the IRR decision process will also result in a negative NPV.4
time out!
13-7  Suppose two projects with normal cash flows, X and Y, have exactly the same required initial investment, but X has a
longer payback. Can we say anything about X’s IRR versus that of Y?
13-8 Assume you are evaluating a project that requires an initial investment of $5,000 at time zero, then another investment of
$4,000 in one year, after which it will have cash inflows of $3,000 per year for five years. How many IRRs could this project
possibly have?
MIRR Strengths and Weaknesses
As we have constructed it, the MIRR statistic explicitly corrects IRR’s faulty and unreasonable reinvestment rate
assumption, implicitly fixing any problems with non-normal cash flows along the way. However, it does not correct

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the problem of IRR choosing the wrong mutually exclusive project for a particular range of rates. For
example, even if we go back to the two sample mutually exclusive projects of Table 13.9 and compute
each project’s MIRR (using a 12 percent rate to move the cash flows), we will still see that the MIRR of project B
(23.39 percent) will always be greater than the MIRR of project A (18.85 percent), causing the MIRR to also choose
the incorrect project to the left of the crossover rate.
There is an old joke in computer programming that gets reused every time a major software product is revised:
“That’s not a bug, it’s a feature!” Well, this “problem” we are experiencing with IRR and MIRR, as well as NPV,
truly is a feature. It’s a feature of all rate-based decision statistics: They tend to focus on the rate of return per dollar
invested at the expense of ignoring how many dollars are getting invested in each project. IRR and MIRR chose
project B all the time because, even though it sometimes had a lower NPV, it was always earning a higher rate of
return per dollar invested.
FIGURE 13-4 Translated NPV Profiles
What causes this confusion? The two cash flows differ in timing and scale. Looking back at the cash flows
associated with our two mutually exclusive projects again (shown again in Table 13.15) we see that project B costs
only half as much as project A. Also, project B has a “flatter,” less steeply sloped, indifference curve.
▼ TABLE 13.15 Sample Mutually Exclusive Projects
Year: 0 1 2 3 4 5
Project A cash flows –$800 $600 $500 $40 $ 0 $200
Project B cash flows –400 250 200 250 50 100
13.7 • PROFITABILITY INDEX  LG13-6
Another popular rate-based decision technique is the profitability index (PI). PI is based upon NPV, so its results will
more closely resemble NPV than will those of IRR or PB/DPB. PI takes the present value of a project’s future cash
flows and standardizes them by simply dividing by the project’s initial investment. The result: We get a decision
statistic that measures “bang per buck invested.” Such a measure comes in handy when the firm faces resource
constraints concerning how much capital is available for new projects.
profitability index (PI) A decision rule and associated methodology for converting the NPV statistic into a rate-based metric.

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time out!
13-9 For a project with normal cash flows, what would you expect the relationship to be between its IRR and its MIRR?
13-10 Describe how you would go about calculating the IRR of a perpetuity.
Profitability Index Statistic
The mathematics of computing the PI are straightforward:
(13-10)
Profitability Index Benchmark
Because of its close linkage to the NPV statistic, PI’s benchmark is, not surprisingly, identical to that of NPV:
(13-11)

EXAMPLE 13-
8
Calculation of Profitability
Index LG13-6
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Turning yet again to the sample project cash flows in Table 13.6, the PI
for that project will be
Similar to Problems 13-13, 13-14, 13-22, 13-28
Though we might be tempted to assume that, like IRR and MIRR, we should compare the PI to the cost of capital,
this is not the case. Remember that the NPV already includes the necessary investment, so any PI above zero is
“found money” or the present value of expected economic profits. In this case, the PI of 1.23 is telling us that the
project will, roughly speaking, earn the equivalent of a 23 percent return on the initial investment of $10,000 above
and beyond the return necessary to repay the initial cost.
time out!
13-11 There is another version of the PI that uses the NPV as its numerator. How would you expect that version’s benchmark to
change from the version of PI we initially discussed?
13-12 Suppose you have a project whose discounted payback is equal to its termination date. What can you say for sure about
its PI? (Hint: What will the project’s NPV be?)

http://mhhe.com/CornettM4e

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Get Online
©JGI/Jamie Grill/Blend Images LLC.
Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. Is the set of cash flows depicted below normal or non-normal? Explain. (LG13-1)
Time: 0 1 2 3 4 5
Cash flow –$100 –$50 –$80 –$0 –$100 –$100
2. Derive an accept/reject rule for IRR similar to equation 13-8 that would make the correct decision on cash
flows that are non-normal, but which always have one large positive cash flow at time zero followed by a series
of negative cash flows. (LG13-1)
Time: 0 1 2 3 4 5
Cash flow + – – – – –
3. Is it possible for a company to initiate two products that target the same market that are not mutually exclusive?
(LG13-1)

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4. Suppose that your company used “APV,” or “All-the-Present Value-Except-CF0,” to analyze capital budgeting
projects. What would this rule’s benchmark value be? (LG13-3)
5. Under what circumstances could payback and discounted payback be equal? (LG13-2)
6. Could a project’s MIRR ever exceed its IRR? (LG13-4)
7. If you had two mutually exclusive, normal-cash-flow projects whose NPV profiles crossed at all points, for
which range of interest rates would IRR give the right accept/reject answer? (LG13-5)
8. Suppose a company wanted to double the firm’s value with the next round of capital budgeting
project decisions. To what would it set the PI benchmark to make this goal? (LG13-6)
9. Suppose a company faced different borrowing and lending rates. How would this range change the way that
you would compute the MIRR statistic? (LG13-4)

Problems
BASIC PROBLEMS
13-1 NPV with Normal Cash Flows Compute the NPV for Project M and accept or reject the project with the
cash flows shown below if the appropriate cost of capital is 8 percent. (LG13-3)
Project M
Time: 0 1 2 3 4 5
Cash flow –$1,000 $350 $480 $520 $600 $100
13-2 NPV with Normal Cash Flows Compute the NPV statistic for Project Y and indicate whether the firm
should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12
percent. (LG13-3)
Project Y
Time: 0 1 2 3 4
Cash flow –$8,000 $3,350 $4,180 $1,520 $300
13-3 NPV with Non-Normal Cash Flows Compute the NPV statistic for Project U and recommend whether
the firm should accept or reject the project with the cash flows shown below if the appropriate cost of
capital is 10 percent. (LG13-3)
Project U
Time: 0 1 2 3 4 5
Cash flow –$1,000 $350 $1,480 –$520 $300 –$100
13-4 NPV with Non-Normal Cash Flows Compute the NPV statistic for Project K and recommend whether
the firm should accept or reject the project with the cash flows shown below if the appropriate cost of
capital is 6 percent. (LG13-3)
Project K
Time: 0 1 2 3 4 5
Cash flow –$10,000 $5,000 $6,000 $6,000 $5,000 –$10,000
13-5 Payback Compute the payback statistic for Project B and decide whether the firm should accept or reject
the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the
maximum allowable payback is three years. (LG13-2)?

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Project B
Time: 0 1 2 3 4 5
Cash flow –$11,000 $3,350 $4,180 $1,520 $0 $1,000
13-6 Payback Compute the payback statistic for Project A and recommend whether the firm should accept or
reject the project with the cash flows shown below if the appropriate cost of capital is 8 percent and the
maximum allowable payback is four years. (LG13-2)
Project A
Time: 0 1 2 3 4 5
Cash flow −$1,000 $350 $480 $520 $300 $100
13-7 Discounted Payback Compute the discounted payback statistic for Project C and recommend
whether the firm should accept or reject the project with the cash flows shown below if the
appropriate cost of capital is 8 percent and the maximum allowable discounted payback is three years.
(LG13-2)
Project C
Time: 0 1 2 3 4 5
Cash flow –$1,000 $480 $480 $520 $300 $100
13-8 Discounted Payback Compute the discounted payback statistic for Project D and recommend whether the
firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is
12 percent and the maximum allowable discounted payback is four years. (LG13-2)
Project D
Time: 0 1 2 3 4 5
Cash flow –$11,000 $3,350 $4,180 $1,520 $300 $1,000
13-9 IRR Compute the IRR statistic for Project E and note whether the firm should accept or reject the project
with the cash flows shown below if the appropriate cost of capital is 8 percent. (LG13-4)
Project E
Time: 0 1 2 3 4 5
Cash flow –$1,000 $350 $480 $520 $300 $100
13-10 IRR Compute the IRR statistic for Project F and note whether the firm should accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 12 percent. (LG13-4)
 Project F
Time: 0 1 2 3 4
Cash flow –$11,000 $3,350 $4,180 $1,520 $2,000
13-11 MIRR Compute the MIRR statistic for Project I and indicate whether to accept or reject the project
with the cash flows shown below if the appropriate cost of capital is 12 percent. (LG13-4)
Project I
Time: 0 1 2 3 4

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Cash flow –$11,000 $5,330 $4,180 $1,520 $2,000
13-12 MIRR Compute the MIRR statistic for Project J and advise whether to accept or reject the project
with the cash flows shown below if the appropriate cost of capital is 10 percent. (LG13-4)
 Project J
Time: 0 1 2 3 4 5
Cash flow –$1,000 $350 $1,480 –$520 $300 –$100
13-13 PI Compute the PI statistic for Project Z and advise the firm whether to accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 8 percent. (LG13-6)
Project Z
Time: 0 1 2 3 4 5
Cash flow –$1,000 $350 $480 $650 $300 $100
13-14 PI Compute the PI statistic for Project Q and indicate whether you would accept or reject the project
with the cash flows shown below if the appropriate cost of capital is 12 percent. (LG13-6)
Project Q
Time: 0 1 2 3 4
Cash flow –$11,000 $3,350 $4,180 $1,520 $2,000
13-15 Multiple IRRs How many possible IRRs could you find for the following set of cash flows? (LG13-
1)
Time: 0 1 2 3 4
Cash flow –$11,000 $3,350 $4,180 $1,520 $2,000
13-16 Multiple IRRs How many possible IRRs could you find for the following set of cash flows? (LG13-
1)
Time: 0 1 2 3 4
Cash flow –$211,000 –$39,350 $440,180 $217,520 –$2,000
INTERMEDIATE PROBLEMS
Use this information to answer the next six questions. If a particular decision method should not be used,
indicate why.
Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate
of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted
payback statistics for the project are 3.5 and 4.5 years, respectively.
Time: 0 1 2 3 4 5 6
Cash flow –$5,000 $1,200 $2,400 $1,600 $1,600 $1,400 $1,200
13-17 Payback Use the payback decision rule to evaluate this project; should it be accepted or rejected?
(LG13-2)
13-18 Discounted Payback Use the discounted payback decision rule to evaluate this project; should it be
accepted or rejected? (LG13-2)
13-19 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected? (LG13-4)
13-20 MIRR Use the MIRR decision rule to evaluate this project; should it be accepted or rejected? (LG13-

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4)
13-21 NPV Use the NPV decision rule to evaluate this project; should it be accepted or rejected? (LG13-3)
13-22 PI Use the PI decision rule to evaluate this project; should it be accepted or rejected? (LG13-6)
Use this information to answer the next six questions. If you should not use a particular decision technique,
indicate why.
Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate
of return on projects of this risk class is 11 percent, and that the maximum allowable payback and discounted
payback statistics for your company are 3 and 3.5 years, respectively.
Time: 0 1 2 3 4 5
Cash flow –$235,000 $65,800 $84,000 $141,000 $122,000 $81,200
13-23 Payback Use the payback decision rule to evaluate this project; should it be accepted or rejected?
(LG13-2)
13-24 Discounted Payback Use the discounted payback decision rule to evaluate this project; should it be
accepted or rejected? (LG13-2)
13-25 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
(LG13-4)
13-26 MIRR Use the MIRR decision rule to evaluate this project; should it be accepted or rejected? (LG13-
4)
13-27 NPV Use the NPV decision rule to evaluate this project; should it be accepted or rejected? (LG13-3)
13-28 PI Use the PI decision rule to evaluate this project; should it be accepted or rejected? (LG13-6)
ADVANCED PROBLEMS
Use the project cash flows for the two mutually exclusive projects shown below to answer the following two
questions.
 Time Project A Cash Flow Project B Cash Flow
 0 –$725 –$850
 1  100  200
 2  250  200
 3  250  200
 4  200  200
 5  100  200
 6  100  200
 7  100  200
13-29 NPV Profiles Graph the NPV profiles for both projects on a common chart, making sure that you
identify all of the “crucial” points. (LG13-5)
13-30 IRR Applicability For what range of possible interest rates would you want to use IRR to choose
between these two projects? For what range of rates would you NOT want to use IRR? (LG13-5)
13-31 Multiple IRRs Construct an NPV profile and determine EXACTLY how many non-negative IRRs
you can find for the following set of cash flows: (LG13-5)
Time: 0 1 2 3 4 5 6 7
Cash flow –$200 $400 $150 –$100 –$100 –$300 $200 –$300
13-32 Multiple IRRs Construct an NPV profile and determine EXACTLY how many non-negative IRRs
you can find for the following set of cash flows: (LG13-5)

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Time: 0 1 2 3 4 5 6 7
Cash flow –$150 $275 $150 –$100 $300 –$300 $200 –$300

Notes
CHAPTER 13
1. As explained in earlier chapters, by definition the expected rate of return incorporates risk.
2. First described by René Descartes in his 1637 manuscript La Geometrie.
3. You will sometimes hear this phenomenon referred to as IRR being “myopic,” which is the technical name for nearsightedness.
4. Actually, in such cases the IRR rule will still choose the wrong project at step 2 of the decision process, the runoff, but the last step of
the decision process, the comparison with the benchmark, will save us. The wrong project may be chosen at the runoff, but if they are
both bad projects, they will be rejected anyway.

Part Seven

page 398
page 399

chapter fourteen
working capital
management and policies
©Stockbyte/Getty Images

I
page 400
n this chapter, we focus on the major trade-off implicit in funding net working capital. By and large, the
trade-off involves comparing the explicit costs of funding an investment in current assets with the
shortage costs associated with the firm not having enough cash, inventory, or accounts receivable.

shortage costs Costs associated with not having sufficient cash, inventory, or accounts receivable.
As we’ll see, the firm’s ideal solution to providing net working capital would be to get someone else to
foot the bill. Though this may be a valid approach to fund some of the firm’s current assets, it’s usually
difficult to get someone else to cover the entire amount of net working capital necessary to run the firm
efficiently. We will, however, discuss how to shift those costs elsewhere as much as possible in this
chapter by covering the following topics:
Depending on the firm’s line of business and the extent to which it provides physical goods versus
services, the management of portions of the current assets may come under a specialized department
responsible for the firm’s operations management. Though beyond the scope of this book, if you ever get a
chance to read about the models used in operations management, you’ll notice that many of the concepts
we’ll discuss here are directly related to the inventory management models used extensively in operations
management. For example, our discussion below of flexible, restrictive, and compromise financing of
current assets would fit right in with the concept of “just in time” (JIT) inventory management, while the
Baumol model we’ll be discussing for determining the target cash balance is a simple extension of the
Barabas Economic Order Quantity (EOQ) model for minimizing total inventory holding and ordering costs.
operations management The area of management concerned with designing and overseeing the process of production.
just in time (JIT) A production strategy that attempts to improve a firm’s return on investment by reducing in-process inventory and
associated carrying costs as much as possible.
Barabas Economic Order Quantity (EOQ) The inventory order quantity that minimizes total holding and ordering costs.
1. How to determine the optimal amount of investment in current assets.
2. How to measure the portion of current assets that the firm is responsible for funding.
3. How to choose the source of funding for that portion of current assets.
LEARNING GOALS
LG14-1 Set overall objectives of a good working capital policy.
LG14-2 Discuss how net working capital serves the firm.
LG14-3 Analyze the firm’s operating and cash cycles to determine what funding for current assets the firm needs.
LG14-4 Model the optimal trade-off between carrying costs and shortage costs that dictates the firm’s current asset investment.
LG14-5 Compare the flexible and restrictive approaches to financing current assets.
LG14-6 Differentiate among sources of short-term financing available for funding current assets.
LG14-7 Justify the firm’s need to hold cash.
LG14-8 Use the Baumol and Miller-Orr models for determining cash policy.
LG14-9 Identify sources of float and show how to control float for the firm’s disbursement and collection functions.
LG14-10 Identify firms’ choices for using excess cash.
LG14-11 Connect the firm’s credit terms and collection policy and the amount of capital the firm has invested in accounts receivable.
LG14-12 Be able to create and interpret a cash budget.

viewpoints
business APPLICATION

page 401
Chewbacca Manufacturing expects sales of $32 million next year. CM’s cost of goods sold normally runs at 55 percent of sales;
inventory requirements are usually 10 percent of annual sales; the average accounts receivable balance is one-sixth of annual sales;
and the average accounts payable balance is 5 percent of sales. If all sales are on credit, what will Chewbacca’s level of net working
capital and its cash cycle be? (See the solution at the end of the book.)
14.1 • REVISITING THE BALANCE-SHEET MODEL OF THE
FIRM LG14-1, 14-2
Recall our discussion of the balance sheet in Chapter 2. At a glance, the balance sheet brings together the firm’s
assets or sources of financing and its liabilities, or investments, as Table 14.1 shows. Net working capital reflects the
need for the firm to generate funds to stay in business and maximize profit.
▼ TABLE 14.1 The Basic Balance Sheet
 Total Assets Total Liabilities and Equity
 Current assets: Net working capital Current liabilities:
  Cash and marketable securities Accrued wages and taxes
  Accounts receivable Accounts payable
  Inventory Notes payable
 Fixed assets: Long-term debt
  Gross plant and equipment Stockholders’ equity:
  Less: Depreciation Preferred stock
 Net plant and equipment Common stock and paid-in surplus
 Other long-term assets Retained earnings

personal APPLICATION
Wanda has saved enough money to go back to grad school. She is planning to put the money in a money market account where it will
earn 3.5 percent. If she anticipates slowly drawing the money out over the course of her time in grad school at a constant rate of
$25,000 per year but is charged a commission of $9.95 every time she sells shares, how much should she take out of the mutual fund
at a time? (See the solution at the end of the book.)
Where else can you park your money . . . for less?
Earlier in the text, we discussed the fact that current assets, while the most liquid, are also usually less profitable
than fixed assets. Because of that, many managers view net working capital as a “necessary evil,” that is, as
something they have to fund, but would really rather not.
time out!
14-1 Why might a firm’s creditors not think of net working capital as a necessary evil, but rather as a good thing?
14-2 If demand for a firm’s products suddenly slows down so that inventory increases while sales decrease, how will the firm’s
needs for net working capital react?


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And they do have to fund it: Most firms can’t sell finished goods without inventory to display, or without offering to
sell to customers on credit, and so forth.
But just because a firm has to fund some current assets does not mean that it has to fund too much of it. Ideally, the
firm should invest in each type of current assets only up to the point where the marginal benefit of each dollar tied
up by doing so just equals the marginal opportunity cost of not having that dollar invested in fixed assets with positive
net present value (NPV).
opportunity cost The dollar cost or forgone opportunity of using an asset already owned by the firm, or a person already employed by
the firm, in a new project.
Also, the firm normally is able to shift part of the burden of funding current assets through the judicious use of
current liabilities. While we normally think of liabilities as the “bad” entries (compared to assets) on a balance sheet,
from a cash flow perspective they actually act as sources of capital, while assets represent, in a sense, “money pits”
that require us to use capital to fund them. To the extent that the firm can partially offset the capital they have tied
up in necessary current assets by buying from suppliers on credit, or by getting employees to work for them in
advance of getting paid, such accounts payable or accrued wages are actually good things.
This line of reasoning helps explain why some managers like to think of net working capital as “the net amount of
current assets that the firm has to fund, above and beyond those that someone else funds for us.”
14.2 • TRACING CASH AND NET WORKING CAPITAL LG14-
3
To trace cash flows through the firm’s operations, we must measure the operating cycle—the time necessary to
acquire raw materials, turn them into finished goods, sell them, and receive payment for them—as well as the firm’s
cash cycle.
operating cycle The time required to acquire raw materials and to produce, sell, and receive payment for the finished goods.
cash cycle The operating cycle minus the average payment period.
If we continue in the vein of thinking of net working capital as the portion of current assets that the firm must fund
(above and beyond those assets funded by current liabilities), then we can similarly think of the firm’s cash cycle as
the portion of the operating cycle that the firm must finance.
FIGURE 14-1 Relationship between Operating and Cash Cycles
The firm’s cash cycle will simply be the operating cycle minus the average payment period.

The Operating Cycle
To measure the firm’s operating cycle, we need to turn to some of the ratios that we discussed in Chapter 3:

(14-1)
The Cash Cycle
The firm’s cash cycle will simply be the operating cycle minus the average payment period as shown in Figure 14.1.
Translating this into a formula yields
(14-2)
time out!
14-3 How will a firm affect its operating cycle if it can reduce inventory on hand?
14-4 When we compare two firms, will the one with the longer cash cycle tend to have more or less net working capital
requirements than the one with a shorter cash cycle, everything held equal? Why?
Note that even though it will take MMK almost 120 days to turn the raw materials into cash, the cash cycle indicates
that the firm will have to foot the bill for its production cycle for only 52.50 days of that time. This is the crux of
managing the firm’s operating and cash cycles: Minimize the number of days that the firm has to pay for its
production cycle.
EXAMPLE 14-
1
Calculation of Operating
Cycle LG14-3
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Suppose that MMK Industries has annual sales of $1 million, cost of
goods sold of $650,000, average inventories of $116,000, and average
accounts receivable of $150,000. Assuming that all MMK’s sales are on
credit, what will be the firm’s operating cycle?
SOLUTION:
The operating cycle will be equal to
So it will take MMK almost 120 days from the time it receives raw
materials to produce, market, sell, and collect the cash for the finished
goods.

http://mhhe.com/CornettM4e

page 403
Similar to Problems 14-13, 14-14

EXAMPLE 14-
2 Calculation of Cash Cycle LG14-3
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Extending the previous example, assume that MMK’s average
accounts payable balance is $120,000. What will be the firm’s cash
cycle?
SOLUTION:
The cash cycle will be equal to
Similar to Problems 14-15, 14-16
14.3 • SOME ASPECTS OF SHORT-TERM FINANCIAL
POLICY LG14-4
In the last section, we derived the cash cycle by first determining the operating cycle and then subtracting the
payment cycle. This derivation suggests two obvious ways that firms can reduce their net working capital needs.
1. They can reduce their cash cycle by managing their need for current assets.
2. They can extend the payment cycle by seeking to obtain as many current liabilities as economically feasible to fund the current assets
that they do need.
The Size of the Current Assets Investment
Choosing the optimal level of investment in each current asset type involves a trade-off between carrying costs and
shortage costs.
Carrying costs are associated with having current assets and fall into two general categories:
carrying costs The opportunity costs associated with having capital tied up in current assets instead of more productive fixed assets
and explicit costs necessary to maintain the value of the current assets.
1. The opportunity costs associated with having capital tied up in current assets instead of more productive fixed assets.
2. Explicit costs necessary to maintain the value of the current assets.
For example, a car dealer who purchases used vehicles and keeps them in inventory would incur not only the
opportunity cost of not being able to invest the money paid for the used vehicles in a more lucrative opportunity,

http://mhhe.com/CornettM4e

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such as new hybrid vehicles, but would also incur explicit costs consisting of rental or lease payments on the piece
of property where the used cars are on display and any maintenance costs necessary to keep the cars ready to sell.
Shortage costs are the costs associated with not having enough current assets and can include opportunity costs such
as sales lost due to not having enough inventory on hand, as well as any explicit transaction fees paid to replenish
the particular type of current asset. For example, consider a camera shop that has a policy to reorder particular lenses
from its supplier only if a customer comes in asking for them, and, even then, to order only one lens at a time. In
today’s business environment, most customers who are seeking an item want it now. If that item is out of stock at
one store, the customer will probably buy it either at another store or online, resulting in lost sales to the store. If, in
addition, we assume that stores pay a shipping fee for every order placed—or that they get quantity discounts if they
order in bulk—then the camera shop’s current policy will probably result in higher shipping fees and missed volume
discounts.

finance at work //: investments
Kaizen ( )
Kaizen is a Japanese approach to productivity improvement that aims to eliminate waste through just-in-time delivery, standardized work
and equipment, and so on. The five basic elements of kaizen are
1. Teamwork
2. Personal discipline
3. Improved morale
4. Quality circles
5. Suggestions for improvement
Studies show that the kaizen approach can reduce (sometimes dramatically) net working capital requirements, with businesses
adopting the approach reporting reductions in finished-goods and in-process inventory of anywhere from 10 to 30 percent.
©master_art/Shutterstock
Want to know more?
Key Words to Search for Updates: The article “Off the shelf: Low inventories drove down working capital last year. But will that
continue as the economy improves?” (www.cfo.com)
Carrying costs will increase, and shortage costs will decrease, as a firm buys more of any particular asset. Therefore,
firms should ideally try to choose the point of an asset’s lowest total cost, which occurs where marginal carrying and
shortage costs are equal. This level is identified as CA* in Figure 14.2.
Alternative Financing Policies for Current Assets LG14-5

http://www.cfo.com



In a perfect world, a firm would use long-term debt and equity to finance long-term (i.e., fixed) assets and short-term
debt to finance current assets. Such an approach would allow the firm to maturity-match assets with their
corresponding liabilities, resulting in a low or nonexistent level for net working capital. As we have previously
discussed, in the real world, net working capital is usually positive for most firms. The implication: At least some
portion of current assets must be financed with long-term debt, equity, or a mixture of both.
Vehicles kept in inventory incur an opportunity cost.
©Comstock Images/Jupiter Images
Assuming that most firms can expect to have some steady, stable need for current assets throughout their calendar
year and additional demand for current assets that fluctuates on some seasonal cycle, a growing firm’s total demand
for assets would resemble that shown in Figure 14.3.
So, a firm in such a situation faces the basic question of whether it should finance the peaks or the valleys of total
asset demand (or somewhere in between) using long-term financing. Figure 14.4, 14.5, and 14.6 illustrate some of
these choices.
FIGURE 14-2 Carrying and Shortage Costs
The point at which marginal carrying and shortage costs are equal (CA) is the optimal level of investment for each current asset category.
FIGURE 14-3 Components of Current Assets

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A firm makes long- or short-term financing decisions by examining the peaks and valleys of total asset demand.
We usually refer to the decision to finance the peaks of asset demand with long-term debt and equity,
shown in Figure 14.4, as a flexible financing policy. It provides the firm with a surplus of cash and
marketable securities most of the time—except during peak asset demand.
On the opposite side of the continuum, we refer to a decision to finance the troughs or valleys of asset demand with
long-term debt and equity, shown in Figure 14.5, as a restrictive financing policy. Under this policy, the firm will
have to seek short-term financing for all peak demand fluctuations for current assets, as well as for in-between
demand situations. In some ways, this policy is the most “conservative”; on the other hand, it’s also the least
convenient for the firm, as it involves seeking some level of short-term financing almost all of the time.
FIGURE 14-4 Flexible Financing of Current Assets
Flexible financing policy reflects the decision to finance the peaks of asset demand with long-term debt and equity.
FIGURE 14-5 Restrictive Financing of Current Assets

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Restrictive financing policy reflects the decision to finance the troughs of asset demand with long-term debt and equity.
A third choice is to follow a compromise financing policy, wherein the firm finances the seasonally
adjusted average level of asset demand with long-term debt and equity. The firm uses both short-term
financing and short-term investing as needed. Figure 14.6 illustrates such a policy.
Which approach works best? As is the case with almost all working capital decisions, it depends on several factors:
Current and future expected interest rate levels. If we expect rates to rise in the future, the firm may want to lock in fixed rates for a longer
time by shifting toward a flexible financing policy. With falling rates, the opposite would of course hold true.
The spread between short-and long-term rates. Long-term borrowing usually costs more than short-term financing, but the “gap” (called
the spread) between the two terms may be historically small or large, encouraging firms to shift to a more flexible or restrictive
policy, respectively.
Alternative financing availability and costs, discussed in the following sections. Firms with easy and sustained access to alternative
sources will want to shift toward more restrictive policies.
FIGURE 14-6 Compromise Financing of Current Assets
Compromise financing policy reflects the decision to finance the seasonally adjusted average level of asset demand with long-term debt and
equity.

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time out!
14-5 Suppose that the gap between short-term rates and long-term rates increases. Would firms tend to shift more toward
flexible current asset financing policies or toward more restrictive policies?
14-6 If a firm offers longer credit terms to its customers, what will happen to its carrying costs?
14.4 • THE SHORT-TERM FINANCIAL PLAN LG14-6
Firms that follow any financing policy other than a flexible financing plan will find themselves forced to seek short-
term financing at times. Depending on their industry, they may find themselves using unsecured loans, secured
loans, or other sources of short-term financing.
Unsecured Loans
For most businesses—particularly smaller ones—the most common way to cover a short-term financing need is to
apply at a bank for a commercial loan. The company may expect to need such short-term loans repeatedly in the
future—perhaps because it is following a restrictive financing policy but faces seasonal fluctuations in asset
demand, as discussed previously. If the bank deems the firm creditworthy enough, the bank will usually grant the
firm a line of credit, upon which the firm can draw and then pay off repeatedly as the firm goes through those
seasonal fluctuations.
Fees for lines of credit can be both explicit (usually taking the form of an interest rate equal to the bank’s prime
lending rate plus a small premium) and implicit (as a compensating balance requirement and/or a bank’s up-front
commitment fee). A compensating balance is a percentage of the borrowed money (usually 5 to 10 percent) that the
bank requires the firm to keep on deposit in the firm’s bank accounts. In return, the bank agrees to lend money to the
firm.1
compensating balance Amount of money required to be kept in a firm’s deposit accounts with a lender according to a lending
arrangement.
Commitment fees, if charged, are usually calculated as a flat percentage of the credit line. But banks also
charge commitment fees based on the portion of the line of credit “taken down” (i.e., used by the firm) or
even of the portion not taken down. The amount of fees the bank charges for a line of credit and their type will
depend on whether the bank is trying to encourage the use of the line of credit or not.
Firms can also use their inventory as collateral for an inventory loan.
©Brand X Pictures/Punchstock
Secured Loans

Asset-based loans are short-term loans secured by a company’s assets. Secured loans carry lower interest rates than
unsecured loans, so it is usually in the firm’s best interest to provide security (or collateral) when it can. Though real
estate, accounts receivable, inventory, and equipment are all sometimes used to back asset-based loans, most firms
seeking such a loan to finance seasonal fluctuations in current assets will typically prefer to use inventory or
accounts receivable as security for the loan, as they won’t wish to encumber long-term assets such as real estate or
equipment.
asset-based loans Short-term loans secured by a company’s assets.
Accounts receivable can either be sold outright to a factor or assigned. A factor is an entity who will buy accounts
receivable on a discounted basis before they are due, with the spread between the discounted price and the
receivable’s face value providing the factor with expected compensation for both the time value of money and the
expected level of defaults among the accounts receivable. Assignment is a process whereby the firm borrows money
from another entity, providing in return a lien on the accounts receivable as well as the right of recourse (i.e., the
legal right to hold the firm responsible for payment of the debt if the accounts receivable debtors do not repay as
promised).
factor An entity that will buy accounts receivable from a firm before they are due on a discounted basis.
assignment A voluntary liquidation proceeding that passes the liquidation of the firm’s assets to a third party that is designated as the
assignee or trustee.
recourse The legal right to hold a firm responsible for payment of a debt if the debtors do not repay as promised.
Firms can also use their inventory as collateral for an inventory loan, a secured short-term loan used to purchase that
inventory. Inventory loans include blanket inventory liens, trust receipts, and field warehousing financing. The
major difference between the three lies with the question of who owns and keeps the inventory in question:
Under a blanket inventory lien, the lender gets a lien against all the firm’s inventory, but the firm retains ownership and possession.
When the borrower holds the inventory in trust for the lender, with any proceed from the sale of the inventory being the property of that
lender, the document acknowledging this loan commitment is referred to as the trust receipt.
In field warehousing financing, a public warehouse company takes possession and supervises the inventory for the lender.
time out!
14-7 If its bank started charging fees to a firm based upon the portion of a line of credit not taken down, how would the firm’s
financing policy for current assets likely change? Why would a bank take such a stance?
14-8 If a firm starts selling its accounts receivable to a factor, how will the firm’s cash cycle change?
Other Sources
Two other primary sources of short-term financing are commercial paper issues and financing through banker’s
acceptances. Commercial paper is a money-market security, issued by large banks and medium-to-large corporations,
that matures in nine months or less. Since these issues have such short durations, and since firms use the proceeds
only for current transactions, commercial paper (or simply paper) is exempt from registering as a security with the
SEC. The corresponding lack of paperwork and regulations to issue short-term debt, along with the fact that
commercial paper is usually issued only by firms with very high credit rankings, makes commercial paper cheaper
than using a bank line of credit.
commercial paper An unsecured short-term promissory note issued by a public firm to raise short-term cash, often to finance working
capital requirements.
A banker’s acceptance (BA) is a short-term promissory note issued by a corporation, bearing the unconditional
guarantee (acceptance) of a major bank. The bank guarantee makes them very safe, and the rates are usually roughly
equivalent to those charged on commercial paper.
banker’s acceptance (BA) A short-term promissory note issued by a corporation, bearing the unconditional guarantee (acceptance) of

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a major bank.

14.5 • CASH MANAGEMENT LG14-7
One common source of confusion when we’re discussing net working capital is the difference between a cash flow
and a cash account. Cash flows, which we have discussed in a number of contexts within this book (such as
estimating cash flows for proposed new projects in Chapter 12) are a good thing. A cash account, on the other hand,
is a current asset account just like all the other current asset accounts we have been discussing, and it has exactly the
same attributes of high liquidity and low profitability that inventory and accounts receivable accounts have: i.e., it is,
relatively speaking, a bad thing from a cash flow perspective.
Reasons for Holding Cash
A firm may keep part of its capital tied up in cash for three primary reasons:
1. Transaction facilitation: Firms need cash to pay employees’ wages, taxes, suppliers’ bills, interest on debts, and stock dividends.
Though the firm will have cash coming in from day-to-day operations and any financing activities, the inflows and outflows are not
usually perfectly synchronized, so the firm will need to keep enough cash on hand to meet reasonable transaction demands.
2. Compensating balances: As we previously discussed, firms must often keep a certain percentage of borrowed funds in their checking
accounts with their lending institution. Since lenders are exempt from paying interest on corporate checking accounts, compensating
balances become a cheap source of funds for the lender and represent opportunity costs for borrowing firms.
3. Investment opportunities: In some industries, investment opportunities come and go very quickly. Sometimes, this happens even too
quickly for the firm to arrange a loan or seek other financing, so having excess cash on hand may allow the firm to take advantage of
investment opportunities that would otherwise be impossible to transact.
transaction facilitation The use of cash to pay employees’ wages, taxes, suppliers’ bills, interest on debts, and dividends on stock.
To determine how much cash to keep on hand, firms must trade off the opportunity costs associated with holding too
much cash against the shortage costs of not holding enough. The two standard models for calculating the trade-offs
are the Baumol Model and the Miller-Orr Model.

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Firms need cash to pay employees’ wages and payroll taxes among other things.
©Stockbyte/Punchstock
Determining the Target Cash Balance: The Baumol Model LG14-8
An economist named William Baumol developed the first model designed to minimize the sum of the opportunity
costs associated with holding cash and the trading costs associated with converting other assets to cash.2 Baumol’s
model is intuitively appealing, and analysts still use it in industries for which cash outflows are fairly predictable.
For other industries, its use is more problematic due to the model’s rather unrealistic assumptions:
The model assumes that the firm has a constant, perfectly predictable disbursement rate for cash. In reality, disbursement rates are much
more variable and unpredictable.
The model assumes that no cash will come in during the period in question. Since most firms hope to make more money than they pay
out, and usually have cash inflows at all times, this assumption is obviously at odds with what we usually see.
The model does not allow for any safety stock of extra cash to buffer the firm against an unexpectedly high demand for cash.
safety stock Excess amounts of a current asset kept on hand to meet unexpected shocks in demand.
In Baumol’s model, cash is assumed to start from a replenishment level, C, and then decline smoothly to a
value of zero. When cash declines to zero, it can be immediately replenished by selling another C worth of
marketable securities, for which the firm has to pay a trading cost of F.
replenishment level The level to which the cash account is ”refilled” when marketable securities are sold to recapitalize it.


time out!
14-9 In what types of industries would firms need more cash on hand for transaction facilitation? In what industries might firms
need less?
14-10 If a firm is going to take a loan with a bank that has a compensating balance requirement, how does that affect the
amount of money the firm must borrow?
Thus the model implies that cash levels will follow a cyclical pattern throughout the year. For example, if a firm
sells $20,000 worth of marketable securities each time it needs to replenish cash and disburses $5,000 in cash each
week, then the cash balance would cycle every four weeks, as shown in Figure 14.7.
Notice another implication of the cash being disbursed at a constant rate. The average cash level should equal one-
half of the replenishment level, C/2. If the firm can earn an interest rate i on marketable securities, then keeping an
average cash balance of C/2 will impose an opportunity cost on the firm of
(14-3)
If we also assume that a particular firm faces an annual demand for cash of T, then the firm will need to sell
marketable securities T/C times during the year, incurring in the process annual trading costs of
(14-4)
The firm’s total annual costs associated with its cash management policy will therefore be
(14-5)
Solving this for the value of C that minimizes annual costs, C*, yields
(14-6)
Determining the Target Cash Balance: The Miller-Orr Model
The Miller-Orr model takes a different approach to calculating the optimal cash management strategy.3 It assumes
that daily net cash flows are random but normally distributed, and allows for both cash inflows and outflows. This
model bases its computations on information about
FIGURE 14-7 Cash Flow Patterns of the Baumol Model

page 411
In this model, when cash declines to zero, it can be immediately replenished by selling marketable securities.

EXAMPLE 14-
3
Optimal Cash Replenishment
under Baumol Models LG14-8
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Suppose that AFS Industries faces an annual demand for cash of $2
million, incurs transaction costs of $150 every time it sells marketable
securities, and can earn 6 percent on its marketable securities. What
will be the firm’s optimal cash replenishment level?
SOLUTION:
The optimal cash replenishment level will be
Similar to Problems 14-19, 14-20, Self-Test Problem 4
The lower control limit, L.
The trading cost for marketable securities per transaction, F.
The standard deviation in net daily cash flows, σ.
The daily interest rate on marketable securities, iday.
Using their model, Miller and Orr show that the optimal cash return point, Z*, and upper limit for cash balances, H*,
are equal to
(14-7)
(14-8)

http://mhhe.com/CornettM4e

page 412
Note that the firm determines L, and that the firm can set it to a non-zero number to recognize the use of safety
stock.
The optimal cash return point, Z*, is analogous to the replenishment level, C*, in Baumol’s model, but with one key
difference. Since Baumol’s model only allowed for cash disbursements, C* was always “replenished to” from a
level of zero. In the Miller-Orr model, Z* will be the replenishment level to which cash is replenished when the cash
level hits L, but it will also be the return level that cash is brought back down to when cash hits H*.
As Figure 14.8 shows, the firm will reduce cash to $126,101.72 by buying marketable securities when the cash
balance gets up to $178,305.16, and it will increase cash to $126,101.72 by selling marketable securities when the
cash balance gets down to $100,000.
Other Factors Influencing the Target Cash Balance
Even the Miller-Orr model, the more realistic of the two models because it deals with both cash inflows and
outflows, still ignores fundamental factors that influence firms’ cash management practices. First, firms also have
the option of borrowing short term to meet unexpected demands for cash. Though the short-term borrowing rate
faced by the firm is likely to be more expensive than the opportunity cost incurred by selling marketable securities,4
this isn’t necessarily the comparison that matters. If the probability of an unexpected demand for cash causing a firm
to borrow in the short term is low enough, or if the amount of interest to be earned by investing in longer-term
securities is sufficiently higher than that to be earned on marketable securities, then it might be worth it for the firm
to risk occasionally paying a relatively high interest rate on short-term borrowing if it can earn a substantially higher
return by investing the funds that would have been tied up in marketable securities in something more lucrative.

EXAMPLE 14-
4
Calculation of Optimal Return
Point and Upper Limit for the
Miller-Orr Model LG14-8
For interactive versions
of this example, log in
to Connect or go to
mhhe.com/CornettM4e.
Suppose that Dandy Candy, Inc., would like to maintain its cash
account at a minimum level of $100,000 but expects the standard
deviation in net daily cash flows to be $5,000; the effective annual rate
on marketable securities will be 8 percent per year, and the trading cost
per sale or purchase of marketable securities will be $200 per
transaction. What will be Dandy Candy’s optimal cash return point and
upper limit?
SOLUTION:
The daily interest rate on marketable securities will equal
And the optimal cash return point and upper limit will equal

http://mhhe.com/CornettM4e

Assuming the random cash balances shown below, Dandy Candy
would buy or sell securities to make adjustments as indicated:
Day
Cash Balance
before
Adjustment Adjustment
Cash after
Adjustment
1 $177,025.21 $177,025.21
2 $158,965.54 $158,965.54
3 $162,488.16 $162,488.16
4 $183,466.74 −
$57,365.02
$126,101.72
5 $132,548.06 $132,548.06
6 $129,816.11 $129,816.11
7 $103,709.38 $103,709.38
8 $77,229.23 $48,872.49 $126,101.72
9 $121,483.60 $121,483.60
10 $109,309.78 $109,309.78
11 $81,609.28 $44,492.44 $126,101.72
12 $128,636.69 $128,636.69
13 $102,121.84 $102,121.84
14 $125,376.66 $125,376.66
15 $145,025.00 $145,025.00
16 $142,320.22 $142,320.22
17 $166,501.15 $166,501.15
18 $191,226.65 −
$65,124.93
$126,101.72


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19 $119,127.54 $119,127.54
20 $109,377.65 $109,377.65
21 $80,841.15 $45,260.57 $126,101.72
22 $125,476.90 $125,476.90
23 $114,416.24 $114,416.24
Similar to Problems 14-21, 14-22, 14-23, 14-24, Self-Test Problem 5
FIGURE 14-8 Cash Flow Patterns of the Miller-Orr Model
The model assumes that the distribution of daily net cash flows is normally distributed and allows for both cash inflows and outflows.
Second, the authors of both models developed their ideas when buying and selling marketable securities
was a relatively expensive and time-consuming proposition. The costs and delays of trading securities have
fallen dramatically since the advent of the Internet. The cost has fallen so much since then that many large firms
now habitually use all or the majority of their available cash to purchase overnight securities. If trading costs are low
enough that it makes sense for the firm to incur at least two sets of trading costs each day—one for selling enough
marketable securities in the morning to make it through the day, and another for purchasing marketable securities at
the end of the business day—then it’s also probable that any unforeseen demand for cash during the day can
probably be met fairly cheaply by selling marketable securities as needed. Or, put another way, the transactions
costs associated with trading securities have fallen so dramatically relative to the opportunity costs of not having
cash invested in marketable securities that keeping any “extra” money idle in cash just doesn’t make sense.
Finally, both models ignore the fact that many firms must keep compensating balances in their deposit accounts as
part of borrowing agreements with their banks. If the compensating balance requirement was a constant amount or
percentage, then we could adjust the Miller-Orr model so that L included the compensating balance, but many firms
must only keep a certain minimum compensating balance on average. This implies that an unforeseen demand for
cash that causes a firm’s deposit account to temporarily dip below the minimum compensating balance can be offset
by keeping a corresponding amount of excess cash in the account in a later period. Even the more modern Miller-
Orr model does not allow for that.


page 414
time out!
14-11 What effect does increasing the standard deviation in daily cash flows have on the cash return point in the Miller-Orr
model?
14-12 If you were asked to adjust the Baumol model to reflect the need to keep a minimum cash balance, how would you go
about doing so?
14.6 • FLOAT CONTROL: MANAGING THE COLLECTION
AND DISBURSEMENT OF CASH LG14-9
The economic definition of cash includes undeposited checks, but as we all know, an undeposited check is not as
liquid as the same amount of cash sitting inside your checking account. So another component of a good cash
management policy involves making sure that checks clear in a timely manner.
FIGURE 14-9 Components of Collection Float
Cash is not always liquid due to collection float.

Accelerating Collections
The period of time between when a check is written and when it clears and the funds are available for use is referred
to as float. The checks sent to a firm experience three different types of collection float, illustrated in Figure 14.9:
float The period of time between when a payment is sent out and when the money is actually received by the collecting firm.
1. Mail float is the length of time that checks are en route to the firm, either through the postal system or through some sort of electronic
transfer.
2. In-house processing float is the length of time needed for the firm to process and deposit check payments from its customers once
they have been received.
3. Availability float is the length of time necessary for a check to clear through the banking system once it has been deposited.
Together, these three types of float span the entire length of time between the customer sending a payment and the
firm receiving cash in its account. Several different techniques can help firms reduce collection float:
A lockbox system is a collection of geographically dispersed post office boxes, each maintained for the firm by a bank local to the
respective box. For firms with hundreds or thousands of customers spread across a large region, the ideal situation is to have enough
locations so that no customer is more than a couple of hundred miles from one of the firm’s post office boxes. By having customers send
their payments to the closest post office box, and then having the local bank pick up and handle the payment processing several times a
day, the firm can reduce both mail float and in-house processing float.
Concentration banking accelerates cash collections from customers by having funds sent to several geographically situated regional banks
and then transferred to a main concentration account in another bank. The funds can be transferred through depository transfer checks
and electronic transfers.
Wire transfers are the fastest way of transmitting money from a local bank into the concentration bank. Banks within the United States
utilize the Society for Worldwide Interbank Financial Telecommunication (SWIFT) system to make payments to banks in countries outside
of the United States. Bank-to-bank transfers conducted within the United States take place over the Fedwire system, which uses the
Federal Reserve System and its assignment of bank routing numbers.
Delaying Disbursements
Disbursement float is the delay between the firm sending out a payment and the money being taken out of the firm’s

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bank account. Two legal ways to increase disbursement float involve keeping the cash available to the firm until the
very last moment:
A zero-balance account is a checking account that the firm sets up so that the bank agrees to automatically transfer funds from an
interest-bearing account to pay off any checks presented. Since zero-balance accounts never contain excess cash, they represent one
way that firms can get around regulations against corporations having interest-bearing checking accounts.
Drafts resemble checks, but differ in that they are payable by the firm issuing them rather than payable by a bank. When a draft is sent to
the firm’s bank for payment, the bank must present the draft to the firm before disbursing the funds.
zero-balance account A corporate checking account which keeps a zero balance, automatically transferring in just enough funds to
cover any checks received on the account from another interest-bearing account.
draft Similar to a check, but payable by the issuing firm rather than by its bank.
The period of time between when a check is written and when it clears is referred to as float.
©iStockPhoto/Getty Images

finance at work //: global
Cultural Differences in Preferences for Paying Bills
Japan’s Postal Savings Bank, the world’s largest bank, has long been used as an example of the efficiencies available to both
individuals and businesses of electronic transactions. Electronic transactions are instantaneous transactions that use security
authentication rather than conventional check-clearing processes to transfer funds from a buyer to the seller.
However, in 2006, one of the Nikkei trade papers summarized the results of a survey among Japanese women regarding payment
methods used for Internet shopping. Not surprisingly, the vast majority (56 percent) of respondents purchasing goods over the Internet
reported that they used credit cards for their transactions. However, the distribution of the rest of the responses illustrates a vast
difference between alternative payment pipelines that American and Japanese consumers use.
For example, 17.6 percent of Japanese respondents ordered online, then paid in cash at their local convenience store; 13.1 percent
paid COD when the mailman delivered the goods; and 4.3 percent paid using electronic transfers from their post office savings accounts.
Though there is some anecdotal evidence that the usage of credits cards has increased slightly since 2006, the use of such
alternative methods of payment in Japan is still much higher than we see elsewhere in the world.

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©Markus Gann/EyeEm/Getty Images
What implications does this have for the money management policies of firms doing business in Japan? Well, given that a far larger
percentage of Americans probably pay for their online purchases with credit cards, and that the alternative methods of payment listed
previously could be expected to have different clearing times than do payments received through a merchant’s credit card account, it’s
something that firms seeking to do business in Japan should consider.
Want to know more?
Key Words to Search for Updates: “Marketing Tip: Payment Methods” (see the Japan Marketing News blog at
www.japanmarketingnews.com)
Ethical and Legal Questions
Using collected cash before actually receiving it, or continuing to use disbursed cash after you have sent a check out,
can earn your firm higher returns, but this practice is illegal. The most extreme form of taking illegal advantage of
disbursement float is a practice called check kiting, which is any sort of fraud that involves drawing out money from
a bank account with insufficient funds to cover the check.
The Check Clearing for the 21st Century Act, which allows for transmitting electronic images of checks rather than
the physical paper checks themselves, has greatly reduced the incidence of check kiting by substantially shortening
the time required for a check to be cleared from one bank to another.
time out!
14-13 In Japan, many consumers pay their bills by electronic deduction from their checking accounts instead of using paper
checks. What effect do you think this has on the collection float of Japanese firms versus that of American firms?
14-14 What’s the difference between a lockbox system and concentration banking?
14.7 • INVESTING IDLE CASH LG14-10
As both the Baumol and Miller-Orr models imply, firms habitually move cash into and out of marketable securities
in order to partially offset the opportunity costs of having capital tied up in current assets. Most large firms will
manage their marketable securities investments themselves. Smaller firms will typically invest through an
independently managed money-market fund or by letting their bank transfer all available excess funds at the end of
each business day into a sweep account, which will then be invested on their behalf.

Why Firms Have Surplus Cash

http://japanmarketingnews.com

Firms tend to have surplus cash available either due to seasonal fluctuations in their cash flow patterns, or in
preparation for planned expenditures. Seasonal fluctuations in the amount of cash on hand can occur as a result of
either cyclical sales or cyclical purchases of raw materials. For example, a firm that produces swimming pool
accessories will obviously experience higher sales from spring through late fall, and a firm that distributes fresh
vegetables purchased on the spot market will have higher cash outflows during the harvest season.
Firms’ cash balances may also temporarily increase immediately prior to a planned expenditure, either because they
have been “saving up” for the expenditure, or because they issued stocks or bonds in advance of the expenditure but
need someplace to “park” the funds until they are needed.
time out!
14-15 Should a firm with nonseasonal cash flows that lacks any good prospective investments keep excess cash on hand? Why
or why not?
14-16 Suppose a firm has a temporary surplus of cash meant to fund an upcoming expansion project. Why might it not wish to
invest these funds in capital-market (as opposed to money-market) securities?
What to Do with Surplus Cash
As mentioned, firms usually put surplus cash into money-market securities. These include Treasury bills, federal
funds and repurchase agreements, commercial paper, negotiable certificates of deposit, and banker’s acceptances.
14.8 • CREDIT MANAGEMENT LG14-11
As is the case with the firm’s cash management policy, the firm’s optimal credit policy will trade off the opportunity
cost of lost sales (if the firm does not grant credit or is too conservative in terms of the credit it does grant) against
the carrying costs associated with funding the accounts receivable plus the expected costs of default on the accounts
receivable.
Credit Policy: Terms of the Sale
As a minimum, the credit terms of sale usually contain at least the credit period, the cash discount, and a description
of the type of credit instrument. The credit period is the maturity of the credit that the firm is willing to extend,
which varies based on attributes of the goods being sold and the customer purchasing the goods. For example,
perishable goods will usually carry a lower credit period, regardless of who is purchasing them. Creditworthy,
established customers will probably be given better credit terms than customers the firm has not dealt with before.
credit terms A listing of the credit period, the cash discount, and the type of credit instrument to be used.
To encourage early repayment, firms will often offer a percentage discount if the bill is paid within a certain time
period. For example, a firm that quotes customers terms of “2/10, net 30” is offering them the choice between
paying the entire bill within 30 days or taking a 2 percent discount off the invoiced price if they pay within 10 days.
For most trade credit, the invoice is the only type of credit instrument involved. When the customer signs a copy
upon receipt of the goods, the customer makes an implicit promise to pay under the terms listed on the invoice. If a
firm wishes for a customer to make a more explicit acknowledgment of its ability and obligation to pay, a firm can
ask the customer to sign a promissory note upon delivery of the goods or to furnish a commercial draft or banker’s
acceptance in advance of the delivery of the goods.
Credit Analysis
Before granting a customer credit, the firm may wish to engage in credit analysis. Such analysis involves a systematic
determination of the potential borrower’s ability and willingness to pay for the goods being provided on credit. A
thorough credit analysis will look at the potential borrower’s past record and its present and forecasted future

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financial condition, which generally involves examining the “five C’s”:
credit analysis A systematic determination of a borrower’s ability and willingness to repay a potential loan.
1. Capacity: Does the borrower have the legal and economic ability to pay?
2. Character: Does the borrower’s reputation indicate a willingness to settle debt obligations?
3. Capital: Having assets at risk makes it more likely that the borrower will repay as promised.
4. Collateral: Goods that can be seized and sold, with the proceeds being used to pay the firm in the event of bankruptcy by the
borrower, also makes it more likely that the customer will repay as promised.
5. Conditions: Any economic conditions that may affect the borrower’s ability to repay the loan should also be taken into account.
Collection Policy
The firm’s collection policy is aimed at collecting past-due debts from customers. The usual procedure for collecting
follows a typical path of
1. Sending one or more delinquency letters informing the customer of the past-due status of the account, asking the customer to contact
the firm to discuss alternative means of repayment and pointing out what legal recourse the firm has.
2. Initiating telephone calls conveying the same information as above.
3. Employing a collection agency.
4. Taking legal action against the customer if all else fails.
To monitor and control this process, firms use a tool called an aging schedule, which stratifies a firm’s accounts
receivable by the age of each account. For example, a firm that offers terms of 2/10, net 60 to its customers might
want to measure the age of accounts receivable using the categories shown in Table 14.2.
Such an aging schedule would allow the firm to see what percentage of its customers are still eligible to take the
discount (i.e., those in the “0–10 days” category), how many are past due by less than 30 days (i.e., those in the “61–
90 days” category), and how many are over 30 days past due (i.e., those in the “Over 90 days” category).
Firms often link their collection policies to their aging schedules. For example, the customers in Table 14.2 that fall
into the “61–90 days” category might be sent a delinquency letter, while those in the “Over 90 days” category might
be phoned.
▼ TABLE 14.2 Sample Aging Schedule
 Age Bracket Percentage of AR in Bracket
 0–10 days 10%
 11–30 days 35
 31–60 days 45
 61–90 days 7
 Over 90 days 3
100
time out!
14-17 Why do firms offer customers discounts for paying early?
14-18 Should a firm always turn far-overdue bills from customers over to a collection agency or sue the customers? Why or why
not?

Get Online

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Log in to your Connect course for study materials including self-test problems with solutions, answers to
the Time Out quizzes, guided example videos, and more.
Your Turn…
Questions
1. Is it possible for a firm to have negative net working capital? How? (LG14-1)
2. Would it be possible for a decision to deny credit to your customers to be value maximizing? How? (LG14-1)
3. Which of the following will result in an increase in net working capital? (LG14-2)
a. An increase in cash.
b. A decrease in accounts payable.
c. An increase in notes payable.
d. A decrease in accounts receivable.
e. An increase in inventory.
4. Would it be possible for a firm to have a negative cash cycle? How? (LG14-3)
5. If a firm’s inventory turnover ratio increases, what will happen to the firm’s operating cycle? (LG14-3)
6. If a firm’s inventory turnover ratio increases, what will happen to the firm’s cash cycle? (LG14-3)
7. Everything else held constant, will an increase in the amount of inventory on hand increase or decrease the
firm’s profitability? (LG14-4)
8. Would a firm ever use short-term debt to finance permanent current assets? Why or why not? (LG14-5)
9. Suppose that short-term borrowing actually becomes more expensive than long-term borrowing: How
would this affect the firm’s choice between a flexible financing policy and a restrictive policy?

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(LG14-5)
10. If asset-backed loans are cheaper than unsecured loans, what is the disadvantage to the firm in using an asset-
backed loan? (LG14-6)
11. Is an increase in the cash account a source of funds or a use of funds? (LG14-7)
12. What will be the carrying cost associated with a compensating balance requirement? (LG14-7)
13. What will be the shortage cost associated with a compensating balance requirement? (LG14-7)
14. What would be the shortage costs associated with a restaurant not having enough cash on hand to make
change? (LG14-7)
15. If a firm needs to keep a minimum cash balance on hand and faces both cash inflows and outflows, which of
the cash management models discussed in this chapter would be more appropriate for the firm to use? (LG14-8)
16. What effect will increasing the trading costs associated with selling marketable securities have on the optimal
replenishment level in the Baumol Model? Why? (LG14-8)
17. What effect will an increase in the standard deviation of daily cash flows have on the return point in the Miller-
Orr model? Why? (LG14-8)
18. Could a firm ever have negative collection float? Why or why not? (LG14-9)
19. Could a firm ever have negative disbursement float? Why or why not? (LG14-9)
20. Would a draft have availability float? Why or why not? (LG14-9)
21. From our discussion of capital markets elsewhere in this book, why would you expect a firm to have a time
delay between raising funds to finance a project and the expenditure of those funds on that project? (LG14-9)
22. What purpose does a discount on credit terms serve? What is the cost of such a discount to the offering firm?
(LG14-9)

Problems
BASIC PROBLEMS
14-1 Net Working Capital Requirements JohnBoy Industries has a cash balance of $45,000, accounts
payable of $125,000, inventory of $175,000, accounts receivable of $210,000, notes payable of
$120,000, and accrued wages and taxes of $37,000. How much net working capital does the firm need
to fund? (LG14-2)
14-2 Net Working Capital Requirements Dandee Lions, Inc., has a cash balance of $105,000, accounts
payable of $220,000, inventory of $203,000, accounts receivable of $319,000, notes payable of
$65,000, and accrued wages and taxes of $75,000. How much net working capital does the firm need
to fund? (LG14-2)
14-3 Days’ Sales in Inventory Dabble, Inc., has sales of $980,000 and cost of goods sold of $640,000. The
firm had a beginning inventory of $36,000 and an ending inventory of $46,000. What is the length of
the days’ sales in inventory? (LG14-3)
14-4 Days’ Sales in Inventory Sow Tire, Inc., has sales of $1,450,000 and cost of goods sold of $980,000.
The firm had a beginning inventory of $97,000 and an ending inventory of $82,000. What is the length
of the days’ sales in inventory? (LG14-3)
14-5 Average Payment Period If a firm has a cash cycle of 67 days and an operating cycle of 104 days,
what is its average payment period? (LG14-3)
14-6 Average Payment Period If a firm has a cash cycle of 45 days and an operating cycle of 77
days, what is its average payment period? (LG14-3)
14-7 Payables Turnover If a firm has a cash cycle of 73 days and an operating cycle of 127 days, what is
its payables turnover? (LG14-3)
14-8 Payables Turnover If a firm has a cash cycle of 54 days and an operating cycle of 77 days, what is its
payables turnover? (LG14-3)

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14-9 Compensating Balance Would it be worthwhile to incur a compensating balance of $10,000 in order
to get a 1 percent lower interest rate on a one-year, pure discount loan of $225,000? (LG14-7)
14-10 Compensating Balance Would it be worthwhile to incur a compensating balance of $7,500 in order
to get a 0.65 percent lower interest rate on a two-year, pure discount loan of $150,000? (LG14-7)
14-11 Collection Float CM Enterprises estimates that it takes, on average, three days for customers’
payments to arrive, one day for the payments to be processed and deposited by the bookkeeping
department, and two more days for the checks to clear once they are deposited. What is CM’s
collection float? (LG14-9)
14-12 Collection Float Smelpank, Inc., estimates that it takes, on average, four days for customers’
payments to arrive, three days for the payments to be processed and deposited by the bookkeeping
department, and three more days for the checks to clear once they are deposited. What is the firm’s
collection float? (LG14-9)
INTERMEDIATE PROBLEMS
14-13 Operating Cycle Suppose that Dunn Industries has annual sales of $2.3 million, cost of goods sold
of $1,650,000, average inventories of $1,116,000, and average accounts receivable of $750,000.
Assuming that all of Dunn’s sales are on credit, what will be the firm’s operating cycle? (LG14-3)
14-14 Operating Cycle Suppose that LilyMac Photography has annual sales of $230,000, cost of goods
sold of $165,000, average inventories of $4,500, and average accounts receivable of $25,000.
Assuming that all of LilyMac’s sales are on credit, what will be the firm’s operating cycle? (LG14-3)
14-15 Cash Cycle Suppose that LilyMac Photography has annual sales of $230,000, cost of goods sold of
$165,000, average inventories of $4,500, average accounts receivable of $25,000, and an average
accounts payable balance of $7,000. Assuming that all of LilyMac’s sales are on credit, what will be
the firm’s cash cycle? (LG14-3)
14-16 Cash Cycle Suppose that Ken-Z Art Gallery has annual sales of $870,000, cost of goods sold of
$560,000, average inventories of $244,500, average accounts receivable of $265,000, and an average
accounts payable balance of $79,000. Assuming that all of Ken-Z’s sales are on credit, what will be
the firm’s cash cycle? (LG14-3)
14-17 Compensating Balance Interest Rate Suppose your firm is seeking an eight-year, amortizing
$800,000 loan with annual payments, and your bank is offering you the choice between an $850,000
loan with a $50,000 compensating balance and an $800,000 loan without a compensating balance. If
the interest rate on the $800,000 loan is 8.5 percent, how low would the interest rate on the loan with
the compensating balance have to be for you to choose it? (LG14-4)
14-18 Compensating Balance Interest Rate Suppose your firm is seeking a four-year, amortizing
$200,000 loan with annual payments and your bank is offering you the choice between a $205,000
loan with a $5,000 compensating balance and a $200,000 loan without a compensating balance. If the
interest rate on the $200,000 loan is 9.8 percent, how low would the interest rate on the loan with the
compensating balance have to be for you to choose it? (LG14-4)
14-19 88Optimal Cash Replenishment Level Rose Axels faces a smooth annual demand for cash of
$5 million, incurs transaction costs of $275 every time the company sells marketable securities,
and can earn 4.3 percent on its marketable securities. What will be its optimal cash replenishment
level? (LG14-8)
14-20 Optimal Cash Replenishment Level Watkins Resources faces a smooth annual demand for cash of
$1.5 million, incurs transaction costs of $75 every time the firm sells marketable securities, and can
earn 3.7 percent on its marketable securities. What will be its optimal cash replenishment level?
(LG14-8)
14-21 Optimal Cash Return Point HotFoot Shoes would like to maintain its cash account at a minimum
level of $25,000, but expects the standard deviation in net daily cash flows to be $4,000, the effective
annual rate on marketable securities to be 6.5 percent per year, and the trading cost per sale or
purchase of marketable securities to be $200 per transaction. What will be its optimal cash return
point? (LG14-8)
14-22 Optimal Cash Return Point Veggie Burgers, Inc., would like to maintain its cash account at a
minimum level of $245,000 but expects the standard deviation in net daily cash flows to be $12,000,

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the effective annual rate on marketable securities to be 4.7 percent per year, and the trading cost per
sale or purchase of marketable securities to be $27.50 per transaction. What will be its optimal cash
return point? (LG14-8)
14-23 Optimal Upper Cash Limit Veggie Burgers, Inc., would like to maintain its cash account at a
minimum level of $245,000 but expects the standard deviation in net daily cash flows to be $12,000,
the effective annual rate on marketable securities to be 3.7 percent per year, and the trading cost per
sale or purchase of marketable securities to be $27.50 per transaction. What will be its optimal upper
cash limit? (LG14-8)
14-24 Optimal Upper Cash Limit HotFoot Shoes would like to maintain its cash account at a minimum
level of $25,000 but expects the standard deviation in net daily cash flows to be $2,000, the effective
annual rate on marketable securities to be 3.5 percent per year, and the trading cost per sale or
purchase of marketable securities to be $200 per transaction. What will be its optimal upper cash
limit? (LG14-8)

chapter fourteen
appendix 14A
the cash budget
LEARNING GOALS
LG14-12 Be able to create and interpret a cash budget.
The production and sales in many firms vary over the year. For example, a toy retailer will have many more sales in
November and December than in March and April. On the other hand, consider the manufacturer of toys. That
company would have to manufacture most of the toys it will sell to the retail stores before November. For the most
part, all businesses have some seasonality in their sales and/or production cycle. This seasonality creates periods
during the year in which the firm will generate large cash surpluses and other periods in which it will generate large
cash deficits. Financial managers must plan ahead for such times so that the firm always has adequate cash to pay its
liabilities. The cash budget is the instrument they use.
cash budget A calculation of the estimated cash flow from receipts and disbursements over a specific time period.
Consider the example of Yellow Jacket, Inc., a manufacturer of coats and jackets that has decided to operate its
factory at a constant pace all year. Thus, inventory builds up until early fall, when it ships large amounts of its
product to retailers. The coats are mostly sold in the fall, depleting inventory. This strategy allows the company to
keep a few full-time workers instead of hiring many seasonal employees and then laying them off during the slow
times of the year. However, incurring costs during most of the year with few sales and then selling the coats in the
fall creates a serious cash flow problem that the financial manager is responsible for resolving.
Cash budgets can be created for daily, monthly, or quarterly time periods. Given the severe seasonality of Yellow
Jacket’s sales, its cash budget is done monthly. The cash budget begins with a projection of sales for the year. In this
case, Yellow Jacket is projecting a 10 percent increase in sales each month from the same month of the previous
year. The top of Table 14A.1 shows these monthly projected sales, which are quite seasonal. Many companies have
sales terms like 2/10 net 45, which means that customers must pay within 45 days of the sale—but if they pay within
10 days they can take a 2 percent discount. Even with terms like this, Yellow Jacket has found that its customers
take the 2 percent discount if they pay in the same month of the sale, which 30 percent do. Then 50 percent pay in
the month after the sale, leaving the final 20 percent to pay in the following month. This is illustrated in the cash
collection row of the table. Note that the firm collects only $1 million in cash payments in July while it collects as
much as $26.4 million in November.
▼ TABLE 14A.1 Cash Collection

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The total sales for the year are $125 million. If the company pursues the level production strategy, then it needs to
produce the coats at a sale value rate of $10.42 million per month (= $125 million/12). Table 14A.2 shows the cash
disbursements per month. The manufacturing costs are assumed to be materials at 50 percent of sales, while wages
are 15 percent of sales. Thus, material cost payments are $5.2 million per month (= $10.42 million × 50%) and wage
payments are $1.6 million per month (= $10.42 million × 15%). Other payments predicted throughout the year are
those for capital investments, interest payments, and dividend payments. Yellow Jacket plans to invest in some
factory upgrades for which it will pay $15 million in June. Interest payments on its bonds are semiannual (March
and September), while quarterly dividends are paid in February, May, August, and November. Notice that the total
cash disbursements have a high degree of variability over time. In addition, the payments do not align well with the
cash collection. For example in June, the firm receives only $1.2 million in cash and expects to pay $24.5 million.
On the other hand, it expects to collect $26.4 million in November and pay only $7.8 million.

▼ TABLE 14A.2 Cash Disbursement
The cash budget can now be completed. Table 14A.3 shows that the next step is to compute the net cash
flow generated each month. This is simply the cash collection for that month minus that month’s
disbursement. Note that Yellow Jacket has seven months in a row (March through September) in which it generates
a negative cash flow. The cumulative net cash flow row shows that the surplus of cash generated in January and
February helps with the deficits from March and April. However, by May, Yellow Jacket enters a cash deficit
situation that lasts the rest of the year. The deficit is increased by the fact that the firm likes to have a cash balance
minimum of $2 million at all times. Finally, the cash budget shows the cash account surplus or deficit during the
year. It is apparent that Yellow Jacket will need to obtain a bank loan or line of revolving credit that can handle a
maximum of $45.4 million (September’s deficit is the highest).
▼ TABLE 14A.3 Cash Budget

Note that Yellow Jacket is a profitable firm. Yet, the seasonality in the sales of coats and jackets causes severe cash
deficit problems during the year. If financial managers do not plan ahead for this situation, then the firm will
experience significant financial stresses that can damage its reputation and relationship with suppliers and
customers. The value of building the cash budget on a spreadsheet (as shown in these tables) is that sensitivity
analysis and what-if scenarios can easily be implemented.
time out!
14A-1 Should all cash payments and receipts made by the firm be included in the cash budget?
14A-2 Due to the nature of Yellow Jacket’s business, they are likely to experience significant cash deficits each year. How is
their bank likely to view this situation?

Problems
BASIC PROBLEMS
14A-1 Cumulative Net Cash Flow The net cash flow for a firm in January, February, and March is −$2.5
million, −$3.0 million, and $2.4 million, respectively. What is the cumulative net cash flow for March?
(LG14-12)
14A-2 Cumulative Net Cash Flow The net cash flow for a firm in January, February, and March is $3.5
million, −$1.0 million, and $1.4 million, respectively. What is the cumulative net cash flow for March?
(LG14-12)
14A-3 Cash Disbursement The Hug-a-Bear company makes its teddy bears the month before they are sold

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and pays for all materials in the month of purchase. If sales of $2.5 million are expected in November
and the firm pays 50 percent of sales in material costs, then what is the materials cash disbursement in
October? (LG14-12)
14A-4 Cash Disbursement The Snow Adventures company makes its snowboards the month before they are
sold and pays for all materials in the month of purchase. If sales of $7.8 million are expected in
November and the firm pays 65 percent of sales in material costs, then what is the materials cash
disbursement in October? (LG14-12)
INTERMEDIATE PROBLEMS

14A-5 Cash Collection Consider a company that has sales in May, June, and July of $10 million, $12
million, and $9 million, respectively. The firm is paid by 35 percent of its customers in the month
of the sale, 40 percent in the following month, and 22 percent in the next month (3 percent are bad sales
and never pay). What is the cash collected in July? (LG14-12)
14A-6 Cash Collection Consider a company that has sales in May, June, and July of $11 million, $10 million,
and $12 million, respectively. The firm is paid by 25 percent of its customers in the month of the sale,
50 percent in the following month, and 23 percent in the next month (2 percent are bad sales and never
pay). What is the cash collected in July? (LG14-12)
14A-7 Cash Surplus or Deficit A firm has estimated the two-month cash budget below. What is the cash
surplus or deficit for these two months? (LG14-12)
14A-8 Cash Surplus or Deficit A firm has estimated the two-month cash budget below. What is the cash
surplus or deficit for these two months? (LG14-12)
 ($ in millions) MAR APR
 Sales 120.0 130.0
 Cash collection 84.0 90.0
 Total cash disbursement 90.0 85.0
 Net cash flow −6.0 5.0
 Cumulative net cash flow −15.0 ?
 Minimum cash balance 10.0 10.0
 Cash surplus or deficit  ?  ?
 ($ in millions) MAR APR
Sales 75.0 68.0
Cash collection 63.0 65.0
Total cash disbursement 60.0 57.0
Net cash flow 3.0 8.0
Cumulative net cash flow 11.0 ?
Minimum cash balance 3.0 3.0
Cash surplus or deficit ? ?
ADVANCED PROBLEMS
14A-9 Cash Budget Spreadsheet Problem The company from the text, Yellow Jacket, has decided to
change its production strategy. Instead of a steady production throughout the year, they will produce
the coats they estimate to sell in the month prior. This will impact the materials and wage
disbursements of the cash budget. (For the December computation, assume that the following January

sales will increase by 10 percent from the prior year.) Build this cash budget. How does this impact
the cash surplus/deficit of the firm? (LG14-12)

Notes
CHAPTER 14
1. If you are sitting there wondering why the bank doesn’t just lend only 95 percent or 90 percent of the money, instead of lending it all
and then asking for part of it back, the answer has to do with bank regulations. Though it’s too complicated to go into great detail, the
simple answer is that bank regulators see a difference between a $900,000 loan and a $1,000,000 loan with a 10 percent
compensating balance requirement, though they may sound the same to us.
2. See W. S. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics 66, no. 4
(November 1952), pp. 545–556.
3 See M. H. Miller and D. Orr, “A Model of the Demand for Money by Firms,” Quarterly Journal of Economics 80, no. 3 (August 1966), pp.
413–435.
4. To see why, go down to your local bank or savings and loan and see which is higher: The rate it pays on savings accounts or the rate it
charges on short-term borrowing.

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page 426
Viewpoints (Revisited)
Chapter one
BUSINESS APPLICATION SOLUTION
Because Caleb is a sole proprietor of a small business, he will have trouble getting loans for large amounts of money
if he wants to expand. Caleb should consider the following options.
First, Caleb can expand slowly. He can get a small loan or self-fund an expansion into one other mall. Once the
new juice stand is making a profit, he can expand again. The advantage of this slow expansion is that he retains full
ownership and control of his business. One significant risk is that others may copy his idea and open their own
stands, thus taking the prime spots in malls before he gets there.
In order to obtain the capital to expand more quickly, Caleb may have to take on a partner. Forming a
partnership with an angel investor or a venture capitalist who can provide business expertise and substantial amounts
of capital would allow for much faster expansion. The disadvantage of this option is that Caleb will have to give up
some ownership of his business.
PERSONAL APPLICATION SOLUTION
Dagmar should know that the market gives no guarantees against losing money investing in company stocks. These
companies failed for different reasons. RadioShack made a series of business mistakes over many years that
included large errors in the products they offered, their marketing, and e-commerce. Wet Seal filed for bankruptcy
protection after failing to stay in tune with its customers and could not compete with rivals like H&M. Finally, THQ
failed because it overinvested in poor gaming products and did not adapt to the changing technology of gaming.
Dagmar should also know that the collapse of firms does occasionally occur. On the other hand, the companies
that competed with these failed firms did very well. There are definitely winners and losers in capitalism.
Nevertheless, she can minimize her loss from a corporate bankruptcy by not putting all her “eggs in one basket.”
Diversification is a finance principle discussed in detail later in this book.
Chapter two
BUSINESS APPLICATION SOLUTION
If the managers of DPH Tree Farm increase the firm’s fixed assets by $27 million and net working capital by $8
million in 2019, the balance sheet would look like the one below (Table 2.6). That is, gross fixed assets increase by
$27 million, to $395 million; cash, accounts receivable, and inventory would increase by $1 million, $5 million, and
$6 million, respectively. DPH Tree Farm’s total assets will thus grow by $39 million to $609 million by ​year-end
2019. This growth in assets would be financed with $4 million in accounts payable, and the remaining $35 million
will be financed with 40 percent long-term debt (0.4 × $35m = $14m) and 60 percent with common stock (0.6 ×
$35m = $21m).
PERSONAL APPLICATION SOLUTION
As Chris Ryan examines the 2018 financial statements for DPH Tree Farm, Inc., she needs to remember that the
balance sheet reports a firm’s assets, liabilities, and equity at a particular point in time, the income statement reports
the total revenues and expenses over a specific period of time, the statement of cash flows shows the firm’s cash
flows over a period of time, and the statement of retained earnings reconciles net income earned during a
given period and any cash dividends paid with the change in retained earnings over the period.
▼ TABLE 2.6 Revised Balance Sheet for DPH Tree Farm, Inc.
DPH TREE FARM, INC. Balance Sheet as of December 31, 2019 (in millions of dollars)

Assets 2019 Liabilities and Equity 2019
Current assets: Current liabilities:
Cash $ 25 ($24 +
$1)
Accrued wages and taxes $ 20
Accounts receivable 75 ($70 +
$5)
Accounts payable 59 ($55 + $4)
Inventory 117 ($111 +
$6)
Notes payable   45
Total $217 Total $124
Fixed assets:
Gross plant and
equipment
$395 ($368 +
$27)
Long-term debt: 209 [$195 +
0.4($39 – $4)]
Less: Accumulated
depreciation
  53 Stockholders’ equity:
Net plant and equipment $342 Preferred stock (5 million shares) $ 5 $5
Common stock and paid-in surplus (20
million shares)
61 [$40 + 0.6($39
– $4)]
Other long-term assets   50 Retained earnings 210
Total $392 Total $276
Total assets $609 ($570 +
$39)
Total liabilities and equity $609 ($570 + $39)
GAAP procedures dictate how each financial statement is prepared. GAAP requires that the firm recognizes
revenue when the firm sells the product, which is not necessarily when the firm receives the cash. Likewise, under
GAAP, expenses appear on the income statement as they match sales. That is, the income statement recognizes
production and other expenses associated with sales when the firm sells the product. Again, the actual cash outflow
associated with producing the goods may actually occur at a very different time than that reported. In addition, the
income statement contains several noncash items, the largest of which is depreciation. As a result, figures shown on
an income statement may not be representative of the actual cash inflows and outflows for a firm during any
particular period.
For investors like Chris Ryan, the actual cash flows are often more important than the accounting profit listed on
the income statement. Cash, not accounting profit, is needed to pay the firm’s obligations as they come due: to fund
the firm’s operations and growth, and to compensate the firm’s owners. So Chris is more likely to find the answers
she seeks in the statement of cash flows, which shows the firm’s cash flows over a given period of time. The
statement of cash flows reports the amounts of cash generated and cash distributed by a firm during the time period
analyzed.
Finally, Chris must remember that firms are required to prepare their financial statements according to GAAP.
GAAP allows managers to have significant discretion over their reported earnings, in other words, to manage
earnings. Indeed, managers can report their results in a way that indicates to investors that the firm’s assets are
growing more steadily than may really be the case. Similarly, the choice of depreciation method—straight-line or
MACRS—for fixed assets may make two firms with identical fixed assets appear to have very different results.
Thus, Chris may need to delve more deeply into research about this firm’s—or any firm’s—financial condition
before she makes any final investment decision.
Chapter three
BUSINESS APPLICATION SOLUTION
The managers of DPH Tree Farm, Inc., have stated that its performance surpasses that of other firms in the industry.
Particularly strong are the firm’s liquidity and asset management positions. The superior performance in these areas
has resulted in superior overall returns for the stockholders of DPH Tree Farm, Inc., according to DPH management.
Having analyzed the financial statements using ratio analysis, we could conclude that these statements are partially
true. All three liquidity ratios show that DPH Tree Farm holds more liquidity on its balance sheet than the industry

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average. Thus, DPH Tree Farm has more cash and other liquid assets (or current assets) available to pay its bills (or
current liabilities) as they come due than the average firm in the tree farm industry. In all cases, the asset
management ratios show that DPH Tree Farm, Inc., is outperforming the industry average in its asset management.
The firm is turning over its inventory faster than the average firm in the tree farm industry, thus producing more
dollars of sales per dollar of inventory. It is also collecting its accounts receivable faster and paying its accounts
payable slower than the average firm. Further, DPH Tree Farm is producing more sales per dollar of fixed assets,
working capital, and total assets than the average firm in the industry. The profitability ratios show that DPH Tree
Farm, Inc., is more profitable than the average firm in the tree farm industry. The profit margin, BEP, and ROA are
all higher than the industry. Despite this, the ROE for DPH Tree Farm is much lower than the average for the
industry.
What the managers do not state is that the debt management ratios show that DPH Tree Farm, Inc., holds less
debt on its balance sheet than the average firm in the tree farm industry. This is a good sign in that this lack of
financial leverage decreases the firm’s potential for financial distress and even failure. If the firm has a bad year, it
has promised relatively few payments to debt holders. Thus, the risk of bankruptcy is small. Further, the firm has
more dollars of operating earnings and cash available to meet each dollar of interest obligations on the firm’s debt.
Further, stockholders are entitled to any residual cash flows—those left after debt holders are paid. When DPH
Tree Farm, Inc., does well, financial leverage increases the reward to shareholders since the amount of cash flows
promised to debt holders is constant and capped. In this case, financial leverage creates more cash flows to share
with stockholders—it magnifies the return to the stockholders of the firm. This magnification is one reason that
stockholders encourage the use of debt financing.
PERSONAL APPLICATION SOLUTION
To evaluate DPH Tree Farm, Inc.’s, financial statements, Chris Ryan would want to perform ratio analysis in which
she uses the financial statements to calculate the most commonly used ratios. These include liquidity ratios, asset
management ratios, debt management ratios, profitability ratios, and market value ratios. The value of these ratios
for DPH Tree Farms and the tree farming industry are presented in Table 3.1. Chris might also want to spread the
financial statements. These calculations yield common-size, easily compared financial statements that can be used to
identify changes in corporate performance as well as how DPH Tree Farm compares to other firms in the industry.
Having calculated these ratios, Chris can identify any interrelationships in the ratios by performing a detailed
analysis of ROA and ROE using the DuPont system of analysis. A critical part of performance analysis lies in the
interpretation of these numbers against some benchmark. To interpret the financial ratios, Chris will also want to
evaluate the performance of the firm over time (time series analysis) and the performance of the firm against one or
more companies in the same industry (cross-sectional analysis). Finally, Chris needs to exercise some cautions when
reviewing data from financial statements. For example, the financial statement data are historical and may not be
representative of future performance. Further, she needs to know what accounting rules DPH Tree Farm uses before
making any comparisons or conclusions about its performance from ratio analysis. Finally, DPH Tree Farm’s
managers may have window-dressed their financial statements to make them look better.

Chapter four
BUSINESS APPLICATION SOLUTION
You must compare the cash flows of buying the wire now at a discount, or waiting one year. The cost of the wire
should include both the supplier’s bill and the storage cost, for a total of $452,000. What interest rate is implied by a
$452,000 cash flow today versus $500,000 in one year? Using equation 4-2:

Whether your company should purchase the wire today depends on the cost of the firm’s capital (discussed in
Chapter 11). If it costs the firm less than 10.6 percent to obtain cash, then you should purchase the wire today.
Otherwise, you should not.
PERSONAL APPLICATION SOLUTION
Since Anthony’s loan of $300 requires an immediate $50 payment, the actual cash flow is $250 (= $300 − $50). He
then must repay the full $300. Use equation 4-2 to compute the interest rate you pay for the period:
Anthony is paying 20 percent for a loan of only two weeks! This is equivalent to paying 11,348 percent per year
(this is shown in Chapter 5). He will never be able to build wealth if he continues to pay interest rates like this.
Indeed, many people get trapped in a continuing cycle, obtaining one payday loan after another.
WARNING: Payday loans are almost always terrible deals for the borrower!
Chapter five
BUSINESS APPLICATION SOLUTION
Walkabout Music, Inc., pays $700,000 (= $20 million × 0.07 ÷ 2) in interest every six months on its existing debt.
The new debt would require payments of $600,000 (= $20 million × 0.06 ÷ 2) every six months, which represents a
$100,000 savings semiannually.
The present value of these savings over the next 20 years is computed using 40 semiannual periods and a 3
percent interest rate per period:

Since this savings is less than the $2.6 million cost of refinancing, the CFO should not refinance the old debt at
this time. The company should wait until it can find more favorable terms.
PERSONAL APPLICATION SOLUTION
Should you switch to a new home mortgage with a lower interest rate? To answer this question, first find the
monthly savings with the new mortgage. Then compare the present value of the savings to the cost of getting the
new mortgage.
The current monthly mortgage payments are
The new mortgage payments would be
The new mortgage would save you $96.99 per month for the next 27 years.
The present value of these savings at the current 7 percent interest rate is
Since the present value of the monthly savings is greater than the $1,000 broker fee, you should refinance the

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mortgage.

Chapter six
BUSINESS APPLICATION SOLUTION
In deciding when to issue new debt, DPH Corporation needs to consider two main factors. First, what might happen
to specific factors that affect interest rates on any debt the firm may issue? Such specific factors include changes in
the firm’s default risk, liquidity risk, any special provisions regarding the use of funds raised by the firm’s security
issuance, and the debt’s term to maturity. An increase (decrease) in any of these risks over the next two years would
increase (decrease) the rate of interest DPH Corp. would be required to pay to holders of the new debt and would
potentially make the debt issue in two years less (more) attractive. Second, what might happen to the general level of
interest rates in the U.S. economy over the next two years? This involves an analysis of any changes in inflation or
the real risk-free rate. DPH can estimate how interest rates may change by examining the term structure of interest
rates or the current yield curve. In addition to any internal analysis of these factors, DPH Corp. can get expert advice
about the timing of its debt issue and get the new debt to the capital market with help from an investment bank.
These financial institutions underwrite securities and engage in related activities, such as making a market in which
securities can trade.
PERSONAL APPLICATION SOLUTION
In deciding which corporate bond to buy, John Adams needs to consider specific factors that affect differences in
interest rates on debt. These specific factors include the general level of inflation and the real risk-free rate in the
U.S. economy, as well as the default risk, liquidity risk, any special provisions regarding the use of funds raised by a
security issuance, and the term to maturity of the two debt issues. While one bond earns more (10.00 percent) than
the other (8.00 percent), it may be that the higher-yielding bond has more default, liquidity, or other risk than the
lower-yielding bond. Thus, the higher yield brings with it more risk. John Adams must consider whether he is
willing to incur higher risk to get higher returns. In addition to his own analysis of these factors, John Adams can get
expert advice about which bond to buy and then buy the bond with a securities firm’s help. These financial
institutions engage in activities such as securities brokerage, securities trading, and making markets in which
securities can trade.
Chapter seven
BUSINESS APPLICATION SOLUTION
To raise $150 million, Beach Sand Resorts would need to issue 150,000 bonds at the customary $1,000 par value (=
$150 million ÷ $1,000). The bonds will have to offer a 7 percent coupon. This means that Beach Sand Resorts will
pay $35 in interest every six months for each bond issued (= 0.07 × $1,000 ÷ 2). So for all 150,000 bonds, they will
pay $5.25 million semiannually (= $35 × 150,000).
PERSONAL APPLICATION SOLUTION
You can calculate that buying 10 of the Trust Media bonds at the quoted price of 96.21 will cost $9,621 (= 0.9621 ×
$1,000 × 10) and would generate $285 (= 0.057 × $1,000 × 10 ÷ 2) in interest payments every six months. Buying
the bond in 2017, it is priced to offer a 6.47 percent yield to maturity. Ten of the Abalon bonds would cost $10,194
(= 1.0194 × $1,000 × 10) and pay $268.75 (= 0.05375 × $1,000 × 10 ÷ 2) in interest payments every six months.
This bond is priced to offer a 5.0 percent yield to maturity. The Trust bonds cost less to purchase, pay more in
interest, and offer a higher return than the Abalon bonds. This is because the Trust bonds have higher credit risk.
You must decide if the higher return of the Trust bonds is worth taking the extra risk.

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Chapter eight
BUSINESS APPLICATION SOLUTION
You can compute the expected return using equation 8-7 as,
Investors expect an 11.32 percent return.
The P/E ratio of 16.25 and the stock price of $65 indicates that earnings were $4.00 per share (= $65 ÷ 16.25). If
the P/E ratio of 16.25 continues, then the price of the stock in three years may be $81.88 [= 16.25 × $4 × (1.08)3].
However, a P/E ratio of 16.25 may seem a little high for a firm with an 8 percent growth rate. So the P/E ratio might
decline a bit to 15. If so, the stock price in three years would be $75.58. On the other hand, P/E ratios in the stock
market may increase in general, thereby inflating this firm’s ratio to 17. In this case, the price would be $85.66.
You should report an expected stock price range of $75.58 to $85.66 with a target of $81.88.
PERSONAL APPLICATION SOLUTION
The information provided allows for two growth rate estimates for stock valuation. The dividend growth from $1.25
to $1.68 in three years implies a 10.36 percent historical growth rate (N = 3, PV = −1.25, PMT = 0, FV = 1.68, CPT
I = 10.36). Since analysts’ mean growth estimate is 10.1 percent, you can use either, or both, rates in the constant-
growth-rate model using a 13.5 percent discount rate:
Both valuation estimates exceed the current price of $54. The current stock price does not appear overvalued, so you
can consider the purchase.
Chapter nine
BUSINESS APPLICATION SOLUTION
We can apply diversification concepts and modern portfolio theory to many more applications than just investment
portfolios. For example, a manufacturing facility can be more efficient by producing different products during the
year as demand dictates the need for one product over another. Salespeople can reduce the volatility of their
commission incomes by having many different products to sell.
Although new project ideas have more risk, they could actually reduce the firm’s overall risk if the projects
diversify the firm’s current business operations. You could evaluate this possibility by determining the
correlation between the expected cash flows from each project idea with the expected cash flows of the
firm’s current business operations. A low or negative correlation would mean that the new projects could actually
reduce risk for the firm. Note that some firms may find that their position is too conservative and that they wish to

increase their risk to increase the possibility of earning a higher return.
PERSONAL APPLICATION SOLUTION
Tables 9.2 and 9.4 show that since 1950 the bond market experienced an average return and standard deviation of
6.6 percent and 11.1 percent, respectively. Stocks earned a 12.6 percent return with a 17.3 percent standard
deviation. The investor is correct in the belief that the stock market is riskier than the bond market.
However, Table 9.6 shows that the correlation between the stock and bond market is very low, at −0.035. This
result allows some diversification opportunity. Indeed, a portfolio of 10 percent stocks and 90 percent bonds would
have experienced an average annual return of 7.2 percent with a standard deviation of 10.1 percent since 1950. The
broker is correct; adding a small portion of stocks to a bond portfolio actually reduces total risk!
Chapter ten
BUSINESS APPLICATION SOLUTION
You need to determine the firm’s level of market risk. If you can obtain a beta, then you can make a required return
estimate using CAPM. To assess the result, you can use the constant-growth model to check the CAPM estimated
required return for comparison’s sake.
If you find the beta of the firm to be 1.8, assume a market return of 11 percent, and note a 5 percent T-bill rate,
the CAPM computations would be
5% + 1.8 × (11% − 5%) = 15.8 percent
The firm will pay a $0.50 dividend next year and the current stock price is $32. Managers believe the company
will grow at 13 percent per year for the foreseeable future. The constant-growth model computation gives
$0.50 ÷ $32 + 0.13 = 0.1456, or 14.56 percent
You can now take these estimates to the team.
PERSONAL APPLICATION SOLUTION
You are investing 57.1 percent (= $200 ÷ $350) of your monthly contribution in stocks. You are also contributing
28.6 percent in bonds and 14.3 percent into a money market account. The diversified stock portfolio has a beta of 1.
The long-term bond portfolio has a beta of 0.18. By definition, the money market account is risk-free and thus has a
beta of zero.
The beta of this portfolio is therefore
0.571 × (1) + 0.286 × (0.18) + 0.143 × (0) = 0.62
With a portfolio beta of 0.62, a market return of 11 percent, and a risk-free rate of 5 percent, you can expect a
return of
5% + 0.62 × (1 1% − 5%) = 8.72 percent
If you want a higher expected return, you will have to take more risk. You can do that by contributing a higher
proportion of your funds to the stock portfolio.
Chapter eleven
BUSINESS APPLICATION SOLUTION
MP3 Devices, Inc., faces current component costs of capital equal to

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gives iD = 0.0891, or 8.91%
Using the target capital structure weights, MP3’s WACC equals
PERSONAL APPLICATION SOLUTION
Mackenzie can expect a total of $17,125 + $29,000 = $46,125 in student loans when she graduates from her master’s
program. At an 8 percent rate of interest, the yearly interest charges will be $3,690 immediately after she graduates
(though they will go down once she starts paying off some of the principal). Since the yearly interest will be more
than the allowable $2,500 deduction, we can express her after-tax interest rate as the following weighted average:

Chapter twelve
BUSINESS APPLICATION SOLUTION
Based on the given information, the yearly sales, levels of NWC, and resulting changes in NWC for McDonald’s
will be:
 Year Yearly Sales Yearly Levels of NWC Changes in NWC
0 $    0 $364,000 $364,000
1 2,800,000  937,300 573,300
2 7,210,000  965,900 28,600
3 7,430,000  994,500 28,600
4 7,650,000  512,200 −482,300
5 3,940,000     0 −512,200
OCF calculations, ΔNWC, and ΔFA for each year are shown as follows:

PERSONAL APPLICATION SOLUTION
Achmed’s purchase of a new computer should not be counted as an incremental cash flow to getting an MBA, as he
has indicated that he would be getting one anyway. Likewise, the $250 that he paid to take the GMAT is a sunk cost
and should not be counted, either. His tuition payments constitute an annuity due, so his incremental cash flows will
equal
Years 0–3 4–23
FCF −$15,000 $10,000
(in millions) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Sales $2.80 $7.21 $7.43 $7.65 $3.94
Less: Variable costs 1.34 3.52 3.70 3.89 2.04
Less: Fixed costs 0.00 0.00 0.00 0.00 0.00
Less: Depreciation 0.00 0.00 0.00 0.00 0.00
Earnings before interest and
taxes
$1.46 $3.69 $3.73 $3.76 $1.90
Less: Taxes 0.00 0.00 0.00 0.00 0.00
Net income $1.46 $3.69 $3.73 $3.76 $1.90
Plus: Depreciation 0.00 0.00 0.00 0.00 0.00
Operating cash flow $1.46 $3.69 $3.73 $3.76 $1.90
Δ Fixed assets $7.00 $0.00 $0.00 $0.00 $0.00 $0.00
Δ Net working capital 0.00 0.00 0.00 0.00 0.00 0.00
Less: Investment in
operating capital
$7.00 0.00 0.00 0.00 0.00 0.00
Free cash flow −$7.00 $1.46 $3.69 $3.73 $3.76 $1.90
Chapter thirteen
BUSINESS APPLICATION SOLUTION
ADK’s project will have an NPV of
and an IRR of
Both the NPV and IRR support accepting the project.

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page 433
We could also calculate MIRR (16.72 percent) and PI (1.10), and these would provide additional support for
accepting the project.
Finally, though we are not given maximum allowable payback or discounted payback, values of 2.96 and 3.70,
respectively, would seem to be in an acceptable range, too.
PERSONAL APPLICATION SOLUTION
First, we should note that, since cash flows occur every three months, we need to convert the APR of 9 percent to a
quarterly rate:
With these types of cash flows, our choice of decision rules is limited to NPV, MIRR, or PI; we cannot use
either the payback rule or IRR because of the non-normality.

The NPV of this project will be
This NPV indicates that the project should be accepted.
Chapter fourteen
BUSINESS APPLICATION SOLUTION
Chewbacca’s operating cycle will be equal to
Their cash cycle will be equal to
Absent any other information about current assets or current liabilities, Chewbacca’s net working capital will be
(0.10 + 0.1667 − 0.05) × $32 million = $6.93 million
PERSONAL APPLICATION SOLUTION
Since Wanda will be drawing out the money smoothly from the account, she can use the Baumol model to determine
the optimal replenishment level for her personal stock of cash:

page 434
chapter equations

chapter 2
2-1 Assets = Liabilities + Equity
2-2 Net working capital = Current assets − Current liabilities
2-3
2-4
2-5
2-6 Market value per share (MVPS) = Market price of the firm’s common stock
2-7

chapter 3
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
3-16
3-17
3-18
3-19
3-20
3-21
3-22
3-23
3-24

page 435
3-25
3-26
3-27

3-28
3-29
3-30
3-31
3-32
3-33
3-34 Retention ratio = 1 – Dividend payout ratio
3-35

chapter 4
4-1 Future value in 1 year = FV1 = PV × (1 + i)
4-2 Future value in N years = FVN = PV × (1 + i)
N
4-3 Futurevaluein Nperiods = FVN = PV × (1 + iperiod 1) × (1 + i period2) × ( 1 + i period3) × . . . × ( 1 + i period N )
4-4 Present value of next period’s cash flow = PV = FV1/(1 + i)
4-5 Present value of cash flow made in Nyears = PV = FVN / (1 + i )
N
4-6 Present value with different discount rates
4-7

chapter 5
5-1 FVN = Future value of first cash flow + Future value of second cash flow + . . . + Future value of last cash flow
= PMTm × (1 + i)
N−m + PMTn × (1 + i)
N−n + . . . + PMTp × (1 + i)
N−p
5-2
5-3
5-4
5-5
5-6 FVAN due = FVAN × (1 + i)
5-7 PVAN due = PVAN × (1 + i)
5-8
5-9

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chapter 6
6-1
6-2 i = Expected IP + RFR
6-3 RFR = i − Expected IP
6-4 DRPj = ijt − iTt
6-5
6-6

6-7
6-8
6-9
6-10
6-11

chapter 7
7-1
7-2 Bond price = PV of annuity (PMT, i, N) + PV(FV, i, N)
7-3
7-4

chapter 8
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
8-9
8-10

chapter 9
9-1
9-2
9-3
9-4
9-5
9-6
9-7 Totalrisk = Firm − specific risk + Market risk
9-8

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chapter 10
10-1
10-2
10-3 Required return = Risk-freerate + Risk premium
10-4 Expected return = Rf + β(RM − Rf)
10-5
10-6

chapter 11
11-1
11-2 iE = Rf + β(RM − Rf)
11-3
11-4
11-5
11-6
11-7
11-8
11-9
11-10

chapter 12
12-1
12-2
12-3 ATCF = Market value − (Market value − Book value )×TC
12-4
12-5

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chapter 13
13-1 Payback Statistic
13-2 Payback Decision Rule
Accept project if calculated payback ≤ Maximum allowable payback
Reject project if calculated payback > Maximum allowable pay back
13-3 Discounted Payback Statistic
13-4 Discounted Payback Decision Rule
Accept project if calculated DPB ≤ Maximum allowable discounted payback
Reject project if calculated DPB > Maximum allowable discounted payback
13-5 NPV Statistic
13-6 NPV Decision Rule
Accept project if NPV ≥ 0
Reject project if NPV < 0 13-7 Formula Comparison (13-5 to 13-8) 13-8 IRR Statistic Solve for IRR: 13-9 IRR Decision Rule Accept project if IRR ≥ Cost of capital Reject project if IRR < Cost of capital 13-10 Profitability Index Statistic 13-11 Profitability Index Decision Rule Accept project if PI ≥ 1 Reject project if PI < 1 chapter 14 14-1 14-2 14-3 14-4 14-5 14-6 14-7 14-8 H* = 3Z* − 2L page 439 index A page number with an e indicates an example; an f, a figure; an n, a note; a t, a table. A ABCP (asset-backed commercial paper), 158 Accelerated depreciation, 349–352 Acceptance, 408–409 Accounting methods depreciation, 30, 45, 349–352 GAAP, 30, 45, 44–45, 57n1 Accounting versus finance, 10–11 Accounts payable, 400–401 Accounts payable management ratios, 63–64 Accounts payable turnover ratio, 63–64 Accounts receivable, 63, 400, 408 Accounts receivable management ratios, 63 Accounts receivable turnover ratio, 63 Accrued wages, 401 Acid-test ratio (quick ratio), 60 ACP (average collection period) ratio, 63 Actual inflation rate, 168 Add-on interest, 136–137 Adjustable-rate mortgages, 206 ADK Industries, 316, 318, 320–321, 370 Adobe Systems Inc., 237 After-tax cash flow (ATCF), 345, 346, 348 Agency bonds, 152, 204 Agency problem, 17–18 Agency relationship, 17 Agency theory, 17–20 Agents, 17 Aging schedule, 417 Alcoa Inc., 246t Alphabet, 252, 262–264 Alternative assets, 354–356 American Express, 253t, 296t, 397t American Spectrum Realty, Inc., 45 American Stock Exchange (AMEX), 235, 237t, 238 American Tower Group, 150 AMEX (American Stock Exchange), 235, 237t, 238 Amortization schedules, 134–136 Amortized loans, 134–137 Anadarko Pete Corp, 223 Analyst opinions, 247 Angel investors, 13 Anginer, Deniz, 300 Anheuser-Busch InBev NV, 14, 223 Annual percentage rate (APR), 130–131 Annual reports, 26–27 Annuity, 118 Annuity cash flow analysis annuity loans, 133–137 compounding frequency and, 129–132 future value of multiple cash flows, 116–122 introduction, 115–116 ordinary annuities versus annuities due, 127–129 present value of multiple cash flows, 122–127 Annuity due, 127–129 Annuity loans, 133–136 Apple, Inc., 20, 253, 253t, 296t, 297t APP (average payment period) ratio, 63 APR (annual percentage rate), 130–131 Arithmetic average returns, 263–264 Ask, 241 Asset allocation, 273, 278 Asset-backed commercial paper (ABCP), 158 Asset-backed securities, 194 Asset-based loans, 408 Asset class, 10 Asset class performance, 265–266 Asset class risk, 269–270 Asset management ratios, 61–65 Asset pricing, 294 Assets alternative, 354–356 on balance sheet, 30 current, 29–32, 401, 408–409 financial versus real, 9–10, 383 fixed, 29–32, 343, 345 Asset transformers, 158 Assignment, 408 ATCF (after-tax cash flow), 345–346, 348 AT&T, 223f Auditors, 19 Auto loans, 166 Availability float, 414 Average collection period (ACP) ratio, 63 Average payment period (APP) ratio, 63–64 Average return, 263–264, 290, 292 Average tax rate, 36–37 B BA (banker’s acceptances), 151, 408 Balance sheet; see also Cash management; Financial statements; Ratio analysis; Working capital management book value versus market value, 32–33 debt versus equity financing, 31–32 definition and introduction, 28 fixed asset depreciation, 30 liquidity, 30–31 net working capital, 30, 408 Banker’s acceptances (BA), 151, 408 Bank loans, 158–159, 424 Bank of America, 148, 150 Bank of America Merrill Lynch, 150, 157 Bank of New York, 277, 279e Barabas Economic Order Quantity (EOQ), 400 Barclays, 150 Barclays Capital, 223 Basic earnings power (BEP) ratio, 68–70 Baumol, William, 409 Baumol model, 409–411 Beach Sand Resorts, 200 Bearer bonds, 202 Behavioral finance, 128, 240, 303–304 Benchmarks, 390 BEP (basic earnings power) ratio, 68–70 Beta (β) calculating, 298–299 concerns about, 300–301 definition, 295 portfolio, 297–298 proxy, 324 security market line and, 296–298 Bid, 240 Bid-ask spread, 207, 241 Blinder, Meyer, 301 Blinder-Robinson, 301 Board of directors, 19 Boeing Company, 115, 252–253, 253t Bond-based securities, 204–206 Bond interest cost of capital and, 343 Bond markets historical returns, 262, 266 historical risks, 266 overview, 222–224 Bond price; see also Bond valuation callable bonds, 215–217 definition, 211 interest rate risk and, 211–213 quotes, 207–208 yield relationship to, 179, 218, 219t Bond rating, 219–221 Bonds; see also Corporate bonds; Debt; Leverage; Treasury bonds; Individual securities and interest rates agency, 204 asset class correlation and, 265–266 bearer, 202 as capital market instruments, 152 capital raised with, 203f characteristics of, 200–202 convertible, 206 credit ratings on, 219–221 default risk premiums on, 169 definition, 200 issuers, 202–203 municipal, 202, 203, 203f, 217–218 premium or discount, 207 state and local, 152 zero-coupon, 209 Bond valuation credit risk and, 219–222 interest rate risk and, 211–213 introduction, 199 present value of cash flows, 209–211 price and yield relationship, 196n, 213–217, 223 quotes, 207–209 yields current, 213–214, 218t summary of, 218–219 taxable equivalent, 217 yield to call, 215–217, 218t yield to maturity, 214–215, 218t Book (historical cost) value, 32–33 Book value per share (BVPS), 45 Boston Red Sox, 124 Brokerage firms, 240 Brokers, 235 Bubbles, 239, 240, 304–305 Budgets, cash, 422–424; see also Capital budgeting Budweiser, 14 Burnside, Tina, 128 Business organization agency problem, 17–18 page 440 characteristics, 13 corporate governance, 18–19 ethics roles, 19–20 executive compensation, 19e firm goals and, 15–16 Business ownership, 233 Business risk, 324 Buy-side analysts, 247 BVPS (book value per share), 45 C Calculators; see Financial calculators Call (bond feature), 201, 201t Call premium, 201 Capital, 4; see also Cost of capital Capital asset pricing model (CAPM) component cost of equity using, 318, 330–331 definition and introduction, 294 required return and, 296–297 Capital budgeting; see also Cash flow estimation; Cost of capital; Internal rate of return benchmark format, 390 decision statistic format, 372–373 introduction, 369–370 net present value, 378–381 payback and discounted payback, 374–378 profitability index, 390–391 separation principle of, 331 technique choices, 371 Capital gain, 247 Capital intensity ratio, 72t Capital market, 151 Capital market efficiency, 301–304 Capital market instruments, 152f, 152–153 Capital market line (CML), 294–296 Capital structure debt versus equity financing, 66–67 definition and introduction, 32 Cargill, 28 Car loans, 131, 134–135 Carrying costs, 403 Cash, surplus or idle, 415–416 Cash, tracing, 401–402 Cash budget, 422–424 Cash coverage ratio, 67–68 Cash cycle, 402 Cash flow after-tax, 345, 348, 355e definition, 4 diagram of, 8f, 9f, 21f financial decisions and, 9–10 incremental, 341–343, 354 moving, 101–102 normal, 374 stock price and, 16 stock valuation and, 241–243 Cash flow estimation accelerated depreciation, 349–352 of alternative assets, 354–356 EAC approach, 354–356 flotation costs, 356–357 guiding principles for, 341, 343 half-year convention, 349–352 introduction, 341 project descriptions, 340–341 special cases, 352–354 total project cash flows, 343–348 Cash flows from financing activities, 40–41 Cash flows from investing activities, 40 Cash flows from operations, 40 Cash management Baumol model, 409–410 cash balance rationale, 409–410 Miller-Orr model, 410–411 Cash ratio, 61 Caterpillar, 253t, 296t, 297t CBC Newscorp, 235 CEO (chief executive officer), 17 Certificates of deposit, 151, 416 CFOs (chief financial officers), 11 Charles Schwab, 240 Check Clearing for the 21st Century Act, 415 Check kiting, 415 Chevron, 252, 253t, 296t, 197t Chewbacca Manufacturing, 400 Chief executive officer (CEO), 17 Chief financial officers (CFOs), 11 China, 154 Cisco Systems, 253t, 296t, 297t Citigroup, 150, 277 Class life, 349 CML (capital market line), 294–295 Coca-Cola Company, 153, 242, 243, 253t, 296t, 297t, 245–247, 251 Coefficient of variation (CoV), 270 Colgate-Palmolive Company, 28 Collection policies, 417 Commercial banks, 148, 155t Commercial paper, 151, 408–409, 416 Commitment fees, 407–408 Common-size financial statements, 75 Common stock, 234–235 Common stock and paid-in surplus, 30 Compensating balance, 407, 413 Complement and substitute, 343 Component costs, 316, 331; see also Cost of capital Compounding, 92–98, 118, 128–132 Compromise financing policy, 406–407 Concentration banking, 414 Consols, 127 Constant-growth model component cost of equity using, 317 component cost of preferred stock, 318 dividend discount models, 243–245 preferred stock and, 245–246 for required return, 304–306 Consumer price index (CPI), 168 Convertible bonds, 206 Corporate bonds as capital market instruments, 152, 203, 203f convertibility, 206 credit risk, 219–222 issuers, 202–203 quotes on, 207–209 secondary market for, 202 Corporate governance, 18–20 Corporate social responsibility (CSR), 15 Corporate stocks, 152; see also Stock Corporate taxes; see also Modigliani-Miller theorem income tax rates, 36t, 321t project WACC and, 322 Corporations; Capital structure; Cost of capital; International corporate finance agency problem, 17–18 definition, 14–15 divisional WACC, 326–330 ethics and, 19–20 firm goals, 15–16 firm versus project WACC, 322–326 governance of, 18–19 Correlation, 276–277 Cost of capital; see also Capital budgeting; Weighted-average cost of capital flotation costs, 330–331, 356–357 introduction, 315–316 preferred stock, 318 Cost of debt, 318–319, 357 Cost of equity component, 317–318, 325, 343 proxy betas and, 324 Costs; see also Cost of capital financing, 343 flotation, 330–331, 356–357 minimizing, 15–16 opportunity, 342, 401, 409–410 sunk, 342 Coupon, 201–202 Coupon rate, 200t, 201, 201t Covenants or special provisions, 171 Coverage ratios, 67–68 CoV (coefficient of variation), 270 CPI (consumer price index), 168–170 Credit analysis, 416–417 Credit analysts, 19 Credit cards, 132, 137 Credit hedge funds, 158 Credit management, 416–417 Credit quality risk, 219 Credit ratings, 219–220 Credit (default) risk, 169–170, 219–222 Credit risk premium, 169 Credit scores, 103 Credit terms, 416 CreditWatch, 220 Cross-sectional analysis, 77–78 CSR (corporate social responsibility), 15 Cultural differences, 415 Current assets, 29–31, 401, 403–404 Current liabilities, 29–30, 401 Current ratio, 60, 72t Current yield, 213–214, 218t D Daily interest rate, 130 Dawa Tech, 234 Days’ sales in inventory, 62 DDB depreciation method, 349–350 Dealers, 237 Debentures, 220 Debt financing; see also Capital structure equity financing versus, 31–32, 35–36, 66–67 Debt management ratios, 66–68, 72t Debt ratio, 66 Debt-to-equity ratio, 66 Decision statistics, 372–373 Default (credit) risk, 169–170, 219–222 Default risk premium, 169 Defined benefit plans, 12 Defined contribution plans, 12 Delegated monitor, 157 Dell, 264 Demand for loanable funds, 162–163, 164f, 164t, 165t Depreciable basis, 344 Depreciation calculating, 344 definition, 30 half-year convention, 349–350 on income statements, 33 MACRS, 30, 45, 349–350 Section 179 deduction, 350 straight-line method, 30 Derivative securities, 154 Derivative securities markets, 154 Descartes, René, 396n Deutsche Bank, 149 Dimmock, Stephen G., 273 Dimon, James, 157 Direct transfers, 155 Disbursement float, 414 Disbursement policies, 414–415 Discount bond, 207, 218 Discounted payback (DPB), 375–378 Discounting, 98–100 Discount rate, 99–100, 209–211 Discount window rate, 160 Disney, 20, 253t, 271, 277t, 296t, 297t, 298, 279e Diversifiable risk, 271 Diversification definition and overview, 270, 271–273 modern portfolio theory and, 274–279 Dividend discount models, 243–245 Dividend payout ratio, 70 Dividends in cash flow estimation, 343 cost of capital and, 316 cost of equity and, 318e received by corporations, 37 stock valuation methods cash flows, 241–243 constant growth model, 246 dividend discount models, 243–245 expected return and, 246–247 future price estimates, 254 P/E model, 251–254, 253t preferred stock, 245–246 variable-growth model, 248–250 tax status of, 316 Dividends per share (DPS), 35 Dividend yield, 246, 247 Divisional WACC, 326–330 DJIA; see Dow Jones Industrial Average Dollar return, 262 Double taxation, 15 Dow, Charles H., 238 Dow Jones Industrial Average (DJIA) bubbles and crashes, 305 page 441 component stock betas, 295 component stock required returns, 296t definition and overview, 238–239 during financial crisis, 152 forward P/E ratios, 253t historical levels, 239f historical P/E ratios, 251f interest rate effects on, 161 DPB (discounted payback), 375–378 DPH Tree Farm, Inc. asset management ratios, 62–65 balance sheet, 28–29, 31t debt management ratios, 66–68 DuPont analysis, 71–75 financial statement analysis, 60, 78 free cash flow, 42–43 income statement, 33–38 internal and sustainable growth rates, 76–77 liquidity ratios, 60–62 profitability ratios, 68–70 ratio summary, 72 statement of cash flows, 38–42 statement of retained earnings, 44 DPS (dividends per share), 35 Drafts, 414 DuPont Corporation, 73, 296t, 297t DuPont system of analysis, 73–75 Dutch Shell Plc, 220 E EAR (effective annual rate), 130–132 Earnings before interest, taxes, depreciation, and amortization (EBITDA), 33 Earnings before interest and taxes (EBIT), 34, 343–345 Earnings before taxes (EBT), 34 Earnings management, 45 Earnings per share (EPS), 35 EBITDA (earnings before interest, taxes, depreciation, and amortization), 33 EBIT (earnings before interest and taxes), 34, 343–345 EBT (earnings before taxes), 34 Economic conditions; see also Financial crisis of 2007–2009 loanable funds theory and, 159–161 market risk and, 271 Economic Policy Institute, 19 Economic profits, 391 Economies of scale, 17 Edward Jones, 240 Effective annual rate (EAR), 130 Efficient frontier, 275, 294–295 Efficient market, 301 Efficient market hypothesis (EMH), 302–303 Efficient portfolios, 274 E.I. DuPont de Nemours & Co., 86, 246t, 253t, 296, 296t, 297t Einstein, Albert, 93, 101 EMC Corporation, 240 EMH (efficient market hypothesis), 302–303 Employee stock option plan (ESOP), 18 Enron Corp., 24n, 45 EOQ (Barabas Economic Order Quantity), 400 EPS (earnings per share), 35 Equilibrium interest rate, 163–165 Equipment trust certificates, 221 Equity component cost of, 317–318, 325, 331, 357 definition, 13, 233 Equity financing; see also Capital structure debt financing versus, 37–38, 66–67 Equity multiplier, 66 Equivalent taxable yield, 217–218 ESOP (employee stock option plan), 18 Ethics, 19–20, 415 E-trade, 240 Euronext, 235 European Central Bank, 7 European Union (EU), 222 Exchange rate risk, 153 Executive compensation, 19e Executive stock options, 304 Expected inflation rate, 168–169 Expected return definition, 291 equations, 246–247, 291–292 IRR statistic as, 381–382 risk and, 290–292, 300, 383 Exxon Mobil, 253t F Factor, 408 Fair interest rate, 173 Fallen angels, 221 Fannie Mae, 204–206 FCF (free cash flows), 42–43, 343–344 Federal Farm Credit System, 204 Federal funds, 151 Federal funds rate, 193f Federal Home Loan Banks, 204 Federal Housing Finance Agency, 205 Federal Reserve bank-to-bank transfers through, 414 financial stability initiatives, 196 monetary policy of, 164–165, 203 Fedwire, 414 Fidelity, 28, 147 FIFO (first-in, first-out), 78 Finance accounting versus, 10–11 application and theory for decision-making, 9–10 in business and life, 4–11 definition, 4 in other business functions, 11–12 in personal life, 12 subareas of, 4, 8–9 Finance companies, 155t Financial analysts, 247 Financial assets, 9, 370, 382–383 Financial calculators AMORT function, 137 annuities, 119 annuity due, 129 bond valuations, 209–213 expected return and standard deviation, 290 interest rates, 103, 175, 202 MIRR calculations, 385 net present value, 376 overview, 97–98 payback and discounted payback, 375 portfolio returns, 278 TVM calculations, 97–98, 103, 125, 379–380 Financial crisis of 2007–2009 causes of, 154, 159, 205–206 derivative securities role, 154 Federal Reserve initiatives, 191t, 193 mortgage-backed securities role, 154, 206 NYSE trading volume during, 151 stock market returns, 153, 266 Financial function, 11–12 Financial institutions definition, 9, 155 direct transfers versus, 155 functions of, 155–159 interest rates and, 159–167 introduction, 155 types, 155t Financial leverage, 295 Financial management, 9f Financial managers, 11, 304–306 Financial markets capital versus money, 151–153 definition, 5, 148 derivative securities, 154 foreign exchange, 153–154 interest rates and, 159–167 introduction, 21, 148 primary versus secondary, 148–151 Financial policy, 403–407 Financial risk, 336n3 Financial statement analysis asset management ratios, 62–65 cautions in using ratios, 78–79 cross-sectional analysis, 77–78 debt management ratios, 67–68 DuPont analysis, 71–75 internal and sustainable growth rates, 76–77 introduction, 78 liquidity ratios, 60–62, 79 market value ratios, 70–71 profitability ratios, 68–70 spreading financial statements, 75 time series analysis, 77–78 Financial statements; see also Financial statement analysis; Working capital management balance sheet book value versus market value, 32–33 debt versus equity financing, 31–2 definition and introduction, 28–29 fixed asset depreciation, 30 liquidity, 30–31 net working capital 30, 408 definition and overview, 28 free cash flow, 42–43 income statement, 33–38 interpretation cautions, 44–45 statement of cash flows, 38–42 statement of retained earnings, 44 Financial theories, 4 Financing costs, 343 Firm-specific risk, 271 Firm values; see Modigliani-Miller theorem Firm WACC divisional WACC, 326–330 project WACC versus, 322–326 First-in, first-out (FIFO), 78 Fisher, Irving, 168 Fisher, Kenneth L., 300 Fisher effect, 168–69 Fitbit, 149 Fitch IBCA, Inc., 219 Fitzpatrick, Dan, 157n Five C’s, 416 Fixed asset ratios, 62 Fixed assets, 29–31, 343, 345, 348 Fixed asset turnover ratio, 64 Fixed-charge coverage ratio, 67–68 Fixed-income securities, 200, 246 Flexible financing policy, 405–406 Float, 414 Float control, 413–415 Florida State transportation bonds, 208e Flotation costs, 330–331, 356–357 Ford Motor Company, 246t Forecasting; see also Financial statement forecasting interest rates, 179–180 Foreign exchange markets, 150, 152 Foreign exchange risk, 153 Forward P/E ratio, 252, 253t Forward rate, 179 401(k) plans, 12 Freddie Mac, 187, 192, 204–205 Free cash flows (FCF), 42–43, 343–344, 348–349, 354 Future price, 254 Future value (FV) of an annuity, 118 of an annuity due, 127–128 compounding effects, 92–93, 96, 129–132 definition, 91 of level cash flows, 118–19 moving cash flows and, 101–102 of multiple annuities, 119–120 of multiple cash flows, 116–122 in N periods, 96 in N years, 98 in one year, 98 solving for time, 105–106 of a stock, 254 FV; see Future value G GAAP (generally accepted accounting principles), 32, 39, 44–45, 57n, 78 GassUp, 322–323 Gates, Bill, 233 General Electric (GE), 253t, 271, 277t, 278, 296, 297t General Motors (GM), 221 General partnerships, 13–14 Geometric mean return, 265 La Geometrie (Descartes), 396n Ginnie Mae, 149 GM (General Motors), 221 Gold, investments in, 103–105, 305 Goldman Sachs, 148, 150, 253t, 296t, 297t Google, 233, 237, 252, 262 Gordon, Myron J., 244 Gordon growth model, 244 page 442 Government agency securities, 152, 204 Great Recession; see Financial crisis of 2007–2009 Greece, 166, 220, 222 Gross fixed assets, 343, 345 Gross profit, 33 Gross profit margin ratio, 68–69 Growth stocks, 246, 247 H Half-year convention, 349–352 Head Phone Gear, Inc., 90 Hedge funds, 157–158 Hewlett-Packard, 264e, 298e, 306e High-yield (junk) bonds, 220 Historical cost (book) value, 32 Historical interest rates, 160f Historical returns by asset class, 265–266, 269–270 asset class correlation and, 277, 277t bond market, 160f, 265–266, 277t computing, 262–265 DJIA levels, 239t S&P 500, 263, 265, 269–272, 278, 294, 300 stock market, 265–266 Treasury securities, 160f, 265–266 Historical risks of asset classes, 269–270 risk versus return, 270 volatility computation, 266–269 Home Depot Inc., 223f, 253t, 296t, 297t, 306e Hoover’s Online, 78 Hybrid organizations, 15 I IBM, 158, 153, 253t, 271, 273, 275, 277t, 279e, 296t, 297 Iksil, Bruno, 157 IMF (International Monetary Fund), 222, 296t Income statement, 33–38, 39 Increasing the discount rate, 211 Incremental cash flows, 341, 354 Indenture agreement, 200, 218 Indian Point Kennels, Inc., 36–37, 45 Indirect transfer, 156 Individual Retirement Accounts (IRAs), 12 Individual securities and interest rates default or credit risk, 169–170 inflation, 168 liquidity risk, 170–171 real risk-free rates, 168–169 special provisions or covenants, 171 term to maturity, 171–173 Inflation definition, 168 Fisher effect and, 168–169 interest rate influences on securities and, 167–173 quantitative easing and, 7 TIPS and, 204 Inflow, 90 In-house processing float, 414 Initial public offerings (IPOs), 419 Insurance companies, 155t Intel Corporation, 20, 237, 253t, 296t, 297 Intercontinental Exchange, 235 Interest bond, 319–320, 343 in cash flow estimation, 343 paid by corporations, 37–38 received by corporations, 37 simple, 93 Interest-rate cognizant, 388 Interest rate risk, 211–213 Interest rates; see also Cost of capital; Yield on annuity loans, 133 bond price relationship to, 211, 212f, 215, 218, 223, 269 computing, 103–105 daily, 130 definition, 90 effects of changes in, 7, 161 equilibrium, 163 federal funds, 190, 193f forecasting, 179–180 forward, 179 future value and, 91–96 historical, 160 influencing factors for securities default or credit risk, 169–170 inflation, 168 liquidity risk, 170–171 real risk-free rates, 168–169 special provisions or covenants, 171 term to maturity, 171–173 IRR calculations and, 381 movement over time, 167 nominal, 167–170 risk-free, 168–169 summary, 218t Intermediaries, 21 Internal growth rate, 76 Internal rate of return (IRR); see also Modified internal rate of return as capital budgeting technique, 381 definition, 381 with mutually exclusive projects, 382, 385–389 with non-normal cash flows, 384 problems with, 383–384 reinvestment rate assumptions, 385 statistic and benchmark, 382 Internal Revenue Service (IRS), 19, 344, 345, 346, 349–350 International finance, 9 International investing, 278 International Monetary Fund (IMF), 222 Inventory, 62–63 Inventory loans, 408 Inventory management, 400 Inventory management ratios, 62–63 Inventory turnover ratio, 62–63 Investment analysts, 19 Investment banks, 9, 148, 155t Investment grade, 220 Investment in operating capital (IOC), 43 Investments cash management policy and, 410, 413, 416 definition, 8 financial analysts and, 247 rate of return on, 103–105 surplus or idle cash and, 415–416 Investors angel, 13 behavior of, 128, 276, 303–304 corporate governance and, 18–19 definition, 6 firm goals, 15–16 organization types, 12–15 Invisible hand, 16 Invoices, 416 IOC (investment in operating capital), 43 Iomega, 240 IPOs (initial public offerings), 149 IRAs (Individual Retirement Accounts), 12 IRR; see Internal rate of return IRS (Internal Revenue Service), 19, 344–346, 349–350 J Japan, 7, 312, 347, 415 JIT (just in time), 400 Jobs, Steven, 20 Johnson & Johnson, 115, 253t, 296 JP Morgan, 157 JP Morgan Chase,157, 223, 296t Junk (high-yield) bonds, 220 Just in time (JIT), 400 K Kaizen, 404 Kohls Corporation, 208e Kouwenberg, Roy, 273n L Last-in, first-out (LIFO), 78 Late payments, 103 Leverage, financial, 31, 295 Liabilities, 29–30, 400–401 Liability, 13–15 LIFO (last-in, first-out), 78 Limited liability, 15 Limited liability companies (LLCs), 15, 24n1 Limited liability partnerships (LLPs), 15 Limited partners, 15 Limited partnerships (LPs), 15 Limited-purpose finance companies, 158 Limit order, 241 Line of credit, 407–408 Lintner, John, 294 Liquidity, 28–31, 158 Liquidity premium theory, 176–177 Liquidity ratios, 60–62, 79 Liquidity risk, 168t, 169, 170–171 LLCs (limited liability companies), 15, 24n1 LLPs (limited liability partnerships), 15 Loanable funds theory definition, 161 demand and, 162–163, 164t, 165f, 166–167 equilibrium interest rate, 163 supply and, 161–162, 163f, 164t Loan principal, 134–135 Loans annuity, 133–137 unsecured, 407–408 Local government bonds, 152 Lockbox system, 414 Long-term debt, 29 Lottery winnings, 127 LPs (limited partnerships), 15 M MACRS method of depreciation, 30, 78, 349–350 Mail float, 414 Major League Baseball, 124 Management; see also Working capital management agency problem and, 17–18 corporate governance and, 18–19 operations, 400 Marginal tax rate, 36–37 Marketable securities, 29–41 Market capitalization, 238 Market interest rate, 218t Market makers, 237 Market order, 241 Market portfolio, 294–295 Market risk beta and, 295–296 definition, 271 market portfolio, 294–295 security market line, 296–298 Market risk premium, 294–296 Market segmentation theory, 177–179 Market share, maximizing, 15–16 Market-to-book ratio, 70 Market value, 32–33, 263 Market value per share (MVPS), 35 Market value ratios, 70–71 Markkula, Mike, 20 Markowitz, Harry, 274 Mattel, Inc., 262–264, 265t, 266–269, 271, 272t Maturity date, 200 Maturity premium, 173–174 Maximization of shareholder wealth, 15–16 Maximizing the current value per share, 16 MBSs (mortgage-backed securities), 152, 154, 158, 205 McDonald’s, 236, 241, 242, 243, 244f, 251f, 252, 253t, 297t, 298, 305–306 Merck & Company, 45, 253t, 296t, 297t Merrill Lynch, 148, 150, 186, 188, 240 Microsoft, 232, 237, 253t, 296t, 297t Miller, M. H., 425n Miller-Orr model, 410–411 MIRR; see Modified internal rate of return Mitchell, Olivia S., 273n MMMFs (money market mutual funds), 158 Modern portfolio theory CAPM and, 294 concept of, 274 diversification and, 275–277 portfolio return, 278–279 Modified internal rate of return (MIRR) as capital budgeting technique, 371–372 definition, 385 with mutually exclusive projects, 385–389 page 443 strengths and weaknesses, 389–390 Molson Coors Brewing, 14 Monetary expansion, 165 Money market instruments, 151 Money market mutual funds (MMMFs), 158 Money markets, 151 Monitoring costs, 157–158 Moody’s Investors Service, 169, 219, 222 Morgan Stanley, 147–149 Morgan Stanley Smith Barney, 240 Mortgage-backed securities (MBSs), 152, 154, 205 Mortgage bonds, 221 Mortgages as capital market instruments, 152 interest rates on, 160f payment calculation, 136 refinancing, 117 subprime, 205–206 MP3 Devices, Inc., 316 MPT; see Modern portfolio theory MSCI Barra indexes, 278 MSN Money, 78, 298 Municipal bonds, 169, 202–203, 203f, 208, 217–218 Mutual funds, 155t Mutually exclusive projects, 374, 385–389 MVPS (market value per share), 35 N NASDAQ 100, 305 NASDAQ Composite Index, 150, 156, 236–238 NASDAQ OMX, 246t NASDAQ Stock Market, 150, 156, 237–238 National Healthcare, 246t Near-term spending needs, 165 Negotiable certificates of deposit, 151t, 416 Net change in cash and marketable securities, 41 Netflix, 237 Net income, 16, 34 Net operating profit after taxes (NOPAT), 43 Net present value (NPV) as capital budgeting technique, 378–381 definition, 378 EAC approach, 355 for non-normal cash flows, 380e, 384 for normal cash flows, 383 NPV profiles, 383–384 reinvestment rate assumptions, 385 statistic and benchmark, 382 strengths and weaknesses, 389 Net working capital (NWC), 30, 346–347, 401–403 Newmont Mining, 271–273, 275, 277–278 New York City Municipal Water Finance Authority, 208 New York Stock Exchange (NYSE) definition and overview, 235–237 delisting from, 46 as secondary market, 150 secondary market trading, 150–151 tracking, 236f, 238 trading volume, 150–151 NeXT Computer, 20 Nike, Inc., 253t, 296t, 297 Nikkei 305 Nominal interest rates, 159, 167 Noncash income statement entries, 39 Nondiversifiable risk, 272 Nonprice terms on loanable funds, 163, 166–167 NOPAT (net operating profit after taxes), 43 Normal cash flows, 374 NPV; see Net present value NPV profiles, 383–384 Nucor Corp., 290–292 NWC (net working capital), 30, 346–347 NYSE; see New York Stock Exchange (NYSE) NYSE MKT LLC, 46 NYSE Regulation, Inc., 46 O Oil prices, 21–22 OMX, 237 Operating cash flow (OCF), 42–43, 344–345 Operating cycle, 401, 402e Operating income, 57n1 Operating profit margin ratio, 68–69 Operations management, 400 Opportunity cost, 342, 401, 409–410, 416 Optimal cash return point, 411, 412e Optimal portfolio, 274 Options, 18 Ordinary annuities, 118, 127–129 Orr, D., 425n Outflow, 90 Overconfidence, 304 Over-the-counter market, 151 P Page, Larry, 233 Paper, commercial, 151, 408–409, 416 Partnerships, 13–14 Par value, 200, 201t Patriot bonds, 205 Payback (PB), 374 Payday lending, 91, 103 Payment on amortized loans, 134–137 PB (payback), 374 Peijnenburg, Kim, 273n Penny stocks, 301 Pension funds asset allocation and, 273 characteristics of, 155t compounding and, 120–122, 131 as investors, 200, 220 P/E (price-earnings) ratio, 71, 251–253, 253t Percentage return, 263–265 Performance of asset classes, 265–266 Perks (perquisites), 17 Perpetuities, 127 Pfizer, 296t, 297t, 253t PG&E Corp., 246t PI (profitability index), 372, 390–391 Pixar, 20 Portfolio beta, 297–298 Portfolio return, 278–279 Portfolios; see also Modern portfolio theory definition, 271 diversification using, 271–273 efficient, 278–279 market, 294–295 optimal, 274–274 Portfolio theory; see Modern portfolio theory Preferred stock, 29, 245–246 Premium bond, 207, 218 Present value (PV); see also Net present value of an annuity, 123–127 of an annuity due, 128–129 of a bond, 209–210, 214 of bond cash flows, 209–211 of cash flow made in N years, 98 definition, 10, 91 with different discount rates, 100 discounting and, 98–100 of dividend cash 123–124 moving cash flows and, 101–102 of multiple annuities, 124–127 of next period’s cash flow, 98 of a perpetuity, 127, 356 of several cash flows, 122–127 Price, David, 124 Price/book value ratio, 253 Price/cash flow ratio, 253 Price-earnings (P/E) ratio, 71, 251, 253t Price of a bond; see Bond price Price risk, 156, 158 Primary markets, 148–150 Prime rate, 160 Principal, 200 Principals, 20 Privately held information, 302 Private placements, 148–149 Probability, 291 Probability distribution, 291–292 Procter & Gamble, 246t, 253t, 296t, 297t Profitability index (PI), 372, 390–391 Profitability ratios, 68–70 Profit margin ratio, 68-69 Pro forma analysis, 340 Project WACC versus firm WACC, 322–326 Proxy beta, 324 Public corporations, 14–15 Public information, 302 Public Storage Inc., 246t Pure-play proxies, 324 PV; see Present value Q Qualcomm, 237 Quantitative easing (QE), 7 Quick ratio (acid-test ratio), 60–61 R RadioShack, 5 Rajan, Raghuram, 24n1 Rappaport, Liz, 157n Rate of return, computation of, 103–105, 133; see also Internal rate of return Ratio analysis asset management ratios, 62–65 cautions in using, 78–79 debt management ratios, 66–68 definition and introduction, 58–59 DuPont analysis, 71–75 internal and sustainable growth rates, 76–77 liquidity ratios, 60–62, 79 market value ratios, 70–71 profitability ratios, 68–70 spreading the financial statements, 75 summary, 72t Real assets, 10, 370, 371, 383 Realized gains, 263 Real markets, 10 Real risk-free rate, 168–169 Recourse, 408 Reinvestment rate risk, 212 Relative value, 251 Replenishment level, 410–411 Repurchase agreements (repos), 151, 416 Required return constant-growth model and, 304–306 cost of capital as, 382 definition, 292 security market line and, 296–297 Residual claimants, 234 Restricted stock, 20, 304 Restrictive financing policy, 405–407 Retained earnings, 6–8, 30 Retention ratio (RR), 76 Retirement plans, 120–121, 131 Return on assets (ROA), 68–69, 73–74 Return on equity (ROE), 68–69, 73–74 Returns; see also Expected return; Historical returns; Internal rate of return; Required return; Risk and return computing, 262–265 portfolio, 278–279 Riley, Charles, 128n Risk; see also Market risk; Risk and return business, 324 credit or default, 169–170 definition, 9 diversifiable, 271 exchange rate, 153 expected return and, 290–292 financial, 336n3 firm-specific, 271 interest rate, 211–213 liquidity, 170–171 loanable funds theory and, 165 market, 271 price, 156, 158 reinvestment rate, 212 systemic, 158 total, 266, 271 Risk and return capital market efficiency, 301–304 expected returns, 290–292 financial manager implications, 304–306 historical returns, 265t, 266t historical risks, 266–270 introduction, 261, 289–290 page 444 market risk beta and, 299–300 market portfolio, 294–295 security market line, 296–298 portfolios diversification, 270–271 modern portfolio theory, 274–279 trade-off between, 270 Risk-free rate, 168–169 Risk premium, 292–294 ROA (return on assets), 68–69, 73–74 Robert Morris Associates, 78 ROE (return on equity), 68–69, 73–74 Royal Dutch Shell, 220 RR (retention ratio), 76 Rule of 72, 101 Rule of Signs, 384 S SABMiller, 14 Safety stock, 409 Sales to working capital ratio, 64 Sallie Mae (Student Loan Marketing Association), 204 Salvage value, 341 Sarbanes-Oxley Act, 24n, 45 Savings bonds, 205 Schoen, John W., 206n S corporations, 15, 24n Scott, Mike, 20 Scottrade, 240 Sculley, John, 20 Secondary markets, 150–151 Secondary securities, 158 Section 179 deduction, 350 Secured loans, 408 Securities; see also Bonds; Stock; Individual securities and interest rates asset-backed, 205 bond-based, 204–206 cash management policy and, 410, 413, 416 definition, 8 derivative, 154 fixed income, 200, 246 government agency, 152, 204 marketable, 29, 41 mortgage-backed, 152, 154, 205 secondary, 158 Treasury, 161–162, 169–171, 203 Securities and Exchange Commission (SEC) corporate governance and, 18–19 as information resource, 27 securities registration with, 149 Securities firms, 153t Security market line (SML), 296–298 Sell-side analysts, 247 Semistrong-form efficiency, 302–303 Senior bonds, 220 Separation principle, 331 Shadow banks, 158 Shareholders, 15–18; see also Investors Sharpe, William, 294 Shortage costs, 399, 400, 403 Short-term financing policy, 403–407 Sidner, Sara, 128n Simple interest, 93 Single cash flow analysis future value compounding and, 92–95 definition, 91 interest rate computation, 105 introduction, 89–90 moving cash flows, 101–102 organizing cash flows, 90–91 present value, 98–100 solving for time, 105–106 Single-period future value, 91–92 SIVs (structured investment vehicles), 158 Small Business Administration, 24n1, 204 Smith, Adam, 16 Smith Barney, 240 SML (security market line), 296–298 Sole proprietorship, 12–13 Sources and uses of cash, 40–42 S&P 500 Index; see Standard & Poor’s 500 Index Special provisions or covenants, 171 Special purpose vehicles (SPVs), 158 Speculative bonds, 220 Spread, 406–407 Spreading financial statements, 75 Spreadsheets annuity computations, 130 beta computations, 296 bond pricing, 216 MIRR calculations, 386 net present value, 378 payback and discounted payback, 377 TVM functions, 97–98, 106 SPVs (special purpose vehicles), 158 Stakeholders, 15, 16–17 Standard deviation beta and, 295 definition and overview, 266–269 expected return and, 291–292 Standard & Poor’s 500 Index (S&P 500) definition and history, 238 diversification and, 270–271 historical returns, 262, 265t, 266t, 292, 299 Standard & Poor’s Corporation, 169, 219–220 Staples, Inc., 264, 265t, 268–271, 272t, 274–275, 277 State government bonds, 152 Statement of cash flows, 42–43 Statement of retained earnings, 44 Statman, Meir, 300n Stock; see also Dividends; Individual securities and interest rates asset class correlation and, 276–277 as capital market instruments, 152 common, 234–235 diversification to reduce risk, 271–273, 278 expected return and risk, 300 news and announcements effect on, 302–303 penny, 301 preferred, 29, 245–246, 318 restricted, 20, 304 trading, 240–241 Stockholders, 15, 17; see also Investors Stockholders’ equity, 29–30 Stock indexes, 238–2392; see also specific index Stock market bubbles, 239–240, 304–305 Stock markets efficient, 301–303 during financial crisis, 151–152 historical returns, 265–266 historical risks, 266–270 introduction, 235–241 tracking, 238–239 trading in, 240–241 Stock price definition, 16 estimating, 254 Stock valuation cash flows, 241–243 constant growth model, 246 dividend discount models, 243–245 expected return and, 246–247 future price estimates, 254 introduction, 241 P/E model, 251–253 preferred stock, 245–246 variable-growth model, 248–250 Straight-line method of depreciation, 30, 341, 344, 349 Strong-form efficiency, 302–303 Structured investment vehicles (SIVs), 158 Student Loan Marketing Association (Sallie Mae), 204 Subprime mortgage market, 205–206 Substitute and complement, 341–343 Sunk cost, 342 Supply of loanable funds, 161–162 Surplus cash, 416 Sustainable growth rate, 76–77 SWIFT system, 414 Systemic risk, 158 T Taxable equivalent yield, 217–219 Taxes; see also Modigliani-Miller (M&M) theorem on bond interest, 316 cash flows and, 7 component cost of capital and, 315–16 corporate, 36–38, 316.320–321 on dividends, 316 TD Ameritrade, 240 Term structure of interest rates definition and overview, 171–172 liquidity premium theory, 176–177 market segmentation theory, 177–179 unbiased expectations theory, 174–176 Term to maturity, 171–173 TheStreet.com Internet Index, 240 THQ, 5 3M Company, 284, 296t, 297t, 253t 3PAR, 264 Thrifts, 155t Ticker symbols, 236 Time line, 90 Time period calculations, 136–137 Time series analysis, 77–78 Times interest earned ratio, 67–68 http://www.TheStreet.com Time to maturity, 200, 201t Time value of money (TVM); see also Annuity cash flow analysis; Capital budgeting; Net present value; Single cash flow analysis definition and introduction, 10, 90 financial calculators for, 97–98, 103, 125, 379–380 spreadsheet functions for, 106 TIPS (Treasury Inflation-Protected Securities), 204 Total asset management ratios, 64–65 Total asset turnover ratio, 64–65 Total cost, 404–410 Total return, 218t Total risk, 266, 268, 271 Toys “R” Us, 28 Trade-off between risk and return, 270 Trading cost, 409–410 Trading posts, 235 Trading volume, 150 Trailing P/E ratio, 251 Transaction facilitation, 409 Travelers, 253t, 296t, 297t Treasurer roles, 11 Treasury bills asset class correlation and, 277t, 278 historical returns, 152f, 265, 266t historical risks, 266 interest rates on, 160f, 161 as money market instrument, 151 as risk-free securities, 169, 292–294 Treasury bonds asset class correlation and, 278 as bond market indicator, 207 credit risk and YTM, 221 historical returns, 265 historical risk, 266 overview, 203 risk-free rate on, 292 TreasuryDirect, 205 Treasury Inflation-Protected Securities (TIPS), 204 Treasury notes and bonds as capital market instruments, 152 capital raised with, 203f purchasing, 205 quotes on, 207–209 yield curves on, 171–173 Treasury securities, 172 Trust Media, 201 Trust receipts, 408 Tulip Mania, 240 TVM; see Time value of money Two-stage growth valuation model, 249 Tyco International, 24n U UBS, 240 Unbiased expectations theory, 174, 176 UnitedHealth Group, 253t, 296t U.S. Commerce Department, 168, 194 U.S. government agency bonds, 152, 204 U.S. government agency securities, 204 U.S. Treasury, 148 U.S. Treasury bills; see Treasury bills U.S. Treasury bonds; see Treasury bonds U.S. Treasury notes and bonds; see Treasury notes and bonds U.S. Treasury securities, 161–162 page 445 United Technologies, 253t, 296t, 297t Unlimited liability, 13 Unrealized gains, 263 Unsecured corporate bonds, 220 Unsecured loans, 407–408 Upper limit for cash balances equation, 412 V Valuation methods; see Bond valuation; Stock valuation Value Line Investment Surveys, 78 Value stocks, 252 Variable-growth rate, 248–250 Variance, 266–268 Venture capitalists, 13 Verizon, 150, 296 Verizon Communications, 253t, 297t Visa, Inc., 223f, 253t, 296t, 297t Volatility, computation of, 266–296 Von Gaudecker, Hans-Martin, 273n W WACC; see Weighted-average cost of capital Wages, accrued, 401 Walkabout Music, Inc., 116 The Wall Street Journal, 207, 223–224 Walmart, 36, 253t, 296t, 297t Walt Disney Company, 253t, 271, 277, 296t, 297t, 298 Warehousing financing, 408 Weak-form efficiency, 302–303 Wealth, loanable funds theory and, 161 Wealth of Nations (Smith), 24n Weighted-average cost of capital (WACC) component cost of debt, 318–319 component cost of equity, 317–318 component cost of preferred stock, 318 definition and equation, 316 divisional, 326–330 firm versus project, 322–326 flotation cost adjustments, 330–331, 356–357 tax rates and, 319–321 weight calculations, 321–322 Weighted-average flotation cost, 356–357 Weights, 278 Wet Seal, 5 Wire transfers, 414 Working capital management balance sheet review, 400–401 cash and net working capital tracing, 401–403 cash budgets, 409–413 cash management, 422 credit management, 416–417 cultural differences in, 415 float control, 413–415 idle cash investment, 415–416 introduction, 399–400 short-term financing plans, 407–408 short-term financing policies, 403–407 Working capital management ratios, 63 WorldCom, 24n, 45 page 446 Wozniak, Stephen, 20 Wulf, Julie, 24n Y Yahoo! Finance, 20, 236f, 245, 247, 298 Yellow Jacket, Inc., 422, 424 Yield current, 213–214, 218t dividend, 246–247 summary of, 218–219 taxable equivalent, 217–218 Yield curves liquidity premium theory and, 176–177 market segmentation theory and, 177–179 overview, 174 unbiased expectations theory and, 174–176 Yield to call, 217, 218t Yield to maturity, 214–215, 218t Z Zero-balance accounts, 414 Zero coupon bonds, 209 Zuckerman, Gregory, 157n Cover Halftitle Title Copyright A Note from the Authors Changes to the Fourth Edition Connect Brief Contents Contents Contents Part One: Introduction Chapter 1: Introduction to Financial Management Part Two: Financial Statements Chapter 2: Reviewing Financial Statements Chapter 3: Analyzing Financial Statements Part Three: Valuing of Future Cash Flows Chapter 4: Time Value of Money 1: Analyzing Single Cash Flows Chapter 5: Time Value of Money 2: Analyzing Annuity Cash Flows Part Four: Valuing of Bonds and Stocks Chapter 6: Understanding Financial Markets and Institutions Chapter 7: Valuing Bonds Chapter 8: Valuing Stocks Part Five: Risk and Return Chapter 9: Characterizing Risk and Return Chapter 10: Estimating Risk and Return Part Six: Capital Budgeting Chapter 11: Calculating the Cost of Capital Chapter 12: Estimating Cash Flows on Capital Budgeting Projects Chapter 13: Weighing Net Present Value and Other Capital Budgeting Criteria Part Seven: Working Capital Management and Financial Planning Chapter 14: Working Capital Management and Policies Viewpoints Revisited Chapter Equations Index

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