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Fundamentals of

Corporate Finance

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Richard A. Brealey London Business School

Stewart C. Myers Sloan School of Management, Massachusetts Institute of Technology

Alan J. Marcus Carroll School of Management, Boston College

Fundamentals of

Corporate Finance

EDITIONTenth

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mheducation.com/highered

FUNDAMENTALS OF CORPORATE FINANCE, TENTH EDITION

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Library of Congress Cataloging-in-Publication Data

Brealey, Richard A., author. | Myers, Stewart C., author. | Marcus, Alan J., author. Fundamentals for corporate finance / Richard A. Brealey, London Business School, Stewart C. Myers, Sloan School of Management, Massachusetts Institute of Technology, Alan J. Marcus, Carroll School of Management, Boston College. Tenth Edition. | Dubuque, IA : McGraw-Hill Education, [2019] | Revised edition of Fundamentals of corporate finance, [2018] | Includes bibliographical references and index. LCCN 2018047649 | ISBN 9781260013962 (student edition : alk. paper) LCSH: Corporations—Finance. LCC HG4026 .B6668 2019 | DDC 658.15—dc23 LC record available at https://lccn.loc.gov/2018047649

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To Our FamiliesDedication

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vi

Alan J. Marcus Mario Gabelli Professor of Finance in the Carroll School of Management at Boston College Professor Marcus’s main research interests are in derivatives and securities markets. He is co-author (with Zvi Bodie and Alex Kane) of the texts Investments and Essentials of Investments (McGraw-Hill Education). Professor Marcus has served as a research fellow at the National Bureau of Economic Research. Professor Marcus also spent two years at Freddie Mac, where he helped to develop mortgage pricing and credit risk models. He currently serves on the Research Foundation Advisory Board of the CFA Institute.

Stewart C. Myers Gordon Y Billard Professor of Finance at MIT’s Sloan School of Management Dr. Myers is past president of the American Finance Association and a research associate of the National Bureau of Economic Research. His research has focused on financing decisions, valuation methods, the cost of capital, and financial aspects of government regulation of business. Dr. Myers is a director of The Brattle Group, Inc. and is active as a financial consultant. He is also the author (with Professor Brealey and Franklin Allen) of this book’s sister text, Principles of Corporate Finance (McGraw-Hill Education).

Richard A. Brealey Professor of Finance at the London Business School Professor Brealey is the former president of the European Finance Association and a former director of the American Finance Association. He is a fellow of the British Academy and has served as Special Adviser to the Governor of the Bank of England and as director of a number of financial institutions. Professor Brealey is also the author (with Professor Myers and Franklin Allen) of this book’s sister text, Principles of Corporate Finance (McGraw-Hill Education).

The AuthorsAbout

Courtesy of Richard A. Brealey

Courtesy of Stewart C. Myers

Courtesy of Alan J. Marcus

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vii

This book is an introduction to corporate finance. It focuses on how companies invest in real assets, how they raise the money to pay for the investments, and how those assets ultimately affect the value of the firm. It also provides a broad overview of the financial landscape, discussing, for example, the major players in financial markets, the role of financial institutions in the economy, and how securities are traded and valued by investors. The book offers a framework for systematically thinking about most of the important financial problems that both firms and individuals are likely to confront.

Financial management is important, interesting, and challenging. It is important because today’s capital investment decisions may determine the businesses that the firm is in 10, 20, or more years ahead. Needless to say, a firm’s success or failure also depends, in large part, on its ability to find the capital that it requires.

Finance is interesting for several reasons. Financial decisions often involve huge sums of money. Large investment projects or acquisitions may involve billions of dol- lars. Also, the financial community is international and fast-moving, with colorful heroes and a sprinkling of unpleasant villains.

Finance is challenging. Financial decisions are rarely cut and dried, and the finan- cial markets in which companies operate are changing rapidly. Good managers can cope with routine problems, but only the best managers can respond to change. To handle new problems, you need more than rules of thumb; you need to understand why companies and financial markets behave as they do and when common practice may not be best practice. Once you have a consistent framework for making financial decisions, complex problems become more manageable.

This book provides that framework. It is not an encyclopedia of finance. It focuses instead on setting out the basic principles of financial management and applying them to the main decisions faced by the financial manager. It explains how managers can make choices between investments that may pay off at different points of time or have different degrees of risk. It also describes the main features of financial markets and discusses why companies may prefer a particular source of finance.

We organize the book around the key concepts of modern finance. These concepts, properly explained, simplify the subject. They are also practical. The tools of financial management are easier to grasp and use effectively when presented in a consistent conceptual framework. This text provides that framework.

Modern financial management is not “rocket science.” It is a set of ideas that can be made clear by words, graphs, and numerical examples. The ideas provide the “why” behind the tools that good financial managers use to make investment and financing decisions.

We wrote this book to make financial management clear, useful, and fun for the beginning student. We set out to show that modern finance and good financial practice go together, even for the financial novice.

Fundamentals and Principles of Corporate Finance

This book is derived in part from its sister text Principles of Corporate Finance. The spirit of the two books is similar. Both apply modern finance to give students a work- ing ability to make financial decisions. However, there are also substantial differences between the two books.

Preface

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viii Preface

First, we provide in Fundamentals much more detailed discussion of the princi- ples and mechanics of the time value of money. This material underlies almost all of this text, and we spend a lengthy chapter providing extensive practice with this key concept.

Second, we use numerical examples in this text to a greater degree than in Principles. Each chapter presents several detailed numerical examples to help the reader become familiar and comfortable with the material.

Third, we have streamlined the treatment of most topics. Whereas Principles has 34 chapters, Fundamentals has only 25. The relative brevity of Fundamentals neces- sitates a broader-brush coverage of some topics, but we feel that this is an advantage for a beginning audience.

Fourth, we assume little in the way of background knowledge. While most users will have had an introductory accounting course, we review the concepts of account- ing that are important to the financial manager in Chapter 3.

Principles is known for its relaxed and informal writing style, and we continue this tradition in Fundamentals. In addition, we use as little mathematical notation as possible. Even when we present an equation, we usually write it in words rather than symbols. This approach has two advantages. It is less intimidating, and it focuses attention on the underlying concept rather than the formula.

Organizational Design Fundamentals is organized in eight parts.

Part 1 (Introduction) provides essential background material. In the first chap- ter, we discuss how businesses are organized, the role of the financial manager, and the financial markets in which the manager operates. We explain how share- holders with many disparate goals might all agree that they want managers to take actions that increase the value of their investment, and we introduce the concept of the opportunity cost of capital and the trade-off that the firm needs to make when assessing investment proposals. We also describe some of the mechanisms that help to align the interests of managers and shareholders. Of course, the task of increasing shareholder value does not justify corrupt and unscrupulous behavior. We, therefore, discuss some of the ethical issues that confront managers.

Chapter 2 surveys and sets out the functions of financial markets and institutions. This chapter also reviews the crisis of 2007–2009. The events of those years illustrate clearly why and how financial markets and institutions matter.

A large corporation is a team effort, so the firm produces financial statements to help the players monitor its progress. Chapter 3 provides a brief overview of these financial statements and introduces two key distinctions—between market and book values and between cash flows and profits. This chapter also discusses some of the shortcomings in accounting practice. The chapter concludes with a summary of fed- eral taxes.

Chapter 4 provides an overview of financial statement analysis. In contrast to most introductions to this topic, our discussion is motivated by considerations of valuation and the insight that financial ratios can provide about how management has added to the firm’s value.

Part 2 (Value) is concerned with valuation. In Chapter 5, we introduce the concept of the time value of money, and because most readers will be more familiar with their own financial affairs than with the big leagues of finance, we motivate our discussion by looking first at some personal financial decisions. We show how to value long-lived

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Preface ix

streams of cash flows and work through the valuation of perpetuities and annuities. Chapter 5 also contains a short concluding section on inflation and the distinction between real and nominal returns.

Chapters 6 and 7 introduce the basic features of bonds and stocks and give stu- dents a chance to apply the ideas of Chapter 5 to the valuation of these securities. We show how to find the value of a bond given its yield, and we show how prices of bonds fluctuate as interest rates change. We look at what determines stock prices and how stock valuation formulas can be used to infer the return that investors expect. Finally, we see how investment opportunities are reflected in the stock price and why analysts focus on the price-earnings multiple. Chapter 7 also introduces the concept of market efficiency. This concept is crucial to interpreting a stock’s valuation; it also provides a framework for the later treatment of the issues that arise when firms issue securities or make decisions concerning dividends or capital structure.

The remaining chapters of Part 2 are concerned with the company’s investment decision. In Chapter 8, we introduce the concept of net present value and show how to calculate the NPV of a simple investment project. We then consider more complex investment proposals, including choices between alternative projects, machine replace- ment decisions, and decisions of when to invest. We also look at other measures of an investment’s attractiveness—its internal rate of return, profitability index, and payback period. We show how the profitability index can be used to choose between invest- ment projects when capital is scarce. The appendix to Chapter 8 shows how to sidestep some of the pitfalls of the IRR rule.

The first step in any NPV calculation is to decide what to discount. Therefore, in Chapter 9, we work through a realistic example of a capital budgeting analysis, show- ing how the manager needs to recognize the investment in working capital and how taxes and depreciation affect cash flows.

We start Chapter 10 by looking at how companies organize the investment process and ensure everyone works toward a common goal. We then go on to look at various techniques to help managers identify the key assumptions in their estimates, such as sensitivity analysis, scenario analysis, and break-even analysis. We explain the distinction between accounting break-even and NPV break-even. We conclude the chapter by describing how managers try to build future flexibil- ity into projects so that they can capitalize on good luck and mitigate the conse- quences of bad luck.

Part 3 (Risk) is concerned with the cost of capital. Chapter 11 starts with a historical survey of returns on bonds and stocks and goes on to distinguish between the specific risk and market risk of individual stocks. Chapter 12 shows how to measure market risk and discusses the relationship between risk and expected return. Chapter 13 intro- duces the weighted-average cost of capital and provides a practical illustration of how to estimate it.

Part 4 (Financing) begins our discussion of the financing decision. Chapter 14 pro- vides an overview of the securities that firms issue and their relative importance as sources of finance. In Chapter 15, we look at how firms issue securities, and we follow a firm from its first need for venture capital, through its initial public offering, to its continuing need to raise debt or equity.

Part 5 (Debt and Payout Policy)  focuses on the two classic long-term financ- ing decisions. In Chapter 16, we ask how much the firm should borrow, and we summarize bankruptcy procedures that occur when firms can’t pay their debts. In

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x Preface

Chapter 17, we study how firms should set dividend and payout policy. In each case, we start with Modigliani and Miller’s (MM’s) observation that in well- functioning markets, the decision should not matter, but we use this initial obser- vation to help the reader understand why financial managers in practice do pay attention to these decisions.

Part 6 (Financial Analysis and Planning)  starts with long-term financial plan- ning in Chapter 18, where we look at how the financial manager considers the com- bined effects of investment and financing decisions on the firm as a whole. We also show how measures of internal and sustainable growth help managers check that the firm’s planned growth is consistent with its financing plans. Chapter 19 is an introduction to short-term financial planning. It shows how managers ensure that the firm will have enough cash to pay its bills over the coming year. Chapter 20 addresses working capital management. It describes the basic steps of credit man- agement, the principles of inventory management, and how firms handle payments efficiently and put cash to work as quickly as possible. It also describes how firms invest temporary surpluses of cash and how they can borrow to offset any temporary deficiency. Chapter 20 is conceptually straightforward, but it contains a large dollop of institutional material.

Part 7 (Special Topics) covers several important but somewhat more advanced topics—mergers (Chapter 21), international financial management (Chapter 22), options (Chapter 23), and risk management (Chapter 24). Some of these topics are touched on in earlier chapters. For example, we introduce the idea of options in Chapter 10, when we show how companies build flexibility into capital proj- ects. However, Chapter 23 generalizes this material, explains at an elementary level how options are valued, and provides some examples of why the financial manager needs to be concerned about options. International finance is also not confined to Chapter 22. As one might expect from a book that is written by an international group of authors, examples from different countries and finan- cial systems are scattered throughout the book. However, Chapter 22 tackles the specific problems that arise when a corporation is confronted by different currencies.

Part 8 (Conclusion) contains a concluding chapter (Chapter 25), in which we review the most important ideas covered in the text. We also introduce some interesting ques- tions that either were unanswered in the text or are still puzzles to the finance profes- sion. Thus, the last chapter is an introduction to future finance courses as well as a conclusion to this one.

Routes through the Book There are about as many effective ways to organize a course in corporate finance as there are teachers. For this reason, we have ensured that the text is modular so that top- ics can be introduced in different sequences.

We like to discuss the principles of valuation before plunging into financial plan- ning. Nevertheless, we recognize that many instructors will prefer to move directly from Chapter 4 (Measuring Corporate Performance) to Chapter 18 (Long-Term Financial Planning) in order to provide a gentler transition from the typical prerequisite accounting course. We have made sure that Part 6 (Financial Analysis and Planning) can easily follow Part 1.

Similarly, we like to discuss working capital only after the student is familiar with the basic principles of valuation and financing, but we recognize that here also

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Preface xi

many instructors prefer to reverse our order. There should be no difficulty in taking Chapter 20 out of order.

When we discuss project valuation in Part 2, we stress that the opportunity cost of capital depends on project risk. But we do not discuss how to measure risk or how return and risk are linked until Part 3. This ordering can easily be modified. For exam- ple, the chapters on risk and return can be introduced before, after, or midway through the material on project valuation.

Changes in the Tenth Edition

Users of previous editions of this book will not find dramatic changes in either the material or the ordering of topics. But, throughout, we have made the book more up to date and easier to read. Here are some of the ways that we have done this.

Beyond the Page The Beyond the Page digital extensions and applications provide additional examples, anecdotes, spreadsheet programs, and more thoroughgoing explanations of some topics. This material is very easily accessed on the web. In this edition, we have updated them and added a number of additional applications and made them easier to access. For example, the applications are seamlessly available with a click on the e-version of the book, but they are also readily accessible in the traditional hard copy of the text using the shortcut URLs provided in the margins of relevant pages.

Improving the Flow  A major part of our effort in revising this text was spent on improving the flow. Often this has meant a word change here or a redrawn diagram there, but sometimes we have made more substantial changes. One example is the dis- cussion of discounted cash flow analysis in Chapter 9. Rather than presenting a series of disconnected examples, we now illustrate the many aspects of cash flow analysis in one integrated application. The material is substantially unchanged, but we think that the flow is much improved.

Updating Major updates in this edition revolved around the implications of recent tax reform legislation. The Tax Cuts and Jobs Act of 2017 mandated substantial changes in corporate and personal tax rates as well as in the tax treatment of depre- ciation and investment income. All of these changes potentially affect firms’ capital budgeting and financing decisions.

Of course, in each new edition we also try to ensure that any statistics are as up to date as possible. For example, since the previous edition, we have available an extra 2 years of data on security returns. These show up in the figures in Chapter 11 of the long-run returns on stocks, bonds, and bills. Measures of EVA, data on security ownership, dividend payments, and stock repurchases are just a few of the other cases where data have been brought up to date.

New Illustrative Boxes  The text contains a number of boxes with illustra- tive real-world examples. Many of these are new. Look, for example, at the box in Chapter  2 that describes prediction markets and what they had to say about the 2016 presidential election. Or look at the box in Chapter 15  that shows how the JOBS Act of 2012 cleared the way for companies to use crowd- funding to raise up to $50 million from small investors who wish to invest in start-up firms.

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xii Preface

More Worked Examples We have added more worked examples in the text, many of them taken from real companies.

Specific Chapter Changes in the Tenth Edition Here are a few of the additions to chapter material:

Chapter 1 contains updated and timely examples of real capital expenditure deci- sions by major corporations. 

Chapter 2 includes a discussion of prediction markets in the most recent presiden- tial election.

Chapter 3 includes updated discussions of recent changes in tax law. Chapter 6 includes a new Finance in Practice box to show how to find bond infor-

mation on the web. Chapter 7 provides new evidence on efficient markets and some of the anomalies

literature. Chapter 9 now illustrates cash flow analysis in one integrated, extended

example. It also discusses and provides several examples of the impact of accelerated depreciation and immediate expensing on the value of a capital investment.

Chapter 14 now includes more coverage of alternative sources of cash as well as extended treatment of the variety of corporate debt.

Chapter 16 reconsiders the present value of interest tax shields at the new, lower, corporate tax rate.

Chapter 20 introduces the components of working capital and the determinants of the cash cycle. It then looks briefly at each of the components including short- term debt. It provides updated discussions on recent trends in the United States concerning investments in working capital.

Chapter 21 features numerous updates to our coverage of the market for corporate control, for example, GE’s divestment of major sectors of the firm, recent activ- ist investor initiatives, and tax inversion strategies in the wake of recent changes to tax law.

Assurance of Learning Assurance of learning is an important element of many accreditation standards. Fundamentals of Corporate Finance, Tenth Edition, is designed specifically to sup- port your assurance-of-learning initiatives. Each chapter in the book begins with a list of numbered learning objectives, which are referred to in the end-of-chap- ter problems and exercises. Every test bank question is also linked to one of these objectives, in addition to level of difficulty, topic area, Bloom’s Taxonomy level, and AACSB skill area. Connect, McGraw-Hill’s online homework solution, and EZ Test, McGraw-Hill’s easy-to-use test bank software, can search the test bank by these and other categories, providing an engine for targeted assurance-of-learning analysis and assessment.

AACSB Statement McGraw-Hill Education is a proud corporate member of AACSB International. Understanding the importance and value of AACSB accreditation, Fundamentals of Corporate Finance, Tenth Edition, has sought to recognize the curricula guidelines detailed in the AACSB standards for business accreditation by connecting selected questions in the test bank to the general knowledge and skill guidelines found in the AACSB standards.

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Preface xiii

The statements contained in Fundamentals of Corporate Finance, Tenth Edition, are provided only as a guide for the users of this text. The AACSB leaves content coverage and assessment within the purview of individual schools, the mission of the school, and the faculty. While Fundamentals of Corporate Finance, Tenth Edition, and the teaching package make no claim of any specific AACSB qualification or evalu- ation, we have, within the test bank, labeled selected questions according to the six general knowledge and skills areas.

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Chapter 5 The Time Value of Money 135

values (column C) therefore appear as positive numbers. Column E shows an alterna- tive to the use of the PV function, where we calculate present values directly. This allows us to see exactly what we are doing.

The Beyond the Page icon will take you to an application that shows how each of the examples in this chapter can be solved using a spreadsheet.

Level Cash Flows: Perpetuities and Annuities

Frequently, you may need to value a stream of equal cash flows. For example, a home mortgage might require the homeowner to make equal monthly payments for the life of the loan. For a 30-year loan, this would result in 360 equal payments. A 4-year car loan might require 48 equal monthly payments. Any such sequence of equally spaced, level cash flows is called an annuity. If the payment stream lasts forever, it is called a perpetuity.

How to Value Perpetuities Some time ago, the British government borrowed by issuing loans known as consols. Consols are perpetuities. In other words, instead of repaying these loans, the British government pays the investors a fixed annual payment in perpetuity (forever).

How might we value such a security? Suppose that you could invest $100 at an interest rate of 10%. You would earn annual interest of .10 × $100 = $10 and could withdraw this amount from your investment account each year without ever running down your balance. In other words, a $100 investment could provide a perpetuity of $10 per year. In general,

Cash payment from perpetuity = interest rate × present value C = r × PV

We can rearrange this relationship to derive the present value of a perpetuity, given the interest rate r and the cash payment C:

PV of perpetuity = C __ r = cash payment ____________ interest rate (5.3)

Suppose some worthy person wishes to endow a chair in finance at your university. If the rate of interest is 10% and the aim is to provide $100,000 a year forever, the amount that must be set aside today is

Present value of perpetuity = C __ r = $100,000 ________ .10 = $1,000,000

5.5

annuity Level stream of cash flows at regular intervals with a finite maturity.

perpetuity Stream of level cash payments that never ends.

SPREADSHEET 5.3 Using a spreadsheet to find the present value of multiple cash flows

A B C D E 1 Finding the present value of multiple cash flows using a spreadsheet 2 3 Time until CF Cash flow Present value Formula in Col C Alternative formula for Col C 4 0 8000 $8,000.00 =PV($B$10, A4, 0, −B4) =B4/(1 + $B$10)^A4 5 1 4000 $3,703.70 =PV($B$10, A5, 0, −B5) =B5/(1 + $B$10)^A5 6 2 4000 $3,429.36 =PV($B$10, A6, 0, −B6) =B6/(1 + $B$10)^A6 7 8 SUM $15,133.06 =SUM(C4:C6) =SUM(C4:C6) 9

10 Discount rate: 0.08 11 12 Notice that the time until each payment is found in column A. 13 Once we enter the formula for present value in cell C4, we can copy it to cells C5 and C6. 14 The present value for other interest rates can be found by changing the entry in cell B10.

178

Alternatively, we could simply enter the following function in Excel:

=PRICE(DATE(2018,2,15), DATE(2021,2,15), .0225, .02391, 100, 1)

The DATE function in Excel, which we use for both the set- tlement and maturity dates, uses the format DATE(year,month,day).

Notice that the coupon rate and yield to maturity are expressed as decimals, not percentages. In most cases, redemption value will be 100 (i.e., 100% of face value), and the resulting price will be expressed as a percent of face value. Occasionally, however, you may encounter bonds that pay off at a premium or discount to face value. One example would be callable bonds, which give the company the right to buy back the bonds at a premium before maturity.

Excel and most other spreadsheet programs provide built- in functions to compute bond values and yields. They typi- cally ask you to input both the date you buy the bond (called the settlement date) and the maturity date of the bond.

The Excel function for bond value is:

=PRICE(settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of face value, number of coupon payments per year)

(If you can’t remember the formula, just remember that you can go to the Formulas tab in Excel, and from the Financial tab pull down the PRICE function, which will prompt you for the necessary inputs.) For our 2.25% coupon bond, we would enter the values shown in the spreadsheet below.

Spreadsheet Solutions Bond Valuation

A B C D E F 1 2.25% annual 2.25% semiannual 6% annual 2 coupon bond, coupon bond, coupon bond, 3 maturing Feb 2021 Formula in column B maturing Feb 2021 30-year maturity 4 5 Settlement date 15-Feb-2018 =DATE(2018,2,15) 15-Feb-2018 15-Feb-2018 6 Maturity date 15-Feb-2021 =DATE(2021,2,15) 15-Feb-2021 15-Feb-2021 7 Annual coupon rate 0.0225 0.0225 0.06 8 Yield to maturity 0.02391 0.02391 0.07 9 Redemption value

(% of face value) 100 100 100

10 Coupon payments per year

1 2 1

11 12 13 Bond price (% of par) 99.596 =PRICE(B5,B6,B7,B8,B9,B10) 99.594 87.591

The solid curve in Figure 6.6 plots the price of a 30-year maturity, 6% coupon bond over time assuming that its yield to maturity is currently 4% and does not change. The price declines gradually until the maturity date, when it finally reaches face value. In each period, the price decline offsets the coupon income by just enough to reduce total return to 4%. The dashed curve in Figure 6.6 shows the corresponding price path for a bond with a 2% coupon that sells at a discount to face value. In this case, the coupon income would provide less than a competitive rate of return, so the bond sells below face value. Its price gradually approaches face value, however, and the price gain each year brings its total return up to the market interest rate.

The Yield Curve

When you buy a bond, you buy a package of coupon payments plus the final repay- ment of face value. But sometimes it is inconvenient to buy things in packages. For example, perhaps you do not need a regular income and would prefer to buy just the final repayment. That’s not a problem. The Treasury is prepared to split its bonds into

6.5

138 Part Two Value

Remembering formulas is about as difficult as remembering other people’s birth- days. But as long as you bear in mind that an annuity is equivalent to the difference between an immediate and a delayed perpetuity, you shouldn’t have any difficulty.

You can use a calculator or spreadsheet to work out annuity factors (we show you how momentarily), or you can use a set of annuity tables. Table 5.4 is an abridged annuity table (an extended version is shown in Table A.3 at the end of the book). Check that you can find the 3-year annuity factor for an interest rate of 10%.

Compare Table 5.4 with Table 5.3, which presented the present value of a single cash flow. In both tables, present values fall as we move across the rows to higher dis- count rates. But in contrast to those in Table 5.3, present values in Table 5.4 increase as we move down the columns, reflecting the greater number of payments made by longer annuities.

TABLE 5.4 An example of an annuity table, showing the present value today of $1 a year received for each of t years

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

 1 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091  2 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355  3 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869  4 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699  5 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908

10 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 20 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 30 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269

If the interest rate is 8%, what is the 4-year discount factor? What is the 4-year annuity factor? What is the relationship between these two numbers? Explain.

Self-Test5.6

Winning Big at the Lottery

In August 2017, a Massachusetts woman bought a Powerball lottery ticket and won a record $758.7 million. We suspect that she received unsolicited congratulations, good wishes, and requests for money from dozens of more or less worthy charities, relations, and newly devoted friends. In response, she could fairly point out that the prize wasn’t really worth $758.7 million. That sum was to be paid in 30 annual installments of about $23 million each. Assuming that the first payment occurred at the end of 1 year, what was the present value of the prize? The interest rate at the time was about 2.7%.

The present value of these payments is simply the sum of the present values of each annual payment. But rather than valuing the payments separately, it is much easier to treat them as a 30-year annuity. To value this annuity, we multiply $23 million by the 30-year annu- ity factor:

PV = 23 × 30-year annuity factor

= 23 × [ 1 __ r − 1 _______ r (1 + r)30 ] At an interest rate of 2.7%, the annuity factor is

[ 1 ____ .027 − 1 ___________ .027(1.027)30 ] = 20.3829

Example 5.8 ⊲

Unique Features

Integrated Examples Numbered and titled examples are integrated in each chapter. Students can learn how to solve specific problems step-by-step as well as gain insight into general principles by seeing how to approach and analyze different problems.

Spreadsheet Solutions Boxes These boxes provide the student with detailed examples of how to use Excel spreadsheets when applying financial concepts. The boxes include questions that apply to the spreadsheet, and their solutions are given at the end of the applicable chapter. These spreadsheets are available for download in Connect.

Excel Exhibits Selected exhibits are set as Excel spreadsheets. The accompanying files are available for instructors and students in Connect.

What makes Fundamentals of Corporate Finance such a powerful learning tool?

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Finance in Practice Boxes These are excerpts that appear in most chapters, often from the financial press, providing real-life illustrations of the chapter’s topics, such as ethical choices in finance, disputes about stock valuation, financial planning, and credit analysis.

Financial Calculator Boxes and Exercises In a continued effort to help students grasp the critical concept of the time value of money, many pedagogical tools have been added throughout the first section of the text. Financial Calculator boxes provide examples for solving a variety of problems, with directions for the most popular financial calculators.

Self-Test Questions Provided in each chapter, these helpful questions enable students to check their understanding as they read. Answers are worked out at the end of each chapter.

Interest Rate Risk We have just seen that bond prices fluctuate as interest rates change. In other words, bonds are subject to interest rate risk. Bond investors cross their fingers that market interest rates will fall, so that the price of their bond will rise. If they are unlucky and the market interest rate rises, the value of their investment falls.

A change in interest rates has only a modest impact on the present value of near-term cash flows but a much greater impact on the value of distant cash flows. Therefore, any change has a greater impact on the price of long-term bonds than the price of short- term bonds. For example, compare the two curves in Figure 6.5. The blue line shows how the value of the 3-year, 2.25% coupon bond varies with the interest rate. The green line shows how the price of a 30-year, 2.25% bond varies. You can see that the 30-year bond is more sensitive to interest rate fluctuations than the 3-year bond. This should not surprise you. If you buy a 3-year bond and rates then rise, you will be stuck with a bad deal—you could have got a better interest rate if you had waited. However, think how much worse it would be if the loan had been for 30 years rather than 3 years. The longer the loan, the more you have lost by accepting what turns out to be a low interest rate. This shows up in a bigger decline in the price of the longer-term bond. Of course, there is a flip side to this effect, which you can also see from Figure 6.5. When interest rates fall, the longer-term bond responds with a greater increase in price.

interest rate risk The risk in bond prices due to fluctuations in interest rates.

BEYOND THE PAGE

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How changes in interest rates affect long- and short-term bonds

BEYOND THE PAGE

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Which is the longer-term bond?

FIGURE 6.5 Plot of bond prices as a function of the interest rate. The price of long- term bonds is more sensitive to changes in the interest rate than is the price of short-term bonds.

B on

d pr

ic e

($ )

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Interest rate (%)

3-year bond

When the interest rate equals the 2.25% coupon rate, both bonds sell for face value.

30-year bond

Suppose that the market interest rate is 4% and then drops overnight to 2%. Calculate the present values of the 2.25%, 3-year bond and of the 2.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5. Use your financial calculator or a spreadsheet. You can find a box on bond pricing using Excel later in this chapter.

Self-Test6.4

Yield to Maturity

Suppose you are considering the purchase of a 3-year bond with a coupon rate of 10%. Your investment adviser quotes a price for the bond. How do you calculate the rate of return the bond offers?

6.3

174 Part Two Value

had reached 138.05% of face value and the yield had fallen to 2.5%. Anyone fortunate enough to have bought the bond at the issue price would have made a capital gain of $1,380.50 − $963.80 = $416.70. In addition, on August 15 the bond made its first coupon payment of $21.875 (this is the semiannual payment on the 4.375% coupon bond with a face value of $1,000). Our lucky investor would therefore have earned a 7-month rate of return of 45.5%:

Rate of return = coupon income + price change

_____________________ investment (6.2)

= $21.875 + $416.70 ______________ $963.80

= .455 = 45.5%

Suddenly, government bonds did not seem quite so boring as before. ■

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Bond pricing using financial calculators

rate of return Total income per period per dollar invested.

Suppose that you purchased 8% coupon, 10-year bonds for $1,324.44 when they were yielding 4% (we assume annual coupon payments). One year later, you receive the annual coupon payment of $80, but the yield to maturity has risen to 6%. Confirm that the rate of return on your bond over the year is less than the original 4% yield to maturity.

Self-Test6.6

Suppose that you buy 8%, 2-year bonds for $1,036.67 when they yield 6%. At the end of the year, they still yield 6%. Show that if you continue to hold the bond until maturity, your return in each of the two years will also be 6%.

Self-Test6.7

177

payments of $11.25. Therefore, we can find the semiannual yield as follows:

This yield to maturity, of course, is a 6-month yield, not an annual one. Bond dealers would typically annualize the semi- annual rate by doubling it, so the yield to maturity would be quoted as 1.19556 × 2 = 2.391%, which exactly matches the value in Table 6.1.

You can use a financial calculator to calculate the yield to maturity on our 2.25% Treasury bond. The inputs are:

Now compute i and you should get an answer of 2.392%, which is just a tick above the yield reported in Table 6.1.

Let’s now redo this calculation but recognize that the cou- pons are paid semiannually. Instead of three annual coupon payments of $22.50, the bond makes six semiannual

Financial Calculator Using a Financial Calculator to Compute Bond Yield

Inputs 3 995.938 22.5 1000 Compute 2.392

n i PV PMT FV

Inputs 6 995.938 11.25 1000 Compute 1.19556

n i PV PMT FV

Is there any connection between the yield to maturity and the rate of return during a particular period? Yes: If the bond’s yield to maturity remains unchanged during the period, the bond price changes with time so that the total return on the bond is equal to the yield to maturity. The rate of return will be less than the yield to maturity if interest rates rise, and it will be greater than the yield to maturity if interest rates fall.

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Bond prices and approaching maturity

20

It is not always easy to know what is ethical behavior, and there can be many gray areas. The nearby box presents three ethical controversies in finance. Think about where you stand on these issues and where you would draw the ethical line.

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Goldman Sachs causes a ruckus

But sometimes raids can enhance shareholder value. For example, in 2012 and 2013, Relational Investors teamed up with the California State Teachers’ Retirement System (CSTRS, a pension fund) to try to force Timken Co. to split into two separate companies, one for its steel business and one for its industrial bearings business. Relational and CSTRS believed that Timken’s combination of unrelated businesses was unfo- cused and inefficient. Timken management responded that breakup would “deprive our shareholders of long-run value— all in an attempt to create illusory short-term gains through financial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding shareholder vote on Relational’s proposal attracted a 53% majority. Finally, in 2014 Timken spun off its steel business in a new corporation, Timken Steel.

How do you draw the ethical line in such examples? Was Relational Investors a “raider” (sounds bad) or an “activist investor” (sounds good)? Breaking up a portfolio of busi- nesses can create difficult adjustments and job losses. Some stakeholders lose. But shareholders and the overall economy can gain if businesses are managed more efficiently.

Tax Avoidance In 2012 it was revealed that during the 14 years that Starbucks had operated in the United Kingdom, it paid hardly any taxes. Public outrage led to a boycott of Starbucks shops, and the company responded by promising that it would voluntarily pay to the taxman about $16 million more than it was required to pay by law. Several months later, a U.S. Senate committee investigating tax avoidance by U.S. technology firms reported that Apple had used a “highly questionable” web of offshore entities to avoid billions of dollars of U.S. taxes.

Multinational companies, such as Starbucks and Apple, could reduce their tax bills using legal techniques with exotic names such as the “Dutch Sandwich,” “Double Irish,” and “Check-the-Box.” But the public outcry over the revelations suggested that many believed that use of these techniques, though legal, was unethical. If they were unethical, that leaves an awkward question: How do companies decide which tax schemes are ethical and which are not? Can a company act in shareholders’ interest if it voluntarily pays more taxes than it is legally obligated to pay?

* We need not go into the mechanics of short sales here, but note that the seller is obligated to buy back the security, even if its price skyrockets far above what he or she sold it for. As the saying goes, “He who sells what isn’t his’n, buys it back or goes to prison.”

† The story of Paulson’s trade is told in G. Zuckerman, The Greatest Trade Ever (New York: Broadway Business, 2009). The trade was controversial for reasons beyond short-selling. Scan the nearby Beyond the Page icon “Goldman Sachs causes a ruckus” to learn more.

Short-Selling Investors who take short positions are betting that securities will fall in price. Usually they do this by borrowing the security, selling it for cash, and then waiting in the hope that they will be able to buy it back cheaply.* In 2007, hedge fund manager John Paulson took a huge short position in mortgage-backed securities. The bet paid off, and that year Paulson’s trade made a profit of $1 billion for his fund.†

Was Paulson’s trade unethical? Some believe not only that he was profiting from the misery that resulted from the crash in mortgage-backed securities, but that his short trades accentuated the collapse. It is certainly true that short-sellers have never been popular. For example, following the crash of 1929, one commentator compared short-selling to the ghoul- ishness of “creatures who, at all great earthquakes and fires, spring up to rob broken homes and injured and dead humans.”

Short-selling in the stock market is the Wall Street Walk on steroids. Not only do short-sellers sell all the shares they may have previously owned, but they borrow more shares and sell them too, hoping to buy them back for less when the stock price falls. Poorly performing companies are natural targets for short-sellers, and the companies’ incumbent managers naturally complain, often bitterly. Governments sometimes lis- ten to such complaints. For example, in 2008 the U.S. govern- ment temporarily banned short sales of financial stocks in an attempt to halt their decline.

But defendants of short-selling argue that selling securi- ties that one believes are overpriced is no less legitimate than buying those that appear underpriced. The object of a well- functioning market is to set the correct stock prices, not always higher prices. Why impede short-selling if it conveys truly bad news, puts pressure on poor performers, and helps corporate governance work?

Corporate Raiders In the movie Pretty Woman, Richard Gere plays the role of an asset stripper, Edward Lewis. He buys companies, takes them apart, and sells the bits for more than he paid for the total package. In the movie Wall Street, Gordon Gekko buys a failing airline, Blue Star, in order to break it up and sell the bits. Real corporate raiders may not be as ruthless as Edward Lewis or Gordon Gekko, but they do target companies whose assets can be profitably split up and redeployed.

This has led some to complain that raiders seek to carve up established companies, often leaving them with heavy debt burdens, basically in order to get rich quick. One German politician has likened them to “swarms of locusts that fall on companies, devour all they can, and then move on.”

Finance in Practice Ethical Disputes in Finance

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164 Part Two Value

MINICASE Old Alfred Road, who is well-known to drivers on the Maine Turnpike, has reached his 70th birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully.

Mr. Road owns his home—the mortgage is paid off—and does not want to move. He is a widower, and he wants to bequeath the house and any remaining assets to his daughter.

He has accumulated savings of $180,000, conservatively invested. The investments are yielding 9% interest. Mr. Road also has $12,000 in a savings account at 5% interest. He wants to keep the savings account intact for unexpected expenses or emergencies.

Mr. Road’s basic living expenses now average about $1,500 per month, and he plans to spend $500 per month on travel and hob- bies. To maintain this planned standard of living, he will have to rely on his investment portfolio. The interest from the portfolio is $16,200 per year (9% of $180,000), or $1,350 per month.

Mr. Road will also receive $750 per month in Social Security payments for the rest of his life. These payments are indexed for

inflation. That is, they will be automatically increased in propor- tion to changes in the consumer price index.

Mr. Road’s main concern is with inflation. The inflation rate has been below 3% recently, but a 3% rate is unusually low by his- torical standards. His Social Security payments will increase with inflation, but the interest on his investment portfolio will not.

What advice do you have for Mr. Road? Can he safely spend all the interest from his investment portfolio? How much could he withdraw at year-end from that portfolio if he wants to keep its real value intact?

Suppose Mr. Road will live for 20 more years and is willing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase along with inflation over that period. In other words, he wants his monthly spending to stay the same in real terms. How much can he afford to spend per month?

Assume that the investment portfolio continues to yield a 9% rate of return and that the inflation rate will be 4%.

192 Part Two Value

32. Credit Risk. (LO6-5) a. Many years ago, Castles in the Sand Inc. issued bonds at face value at a yield to maturity of

7%. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is now the price of the bond? (Assume semiannual coupon payments.)

b. Suppose that investors believe that Castles can make good on the promised coupon pay- ments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

33. Credit Risk. Suppose that Casino Royale has issued bonds that mature in 1 year. They currently offer a yield of 20%. However, there is a 50% chance that Casino will default and bondholders will receive nothing. What is the expected yield on the bonds? (LO6-5)

34. Credit Risk. Bond A is a 10-year U.S. Treasury bond. Bond B is a 10-year corporate bond. True or false? (LO6-3 and LO6-5) a. If you hold bond A to maturity, your return will be equal to the yield to maturity. b. If you hold bond B to maturity, your return will be equal to or less than the yield to

maturity. c. If you hold bond A for 5 years and then sell it, your return could be greater than the yield to

maturity.

35. Credit Risk. A bond’s credit rating provides a guide to its risk. Suppose that long-term bonds rated Aa currently offer yields to maturity of 7.5%. A-rated bonds sell at yields of 7.8%. Sup- pose that a 10-year bond with a coupon rate of 7.6% is downgraded by Moody’s from an Aa to A rating. (LO6-5) a. Is the bond likely to sell above or below par value before the downgrade? b. Is the bond likely to sell above or below par value after the downgrade?

36. Credit Risk. Sludge Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is a senior bond; bond B is subordinated. Sludge has suffered a severe downturn in demand, and its assets are now worth only $3 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

37. Credit Risk. Slush Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is secured on the company’s head office building; bond B is unsecured. Slush has suffered a severe downturn in demand. Its head office building is worth $1 million, but its remaining assets are now worth only $2 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

WEB EXERCISES 1. Log on to www.investopedia.com to find a simple calculator for working out bond prices.

(Start by clicking the Investing link and then look for another link to Calculators.) Check whether a change in yield has a greater effect on the price of a long-term or a short-term bond.

2. When we plotted the yield curve in Figure 6.7, we used the prices of Treasury strips. You can find current prices of strips by logging on to The Wall Street Journal website (www.wsj.com) and clicking on Markets, Market Data, and then Rates. Try plotting the yields on stripped cou- pons against maturity. Do they currently increase or decline with maturity? Can you explain why? You can also use The Wall Street Journal site to compare the yields on nominal Treasury bonds with those on TIPS. Suppose that you are confident that inflation will be 3% per year. Which bonds are the better buy?

3. In Figure 6.9, we showed how bonds with greater credit risk have promised higher yields to maturity. This yield spread goes up when the economic outlook is particularly uncertain. You can check how much extra yield lower-grade bonds offer today by logging on to the Federal Reserve Economic Database (FRED) at the St. Louis Fed website (fred.stlouisfed.org). Search for Corporate Bonds and compare the yields on Aaa and Baa bonds. How does the current spread in yields compare with the spread in November 2008 at the height of the financial crisis?

Interest Rate Risk We have just seen that bond prices fluctuate as interest rates change. In other words, bonds are subject to interest rate risk. Bond investors cross their fingers that market interest rates will fall, so that the price of their bond will rise. If they are unlucky and the market interest rate rises, the value of their investment falls.

A change in interest rates has only a modest impact on the present value of near-term cash flows but a much greater impact on the value of distant cash flows. Therefore, any change has a greater impact on the price of long-term bonds than the price of short- term bonds. For example, compare the two curves in Figure 6.5. The blue line shows how the value of the 3-year, 2.25% coupon bond varies with the interest rate. The green line shows how the price of a 30-year, 2.25% bond varies. You can see that the 30-year bond is more sensitive to interest rate fluctuations than the 3-year bond. This should not surprise you. If you buy a 3-year bond and rates then rise, you will be stuck with a bad deal—you could have got a better interest rate if you had waited. However, think how much worse it would be if the loan had been for 30 years rather than 3 years. The longer the loan, the more you have lost by accepting what turns out to be a low interest rate. This shows up in a bigger decline in the price of the longer-term bond. Of course, there is a flip side to this effect, which you can also see from Figure 6.5. When interest rates fall, the longer-term bond responds with a greater increase in price.

interest rate risk The risk in bond prices due to fluctuations in interest rates.

BEYOND THE PAGE

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How changes in interest rates affect long- and short-term bonds

BEYOND THE PAGE

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Which is the longer-term bond?

FIGURE 6.5 Plot of bond prices as a function of the interest rate. The price of long- term bonds is more sensitive to changes in the interest rate than is the price of short-term bonds.

B on

d pr

ic e

($ )

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Interest rate (%)

3-year bond

When the interest rate equals the 2.25% coupon rate, both bonds sell for face value.

30-year bond

Suppose that the market interest rate is 4% and then drops overnight to 2%. Calculate the present values of the 2.25%, 3-year bond and of the 2.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5. Use your financial calculator or a spreadsheet. You can find a box on bond pricing using Excel later in this chapter.

Self-Test6.4

Yield to Maturity

Suppose you are considering the purchase of a 3-year bond with a coupon rate of 10%. Your investment adviser quotes a price for the bond. How do you calculate the rate of return the bond offers?

6.3

174 Part Two Value

“Beyond the Page” Interactive Content and Applications Additional resources and hands-on applications are just a click away. Students can tap or click the icons in the e-version or use the direct web links to learn more about key concepts and try out calculations, tables, and figures when they go “Beyond the Page.”

Web Exercises Select chapters include Web Exercises that allow students to utilize the Internet to apply their knowledge and skills with real-world companies.

Minicases Integrated minicases allow students to apply their knowledge to relatively complex, practical problems and typical real-world scenarios.

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xvii

∙ Offers students quick access to the Beyond the Page features, Excel files and templates, lectures, eBooks, and more.

∙ Provides instant practice material and study questions, easily accessible on the go.

Student Progress Tracking  Connect keeps instructors informed about how each student, section, and class is per- forming, allowing for more productive use of lecture and office hours. The progress- tracking function enables you to

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McGraw-Hill’s test bank content. The instructors can then organize, edit, and customize questions and answers to rapidly generate tests for paper or online admin- istration. Questions can include stylized text, symbols, graphics, and equations that are inserted directly into questions using built-in mathematical templates. TestGen’s random generator provides the option to display different text or calculated number values each time questions are used. With both quick-and-simple test creation and flexible and robust editing tools, TestGen is a complete test generator system for today’s educators.

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Beyond the Page Content The authors have created a wealth of additional examples, explanations, and applications, available for quick access by instructors and students. Each “Beyond the Page” feature is called out in the text with an icon that links directly to the content.

Excel Solutions and Templates Excel templates are available in Connect for select exhibits and various end-of-chapter problems that have been set as Excel spreadsheets. They correlate with specific concepts in the text and allow students to work through financial problems and gain experience using spreadsheets. Also refer to the valuable Spreadsheet Solutions Boxes that are sprinkled throughout the text for some helpful prompts on working in Excel.

Student Study Center The Connect Student Study Center is the place for students to access additional resources. The Student Study Center

Instructor Library  The Connect Instructor Library is your repository for additional resources to improve student engagement in and out of class. You can select and use any asset that enhances your lecture. The Connect Instructor Library includes all of the instructor supplements for this text.

Solutions Manual Andrew Hession-Kunz worked with the authors to prepare this resource containing detailed and thoughtful solutions to all the end-of-chapter problems.

Instructor’s Manual This manual, updated and enhanced by Matthew Will at the University of Indianapolis, includes a descriptive preface containing alternative course formats and case teaching methods, a chapter overview and outline, key terms and concepts, a description of the PowerPoint slides, video teaching notes, related web links, and pedagogical ideas.

Test Bank Matthew Will has also thoroughly reviewed and revised the test bank, add- ing new questions and ensuring that all of the content is closely correlated to the text. More than 2,000 true/false, multiple- choice, and discussion questions/problems are available to the instructor at varying levels of difficulty and comprehension. All questions are tagged by learning objec- tive, topic, AACSB category, and Bloom’s Taxonomy level. Complete answers are provided for all test questions and prob- lems. The test bank is available as down- loadable Word files, and tests can also be created online within McGraw-Hill’s Connect or through TestGen.

TestGen is a complete, state-of-the- art test generator and editing applica- tion software that allows instructors to quickly and easily select test items from

In addition to the overall refinement and improvement of the text material, considerable effort was put into develop- ing an exceptional supplement package to provide students and instructors with an abundance of teaching and learn- ing resources.

Supplements

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They’ll thank you for it. Adaptive study resources like SmartBook® help your students be better prepared in less time. You can transform your class time from dull definitions to dynamic debates. Hear from your peers about the benefits of Connect at www.mheducation.com/highered/connect

Make it simple, make it affordable. Connect makes it easy with seamless integration using any of the major Learning Management Systems—Blackboard®, Canvas, and D2L, among others—to let you organize your course in one convenient location. Give your students access to digital materials at a discount with our inclusive access program. Ask your McGraw-Hill representative for more information.

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We take this opportunity to thank all of the individuals who helped us prepare this and previous editions. We want to express our appreciation to those instructors whose insightful comments and suggestions were invaluable to us during this revision.

Acknowledgments

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xxi

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xxii

In addition, we would like to thank the dedicated experts who have helped with updates to our instructor materials and online content in Connect and LearnSmart, including Andrew Hession-Kunz, Matt Will, Marc-Anthony Isaacs, and Nicholas Racculia. Their efforts are much appreciated as they will help both students and instructors. We also appreciate help from Aleijda de Cazenove Balsan and Malcolm Taylor.

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Finally, as was the case with the last nine editions, we cannot overstate the thanks due to our families.

Richard A. Brealey Stewart C. Myers Alan J. Marcus

bre13960_fm_i-xxxi.indd 22 1/29/19 4:35 PM

1 Goals and Governance of the Corporation 2

2 Financial Markets and Institutions 32

3 Accounting and Finance 56

4 Measuring Corporate Performance 86

5 The Time Value of Money 118

6 Valuing Bonds 166

7 Valuing Stocks 196

8 Net Present Value and Other Investment Criteria 238

9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 274

10 Project Analysis 304

11 Introduction to Risk, Return, and the Opportunity Cost of Capital 332

12 Risk, Return, and Capital Budgeting 362

13 The Weighted-Average Cost of Capital and Company Valuation 392

14 Introduction to Corporate Financing 420

15 How Corporations Raise Venture Capital and Issue Securities 440

16 Debt Policy 466

17 Payout Policy 504

18 Long-Term Financial Planning 528

19 Short-Term Financial Planning 550

20 Working Capital Management 572

21 Mergers, Acquisitions, and Corporate Control 612

22 International Financial Management 640

23 Options 666

24 Risk Management 694

25 What We Do and Do Not Know about Finance 714

Appendix: Present Value and Future Value Tables A-1

Glossary G-1

Index IND-1

in Brief

Part One Introduction

Part Two Value

Part Three Risk

Part Four Financing

Part Five Debt and Payout

Policy

Part Six Financial Analysis

and Planning

Part Seven Special Topics

Part Eight Conclusion

xxiii

Contents

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xxv

Chapter 1 Goals and Governance of the Corporation 2 1.1 Investment and Financing Decisions 4

The Investment (Capital Budgeting) Decision 6

The Financing Decision 6

1.2 What Is a Corporation? 8

Other Forms of Business Organization 9

1.3 Who Is the Financial Manager? 10

1.4 Goals of the Corporation 12

Shareholders Want Managers to Maximize Market Value 12

1.5 Agency Problems, Executive Compensation, and Corporate Governance 15

Executive Compensation 16

Corporate Governance 17

1.6 The Ethics of Maximizing Value 18

1.7 Careers in Finance 21

1.8 Preview of Coming Attractions 22

1.9 Snippets of Financial History 23

Summary 25

Questions and Problems 26

Chapter 2 Financial Markets and Institutions 32 2.1 The Importance of Financial Markets

and Institutions 34

2.2 The Flow of Savings to Corporations 35

The Stock Market 37

Other Financial Markets 38

Financial Intermediaries 40

Financial Institutions 42

Total Financing of U.S. Corporations 44

2.3 Functions of Financial Markets and Intermediaries 45

Transporting Cash across Time 45

Risk Transfer and Diversification 45

Liquidity 46

The Payment Mechanism 47

Information Provided by Financial Markets 47

2.4 The Crisis of 2007–2009 49

Summary 51

Questions and Problems 52

Chapter 3 Accounting and Finance 56 3.1 The Balance Sheet 58

Book Values and Market Values 61

3.2 The Income Statement 63

Income versus Cash Flow 64

3.3 The Statement of Cash Flows 67

Free Cash Flow 69

3.4 Accounting Practice and Malpractice 70

3.5 Taxes 73

Corporate Tax 73

Personal Tax 74

Summary 75

Questions and Problems 76

Chapter 4 Measuring Corporate Performance 86 4.1 How Financial Ratios Relate to Shareholder

Value 88

4.2 Measuring Market Value and Market Value Added 89

4.3 Economic Value Added and Accounting Rates of Return 91

Accounting Rates of Return 93

Problems with EVA and Accounting Rates of Return 95

4.4 Measuring Efficiency 96

4.5 Analyzing the Return on Assets: The Du Pont System 98

The Du Pont System 98

4.6 Measuring Financial Leverage 100

Leverage and the Return on Equity 102

4.7 Measuring Liquidity 103

4.8 Interpreting Financial Ratios 104

4.9 The Role of Financial Ratios 108

Summary 109

Questions and Problems 110

Minicase 116

Part One Introduction

Contents

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xxvi Contents

Part Two Value

Chapter 5 The Time Value of Money 118 5.1 Future Values and Compound Interest 120

5.2 Present Values 123

Finding the Interest Rate 127

5.3 Multiple Cash Flows 128

Future Value of Multiple Cash Flows 128

Present Value of Multiple Cash Flows 129

5.4 Reducing the Chore of the Calculations: Part 1 131

Using Financial Calculators to Solve Simple Time-Value-of-Money Problems 131

Using Spreadsheets to Solve Simple Time-Value-of-Money Problems 132

5.5 Level Cash Flows: Perpetuities and Annuities 135

How to Value Perpetuities 135

How to Value Annuities 136

Future Value of an Annuity 140

Annuities Due 143

5.6 Reducing the Chore of the Calculations: Part 2 144

Using Financial Calculators to Solve Annuity Problems 144

Using Spreadsheets to Solve Annuity Problems 145

5.7 Effective Annual Interest Rates 145

5.8 Inflation and the Time Value of Money 147

Real versus Nominal Cash Flows 147

Inflation and Interest Rates 149

Valuing Real Cash Payments 151

Real or Nominal? 152

Summary 152

Questions and Problems 153

Minicase 164

Chapter 6 Valuing Bonds 166 6.1 The Bond Market 168

Bond Characteristics 168

6.2 Interest Rates and Bond Prices 170

How Bond Prices Vary with Interest Rates 172

Interest Rate Risk 174

6.3 Yield to Maturity 174

Calculating the Yield to Maturity 176

6.4 Bond Rates of Return 176

6.5 The Yield Curve 178

Nominal and Real Rates of Interest 181

6.6 Corporate Bonds and the Risk of Default 182

Protecting against Default Risk 185

Not All Corporate Bonds Are Plain Vanilla 187

Summary 187

Questions and Problems 188

Chapter 7 Valuing Stocks 196 7.1 Stocks and the Stock Market 198

Reading Stock Market Listings 199

7.2 Market Values, Book Values, and Liquidation Values 201

7.3 Valuing Common Stocks 203

Valuation by Comparables 203

Price and Intrinsic Value 204

The Dividend Discount Model 206

7.4 Simplifying the Dividend Discount Model 209

Case 1: The Dividend Discount Model with No Growth 209

Case 2: The Dividend Discount Model with Constant Growth 209

Case 3: The Dividend Discount Model with Nonconstant Growth 214

7.5 Valuing a Business by Discounted Cash Flow 218

Valuing the Concatenator Business 218

Repurchases and the Dividend Discount Model 219

7.6 There Are No Free Lunches on Wall Street 220

Random Walks and Efficient Markets 221

7.7 Market Anomalies and Behavioral Finance 224

Market Anomalies 224

Bubbles and Market Efficiency 226

Behavioral Finance 227

Summary 228

Questions and Problems 229

Minicase 236

Chapter 8 Net Present Value and Other Investment Criteria 238 8.1 Net Present Value 240

A Comment on Risk and Present Value 241

Valuing Long-Lived Projects 242

Choosing between Alternative Projects 244

8.2 The Internal Rate of Return Rule 245

A Closer Look at the Rate of Return Rule 246

Calculating the Rate of Return for Long-Lived Projects 246

A Word of Caution 248

Some Pitfalls with the Internal Rate of Return Rule 248

8.3 The Profitability Index 253

Capital Rationing 254

Pitfalls of the Profitability Index 254

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Contents xxvii

8.4 The Payback Rule 255

Discounted Payback 256

8.5 More Mutually Exclusive Projects 256

Problem 1: The Investment Timing Decision 257

Problem 2: The Choice between Long- and Short-Lived Equipment 258

Problem 3: When to Replace an Old Machine 260

8.6 A Last Look 261

Summary 262

Questions and Problems 263

Minicase 270

Appendix: More on the IRR Rule 271

Using the IRR to Choose between Mutually Exclusive Projects 271

Using the Modified Internal Rate of Return When There Are Multiple IRRs 271

Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 274 9.1 Identifying Cash Flows 276

Discount Cash Flows, Not Profits 276

Discount Incremental Cash Flows 278

Discount Nominal Cash Flows by the Nominal Cost of Capital 281

Separate Investment and Financing Decisions 282

9.2 Corporate Income Taxes 283

9.3 An Example—Blooper Industries 283

Forecasting Blooper’s Cash Flows 284

Calculating the NPV of Blooper’s Mine 287

Further Notes and Wrinkles Arising from Blooper’s Project 288

Summary 293

Questions and Problems 294

Minicase 302

Chapter 10 Project Analysis 304 10.1 How Firms Organize the Investment Process to Draw on

Their Competitive Strengths 306

The Capital Budget 306

Problems and Some Solutions 307

10.2 Reducing Forecast Bias 307

10.3 Some “What-If” Questions 308

Sensitivity Analysis 309

Scenario Analysis 312

10.4 Break-Even Analysis 312

Accounting Break-Even Analysis 313

NPV Break-Even Analysis 314

Operating Leverage 317

10.5 Real Options and the Value of Flexibility 319

The Option to Expand 319

A Second Real Option: The Option to Abandon 321

A Third Real Option: The Timing Option 321

A Fourth Real Option: Flexible Production Facilities 322

Summary 323

Questions and Problems 324

Minicase 330

Part Three Risk

Chapter 11 Introduction to Risk, Return, and the Opportunity Cost of Capital 332 11.1 Rates of Return: A Review 334

11.2 A Century of Capital Market History 335

Market Indexes 335

The Historical Record 335

Using Historical Evidence to Estimate Today’s Cost of Capital 338

11.3 Measuring Risk 340

Variance and Standard Deviation 340

A Note on Calculating Variance 343

Measuring the Variation in Stock Returns 343

11.4 Risk and Diversification 345

Diversification 345

Asset versus Portfolio Risk 346

Market Risk versus Specific Risk 352

11.5 Thinking about Risk 353

Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable 353

Message 2: Market Risks Are Macro Risks 354

Message 3: Risk Can Be Measured 355

Summary 356

Questions and Problems 357

Chapter 12 Risk, Return, and Capital Budgeting 362 12.1 Measuring Market Risk 364

Measuring Beta 364

Betas for Ford and PG&E 367

Total Risk and Market Risk 367

12.2 What Can You Learn from Beta? 369

Portfolio Betas 369

The Portfolio Beta Determines the Risk of a Diversified Portfolio 372

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xxviii Contents

12.3 Risk and Return 373

Why the CAPM Makes Sense 375

The Security Market Line 376

Using the CAPM to Estimate Expected Returns 377

How Well Does the CAPM Work? 377

12.4 The CAPM and the Opportunity Cost of Capital 380

The Company Cost of Capital 382

What Determines Project Risk? 382

Don’t Add Fudge Factors to Discount Rates 383

Summary 383

Questions and Problems 384

Chapter 13 The Weighted-Average Cost of Capital and Company Valuation 392 13.1 Geothermal’s Cost of Capital 394

13.2 The Weighted-Average Cost of Capital 395

Calculating Company Cost of Capital as a Weighted Average 396

Use Market Weights, Not Book Weights 398

Taxes and the Weighted-Average Cost of Capital 398

What If There Are Three (or More) Sources of Financing? 400

The NPV of Geothermal’s Expansion 400

Checking Our Logic 401

13.3 Interpreting the Weighted-Average Cost of Capital 402

When You Can and Can’t Use WACC 402

Some Common Mistakes 402

How Changing Capital Structure Affects Expected Returns 403

What Happens When the Corporate Tax Rate Is Not Zero 403

13.4 Practical Problems: Measuring Capital Structure 403

13.5 More Practical Problems: Estimating Expected Returns 405

The Expected Return on Bonds 405

The Expected Return on Common Stock 406

The Expected Return on Preferred Stock 407

Adding It All Up 408

Real-Company WACCs 408

13.6 Valuing Entire Businesses 409

Calculating the Value of the Deconstruction Business 410

Summary 411

Questions and Problems 412

Minicase 417

Part Four Financing

Chapter 14 Introduction to Corporate Financing 420 14.1 Creating Value with Financing Decisions 422

14.2 Patterns of Corporate Financing 422

Are Firms Issuing Too Much Debt? 424

14.3 Common Stock 425

Ownership of the Corporation 427

Voting Procedures 428

Classes of Stock 429

14.4 Preferred Stock 429

14.5 Corporate Debt 430

Debt Comes in Many Forms 431

Innovation in the Debt Market 433

14.6 Convertible Securities 435

Summary 436

Questions and Problems 437

Chapter 15 How Corporations Raise Venture Capital and Issue Securities 440 15.1 Venture Capital 442

Venture Capital Companies 443

15.2 The Initial Public Offering 445

Arranging a Public Issue 446

Other New-Issue Procedures 450

The Underwriters 450

15.3 General Cash Offers by Public Companies 451

General Cash Offers and Shelf Registration 452

Costs of the General Cash Offer 452

Market Reaction to Stock Issues 453

15.4 The Private Placement 454

Summary 454

Questions and Problems 455

Minicase 460

Appendix: Hotch Pot’s New-Issue Prospectus 461

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Contents xxix

Chapter 16 Debt Policy 466 16.1 How Borrowing Affects Value in a Tax-Free

Economy 468

MM’s Argument—A Simple Example 469

How Borrowing Affects Earnings per Share 470

How Borrowing Affects Risk and Return 472

16.2 Debt and the Cost of Equity 474

No Magic in Financial Leverage 476

16.3 Debt, Taxes, and the Weighted-Average Cost of Capital 478

Debt and Taxes at River Cruises 478

How Interest Tax Shields Contribute to the Value of Stockholders’ Equity 480

Corporate Taxes and the Weighted-Average Cost of Capital 480

The Implications of Corporate Taxes for Capital Structure 482

16.4 Costs of Financial Distress 482

Bankruptcy Costs 483

Costs of Bankruptcy Vary with Type of Asset 484

Financial Distress without Bankruptcy 485

16.5 Explaining Financing Choices 487

The Trade-Off Theory 487

A Pecking Order Theory 488

The Two Faces of Financial Slack 489

Is There a Theory of Optimal Capital Structure? 490

Summary 491

Questions and Problems 492

Minicase 499

Appendix: Bankruptcy Procedures 501

Chapter 17 Payout Policy 504 17.1 How Corporations Pay Out Cash to Shareholders 506

How Firms Pay Dividends 507

Limitations on Dividends 507

Stock Dividends and Stock Splits 508

Stock Repurchases 509

17.2 The Information Content of Dividends and Repurchases 509

17.3 Dividends or Repurchases? The Payout Controversy 511

Dividends or Repurchases? An Example 511

Repurchases and the Dividend Discount Model 513

Dividends and Share Issues 514

17.4 Why Dividends May Increase Value 515

17.5 Why Dividends May Reduce Value 517

Taxation of Dividends and Capital Gains under Current Tax Law 518

Taxes and Payout—A Summary 518

17.6 Payout Policy and the Life Cycle of the Firm 518

Summary 519

Questions and Problems 520

Minicase 526

Part Five Debt and Payout Policy

Part Six Financial Analysis and Planning

Chapter 18 Long-Term Financial Planning 528 18.1 What Is Financial Planning? 530

Why Build Financial Plans? 530

18.2 Financial Planning Models 531

Components of a Financial Planning Model 531

18.3 A Long-Term Financial Planning Model for Dynamic Mattress 532

Pitfalls in Model Design 537

Choosing a Plan 538

18.4 External Financing and Growth 539

Summary 542

Questions and Problems 543

Minicase 549

Chapter 19 Short-Term Financial Planning 550 19.1 Links between Long-Term and Short-Term Financing 552

Tax Strategies 553

Reasons to Hold Cash 554

19.2 Tracing Changes in Cash 554

19.3 Cash Budgeting 556

Preparing the Cash Budget 556

19.4 Dynamic’s Short-Term Financial Plan 559

Dynamic Mattress’s Financing Plan 560

Evaluating the Plan 561

A Note on Short-Term Financial Planning Models 562

Summary 564

Questions and Problems 564

Minicase 569

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xxx Contents

Chapter 20 Working Capital Management 572 20.1 Working Capital 574

Components of Working Capital 574

Working Capital and the Cash Cycle 574

20.2 Accounts Receivable and Credit Policy 577

Terms of Sale 578

Credit Agreements 579

Credit Analysis 580

The Credit Decision 581

Collection Policy 586

20.3 Inventory Management 587

20.4 Cash Management 590

Check Handling and Float 591

Other Payment Systems 592

Electronic Funds Transfer 593

International Cash Management 594

20.5 Investing Idle Cash: The Money Market 595

Money Market Investments 595

Calculating the Yield on Money Market Investments 596

Yields on Money Market Investments 597

The International Money Market 597

20.6 Managing Current Liabilities: Short-Term Debt 598

Bank Loans 598

Commercial Paper 599

Summary 600

Questions and Problems 602

Minicase 610

Part Seven Special Topics

Chapter 21 Mergers, Acquisitions, and Corporate Control 612 21.1 Sensible Motives for Mergers 614

Economies of Scale 616

Economies of Vertical Integration 616

Combining Complementary Resources 617

Mergers as a Use for Surplus Funds 618

Eliminating Inefficiencies 618

Industry Consolidation 618

Taxes and Cross-Border Mergers 619

21.2 Dubious Reasons for Mergers 619

Diversification 619

The Bootstrap Game 619

21.3 The Mechanics of a Merger 621

The Form of Acquisition 621

Mergers, Antitrust Law, and Popular Opposition 621

21.4 Evaluating Mergers 622

Mergers Financed by Cash 622

Mergers Financed by Stock 624

A Warning 625

Another Warning 625

21.5 The Market for Corporate Control 626

21.6 Method 1: Proxy Contests 626

21.7 Method 2: Takeovers 627

21.8 Method 3: Leveraged Buyouts 629

Barbarians at the Gate? 630

21.9 Method 4: Divestitures, Spin-Offs, and Carve-Outs 632

21.10 The Benefits and Costs of Mergers 633

Merger Waves 633

Summary 634

Questions and Problems 635

Minicase 639

Chapter 22 International Financial Management 640 22.1 Foreign Exchange Markets 642

Spot Exchange Rates 642

Forward Exchange Rates 644

22.2 Some Basic Relationships 645

Exchange Rates and Inflation 645

Real and Nominal Exchange Rates 648

Inflation and Interest Rates 648

The Forward Exchange Rate and the Expected Spot Rate 650

Interest Rates and Exchange Rates 651

22.3 Hedging Currency Risk 652

Transaction Risk 652

Economic Risk 653

22.4 International Capital Budgeting 654

Net Present Values for Foreign Investments 654

Political Risk 656

The Cost of Capital for Foreign Investment 657

Avoiding Fudge Factors 658

Summary 658

Questions and Problems 659

Minicase 664

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Contents xxxi

Chapter 23 Options 666 23.1 Calls and Puts 668

Selling Calls and Puts 670

Payoff Diagrams Are Not Profit Diagrams 671

Financial Alchemy with Options 672

Some More Option Magic 673

23.2 What Determines Option Values? 674

Upper and Lower Limits on Option Values 674

The Determinants of Option Value 675

Option-Valuation Models 677

23.3 Spotting the Option 680

Options on Real Assets 680

Options on Financial Assets 681

Summary 684

Questions and Problems 685

Chapter 24 Risk Management 694 24.1 Why Hedge? 696

The Evidence on Risk Management 697

24.2 Reducing Risk with Options 698

24.3 Futures Contracts 698

The Mechanics of Futures Trading 701

Commodity and Financial Futures 702

24.4 Forward Contracts 703

24.5 Swaps 704

Interest Rate Swaps 704

Currency Swaps 706

And Some Other Swaps 707

24.6 Innovation in the Derivatives Market 707

24.7 Is “Derivative” a Four-Letter Word? 707

Summary 708

Questions and Problems 709

Chapter 25 What We Do and Do Not Know about Finance 714 25.1 What We Do Know: The Six Most Important

Ideas in Finance 716

Net Present Value (Chapter 5) 716

Risk and Return (Chapters 11 and 12) 716

Efficient Capital Markets (Chapter 7) 717

MM’s Irrelevance Propositions (Chapters 16 and 17) 717

Option Theory (Chapter 23) 717

Agency Theory 718

25.2 What We Do Not Know: Nine Unsolved Problems in Finance 718

What Determines Project Risk and Present Value? 718

Risk and Return—Have We Missed Something? 719

Are There Important Exceptions to the Efficient-Market Theory? 720

Is Management an Off-Balance-Sheet Liability? 720

How Can We Explain Capital Structure? 721

How Can We Resolve the Payout Controversy? 721

How Can We Explain Merger Waves? 721

What Is the Value of Liquidity? 722

Why Are Financial Systems Prone to Crisis? 722

25.3 A Final Word 723

Questions and Problems 723

Appendix A A-1

Glossary G-1

Index IND-1

Part Eight Conclusion

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2

Goals and Governance of the Corporation

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

1-1 Give examples of the investment and financing decisions that financial managers make.

1-2 Distinguish between real and financial assets.

1-3 Cite some of the advantages and disadvantages of organizing a business as a corporation.

1-4 Describe the responsibilities of the CFO, treasurer, and controller.

1-5 Explain why maximizing market value is the natural financial goal of the corporation.

1-6 Understand what is meant by “agency problems,” and cite some of the ways that corporate governance helps mitigate them.

1-7 Understand why maximizing market value does not justify behaving unethically.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

1

bre13960_ch01_002-031.indd 2 1/26/19 10:36 AM

3

P A

R T

O N

E In

tr od

uc tio

n

To grow from small beginnings to a major corporation, FedEx needed to make good investment and financing decisions. @Duy Phuong Nguyen/Alamy

To carry on business, a corporation needs an almost endless variety of assets. Some assets are tangible, for example, plant and machinery, office buildings, and vehicles; others are intangible, for exam- ple, brand names and patents. Corporations finance these assets by borrowing, by reinvesting profits back into the firm, and by selling additional shares to the firm’s shareholders.

Financial managers, therefore, face two broad ques- tions. First, what investments should the corporation make? Second, how should it pay for these investments? Investment decisions spend money. Financing decisions raise money for investment.

We start this chapter with examples of recent invest- ment and financing decisions by major U.S. and foreign corporations. We review what a corporation is and describe the roles of its top financial managers. We then turn to the financial goal of the corporation, which is usu- ally expressed as maximizing value, or at least adding

value. Financial managers add value whenever the cor- poration can invest to earn a higher return than its share- holders can earn for themselves.

But managers are human beings; they cannot be per- fect servants who always and everywhere maximize value. We will consider the conflicts of interest that arise in large corporations and how corporate governance helps to align the interests of managers and shareholders.

If we ask managers to maximize value, can the corpo- ration also be a good citizen? Won’t the managers be tempted to try unethical or illegal financial tricks? They sometimes may be tempted, but wise managers realize that such tricks are not just dishonest; they almost always destroy value, not increase it. More challeng- ing for the financial manager are the gray areas where the line between ethical and unethical financial actions is hard to draw.

Finally, we look ahead to the rest of this book and look back to some entertaining snippets of financial history.

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4 Part One Introduction

Investment and Financing Decisions

Fred Smith is best known today as the founder of FedEx. But in 1965 he was still a sophomore at Yale, where he wrote an economics term paper arguing that delivery systems were not keeping up with increasing needs for speed and dependability.1 He later joined his stepfather at a struggling equipment and maintenance firm for air car- riers. He observed firsthand the difficulties of shipping spare parts on short notice. He saw the need for an integrated air and ground delivery system with a central hub that could connect a large number of points more efficiently than a point-to-point delivery system. In 1971, at the age of 27, Smith founded Federal Express.

Like many start-up firms, Federal Express flirted again and again with failure. Smith and his family had an inheritance of a few million dollars, but this was far from enough. The young company needed to purchase and retrofit a small fleet of aging Dassault Falcon jets; build a central-hub facility; and hire and train pilots, delivery, and office staff. The initial source of capital was short-term bank loans. Because of the company’s shaky financial position, the bank demanded that the planes be used as col- lateral and that Smith personally guarantee the loan with his own money.

In April 1973, the company went live with a fleet of 14 jets, servicing 25 U.S. cities out of its Memphis hub. By then, the company had spent $25 million and was effec- tively flat broke, without enough funds to pay for its weekly delivery of jet fuel. In desperation, it managed to acquire a bank loan for $23.7 million. This loan had to be backed by a guarantee from General Dynamics, which in return acquired an option to buy the company. (Today, General Dynamics must regret that it never exercised this option.)

In November of that year, the company finally achieved some financial stability when it raised $24.5 million from venture capitalists, investment firms that provide funds and advice to young companies in return for a partial ownership share. Eventu- ally, venture capitalists invested about $90 million in Federal Express.

In 1977, private firms were allowed for the first time to compete with the Postal Service in package delivery. Federal Express responded by expanding its operations. It acquired seven Boeing 727s, each with about seven times the capacity of the Falcon jets. To pay for these new investments, Federal Express raised about $19 million by selling shares of stock to the general public in an initial public offering (IPO). The new stockholders became part-owners of the company in proportion to the number of shares they purchased.

From this point on, success followed success, and the company invested heavily to expand its air fleet as well as its supporting infrastructure. It introduced an automated shipping system and a bar-coded tracking system. In 1994, it launched its fedex.com website for online package tracking. It opened several new hubs across the United States as well as in Canada, France, the Philippines, and China. In 2007, FedEx (as the company was now called) became the world’s largest airline measured by number of planes. FedEx also invested in other companies, capped by the acquisition of TNT Express for $4.4 billion in 2016. By 2017, FedEx had 400,000 employees, annual rev- enue of $60 billion, and a stock market value of $67 billion. Its name had become a verb—to “FedEx a package” was to ship it overnight.

Even in retrospect, FedEx’s success was hardly a sure thing. Fred Smith’s idea was inspired, but its implementation was complex and difficult. FedEx had to make good investment decisions. In the beginning, these decisions were constrained by lack of financing. For example, used Falcon jets were the only option, given the young com- pany’s precarious financial position. At first it could service only a short list of major cities. As the company grew, its investment decisions became more complex. Which type of planes should it buy? When should it expand coverage to Europe and Asia?

1.1

1 Legend has it that Smith received a grade of C on this paper. In fact, he doesn’t remember the grade.

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Chapter 1 Goals and Governance of the Corporation 5

How many operations hubs should it build? What computer and tracking systems were necessary to keep up with the increasing package volume and geographic coverage? Which companies should it acquire as it expanded its range of services?

FedEx also needed to make good financing decisions. For example, how should it raise the money it needed for investment? In the beginning, these choices were limited to family money and bank loans. As the company grew, its range of choices expanded. Eventually it was able to attract funding from venture capitalists, but this posed new questions. How much cash did the firm need to raise from the venture capitalists? How big a share in the firm would the venture capitalists demand in return? The initial public offering of stock prompted similar questions. How many shares should the company try to sell? At what price? As the company grew, it raised more funds by bor- rowing money from its banks and by selling publicly traded bonds to investors. At each point, it needed to decide on the proper form and terms of financing as well as the amounts to be raised.

In short, FedEx needed to be good at finance. It had a head start over potential com- petitors, but a series of bad financial decisions would have sunk the company. No two companies’ histories are the same, but, like FedEx, all successful companies must make good investment and financing decisions. And, as with FedEx, those decisions range from prosaic and obvious to difficult and strategically crucial.

Let’s widen our discussion. Table 1.1 gives an example of a recent investment and financing decision for 10 corporations. Five are U.S. corporations and five are foreign. We have chosen very large public corporations that you are likely to be familiar with. You may have shopped at Walmart, posted a picture on Facebook, or dreamed of buy- ing a Ferrari.

Take a look at the decisions now. We think you will agree that they appear sensible— at least there is nothing obviously wrong with them. But if you are new to finance, it may be difficult to think about why these companies made these decisions and not others.

Company Recent Investment Decisions Recent Financing Decisions

Delta Air Lines (U.S.) Places order for 100 Airbus A321 airliners. Issues $1 billion 5-year bond. ExxonMobil (U.S.) Announces decision to proceed with development

of a huge offshore oil discovery in Guyana. Reinvests $8.5 billion of the cash that it generates from operations.

Facebook (U.S.) Acquires Two Big Ears, a British virtual reality audio company

Leases large new office building in San Francisco.

Fiat Chrysler (Italy) Spins off its Ferrari luxury car unit. Repays $1.8 billion of bank debt. GlaxoSmithKline (U.K.) Spends $3.6 billion on research and development

for new drugs. Issues additional short-term euro debt.

Lenovo (China) Announces plans to build a new manufacturing facility in India to produce PCs and smartphones

Issues $500 million of dollar bonds and $850 million of preferred shares.

LVMH2 (France) Acquires high-end perfumery, Maison Francis Kurkdjian

Partly finances acquisitions by issue of debt.

Procter & Gamble (U.S.) Spends over $7 billion on advertising. Buys back $4.6 billion of stock and pays a $7.2 billion dividend.

Toshiba (Japan) Agrees to sell off its bankrupt U.S. nuclear business for $4.6 billion.

Makes $5.4 billion issue of common stock.

Walmart (U.S.) Announces plan to invest $800 million in Chile over 3 years.

Announces offer to buy back some of its bonds.

TABLE 1.1 Examples of recent investment and financing decisions by major public corporations

2 LVMH (Moët Hennessy Louis Vuitton) markets perfumes and cosmetics, wines and spirits, leather goods, watches, and other luxury products. And, yes, we know what you are thinking, but “LVMH” really is short for “Moët Hennessy Louis Vuitton.”

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6 Part One Introduction

The Investment (Capital Budgeting) Decision Investment decisions, such as those shown in Table 1.1, are also called capital bud- geting or capital expenditure (CAPEX) decisions. Some of the investments in the table, such as ExxonMobil’s oil platforms or Lenovo’s new factory, involve tangible assets—assets that you can touch and kick. Others involve intangible assets, such as research and development (R&D), advertising, and the design of computer software. For example, major pharmaceutical manufacturers invest billions every year on R&D for new drugs.

Sometimes investments can have very-long-term consequences. For example, many U.S. nuclear power plants, which were initially licensed by the Nuclear Regulatory Commission to operate for 40 years, are now being relicensed for 20 more years, and may be able to operate efficiently for 80 years overall. Other investments may pay off in only a few months. For example, with the approach of the Christmas holidays, Walmart spends nearly $50 billion to stock up its warehouses and retail stores. As the goods are sold over the following months, the company recovers its investment in these inventories.

The world of business can be intensely competitive, and corporations prosper only if they can keep launching new products or services. In some cases, the costs and risks of doing so are amazingly large. For example, the cost of developing the Gorgon natu- ral gas field in Australia has been estimated at over $40 billion. It’s not surprising that this cost is being shared among several major energy companies. But do not think of companies as making billion-dollar investments on a daily basis. Most investment decisions are smaller, such as the purchase of a truck, machine tool, or computer sys- tem. Corporations make thousands of such investments each year. The cumulative amount of these small expenditures can be just as large as the occasional jumbo invest- ments, such as those shown in Table 1.1.

Not all investments succeed. In October 2011 Hewlett-Packard (HP) paid $11.1 billion to acquire the British software company Autonomy. Just 13 months later, HP wrote down the value of this investment by $8.8 billion. HP claimed that it was misled by improper accounting at Autonomy. Nevertheless, the Autonomy acquisition was a disastrous investment for HP. HP’s CEO was fired in short order.

There are no free guarantees in finance. But you can tilt the odds in your favor if you learn the tools of investment analysis and apply them intelligently. We cover these tools in detail later in this book.

The Financing Decision The financial manager’s second main responsibility is to raise the money that the firm requires for its investments and operations. This is the financing decision. When a company needs to raise money, it can invite investors to put up cash in exchange for a share of future profits, or it can promise to pay back the investors’ cash plus a fixed rate of interest. In the first case, the investors receive shares of stock and become shareholders, part-owners of the corporation. The investors in this case are referred to as equity investors, who contribute equity financing. In the second case, the investors are lenders, that is, debt investors, who one day must be repaid. The choice between debt and equity financing is often called the capital structure decision. Here “capital” refers to the firm’s sources of long-term financing. A firm that is seeking to raise long- term financing is said to be “raising capital.”

Notice the essential difference between the investment and financing decisions. When the firm invests, it acquires real assets, which are then used to produce the firm’s goods and services. The firm finances its investment in real assets by issuing financial assets to investors. A share of stock is a financial asset, which has value as a claim on the firm’s real assets and on the income that those assets will produce. A bank loan is a financial asset also. It gives the bank the right to get its money back plus interest. If the firm’s operations can’t generate enough income to repay the bank,

capital budgeting or capital expenditure (CAPEX) decision Decision to invest in tangible or intangible assets.

financing decision Decision on the sources and amounts of financing.

real assets Assets used to produce goods and services.

financial assets Financial claims to the income generated by the firm’s real assets.

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Chapter 1 Goals and Governance of the Corporation 7

the bank can force the firm into bankruptcy and stake a claim on its real assets. Finan- cial assets that can be purchased and traded by investors in public markets are called securities. The shares of stock issued by the public corporations in Table 1.1 are all securities. Delta’s 5-year bond in Table 1.1 also is a security. But a bank loan from JPMorgan to Delta is not called a security unless the bank resells the loan to public investors.

The firm can issue an almost endless variety of financial assets. Suppose it decides to borrow. It can issue debt to investors, or it can borrow from a bank. It can borrow for 1 year or 20 years. If it borrows for 20 years, it can reserve the right to pay off the debt early. It can borrow in Paris, receiving and promising to repay euros, or it can borrow dollars in New York. (As Table 1.1 shows, GlaxoSmithKline chose to borrow euros, but it could have borrowed U.S. dollars or British pounds instead.)

In some ways, financing decisions are less important than investment decisions. Financial managers say that “value comes mainly from the investment side of the bal- ance sheet.” Also, the most successful corporations sometimes have the simplest financing strategies. Take Microsoft as an example. It is one of the world’s most valu- able corporations. In mid-2018, Microsoft shares traded for $94 each. There were 7.71 billion shares outstanding. Therefore Microsoft’s market value—its market capi- talization or market cap—was 7.71 × $94 = $725 billion. Where did this market value come from? It came from Microsoft’s products, from its brand name and worldwide customer base, from its R&D, and from its ability to make profitable future invest- ments. It did not come from sophisticated financing. Microsoft’s financing strategy is very simple: It finances almost all investment by retaining and reinvesting operating cash flow.

Financing decisions may not add much value compared to good investment deci- sions, but they can destroy value if they are stupid or ambushed by bad news. For example, when a consortium of investment companies bought the energy giant TXU in 2007, the company took on an additional $40 billion in debt. This may not have been a stupid decision, but it did prove fatal. The consortium did not foresee the expan- sion of shale gas production and the resulting sharp fall in natural gas and electricity prices. By April 2014 the company (renamed Energy Future Holdings) was bankrupt.

Are the following capital budgeting or financing decisions? (Hint: In one case the answer is “both.”)

a. Intel decides to spend $7 billion to develop a new microprocessor factory. b. BMW borrows 350 million euros (€350 million) from Deutsche Bank. c. Royal Dutch Shell constructs a pipeline to bring natural gas onshore from a

production platform in Australia. d. Avon spends €200 million to launch a new range of cosmetics in European

markets. e. Pfizer issues new shares to buy a small biotech company.

Self-Test1.1

We have emphasized the financial manager’s responsibility for two decisions:

The investment decision = purchase of real assets   The financing decision = sale of financial assets

But this is an oversimplification because the financial manager is also involved in many other day-to-day activities that are essential to the smooth operation of a busi- ness. For example, if the firm sells goods or services on credit, it needs to make sure

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8 Part One Introduction

What Is a Corporation?

We have been referring to “corporations.” But before going too far or too fast, we need to offer some basic definitions.

A corporation is a distinct, permanent legal entity. Suppose you decide to create a new corporation.3 You would work with a lawyer to prepare articles of incorporation, which set out the purpose of the business and how it is to be financed, managed, and governed. These articles must conform to the laws of the state in which the business is incorporated. For many purposes, the corporation is considered a resident of its state. For example, it can enter into contracts, borrow or lend money, and sue or be sued. It pays its own taxes (but it cannot vote!).

A corporation’s owners are called shareholders or stockholders.4 The shareholders do not directly own the business’s real assets (factories, oil wells, stores, etc.). Instead they have indirect ownership via financial assets (the shares of the corporation).

A corporation is legally distinct from the shareholders. Therefore, the shareholders have limited liability and cannot be held personally responsible for the corporation’s debts. When the U.S. financial corporation Lehman Brothers failed in 2008, no one demanded that its stockholders put up more money to cover Lehman’s massive debts. Shareholders can lose their entire investment in a corporation, but no more.

1.2

corporation A business organized as a separate legal entity owned by stockholders.

limited liability The owners of a corporation are not personally liable for its obligations.

Which of the following are financial assets, and which are real assets?

a. A patent. b. A share of stock issued by Wells Fargo Bank. c. A blast furnace in a steelmaking factory. d. A mortgage loan taken out to help pay for a new home. e. After a successful advertising campaign, potential customers trust FedEx to

deliver packages promptly and reliably. f. An IOU (“I owe you”) from your brother-in-law.

Self-Test1.2

Business Organization

Suppose you buy a building and open a restaurant. You have invested in the building itself, kitchen equipment, dining-room furnishings, plus various other assets. If you do not incorpo- rate, you own these assets personally, as the sole proprietor of the business. If you have borrowed money from a bank to start the business, then you are personally responsible for this debt. If the business loses money and cannot pay the bank, then the bank can demand

Example 1.1 ⊲

3 In the United States, corporations are identified by the label “Corporation,” “Incorporated,” or “Inc.,” as in Caterpillar Inc. The United Kingdom identifies public corporations by “plc” (short for “Public Limited Corpo- ration”). French corporations have the suffix “SA” (“Société Anonyme”). The corresponding labels in Germany are “GmbH” (“Gesellschaft mit beschränkter Haftung”) and “AG” (“Aktiengesellschaft”). 4 “Shareholder” and “stockholder” mean exactly the same thing and are used interchangeably.

that its customers pay on time. Corporations that operate internationally must con- stantly transfer cash from one currency to another. And the manager must keep an eye on the risks that the firm runs and ensure that they don’t land the firm in a pickle.

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Chapter 1 Goals and Governance of the Corporation 9

When a corporation is first established, its shares may be privately owned by a small group of investors, perhaps the company’s managers and a few backers. In this case, the shares are not publicly traded and the company is said to be closely held. Eventually, when the firm grows and new shares are issued to raise additional capital, its shares are traded in public markets such as the New York Stock Exchange. Such corporations are known as public companies. Most well-known corporations in the United States are public companies with widely dispersed shareholdings. In other countries, it is more common for large corporations to remain in private hands, and many public companies may be controlled by just a handful of investors.

A large public corporation may have hundreds of thousands of shareholders, who together own the business. An individual may have 100 shares, receive 100 votes, and be entitled to a tiny fraction of the firm’s income and value. On the other hand, a pen- sion fund or insurance company may own millions of shares, receive millions of votes, and have a correspondingly large stake in the firm’s performance.

Public shareholders cannot possibly manage or control the corporation directly. Instead, they elect a board of directors, who in turn appoint the top managers and monitor their performance. This separation of ownership and control gives corpora- tions permanence. Even if managers quit or are dismissed, the corporation survives. Today’s stockholders can sell all their shares to new investors without disrupting the operations of the business. Corporations can, in principle, live forever, and in prac- tice they may survive many human lifetimes. One of the oldest corporations is the Hudson’s Bay Company, which was formed in 1670 to profit from the fur trade between northern Canada and England. The company still operates as one of Canada’s leading retail chains.

The separation of corporate ownership and control can also have a downside, for it can open the door for managers and directors to act in their own interests rather than in the stockholders’ interest. We return to this problem later in the chapter.

There are other disadvantages to being a corporation. One is the cost, in both time and money, of managing the corporation’s legal machinery. These costs are particu- larly burdensome for small businesses.

There is also an important tax drawback to corporations in the United States. Because the corporation is a separate legal entity, it is taxed separately. So corpora- tions pay tax on their profits, and shareholders are taxed again when they receive divi- dends from the company or sell their shares at a profit. By contrast, income generated by businesses that are not incorporated is taxed just once as personal income.6

Other Forms of Business Organization Corporations do not have to be prominent, multinational businesses such as those listed in Table 1.1. You can organize a local plumbing contractor or barber shop as a

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S-corporations

that you raise cash by selling other assets—your car or house, for example—in order to repay the loan. But if you incorporate the restaurant business, and then the corporation borrows from the bank, your other assets are shielded from the restaurant’s debts. Of course, incor- poration also means that the bank will be more cautious in lending to you because it will have no recourse to your other assets.5

Notice that if you incorporate your business, you exchange direct ownership of its real assets (the building, kitchen equipment, etc.) for indirect ownership via financial assets (the shares of the new corporation). ■

5 The bank may ask you to put up personal assets as collateral for the loan to your restaurant corporation. But it has to ask and get your agreement. It doesn’t have to ask if your business is a sole proprietorship. 6 The U.S. tax system is somewhat unusual in this respect. To avoid taxing the same income twice, many other countries give shareholders at least some credit for the taxes that the corporation has already paid.

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10 Part One Introduction

corporation if you want to take the trouble. But most corporations are larger businesses or businesses that aspire to grow. Small “mom-and-pop” businesses are usually orga- nized as sole proprietorships.

What about the middle ground? What about businesses that grow too large for sole proprietorships but don’t want to reorganize as corporations? For example, suppose you wish to pool money and expertise with some friends or business associates. You can form a partnership and enter into a partnership agreement that sets out how deci- sions are to be made and how profits are to be split up. Partners, like sole proprietors, face unlimited liability. If the business runs into difficulties, each partner can be held responsible for all the business’s debts.

Partnerships have a tax advantage. Partnerships, unlike corporations, do not have to pay income taxes. The partners pay personal income taxes on their shares of the profits.

Some businesses are hybrids that combine the tax advantage of a partnership with the limited liability advantage of a corporation. In a limited partnership, partners are classified as general or limited. General partners manage the business and have unlim- ited personal liability for its debts. Limited partners are liable only for the money they invest and do not participate in management.

Many states allow limited liability partnerships (LLPs) or limited liability compa- nies (LLCs). These are partnerships in which all partners have limited liability. Another variation on the theme is the professional corporation (PC), which is commonly used by doctors, lawyers, and accountants. In this case, the business has limited liability, but the professionals can still be sued personally, for example, for malpractice.

Most large investment banks such as Morgan Stanley and Goldman Sachs started life as partnerships. But eventually these companies and their financing requirements grew too large for them to continue as partnerships, and they reorganized as corpora- tions. The partnership form of organization does not work well when ownership is widespread and separation of ownership and management is essential.

Who Is the Financial Manager?

What do financial managers do for a living? That simple question can be answered in several ways. We can start with financial managers’ job titles. Most large corporations have a chief financial officer (CFO), who oversees the work of all financial staff. As you can see from Figure 1.1, the CFO is deeply involved in financial policy and finan- cial planning and is in constant contact with the chief executive officer (CEO) and other top management. The CFO is the most important financial voice of the corpora- tion and explains earnings results and forecasts to investors and the media.

1.3

chief financial officer (CFO) Supervises all financial functions and sets overall financial strategy.

Treasurer Responsible for: Cash management Raising of capital Banking relationships

Controller Responsible for: Preparation of financial statements Accounting Taxes

Chief Financial O�cer (CFO) Responsible for: Financial policy Corporate planning

FIGURE 1.1 Financial managers in large corporations

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Chapter 1 Goals and Governance of the Corporation 11

Below the CFO are usually a treasurer and a controller. The treasurer looks after the firm’s cash, raises new capital, and maintains relationships with banks and other investors that hold the firm’s securities. The controller prepares the financial state- ments, manages the firm’s internal budgets and accounting, and looks after its tax affairs. Thus, the treasurer’s main function is to obtain and manage the firm’s capital, whereas the controller ensures that the money is used efficiently.

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The financial managers

treasurer Responsible for financing, cash management, and relationships with banks and other financial institutions.

controller Responsible for budgeting, accounting, and taxes.

Fritz and Frieda went to business school together 10 years ago. They have just been hired by a midsize corporation that wants to bring in new financial manag- ers. Fritz studied finance, with an emphasis on financial markets and institutions. Frieda majored in accounting and became a CPA 5 years ago. Who is more suited to be treasurer and who controller? Briefly explain.

Self-Test1.3

In large corporations, financial managers are responsible for organizing and super- vising the capital budgeting process. However, major capital investment projects are so closely tied to plans for product development, production, and marketing that man- agers from these other areas are inevitably drawn into planning and analyzing the proj- ects. If the firm has staff members specializing in corporate planning, they are naturally involved in capital budgeting too. For this reason, we will use the term financial man- ager to refer to anyone responsible for an investment or financing decision. Often we will use the term collectively for all the managers drawn into such decisions.

Now let’s go beyond job titles. What is the essential role of the financial manager? Figure 1.2 gives one answer. The figure traces how money flows from investors to the corporation and back again to investors. The flow starts when cash is raised from investors (arrow 1 in the figure). The cash could come from banks or from securities sold to investors in financial markets. The cash is then used to pay for the real assets (investment projects) needed for the corporation’s business (arrow 2). Later, as the business operates, the assets generate cash inflows (arrow 3). That cash is either rein- vested (arrow 4a) or returned to the investors who furnished the money in the first place (arrow 4b). Of course, the choice between arrows 4a and 4b is constrained by the promises made when cash was raised at arrow 1. For example, if the firm borrows money from a bank at arrow 1, it must repay this money plus interest at arrow 4b.

You can see examples of arrows 4a and 4b in Table 1.1. ExxonMobil partly financed its investments by reinvesting earnings (arrow 4a). Procter & Gamble decided to return cash to shareholders by buying back its stock (arrow 4b). It could have chosen instead to pay the money out as additional cash dividends, also on arrow 4b.

Notice how the financial manager stands between the firm and outside investors. On the one hand, the financial manager is involved in the firm’s operations, particularly by

FIGURE 1.2 Flow of cash between investors and the firm’s operations. Key: (1) Cash raised by selling financial assets to investors; (2) cash invested in the firm’s operations; (3) cash generated by the firm’s operations; (4a) cash reinvested; (4b) cash returned to investors.

(2)

(3)

(1)

(4b)

(4a)Financial Manager

Firm’s Operations

Real Assets

Investors

Financial Assets

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12 Part One Introduction

helping to make good investment decisions. On the other hand, he or she deals with financial institutions and other investors and with financial markets such as the New York Stock Exchange. We say more about these financial institutions and markets in the next chapter.

Goals of the Corporation

Shareholders Want Managers to Maximize Market Value For small corporations, shareholders and management may be one and the same. But for large corporations, separation of ownership and management is a practical neces- sity. For example, Walmart has more than 100,000 distinct shareholders. There is no way that these shareholders can be actively involved in management; it would be like trying to run New York City by town meetings. Authority has to be delegated.

How can shareholders effectively delegate decision making when they all have dif- ferent tastes, wealth, time horizons, personal opportunities, and tolerance for risk? Delegation can work only if the shareholders have a common goal. Fortunately there is a natural financial objective on which almost all shareholders can agree: Maximize the current market value of shareholders’ investment in the firm.

This simple, unqualified goal makes sense when the shareholders have access to well-functioning financial markets and institutions. Access gives them the flexibility to manage their own savings and consumption plans, leaving the corporation’s finan- cial managers with only one task, to increase market value. For example, a corpora- tion’s roster of shareholders will usually include both risk-averse and risk-tolerant investors. You might expect the risk-averse to say, “Sure, maximize value, but don’t touch too many high-risk projects.” Instead, they say, “Risky projects are okay, pro- vided that expected profits are more than enough to offset the risks. If this firm ends up too risky for my taste, I’ll adjust my investment portfolio to make it safer.” For example, the risk-averse shareholder can shift more of his or her portfolio to safe assets, such as U.S. government bonds. Shareholders can also just say good-bye, sell- ing off shares of the risky firm and buying shares in a safer one. If the risky invest- ments increase market value, the departing shareholders are better off than they would be if the risky investments were turned down.

1.4

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Foundations of the NPV rule

Value Maximization

Fast-Track Wireless shares trade for $20. It has just announced a “bet the company” investment in a high-risk, but potentially revolutionary, WhyFi technology. Investors note the risk of failure but are even more impressed with the technology’s upside. They con- clude that the possibility of very high future profits justifies a higher share price. The price goes up to $23.

Caspar Milquetoast, a thoughtful but timid shareholder, notes the downside risks and decides that it’s time for a change. He sells out to more risk-tolerant investors. But he sells at $23 per share, not $20. Thus, he captures the value added by the WhyFi project without hav- ing to bear the project’s risks. Those risks are transferred to other investors, who are more risk-tolerant or more optimistic.

In a well-functioning stock market, there is always a pool of investors ready to bear down- side risks if the upside potential is sufficiently attractive. We know that the upside potential was sufficient in this case because Fast-Track stock attracted investors willing to pay $23 per share. ■

Example 1.2 ⊲

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Chapter 1 Goals and Governance of the Corporation 13

Sometimes you hear managers speak as if the corporation has other goals. For example, they may say that their job is to “maximize profits.” That sounds reasonable. After all, don’t shareholders want their company to be profitable? But taken literally, profit maximization is not a well-defined corporate objective. Here are two reasons:

1. Maximize profits? Which year’s profits? A corporation may be able to increase current profits by cutting back on outlays for maintenance or staff training, but that will not add value unless the outlays were wasteful in the first place. Shareholders will not welcome higher short-term profits if long-term profits are damaged.

2. A company may be able to increase future profits by cutting this year’s dividend and investing the freed-up cash in the firm. That is not in the shareholders’ best interest if the company earns only a very low rate of return on the extra investment.

Maximizing—or at least maintaining—value is necessary for the long-run survival of the corporation. Suppose, for example, that its managers forget about value and decide that the only goal is to increase the market share of its products. So the manag- ers cut prices aggressively to attract new customers, even when this leads to continu- ing losses. As losses mount, the corporation finds it more and more difficult to borrow money and sooner or later cannot pay existing debts. Nor can it raise new equity financing if shareholders see that new equity investment will follow previous invest- ments down the drain.

This firm’s managers would probably pay the price for this business malpractice. For example, outside investors would see an opportunity for easy money. They could buy the firm from its current shareholders, toss out the managers, and reemphasize value rather than market share. The investors would profit from the increase in value under new management.

Managers who pursue goals that destroy value often end in early retirement—another reason that the natural financial goal of the corporation is to maximize market value.

The Investment Trade-Off Okay, let’s take the objective as maximizing market value, or at least adding market value. But why do some investments increase market value, while others reduce it? The answer is given by Figure 1.3, which sets out the fundamental trade-off for corporate investment decisions. The corporation has a pro- posed investment project (the purchase of a real asset). Suppose it has sufficient cash on hand to finance the project. The financial manager is trying to decide whether to go ahead. If he or she decides not to invest, the corporation can pay out the cash to share- holders, say as an extra dividend. (The investment and dividend arrows in Figure 1.3 are arrows 2 and 4b in Figure 1.2.)

Assume that the financial manager is acting in the interests of the corporation’s owners, its stockholders. What do these stockholders want the financial manager

Rhonda and Reggie Hotspur are working hard to save for their children’s college education. They don’t need more cash for current consumption but will face big tuition bills in 2028. Should they therefore avoid investing in stocks that pay generous current cash dividends? (Hint: Are they required to spend the divi- dends on current consumption?) Explain briefly.

Self-Test1.4

The same principles apply to the timing of a corporation’s cash flows, as the follow- ing Self-Test illustrates.

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14 Part One Introduction

to do? The answer depends on the rate of return on the investment project and on the rate of return that stockholders can earn by investing in financial markets. If the return offered by the investment project is higher than the rate of return that shareholders can get by investing on their own, then the shareholders would vote for the investment project. If the investment project offers a lower return than shareholders can achieve on their own, the shareholders would vote to cancel the project and take the cash instead.

Figure 1.3 could apply to Delta’s decision to invest in new aircraft. Suppose the company has cash set aside to buy five more Airbus A321s. It could go ahead with the purchase, or it could choose to cancel the investment and instead pay out the cash to its stockholders. If it pays out the cash, the stockholders could then invest for themselves.

Suppose that Delta’s investment in new planes is just about as risky as the stock market and that investment in the stock market offers a 10% expected rate of return. If the new planes offer a superior rate of return, say 20%, then Delta’s stockholders would be happy to let the company keep the cash and invest it in the new planes. If the planes offer only a 5% return, then the stockholders are better off with the cash and without the new project; in that case, the financial manager should turn down the project.

As long as a corporation’s proposed investments offer higher rates of return than its shareholders can earn for themselves in the stock market (or in other financial mar- kets), its shareholders will applaud the investments and the market value of the firm will increase. But if the company earns an inferior return, shareholders boo, market value falls, and stockholders clamor to get their money back so that they can invest on their own.

In our example, the minimum acceptable rate of return on Delta’s new aircraft is 10%. This minimum rate of return is called the hurdle rate or opportunity cost of capital. It is called an opportunity cost of capital because it depends on the alternative investment opportunities available to shareholders in financial markets. Whenever a corporation invests cash in a new project, its shareholders lose the opportunity to invest the cash on their own. Corporations increase value by accepting investment projects that earn more than the opportunity cost of capital.

Figure 1.3, which compares rates of return on investment projects with the opportu- nity cost of capital, illustrates a general principle: A corporation should direct cash to investments that add market value, compared with the investments that shareholders could make on their own.7

opportunity cost of capital The minimum acceptable rate of return on capital investment set by the investment opportunities available to shareholders in financial markets.

FIGURE 1.3 The firm can either keep and reinvest cash or return it to investors. (Arrows represent possible cash flows or transfers.) If cash is reinvested, the opportunity cost is the expected rate of return that shareholders could have obtained by investing in financial assets.

Investment opportunity (real asset)

Invest Alternative: pay out cash

to shareholders

Shareholders invest for

themselves

Firm Shareholders Investment

opportunities (financial assets)

Cash

7 We have mentioned 5% or 20% as possible future rates of return on Delta’s new planes. We will see in Chapter 8 that future rates of return are sometimes difficult to calculate and interpret. The general principle always holds, however. In Chapters 8 and 9 we show you how to apply the principle by calculating the net present value (NPV) of investment projects.

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Chapter 1 Goals and Governance of the Corporation 15

Agency Problems, Executive Compensation, and Corporate Governance

Sole proprietors face no conflicts in financial management. They are both owners and managers, reaping the rewards of good decisions and hard work and suffering when they make bad decisions or slack off. Their personal wealth is tied to the value of their businesses.

In most large corporations, however, the owners are mostly outside investors, and so the managers may be tempted to act in their own interests rather than maximize shareholder value. For example, they may shy away from valuable but risky invest- ment projects because they worry more about job security than maximizing value. They may build empires by overaggressive investment or overconfident acquisitions of other companies.

The temptation for such value-destroying actions arises because the managers are not the shareholders, but agents of the shareholders. Therefore, the actions are called agency problems. Losses in value from agency problems—or from costs incurred to mitigate the problems—are called agency costs.

Agency problems sometimes lead to outrageous behavior. When Dennis Kozlowski, the former CEO of Tyco, threw a $2 million birthday bash for his wife, he charged half the cost to the company. Conrad Black, the former boss of Hollinger International, used the company jet for a trip with his wife to Bora Bora. These, of course, are extreme examples. The agency problems encountered in the ordinary course of busi- ness are often subtle and mundane. But agency problems do arise whenever managers think just a little less hard about spending money that is not their own.

1.5

Investing $100,000 in additional raw materials, mostly palladium, should allow Cryogenic Concepts to increase production and earn an additional $112,000 next year. This payoff could cover the investment, plus a 12% return. Palladium is traded in commodity markets. The CFO has studied the history of returns from investments in palladium and believes that investors in the precious metal can reasonably expect a 15% return. What is the opportunity cost of capital? Is Cryo- genic’s proposed investment in palladium a good idea? Why or why not?

Self-Test1.5

Notice that the opportunity cost of capital depends on the risk of the proposed investment project. Why? It’s not just because shareholders are risk-averse. It’s also because shareholders have to trade off risk against return when they invest on their own. The safest investments, such as U.S. government debt, offer low rates of return. Investments with higher expected rates of return—the stock market, for example—are riskier and sometimes deliver painful losses. (The U.S. stock market fell 38% in 2008, for example.) Other investments are riskier still. For example, high-tech growth stocks offer the prospect of higher rates of return than typical stocks but are also more volatile than typical stocks.

Managers look to the financial markets to measure the opportunity cost of capital for the firm’s investment projects. They can observe the opportunity cost of capital for safe investments by looking up current interest rates on safe debt securities. For risky investments, the opportunity cost of capital has to be estimated. We start to tackle this task in Chapter 11.

agency problem Managers are agents for stockholders and are tempted to act in their own interests rather than maximizing value.

agency cost Value lost from agency problems or from the cost of mitigating agency problems.

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16 Part One Introduction

Agency problems are controlled in practice in three ways. First, corporations set up internal controls and decision-making procedures to prevent wasteful spending and discourage careless investment. We discuss the controls and procedures in several later chapters. For example, Chapters 8, 9, and 10 cover procedures for disciplined, value- maximizing capital investment decisions. Second, corporations try to design compen- sation schemes that align managers’ and shareholders’ interests. Third, the corporations are constrained by systems of corporate governance. We comment on compensation and governance here.

Executive Compensation The compensation packages of top executives are almost always tied to the financial performance of their companies. The package typically includes a fixed base salary plus an annual award tied to earnings or other measures of financial performance. The more senior the manager, the smaller the base salary as a fraction of total com- pensation. Also, compensation is not all in cash, but partly in shares.8 Many corpo- rations also include stock options in compensation packages. Stock options, which we cover in Chapter 23, give especially powerful incentives to maximize stock price per share.

The upside compensation potential for a few top managers is enormous. For exam- ple, Larry Ellison, CEO of the business software giant Oracle, received total compen- sation of $21 million for 2017. Only $1 of that amount was base salary. The rest came from grants of stock and options. The options will be worthless if Oracle’s stock price falls from its 2017 level but will pay off handsomely if the price rises. In addition, as a founder of Oracle, Ellison owns shares worth $60 billion. No one can say for certain how hard Ellison would have worked with a different compensation package, but one thing is clear: He has a huge personal stake in Oracle’s market value.

Well-designed compensation schemes alleviate agency problems by encouraging managers to maximize shareholder wealth. But some schemes are not well designed; they reward managers even when value is destroyed. For example, during Robert Nardelli’s 6-year tenure as CEO, The Home Depot’s stock price fell by 20% while shares of its rival Lowe’s nearly doubled. When Nardelli was ousted in January 2007, he received a farewell package worth $210 million. Needless to say, many sharehold- ers were livid.

In 2010, the Dodd-Frank financial reform law gave U.S. shareholders the right to express their opinion on executive compensation through nonbinding “say on pay” votes at 1- or 3-year intervals. (Shareholders of U.K. companies have a similar right.)

What are agency problems and agency costs? Give two or three examples of decisions by managers that can lead to agency costs.

Self-Test1.6

Think of the corporation’s value as a pie that is divided among several classes of claimants. These include managers and workers as well as shareholders and lenders. The government is a claimant, too, because it taxes sales and profits. The claimants are called stakeholders because each has a stake in the firm. Agency problems arise whenever the stakeholders’ interests do not coincide.

stakeholder Anyone with a financial interest in the corporation.

8 The manager may get to keep these shares only if he or she stays with the corporation or meets certain perfor- mance targets.

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Chapter 1 Goals and Governance of the Corporation 17

Most votes have endorsed compensation policy, but occasionally shareholders refuse. For example, when the shareholders of auto supplier BorgWarner voted “no” in 2015, the company cut the CEO’s incentive award by $2.4 million. Other CEOs looked anx- iously over their shoulders to check that their compensation package would not be next in the spotlight.

Corporate Governance Financial markets and institutions are supposed to direct financing to firms that can invest to add value. But financing moves from investors to firms only if investors are protected and if agency problems within firms are absent or at least tolerable. Thus there is a need for a system of corporate governance so that money can flow to the right firms at the right times. “Corporate governance” refers to the laws, regulations, institutions, and corporate practices that protect shareholders and other investors. When scandals happen, we say that corporate governance has broken down. When corporations compete to deliver value to shareholders, we are comforted that corporate governance is working properly.

Good corporate governance relies in part on well-designed management compensa- tion packages. Other elements of good corporate governance include the following.

Legal Requirements Good governance requires laws and regulations that protect investors from self-dealing by insiders. CEOs and financial managers have a fiduciary duty to stockholders. That is, they are required to act fairly and responsibly in the stockholders’ interests. If they don’t, they may end up in jail like Tyco’s Dennis Kozlowski and Hollinger’s Conrad Black.

Boards of Directors The board of directors appoints top managers, including the CEO and CFO, and must approve important financial decisions. For example, only the board has legal authority to approve a dividend or a public issue of securities. The board approves compensation schemes and awards to top management. Boards usually delegate decision making for small and medium-size investments, but the authority to approve large investments is almost never delegated.

The board of directors is elected by shareholders and is supposed to represent their interests. Boards have been portrayed as passive supporters of top management, but the balance has tipped toward independence. The Sarbanes-Oxley Act of 2002 (SOX) requires that more directors be independent—that is, not affiliated with management. The majority of directors are now independent. Boards must meet in executive sessions with the CEO not present. SOX also requires CEOs and CFOs to sign off personally on the corporation’s accounting procedures and results.

Activist Shareholders Institutional shareholders, including pension funds, have become more active in monitoring management and pushing for changes. CEOs have been forced out as a result, including the CEOs of GE, Ford, CSX, AIG, and Wells Fargo. Boards outside the United States, which have traditionally been more management-friendly, also have become more willing to replace underper- formers. The list of foreign companies with CEO departures includes Cathay Pacific, Thyssenkrup, LafargeHolcim, Toshiba, Marks and Spencer, and Deutsche Bank.

Although U.S. corporations typically have thousands of individual shareholders, they often also have blockholders, that is, investors who own 5%, 10%, or more of outstanding shares. The blockholders may include wealthy individuals or families— for example, descendants of a founder. They may also include other corporations, pen- sion funds, or foundations.9 When a 5% blockholder calls, the CFO answers.

corporate governance The laws, regulations, institutions, and corporate practices that protect shareholders and other investors.

9 A large block of shares may give effective control even when there is no majority owner. For example, Larry Ellison’s billion-plus shares give him a 25% stake in Oracle. Barring some extreme catastrophe, this holding means that he can run the company as long as he wants to.

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18 Part One Introduction

Disgruntled shareholders can also take the “Wall Street Walk” by selling out and moving on to other investments. The Wall Street Walk can send a powerful message. If enough shareholders bail out, the stock price tumbles, which damages top managers’ compensation and reputation.

Takeovers The Wall Street Walk opens the door for takeovers. The further the stock price falls, the easier it is for another company to buy up the majority of shares and take over. The old management team is then likely to find itself out on the street. We discuss takeovers in Chapter 21.

Information for Investors Corporate governance can’t work unless outside inves- tors get detailed, up-to-date information. If a firm is transparent—if investors can see its true profitability and prospects—then problems will show up right away in a falling stock price. That in turn generates extra scrutiny from security analysts, bond rating agencies, and banks and other lenders, who keep an eagle eye on the progress of their borrowers.

The U.S. Securities and Exchange Commission (SEC) sets accounting and report- ing standards for public companies. We cover accounting and finance in Chapter 3.

The Ethics of Maximizing Value

Shareholders want managers to maximize the market value of their shares. But perhaps this begs the question: Is it desirable for managers to act in the narrow, selfish interest of their shareholders? Does a focus on shareholder value mean that the managers must act as greedy mercenaries riding roughshod over widows and orphans?

Most of this book is devoted to financial policies that increase value. None of these policies requires galloping over widows and orphans. In most instances, there is little conflict between doing well (maximizing value) and doing good. The first step in doing well is doing good by your customers. Here is how Adam Smith put the case in 1776:

It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our din- ner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love, and never talk to them of our own necessities but of their advantages.10

Profitable firms are those with satisfied customers and loyal employees; firms with dissatisfied customers and a disgruntled workforce will probably end up with declin- ing profits and a low stock price.11

Of course, ethical issues do arise in business as in other walks of life. When the stakes are high, it is often tempting for managers to cut corners. Laws and regulations seek to prevent managers from undertaking dishonest actions. But written rules and laws can help only so much. In business, as in other day-to-day affairs, there are also unwritten rules of behavior. They are reinforced because good managers know that their firm’s reputation is one of its most important assets, and therefore playing fair

1.6

BEYOND THE PAGE

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Things are not always fair in love or business

10 Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations (New York: Random House, 1937; first published 1776), p. 14. 11 Shareholders value integrity. Firms that are regarded as trustworthy by their employees and that are voted as good places to work tend to be more highly valued by investors and to perform better. See A. Edmans, “Does the Stock Market Fully Value Intangibles? Employee Satisfaction and Equity Prices,” Journal of Financial Economics 101, no. 3 (September 2011), pp. 621–640; and L. Guiso, P. Sapienza, and L. Zingales, “The Value of Corporate Culture,” Journal of Financial Economics 117, no. 1 (July 2015), pp. 60–76.

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B Corporations

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Chapter 1 Goals and Governance of the Corporation 19

and keeping one’s word are simply good business practices. Thus financial deals are regularly sealed by a handshake, and each side knows that the other will not renege later if things turn sour.

When something happens to undermine reputations, the costs can be enormous. Volkswagen (VW) is a recent case in point. VW had installed secret software that cut back pollution from its diesel cars, but only when the cars were tested. Actual pollu- tion in regular driving was much higher—and far in excess of legal maximums. Dis- covery of the software scandal in 2015 caused a tidal wave of opprobrium. VW’s stock price dropped by 35%. Its CEO was fired. VW diesel vehicles piled up unsold on car dealers’ lots. In the United States alone, the scandal is likely to cost the company over $20 billion in fines and compensation payments.

Reputation is particularly important in finance. If you buy a well-known brand in a supermarket, you can be fairly sure of what you are getting. But in financial transac- tions, the other party often has more information than you, and it is less easy to be sure of the quality of what you are buying. Therefore, honest financial firms seek to build long-term relationships with their customers and to establish a name for fair dealing and financial integrity.

Of course, there are always charlatans and swindlers who prey on individual inves- tors, especially in booming markets. (It’s only “when the tide goes out that you learn who’s been swimming naked.”12) The tide went out in 2008 and a number of frauds were exposed. One notorious example was the Ponzi scheme run by the disgraced financier Bernard Madoff (pronounced “Made-off”).13 Individuals and institutions invested around $20 billion with Madoff and were told that their investments had grown to $65 billion. That figure turned out to be completely fictitious. (It’s not clear what Madoff did with all this money, but much of it was apparently paid out to early investors in the scheme to create an impression of superior investment performance.) With hindsight, the investors should not have trusted Madoff or the financial advisers who steered money to him.

Madoff’s Ponzi scheme was (we hope) a once-in-a-lifetime event. (Ponzi schemes pop up frequently, but few have approached the scope and duration of Madoff’s.) It was astonishingly unethical and illegal and was bound to end in tears. Needless to say, it was not designed to add value for investors.

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Business culture and unethical behavior

BEYOND THE PAGE

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The Great Albanian Ponzi Scheme

12 The quotation is from Warren Buffett’s annual letter to the shareholders of Berkshire Hathaway, March 2008. 13 Ponzi schemes are named after Charles Ponzi, who founded an investment company in 1920 that promised investors unbelievably high returns. He was soon deluged with funds from investors in New England, taking in $1 million during one 3-hour period. Ponzi invested only about $30 of the money that he raised. But he used part of the cash provided by later investors to pay generous dividends to the original investors, thus promoting the illusion of high profits and quick payoffs. Within months the scheme collapsed and Ponzi started a 5-year prison sentence.

Without knowing anything about the personal ethics of the owners, which com- pany would you trust more to keep its word in a business deal?

a. Harry’s Hardware has been in business for 50 years. Harry’s grandchildren, now almost adults, plan to take over and operate the business. Successful hardware stores depend on long-term loyal customers.

b. Pete’s Pizza just opened for business. It rents a storefront in a strip mall and has financed its inventory with a bank loan. Pete has little of his own money invested in the business. Pizza shops usually command little customer loyalty.

Self-Test1.7

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20

It is not always easy to know what is ethical behavior, and there can be many gray areas. The nearby box presents three ethical controversies in finance. Think about where you stand on these issues and where you would draw the ethical line.

BEYOND THE PAGE

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Goldman Sachs causes a ruckus

But sometimes raids can enhance shareholder value. For example, in 2012 and 2013, Relational Investors teamed up with the California State Teachers’ Retirement System (CSTRS, a pension fund) to try to force Timken Co. to split into two separate companies, one for its steel business and one for its industrial bearings business. Relational and CSTRS believed that Timken’s combination of unrelated businesses was unfo- cused and inefficient. Timken management responded that breakup would “deprive our shareholders of long-run value— all in an attempt to create illusory short-term gains through financial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding shareholder vote on Relational’s proposal attracted a 53% majority. Finally, in 2014 Timken spun off its steel business in a new corporation, Timken Steel.

How do you draw the ethical line in such examples? Was Relational Investors a “raider” (sounds bad) or an “activist investor” (sounds good)? Breaking up a portfolio of busi- nesses can create difficult adjustments and job losses. Some stakeholders lose. But shareholders and the overall economy can gain if businesses are managed more efficiently.

Tax Avoidance In 2012 it was revealed that during the 14 years that Starbucks had operated in the United Kingdom, it paid hardly any taxes. Public outrage led to a boycott of Starbucks shops, and the company responded by promising that it would voluntarily pay to the taxman about $16 million more than it was required to pay by law. Several months later, a U.S. Senate committee investigating tax avoidance by U.S. technology firms reported that Apple had used a “highly questionable” web of offshore entities to avoid billions of dollars of U.S. taxes.

Multinational companies, such as Starbucks and Apple, could reduce their tax bills using legal techniques with exotic names such as the “Dutch Sandwich,” “Double Irish,” and “Check-the-Box.” But the public outcry over the revelations suggested that many believed that use of these techniques, though legal, was unethical. If they were unethical, that leaves an awkward question: How do companies decide which tax schemes are ethical and which are not? Can a company act in shareholders’ interest if it voluntarily pays more taxes than it is legally obligated to pay?

* We need not go into the mechanics of short sales here, but note that the seller is obligated to buy back the security, even if its price skyrockets far above what he or she sold it for. As the saying goes, “He who sells what isn’t his’n, buys it back or goes to prison.”

† The story of Paulson’s trade is told in G. Zuckerman, The Greatest Trade Ever (New York: Broadway Business, 2009). The trade was controversial for reasons beyond short-selling. Scan the nearby Beyond the Page icon “Goldman Sachs causes a ruckus” to learn more.

Short-Selling Investors who take short positions are betting that securities will fall in price. Usually they do this by borrowing the security, selling it for cash, and then waiting in the hope that they will be able to buy it back cheaply.* In 2007, hedge fund manager John Paulson took a huge short position in mortgage-backed securities. The bet paid off, and that year Paulson’s trade made a profit of $1 billion for his fund.†

Was Paulson’s trade unethical? Some believe not only that he was profiting from the misery that resulted from the crash in mortgage-backed securities, but that his short trades accentuated the collapse. It is certainly true that short-sellers have never been popular. For example, following the crash of 1929, one commentator compared short-selling to the ghoul- ishness of “creatures who, at all great earthquakes and fires, spring up to rob broken homes and injured and dead humans.”

Short-selling in the stock market is the Wall Street Walk on steroids. Not only do short-sellers sell all the shares they may have previously owned, but they borrow more shares and sell them too, hoping to buy them back for less when the stock price falls. Poorly performing companies are natural targets for short-sellers, and the companies’ incumbent managers naturally complain, often bitterly. Governments sometimes lis- ten to such complaints. For example, in 2008 the U.S. govern- ment temporarily banned short sales of financial stocks in an attempt to halt their decline.

But defendants of short-selling argue that selling securi- ties that one believes are overpriced is no less legitimate than buying those that appear underpriced. The object of a well- functioning market is to set the correct stock prices, not always higher prices. Why impede short-selling if it conveys truly bad news, puts pressure on poor performers, and helps corporate governance work?

Corporate Raiders In the movie Pretty Woman, Richard Gere plays the role of an asset stripper, Edward Lewis. He buys companies, takes them apart, and sells the bits for more than he paid for the total package. In the movie Wall Street, Gordon Gekko buys a failing airline, Blue Star, in order to break it up and sell the bits. Real corporate raiders may not be as ruthless as Edward Lewis or Gordon Gekko, but they do target companies whose assets can be profitably split up and redeployed.

This has led some to complain that raiders seek to carve up established companies, often leaving them with heavy debt burdens, basically in order to get rich quick. One German politician has likened them to “swarms of locusts that fall on companies, devour all they can, and then move on.”

Finance in Practice Ethical Disputes in Finance

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Chapter 1 Goals and Governance of the Corporation 21

Careers in Finance

Well over 1 million people work in the financial services industry in the United States, and many others work as financial managers in corporations. We can’t tell you what each one does all day, but we can give you some idea of the variety of careers in finance. The nearby box summarizes the experience of a small sample of recent graduates.14

We explained earlier that corporations face two principal financial decisions: the investment decision and the financing decision. Therefore, as a newly recruited finan- cial analyst, you may help to analyze a major new investment project. Or you may instead help to raise the money to pay for it, perhaps by negotiating a bank loan or by arranging to lease the plant and equipment. Other financial analysts work on short- term finance, managing collection and investment of the company’s cash or checking whether customers are likely to pay their bills. Financial analysts are also involved in monitoring and controlling risk. For example, they may help to arrange insurance for the firm’s plant and equipment, or they may assist with the purchase and sale of options, futures, and other exotic tools for managing risk.

Instead of working in the finance department of a corporation, you may join a financial institution. The largest employers are banks. Banks collect deposits and relend the cash to corporations and individuals. If you join a bank, you may start in a branch office, where individuals and small businesses come to deposit cash or to seek a loan. You could also work in the head office, helping to analyze a $500 million loan to a large corporation.

Banks do many things in addition to lending money, and they probably provide a greater variety of jobs than other financial institutions. For example, if you work in the cash man- agement department of a large bank, you may help companies to transfer huge sums of money electronically as wages, taxes, and payments to suppliers. Banks also buy and sell foreign exchange, so you could find yourself working in front of one of those computer screens in a foreign exchange trading room. Another glamorous bank job is in the deriva- tives group, which helps companies to manage their risk by buying and selling options, futures, and so on. This is where the mathematicians and the computer buffs thrive.

Investment banks, such as Goldman Sachs or Morgan Stanley, help companies sell their securities to investors. They also have large corporate finance departments that assist firms in mergers and acquisitions. When firms issue securities or try to take over another firm, a lot of money is at stake and the firms may need to move fast. Thus, working for an investment bank can be a high-pressure activity with long hours. It can also pay very well.

The insurance industry is another large employer. Much of the insurance industry is involved in designing and selling insurance policies on people’s lives and property, but businesses are also major customers. So, if you work for an insurance company or a large insurance broker, you could find yourself arranging insurance on a Boeing 787 in the United States or an oil rig in Indonesia.

Life insurance companies are major lenders to corporations and to investors in com- mercial real estate. (Life insurance companies deploy the insurance premiums received from policyholders into medium- or long-term loans; banks specialize in shorter-term financing.) So you could end up negotiating a $50 million loan for construction of a new shopping center or investigating the creditworthiness of a family-owned manufac- turing company that has applied for a loan to expand production.

Then there is the business of “managing money,” that is, deciding which compa- nies’ shares to invest in or how to balance investment in shares with safer securities, such as the bonds (debt securities) issued by the U.S. Treasury. Take mutual funds, for example. A mutual fund collects money from individuals and invests in a portfolio of stocks or bonds. A financial analyst in a mutual fund analyzes the prospects for the securities and works with the investment manager to decide which should be bought

1.7

14 The careers are fictitious but based on the actual experiences of several of the authors’ students.

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22

and sold. Many other financial institutions also contain investment management departments. For example, you might work as a financial analyst in the investment department of an insurance company. (Insurance companies also invest in traded secu- rities.) Or you could be a financial analyst in the trust department of a bank that man- ages money for retirement funds, universities, and charities.

Stockbroking firms help investment management companies and private individu- als to invest in securities. They employ sales staff and dealers who make the trades. They also employ financial analysts to analyze the securities and help customers to decide which to buy or sell.

Investment banks and stockbroking firms are largely headquartered in New York, as are many of the large commercial banks. Insurance companies and investment manage- ment companies tend to be more scattered. For example, some of the largest insurance companies are headquartered in Hartford, Connecticut, and many investment manage- ment companies are located in Boston. Of course, some U.S. financial institutions have large businesses outside the United States. Finance is a global business. So you may spend some time working in a branch overseas or making the occasional trip to one of the other major financial centers, such as London, Tokyo, Hong Kong, or Singapore.

Preview of Coming Attractions

This book covers investment decisions, then financing decisions, and finally a variety of planning issues that require an understanding of both investment and financing. But first there are three further introductory chapters that should be helpful to readers who are making a first acquaintance with financial management. Chapter 2 is an overview

1.8

Albert Rodriguez, European Markets Group, Major New York Bank I joined the bank after majoring in finance. I spent the first 6 months in the bank’s training program, rotating among departments. I was assigned to the European markets team just before the 2010 Greek crisis, when worries about a pos- sible default caused interest rates on Greek government debt to jump to more than 4% above the rate on comparable German government debt. Those rates soon went much higher! There was a lot of activity, with everyone trying to fig- ure out whether Greece might be forced to abandon the euro and how this would affect our business. My job is largely con- cerned with analyzing economies and assessing the pros- pects for bank business. There are plenty of opportunities to work abroad, and I hope to spend some time in Madrid or one of our other European offices.

Sherry Solera, Branch Manager, Regional Bank I took basic finance courses in college, but nothing spe- cific for banking. I started here as a teller. I was able to learn about banking through the bank’s training program and also by evening courses at a local college. Last year I was promoted to branch manager. I oversee the branch’s operations and help customers with a wide variety of prob- lems. I’m also spending more time on credit analysis of business loan applications. I want to expand the branch’s business customers, but not by making loans to shaky companies.

Susan Webb, Research Analyst, Mutual Fund Group After majoring in biochemistry, I joined the research department of a large mutual fund group. Because of my background, I was assigned to work with the senior pharmaceuticals analyst. I start the day by reading The Wall Street Journal and reviewing the analyses that come in each day from stockbroking firms. Some- times we need to revise our earnings forecasts and meet with the portfolio managers to discuss possible trades. The remain- der of my day is spent mainly in analyzing companies and developing forecasts of revenues and earnings. I meet fre- quently with pharmaceutical analysts in stockbroking firms, and we regularly visit company management. In the evenings I study for the Chartered Financial Analyst (CFA) exam. I did not study finance at college, so this is quite challenging. I hope eventually to move from a research role to become a portfolio manager.

Richard Gradley, Project Finance, Large Energy Company After leaving college, I joined the finance department of a large energy company. I spent my first year helping to analyze capital investment proposals. I then moved to the project finance group, which is responsible for analyzing indepen- dent power projects around the world. Recently, I have been involved in a proposal to set up a company that would build and operate a large new electricity plant in southeast Asia. We built a spreadsheet model of the project to make sure that it was viable. We had to check that the contracts with the builders, operators, suppliers, and so on, were all in place before we could arrange bank financing for the project.

Finance in Practice Working in Finance

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Chapter 1 Goals and Governance of the Corporation 23

of financial markets and institutions. Chapter 3 reviews the basic concepts of account- ing, and Chapter 4 demonstrates the techniques of financial statement analysis.

We have said that the financial manager’s task is to make investment and financing decisions that add value for the firm’s shareholders. But that statement opens up a treasure chest of follow-up questions that will occupy us from Chapter 4 onward:

∙ How do I calculate the value of a stream of future cash flows? A dollar that you receive today is worth more than the promise of a dollar in 10 or 20 years’ time. So, when measuring the effect of a new project on firm value, the financial manager needs to recognize the timing of the cash flows. In Chapters 5 through 10, we show how to calculate the present value of an investment that produces a stream of future cash flows. We begin by calculating the present value of bonds and stocks and then look at how to value the cash flows resulting from capital investment projects. Present value is a workhorse concept of corporate finance that shows up in almost every chapter.

∙ How do I measure risk? In Chapters 5 through 10, we largely ignore the issue of risk. But risky cash flows are less valuable than safe ones. In Chapters 11, 12, and 13, we look at how to measure risk and how it affects present values.

∙ Where does financing come from? Broadly speaking, it comes from borrowing or from cash invested or reinvested by stockholders. But financing can get complicated when you get down to specifics. Chapter 14 gives an overview of the sources of finance. Chapters 15, 16, and 17 then look at how companies sell their securities to investors, the choice between debt and equity, and the decision to pay out cash to stockholders.

∙ How do I ensure that the firm’s financial decisions add up to a sensible whole? There are two parts to this question. The first is concerned with making sure that the firm can finance its future growth strategy. This is the role of long-term planning. The second is concerned with ensuring that the firm has a sensible plan for managing and financing its short-term assets such as cash, inventories, and money due from customers. We cover long- and short-term planning in Chapters 18, 19, and 20.

∙ What about some of those other responsibilities of the financial manager that you mentioned earlier? Not all of the financial manager’s responsibilities can be classified simply as an investment decision or a financing decision. In Chapters 21 through 24, we review four such topics. First we look at mergers and acquisitions. Then we consider international financial management. All the financial problems of doing business at home are present overseas, but the international financial manager faces the additional complications created by multiple currencies, different tax systems, and special regulations imposed by foreign institutions and governments. Finally, we look at risk management and the specialized securities, including futures and options, which managers can use to hedge or lay off risks.

That’s enough material to start, but as you reflect on this chapter, you can see cer- tain themes emerging that you will encounter again and again throughout this book:

1. Corporate finance is about adding value. 2. The opportunity cost of capital sets the standard for investments. 3. A safe dollar is worth more than a risky one. 4. Smart investment decisions create more value than smart financing decisions. 5. Good governance matters.

Snippets of Financial History

Now let’s lighten up a little. In this book we are going to describe how financial deci- sions are made today. But financial markets also have an interesting history. Look at the nearby box, which lays out bits of this history, starting in prehistoric times, when the growth of bacteria anticipated the mathematics of compound interest, and continu- ing nearly to the present. We have keyed each of these episodes to the chapter of the book that discusses its topic.

1.9

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enterprising individual announced a company “for carry- ing on an undertaking of great advantage but nobody to know what it is.” Within 5 hours he had raised £2,000; within 6 hours he was on his way out of the country. Read- ers nearly two centuries later could only wonder at the naïve or foolhardy investors in these ventures—that is, until they had a chance to participate in the follies unearthed by the financial crisis of 2008–2009. (Chapter 2)

1792 Formation of the New York Stock Exchange The New York Stock Exchange (NYSE) was founded in 1792 when a group of brokers met under a buttonwood tree* and arranged to trade shares with one another at agreed rates of commission. Today the NYSE is the largest stock exchange in the world, trading on average over a billion shares a day. (Chapter 7)

1929 Stock Market Crashes Common stocks are risky investments. In September 1929 stock prices in the United States reached an all-time high, and the economist Irving Fisher forecast that they were at “a permanently high plateau.” Some 3 years later, stock prices were almost 90% lower, and it was to be a quarter of a century before the prices of September 1929 were seen again. Eighty years later, history came close to repeating itself. After stock prices peaked in July 2007, they slumped over the next 20 months by 54%. (Chapter 11)

1960s Eurodollar Market In the 1950s the Soviet Union transferred its dollar holdings from the United States to a Russian-owned bank in Paris. This bank was best known by its telex address, eurobank, and consequently dollars held outside the United States came to be known as eurodollars. In the 1960s, U.S. taxes and regulation made it much cheaper to borrow and lend dollars in Europe than in the United States, and a huge market in eurodol- lars arose. (Chapter 14)

1971 Corporate Bankruptcies Every generation of investors is shocked and surprised by a major corporate bank- ruptcy. In 1971 the Penn Central Railroad, a pillar of American industry, suddenly collapsed. At that time, it was the largest corporate bankruptcy in history. In 2008, the investment bank Lehman Brothers smashed Penn Central’s record. (Chapter 16)

1972 Financial Futures Financial futures allow companies to protect themselves against fluctuations in interest rates, exchange rates, and so on. It is said that they originated from a remark by the economist Milton Friedman that he was unable to profit from his view that sterling (the U.K. currency) was overpriced. The Chicago Mercantile Exchange founded the first financial futures market. Today futures exchanges trade 6 billion contracts a year of finan- cial futures. (Chapter 24)

1986 Capital Investment Decisions When it was com- pleted in 1994 at a cost of $15 billion, the tunnel under the English Channel was the largest investment project undertaken by a single private investment company. (Chapters 8, 9)

1988 Mergers The 1980s saw a wave of takeovers culminat- ing in the $25 billion takeover of RJR Nabisco. Over a period of 6 weeks, three groups battled for control of the

Date unknown Compound Growth Bacteria start to propa- gate by subdividing. They thereby demonstrate the power of compound growth. (Chapter 5)

c. 1800 b.c. Interest Rates In Babylonia, Hammurabi’s Code established maximum interest rates on loans. Borrowers often mortgaged their property and sometimes their spouses, but lenders were obliged to return spouses in good condition within 3 years. (Chapter 6)

c. 1000 b.c. Options One of the earliest recorded options is described by Aristotle. The philosopher Thales knew by the stars that there would be a great olive harvest, so, having a little money, he bought options for the use of olive presses. When the harvest came, Thales was able to rent the presses at great profit. Today financial managers need to be able to evaluate options to buy or sell a wide variety of assets. (Chapter 23)

15th century International Banking Modern international banking had its origins in the great Florentine banking houses. But the entire European network of the Medici empire employed only 57 people in eight offices. Today the London-based bank HSBC has around 260,000 employees in 71 different countries. (Chapter 14)

1650 Futures Futures markets allow companies to protect themselves against fluctuations in commodity prices. Dur- ing the Tokugawa era in Japan, feudal lords collected rents in the form of rice, but often they wished to trade their future rice deliveries. Rice futures therefore came to be traded on what was later known as the Dojima Rice Market. Rice futures are still traded, but now companies also can trade in futures on a range of items from pork bellies to stock market indexes. (Chapter 24)

17th century Joint Stock Corporations Although investors have for a long time combined together as joint owners of an enterprise, the modern corporation with a large number of stockholders originated with the formation in England of trading firms like the East India Company (est. 1599). (Chapter 15)

17th century Money America has been in the forefront in the development of new types of money. Early settlers often used a shell known as wampum. For example, Peter Stuyvesant raised a loan in wampum, and in Massachusetts it was legal tender. Unfortunately, the enterprising settlers found that with a little dye the rela- tively common white wampum shells could be con- verted profitably into the more valuable black ones, which confirmed Gresham’s law that bad money drives out good. Paper money was used in China during the 7th century, but the first issue of paper money in America was by the Massachusetts Bay Colony in 1690, and other colonies soon set their printing presses to producing money. In 1862 Congress agreed to an issue of paper money that would be legal tender. These notes, printed in green ink, immediately became known as “greenbacks.” (Chapters 19, 20)

1720 New-Issue Speculation From time to time investors have been tempted by speculative new issues. During the South Sea Bubble in England, one company was launched to develop perpetual motion. Another

Finance in Practice Finance through the Ages

24

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In 1865 France, Belgium, Switzerland, and Italy came together in the Latin Monetary Union, and they were joined by Greece and Romania the following year. Mem- bers of the European Monetary Union (EMU) hope that the euro will be a longer-lasting success than this earlier experiment. As we write this in 2018, the euro appears to have weathered the worst of the crisis caused by the Greek government’s debt default. (Chapter 23)

2002 Financial Scandals A seemingly endless series of financial and accounting scandals climaxed in this year. Resulting bankruptcies included the icons Enron (and its accounting firm, Arthur Andersen), WorldCom, and the Italian food company Parmalat. Congress passed the Sarbanes-Oxley Act to increase the accountability of corporations and executives. (Chapters 1, 14)

2007–2009 Subprime Mortgages Subprime mortgages are housing loans made to homeowners with shaky credit standing. After a decade in which housing prices had con- sistently gone up, lenders became complacent about the risks of these home loans and progressively loosened lending standards. When housing prices stalled and inter- est rates increased in 2007, many of these loans went bad. Some large banks such as Lehman Brothers went to the wall, while others such as Wachovia and Merrill Lynch were rescued with the aid of government money. (Chapters 2, 14)

2011 Defaults on Sovereign Debt By 2010 the Greek gov- ernment had amassed a huge $460 billion of debt. Other eurozone governments and the International Monetary Fund (IMF) rushed to Greece’s aid, but their assistance was insufficient, and in 2011 the Greek government defaulted on $100 billion of debt. It was the largest-ever sovereign default. Investors nervously eyed other highly indebted eurozone countries. (Chapter 2)

2016 Brexit The United Kingdom voted to withdraw from the European Union (the EU), thereby reversing a decades- long trend of increased integration among European econ- omies. Terms of the departure were still being negotiated in 2018.

company. As one of the contestants put it, “We were charging through the rice paddies, not stopping for any- thing and taking no prisoners.” The takeover was the larg- est in history and generated almost $1 billion in fees for the banks and advisers. (Chapter 21)

1993 Inflation Financial managers need to recognize the effect of inflation on interest rates and on the profitability of the firm’s investments. In the United States inflation has been relatively modest, but some countries have suffered from hyperinflation. In Hungary after World War II, the gov- ernment issued banknotes worth 1,000 trillion pengoes. In Yugoslavia in October 1993, prices rose by nearly 2,000% and a dollar bought 105 million dinars. In the latter part of 2018, the inflation rate in Venezuela was running at more than 1 million percent per year. (Chapter 5)

1780 and 1997 Inflation-Indexed Debt In 1780, Massachusetts paid Revolutionary War soldiers with interest-bearing notes rather than its rapidly eroding currency. Interest and princi- pal payments on the notes were tied to the subsequent rate of inflation. After a 217-year hiatus, the U.S. Treasury issued inflation-indexed notes called TIPS (Treasury Infla- tion Protected Securities). Many other countries, including Britain and Israel, had done so previously. (Chapter 6)

1993 Controlling Risk When a company fails to keep close tabs on the risks being taken by its employees, it can get into serious trouble. This was the fate of Barings, a 220-year-old British bank that numbered the queen among its clients. In 1993 it discovered that Nick Leeson, a trader in its Singapore office, had hidden losses of $1.3 billion (£869 million) from unauthorized bets on the Japanese equity market. The losses wiped out Barings and landed Leeson in jail, with a 6-year sentence. In 2008 a rogue trader at Morgan Stanley established a new record by los- ing $9 billion on unauthorized deals. (Chapter 24)

1999 The Euro Large corporations do business in many cur- rencies. In 1999 a new currency came into existence when 11 European countries adopted the euro in place of their separate currencies. They have since been joined by eight other countries. This is not the first time that differ- ent countries have agreed on a common currency.

SUMMARY Financial management can be broken down into (1) the investment or capital budgeting decision and (2) the financing decision. The firm has to decide (1) which real assets to invest in and (2) how to raise the funds necessary to pay for those investments.

Real assets include all assets used in the production or sale of the firms’ products or ser- vices. They can be tangible (plant and equipment, for example) or intangible (patents or trademarks, for example). In contrast, financial assets (such as stocks or bonds) are claims on the income generated by real assets.

Corporations are distinct, permanent legal entities. They allow for separation of owner- ship and control, and they can continue operating without disruption even as management or ownership changes. They provide limited liability to their owners. On the other hand,

What are the two major decisions made by financial managers? (LO1-1)

What does “real asset” mean? (LO1-2)

What are the advantages and disadvantages of forming a corporation? (LO1-3)

25

*The American sycamore, Planatus occidentalis.

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26 Part One Introduction

managing the corporation’s legal machinery is costly. Also, corporations are subject to double taxation because they pay taxes on their profits and the shareholders are taxed again when they receive dividends or sell their shares at a profit.

Almost all managers are involved to some degree in investment decisions, but some man- agers specialize in finance, for example, the treasurer, controller, and CFO. The treasurer is most directly responsible for raising capital and maintaining relationships with banks and investors that hold the firm’s securities. The controller is responsible for preparing financial statements and managing budgets. In large firms, a chief financial officer over- sees both the treasurer and the controller and is involved in financial policymaking and corporate planning.

Value maximization is the natural financial goal of the firm. Shareholders can invest or consume the increased wealth as they wish, provided that they have access to well- functioning financial markets.

Companies either can invest in real assets or can return the cash to shareholders, who can invest it for themselves. The return that shareholders can earn for themselves is called the opportunity cost of capital. Companies create value for shareholders whenever they can earn a higher return on their investments than the opportunity cost of capital.

Conflicts of interest between managers and stockholders can lead to agency problems and agency costs. Agency problems are kept in check by financial controls, by well-designed compensation packages for managers, and by effective corporate governance.

Shareholders do not want the maximum possible stock price; they want the maximum hon- est price. But there need be no conflict between value maximization and ethical behavior. The surest route to maximum value starts with products and services that satisfy custom- ers. A good reputation with customers, employees, and other stakeholders is important for the firm’s long-run profitability and value.

Who are the principal financial managers in a corporation? (LO1-4)

Why does it make sense for corporations to maximize shareholder wealth? (LO1-5)

What is the fundamental trade-off in investment decisions? (LO1-5)

Is value maximization ethical? (LO1-7)

How do corporations ensure that managers act in the interest of stockholders? (LO1-6)

QUESTIONS AND PROBLEMS 1. Vocabulary Check. Choose the term within the parentheses that best matches each of the fol-

lowing descriptions. (LO1-1–LO1-7) a. Expenditure on research and development (financing decision / investment decision) b. A bank loan (real asset / financial asset) c. Listed on a stock exchange (closely held corporation / public corporation) d. Has limited liability (partnership / corporation) e. Responsible for bank relationships (the treasurer / the controller) f. Agency cost (the cost resulting from conflicts of interest between managers and shareholders /

the amount charged by a company’s agents such as the auditors and lawyers)

2. Financial Decisions. Which of the following are investment decisions, and which are financing decisions? (LO1-1) a. Should we stock up with inventory ahead of the holiday season? b. Do we need a bank loan to help buy the inventory? c. Should we develop a new software package to manage our inventory? d. With a new automated inventory management system, it may be possible to sell off our Birdlip

warehouse. e. With the savings we make from our new inventory system, it may be possible to increase our

dividend. f. Alternatively, we can use the savings to repay some of our long-term debt.

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Chapter 1 Goals and Governance of the Corporation 27

3. Financial Decisions. What is the difference between capital budgeting decisions and capital structure decisions? (LO1-1)

4. Real versus Financial Assets. Which of the following are real assets, and which are financial? (LO1-2) a. A share of stock b. A personal IOU c. A trademark d. A truck e. Undeveloped land f. The balance in the firm’s checking account g. An experienced and hardworking sales force h. A bank loan agreement

5. Real and Financial Assets. Read the following passage and fit each of the following terms into the most appropriate space: financing, real, bonds, investment, executive airplanes, financial, capital budgeting, brand names. (LO1-2)

Companies usually buy _____ assets. These include both tangible assets such as _____ and intangible assets such as _____. To pay for these assets, they sell _____ assets such as _____. The decision about which assets to buy is usually termed the _____ or _____ decision. The decision about how to raise the money is usually termed the _____ decision.

6. Corporations. Choose in each case the type of company that best fits the description. (LO1-3) a. The business is owned by a small group of investors. (private corporation / public corporation) b. The business does not pay income tax. (private corporation / partnership) c. The business has limited liability. (sole proprietorship / public corporation) d. The business is owned by its shareholders. (partnership / public corporation)

7. Corporations. What do we mean when we say that corporate income is subject to double taxa- tion? (LO1-3)

8. Corporations. Which of the following statements always apply to corporations? (LO1-3) a. Unlimited liability b. Limited life c. Ownership can be transferred without affecting operations d. Managers can be fired with no effect on ownership

9. Corporations. What is limited liability, and who benefits from it? (LO1-3) 10. Corporations. Which of the following are correct descriptions of large corporations? (LO1-3)

a. Managers no longer have the incentive to act in their own interests. b. The corporation survives even if managers are dismissed. c. Shareholders can sell their holdings without disrupting the business. d. Corporations, unlike sole proprietorships, do not pay tax; instead, shareholders are taxed on

any dividends they receive.

11. Corporations. Is limited liability always an advantage for a corporation and its shareholders? (Hint: Could limited liability reduce a corporation’s access to financing?) (LO1-3)

12. Financial Managers. Which of the following statements more accurately describes the trea- surer than the controller? (LO1-4) a. Monitors capital expenditures to make sure that they are not misappropriated b. Responsible for investing the firm’s spare cash c. Responsible for arranging any issue of common stock d. Responsible for the company’s tax affairs

13. Financial Managers. Explain the differences between the CFO’s responsibilities and the trea- surer’s and controller’s responsibilities. (LO1-4)

14. Goals of the Firm. Give an example of an action that might increase short-run profits but at the same time reduce stock price and the market value of the firm. (LO1-5)

15. Cost of Capital. Why do financial managers refer to the opportunity cost of capital? How would you find the opportunity cost of capital for a safe investment? (LO1-5)

16. Goals of the Firm. You may have heard big business criticized for focusing on short-term per- formance at the expense of long-term results. Explain why a firm that strives to maximize stock

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28 Part One Introduction

price should be less subject to an overemphasis on short-term results than one that simply maxi- mizes profits. (LO1-5)

17. Goals of the Firm. Fritz is risk-averse and is content with a relatively low but safe return on his investments. Frieda is risk-tolerant and seeks a very high rate of return on her invested savings. Yet both shareholders will applaud a high-risk capital investment if it offers an attractive rate of return. Why? What is meant by “attractive”? (LO1-5)

18. Goals of the Firm. We claim that the goal of the firm is to maximize current market value. Could the following actions be consistent with that goal? (LO1-5) a. The firm adds a cost-of-living adjustment to the pensions of its retired employees. b. The firm reduces its dividend payment, choosing to reinvest more earnings in the business. c. The firm buys a corporate jet for its executives. d. The firm drills for oil in a remote jungle. The chance of finding oil is only 1 in 5.

19. Goals of the Firm. Fill in the blanks in the following passage by choosing the most appropriate term from the following list (some of the terms may be used more than once or not used at all): expected return, financial assets, lower, market value, higher, opportunity cost of capital, real assets, dividend, shareholders. (LO1-5)

Shareholders want managers to maximize the _____ of their investments. The firm faces a trade-off. Either it can invest its cash in _____ or it can give the cash back to _____ in the form of a(n) _____ and they can invest it in _____. Shareholders want the company to invest in _____ only if the _____ is _____ than they could earn for themselves in equivalent risk invest- ments. The return that shareholders could earn for themselves is therefore the _____ for the firm.

20. Goals of the Firm. Explain why each of the following may not be appropriate corporate goals. (LO1-5) a. Increase market share b. Minimize costs c. Underprice any competitors d. Expand profits

21. Goals of the Firm. We can imagine the financial manager doing several things on behalf of the firm’s stockholders. For example, the manager might do the following:  a. Make shareholders as wealthy as possible by investing in real assets. b. Modify the firm’s investment plan to help shareholders achieve a particular time pattern of

consumption. c. Choose high- or low-risk assets to match shareholders’ risk preferences. d. Help balance shareholders’ checkbooks.

However, in well-functioning capital markets, shareholders will vote for only one of these goals. Which one will they choose? (LO1-5)

22. Cost of Capital. British Quince comes across an average-risk investment project that offers a rate of return of 9.5%. This is less than the company’s normal rate of return, but one of Quince’s directors notes that the company can easily borrow the required investment at 7%. “It’s simple,” he says. “If the bank lends us money at 7%, then our cost of capital must be 7%. The project’s return is higher than the cost of capital, so let’s move ahead.” How would you respond? (LO1-5)

23. Cost of Capital. In a stroke of good luck, your company has uncovered an opportunity to invest for 10 years at a guaranteed 6% rate of return. How would you determine the opportunity cost of capital for this investment? (LO1-5)

24. Cost of Capital. Pollution Busters Inc. is considering a purchase of 10 additional carbon sequesters for $100,000 apiece. The sequesters last for only 1 year before becoming saturated. Then the carbon is sold to the government. (LO1-5) a. Suppose the government guarantees the price of carbon. At this price, the payoff after 1 year

is $115,000 for sure. How would you determine the opportunity cost of capital for this investment?

b. Suppose instead that the sequestered carbon has to be sold on the London Carbon Exchange. Carbon prices have been extremely volatile, but Pollution Busters’ CFO learns that average rates of return from investments on that exchange have been about 20%. She thinks this is a reasonable forecast for the future. What is the opportunity cost of capital in this case?

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Chapter 1 Goals and Governance of the Corporation 29

c. If the expected return on the investment is still 15%, but now depends on the price of carbon (so that it is no longer risk-free), then is the purchase of additional sequesters still an attrac- tive investment for the firm?

25. Goals of the Firm. It is sometimes suggested that instead of seeking to maximize shareholder value and, in the process, pursuing profit, the firm should seek to maximize the welfare of all its stakeholders, such as its employees, its customers, and the community in which it operates. How far would this objective conflict with one of maximizing shareholder value? Do you think such an objective is feasible or desirable? (LO1-5)

26. Agency Issues. Many firms have devised defenses that make it much more costly or difficult for other firms to take them over. How might such takeover defenses affect the firm’s agency prob- lems? Are managers of firms with formidable takeover defenses more or less likely to act in the firm’s interest rather than their own? (LO1-6)

27. Agency Issues. Sometimes lawyers work on a contingency basis. They collect a percentage of their clients’ settlements instead of receiving fixed fees. Why might clients prefer this arrange- ment? Would the arrangement mitigate an agency problem? Explain. (LO1-6)

28. Agency Issues. One of the “Finance through the Ages” episodes that we cited is the 1993 col- lapse of Barings Bank, when one of its traders lost $1.3 billion. Traders are compensated in large part according to their trading profits. How might this practice have contributed to an agency problem? (LO1-6)

29. Agency Issues. When a company’s stock is widely held, it may not pay an individual share- holder to spend time monitoring managers’ performance and trying to replace poor performers. Explain why. Do you think that a bank that has made a large loan to the company is in a different position? (LO1-6)

30. Agency Issues. Company A pays its managers a fixed salary. Company B ties compensation to the performance of the stock. Which company’s compensation package would most effectively mitigate conflicts of interest between managers and shareholders? (LO1-6)

31. Corporate Governance. How do clear and comprehensive financial reports promote effective corporate governance? (LO1-6)

32. Corporate Governance. Some commentators have claimed that the U.S. system of corporate governance is “broken” and needs thorough reform. What do you think? Do you see systematic failures in corporate governance or just a few “bad apples”? (LO1-6)

33. Agency Issues. Which of the following forms of compensation is most likely to align the inter- ests of managers and shareholders? (LO1-6) a. A fixed salary b. A salary linked to company profits c. A salary that is paid partly in the form of the company’s shares

34. Agency Costs. What are agency costs? List some ways by which agency costs are mitigated. (LO1-6)

35. Reputation. As you drive down a deserted highway, you are overcome with a sudden desire for a hamburger. Fortunately, just ahead are two hamburger outlets; one is owned by a national brand, and the other appears to be owned by “Joe.” Which outlet has the greater incentive to serve you cat meat? Why? (LO1-7)

36. Ethics. In some countries, such as Japan and Germany, corporations develop close long-term relationships with one bank and rely on that bank for a large part of their financing needs. In the United States, companies are more likely to shop around for the best deal. Do you think that this practice is more or less likely to encourage ethical behavior on the part of the corporation? (LO1-7)

37. Ethics. Is there a conflict between “doing well” and “doing good”? In other words, are policies that increase the value of the firm (doing well) necessarily at odds with socially responsible policies (doing good)? When there are conflicts, how might government regulations or laws tilt the firm toward doing good? For example, how do taxes or fees charged on pollutants affect the firm’s decision to pollute? Can you cite other examples of “incentives” used by governments to align private interests with public ones? (LO1-7)

38. Ethics. Look at some of the practices described in the Finance in Practice box on ethic disputes in finance. What, if any, do you believe are the ethical issues involved? (LO1-7)

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30 Part One Introduction

SOLUTIONS TO SELF-TEST QUESTIONS 1.1 a. The development of a microprocessor is a capital budgeting decision. The investment of

$7 billion will purchase a real asset, the microprocessor production facilities. b. The bank loan is a financing decision. This is how BMW will raise money for its

investment. c. Capital budgeting. d. Capital budgeting. The marketing campaign should generate a real, though intangible,

asset. e. Both. The acquisition is an investment decision. The decision to issue shares is a financing

decision.

1.2 a. A real asset. Real assets can be intangible assets. b. Financial. c. Real. d. Financial. e. Real. f. Financial.

1.3 Fritz would more likely be the treasurer and Frieda the controller. The treasurer raises money from the financial markets and requires a background in financial institutions. The controller requires a background in accounting.

1.4 There is no reason for the Hotspurs to avoid high-dividend stocks, even if they wish to invest for tuition bills in the distant future. Their concern should be only with the risk and expected return of the shares. If a particular stock pays a generous cash dividend, they always have the option of reinvesting the dividend in that stock or, for that matter, in other securities. The divi- dend payout does not affect their ability to redirect current investment income to their future needs as they plan for their anticipated tuition bills.

1.5 Because investors can reasonably expect a 15% return in other investments in palladium, the firm should take this as the opportunity cost of capital for its proposed investment. Although the project is expected to show an accounting profit, its expected return is only 12%. There- fore, the firm should reject the project: Its expected return is less than the 15% expected return offered by equivalent-risk investments.

1.6 Agency problems arise when managers and shareholders have different objectives. Managers may empire-build with excessive investment and growth. Managers may be unduly risk- averse, or they may try to take excessive salaries or perquisites.

1.7 Harry’s has a far bigger stake in the reputation of its business than Pete’s. The store has been in business for a long time. The owners have spent years establishing customer loyalty. In contrast, Pete’s has just been established. The owner has little of his own money tied up in the firm, and so has little to lose if the business fails. In addition, the nature of the business results in little customer loyalty. Harry’s is probably more reliable.

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32

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

2-1 Understand how financial markets and institutions channel savings to corporate investment.

2-2 Understand the basic structure of banks, insurance compa- nies, mutual funds, and pension funds.

2-3 Explain the functions of financial markets and institutions.

2-4 Understand the main events behind the financial crisis of 2007–2009 and the subsequent eurozone crisis.

C H A P T E R

2 Financial Markets and Institutions

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

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33

If a corporation needs to issue more shares of stock, then its financial manager had better understand how the stock market works. If it wants to take out a bank loan, the financial manager had better understand how banks and other financial institutions work. If the firm contemplates a capital investment, such as a factory expansion or a new product launch, the financial man- ager needs to think clearly about the cost of the capital that the firm raises from outside investors. As we pointed out in Chapter 1, the opportunity cost of capital for the firm is the rate of return that its stockholders expect to get by investing on their own in financial markets. This means that the financial manager must understand how prices are determined in the financial markets in order to make wise investment decisions.

Financial markets and institutions are the firm’s finan- cial environment. You don’t have to know everything about that environment to begin the study of financial management, but a general understanding provides useful context for the work ahead. For example, it will help you to understand why you are calculating the yield to maturity of a bond in Chapter 6, the net present value of a capital investment in Chapter 9, or the weighted- average cost of capital for a company in Chapter 13.

This chapter does three things. First, it surveys finan- cial markets and institutions. We will cover the stock and bond markets, banks and insurance companies, and mutual and pension funds. Second, we will set out the functions of financial markets and institutions and look at how they help corporations and the economy. Third, we will discuss the financial crisis of 2007–2009 and the eurozone crisis that followed. An understanding of what happens when financial markets do not function well is important for understanding why and how finan- cial markets and institutions matter.

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Read this chapter before you visit the New York Stock Exchange. @Ingram Publishing

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34 Part One Introduction

The Importance of Financial Markets and Institutions

In the previous chapter, we explained why corporations need to be good at finance in order to survive and prosper. All corporations face important investment and financing decisions. But, of course, those decisions are not made in a vacuum. They are made in a financial environment. That environment has two main segments: financial markets and financial institutions.

Businesses have to go to financial markets and institutions for the financing they need to grow. When they have a surplus of cash, and no need for immediate financing, they have to invest the cash, for example, in bank accounts or in securities. Let’s take Apple Computer Inc. as an example.

Table 2.1 presents a time line for Apple and examples of the sources of financing tapped by Apple from its start-up in a California garage in 1976 to its cash-rich status in 2018. The initial investment in Apple stock was $250,000. Apple was also able to get short-term financing from parts suppliers who did not demand immediate pay- ment. Apple got the parts, assembled and sold the computers, and afterward paid off its accounts payable to the suppliers. (We discuss accounts payable in Chapter 19.)

2.1

April 1976: Apple Computer Inc. founded

Mike Makkula, Apple’s first chairman, invests $250,000 in Apple shares.

1976: First 200 computers sold

Parts suppliers give Apple 30 days to pay. (Financing from accounts payable.)

1978–79 Apple raises $3.5 million from venture capital investors.

December 1980: Initial public offering

Apple raises $91 million, after fees and expenses, by selling shares to public investors.

May 1981 Apple sells 2.6 million additional shares at $31.25 per share.

April 1987 Apple pays its first dividend at an annual rate of $.12 per share.

Early 1990s Apple carries out several share repurchase programs.

1994 Apple issues $300 million of debt at an interest rate of 6.5%.

1996–97: Apple reports a $740 million loss in the second quarter of 1996. Lays off 2,700 employees in 1997.

Dividend is suspended in February 1996. Apple sells $661 million of debt to private investors in June 1996. The borrowing provides “sufficient liquidity” to execute Apple’s strategic plans and to “return the company to profitability.”

September 1997: Acquires assets of Power Computing Corp.

Acquisition is financed with $100 million of Apple stock.

2004: Apple is healthy and profitable, thanks to iMac, iPod, and other products.

Apple pays off the $300 million in long-term debt issued in 1994, leaving the company with no long-term debt outstanding.

2005–13 Apple’s profits grow rapidly. It invests in marketable securities, which accumulate to $147 billion by June 2013.

2012–13 Apple announces plans to pay out $100 billion to shareholders over the next 3 years. It also borrows a record $17 billion.

2013–15 Apple’s Capital Return Program distributes cash to shareholders by paying dividends and repurchasing shares. The planned total distribution is $200 billion by 2017.

2015 Apple issues $14.5 billion in dollar-denominated debt, €4.8 billion in euro debt, as well as debt issued in U.K. pounds, Swiss francs, and Japanese yen.

December 2017 Apple’s market capitalization, the total market value of all its outstanding shares, is $851 billion, far in excess of the $140 billion cumulative investment by Apple’s shareholders. The cumulative investment includes $105 billion of retained earnings.

TABLE 2.1 Examples of financing decisions by Apple Computer

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Chapter 2 Financial Markets and Institutions 35

Then, as Apple grew, it was able to obtain several rounds of financing by selling Apple shares to private venture capital investors. (We discuss venture capital in Chapter 15.) In December 1980, it raised $91 million in an initial public offering (IPO) of its shares to public investors. There was also a follow-up share issue in May 1981.1

After Apple became a public company, it could raise financing from many sources, and it was able to pay for acquisitions by issuing more shares. We show a few exam- ples in Table 2.1.

Apple started paying cash dividends to shareholders in 1987, and it also distributed cash to investors by stock repurchases in the early 1990s. But Apple hit a rough patch in 1996 and 1997, and regular dividends were eliminated. The company had to borrow $661 million from a group of private investors in order to cover its losses and finance its recovery plan. However, the rough patch ended with the release of the iMac in 1998 and the iPod in 2001. Apple’s profitability increased rapidly, and it was able to finance its growth by plowing back earnings into operations.

As the twenty-first century progressed, Apple’s profits grew so fast that it piled up a cash mountain. In 2012, Apple resumed cash dividends and started a massive program of share repurchases. Between September 2012 and December 2017, it distributed $226 billion of cash to its shareholders. But this did not stop its cash mountain from growing, and by February 2018 Apple had $285 billion in cash and securities.

Apple is well known for its product innovations, including the Macintosh computer, the iPhone, and the iPad. Apple is not special because of financing. In fact, the story of its financing is not too different from that of many other successful companies. But access to financing was vital to Apple’s growth and profitability. Would we have Macintosh computers, iPhones, or iPads if Apple had been forced to operate in a coun- try with a primitive financial system? Definitely not. A prosperous economy requires a well-functioning financial system.

A modern financial system offers financing in many different forms, depending on the company’s age, its growth rate, and the nature of its business. For example, Apple relied on venture capital financing in its early years and only later floated its shares in public stock markets. Still later, as the company matured, it turned to other forms of financing, including the examples given in Table 2.1. But the table does not begin to cover the range of financing channels open to modern corporations. We will encounter many other channels later in the book, and new channels are opening up regularly. The nearby box describes one recent financial innovation, micro-lending funds that make small loans to businesspeople in the poorer parts of the world.

The Flow of Savings to Corporations

The money that corporations invest in real assets comes ultimately from savings by investors. But there can be many stops on the road between savings and corpo- rate investment. The road can pass through financial markets, financial interme- diaries, or both.

Let’s start with the simplest case of a small, closely held corporation, like Apple in its earliest years. The orange arrows in Figure 2.1 show the flow of savings from share- holders in this simple setting. There are two possible paths: The firm can sell new shares, or it can reinvest cash back into the firm’s operations. Reinvestment means additional savings by existing shareholders. The reinvested cash could have been paid out to those shareholders and spent by them on personal consumption. By not taking and spending the cash, shareholders have reinvested their savings in the corporation.

2.2

1Many of the shares sold in the 1981 sale were previously held by Apple employees. Sale of these shares allowed the employees to cash out and diversify some of their Apple holdings but did not raise additional financing for Apple.

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36

Cash retained and reinvested in the firm’s operations is cash saved and invested on behalf of the firm’s shareholders.

Of course, a small corporation has other financing choices. It could take out a bank loan, for example. The bank in turn may have raised money by attracting savings accounts. In this case, investors’ savings flow through the bank to the firm.

Now consider a large, public corporation, for example, Apple Computer at the start of 2018. What’s different? Scale, for one thing: Apple’s annual revenues for the previ- ous 12 months were $239 billion, and its balance sheet showed total assets of $407 billion. The scope of Apple’s activities has also expanded: It now has dozens of prod- uct lines and operates worldwide. Because of this scale and scope, Apple attracts investors’ savings by a variety of different routes. It can do so because it is a large, profitable, public firm.

The flow of savings to large public corporations is shown in Figure 2.2. Notice two key differences from Figure 2.1. First, public corporations can draw savings from investors worldwide. Second, the savings flow through financial markets, financial intermediaries, or both. Suppose, for example, that Bank of America raises $900 mil- lion by a new issue of shares. An Italian investor buys 2,000 of the new shares for $30 per share. Now Bank of America takes that $60,000, along with money raised by the rest of the issue, and makes a $300 million loan to Apple. The Italian investor’s sav- ings end up flowing through financial markets (the stock market), to a financial inter- mediary (Bank of America), and finally to Apple.

Of course, our Italian friend’s $60,000 doesn’t literally arrive at Apple in an enve- lope marked “From L. DaVinci.” Investments by the purchasers of the Bank of America’s stock issue are pooled, not segregated. Signor DaVinci would own a share of all of Bank of America’s assets, not just one loan to Apple. Nevertheless, investors’ savings are flowing through the financial markets and the bank to finance Apple’s capital investments.

The interest rates on these micro loans are relatively high; this is because the cost of writing and administering such small loans is high and the loans are made in nations with weak currencies. However, default rates on the loans are only about 4%. “There is a deep pride in keeping up with payments,” says Deidre Wagner, an executive vice president of Starbucks, which invested $100,000 in a microfinance fund. “In some instances, when an individual is behind on payments, others in the village may make up the difference.” Investors and borrowers know that when the micro loans are repaid, the money gets recycled into new loans, giving still more borrowers a chance to move up the economic ladder. Source: Adapted from Eric Uhlfelder, “Micro Loans, Solid Returns,” Business- Week, May 9, 2005, pp. 100–102.

Vahid Hujdur had dreams of opening his own business. With about $200 of his own money and a $1,500 loan, he was able to rent space in the old section of Sarajevo, and he began repairing and selling discarded industrial sewing machines. After just 8 years, Hujdur had 10 employees building, install- ing, and fixing this industrial machinery. Hujdur didn’t get his initial loan from a local bank. “They were asking for guaran- tees that were impossible to get,” he recalls. Instead, the capi- tal came from LOKmicro, a local financial institution specializing in microfinance—the lending of small amounts to the poor in developing nations to help them launch small enterprises.

Microfinance institutions get capital from individual and institutional investors via microfinance funds, which collect the investors’ money, vet the local lenders, offer them man- agement assistance, and administer investors’ accounts.

Finance in Practice Micro Loans, Solid Returns

FIGURE 2.1 Flow of savings to investment in a closely held corporation. Investors use savings to buy additional shares. Investors also save when the corporation reinvests on their behalf.

Investment in real assets

Corporation Shareholders

in closely held corporation

InvestorsCash raised from share issues

Cash reinvested

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Chapter 2 Financial Markets and Institutions 37

The Stock Market A financial market is a market where securities are issued and traded. A security is just a traded financial asset, such as a share of stock. For a corporation, the stock mar- ket is probably the most important financial market.

As corporations grow, their requirements for outside capital can expand dramati- cally. At some point the firm may decide to “go public” by issuing shares on an orga- nized exchange such as the New York Stock Exchange (NYSE) or NASDAQ; that first issue is called an initial public offering or IPO. The buyers of the IPO are helping to finance the firm’s investment in real assets. In return, the buyers become part-owners of the firm and participate in its future success or failure. (Most investors in the Inter- net IPOs of 1999 and 2000 were sorely disappointed, but many IPOs pay off hand- somely. If only we had bought Apple shares on their IPO day in 1980 …) Of course a corporation’s IPO is not its last chance to issue shares. For example, Bank of America went public in the 1930s, but it could make a new issue of shares tomorrow.

A new issue of shares increases both the amount of cash held by the company and the number of shares held by the public. Such an issue is known as a primary issue, and it is sold in the primary market. But in addition to helping companies raise new cash, financial markets also allow investors to trade securities among themselves. For example, Smith might decide to raise some cash by selling her Apple stock at the same time that Jones invests his spare cash in Apple. The result is simply a transfer of own- ership from Smith to Jones, which has no effect on the company itself. Such purchases and sales of existing securities are known as secondary transactions, and they take place in the secondary market. Notice that Smith and Jones might be less happy for Apple to raise new capital and invest in long-term projects if they could not sell their stock in the secondary market when they needed the cash for personal use.

Stock markets are called equity markets  because stockholders are said to own the common equity of the firm. You will hear financial managers refer to the capital structure decision as “the choice between debt and equity financing.”

Now may be a good time to stress that the financial manager plays on a global stage and needs to be familiar with markets around the world. For example, Apple’s stock is traded on the NASDAQ market and also in Germany on the Deutsche Börse. China Telecom, Deutsche Bank, Ferrari, Novartis, Petrobras (Brazil), Sony, Unilever, Manchester United football club, and more than 500 other overseas firms have listed their shares on the NYSE. We return to the trading and pricing of shares in Chapter 7.

financial market Market where securities are issued and traded.

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Stock exchanges: From clubs to commercial businesses

primary market Market for the sale of new securities by corporations.

secondary market Market in which previously issued securities are traded among investors.

FIGURE 2.2 Flow of savings to investment for a large, public corporation. Savings come from investors worldwide. The savings may flow through financial markets or financial intermediaries. The corporation also reinvests on shareholders’ behalf.

Stock markets Fixed-income markets Money markets

Financial Markets

Mutual funds Pension funds

Financial Intermediaries

Banks Insurance companies

Financial Institutions

Investors WorldwideInvestment

in real assets

Corporation Reinvestment

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38 Part One Introduction

Other Financial Markets Debt securities as well as equities are traded in financial markets. The Apple bond issue in 1994 was sold publicly to investors (see Table 2.1). Table 1.1 in the previous chapter also gives examples of debt issues, including issues by Delta Airlines and Lenovo.

A few corporate debt securities are traded on the NYSE and other exchanges, but most corporate debt securities are traded over the counter, through a network of banks and securities dealers. Government debt is also traded over the counter.

A bond is a more complex security than a share of stock. A share is just a propor- tional ownership claim on the firm, with no definite maturity. Bonds and other debt securities can vary in maturity, in the degree of protection or collateral offered by the issuer, and in the level and timing of interest payments. Some bonds make “floating” interest payments tied to the future level of interest rates. Many can be “called” (repur- chased and retired) by the issuing company before the bonds’ stated maturity date. Some bonds can be converted into other securities, usually the stock of the issuing company. You don’t need to master these distinctions now; just be aware that the debt or fixed-income market is a complicated and challenging place. A corporation must not only decide between debt and equity finance. It must also consider the design of debt. We return to the trading and pricing of debt securities in Chapter 6.

The markets for long-term debt and equity are called capital markets. A firm’s capital is its long-run financing. Short-term securities are traded in the money mar- kets. “Short term” means less than 1 year. For example, large, creditworthy corpora- tions raise short-term financing by issues of commercial paper, which are debt issues with maturities of no more than 270 days. Commercial paper is issued in the money market.

fixed-income market Market for debt securities.

capital markets Markets for long-term financing.

money market Market for short-term financing (less than 1 year).

Do you understand the following distinctions? Briefly explain in each case.

a. Primary market vs. secondary market. b. Capital market vs. money market. c. Stock market vs. fixed-income market.

Self-Test2.1

The financial manager regularly encounters other financial markets. Here are three examples, with references to the chapters where they are discussed:

∙ Foreign exchange markets (Chapter 22). Any corporation engaged in international trade must be able to transfer money back and forth between dollars and other currencies. Foreign exchange is traded over the counter through a network of the largest international banks.

∙ Commodities markets (Chapter 24). Dozens of commodities are traded on organized exchanges, such as the Chicago Mercantile Exchange (CME) or the Intercontinental Exchange. You can buy or sell corn, wheat, cotton, fuel oil, natural gas, copper, silver, platinum, and so on.

∙ Markets for options and other derivatives (Chapters 23 and 24). Derivatives are securities whose payoffs depend on the prices of other securities or commodities. For example, you can buy an option to purchase IBM shares at a fixed price on a fixed future date. The option’s payoff depends on the price of IBM shares on that date. Commodities can be traded by a different kind of derivative security called a futures contract.

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Panel a of the accompanying figure shows contract prices through 2012 for a victory by Obama or Romney. For all of this period, those prices pointed to the likelihood of an Obama victory, and those predictions turned out to be correct.

Of course, no individuals are perfect forecasters, and pre- diction markets are not unique in performing poorly when the participants have common biases or are focusing on the same information sources. That is what happened in the 2016 presidential election. Panel b of the figure shows that at no point during the contest did participants rank Donald Trump’s chances as better than even.

Nevertheless, because prediction markets can pool ideas efficiently, some businesses have also formed internal prediction markets to survey the views of their staff. For example, Google operates an internal market to forecast product launch dates, the number of Gmail users, and other strategic questions.*

Stock markets allow investors to bet on their favorite stocks. Prediction markets allow them to bet on almost anything else. These markets reveal the collective guess of traders on issues as diverse as New York City snowfall, an avian flu out- break, and the occurrence of a major earthquake.

Prediction markets are conducted on a number of online exchanges such as the Iowa Electronic Markets and Predic- tit. Take presidential elections as an example. Prediction markets allow you to bet that a particular candidate will win. To do so, you can buy a contract that pays $1 if he or she wins and nothing otherwise. If you think the probability of victory is 55% (say), you will be prepared to pay up to $.55 for this contract. Someone who is relatively pessimistic about that candidate’s chances will be happy to sell you such a contract, for that sale will turn a profit if that candi- date loses.

With many participants buying and selling, the market price of a contract reveals the collective wisdom of the crowd (or at least of those people who participated in the market). But even the crowd is not clairvoyant.

* See B. Cowgill and E. Zitzewitz, “Corporate Prediction Markets: Evidence from Google, Ford, and Firm X,” Review of Economic Studies 82, no. 4 (Octo- ber 2015), pp. 1309–41.

Finance in Practice Prediction Markets

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40 Part One Introduction

Commodity and derivative markets are not sources of financing but markets where the financial manager can adjust the firm’s exposure to business risks. For example, an electric generating company may wish to lock in the future price of natural gas by trad- ing in commodity markets, thus eliminating the risk of a sudden jump in the price of its raw materials.

Wherever there is uncertainty, investors may be interested in trading, either to spec- ulate or to lay off their risks, and a market may arise to meet that trading demand. In recent years, several smaller markets have been created that allow punters to bet on a single event. The nearby box discusses how prices in these markets can reveal people’s predictions about the future.

Financial Intermediaries A financial intermediary is an organization that raises money from investors and provides financing for individuals, companies, and other organizations. For corpora- tions, intermediaries are important sources of financing.

Why is a financial intermediary different from a manufacturing corporation? First, it may raise money in different ways, for example, by taking deposits or selling insur- ance policies. Second, it invests that money in financial assets, for example, in stocks, bonds, or loans to businesses or individuals. In contrast, a manufacturing company’s main investments are in plant, equipment, or other real assets.

We will start with two important classes of intermediaries, mutual funds and pen- sion funds.

Mutual funds raise money by selling shares to investors. The investors’ money is pooled and invested in a portfolio of securities. Investors can buy or sell shares in mutual funds as they please, and initial investments are often $3,000 or less. Van- guard’s Explorer Fund, for example, held a portfolio of about 550 stocks with a market value of $13.6 billion in early 2018. An investor in Explorer can increase her stake in the fund’s portfolio by buying additional shares, and so gain a higher share of the port- folio’s subsequent dividends and price appreciation.2 She can also sell her shares back to the fund if she decides to cash out of her investment.3

The advantages of a mutual fund should be clear: Unless you are very wealthy, you cannot buy and manage a 550-stock portfolio on your own, at least not efficiently. Mutual funds offer investors low-cost diversification and professional manage- ment. For most investors, it’s more efficient to buy a mutual fund than to assem- ble a diversified portfolio of stocks and bonds.

Most mutual fund managers also try their best to “beat the market,” that is, to gener- ate superior performance by finding the stocks with better-than-average returns. Whether they can pick winners consistently is another question, which we address in Chapter 7.

In exchange for their services, the fund’s managers charge a management fee. There are also the expenses of running the fund. For Explorer, fees and expenses absorb about .3% of portfolio value each year. This seems reasonable, but watch out: The typical mutual fund charges more than Explorer does. In some cases, fees and expenses add up to more than 1% per year. That’s a big bite out of your investment return.

financial intermediary An organization that raises money from investors and provides financing for individuals, corporations, or other organizations.

mutual fund An investment company that pools the savings of many investors and invests in a portfolio of securities.

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U.S. mutual funds

2Mutual funds are not corporations but investment companies. They pay no tax, providing that all income from dividends and price appreciation is passed on to the funds’ shareholders. The shareholders pay personal tax on this income. 3Explorer, like most mutual funds, is an open-end fund. It stands ready to issue shares to new investors in the fund and to buy back existing shares when its shareholders decide to cash out. The purchase and sale prices depend on the fund’s net asset value (NAV) on the day of purchase or redemption. Closed-end funds have a fixed number of shares traded on an exchange. If you want to invest in a closed-end fund, you must buy shares from another stockholder in the fund.

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Chapter 2 Financial Markets and Institutions 41

Mutual funds are a stop on the road from savings to corporate investment. Suppose Explorer purchases part of the new issue of shares by Bank of America. Again we show the flow of savings to investment by orange arrows:

Bank of America Explorer Fund Sells shares

$ Investors

Issues shares

$

There are about 8,000 mutual funds in the United States. In fact, there are more mutual funds than public companies! The funds pursue a wide variety of investment strategies. Some funds specialize in safe stocks with generous dividend payouts. Some specialize in high-tech growth stocks. Some “balanced” funds offer mixtures of stocks and bonds. Some specialize in particular countries or regions. For example, the Fidelity Investments mutual fund group sponsors funds for Canada, Japan, China, Europe, and Latin America.

Like mutual funds, hedge funds also pool the savings of different investors and invest on their behalf. But they differ from mutual funds in at least two ways. First, because hedge funds usually follow complex, high-risk investment strategies, access is usually restricted to knowledgeable investors such as pension funds, endowment funds, and wealthy individuals. Don’t try to send a check for $3,000 or $5,000 to a hedge fund; most hedge funds are not in the “retail” investment business. Second, hedge funds try to attract the most talented managers with high compensation packages that they can pay because they charge investors potentially hefty, performance-related fees.4 In contrast, mutual funds usually charge a fixed percentage of assets under management.

Hedge funds follow many different investment strategies. Some try to make a profit by identifying overvalued stocks or markets and selling short. (We will not go into procedures for short-selling here. Just remember that short-sellers profit when prices fall.5) “Vulture funds” specialize in the securities of distressed corporations. Some hedge funds take bets on firms involved in merger negotiations, others look for mis- priced convertible bonds, and some take positions in currencies and interest rates. Hedge funds manage less money than mutual funds, but they sometimes take very big positions and have a large impact on the market.

There are other ways of pooling and investing savings. Consider a pension plan set up by a corporation or other organization on behalf of its employees. There are several types of pension plan. The most common type of plan is the defined-contribution plan. In this case, a percentage of the employee’s monthly paycheck is contributed to a pension fund. (The employer and employee may each contribute 5%, for example.) Contributions from all participating employees are pooled and invested in securities or mutual funds. (Usually the employees can choose from a menu of funds with different investment strategies.) Each employee’s balance in the plan grows over the years as contributions continue and investment income accumulates. The balance in the plan can be used to finance living expenses after retirement. The amount available for retirement depends on the accumulated contributions and on the rate of return earned on the investments.6

hedge fund Private investment fund that pursues complex, high-risk investment strategies.

pension fund Fund set up by an employer to provide for employees’ retirement.

4Sometimes these fees can be very large indeed. For example, Forbes estimated that the top hedge fund manager in 2017 earned $1.5 billion in fees. 5A short-seller borrows a security from another investor and sells it. Of course, the seller must sooner or later buy the security back and return it to its original owner. The short-seller earns a profit if the security can be bought back at a lower price than it was sold for. 6In contrast, in a defined-benefit plan, the employer promises a certain level of retirement benefits (set by a for- mula) and the employer invests in the pension plan. The plan’s accumulated investment value has to be large enough to cover the promised benefits. If not, the employer must put in more money. Defined-benefit plans are gradually giving way to defined-contribution plans.

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42 Part One Introduction

Pension funds are designed for long-run investment. They provide professional management and diversification. They also have an important tax advantage: Contri- butions are tax-deductible, and investment returns inside the plan are not taxed until cash is finally withdrawn.7

Pension plans are among the most important vehicles for savings. Total assets held by U.S. pension plans exceeded $22 trillion in June 2018.

Individual investors can buy bonds and stocks directly, or they can put their money in a mutual fund or a defined-contribution pension fund. What are the advantages of the second strategy?

Self-Test2.2

Financial Institutions Banks and insurance companies are financial institutions.8 A financial institution is an intermediary that does more than just pool and invest savings. Institutions raise financing in special ways, for example, by accepting deposits or selling insurance policies, and they provide additional financial services. Unlike a mutual fund, they not only invest in secu- rities but also lend money directly to individuals, businesses, or other organizations.

Commercial Banks There are about 4,900 commercial banks in the United States.9 They vary from giants such as JPMorgan Chase with $2.1 trillion of assets to relative dwarfs like Emigrant Mercantile Bank with assets of $3.4 million.

Commercial banks are major sources of loans for corporations. (In the United States, they generally are not allowed to make equity investments in corporations, although banks in most other countries can do so.) Suppose that a local forest products company negotiates a 9-month bank loan for $2.5 million. The flow of savings is:

financial institution A bank, insurance company, or similar financial intermediary.

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The world’s largest banks

7Defined-benefit pension plans share these same advantages, except that the employer invests rather than the employees. In a defined-benefit plan, the advantage of tax deferral on investment income accrues to the employer. This deferral reduces the cost of funding the plan. 8We may be drawing too fine a distinction between financial intermediaries and institutions. A mutual fund could be considered a financial institution. But “financial institution” usually suggests a more complicated inter- mediary, such as a bank. 9Banks that accept deposits and provide financing mostly to businesses are called commercial banks. Savings banks and savings & loans (S&Ls) accept deposits and lend mostly to individuals, for example, as mortgage loans to home buyers. 10Investment banks do not take deposits and do not lend money to businesses or individuals, except as bridge loans made as temporary financing for takeovers or other transactions. Investment banks are sometimes called merchant banks.

Company Bank(Institution) Issues debt to bank

$2.5 million Investors

(Depositors) Accepts deposits

$2.5 million

The bank provides debt financing for the company and, at the same time, provides a place for depositors to park their money safely and withdraw it as needed.

Investment Banks We have discussed commercial banks, which raise money from depositors and other investors and then make loans to businesses and individuals. Investment banks are different. Investment banks do not generally take deposits or make loans to companies.10 Instead, they advise and assist companies in obtaining

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Chapter 2 Financial Markets and Institutions 43

finance. For example, investment banks underwrite stock offerings by purchasing the new shares from the issuing company at a negotiated price and reselling the shares to investors. Thus, the issuing company gets a fixed price for the new shares, and the investment bank takes responsibility for distributing the shares to investors. We dis- cuss share issues in more detail in Chapter 15.

Investment banks also advise on takeovers, mergers, and acquisitions. They offer investment advice and manage investment portfolios for individual and institutional investors. They run trading desks for foreign exchange, commodities, bonds, options, and other derivatives.

Investment banks can invest their own money in start-ups and other ventures. For example, the Australian Macquarie Bank has invested in airports, toll highways, elec- tric transmission and generation, and other infrastructure projects around the world.

The largest investment banks are financial powerhouses. They include Goldman Sachs, Morgan Stanley, Lazard, Nomura (Japan), and Macquarie Bank.11 In addition, the major commercial banks, including Bank of America and Citigroup, all have investment banking operations.12

Insurance Companies Insurance companies are more important than banks for the long-term financing of business. They are massive investors in corporate stocks and bonds, and they often make long-term loans directly to corporations.

Suppose a company needs a loan of $2.5 million for 9 years, not 9 months. It could issue a bond directly to investors, or it could negotiate a 9-year loan with an insurance company:

11The distinction between investment and commercial banks is not a legal one. Since 2008 both Goldman Sachs and Morgan Stanley have held banking licenses and are supervised by the Federal Reserve. However, they are not in the business of taking retail deposits or providing loans. 12Bank of America owns Merrill Lynch, one of the largest investment banks. Merrill was rescued by Bank of America in 2009 after suffering huge losses on mortgage-related investments.

Company Insurance company(Institution) Issues debt

$2.5 million Investors

(Policyholders) Sells policies

$2.5 million

The money to make the loan comes mainly from the sale of insurance policies. Say you buy a fire insurance policy on your home. You pay cash to the insurance company and get a financial asset (the policy) in exchange. You receive no interest payments on this financial asset, but if a fire does strike, the company is obliged to cover the dam- ages up to the policy limit. This is the return on your investment. (Of course, a fire is a sad and dangerous event that you hope to avoid. But if a fire does occur, you are better off getting a payoff on your insurance policy than not having insurance at all.)

The company will issue not just one policy but thousands. Normally the incidence of fires “averages out,” leaving the company with a predictable obligation to its policy- holders as a group. Of course, the insurance company must charge enough for its poli- cies to cover selling and administrative costs, pay policyholders’ claims, and generate a profit for its stockholders.

What are the key differences between a mutual fund and a bank or an insurance company?

Self-Test2.3

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44 Part One Introduction

Total Financing of U.S. Corporations The pie chart in Figure 2.3 shows the investors in bonds and other debt securities. Notice the importance of institutional investors—mutual funds, pension funds, insur- ance companies, and banks. Households (individuals and non-profit organizations) hold less than 10% of the debt pie. The other slices represent the rest of the world (investors from outside the United States) and other, smaller categories of investors.

The pie chart in Figure 2.4 shows holdings of the shares issued by U.S. corpora- tions. Here, households make a stronger showing, with 38.7% of the total. Pension funds, insurance companies, and mutual funds add up to 43.9% of the total. Remem- ber, banks in the United States do not usually hold stock in other companies. The rest- of-the-world slice is 15.5%.

The aggregate amounts represented in these figures are enormous. There is $13.0 tril- lion of debt behind Figure 2.3 and $46.8 trillion of equity behind Figure 2.4 ($46,800,000,000,000).

Chapter 14 reviews corporate financing patterns in more detail.

Pension funds (10.3%)

Mutual funds, etc. (19.6%)

Banks & savings institutions

(4.9%) Insurance companies

(23.9%)

Rest of world (28.3%)

Other (3.6%)

Household sector (9.4%)

FIGURE 2.3 Holdings of corporate and foreign bonds, June 2018. The total amount is $13.0 trillion.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts, Table L.213 (www.federalreserve.gov).

Pension funds (12.2%)

Mutual funds, etc. (29.8%)

Insurance companies

(1.9%)

Rest of world (15.5%)

Household sector (38.7%)

Other (1.9%)

FIGURE 2.4 Holdings of corporate equities, June 2018. The total amount is $46.8 trillion.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts, Table L.223 (www.federalreserve.gov).

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Chapter 2 Financial Markets and Institutions 45

Functions of Financial Markets and Intermediaries

Financial markets and intermediaries provide financing for business. They channel savings to real investment. That much should be loud and clear from Sections 2.1 and 2.2 of this chapter. But there are other functions that may not be quite so obvious.

Transporting Cash across Time Individuals need to transport expenditures in time. If you have money now that you wish to save for a rainy day, you can (for example) put the money in a savings account at a bank and withdraw it with interest later. If you don’t have money today, say to buy a car, you can borrow money from the bank and pay off the loan later. Modern finance provides a kind of time machine. Lenders transport money forward in time; borrowers transport it back. Both are happier than if they were forced to spend income as it arrives. Of course, individuals are not alone in needing to raise cash from time to time. Firms with good investment opportunities, but a shortage of internally generated cash, raise cash by borrowing or selling new shares. Many governments run deficits and finance current outlays by issuing debt.

Young people saving for retirement may transport their current earnings 30 or 40 years into the future by means of a pension fund. They can even transport income to their heirs by purchase of a life insurance policy.

In principle, individuals or firms with cash surpluses could take out newspaper advertisements or surf the web looking for counterparties with cash shortages. But it is usually cheaper and more convenient to use financial markets and intermediaries. It is not just a matter of avoiding the cost of searching for the right counterparty. Follow-up is needed. For example, banks don’t just lend money and walk away. They monitor the borrower to make sure that the loan is used for its intended purpose and that the bor- rower’s credit stays solid.

Risk Transfer and Diversification Financial markets and intermediaries allow investors and businesses to reduce and reallocate risk. Insurance companies are an obvious example. When you buy homeowner’s insurance, you greatly reduce the risk of loss from fire, theft, or acci- dents. But your policy is not a very risky bet for the insurance company. It diversifies by issuing thousands of policies, and it expects losses to average out over the policies.13 The insurance company allows you to pool risk with thousands of other homeowners.

Investors should diversify too. For example, you can buy shares in a mutual fund that holds hundreds of stocks. In fact, you can buy index funds that invest in all the stocks in the popular market indexes. For example, the Vanguard 500 Index Fund holds the stocks in the Standard & Poor’s Composite stock market index. (The “S&P 500” tracks the performance of the largest U.S. stocks. It is the index most used by profes- sional investors.) If you buy this fund, you are insulated from the company-specific risks of the approximately 500 companies in the index. These risks are averaged out by diversification. Of course, you are still left with the risk that the level of the stock mar- ket as a whole will fall. In fact, we will see in Chapter 11 that investors are mostly concerned with market risk, not the specific risks of individual companies.

Index mutual funds are one way to invest in widely diversified portfolios at low cost. Another route is provided by exchange-traded funds (ETFs), which are portfolios of stocks that can be bought or sold in a single trade. For example, Standard & Poor’s Depositary Receipts (SPDRs, or “spiders”) invest in portfolios that match Standard &

2.3

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How ETFs work

13Unfortunately for insurance companies, the losses don’t always average out. Hurricanes and earthquakes can damage thousands of homes at once. The potential losses are so great that property insurance companies buy reinsurance against such catastrophes.

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46 Part One Introduction

Poor’s stock market indexes. The total amount invested in the spider that tracks the benchmark S&P 500 index was $253 billion in early 2018.

ETFs are in some ways more efficient than mutual funds. To buy or sell an ETF, you simply make a trade, just as if you bought or sold shares of stock.14 This is differ- ent from investing in an open-end mutual fund. In that case you have to send money to the fund in exchange for newly issued shares. And, if you want to withdraw the invest- ment, you have to notify the fund, which redeems your shares and sends you a check. Also, many of the larger ETFs charge lower fees than mutual funds. State Street Global Advisors charges just .0945% a year for managing the Standard & Poor’s 500 Index Spider. For a $100,000 investment, the fee is only .000945 × 100,000 = $94.50.

Financial markets provide other mechanisms for sharing risks. For example, a wheat farmer and a baking company are each exposed to fluctuations in the price of wheat after the harvest. The farmer worries about low prices, the baker about high prices. They can both rest easier if the baker can agree with the farmer to buy wheat in the future at a fixed price. Of course, it would be difficult, to say the least, if the baker and the farmer each had to contact an Internet dating service to get together to make a deal. Fortunately, no dating service is needed: Each can trade in commodity markets, the farmer as a seller and the baker as a buyer.

Liquidity Markets and intermediaries also provide liquidity, that is, the ability to turn an invest- ment back into cash when needed. Suppose you deposit $5,000 in a savings bank on February 1. During that month, the bank uses your deposit and other new deposits to make a 6-month construction loan to a real estate developer. On March 1, you realize that you need your $5,000 back. The bank can give it to you. Because the bank has thousands of depositors, and other sources of financing if necessary, it can make an illiquid loan to the developer financed by liquid deposits made by you and other cus- tomers. If you lend your money for 6 months directly to the real estate developer, you will have a hard time retrieving it 1 month later.15

The shares of public companies are liquid because they are traded more or less con- tinuously in the stock market. An Italian investor who puts $60,000 into Bank of America shares can recover that money on short notice. (A $60,000 sell order is a drop in the bucket compared with the normal trading volume of Bank of America shares.) Mutual funds can redeem their shares for cash on short notice because the funds invest in traded securities, which can be sold as necessary.

Of course, liquidity is a matter of degree. Foreign exchange markets for major currencies are exceptionally liquid. Bank of America or Deutsche Bank could buy $200 million worth of yen or euros in the blink of an eye, with hardly any effect on for- eign exchange rates. U.S. Treasury securities are also very liquid, and the shares of the largest companies on the major international stock exchanges are only slightly less so.

Liquidity is most important when you’re in a hurry. If you try to sell $500,000 worth of the shares of a small, thinly traded company all at once, you will probably knock down the price to some extent. If you’re patient and don’t surprise other inves- tors with a large, sudden sell order, you may be able to unload your shares on better terms. It’s the same problem that you may face in selling real estate. A house or con- dominium is not a liquid asset in a panic sale. If you’re determined to sell in an after- noon, you’re not going to get full value.

liquidity The ability to sell an asset on short notice at close to the market value.

14ETFs are in this respect like closed-end mutual funds (see footnote 3). But ETFs generally do not give manag- ers the discretion to try to “pick winners.” ETF portfolios are tied down to indexes or fixed baskets of securities. ETF issuers make sure that the ETF price tracks the price of the underlying index or basket. 15Of course, the bank can’t repay all depositors simultaneously. To do so, it would have to sell off its loans to the real estate developer and other borrowers. These loans are not liquid. This raises the specter of bank runs, where doubts about a bank’s ability to pay off its depositors cause a rush of withdrawals, with each depositor trying to get his or her money out first. Bank runs are rare because bank deposits are backed up by the U.S. Federal Deposit Insurance Corporation, which insures bank accounts up to $250,000 per account.

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Chapter 2 Financial Markets and Institutions 47

The Payment Mechanism Think how inconvenient life would be if you had to pay for every purchase in cash or if Boeing had to ship truckloads of hundred-dollar bills around the country to pay its suppliers. Checking accounts, credit cards, and electronic transfers allow individuals and firms to send and receive payments quickly and safely over long distances. Banks are the obvious providers of payment services, but they are not alone. For example, if you buy shares in a money market mutual fund, your money is pooled with that of other investors and used to buy safe, short-term securities. You can then write checks on this mutual fund investment, just as if you had a bank deposit.

Information Provided by Financial Markets In well-functioning financial markets, you can see what securities and commodities are worth, and you can see—or at least estimate—the rates of return that investors can expect on their savings. The information provided by financial markets is often essen- tial to a financial manager’s job. Here are three examples of how this information can be used.

Commodity Prices Catalytic converters are used in the exhaust systems of cars and light trucks to reduce pollution. The catalysts include platinum, which is traded on the New York Mercantile Exchange (NYMEX).

In March a manufacturer of catalytic converters is planning production for October. How much per ounce should the company budget for purchases of platinum in that month? Easy: The company’s CFO looks up the futures price of platinum on the New York Mercantile Exchange—$943 per ounce for delivery in October (this was the closing price for platinum in April 2018, for delivery in October). The CFO can lock in that price if she wishes. The details of such a trade are covered in Chapter 24.

Interest Rates The CFO of Catalytic Concepts has to raise $400 million in new financing. She considers an issue of long-term bonds. What will the interest rate on the bonds be? To find out, the CFO looks up interest rates on existing bonds traded in financial markets.

The results are shown in Table 2.2. Notice how the interest rate climbs as credit quality deteriorates: The largest, safest companies, which are rated AAA (“triple-A”), can raise long-term debt at a 3.5% interest rate. Yields start to rise as credit quality declines. BBB bonds, which are still regarded as investment grade, yield 0.8% more than AAAs. The next step down takes the investor into junk bond territory. The inter- est rate for BB debt climbs to 5.1%. Single-B companies are riskier still, so investors demand 6.5%.

There will be more on bond ratings and interest rates in Chapter 6. But you can see how a financial manager can use information from fixed-income markets to forecast the interest rate on new debt financing. For example, if Catalytic Concepts can qualify as a BBB-rated company, and interest rates are as shown in Table 2.2, it should be able to raise new debt financing for approximately 4.3%.

Credit Rating Interest Rate

AAA 3.5%

AA 3.5

A 3.8

BBB 4.3

BB 5.1

B 6.5

TABLE 2.2 Interest rates on long-term corporate bonds, May 2018. The interest rate is lowest for top-quality (AAA and AA) issuers. The rate rises as credit quality declines.

Source: ICE Bank of America Merrill Lynch indices.

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48 Part One Introduction

Company Values How much was Callaway Golf worth in March 2018? How about Alaska Air Group, Yum! Brands, Caterpillar, or Microsoft? Table 2.3 shows the mar- ket capitalization of each company. We simply multiply the number of shares out- standing by the price per share in the stock market. Investors valued Callaway Golf at $1.55 billion and Microsoft at $703 billion.

Stock prices and company values summarize investors’ collective assessment of how well a company is doing, both its current performance and its future prospects. Thus, an increase in stock price sends a positive signal from investors to managers.16 That is why top management’s compensation is linked to stock prices. A manager who owns shares in his or her company will be motivated to increase the company’s market value. This reduces agency costs by aligning the interests of managers and stockholders.

This is one important advantage of going public. A private company can’t use its stock price as a measure of performance. It can still compensate managers with shares, but the shares will not be valued in a financial market.

Cost of Capital Financial managers look to financial markets to measure, or at least estimate, the cost of capital for the firm’s investment projects. The cost of capital is the minimum acceptable rate of return on the project. Investment projects offering rates of return higher than their cost of capital are worthwhile because they add value; they make both the firm and its shareholders better off financially. Projects offering rates of return less than the cost of capital subtract value and should not be undertaken.17

Thus, the hurdle rate for investments inside the corporation is actually set outside the corporation. The expected rate of return on investments in financial markets deter- mines the opportunity cost of capital.

The opportunity cost of capital is generally not the interest rate that the firm pays on a loan from a bank or insurance company. If the company is making a risky invest- ment, the opportunity cost of capital is the expected rate of return that investors can achieve in financial markets at the same level of risk. The expected rate of return on risky securities is normally well above the interest rate on corporate borrowing.

We introduced the cost of capital in Chapter 1, but this brief reminder may help to fix the idea. We cover the cost of capital in detail in Chapters 11 and 12.

cost of capital Minimum acceptable rate of return on capital investment.

Number of Shares (millions) × Stock Price =

Market Capitalization  ($ millions)

Callaway Golf (ELY) 94.6 × $16.36 = $1,548 Alaska Air Group (ALK) 123.4 × $61.76 = $7,621 Yum! Brands (YUM) 332.5 × $85.13 = $28,306 Caterpillar Tractor (CAT) 597.6 × 147.38 = $88,074 Microsoft (MSFT) 7,690 × 91.39 = $702,789

TABLE 2.3 Calculating the market capitalization of Callaway Golf and other companies in March 2018. (Shares and market values in millions. Ticker symbols in parentheses.)

Source: Yahoo! Finance, finance.yahoo.com.

16 We can’t claim that investors’ assessments of value are always correct. Finance can be a risky and dangerous business—dangerous for your wealth, that is. With hindsight we see horrible mistakes by investors, for example, the gross overvaluation of Internet and telecom companies in 2000. On average, however, it appears that finan- cial markets collect and assess information quickly and accurately. We’ll discuss this issue again in Chapter 7. 17 Of course, the firm may invest for other reasons. For example, it may invest in pollution control equipment for a factory. The equipment may not generate a cash return but may still be worth investing in to meet legal and ethical obligations.

Which of the functions described in this section require financial markets? Explain briefly.

Self-Test2.4

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Chapter 2 Financial Markets and Institutions 49

The Crisis of 2007–2009

The financial crisis of 2007–2009 raised many questions, but it settled one question conclusively: Yes, financial markets and institutions are important. When financial markets and institutions ceased to operate properly, the world was pushed into a global recession.

The financial crisis had its roots in the easy-money policies that were pursued by the U.S. Federal Reserve and other central banks following the collapse of the Internet and telecom stock bubble in 2000. At the same time, large balance-of-payments sur- pluses in Asian economies were invested back into U.S. debt securities. This also helped to push down interest rates and contribute to lax credit.

Banks took advantage of this cheap money to expand the supply of subprime mort- gages to low-income borrowers. Many banks tempted would-be homeowners with low initial payments, offset by significantly higher payments later.18 (Some home buyers were betting on escalating housing prices so that they could resell or refinance before the higher payments kicked in.) One lender is even said to have advertised what it dubbed its “NINJA” loan—NINJA standing for “No Income, No Job, and No Assets.” Most subprime mortgages were then packaged together into mortgage-backed securi- ties (MBSs) that could be resold. But, instead of selling these securities to investors who could best bear the risk, many banks kept large quantities of the loans on their own books or sold them to other banks.

The widespread availability of mortgage finance fueled a dramatic increase in house prices, which doubled in the 5 years ending June 2006. At that point, prices started to slide and homeowners began to default on their mortgages. A year later, Bear Stearns, a large investment bank, announced huge losses on the mortgage invest- ments that were held in two of its hedge funds. By the spring of 2008, Bear Stearns was on the verge of bankruptcy, and the U.S. Federal Reserve arranged for it to be acquired by JPMorgan Chase.

The crisis peaked in September 2008, when the U.S. government was obliged to take over the giant federal mortgage agencies Fannie Mae and Freddie Mac, both of which had invested several hundred billion dollars in subprime mortgage-backed securities. Over the next few days, the financial system started to melt down. Both Merrill Lynch and Lehman Brothers were in danger of failing. On September 14, the government arranged for Bank of America to take over Merrill in return for financial guarantees. However, it did nothing to rescue Lehman Brothers, which filed for bankruptcy protec- tion the next day. Two days later, the government reluctantly lent $85 billion to the giant insurance company AIG, which had insured huge volumes of mortgage-backed securities and other bonds against default. The following day, the Treasury unveiled its first proposal to spend $700 billion to purchase “toxic” mortgage-backed securities.

After the failure of Lehman and the forced rescues of Bear Stearns, Fannie Mae, Freddie Mac, Merrill Lynch, and AIG, investors and financial institutions had to ask, “Who will be next? Do I dare trade with or lend money to Bank X?” In many situa- tions, the cautious answer was “No.” Customary day-to-day financial transactions were canceled or completed on onerous terms.19 At the same time, trading in MBSs and other hard-to-value securities dried up; it therefore became even harder to know what these securities were worth. As banks and other financial institutions became reluctant to trade securities or lend to one another, the supply of credit to the economy contracted and busi- ness investment was cut back. The U.S. economy suffered one of its worst setbacks since the Great Depression. Unemployment rose rapidly and business bankruptcies tripled.

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Housing prices in the financial crisis

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Time line of the financial crisis

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The rise and fall of Lehman Brothers

18 With a so-called option ARM loan, the minimum mortgage payment was often not even sufficient to cover that month’s interest on the loan. The unpaid interest was then added to the amount of the mortgage, so the homeowner was burdened by an ever-increasing mortgage that one day would need to be paid off. 19 The interest rate on interbank loans rose in 2008 to 4.6% above the rate on U.S. Treasury debt. The normal spread over Treasuries is less than .5%.

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50

The invention of MBSs also made mortgages liquid. They are actively traded among banks, insurance companies, mutual funds, pension funds, and endowments.

The MBS market grew explosively through 2005. With the growth came more and more complexity. Issuers were not content with the simple pass-through MBS described earlier. They issued complicated packages of securities called tranches. The most senior tranches were given first call on all cash flows from the mortgage portfolio and were viewed as almost risk-free. Bond-rating agencies gave their highest, triple-A ratings to the senior tranches, even for MBSs based on subprime mortgages for homeowners with weak credit. Many investors in triple-A tranches lost a lot of money in the crisis of 2007–2009. We discuss bond ratings in Chapter 6.

The MBS market survived. It is still by far the largest source of mortgage financing. By 2018, the aggregate value of mortgage-related securities outstanding exceeded $9 trillion. MBSs are part of a broader market for asset-backed securi- ties, which include securities that work like MBSs but are based on portfolios of other types of assets, including car loans, bank loans to businesses, and financing for commer- cial real estate.

Mortgage-backed securities (MBSs) provide another example of how financial markets convey savings to finance invest- ment in real assets. In this case, the real assets are homes, which homeowners finance in part with mortgage loans.

In the old days—the 1960s, for example—most mortgage loans were made by local banks, savings banks, and savings and loan institutions (S&Ls), which accepted deposits and savings accounts and made mortgage and other local loans. We will use an S&L as the example. The flow of savings would be as described by the figure in Panel a, at the bottom of this box.

The typical mortgage was long term, up to 30 years matu- rity, with a fixed interest rate. The S&Ls’ liabilities—chiefly sav- ings accounts—had much shorter maturities, perhaps a year or two on average. The S&Ls were therefore “borrowing short, lending long,” a dangerous investment strategy. When interest rates rose in the 1970s and 1980s, the S&Ls’ interest costs on savings accounts rose, too, but their interest income was locked up in long-term, fixed-rate mortgages. Losses mounted. The S&L crisis of the 1980s followed.*

The invention of the MBS allowed S&Ls to eliminate the risks of borrowing short and lending long. You can still get a mortgage from your local S&L, but now the S&L does not have to keep it. The S&L originates the mortgage but will probably resell it to an MBS issuer—for example, Fannie Mae (Federal National Mortgage Association or FNMA†) or Bank of America. The issuer combines your mortgage with hundreds or thousands of others and issues an MBS backed by the combined portfolio. The MBS is sold to investors such as life insurance companies that want to hold long-term, fixed-rate obligations. Cash flows from the mortgage portfolio are passed through to investors.‡

Suppose a life insurance company purchases an MBS. The flow of savings would now match the figure in Panel b.

Finance in Practice Mortgage-Backed Securities

*For a history of the crisis, see Edward J. Kane, The S&L Insurance Mess: How Did It Happen? (Washington, D.C.: Urban Institute Press, 1989).

†Fannie Mae and Freddie Mac (Federal Home Loan Mortgage Corp.) are gov- ernment-sponsored entities (GSEs) charged with increasing the availability of mortgage credit. The GSEs purchase “conforming loans” and package and resell them as MBSs. Nonconforming loans—for example, large, “jumbo” mort- gages—are packaged by banks such as Citigroup or Bank of America.

‡You still send monthly payments to your local S&L. The S&L extracts a small servicing fee and sends your payments along to the MBS issuer, which also extracts a small fee. Net cash flows from the portfolio of mortgages then go to the MBS investors.

Homeowner S&L Mortgage loan

(a) $

Investors (Depositors)

Savings account

$

Homeowner

(b)

S&L Mortgage

loan

$ MBS

Issuer Mortgage

loan

Issuer assembles portfolio of mortgages

$ Insurance Company

MBS

$

Few developed economies escaped the crisis. As well as suffering from a collapse in their own housing markets, a number of foreign banks had made large investments in U.S. subprime mortgages and had to be rescued by their governments. Many European governments were already heavily in debt and, as the cost of the bank bailouts mounted, investors began to worry about the ability of the governments to repay their debts. Thus, in Europe, the banking crisis became entwined with a sovereign debt crisis.

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Chapter 2 Financial Markets and Institutions 51

Greece was in the worst shape. It had accumulated €350 billion (about $460 billion) of government debt. Greece is a member of the single-currency euro club, so it had no control over its currency and could not just print more euros to service its debts. In 2011 it defaulted on debts totaling €100 billion.

What lessons can you, as a student of finance, draw from these financial crises? Here are three. First, note the sorry consequences for the economy when financial markets and institutions do not carry out the functions described in this chapter. For example, the crisis was amplified by the sudden disappearance of liquidity in many markets, including the market for MBSs. That meant that potential buyers of the illiq- uid assets could not know for sure what they were worth. Thus, the informational func- tion of financial markets was also compromised.

Second, why were Bear Stearns, Lehman, Merrill Lynch, and the other dis- tressed firms so fragile? One reason is that they were mostly financed with bor- rowed money, much of it short-term debt that had to be refinanced frequently. Investment banks like Lehman typically were financed with more than 95% debt and less than 5% equity capital. Thus, a 5% fall in their asset values could wipe out their equity “cushions” and leave the banks insolvent. Regulators since the crisis have therefore required banks to finance with much more equity. This requirement has also affected payout to shareholders. A U.S. bank’s dividend payments can be stopped by regulators if the bank’s equity capital ratio is not up to snuff. We cover decisions about debt versus equity financing and payout in Chapters 16 and 17.

Third, some causes of the crisis can be traced back to agency problems noted in Chapter 1. Managers in the mortgage business were probably at least dimly aware that promoting and selling massive amounts of subprime MBSs was likely to end badly. They didn’t wake up in the morning thinking, “Hey, maybe I can cause a financial crisis,” but their incentives did call for trying to squeeze out one more fat bonus before the game ended. Their incentives were not aligned with shareholders’. The value of their firms suffered accordingly.

BEYOND THE PAGE

mhhe.com/brealey10e

The Dodd- Frank Act

SUMMARY The ultimate source of financing is individuals’ savings. The savings may flow through financial markets and intermediaries. The intermediaries include mutual funds, pension funds, and financial institutions, such as banks and insurance companies.

Corporations need access to financing in order to innovate and grow. A modern financial system offers different types of financing, depending on a corporation’s age and the nature of its business. A high-tech start-up will seek venture capital financing, for example. A mature firm will rely more on bond markets.

In that case, the corporation is saving on behalf of its shareholders.

Mutual and pension funds allow investors to diversify in professionally managed portfo- lios. Pension funds offer an additional tax advantage because the returns on pension investments are not taxed until withdrawn from the plan.

Where does the financing for corporations come from? (LO2-1)

Why do nonfinancial corporations need modern financial markets and institutions? (LO2-1)

What if a corporation finances investment by retaining and reinvesting cash generated from its operations? (LO2-1)

What are the key advantages of mutual funds and pension funds? (LO2-2)

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52 Part One Introduction

Financial markets help channel savings to corporate investment, and they help match up borrowers and lenders. They provide liquidity and diversification opportunities for inves- tors. Trading in financial markets provides a wealth of useful information for the financial manager.

Financial institutions carry out a number of similar functions to financial markets but in different ways. They channel savings to corporate investment, and they serve as financial intermediaries between borrowers and lenders. Banks also provide liquidity for deposi- tors and, of course, play a special role in the economy’s payment systems. Insurance com- panies allow policyholders to pool risks.

The financial crisis of 2007–2009 provided a dramatic illustration. The huge expansion in subprime mortgage lending in the United States led to a collapse of the banking system. The government was forced into costly bailouts of banks and other financial institutions. As the credit markets seized up, the country suffered a deep recession. In much of Europe, the financial crisis did not end in 2009. As governments struggled to reduce their debt mountains and to strengthen their banking systems, many countries suffered sharp falls in economic activity and severe unemployment.

What are the functions of financial markets? (LO2-3)

Do financial institutions have different functions? (LO2-3)

What happens when financial markets and institutions no longer function well? (LO2-4)

QUESTIONS AND PROBLEMS 1. Corporate Financing. How can a small, private firm finance its capital investments? Give two

or three examples of financing sources. (LO2-1)

2. Financial Markets. The stock and bond markets are not the only financial markets. Give two or three additional examples. (LO2-1)

3. Financial Markets and Institutions. True or false? (LO2-1) a. Financing for public corporations must flow through financial markets. b. Financing for private corporations must flow through financial intermediaries. c. Almost all foreign exchange trading occurs on the floors of the FOREX exchanges in New

York and London. d. Derivative markets are a major source of finance for many corporations. e. The opportunity cost of capital is the capital outlay required to undertake a real investment

opportunity. f. The cost of capital is the interest rate paid on borrowing from a bank or other financial

institution.

4. Corporate Financing. Financial markets and intermediaries channel savings from investors to corporate investment. The savings make this journey by many different routes. Give a specific example for each of the following routes: (LO2-1) a. Investor to financial intermediary, to financial markets, and to the corporation b. Investor to financial markets, to a financial intermediary, and to the corporation c. Investor to financial markets, to a financial intermediary, back to financial markets, and to

the corporation

5. Financial Intermediaries. You are a beginning investor with only $5,000 in savings. How can you achieve a widely diversified portfolio at reasonable cost? (LO2-2)

6. Financial Intermediaries. Is an insurance company also a financial intermediary? How does the insurance company channel savings to corporate investment? (LO2-2)

7. Corporate Financing. Choose the most appropriate term to complete each sentence. (LO2-2) a. Households hold a greater percentage of (corporate equities / corporate bonds). b. (Pension funds / Banks) are major investors in corporate equities. c. (Investment banks / Commercial banks) raise money from depositors and make loans to

individuals and businesses.

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Chapter 2 Financial Markets and Institutions 53

8. Financial Markets. Which of the following are financial markets? (LO2-2) a. NASDAQ b. Vanguard Explorer Fund c. JPMorgan Chase d. Chicago Mercantile Exchange

9. Financial Intermediaries. True or false? (LO2-2) a. Exchange traded funds are hedge funds that can be bought and sold on the stock exchange. b. Hedge funds provide small investors with low-cost diversification. c. The sale of insurance policies is a source of financing for insurance companies. d. In defined-contribution pension plans, the pension pot depends on the rate of return earned

on the contributions by the employer and employee.

10. Liquidity. Securities traded in active financial markets are liquid assets. Explain why liquidity is important to individual investors and to mutual funds. (LO2-2)

11. Liquidity. Bank deposits are liquid; you can withdraw money on demand. How can the bank provide this liquidity and at the same time make illiquid loans to businesses? (LO2-2)

12. Financial Institutions. Summarize the differences between a commercial bank and an invest- ment bank. (LO2-2)

13. Mutual Funds. Why are mutual funds called financial intermediaries? Why does it make sense for an individual to invest her savings in a mutual fund rather than directly in financial markets? (LO2-2)

14. Functions of Financial Markets. Fill in the blanks in the following passage by choosing the most appropriate term from the following list: CFO, save, financial intermediaries, stock mar- ket, savings, real investment, bonds, commodity markets, mutual funds, shares, liquid, ETFs, banks. Each term should be used once only. (LO2-3) Financial markets and _____ channel _____ to _____. They also channel money from individu- als who want to _____ for the future to those who need cash to spend today. A third function of financial markets is to allow individuals and businesses to adjust their risk. For example, _____, such as the Vanguard Index fund, and _____, such as SPDRs or “spiders,” allow individuals to spread their risk across a large number of stocks. Financial markets provide other mechanisms for sharing risks. For example, a wheat farmer and a baker may use the _____ to reduce their exposure to wheat prices. Financial markets and intermediaries allow investors to turn an invest- ment into cash when needed. For example, the _____ of public companies are _____ because they are traded in huge volumes on the _____. _____ are the main providers of payment ser- vices by offering checking accounts and electronic transfers. Finally, financial markets provide information. For example, the _____ of a company that is contemplating an issue of debt can look at the yields on existing _____ to gauge how much interest the company will need to pay.

15. Financial Markets and Intermediaries. List the major functions of financial markets and intermediaries in a modern financial system. (LO2-3)

16. Functions of Financial Markets. On a mountain trek, you discover a 6-ounce gold nugget. A friend offers to pay you $2,500 for it. How do you check whether this is a fair price? (LO2-3)

17. Functions of Financial Markets. What kinds of useful information can a financial manager obtain from financial markets? Give examples. (LO2-3)

18. Functions of Financial Markets. Look back at Section 2.3 and then answer the following ques- tions: (LO2-3) a. The price of Yum! Brands stock has risen to $180. What is the market value of the firm’s

equity if the number of outstanding shares does not change? b. The rating agency has revised Catalytic Concepts’ bond rating to A. What interest rate,

approximately, would the company now need to pay on its bonds? c. A farmer and a meatpacker use the commodity markets to reduce their risk. One agrees to

buy live cattle in the future at a fixed price, and the other agrees to sell. Which one sells?

19. The Financial Crisis. True or false? (LO2-4) a. The financial crisis was largely caused by banks taking large positions in the options and

futures markets. b. The prime cause of the financial crisis was an expansion in bank lending for the overheated

commercial real estate market.

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54 Part One Introduction

c. Many subprime mortgages were packaged together by banks for resale as mortgage-backed securities (MBSs).

d. The crisis could have been much more serious if the government had not stepped in to rescue Merrill Lynch and Lehman Brothers.

e. The crisis in the eurozone finally ended when other eurozone countries and the IMF pro- vided a massive bailout package to stop Greece from defaulting on its debts.

WEB EXERCISES 1. Log on to finance.yahoo.com and use the website to update Table 2.3. Search for each firm

using its ticker symbol. You can find total market capitalization under the Statistics tab. How have market values of these companies changed?

2. Find the websites for the Vanguard Group and Fidelity Investments. Pick three or four funds from these sites and compare their investment objectives, risks, past returns, fund fees, and so on. Read the prospectuses for each fund. Who do you think should, or should not, invest in each fund?

3. Morningstar provides data on mutual fund performance. Log on to its website. Which category of funds has performed unusually well or badly?

SOLUTIONS TO SELF-TEST QUESTIONS 2.1 a. Corporations sell securities in the primary market. The securities are later traded in the

secondary market. b. The capital market is for long-term financing; the money market, for short-term

financing. c. The market for stocks versus the market for bonds and other debt securities.

2.2 Efficient diversification and professional management. Pension funds offer an additional advantage because investment returns are not taxed until withdrawn from the fund.

2.3 Mutual funds pool investor savings and invest in portfolios of traded securities. Financial institutions such as banks or insurance companies raise money in special ways, for example, by accepting deposits or selling insurance policies. They not only invest in securities but also lend directly to businesses. They provide various other financial services.

2.4 Liquidity, risk reduction by investment in diversified portfolios of securities (through a mutual fund, for example), information provided by trading.

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56

Accounting and Finance

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

3-1 Interpret the information contained in the balance sheet, income statement, and statement of cash flows.

3-2 Distinguish between market and book values.

3-3 Explain how income differs from cash flow.

3-4 Understand the essential features of the taxation of corporate and personal income.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

3

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57

P A

R T

O N

E In

tr od

uc tio

n

In Chapter 1 we pointed out that a large corporation is a team effort. All the players—the shareholders, lend-ers, directors, management, and employees—have a stake in the company’s success, and all therefore need to monitor its progress. For this reason, the company prepares regular financial accounts and arranges for an independent firm of auditors to certify that these accounts present a “true and fair view.”

Until the mid-nineteenth century, most businesses were owner-managed and seldom required outside capital beyond personal loans to the proprietor. There was little need, therefore, for firms to produce compre- hensive accounting information. But with the industrial revolution and the creation of large railroad and canal companies, the shareholders and bankers demanded information that would help them gauge a firm’s finan- cial strength. That was when the accounting profession began to come of age.

We don’t want to get lost in the details of accounting practice. But because we will refer to financial state- ments throughout this book, it may be useful to review briefly their main features. In this chapter, we introduce the major financial statements: the balance sheet, the income statement, and the statement of cash flows. We discuss the important differences between income and cash flow and between book values and market values. We also discuss the federal tax system.

This chapter is our first look at financial statements and is meant primarily to serve as a brief review of your accounting class. It will be far from our last look. For example, we will see in the next chapter how managers use financial statements to analyze a firm’s performance and assess its financial strength.

Accounting is not the same as finance, but the two are related. ©g-stockstudio/Getty Images

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58 Part One Introduction

The Balance Sheet

Public companies are obliged to file their financial statements with the SEC each quar- ter. These quarterly reports (or 10Qs) provide the investor with information about the company’s earnings during the quarter and its assets and liabilities at the end of the quarter. In addition, companies need to file annual financial statements (or 10Ks) that provide rather more detailed information about the outcome for the entire year.

The financial statements show the firm’s balance sheet, the income statement, and a statement of cash flows. We will review each in turn.1

Firms need to raise cash to pay for the many assets used in their businesses. In the process of raising that cash, they also acquire obligations or “liabilities” to those who provide the funding. The balance sheet presents a snapshot of the firm’s assets and liabilities at one particular moment. The assets—representing the uses of the funds raised—are listed on the left-hand side of the balance sheet. The liabilities— representing the sources of that funding—are listed on the right.

Some assets can be turned more easily into cash than others; these are known as liquid assets. The accountant puts the most liquid assets at the top of the list and works down to the least liquid. Look, for example, at Table 3.1, which shows the consoli- dated balance sheet for The Home Depot (HD), at the end of its 2017 fiscal year.2 (“Consolidated” simply means that the balance sheet shows the position of Home Depot and any companies it owns.) You can see that Home Depot had $3,595 million of cash and marketable securities. In addition, it had sold goods worth $1,952 million but had not yet received payment. These payments are due soon, and therefore the bal- ance sheet shows the unpaid bills or accounts receivable (or simply receivables) as a current asset. The next asset consists of inventories. These may be (1) raw materials and ingredients that the firm bought from suppliers, (2) work in progress, and (3) finished products waiting to be shipped from the warehouse. For Home Depot, inventories consist largely of goods in the warehouse or on the store shelves; for manu- facturing companies, inventories would be more skewed toward raw materials and work in progress. Of course, there are always some items that don’t fit into neat cate- gories. So there is a fourth entry, other current assets.

Up to this point, all the assets in Home Depot’s balance sheet are likely to be used or turned into cash in the near future. They are therefore described as current assets. The next assets listed in the balance sheet are longer-lived or fixed assets and include items such as buildings, equipment, and vehicles.

The balance sheet shows that the gross value of Home Depot’s property, plant, and equipment is $41,414 million. This is what the assets originally cost. But they are unlikely to be worth that now. For example, suppose the company bought a delivery van 2 years ago; that van may be worth far less now than Home Depot paid for it. It might, in principle, be possible for the accountant to estimate separately the value today of the van, but this would be costly and somewhat subjective. Accountants rely instead on rules of thumb to estimate the depreciation in the value of assets, and with rare exceptions they stick to these rules. For example, in the case of that delivery van, the accountant may deduct a third of the original cost each year to reflect its declining value. So if Home Depot bought the van 2 years ago for $15,000, the balance sheet would show that accumulated depreciation is 2 × $5,000 = $10,000. Net of deprecia- tion the value is only $5,000. Table 3.1 shows that Home Depot’s total accumulated

3.1

balance sheet Financial statement that shows the firm’s assets and liabilities at a particular time.

1 In addition, the company provides a statement of the shareholders’ equity, which shows how much of the firm’s earnings has been retained in the business rather than paid out as dividends and how much money has been raised by issuing new shares or spent by repurchasing stock. We will not review in detail the statement of shareholders’ equity. 2 Home Depot’s fiscal 2017 ended January 28, 2018. The balance sheet in Table 3.1, therefore, shows the firm’s assets and liabilities on this date. We have simplified and eliminated some of the detail in the company’s published financial statements.

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Chapter 3 Accounting and Finance 59

depreciation on fixed assets is $19,339 million. So while the assets cost $41,414 mil- lion, their net value in the accounts is only $41,414 − $19,339 = $22,075 million.

In addition to its tangible assets, Home Depot also has valuable intangible assets, such as its brand name, skilled management, and a well-trained labor force. Accoun- tants are generally reluctant to record these intangible assets in the balance sheet unless they can be readily identified and valued.

There is, however, one important exception. When Home Depot has acquired other businesses in the past, it has paid more for their assets than the value shown in the firms’ accounts. This difference is shown in Home Depot’s balance sheet as “goodwill.” Most of the intangible assets on Home Depot’s balance sheet consist of goodwill.

Now look at the right-hand portion of Home Depot’s balance sheet, which shows where the money to buy its assets came from. The accountant starts by looking at the company’s liabilities—that is, the money owed by the company. First come those liabili- ties that are likely to be paid off most rapidly. For example, Home Depot has borrowed $2,761 million, due to be repaid shortly. It also owes its suppliers $7,244 million for goods that have been delivered but not yet paid for. These unpaid bills are shown as accounts payable (or payables). Both the borrowings and the payables are debts that Home Depot must repay within the year. They are therefore classified as current liabilities.

Home Depot’s current assets total $18,933 million; its current liabilities amount to $16,194 million. Therefore, the difference between the value of Home Depot’s current assets and its current liabilities is $18,933 − $16,194 = $2,739 million. This figure is known as Home Depot’s net current assets or net working capital. It roughly measures the company’s potential reservoir of cash.

Below the current liabilities, Home Depot’s accountants have listed the firm’s long- term liabilities, such as debts that come due after the end of a year. You can see that banks and other investors have made long-term loans to Home Depot of $24,267 million.

Home Depot’s liabilities are financial obligations to various parties. For example, when Home Depot buys goods from its suppliers, it has a liability to pay for them; when it borrows from the bank, it has a liability to repay the loan. Thus, the suppliers and the bank have first claim on the firm’s assets. What is left over after the liabilities

End of Fiscal End of Fiscal

Assets 2017 2016 Liabilities and Shareholders’ Equity 2017 2016

Current assets Cash and marketable securities 3,595 2,538 Current liabilities Receivables 1,952 2,029 Debt due for repayment 2,761 1,252 Inventories 12,748 12,549 Accounts payable 7,244 7,000 Other current assets 638 608 Other current liabilities 6,189 5,881 Total current assets 18,933 17,724 Total current liabilities 16,194 14,133 Fixed assets Long-term debt 24,267 22,349 Tangible fixed assets Other long-term liabilities 2,614 2,151 Property, plant, and equipment 41,414 40,426 Less accumulated depreciation 19,339 18,512 Total liabilities 43,075 38,633 Net tangible fixed assets 22,075 21,914

Shareholders’ equity: Intangible asset (goodwill) 2,275 2,093 Common stock and other paid-in capital 9,715 9,010 Other assets 1,246 1,235 Retained earnings 39,935 35,517

Treasury stock −48,196 −40,194 Total shareholders’ equity 1,454 4,333

Total assets 44,529 42,966 Total liabilities and shareholders’ equity 44,529 42,966

Note: Column sums subject to rounding error. Source: Derived from Home Depot annual reports.

TABLE 3.1 Home Depot’s balance sheet (figures in $ millions)

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60 Part One Introduction

have been paid off belongs to the shareholders. This figure is known as the sharehold- ers’ equity. For Home Depot the total value of shareholders’ equity amounts to $1,454 million. Table 3.1 shows that Home Depot’s equity is made up of three parts. One portion, $9,715 million, has resulted from the occasional sale of new shares to investors. A much larger amount, $39,935 million, has come from earnings that Home Depot has retained and reinvested in the business on the shareholders’ behalf.3 Finally, treasury stock is a large negative number, −$48,196 million. This represents the amount that Home Depot has spent on buying back its shares. The money to repur- chase them has gone out of the firm and reduced shareholders’ equity.

Figure 3.1 shows how the separate items in the balance sheet link together. There are two classes of assets—current assets, which will soon be used or turned into cash, and long-term or “fixed” assets, which may be either tangible or intangible. There are also two classes of liability—current liabilities, which are due for payment shortly, and long-term liabilities.

The difference between the assets and the liabilities represents the amount of the shareholders’ equity. This is the basic balance sheet identity. Shareholders are some- times called “residual claimants” on the firm. We mean by this that shareholders’ equity is what is left over when the liabilities of the firm are subtracted from its assets:

Shareholders’ equity = net assets = total assets − total liabilities (3.1)

FIGURE 3.1 Assets and liabilities on the balance sheet

Current assets Cash & securities Receivables Inventories + Fixed assets Tangible assets Intangible assets

=

THE MAIN BALANCE SHEET ITEMS

Current liabilities Payables Short-term debt

+ Long-term liabilities

+ Shareholders’ equity

Suppose that Home Depot borrows $500 million by issuing new long-term bonds. It places $100 million of the proceeds in the bank and uses $400 million to buy new machinery. What items of the balance sheet would change? Would shareholders’ equity change?

Self-Test3.1

When comparing financial statements, analysts often calculate a common-size balance sheet, which re-expresses all items as a percentage of total assets. Table 3.2 is Home Depot’s common-size balance sheet. The financial manager might look at this common-size balance sheet and notice right away that while current assets in 2017 were a slightly higher proportion of assets than in the previous year, current liabilities increased by a greater proportion. Net working capital therefore declined. This is not

common-size balance sheet All items in the balance sheet are expressed as a percentage of total assets.

3 Here is an occasional source of confusion. You may be tempted to think of retained earnings as a pile of cash that the company has built up from its past operations. But there is absolutely no link between retained earnings and cash balances. The earnings that Home Depot has plowed back into the business may have been used to buy new equipment, trucks, warehouses, and so on. Typically, only a small proportion will be kept in the bank. Notice that Home Depot’s balance sheet lists $39,935 million in retained earnings but only $3,595 million in cash and marketable securities.

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Chapter 3 Accounting and Finance 61

necessarily something to worry about, but the manager might wish to check that this pattern is not likely to persist.

By the way, it is easy to obtain the financial statements of almost any publicly traded firm. Most firms make their annual reports available on the web. You also can find key financial statements of most firms at Yahoo! Finance (finance.yahoo.com) or Google Finance (finance.google.com).

Book Values and Market Values Throughout this book, we will frequently make a distinction between the book values of the assets shown in the balance sheet and their market values.

Items in the balance sheet are valued according to generally accepted accounting principles, commonly called GAAP. These state that assets must be shown in the bal- ance sheet at their historical cost adjusted for depreciation. Book values are therefore “backward-looking” measures of value. They are based on the past cost of the asset, not its current market price or value to the firm. For example, suppose that 2 years ago Home Depot built an office building for $30 million and that in today’s market the building would sell for $40 million. The book value of the building would be less than its market value, and the balance sheet would understate the value of Home Depot’s asset.

Or consider a specialized plant that Intel develops for producing special-purpose computer chips at a cost of $800 million. The book value of the plant is $800 million less accumulated depreciation. But suppose that shortly after the plant is constructed, a new chip makes the existing one obsolete. The market value of Intel’s new plant could fall by 50% or more. In this case, market value would be less than book value.

The difference between book value and market value is greater for some assets than for others. It is zero in the case of cash but potentially very large for fixed assets where the accountant starts with initial cost and then depreciates that figure according to a prespecified schedule. The purpose of depreciation is to allocate the original cost of the asset over its life, and the rules governing the depreciation of asset values do not reflect actual loss of market value. Usually the market value of fixed assets is much higher than the book value, but sometimes it is less.

generally accepted accounting principles (GAAP) U.S. procedures for preparing financial statements.

book value Net worth of the firm according to the balance sheet.

End of Fiscal End of Fiscal

Assets 2017 2016 Liabilities and Shareholders’ Equity 2017 2016

Current assets Current liabilities Cash and marketable securities 8.1% 5.9% Debt due for repayment 6.2% 2.9% Receivables 4.4% 4.7% Accounts payable 16.3% 16.3% Inventories 28.6% 29.2% Other current liabilities             13.9%    13.7% Other current assets   1.4%    1.4% Total current liabilities 36.4% 32.9% Total current assets 42.5% 41.3%

Long-term debt 54.5% 52.0% Fixed assets Other long-term liabilities             5.9%       5.0% Tangible fixed assets Property, plant, and equipment 93.0% 94.1% Total liabilities 96.7% 89.9% Less accumulated depreciation 43.4% 43.1% Net tangible fixed assets 49.6% 51.0% Shareholders’ equity:

Common stock and other paid-in capital 21.8% 21.0% Intangible asset (goodwill) 5.1% 4.9% Retained earnings 89.7% 82.7% Other assets   2.8%    2.9% Treasury stock −108.2% −93.5%

Total shareholders’ equity             3.3%    10.1% Total assets 100.0% 100.0% Total liabilities and shareholders’ equity 100.0% 100.0%

TABLE 3.2 Home Depot’s common-size balance sheet (all items expressed as a percentage of total assets)

Source: Derived from Home Depot annual reports.

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62 Part One Introduction

The same goes for the right-hand side of the balance sheet. In the case of liabilities, the accountant simply records the amount of money that you have promised to pay. For short-term liabilities, this figure is generally close to the market value of that promise. For example, if you owe the bank $1 million tomorrow, the accounts show a book lia- bility of $1 million. As long as you are not bankrupt, that $1 million is also roughly the value to the bank of your promise. But now suppose that $1 million is not due to be repaid for several years. The accounts still show a liability of $1 million, but how much your debt is worth depends on what happens to interest rates. If interest rates rise after you have issued the debt, lenders may not be prepared to pay as much as $1 million for your debt; if interest rates fall, they may be prepared to pay more than $1 million.4 Thus, the market value of a long-term liability may be higher or lower than the book value. Market values of assets and liabilities do not generally equal their book values. Book values are based on historical or original values. Market values mea- sure current values of assets and liabilities.

The difference between book value and market value is likely to be greatest for shareholders’ equity. The book value of equity measures the cash that shareholders have contributed in the past plus the cash that the company has retained and reinvested in the business on their behalf. But this often bears little resemblance to the total mar- ket value that investors place on the shares.

If the market price of the firm’s shares falls through the floor, don’t try telling the shareholders that the book value is satisfactory—they won’t want to hear. Sharehold- ers are concerned with the market value of their shares; market value, not book value, is the price at which they can sell their shares. Managers who wish to keep their share- holders happy will focus on market values.

We will often find it useful to think about the firm in terms of a market-value bal- ance sheet. Like a conventional balance sheet, a market-value balance sheet lists the firm’s assets, but it records each asset at its current market value rather than at histori- cal cost less depreciation. Similarly, each liability is shown at its market value. The difference between the market values of assets and liabilities is the market value of the shareholders’ equity claim. The stock price is simply the market value of shareholders’ equity divided by the number of outstanding shares.

market-value balance sheet Balance sheet showing market rather than book values of assets, liabilities, and stockholders’ equity.

Market- versus Book-Value Balance Sheets

Jupiter has developed a revolutionary auto production process that enables it to produce cars 20% more efficiently than any rival. It has invested $10 billion in building its new plant. To finance the investment, Jupiter borrowed $4 billion and raised the remaining funds by selling new shares of stock in the firm. There are currently 100 million shares of stock outstanding. Investors are very excited about Jupiter’s prospects. They believe that the flow of profits from the new plant justifies a stock price of $75.

If these are Jupiter’s only assets, the book-value balance sheet immediately after it has made the investment is as follows:

4 We will show you how changes in interest rates affect the market value of debt in Chapter 6.

BOOK-VALUE BALANCE SHEET FOR JUPITER MOTORS (Figures in $ billions)

Assets Liabilities and Shareholders’ Equity

Auto plant 10 Debt 4 Shareholders’ equity 6

Example 3.1 ⊲

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Chapter 3 Accounting and Finance 63

Is it surprising that market value generally exceeds book value? It shouldn’t be. Firms find it attractive to raise money to invest in various projects because they believe the projects will be worth more than they cost. Otherwise, why bother? You usually will find that shares of stock sell for more than the value shown in the company’s books.

Investors are placing a market value on Jupiter’s equity of $7.5 billion ($75 per share times 100 million shares). We assume that the debt outstanding is worth $4 billion.5 There- fore, if you owned all Jupiter’s shares and all its debt, the value of your holdings would be $7.5 + $4 = $11.5 billion. In this case, you would own the company lock, stock, and barrel and would be entitled to all its cash flows. Because you can buy the entire company for $11.5 bil- lion, the total value of Jupiter’s assets must also be $11.5 billion. In other words, the market value of the assets must be equal to the market value of the liabilities plus the market value of the shareholders’ equity.

We can now draw up the market-value balance sheet as follows:

MARKET-VALUE BALANCE SHEET FOR JUPITER MOTORS (Figures in $ billions)

Assets Liabilities and Shareholders’ Equity

Auto plant 11.5 Debt 4 Shareholders’ equity 7.5

Notice that the market value of Jupiter’s plant is $1.5 billion more than the plant cost to build. The difference is due to the superior profits that investors expect the plant to earn. Thus, in contrast to the balance sheet shown in the company’s books, the market-value balance sheet is forward-looking. It depends on the profits that investors expect the assets to provide. ■

a. What would be Jupiter’s price per share if the auto plant had a market value of $14 billion?

b. How would you reassess the value of the auto plant if the value of outstand- ing stock was $8 billion?

Self-Test3.2

The Income Statement

If Home Depot’s balance sheet resembles a snapshot of the firm at a particular time, its income statement is like a video. It shows how profitable the firm has been during the past year.

Look at the summary income statement in Table 3.3. You can see that during fiscal 2017, Home Depot sold goods worth $100,904 million and that the total cost of acquir- ing and selling those goods was $66,548 + $17,864 = $84,412 million. The largest expense item, amounting to $66,548 million, consisted of the cost of goods sold. This included the acquisition cost of Home Depot’s goods, the wages of its employees, and the other expenses incurred to obtain and sell its wares. Almost all the remaining

3.2

income statement Financial statement that shows the revenues, expenses, and net income of a firm over a period of time.

5 Jupiter has borrowed $4 billion to finance its investment, but if the interest rate has changed in the meantime, the debt could be worth more or less than $4 billion.

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64 Part One Introduction

expenses were administrative expenses such as head office costs, advertising, and distribution.

In addition to these out-of-pocket expenses, Home Depot also made a deduction for the value of the plant and equipment used up in producing the goods. In 2017, this charge for depreciation was $1,811 million. Thus, Home Depot’s earnings before interest and taxes (EBIT) were

EBIT = total revenues − costs − depreciation = 100,904 − (66,548 + 17,864) − 1,811 = $14,681 million

The remainder of the income statement shows where these earnings went. As we saw earlier, Home Depot has partly financed its investment in plant and equipment by borrowing. In 2017, it paid $983 million of interest on this borrowing. A further slice of the profit went to the government in the form of taxes. This amounted to $5,068 million. The $8,630 million that was left over after paying interest and taxes belonged to the shareholders. Of this sum, Home Depot paid out $4,212 million in dividends and reinvested the remaining $4,418 million in the business. Presumably, these reinvested funds made the company more valuable.

The $4,418 million of earnings that Home Depot reinvested in the firm show up on its balance sheet as an increase in retained earnings. Notice that retained earnings in Table 3.1 increased by $4,418 million in 2017, from $35,517 million to $39,935 mil- lion. However, shareholders’ equity fell during the year because Home Depot also repurchased some of its stock.

Just as it is sometimes useful to prepare a common-size balance sheet, we also can prepare a common-size income statement. In this case, all items are expressed as a percentage of revenues. The last column of Table 3.3 is Home Depot’s common-size income statement. You can see, for example, that the cost of goods sold consumed 66.0% of revenues and that selling, general, and administrative expenses absorbed a further 17.7%.

Income versus Cash Flow It is important to distinguish between Home Depot’s income and the cash that the company generated. Here are two reasons that income and cash are not the same:

1. Depreciation. When Home Depot’s accountants prepare the income statement, they do not simply count the cash coming in and the cash going out. Instead, the accountant starts with the cash payments but then divides these payments into two groups—current expenditures (such as wages) and capital expenditures (such as the

common-size income statement All items on the income statement are expressed as a percentage of revenues.

TABLE 3.3 Home Depot’s income statement, fiscal 2017

$ Million % of Sales

Net sales 100,904 100.0% Cost of goods sold 66,548 66.0% Selling, general & administrative expenses 17,864 17.7% Depreciation 1,811 1.8% Earnings before interest and income taxes (EBIT) 14,681 14.5% Interest expense 983 1.0% Taxable income 13,698 13.6% Taxes 5,068 5.0% Net income 8,630 8.6% Allocation of net income Dividends 4,212 4.2% Addition to retained earnings 4,418 4.4%

Source: Derived from Home Depot annual reports.

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Chapter 3 Accounting and Finance 65

purchase of new machinery). Current expenditures are deducted from current profits. However, rather than deducting the cost of long-lived machinery in the year it is purchased, the accountant spreads its acquisition cost over its forecasted life by making an annual charge for depreciation. 

Thus, when calculating profits, the accountant does not deduct the expenditure on new equipment that year, even though cash is paid out. However, the accountant does deduct depreciation on assets previously purchased, even though no cash is currently paid out. For example, suppose a $100,000 investment is depreciated by $10,000 a year for 10 years.6 This depreciation is treated as an annual expense, although the cash actually went out of the door when the asset was first purchased. For this reason, the deduction for depreciation is classified as a noncash expense.

To calculate the cash produced by the business, it is necessary to add the depreciation charge (which is not a cash payment) back to accounting profits and to subtract the expenditure on new capital equipment (which is a cash payment).

2. Cash versus accrual accounting. Consider a manufacturer that spends $60 to produce goods in period 1. In period 2 it sells these goods for $100, but its customers pay their bills with a delay, so payment is not received until period 3. The following diagram shows the firm’s cash flows. In period 1 there is a cash outflow of $60. Then, when customers pay their bills in period 3, there is an inflow of $100.

+$100 (collect payment)

-$60 (pay for goods)

1 2 3 Period

It would be misleading to say that the firm was running at a loss in period 1 (when cash flow was negative) or that it was extremely profitable in period 3 (when cash flow was positive). Therefore, to construct the income statement, the accountant looks at when the sale was made (period 2 in our example) and gathers together all the revenues and expenses associated with that sale. For our company, the income statement would show:

Revenue $100 Less cost of goods sold 60 Profit $ 40

This practice of matching revenues and expenses is known as accrual accounting. Of course, the accountant does not ignore the actual timing of the cash expenditures and payments. So the cash outlay in the first period will be treated not as an expense but as an investment in inventories. Subsequently, in period 2, when the goods are taken out of inventory and sold, the accountant shows a reduction in inventories.

To go from the cost of goods sold in the income statement to the cash outflows, we need to subtract the investment in inventories that is shown in the balance sheet:

Period: 1 2

Cost of goods sold (income statement) 0 60 + Investment in inventories (balance sheet) 60 −60 = Cash paid out 60 0

6 In the United States, firms may maintain two sets of accounts, one for reporting and one for taxes. While recent changes to tax law allow most investments to be depreciated or “expensed” immediately, financial reports will typically spread the cost of acquisition out over several years.

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66 Part One Introduction

The accountant also does not ignore the fact that the firm has to wait until period 3 to collect its bills. When the sale is made in period 2, the figure for accounts receivable in the balance sheet is increased to show that the company’s customers owe an extra $100 in unpaid bills. Later, when the customers pay those bills in period 3, accounts receivable are reduced by $100. Therefore, to go from the sales shown in the income statement to the cash inflows, we need to subtract the investment in receivables:

Period: 2 3

Sales (income statement) 100 0 − Investment in receivables (balance sheet) 100 −100 = Cash received 0 +100

We will return to these issues in more detail in Chapter 9, but for now we summarize the key points as follows: Cash outflow is equal to the cost of goods sold, which is shown in the income statement, plus the change in inventories. Cash inflow is equal to the sales shown in the income statement less the change in uncollected bills.

Profits versus Cash Flows

Suppose our manufacturer spends a further $80 to produce goods in period 2. It sells these goods in period 3 for $120, but customers do not pay their bills until period 4.

The cash flows from these transactions are now as follows:

$100 (collect payment)

$120 (collect further payment)

-$60 (pay for goods) -$80

(pay for more goods)

1 2 3 4 Period

Example 3.2 ⊲

How do the new transactions affect the income statement and the balance sheet? The income statement will match costs with revenues and record the cost of goods sold when the sales are made in periods 1 and 2. The difference between the costs shown in the income statement and the cash flows is recorded as an investment (and later, disinvestment) in inventories. Thus, in period 1 the accountant shows an investment in inventories of $60 just as before. In period 2, these goods are taken out of inventory and sold, but the firm also produces a further $80 of goods. Thus, there is a net increase in inventories of $20. As these goods in turn are sold in period 3, inventories are reduced by $80. The following table con- firms that the cash outflow in each period is equal to the cost of goods sold that is shown in the income statement plus the change in inventories.

Period: 1 2 3

Cost of goods sold (income statement) 0 60 80 + Investment in inventories (balance sheet) 60 −60 + 80 = 20 −80 = Cash paid out 60 80 0

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Chapter 3 Accounting and Finance 67

The Statement of Cash Flows

The firm requires cash when it buys new plant and machinery or when it pays interest to the bank and dividends to the shareholders. Therefore, the financial manager needs to keep track of the cash that is coming in and going out.

We have seen that the firm’s cash flow can be quite different from its net income. These differences can arise for at least two reasons:

1. The income statement does not recognize capital expenditures as expenses in the year that the capital goods are paid for. Instead, it spreads those expenses over time in the form of an annual deduction for depreciation.

2. The income statement uses the accrual method of accounting, which means that revenues and expenses are recognized when sales are made, rather than when the cash is received or paid out.

The statement of cash flows shows the firm’s cash inflows and outflows from opera- tions as well as from its investments and financing activities. Table 3.4 is the cash-flow statement for Home Depot. It contains three sections. The first shows the cash flow from operations. This is the cash generated from Home Depot’s normal business activities. Next comes the cash that Home Depot has invested in plant and equipment or in the acquisition of new businesses. The final section reports cash flows from financing activ- ities such as the sale of new debt or stock. We will look at each of these sections in turn.

The first section, cash flow from operations, starts with net income but adjusts that figure for those parts of the income statement that do not involve cash coming in or going out. Therefore, it adds back the allowance for depreciation because depreciation is not a cash outflow, even though it is treated as an expense in the income statement. Similarly, employee stock compensation is considered an expense, but because it is paid in shares in the firm, it does not represent a cash outflow.

Any additions to current assets (other than cash itself) need to be subtracted from net income because these absorb cash but do not show up in the income statement.

3.3

statement of cash flows Financial statement that shows the firm’s cash receipts and cash payments over a period of time.

The following table provides a similar reconciliation of the difference between the reve- nues shown in the income statement and the cash inflow:

Period: 2 3 4

Sales (income statement) 100 120 0 − Investment in receivables (balance sheet) 100 −100 + 120 = 20 −120 = Cash received 0 +100 +120

In the income statement, the accountant records sales of $100 in period 1 and $120 in period 2. The fact that the firm has to wait for payment is recognized in the balance sheet as an investment in receivables. The cash that the company receives is equal to the sales shown in the income statement less the investment in receivables. ■

Consider a firm that spends $200 to produce goods in period 1. In period 2, it sells half of those goods for $150, but it doesn’t collect payment until one period later. In period 3, it sells the other half of the goods for $150, and it collects payment on these sales in period 4. Calculate the profits and the cash flows for this firm in periods 1 to 4.

Self-Test3.3

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68 Part One Introduction

Conversely, any additions to current liabilities need to be added to net income because these release cash. For example, you can see that over the year the company spent $84 million building up its inventories. On the other hand, it freed up $352 million of cash by deferring payment to its own suppliers, as reflected in the increase in its accounts payable. After making these adjustments, Home Depot’s operations contrib- uted $12,031 to its cash holdings.

The second section of the cash-flow statement shows the cash expenditures on capi- tal equipment. The net expenditure on such investments was $2,228.

The third section shows the cash flows from financing activity. Home Depot raised over $3 billion of cash in the form of long- and short-term debt, but it paid out nearly $12 billion to shareholders in the form of dividends and stock repurchases.7

The total effect of these activities was to increase Home Depot’s holdings of cash and short-term investments by $933 billion:

In Millions

Cash flow from operations $12,031

− Cash flow for new investment −2,228 + Cash provided by new financing   −8,870 = Change in cash balance $     933

TABLE 3.4 Home Depot’s statement of cash flows (figures in $ millions)

Cash Provided by Operations:

Net income 8,630 Depreciation plus amortization 2,062 Changes in working capital items Decrease (increase) in accounts receivable 139 Decrease (increase) in inventories −84 Decrease (increase) in other current assets −10 Increase (decrease) in accounts payable 352 Increase (decrease) in other current liabilities 669 Total decrease (increase) in working capital 1,066 Stock-based compensation expense 273 Cash provided by operations 12,031

Cash Flows from Investments:

Capital expenditure −1,897 Sales (acquisitions) of long-term assets 47 Other investing activities −378 Cash provided by (used for) investments −2,228

Cash Provided for (used by) Financing Activities:

Increase (decrease) in short-term debt 850 Increase (decrease) in long-term debt 2,448 Dividends −4,212 Repurchases of stock −7,745 Other −211 Cash provided by (used for) financing activities −8,870 Net increase (decrease) in cash and cash equivalents 933

Source: Calculated from data in Tables 3.1 and 3.3.

7 You might think that interest payments also ought to be listed in this section. However, it is usual to include interest in the first section with cash flow from operations. This is because, unlike dividends, interest payments are not discretionary. The firm must pay interest when a payment comes due, so these payments are treated as a business expense rather than as a financing decision.

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Chapter 3 Accounting and Finance 69

Now here is a matter that may have been puzzling you. The cash-flow statement shows that Home Depot raised $139 million of cash by collecting unpaid bills from its customers. However, the balance sheet in Table 3.1 showed that receivables fell by only $77 million (from $2,029 to $1,952 million). Indeed, when you compare the changes shown in the balance sheet with the cash flows reported in the cash-flow statement, there are several other apparent discrepancies. For example, the cash-flow statement shows that inventories increased by $84 million, whereas the balance sheet shows that they rose by $199 million. There are several reasons for this, but the princi- pal one is that Home Depot made two important business acquisitions during the year. The 2017 balance sheet adds in the assets and liabilities of these businesses and there- fore the changes in the items shown in the balance sheet do not necessarily represent a source or use of cash. To understand the movements of cash, you need to look at the company’s statement of cash flows.

Would the following activities increase or decrease the firm’s cash balance?

a. Inventories are increased.   b. The firm reduces its accounts payable.   c. The firm issues additional common stock.   d. The firm buys new equipment.

Self-Test3.4

Free Cash Flow The value of a company depends on how much cash it can generate for all investors, both debt and equity investors, after paying for any new capital investments. This is called the company’s free cash flow. There are three elements to free cash flow. The first is the interest paid to holders of the company’s debt. The second is the cash available to the shareholders, which is the company’s operating cash flow. From these first two elements, we subtract the cash necessary to pay for new investments.

To calculate operating cash flow, we start with the company’s net income, but then we adjust that figure for those parts of the income statement that do not involve cash coming in or going out. That involves adding back depreciation (which is not a cash outflow) and adjusting for changes in working capital that absorb cash but do not show up in the income statement. The operating cash flow is not all available to be paid out to investors, for the company needs some of that cash to pay for new capital expendi- tures. So the capital that is free to be distributed is

Free cash flow = interest payments to debt investors + shareholders’ operating cash flow − capital expenditures

free cash flow (FCF) Cash flow available for distribution to investors after firm pays for new investments or additions to working capital.

Free Cash Flow for Home Depot

Let’s use Home Depot’s income and cash-flow statements to calculate its free cash flow in 2017. We start with debt interest. The income statement in Table 3.3 tells us that in 2017 the company paid out $983 million in interest to its debtholders.

The second step is to calculate the operating cash flow generated for the shareholders. We worked through these calculations when we set out Home Depot’s statement of cash flows in Table 3.4, so we won’t repeat those calculations here. Table 3.4 showed that in 2017 Home Depot’s operating cash flow was $12,031.

Example 3.3 ⊲

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70 Part One Introduction

Accounting Practice and Malpractice

Managers of public companies face constant scrutiny. Much of that scrutiny focuses on earnings. Security analysts forecast earnings per share, and investors then wait to see whether the company can meet or beat the forecasts. A shortfall, even if it is only a cent or two, can be a big disappointment. Investors might judge that if you could not find that extra cent or two of earnings, the firm must be in a really bad way.

Managers complain about this pressure, but do they do anything about it? Unfortu- nately, the answer appears to be yes, according to Graham, Harvey, and Rajgopal, who surveyed about 400 senior managers.11 Most of the managers said that accounting earnings were the single most important number reported to investors. Most admitted to adjusting their firms’ operations and investments to produce the earnings that inves- tors were looking for. For example, 80% were prepared to decrease discretionary spending on R&D, advertising, or plant maintenance to meet earnings targets.

Of course, managers may not need to adjust the firm’s operations if they can instead adjust their accounting methods. U.S. accounting rules are spelled out by the Financial Accounting Standards Board (FASB) and its generally accepted accounting principles

3.4

Finally, we need to subtract the cash that Home Depot spent on new capital investment. The statement of cash flows in Table 3.4 shows that this amounted to $2,228. Thus, the company’s free cash flow in 2017 was

Free cash flow = interest payments + operating cash flow − capital expenditures = $983 + $12,031 − $2,228 = $10,786 million

Notice that free cash flow differs from the addition-to-cash balances found in the state- ment of cash flows (Table 3.4). First, when we calculate free cash flow, we ignore altogether items in the last panel of Table 3.4, “Cash provided by financing activities.”8 This is because free cash flow measures how much cash the company’s operations generate for possible distribution to investors. The available amount should not be confused with the amount that the company actually raised by financing activities. Second, we add back interest payments when computing free cash flow, as those payments are part of the distributions made to investors.9

It is often useful to ask what Home Depot’s free cash flow would have been if the com- pany had been financed entirely by equity. In that case, all the free cash flow would belong to the shareholders. However, if Home Depot had no longer paid out $983 million as inter- est, pretax income would have increased by that amount, and the company would have paid an additional .35 × 983 = $344 million in tax.10 Thus, if the company had been financed solely by equity, free cash flow would have been $10,786 − $344 = $10,442 million. ■

8 For this reason, when we calculated cash flow from operations, we ignored the change in holdings of short- term debt, even though that debt is listed under current liabilities. We were interested only in the items of working capital that arose from the firm’s operations. 9 We can check the logic linking free cash flow to the statement of cash flows as follows:

Increase in cash balance (from Table 3.4) $ 933 + Cash used for financing activities (from Table 3.4) 8,870 + Interest payments 983 Free cash flow $10,786

10 The U.S. corporate tax rate in 2017 was 35%, so for every dollar of interest that HD paid, its taxable income fell by $1 and taxes fell by $.35. The corporate tax rate today is only 21%. 11 J. R. Graham, C. R. Harvey, and S. Rajgopal, “The Economic Implications of Corporate Financial Reporting,” Journal of Accounting and Economics 40 (2005), pp. 3–73.

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Chapter 3 Accounting and Finance 71

(GAAP). Yet, inevitably, rules and principles leave room for discretion, and managers under pressure to perform are tempted to take advantage of this leeway to satisfy inves- tors. Investors worry about the fact that some companies seem particularly prone to inflate their earnings by playing fast and loose with accounting practice. They refer to such companies as having “low-quality” earnings, and they place a correspondingly lower value on the firms’ stock.

Here are some examples of ambiguities in accounting rules that have been used by companies to conceal unflattering information:

∙ Revenue recognition. As we saw earlier, firms record a sale when it is made, not when the customer actually pays. But the date of sale is not always obvious. Suppose it is November and you are concerned that if your firm does not meet its sales target, you can forget about your annual bonus. You contact your main customers, and they agree to increase their December orders as long as they have the right to return any unsold goods. Your firm then books these shipments as “sales,” even though there is a high likelihood that many of the goods will be returned. That is almost certainly illegal and will get you into serious trouble. But suppose instead that you tell your customers that the price of your product may rise in the new year and suggest that they place an extra order in December. This practice, known as “channel stuffing,” increases this year’s sales at the expense of next year’s sales.

Many companies have been thought to use channel stuffing to overstate their earnings, but very blatant instances are liable to attract the SEC’s attention. For example, in 2002 the pharmaceutical giant Bristol Myers Squibb disclosed that wholesalers were holding hundreds of millions of dollars in excessive inventories of its products and the company’s earnings for 2002 might be just half of its 2001 earnings as wholesalers worked down these inventories. Following an investigation by the SEC, the company agreed to pay $150 million to settle accusations that this channel stuffing had improperly inflated its sales and earnings. In Chapter 1, we mentioned Hewlett-Packard’s disastrous acquisition of the British company Autonomy. Hewlett-Packard paid $11.1 billion for Autonomy. Just over a year later, it wrote down the value of the company by $8.8 billion, alleging that Autonomy had used channel stuffing to greatly inflate its revenues.

∙ Cookie-jar reserves. The giant mortgage-pass-through firm Freddie Mac earned the Wall Street nickname “Steady Freddie” for its unusually smooth and predictable pattern of earnings growth, at least until 2008 when it suddenly collapsed in the wake of the meltdown in subprime mortgages. Unfortunately, it emerged in 2003 that Freddie achieved this predictability in part by misusing its reserve accounts. Normally, such accounts are intended to allow for the likely impact of events that might reduce earnings, such as the failure of customers to pay their bills. But Freddie seemed to “overreserve” against such contingencies so that it could “release” those reserves and bolster income in a bad year. Its steady growth was largely a matter of earnings management.

∙ Off–balance sheet assets and liabilities. Before its bankruptcy in 2001 (at that time, the second largest in U.S. history), Enron had accumulated large debts and had also guaranteed the debts of other companies in which it had an ownership stake. To present a fair view of the firm, Enron should have recognized these potential liabilities on its balance sheet. But the firm created and placed paper firms— so-called special-purpose entities (SPEs)—in the middle of its transactions and excluded these liabilities from its financial statements.

The collapse of Enron illustrates how dishonest managers with creamy compensa- tion packages may be tempted to conceal the truth from investors. If the company had been more transparent to outsiders—that is, if they could have assessed its true profit- ability and prospects—its problems would have shown up right away in a falling stock price. This in turn would have generated extra scrutiny from security analysts, bond rating agencies, lenders, and investors.

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72

With transparency, corporate troubles generally lead to corrective action. But the top management of a troubled and opaque company may be able to maintain its stock price and postpone the discipline of the market. Market discipline caught up with Enron only a month or two before bankruptcy.

Enron was not the only company to be mired in accounting scandals in the early years of the century. Firms such as Global Crossing, Qwest Communications, and WorldCom misstated profits by billions of dollars. Overseas, the Italian dairy com- pany Parmalat falsified the existence of a bank account to the tune of $5.5 billion, and the French media and entertainment company Vivendi came close to bankruptcy after it was accused of accounting fraud. In response to these scandals, Congress passed the Sarbanes-Oxley Act, widely known as SOX. A major goal of SOX is to increase transparency and ensure that companies and their accountants provide directors, lenders, and shareholders with the information they need to monitor progress.

SOX created the Public Company Accounting Oversight Board (PCAOB) to over- see the auditing of public companies; it banned accounting firms from offering other services to companies whose accounts they audit; it prohibited any individual from heading a firm’s audit for more than 5 years; and it required that the board’s audit committee consist of directors who are independent of the company’s management. Sarbanes-Oxley also required that management certify that the financial statements present a fair view of the firm’s financial position and demonstrate that the firm has adequate controls and procedures for financial reporting. All this has come at a price. Managers and investors worry that the costs of SOX and the burden of meeting detailed, inflexible regulations are pushing some corporations to return from public to private ownership. Some blame SOX and onerous regulation in the United States for the fact that an increasing number of foreign companies have chosen to list their shares in London rather than New York.

There is also a vigorous debate over “rules-based” versus “principles-based” ap- proaches to accounting standards. The United States follows a rules-based approach, with detailed rules governing virtually every circumstance that possibly can be anticipated. In contrast, the European Union takes a principles-based approach

This shift from GAAP to IFRS would involve a major change in the way that accountants in the United States approach their task. IFRS tend to be “principles-based,” which means that there are no hard-and-fast codes to follow. Instead, com- panies must be ready to defend their accounting practices in light of the general principles laid out in the IFRS. By contrast, in the United States, GAAP are accompanied by thousands of pages of prescriptive regulatory guidance and interpretations from auditors and accounting groups. For example, more than 160 pieces of authoritative literature relate to how and when companies record revenue. This leaves less room for judgment, but detailed rules rapidly become out of date, and unscrupulous companies have been able to structure trans- actions so that they keep to the letter but not the spirit of the rules.

By 2014, it had become clear that the SEC’s plan to move to IFRS was effectively dead and that, while the SEC and IASB would continue to collaborate on accounting rules, there was little prospect of any agreement over a single global standard that included the United States.

The International Financial Reporting Standards (IFRS), which are set by the London-based International Accounting Stan- dards Board (IASB), aim to harmonize financial reporting around the world. They are the basis for reporting by listed firms throughout the European Union. In addition, some 100 other countries, such as Australia, Canada, Brazil, and India, have adopted them or plan to do so, while China has modi- fied its accounting standards to be largely in line with IFRS.

For some years, the SEC has worked to bring U.S. account- ing standards more in line with international rules. For exam- ple, until 2007 foreign companies that traded on U.S. stock exchanges were required to show how their accounts dif- fered from U.S. GAAP. This was a very expensive exercise that cost some companies millions of dollars annually and caused many to delist their stocks. These companies can now simply report results using international accounting stan- dards. Subsequently, in August 2008, the SEC released its plans to allow some large U.S. multinationals, representing approximately $2.5 trillion in market capitalization, to eventu- ally use IFRS for financial statements.

Finance in Practice The Rise and Stall of Convergence in Accounting Standards

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Chapter 3 Accounting and Finance 73

to accounting. Its International Financial Reporting Standards set out general ap- proaches that financial statements should take to valuing assets. Europe and the United States have been engaged for years in attempts to coordinate their systems, and many in the United States have lobbied for the greater simplicity that principles- based accounting standards might offer. The nearby box reports on these efforts.

Taxes

Taxes often have a major effect on financial decisions. Therefore, we should explain how corporations and investors are taxed.

Corporate Tax Companies pay tax on their income. The U.S. Tax Cuts and Jobs Act, passed in December 2017, reduced the corporate tax rate from 35% to 21%. Thus, for every $100 that the company earns, it pays $21 in federal tax.12

When firms calculate taxable income, they are allowed to deduct expenses. These expenses include an allowance for depreciation. The new tax law allows companies to take bonus depreciation sufficient to write off 100% of investment immediately.13 With 100% bonus depreciation, the firm can treat investments in plant and equipment as immediate expenses. Bonus depreciation is a temporary provision, however. It is scheduled for phase-out starting in 2023. By 2027, it will be gone.

The company is also allowed to deduct interest paid to debtholders when calculat- ing its taxable income, but dividends paid to shareholders are not deductible. These dividends are therefore paid out of after-tax income. Table 3.5 provides an example of how interest payments reduce corporate taxes. Although EBIT for both firms A and B is $100 million, firm A, which has $40 million of interest expense, has lower pretax income and therefore pays less taxes.

The bad news about taxes is that each extra dollar of revenue increases taxable income by $1 and results in 21 cents of extra taxes. The good news is that each extra dollar of expense reduces taxable income by $1 and therefore reduces taxes by 21 cents. For example, if the firm borrows money, every dollar of interest it pays on the loan reduces taxes by 21 cents. Therefore, a dollar of interest reduces after-tax income by only 79 cents.

3.5

TABLE 3.5 Firms A and B both have earnings before interest and taxes (EBIT) of $100 million, but A pays out part of its profits as debt interest. This reduces the corporate tax paid by A.

Firm A Firm B

EBIT $100 $100 Interest  40   0 Pretax income $ 60 $100 Tax (21% of pretax income) 12.6   21 Net income $47.4 $  79

Note: Figures in millions of dollars.

12 In addition, most states also impose corporate taxes, which range from 3 percent in North Carolina to 12 percent in Iowa. For simplicity, we will ignore these. 13 Companies are allowed to maintain separate accounts for tax and reporting purposes, and are not obliged to show 100% deprecation in their income statement. Instead they usually write off a constant proportion of the investment over its forecast life. If the company assumes a slower rate of depreciation in its income statement, the tax charge shown in the income statement will be higher in the early years of an asset’s life than the actual tax payment. This difference is recorded in the balance sheet as a liability for deferred tax.

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74 Part One Introduction

Recalculate the figures in Table 3.5, assuming that firm A now has to make inter- est payments of $60 million. What happens to taxes paid? Does net income fall by the additional $20 million interest payment compared with the case consid- ered in Table 3.5, where interest expense was only $40 million?

Self-Test3.5

When firms make profits, they pay 21% of the profits to the Internal Revenue Service. But the process doesn’t work in reverse; if the firm suffers a loss, the IRS does not send it a check for 21% of the loss. However, the firm can carry the losses forward, using the losses to offset up to 80% of future years’ income. Suppose, for example, that a manufacturer of gargle blasters loses $100,000 in 2018 but earns $100,000 in 2019 and 2020. It pays no tax in 2018, but carries forward the loss. In 2019, it uses $80,000 of the loss to offset income, paying tax of $4,200 (21% of $20,000). In 2020, it uses the remaining $20,000 carried forward, paying tax of $16,800 (21% of $80,000).

Personal Tax Table 3.6 shows the U.S. rates of personal tax. Notice that as income increases, the tax rate also increases. Notice also that the top personal tax rate is higher than the top cor- porate rate.

The tax rates presented in Table 3.6 are marginal tax rates. The marginal tax rate is the tax that the individual pays on each extra dollar of income. For example, as a single taxpayer, you would pay 10 cents of tax on each extra dollar you earn when your income is below $9,525, but once income exceeds $9,525, you would pay 12 cents of tax on each extra dollar of income up to an income of $38,700. If your total income is

marginal tax rate Additional taxes owed per dollar of additional income.

Taxable Income ($)

Single Taxpayers Married Taxpayers Filing Joint Returns Tax Rate (%)

$0−$9,525 $0−$19,050 10

$9,526−$38,700 $19,051−$77,400 12 $38,701−$82,500 $77,401−$165,000 22 $82,501−$157,500 $165,001−$315,000 24

$157,501−$200,000 $315,001−$400,000 32 $200,001–$500,000 $400,001−$600,000 35 $500,001 and above $600,001 and above 37

TABLE 3.6 Personal tax rates, 2018

Taxable Income (dollars)

Single Taxpayers Married Taxpayers Filing Joint Returns Tax Rate

0−38,600 0−77,200 0.0%

38,601−425,800   77,201−479,000 15.0% 425,801 and above 479,001 and above 20.0%

TABLE 3.7 Tax rates on investment income for various levels of taxable income, 2018*

*These rates apply to capital gains and dividends on assets held for at least one year. In addition to these nominal rates, an additional 3.8% surtax is assessed on net investment income for taxpayers with total income over $200,000 (single filers) or $250,000 (married filing jointly).

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Chapter 3 Accounting and Finance 75

The tax rates in Table 3.6 apply to “ordinary income,” primarily income earned as salary or wages. Interest earnings also are treated as ordinary income.

The U.S. government also taxes investment earnings, for example, dividends or capital gains. The treatment of dividend income in the United States leads to what is commonly dubbed the “double taxation” of corporate earnings. Each dollar the company earns is taxed at the corporate rate. Then, if the company pays a dividend out of this after-tax income, the shareholder pays personal income taxes on the distribu- tion. The original earnings are taxed first as corporate income and again as dividend income. Suppose instead that the company earns a dollar that is paid out as interest. The dollar escapes corporate tax because the interest payment is considered a business expense that reduces the firm’s taxable income.

Capital gains are also taxed, but only when the gains are realized. Suppose that you bought Bio-technics stock when it was selling for 10 cents a share. Its market price today is $1 a share. As long as you hold on to your stock, there is no tax to pay on your gain. But if you sell, the 90 cents of capital gain is taxed. 

Table 3.7 shows tax rates on investment income. In addition many high-income investors will be subject to a 3.8% Medicare surtax on their investment income, so these investors pay an effective rate of 23.8%.

Financial managers need to worry about the tax treatment of investment income because tax policy will affect the prices individuals are willing to pay for the company’s stock or bonds. We will return to these issues in Part 5 of the text.

The tax rates in Table 3.6 and Table 3.7 apply to individuals. But financial institu- tions are major investors in corporate securities. These institutions often have special tax provisions. For example, pension funds are not taxed on interest or dividend income or on capital gains.

What are the average and marginal tax rates for a single taxpayer with a taxable income of $80,000? What are the average and marginal tax rates for married taxpayers filing joint returns if their joint taxable income is also $80,000?

Self-Test3.6 BEYOND THE PAGE

mhhe.com/brealey10e

Average and marginal tax rates

SUMMARY Investors and other stakeholders in the firm need regular financial information to help them monitor the firm’s progress. Accountants summarize this information in a balance sheet, income statement, and statement of cash flows.

The balance sheet provides a snapshot of the firm’s assets and liabilities. The assets consist of current assets that can be rapidly turned into cash and fixed assets such as plant and machinery. The liabilities consist of current liabilities that are due for payment within

What information is contained in the balance sheet, income statement, and statement of cash flows? (LO3-1)

$50,000, your tax bill is 10% of the first $9,525 of income, 12% of the next $29,175 (i.e., 38,700 − 9,525), and 22% of the remaining $11,300:

Tax = (.10 × $9,525) + (.12 × $29,175) + (.22 × $11,300) = $6,939.50

The average tax rate is simply the total tax bill divided by total income. In this example it is $6,939.50/$50,000 = .139, or 13.9%. Notice that the average rate is lower than the marginal rate. This is because of the lower rates on the first $38,700 of income.

average tax rate Total taxes owed divided by total income.

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76 Part One Introduction

a year and long-term debts. The difference between the assets and the liabilities represents the amount of the shareholders’ equity.

The income statement measures the profitability of the company during the year. It shows the difference between revenues and expenses.

The statement of cash flows measures the sources and uses of cash during the year. The change in the company’s cash balance is the difference between sources and uses.

It is important to distinguish between the book values that are shown in the company accounts and the market values of the assets and liabilities. Book values are historical measures based on the original cost of an asset. For example, the assets in the balance sheet are shown at their historical cost less an allowance for depreciation. Similarly, the figure for shareholders’ equity measures the cash that shareholders have contributed in the past or that the company has reinvested on their behalf. In contrast, market value is the current price of an asset or liability.

Income is not the same as cash flow. There are two reasons for this: (1) On the reported income statement, investment in fixed assets is not deducted immediately from income but is instead spread (as charges for depreciation) over the expected life of the equipment, and (2) the accountant records revenues when the sale is made, rather than when the customer actually pays the bill, and at the same time deducts the production costs even though those costs may have been incurred earlier.

For corporations, the marginal rate of tax on income is 21%. In calculating taxable income, the company deducts an allowance for depreciation and interest payments. It can- not deduct dividend payments to the shareholders.

Individuals are also taxed on their income, which includes dividends and interest on their investments. Capital gains are taxed, but only when the investment is sold and the gain realized.

What is the difference between market and book values? (LO3-2)

Why does accounting income differ from cash flow? (LO3-3)

What are the essential features of the taxation of corporate and personal income? (LO3-4)

LISTING OF EQUATION

3.1 Shareholders’ equity = net assets = total assets − total liabilities

QUESTIONS AND PROBLEMS 1. Financial Statements. Earlier in the chapter, we characterized the balance sheet as providing

a snapshot of the firm at one point in time and the income statement as providing a video. What did we mean by this? Is the statement of cash flow more like a snapshot or a video? (LO3-1)

2. Balance Sheet. Balance sheet items are usually entered in order of declining liquidity. Place each of the terms below in the appropriate place in the following balance sheet. (LO3-1)

Accounts payable Total current assets Net fixed assets Accounts receivable Debt due for repayment Total current liabilities Cash and marketable securities Inventories Equity Long-term debt

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Chapter 3 Accounting and Finance 77

3. Balance Sheet. Construct a balance sheet for Sophie’s Sofas given the following data. What is shareholders’ equity? (LO3-1) Cash balances = $10,000 Inventory of sofas = $200,000 Store and property = $100,000 Accounts receivable = $22,000 Accounts payable = $17,000 Long-term debt = $170,000

4. Income Statement. A firm’s income statement included the following data. The firm’s average tax rate was 20%. (LO3-1)

Assets Liabilities and Equity

a. f. b. g. c. h. d. i. e.  j.

Total assets Total liabilities and equity

Cost of goods sold $8,000 Income taxes paid $2,000 Administrative expenses $3,000 Interest expense $1,000 Depreciation $1,000 a. What was the firm’s net income? b. What must have been the firm’s revenues? c. What was EBIT?

5. Balance Sheet/Income Statement. The year-end 2018 balance sheet of Brandex Inc. listed common stock and other paid-in capital at $1,100,000 and retained earnings at $3,400,000. The next year, retained earnings were listed at $3,700,000. The firm’s net income in 2019 was $900,000. There were no stock repurchases during the year. What were the dividends paid by the firm in 2019? (LO3-1)

6. Financial Statements. South Sea Baubles has the following (incomplete) balance sheet and income statement. (LO3-1, LO3-4)

INCOME STATEMENT, 2019 (Figures in $ millions)

Revenue $1,950 Cost of goods sold 1,030 Depreciation 350 Interest expense 240

BALANCE SHEET AT END OF YEAR (Figures in $ millions)

Assets 2018 2019 Liabilities and Shareholders’ Equity 2018 2019

Current assets $  90 $140 Current liabilities $  50 $  60 Net fixed assets 800 900 Long-term debt 600 750

a. What is shareholders’ equity in 2018? b. What is shareholders’ equity in 2019? c. What is net working capital in 2018?  d. What is net working capital in 2019? e. What are taxes paid in 2019? Assume the firm pays taxes equal to 21% of taxable income.

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78 Part One Introduction

f. What is cash provided by operations during 2019? Pay attention to changes in net working capital, using Table 3.4 as a guide.

g. Net fixed assets increased from $800 million to $900 million during 2019. What must have been South Sea’s gross investment in fixed assets during 2019?

h. If South Sea reduced its outstanding accounts payable by $35 million during the year, what must have happened to its other current liabilities?

7. Financial Statements. Here are the 2018 and 2019 (incomplete) balance sheets for Newble Oil Corp. (LO3-1)

BALANCE SHEET AT END OF YEAR (Figures in $ millions)

Assets 2018 2019 Liabilities and Shareholders’ Equity 2018 2019

Current assets $  310 $  420 Current liabilities $210 $240 Net fixed assets 1,200 1,420 Long-term debt 830 920

a. What was shareholders’ equity at the end of 2018? b. What was shareholders’ equity at the end of 2019? c. If Newble paid dividends of $100 in 2019 and made no stock issues, what must have been

net income during the year? d. If Newble purchased $300 in fixed assets during 2019, what must have been the depreciation

charge on the income statement? e. What was the change in net working capital between 2018 and 2019? f. If Newble issued $200 of new long-term debt, how much debt must have been paid off

during the year?

8. Financial Statements. Henry Josstick has just started his first accounting course and has pre- pared the following balance sheet and income statement for Omega Corp. Unfortunately, although the data for the individual items are correct, he is very confused as to whether an item should go in the balance sheet or income statement and whether it is an asset or liability. Help him by rear- ranging the items and filling in the blanks.

BALANCE SHEET

Payables $  35 Inventories $50 Less accumulated depreciation 120 Receivables 35 Total current assets Total current liabilities Long-term debt $350 Interest expense $25 Property, plant, and equipment 520 Total liabilities Net fixed assets Shareholders’ equity $90 Total assets Total liabilities and shareholders’ equity

INCOME STATEMENT

Net sales $700 Cost of goods sold 580 Selling, general, and administrative expenses 38 EBIT Debt due for repayment $  25 Cash 15 Taxable income Federal plus other taxes $  15 Depreciation 12 Net income

What is the correct total for the following? (LO3-1) a. Current assets b. Net fixed assets c. Total assets

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Chapter 3 Accounting and Finance 79

d. Current liabilities e. Total liabilities f. Total liabilities and shareholders’ equity g. EBIT h. Taxable income i. Net income

9. Market versus Book Values. The founder of Alchemy Products Inc. discovered a way to turn gold into lead and patented this new technology. He then formed a corporation and invested $200,000 in setting up a production plant. He believes that he could sell his patent for $50 mil- lion. (LO3-2) a. What is the book value of the firm? b. What is the market value of the firm? c. If there are 2 million shares of stock in the new corporation, what is the book value per share? d. What is the price per share?

10. Market versus Book Values. State whether each of the following events would increase or decrease the ratio of market value to book value. (LO3-2) a. Big Oil announces the discovery of a major new oil field in Costaguana. b. Big Autos increases its depreciation provision. c. Since Big Stores purchased its assets, inflation has risen sharply.

11. Market versus Book Values. (LO3-2) a. In early 2018, the market values of the shares of many banks (e.g., Bank of America or

Citigroup) were barely greater than book value per share. How would you interpret this pattern?

b. At the same time, Apple’s market value per share was more than six times its book value. Is this consistent with your analysis in part (a)?

12. Income versus Cash Flow. Explain why accounting income generally differs from a firm’s cash inflows. (LO3-3)

13. Cash Flows. Will the following actions increase or decrease the firm’s cash balance? (LO3-3) a. The firm sells some goods from inventory. b. The firm sells some machinery to a bank and leases it back for a period of 20 years. c. The firm buys back 1 million shares of stock from existing shareholders.

14. Income versus Cash Flow. Butterfly Tractors had $14 million in sales last year. Cost of goods sold was $8 million, depreciation expense was $2 million, interest payment on outstanding debt was $1 million, and the firm’s tax rate was 21%. (LO3-3) a. What was the firm’s net income? b. What was the firm’s cash flow? c. What would happen to net income and cash flow if depreciation were increased by $1 million? d. Would you expect the change in depreciation to have a positive or negative impact on the

firm’s stock price? e. What would be the impact on net income if depreciation was $1 million and interest expense

was $2 million? f. What would be the impact on cash flow if depreciation was $1 million and interest expense

was $2 million?

15. Working Capital. QuickGrow is in an expanding market, and its sales are increasing by 25% per year. Would you expect its net working capital to be increasing or decreasing? (LO3-3)

16. Income Statement. Sheryl’s Shipping had sales last year of $10,000. The cost of goods sold was $6,500, general and administrative expenses were $1,000, interest expenses were $500, and depreciation was $1,000. The firm’s tax rate is 21%. (LO3-3) a. What are earnings before interest and taxes? b. What is net income? c. What is cash flow from operations?

17. Income versus Cash Flow. Start-up firms typically have negative net cash flows for several years. (LO3-3) a. Does this mean that they are failing? b. Accounting profits for these firms are also commonly negative. How would you interpret

this pattern? Is there a shortcoming in our accounting rules?

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80 Part One Introduction

18. Income versus Cash Flow. Can cash flow from operations be positive if net income is nega- tive? Can it be negative if net income is positive? Give examples. (LO3-3)

19. Income versus Cash Flow. During the last year of operations, Theta’s accounts receivable increased by $10,000, accounts payable increased by $5,000, and inventories decreased by $2,000. What is the total impact of these changes on the difference between profits and cash flow? (LO3-3)

20. Income versus Cash Flow. Candy Canes Inc. spends $100,000 to buy sugar and peppermint in April. It produces its candy and sells it to distributors in May for $150,000, but it does not receive payment until June. Assuming that sales in April and June are zero, fill in the following table. (LO3-3)

Sales Net Income Cash Flow

April a. b. c. May d. e. f. June g. h. i.

21. Income versus Cash Flow. Ponzi Products produced 100 chain-letter kits this quarter, resulting in a total cash outlay of $10 per unit. It will sell 50 of the kits next quarter at a price of $11, and the other 50 kits in the third quarter at a price of $12. It takes a full quarter for Ponzi to collect its bills from its customers. (Ignore possible sales in earlier or later quarters.) (LO3-3) a. What is the net income for Ponzi next quarter? b. What are the cash flows for the company this quarter? c. What are the cash flows for the company in the third quarter? d. What is Ponzi’s net working capital in the next quarter?

22. Income versus Cash Flow. Value Added Inc. buys $1 million of sow’s ears at the beginning of January but doesn’t pay immediately. Instead, it agrees to pay the bill in March. It processes the ears into silk purses, which it sells for $2 million in February. However, it will not collect pay- ment on the sales until April. (LO3-3) a. What is the firm’s net income in February? b. What is its net income in March? c. What is the firm’s net new investment in working capital in January? d. What is its net new investment in working capital in April? e. What is the firm’s cash flow in January? f. What is the firm’s cash flow in February? g. What is the cash flow in March? h. What is the cash flow in April?

23. Free Cash Flow. Free cash flow measures the cash available for distribution to debtholders and shareholders. Look at Section 3.3, where we calculate free cash flow for Home Depot. Show how this cash was distributed to investors. How much was used to build up cash reserves? (LO3-3)

24. Free Cash Flow. The following table shows an abbreviated income statement and balance sheet for Quick Burger Corporation for 2019.

INCOME STATEMENT OF QUICK BURGER CORP., 2019 (Figures in $ millions)

Net sales $27,567 Costs 17,569 Depreciation 1,402 Earnings before interest and taxes (EBIT) $  8,596 Interest expense 517 Pretax income 8,079 Federal plus other taxes 2,614 Net income $  5,465

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Chapter 3 Accounting and Finance 81

In 2019 Quick Burger had capital expenditures of $3,049. (LO3-3) a. Calculate Quick Burger’s free cash flow in 2019. b. If Quick Burger was financed entirely by equity, how much more tax would the company

have paid? (Assume a tax rate of 21%.) c. What would the company’s free cash flow have been if it was all-equity financed?

25. Tax Rates.  Use Table 3.6 to answer the following. (LO3-4) a. What would be the marginal tax rate for a married couple with income of $90,000? b. What would be the average tax rate for a married couple with income of $90,000? c. What would be the marginal tax rate for an unmarried taxpayer with income of $90,000? d. What would be the average tax rate for an unmarried taxpayer with income of $90,000?

26. Tax Rates. Using Table 3.6, calculate the marginal and average tax rates for a single taxpayer with the following incomes: (LO3-4) a. $20,000 b. $50,000 c. $300,000 d. $3,000,000

27. Taxes. A married couple earned $95,000 in 2018. How much did they pay in taxes? (LO3-4) a. What was their marginal tax bracket? b. What was their average tax bracket?

28. Tax Rates. What would be the marginal and average tax rates for a corporation with an income level of $100,000? (LO3-4)

29. Tax Rates. You have set up your tax preparation firm as an incorporated business. You took $80,000 from the firm as your salary. The firm’s taxable income for the year (net of your salary) was $30,000. Assume you pay personal taxes as an unmarried taxpayer. (LO3-4) a. How much tax must be paid to the federal government, including both your personal taxes

and the firm’s taxes? Use the tax rates presented in Tables 3.6. b. By how much will you reduce the total tax bill if you cut your salary to $50,000, thereby

leaving the firm with taxable income of $60,000? c. What allocation will minimize the total tax bill? Hint: Think about marginal tax rates and

the ability to shift income from a higher marginal bracket to a lower one.

30. Tax Rates. Turn back to Table 3.6, which shows marginal personal tax rates. Make a table in Excel that calculates taxes due for income levels ranging from $10,000 to $10 million. (LO3-4) a. For each income, calculate the average tax rate of a single taxpayer. Plot the average tax rate

as a function of income. b. What happens to the difference between the average and top marginal tax rates as income

becomes very large?

BALANCE SHEET OF QUICK BURGER CORP., 2019 (Figures in $ millions)

Assets 2019 2018 Liabilities and Shareholders’ Equity 2019 2018

Current assets Current liabilities

Cash and marketable securities $  2,336 $  2,336 Debt due for repayment — $  367 Receivables 1,375 1,335 Accounts payable $  3,403 3,143 Inventories 122 117 Total current liabilities $  3,403 $  3,509 Other current assets 1,089 616 Total current assets $  4,922 $  4,403 Fixed assets Long-term debt $13,633 $12,134 Property, plant, and equipment $24,677 $22,835 Other long-term liabilities 3,057 2,957 Intangible assets (goodwill) 2,804 2,653 Total liabilities $20,093 $18,600 Other long-term assets 2,983 3,099 Total shareholders’ equity 15,294 14,390 Total assets $35,387 $32,990 Total liabilities and shareholders’ equity $35,387 $32,990

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82 Part One Introduction

The table below contains data on Fincorp Inc. that you should use for Problems 31–38. The balance sheet items correspond to values at year-end 2018 and 2019, while the income statement items correspond to revenues or expenses during the year ending in either 2018 or 2019. All values are in thousands of dollars.

2018 2019

Revenue $4,000 $4,100 Cost of goods sold 1,600 1,700 Depreciation 500 520 Inventories 300 350 Administrative expenses 500 550 Interest expense 150 150 Federal and state taxes* 400 420 Accounts payable 300 350 Accounts receivable 400 450 Net fixed assets† 5,000 5,800 Long-term debt 2,000 2,400 Notes payable 1,000 600 Dividends paid 410 410 Cash and marketable securities 800 300

* Taxes are paid in their entirety in the year that the tax obligation is incurred. † Net fixed assets are fixed assets net of accumulated depreciation since the asset was installed.

31. Balance Sheet. Construct a balance sheet for Fincorp for 2018 and 2019. What is shareholders’ equity? (LO3-1)

32. Working Capital. What was the change in net working capital during the year? (LO3-1) 33. Income Statement. Construct an income statement for Fincorp for 2018 and 2019. What were

reinvested earnings for 2019? (LO3-1)

34. Earnings per Share. Suppose that Fincorp has 500,000 shares outstanding. What were earn- ings per share in 2019? (LO3-1)

35. Balance Sheet. Examine the values for depreciation in 2019 and net fixed assets in 2018 and 2019. What was Fincorp’s gross investment in plant and equipment during 2019? (LO3-1)

36. Book versus Market Value. Suppose that the market value (in thousands of dollars) of Fin- corp’s fixed assets in 2019 is $6,000 and that the value of its long-term debt is only $2,200. In addition, the consensus among investors is that Fincorp’s past investments in developing the skills of its employees are worth $2,900. This investment, of course, does not show up on the balance sheet. What will be the price per share of Fincorp stock? (LO3-2)

37. Income versus Cash Flows. Construct a statement of cash flows for Fincorp for 2019. (LO3-3) 38. Tax Rates. What was the firm’s average tax bracket for each year? (LO3-4)

WEB EXERCISES 1. Find Microsoft (MSFT) and Ford (F) on finance.yahoo.com, and examine the financial state-

ments of each. Which firm uses more debt finance? Which firm has higher cash as a percentage of total assets? Which has higher EBIT per dollar of total assets? Which has higher profits per dollar of shareholders’ equity?

2. Now choose two highly profitable technology firms, such as Intel (INTC) and Microsoft (MSFT), and two electric utilities, such as American Electric Power (AEP) and Duke Energy (DUK). Which firms have the higher ratio of market value to book value of equity? Does this make sense to you? Which firms pay out a higher fraction of their profits as dividends to share- holders? Does this make sense?

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Chapter 3 Accounting and Finance 83

3. Log on to the website of a large nonfinancial company and find its latest financial statements. Draw up a simplified balance sheet, income statement, and statement of cash flows as in Tables 3.1, 3.3, and 3.4. Some companies’ financial statements can be extremely complex; try to find a relatively straightforward business. Also, as far as possible, use the same headings as in these tables, and don’t hesitate to group some items as “other current assets,” “other expenses,” and so on. Look first at your simplified balance sheet. How much was the com- pany owed by its customers in the form of unpaid bills? What liabilities does the company need to meet within a year? What was the original cost of the company’s fixed assets? Now look at the income statement. What were the company’s earnings before interest and taxes (EBIT)? Finally, turn to the cash-flow statement. Did changes in working capital add to cash or use it up?

4. The schedule of tax rates for individuals changes frequently. If you search for federal tax brackets on the web, you will find many sites with up-to-date information.What is your marginal tax rate if you are single with a taxable income of $70,000? What is your average tax rate?

SOLUTIONS TO SELF-TEST QUESTIONS 3.1 Cash and equivalents would increase by $100 million. Property, plant, and equipment would

increase by $400 million. Long-term debt would increase by $500 million. Shareholders’ equity would not increase: Assets and liabilities have increased equally, leaving shareholders’ equity unchanged.

3.2 a. If the auto plant were worth $14 billion, the equity in the firm would be worth $14 − $4 = $10 billion. With 100 million shares outstanding, each share would be worth $100.

b. If the outstanding stock were worth $8 billion, we would infer that the market values the auto plant at $8 + $4 = $12 billion.

3.3 The profits for the firm are recognized in periods 2 and 3 when the sales take place. In both of those periods, profits are $150 − $100 = $50. Cash flows are derived as follows.

Period: 1 2 3 4

1. Sales $ 0 $150 $150 $ 0 2. Change in accounts receivable 0 150 0 − 150 3. Cost of goods sold 0 100 100 0 4. Change in inventories 200 −100 − 100 0 5. Net cash flow [= (1) − (2) − (3) − (4)] −$200 $ 0 +$150 +$150

In period 2, half the units are sold for $150 but no cash is collected, so the entire $150 is treated as an increase in accounts receivable. Half the $200 cost of production is recognized, and a like amount is taken out of inventory. In period 3, the firm sells another $150 of product but collects $150 from its previous sales, so there is no change in outstanding accounts receivable. Net cash flow is the $150 collected in this period on the sale that occurred in period 2. In period 4, cash flow is again $150, as the accounts receivable from the sale in period 3 are collected.

3.4 a. An increase in inventories uses cash, reducing the firm’s net cash balance. b. A reduction in accounts payable uses cash, reducing the firm’s net cash balance. c. An issue of common stock is a source of cash. d. The purchase of new equipment is a use of cash, and it reduces the firm’s net cash balance.

3.5 Firm A Firm B

EBIT 100 100 Interest 60 0 Pretax income 40 100 Tax (21% of pretax income) 8.4 21 Net income 31.6 79

Note: Figures in millions of dollars.

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84 Part One Introduction

Taxes owed by firm A fall from $12.6 million (when debt was $40 million) to $8.4 million. The reduction in taxes is 21% of the extra $20 million of interest expense. Net income does not fall by the full $20 million of extra interest expense. It instead falls by interest expense less the reduction in taxes, or $20 million − $4.2 million = $15.8 million.

3.6 For a single taxpayer with taxable income of $80,000, total taxes paid are

(.10 × $9,525) + (.12 × $29,175) + (.22 × $41,300) = $13,539.50

The marginal tax rate is 22%, but the average tax rate is only 13,539.50/80,000 = .169, or 16.9%. For the married taxpayers filing jointly with taxable income of $80,000, total taxes paid are

(.10 × $19,050) + (.12 × $58,350) + (.22 × $2,600) = $9,479

The marginal tax rate is 22%, and the average tax rate is 9,479/80,000 = .118, or 11.8%.

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86

Measuring Corporate Performance

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

4-1 Calculate and interpret the market value and market value added of a public corporation.

4-2 Calculate and interpret key measures of financial performance, including economic value added (EVA) and rates of return on capital, assets, and equity.

4-3 Calculate and interpret key measures of operating efficiency, leverage, and liquidity.

4-4 Show how profitability depends on the efficient use of assets and on profits as a fraction of sales.

4-5 Compare a company’s financial standing with that of its com- petitors and its own position in previous years.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

4

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87

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When managers need to judge a firm’s performance, they start with some key financial ratios. ©Wavebreakmedia Ltd UC4/Alamy

In Chapter 1 we introduced the basic objective of corporate finance: Maximize the current value of shareholders’ investment in the firm. For public cor- porations, this value is set in the stock market. It equals market price per share multiplied by the num- ber of shares outstanding. Of course, fluctuations in market value partly reflect events that are outside the manager’s control. Nevertheless, good managers strive to add value by superior investment and financ- ing decisions.

How can we judge whether managers are doing a good job at adding value or where there may be scope for improvement? We need measures of value added. We also need measures that help explain where the value added comes from. For example, value added depends on profitability, so we need measures of profit- ability. Profitability depends in turn on profit margins and on how efficiently the firm uses its assets. We will describe the standard measures of profitability and effi- ciency in this chapter.

Value also depends on sound financing. Value is destroyed if the firm is financed recklessly and can’t pay its debts. Value is also destroyed if the firm does not maintain adequate liquidity and therefore has difficulty finding the cash to pay its bills. Therefore, we will describe the measures that financial managers and investors use to assess debt policy and liquidity.

These financial measures are mostly financial ratios calculated from the firm’s income statement and bal- ance sheet. Therefore, we will have to take care to remember the limitations of these accounting data.

You have probably heard stories of whizzes who can take a company’s accounts apart in minutes, calculate a list of financial ratios, and divine the company’s future. Such people are like abominable snowmen: often spoken of but never truly seen. Financial ratios are no substitute for a crystal ball. They are just a convenient way to summarize financial data and to assess and com- pare financial performance. The ratios help you to ask the right questions, but they seldom answer them.

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88 Part One Introduction

How Financial Ratios Relate to Shareholder Value

The good news about financial ratios is that they are usually easy to calculate. The bad news is that there are so many of them. To make it worse, the ratios are often presented in long lists that seem to require memorization first and understanding maybe later.

We can mitigate the bad news by taking a moment to preview what the ratios are measuring and how the ratios connect to the ultimate objective of value added for shareholders.

Shareholder value depends on good investment decisions. The financial manager evaluates investment decisions by asking several questions, including: How profitable are the investments relative to the cost of capital? How should profitability be mea- sured? What does profitability depend on? (We will see that it depends on efficient use of assets and on the bottom-line profits on each dollar of sales.)

Shareholder value also depends on good financing decisions. Again, there are obvi- ous questions: Is the available financing sufficient? The firm cannot grow unless financing is available. Is the financing strategy prudent? The financial manager should not put the firm’s assets and operations at risk by operating at a dangerously high debt ratio, for example. Does the firm have sufficient liquidity (a cushion of cash or assets that can be readily sold for cash)? The firm has to be able to pay its bills and respond to unexpected setbacks.

Figure 4.1 summarizes these questions in somewhat more detail. The boxes on the left are for investment, the boxes on the right for financing. In each box, we have posed a question and, where appropriate, given examples of financial ratios or other mea- sures that the financial manager can use to answer the question. For example, the bot- tom box on the far left of Figure 4.1 asks about efficient use of assets. Three financial ratios that measure asset efficiency are turnover ratios for assets, inventory, and accounts receivable.

The two bottom boxes on the right ask whether financial leverage (the amount of debt financing) is prudent and whether the firm has enough liquidity for the coming year. The ratios for tracking financial leverage include debt ratios, such as the ratio of debt to equity, and interest coverage ratios. The ratios for liquidity are the current, quick, and cash ratios.

4.1

Shareholder Value How much value has been generated?

Turnover ratios for assets, inventory, and receivables

E�cient use of assets? Profits from sales?

Operating profit margin

Prudent financial leverage?

Su�cient liquidity for the coming year?

Current, quick, and cash ratios

Debt ratios Interest coverage ratios

Economic value added (EVA) Returns on capital, assets, and equity

How profitable? How can the firm safely finance future growth?

Investment Financing

Market value added Market-to-book ratio

FIGURE 4.1 An organization chart for financial ratios. The figure shows how common financial ratios and other measures relate to shareholder value.

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Chapter 4 Measuring Corporate Performance 89

We will explain how to calculate and interpret these and the other ratios in Figure 4.1. For now you can read the figure as an organization chart that locates some important financial ratios and shows how they relate to the objective of shareholder value.

Now we start at the top of the figure. Our first task is to measure value. We will explain market capitalization, market value added, and the market-to-book ratio.

Measuring Market Value and Market Value Added

Twenty years have passed since your introductory finance class. You are well into your career, and Home Depot is on your mind. Perhaps you are a mutual fund manager try- ing to decide whether to allocate $25 million of new money to Home Depot stock. Perhaps you are a major shareholder pondering a sellout. You could be an investment banker seeking business from Home Depot or a bondholder concerned with Home Depot’s credit standing. You could be the treasurer or CFO of Home Depot or of one of its competitors. You want to understand Home Depot’s value and financial perfor- mance. How would you start?

Home Depot’s common stock closed fiscal 2017 at a price of $190.21 per share. There were 1,170 million shares outstanding, so Home Depot’s market capitalization or “market cap” was $190.21 × 1,170 = $222,546 million, or more than $220 billion. This is a big number, of course, but Home Depot is a big company. Home Depot’s shareholders have, over the years, invested billions in the company. Therefore, you decide to compare Home Depot’s market capitalization with the book value of Home Depot’s equity. The book value measures shareholders’ cumulative investment in the firm.

You turn to Home Depot’s income statement and balance sheet, which are repro- duced in Tables 4.1 and 4.2.1 At the end of 2017, the book value of Home Depot’s equity was $1,454 million. Therefore, Home Depot’s market value added, the differ- ence between the market value of the firm’s shares and the amount of money that shareholders have invested in the firm, was $222,546 − $1,454 = $221,092 million. Home Depot shareholders have contributed about $1.45 billion and ended up with shares worth $222.55 billion. They have accumulated $221.1 billion in market value added.

4.2

market capitalization Total market value of equity, equal to share price times number of shares outstanding.

market value added Market capitalization minus book value of equity.

1 For convenience the statements are repeated from Chapter 3. We are pretending that you actually had these statements on January 28, 2018, the close of Home Depot’s 2017 fiscal year. They were not published until March.

$ Million % of Sales

Net sales 100,904 100.0% Cost of goods sold 66,548 66.0% Selling, general & administrative expenses 17,864 17.7% Depreciation 1,811 1.8% Earnings before interest and income taxes (EBIT) 14,681 14.5% Interest expense 983 1.0% Taxable income 13,698 13.6% Taxes 5,068 5.0% Net income 8,630 8.6% Allocation of net income Dividends 4,212 4.2% Addition to retained earnings 4,418 4.4%

TABLE 4.1 Income statement for Home Depot, fiscal 2017

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90 Part One Introduction

We see from the income statement and balance sheet that Home Depot has earned in just one year more than the net amount of capital contributed by its shareholders. This may seem an accomplishment. But remember that when the firm buys back its own shares from investors in the stock market, the repurchase reduces the book value of shareholders’ equity by the amount of the repurchase. As it has grown, HD has steadily issued more debt and bought back ever-more of its shares. So the current mar- ket value of the firm is many multiples of the book value of outstanding shares. This example serves to remind us that market values of equity are far more revealing about the earning power of the firm as a going concern than are book values.

The consultancy firm EVA Dimensions calculates market value added for a large sample of U.S. companies. Table 4.3 shows a few of the firms from EVA’s list. They include some of the most and least successful companies. Apple heads the group. It has created $782.2 billion of wealth for its shareholders. Bank of America languishes

Assets

End of fiscal

Liabilities and shareholders’ equity

End of fiscal

2017 2016 2017 2016

Current assets Current liabilities Cash and marketable securities 3,595 2,538 Receivables 1,952 2,029 Debt due for repayment 2,761 1,252 Inventories 12,748 12,549 Accounts payable 7,244 7,000 Other current assets 638 608 Other current liabilities 6,189 5,881 Total current assets 18,933 17,724 Total current liabilities 16,194 14,133

Fixed assets Long-term debt 24,267 22,349 Tangible fixed assets Other long-term liabilities 2,614 2,151 Property, plant, and equipment 41,414 40,426 Less accumulated depreciation 19,339 18,512 Total liabilities 43,075 38,633 Net tangible fixed assets 22,075 21,914

Shareholders’ equity: Intangible asset (goodwill) 2,275 2,093 Common stock and other paid-in capital 9,715 9,010 Other assets 1,246 1,235 Retained earnings 39,935 35,517

Treasury stock −48,196 −40,194 Total shareholders’ equity      1,454 4,333

Total assets 44,529 42,966 Total liabilities and shareholders’ equity 44,529 42,966

TABLE 4.2 Home Depot’s balance sheet (figures in $ millions)

Note: Column sums subject to rounding error.

Stock

Market Value Market-to-Book

Added Ratio

Apple 782,164 7.15 Microsoft 461,134 5.84 Johnson & Johnson 277,722 3.38 Walmart 209,010 3.41 Coca-Cola 202,102 8.59 Freeport −5,781 0.85 CBS −16,858 0.65 AIG −30,134 0.64 Conoco −53,141 0.47 Bank of America −65,878 0.80

TABLE 4.3 Stock market measures of company performance, September 2017. Companies are ranked by market value added (dollar values in millions).

Source: We are grateful to EVA Dimensions for providing these statistics.

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Chapter 4 Measuring Corporate Performance 91

near the bottom: The market value of its shares is $65.9 billion less than the amount of shareholders’ money invested in the firm.

The top-listed companies in Table 4.3 are large firms. Their managers have lots of assets to work with. A small firm could not hope to create so much extra value. There- fore, financial managers and analysts also like to calculate how much value has been added for each dollar that shareholders have invested. To do this, they compute the ratio of market value to book value. For example, Home Depot’s market-to-book ratio in early 2018 (at the end of its 2017 fiscal year) was2

Market-to-book ratio = market value of equity ________________ book value of equity = $222.5 _____ 1.454 = 153.0

In other words, Home Depot has multiplied the value of its shareholders’ invest - ment 153 times.

Table 4.3 shows a sample of market-to-book ratios for 2017. Notice that Coca-Cola has a much higher market-to-book ratio than Microsoft. But Microsoft’s market value added is higher because of its larger scale.

market-to-book ratio Ratio of market value of equity to book value of equity.

2 The market-to-book ratio can also be calculated by dividing stock price by book value per share.

Shares of Notung Cutlery Corp. closed 2018 at $75 per share. Notung had 14.5 million shares outstanding. The book value of equity was $610 million. Com- pute Notung’s market capitalization, market value added, and market-to-book ratio.

Self-Test4.1

The market-value performance measures in Table 4.3 have three drawbacks. First, the market value of the company’s shares reflects investors’ expectations about future performance. Investors pay attention to current profits and investment, of course, but they also avidly forecast investment and growth. Second, market values fluctuate because of many risks and events that are outside the financial manager’s control. Thus, market values are noisy measures of how well the corporation’s management is performing. Third, you can’t look up the market value of privately owned companies whose shares are not traded. Nor can you observe the market value of divisions or plants that are parts of larger companies. You may use market values to satisfy your- self that Home Depot as a whole has performed well, but you can’t use them to drill down to compare the performance of the lumber and home improvement divisions. To do this, you need accounting measures of profitability. We start with economic value added (EVA).

Economic Value Added and Accounting Rates of Return

When accountants draw up an income statement, they start with revenues and then deduct operating and other costs. But one important cost is not included: the opportu- nity cost of the capital the firm employs. Therefore, to see whether the firm has truly created value, we need to measure whether it has earned a profit after deducting all costs, including the cost of its capital.

Recall from Chapters 1 and 2 that the cost of capital is the minimum acceptable rate of return on capital investment. It is an opportunity cost of capital because it equals the expected rate of return on opportunities open to investors in financial markets. The firm

4.3

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92 Part One Introduction

creates value only if it can earn more than its cost of capital, that is, more than its inves- tors can earn by investing on their own.

The profit after deducting all costs, including the cost of capital, is called the com- pany’s economic value added or EVA. The term “EVA” was coined by Stern Stewart & Co., which did much to develop and promote the concept. EVA is also called resid- ual income.

In calculating EVA, it’s customary to take account of all the long-term capital con- tributed by investors in the corporation. That means including bonds and other long- term debt as well as equity capital. Total long-term capital, usually called total capitalization, is the sum of long-term debt and shareholders’ equity.

Home Depot entered fiscal 2017 with a total capitalization of $26,682 million, which was made up of $22,349 million of long-term debt and $4,333 million of share- holders’ equity. (See the entries in Table 4.2 for the end of the 2016 fiscal year.) This was the cumulative amount that had been invested by Home Depot’s debt and equity investors. Home Depot’s cost of capital was about 8.2%.3 So we can convert the cost of capital into dollars by multiplying total capitalization by 8.2%: .082 × 26,682 million = $2,188 million. To satisfy its debt and equity investors, Home Depot needed to earn total income of $2,188 million.

Now we can compare this figure with the income that Home Depot actually generated for its debt and equity investors. In 2017, debt investors received interest income of $983 mil- lion. The after-tax equivalent, using Home Depot’s 2017 35% tax rate, is (1 − .35) × $983 = $639 million.4 Net income to shareholders was $8,630 million. Therefore, Home Depot’s after-tax interest and net income totaled 639 + 8,630 = $9,269 million. If you deduct the dollar cost of capital from this figure, you can see that the company earned 9,269 − 2,188 = $7,081 million more than investors required. This was Home Depot’s EVA or residual income:

EVA

= after-tax interest + net income − (cost of capital × total capitalization)

= 639 + 8,630 − 2,188 = $7,081 million

The sum of Home Depot’s net income and after-tax interest is its after-tax operating income. This is what Home Depot would earn if it had no debt and could not take interest as a tax-deductible expense. After-tax operating income is what the company would earn if it were all-equity-financed. In that case it would have no (after-tax) inter- est expense and all operating income would go to shareholders.

Thus EVA also equals:

EVA

= after-tax operating income − (cost of capital × total capitalization)

= 9,269 − 2,188 = $7,081 million

Of course, Home Depot and its competitors do use debt financing. Nevertheless, EVA comparisons are more useful if focused on operating income, which is not affected by interest tax deductions.

Table 4.4 shows estimates of EVA for our sample of large companies. Apple again heads the list. It earned $37.6 billion more than was needed to cover its cost of capital. By contrast, Bank of America was among the laggards. Although it earned an accounting

economic value added (EVA) Net income minus a charge for the cost of capital employed. Also called residual income.

3 This is an after-tax weighted-average cost of capital, or WACC. A company’s WACC depends on the risk of its business. The WACC is almost the same as the opportunity cost of capital, but with the cost of debt calculated after tax. We will explain WACC and how to calculate it in Chapter 13. 4 The corporate tax rate in 2017 was 35%. Today it is 21%. Why do we take interest after tax? Remember from Chapter 3 that when a firm pays interest, it reduces its taxable income and therefore its tax bill. This tax saving, or tax shield, will vary across firms depending on the amounts of debt financing. But we want to focus here on operating results. To put all firms on a common basis, we subtract the interest tax shield from reported income, or, equivalently, we look at after-tax interest payments. By ignoring the tax shield, we calculate each firm’s income as if it had no debt outstanding and shareholders got the (after-tax) interest. To be consistent, the cost of capital is defined as an after-tax weighted-average cost of capital (WACC). We have more to say about these issues in Chapters 13 and 16.

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Chapter 4 Measuring Corporate Performance 93

profit of $18.37 billion, this figure was calculated before deducting the cost of capital. After deducting the cost of capital, the company made an EVA loss of $2.4 billion.

Notice how the cost of capital differs across the 10 firms in Table 4.4. The variation is due to differences in business risk. Relatively safe companies like Walmart tend to have low costs of capital. Riskier companies like Apple and Microsoft have high costs of capital.

EVA, or residual income, is a better measure of a company’s performance than is accounting income. Accounting income is calculated after deducting all costs except the cost of capital. By contrast, EVA recognizes that companies need to cover their opportunity costs before they add value.

EVA makes the cost of capital visible to operating managers. There is a clear target: Earn at least the cost of capital on assets employed. A plant or divisional manager can improve EVA by reducing assets that aren’t making an adequate contribution to prof- its. Evaluating performance by EVA pushes managers to flush out and dispose of such underutilized assets. Therefore, a growing number of firms now calculate EVA and tie managers’ compensation to it.

1. After-Tax Interest + Net Income

2. Cost of Capital (WACC), %

3. Total Long-Term Capital

4. EVA = 1 − (2 × 3)

5. Return on Capital (ROC),

% (1 ÷ 3)

6. Excess return, % (5 − 2)

Apple $52,051 7.1% $203,569 $37,638 25.6% 18.5% Microsoft 20,626 7.1% 61,619 16,270 33.5% 26.4% Johnson & Johnson 17,599 5.7% 112,367 11,160 15.7% 9.9% Walmart 14,891 2.8% 206,206 9,076 7.2% 4.4% Coca-Cola 8,713 5.8% 44,678 6,144 19.5% 13.8% CBS 1,863 6.1% 55,820 −1,559 3.3% −2.8% Freeport 1,710 7.1% 52,991 −2,068 3.2% −3.9% Bank of America 18,370 6.7% 310,587 −2,439 5.9% −0.8% AIG 457 6.4% 90,107 −5,300 0.5% −5.9% Conoco −1,494 6.7% 102,820 −8,373 −1.5% −8.2%

Source: We are grateful to EVA Dimensions for providing these statistics.

TABLE 4.4 EVA and ROC, September 2017. Companies are ranked by EVA (dollar values in millions).

Roman Holidays Inc. had operating income of $30 million on a start-of-year total capitalization of $188 million. Its cost of capital was 11.5%. What was its EVA?

Self-Test4.2

Accounting Rates of Return EVA measures how many dollars a business is earning after deducting the cost of capi- tal. Other things equal, the more assets the manager has to work with, the greater the opportunity to generate a large EVA. The manager of a small division may be highly competent, but if that division has few assets, she is unlikely to rank high in the EVA stakes. Therefore, when comparing managers, it can be helpful to measure the firm’s profits per dollar of assets. Three common measures are the return on capital (ROC), the return on equity (ROE), and the return on assets (ROA). These are called book rates of return because they are based on accounting information.

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94 Part One Introduction

Return on Capital (ROC) The return on capital is equal to after-tax operating income divided by total capitalization. In 2017, Home Depot’s after-tax operating income was $9,269 million. It started the year with total capitalization (long-term debt plus share- holders’ equity) of $26,682 million. Therefore, its return on capital (ROC) was5

ROC =  after-tax operating income _______________________ total capitalization at start of year = 9,269 _____ 26,682  = .347, or 34.7%

As we noted earlier, Home Depot’s cost of capital was about 8.2%. This was the return that investors could have expected to earn at the start of 2017 if they invested their money in other companies or securities with the same risk as Home Depot’s busi- ness. So in 2017 the company earned 34.7 − 8.2 = 26.5% more than investors required.

When we calculated ROC, we compared a flow measure (income earned over the year) with a snapshot measure (capital at the start of the year). We therefore ignored the company’s additional financing during that year. If the additional financing con- tributed a significant part of the year’s operating income, it may be better to divide by the average of the total capitalization at the beginning and end of the year. In the case of Home Depot, the company increased long-term debt in 2017, but it repurchased some of its stock. It actually ended the year with less capital than it had at the start. Therefore, if we divide operating income by average capitalization, Home Depot’s ROC for 2017 increases slightly to

ROC =  after-tax operating income ___________________ average total capitalization = 9,269 ______________ (25,721 + 26,682)/2  = .354, or 35.4%

Is one measure better than another? It is difficult to generalize, but if you would like to know more about when one might prefer to use average rather than start-of-year figures to calculate a financial ratio, the icon in the margin provides a link to a short discussion of the issue.6

The last column in Table 4.4 shows ROC for our sample of well-known companies. Notice that Coke’s return on capital was 19.5%, over 13 percentage points above its cost of capital. Although Coke had a higher return on capital than Walmart, it had a lower EVA. This was partly because it was riskier than Walmart and so had a higher cost of capital, but also because it had far fewer dollars invested than Walmart.

The five companies in Table 4.4 with negative EVAs all have ROCs less than their cost of capital. The spread between ROC and the cost of capital is really the same thing as EVA but expressed as a percentage return rather than in dollars.

Return on Assets (ROA) Return on assets (ROA) measures after-tax operating income as a fraction of the firm’s total assets. Total assets (which equal total liabilities plus shareholders’ equity) are greater than total capitalization because total capitaliza- tion does not include current liabilities. For Home Depot, ROA was

Return on assets =  after-tax operating income ___________________ total assets at start of year = 9,269 _____ 42,966  = .216, or 21.6%

Using average total assets, ROA was slightly lower:

ROA =  after-tax operating income ___________________ average total assets = 9,269 ______________ (44,529 + 42,966)/2 = .212, or 21.2%

return on capital (ROC) Net income plus after-tax interest as a percentage of long-term capital.

return on assets (ROA) Net income plus after-tax interest as a percentage of total assets.

BEYOND THE PAGE

mhhe.com/brealey10e

Average or start- of-year assets

5 The numerator of Home Depot’s ROC is again its after-tax operating income, calculated by adding back after- tax interest to net income. More often than not, financial analysts forget that interest is tax-deductible and use pretax interest to calculate operating income. This complicates comparisons of ROC for companies that use dif- ferent fractions of debt financing. It also muddies comparisons of ROC with the after-tax weighted-average cost of capital (WACC). We cover WACC in Chapter 13. 6 Sometimes it’s convenient to use a snapshot figure at the end of the year, although this procedure is not strictly correct.

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Chapter 4 Measuring Corporate Performance 95

Return on Equity (ROE) We measure the return on equity (ROE) as the income to shareholders per dollar that they have invested. Home Depot had net income of $8,630 million in fiscal 2017 and shareholders’ equity of $4,333 million at the start of the year. So Home Depot’s ROE was

Return on equity = ROE =  net income ________ equity = 8,630 ____ 4,333 = 1.992, or 199.2%

Using average equity, ROE was even higher:

ROE =  net income ___________ average equity = 8,630 ____________ (1,454 + 4,333) / 2 = 2.983, or 298.3%

This appears to be an implausibly high value for return on equity. Remember though that HD has driven the book value of shareholders’ equity down to quite low levels through its sustained program of share repurchases. As a percentage of the book value of remaining equity, ROE is very high, but we certainly would not expect to see HD (or many other firms) earning 200% returns on their new investments.

return on equity (ROE) Net income as a percentage of shareholders’ equity.

What is the difference between after-tax operating income and net income to shareholders? How is after-tax operating income calculated? Why is it useful in calculating EVA, ROC, and ROA?

Self-Test4.3

Explain the differences among ROE, ROC, and ROA.

Self-Test4.4

For both ROA and ROC, we use after-tax operating income, which is calculated by adding after-tax interest to net income. We are again asking how profitable the com- pany would have been if it were all-equity-financed. This what-if calculation is helpful when comparing the profitability of firms with different capital structures. The tax deduction for interest is often ignored, however, and operating income is calculated using pretax interest. Some financial analysts take no account of interest payments and measure ROA as net income for shareholders divided by total assets. This calculation is really—we were about to say “stupid” but don’t want to offend anyone. The calcula- tion ignores entirely the income that the firm’s assets have generated for debt investors.

Problems with EVA and Accounting Rates of Return Rates of return and economic value added have some obvious attractions as measures of performance. Unlike market-value-based measures, they show current performance and are not affected by all the other things that move stock market prices. Also, they can be calculated for an entire company or for a particular plant or division. However, remember that both EVA and accounting rates of return are based on book (balance sheet) values for assets. Debt and equity are also book values. As we noted in the pre- vious chapter, accountants do not show every asset on the balance sheet, yet our calcu- lations take accounting data at face value. For example, we ignored the fact that Home

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96 Part One Introduction

Depot has invested large sums in marketing in order to establish its brand name. This brand name is an important asset, but its value is not shown on the balance sheet. If it were shown, the book values of assets, capital, and equity would increase, and Home Depot would not appear to earn such high returns.

EVA Dimensions, which produced the figures in Tables 4.3 and 4.4, does make a number of adjustments to the accounting data. However, it is impossible to include the value of all assets or to judge how rapidly they depreciate. For example, did Microsoft really earn a return on capital of 33.5%? It’s difficult to say because its investment over the years in operating systems and other software is not shown in the balance sheet and cannot be measured exactly.

Remember also that the balance sheet does not show the current market values of the firm’s assets. The assets in a company’s books are valued at their original cost less any depreciation. Older assets may be grossly undervalued in today’s market condi- tions and prices. So a high return on assets indicates that the business has performed well by making profitable investments in the past, but it does not necessarily mean that you could buy the same assets today at their reported book values. Conversely, a low return suggests some poor decisions in the past, but it does not always mean that today the assets could be employed better elsewhere.

Measuring Efficiency

We began our analysis of Home Depot by calculating how much value that company has added for its shareholders and how much profit the company is earning after deducting the cost of the capital that it employs. We examined its rates of return on equity, capital, and total assets, which were all impressively high. Our next task is to probe a little deeper to understand the reasons for Home Depot’s success. What factors contribute to this firm’s overall profitability? One is the efficiency with which it uses its various assets.

Asset Turnover Ratio The asset turnover, or sales-to-assets, ratio shows how much sales are generated by each dollar of total assets, and therefore it measures how hard the firm’s assets are working. For Home Depot, each dollar of assets produced $2.35 of sales:

Asset turnover =  sales __________________ total assets at start of year = 100,904 ______ 42,966 = 2.35

Like some of our profitability ratios, the sales-to-assets ratio compares a flow measure (sales over the entire year) to a snapshot measure (assets on one day). Therefore, finan- cial managers and analysts often calculate the ratio of sales over the entire year to the average level of assets over the same period. In this case, the value is about the same:

Asset turnover =  sales ______________ average total assets = 100,904 ______________ (44,529 + 42,966) / 2  = 2.31

The asset turnover ratio measures how efficiently the business is using its entire asset base. But you also might be interested in how hard particular types of assets are being put to use. A couple of examples are provided next.

Inventory Turnover Efficient firms don’t tie up more capital than they need in raw materials and finished goods. They hold only a relatively small level of inventories of raw materials and finished goods, and they turn over those inventories rapidly.

The balance sheet shows the cost of inventories rather than the amount that the fin- ished goods will eventually sell for. So it is usual to compare the level of inventories with the cost of goods sold rather than with sales. In Home Depot’s case,

Inventory turnover =  cost of goods sold _________________ inventory at start of year = 66,548 _____ 12,549 = 5.3

4.4

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Chapter 4 Measuring Corporate Performance 97

Another way to express this measure is to look at how many days of output are rep- resented by inventories. This is equal to the level of inventories divided by the daily cost of goods sold:

Average days in inventory =  inventory at start of year _________________ daily cost of goods sold = 12,549 _________ 66,548 / 365 = 68.8 days

You could say that on average Home Depot has sufficient inventories to maintain operations for about 69 days.

In Chapter 20 we will see that many firms have managed to increase their inventory turnover in recent years. Toyota has been the pioneer in this endeavor. Its just-in-time inventory system ensures that auto parts are delivered exactly when they are needed. Toyota now keeps only about one month’s supply of parts and finished cars in inven- tory and turns over its inventory about 11 times a year.

Receivables Turnover Receivables are sales for which you have not yet been paid. The receivables turnover ratio measures the firm’s sales as a multiple of its receiv- ables. For Home Depot,

Receivables turnover =  sales ___________________ receivables at start of year = 100,904 ______ 2,029 = 49.7

If customers are quick to pay, unpaid bills will be a relatively small proportion of sales and the receivables turnover will be high. Therefore, a high ratio often indicates an efficient credit department that is quick to follow up on late payers. Sometimes, however, a high ratio may indicate that the firm has an unduly restrictive credit policy and offers credit only to customers who can be relied on to pay promptly.7

Another way to measure the efficiency of the credit operation is by calculating the average length of time for customers to pay their bills. The faster the firm turns over its receivables, the shorter the collection period. On average, Home Depot’s customers pay their bills in about 7.3 days:

Average collection period =  receivables at start of year ___________________ average daily sales = 2,029 _________ 100,904/365 = 7.3 days

The average collection period measures the number of days it takes Home Depot to collect its bills. But Home Depot also delays paying its own bills. Use the information in Tables 4.1 and 4.2 to calculate the average number of days that it takes Home Depot to pay its bills. [Like days in inventory, payment delay should be calculated using only direct cost of goods sold–these do not include indirect costs (i.e., selling, general, and administrative).]

Self-Test4.5

The receivables turnover ratio and the inventory turnover ratio may help to highlight particular areas of inefficiency, but they are not the only possible indicators. For exam- ple, a retail chain might compare its sales per square foot with those of its competitors, an airline might look at revenues per passenger-mile, and a law firm might look at revenues per partner. A little thought and common sense should suggest which mea- sures are likely to produce the most helpful insights into your company’s efficiency.

7 Where possible, it makes sense to look only at credit sales. Otherwise, a high receivables turnover ratio (or, equivalently, a low average collection period) might simply indicate that a small proportion of sales are made on credit. For example, if a retail customer pays cash for a purchase at Home Depot, that transaction will have a collection period of zero, regardless of any policies of the firm’s credit department.

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98 Part One Introduction

Analyzing the Return on Assets: The Du Pont System

We have seen that every dollar of Home Depot’s assets generates $2.35 of sales. But Home Depot’s success depends not only on the efficiency with which it uses its assets to generate sales but also on how profitable those sales are. This is measured by Home Depot’s profit margin.

Profit Margin The profit margin measures the proportion of sales that finds its way into profits. It is sometimes defined as

Profit margin = net income ________ sales = 8,630 ______ 100,904 = .086, or 8.6%

This definition can be misleading. When companies are partly financed by debt, a portion of the revenue produced by sales must be paid as interest to the firm’s lenders. So profits from the firm’s operations are divided between the debtholders and the shareholders. We would not want to say that a firm is less profitable than its rivals simply because it employs debt financing and pays out part of its income as interest. Therefore, when we are calculating the profit margin, it makes sense to add back the after-tax debt interest to net income. This leads us again to after-tax operating income and to the operating profit margin:

Operating profit margin

=

after-tax operating income ___________________ sales

= 8,630 + (1 − .35) × 983 __________________ 100,904 = .0919, or 9.19%

The Du Pont System We calculated earlier that Home Depot has earned a return of 21.6% on its assets. The following equation shows that this return depends on two factors—the sales that Home Depot generates from its assets (asset turnover) and the profit that it earns on each dol- lar of sales (operating profit margin):

Return on assets = after-tax operating income ______________________ assets (4.1)

= sales _____ assets × after-tax operating income ______________________ sales

This breakdown of ROA into the product of turnover and margin is often called the Du Pont formula, after the chemical company that popularized the procedure. In Home Depot’s case, the formula gives the following breakdown of ROA:

ROA = asset turnover × operating profit margin

= 2.35 × .0919 = .216

The Du Pont formula is a useful way to think about a company’s strategy. For exam- ple, a retailer may strive for high turnover at the expense of a low profit margin (a “Walmart strategy”), or it may seek a high profit margin even if that results in low turnover (a “Bloomingdales strategy”). You would naturally prefer both high profit margin and high turnover, but life isn’t that easy. A high-price and high-margin strat- egy will typically result in lower sales per dollar of assets, so firms must make trade- offs between these goals. The Du Pont formula can help sort out which strategy the firm is pursuing.

4.5

operating profit margin After-tax operating income as a percentage of sales.

↑ asset turnover

↑ operating

profit margin

Du Pont formula ROA equals the product of asset turnover and operating profit margin.

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Chapter 4 Measuring Corporate Performance 99

All firms would like to earn a higher return on their assets, but their ability to do so is limited by competition. The Du Pont formula helps to identify the constraints that firms face. Fast-food chains, which have high asset turnover, tend to operate on low margins. Classy hotels have relatively low turnover ratios but tend to compensate with higher margins.

Turnover versus Margin

Firms often seek to improve their profit margins by acquiring a supplier. The idea is to cap- ture the supplier’s profit as well as their own. Unfortunately, unless they have some special skill in running the new business, they are likely to find that any gain in profit margin is offset by a decline in asset turnover.

A few numbers may help to illustrate this point. Table 4.5 shows the sales, profits, and assets of Admiral Motors and its components supplier, Diana Corporation. Both earn a 10% return on assets, though Admiral has a lower operating profit margin (20% versus Diana’s 25%). Because all of Diana’s output goes to Admiral, Admiral’s management reasons that it would be better to merge the two companies. That way, the merged company would capture the profit margin on both the auto components and the assembled car.

The bottom row of Table 4.5 shows the effect of the merger. The merged firm does indeed earn the combined profits. Total sales remain at $20 million, however, because all the com- ponents produced by Diana are used within the company. With higher profits and unchanged sales, the profit margin increases. Unfortunately, the asset turnover is reduced by the merger because the merged firm has more assets. This exactly offsets the benefit of the higher profit margin. The return on assets is unchanged. ■

Example 4.1 ⊲

Figure 4.2 shows evidence of the trade-off between turnover and profit margin. You can see that industries with high average turnover ratios tend to have lower average profit margins. Conversely, high margins are typically associated with low turnover. The classic examples here are electric or water utilities, which have enormous capital requirements and therefore low asset turnover ratios. However, they have extremely low marginal costs for each unit of additional output and therefore earn high markups. The two curved lines in the figure trace out the combinations of profit margin and turnover that result in an ROA of either 3% or 10%. Despite the enormous dispersion across industries in both margin and turnover, that variation tends to be offsetting, so for most industries the return on assets lies between 3% and 10%.

The Du Pont formula (Equation 4.1) seems to suggest that companies with above-average asset turnover ratios generally will have above-average ROAs. Why may this not be so?

Self-Test4.6

Sales Profits Assets Asset

Turnover Profit

Margin ROA

Admiral Motors $20 $4 $40 0.50 20% 10%

Diana Corp. 8 2 20 0.40 25 10

Diana Motors (the merged firm) 20 6 60 0.33 30 10

TABLE 4.5 Merging with suppliers or customers will generally increase the profit margin, but this will be offset by a reduction in asset turnover

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100 Part One Introduction

Measuring Financial Leverage

As Figure 4.1 indicates, shareholder value depends not only on good investment deci- sions and profitable operations, but also on sound financing decisions. We look first at measures of financial leverage and then at measures of liquidity.

When a firm borrows money, it promises to make a series of interest payments and then to repay the amount that it has borrowed. If profits rise, the debtholders continue to receive only the fixed interest payment, so all the gains go to the shareholders. Of course, the reverse happens if profits fall. In this case, shareholders bear most of the pain. If times are sufficiently hard, a firm that has borrowed heavily may not be able to pay its debts. The firm is then bankrupt, and shareholders lose most or all of their entire investment.

Because debt increases returns to shareholders in good times and reduces them in bad times, it is said to create financial leverage. Leverage ratios measure how much financial leverage the firm has taken on. CFOs keep an eye on leverage ratios to ensure that lenders are happy to continue to take on the firm’s debt.

Debt Ratio Financial leverage is usually measured by the ratio of long-term debt to total long-term capital (that is, to total capitalization). Here long-term debt should include not just bonds or other borrowing, but also financing from long-term leases.8 For Home Depot,

Long-term debt ratio = long-term debt _________________ long-term debt + equity = 24,267 ___________ 24,267 + 1,454 = .94, or 94%

This means that 94 cents of every dollar of long-term capital is in the form of debt.

4.6

0%

5%

10%

15%

20%

25%

30%

35%

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

O pe

ra tin

g pr

ofi t m

ar gi

n %

Asset Turnover

Beverages

Mining

Retail stores

ROA = 10%

ROA = 3%

FIGURE 4.2 Operating profit margin and asset turnover for 45 industries

Source: U.S. Census Bureau, Quarterly Report for Manufacturing and Trade Corporations, Third Quarter 2017.

8 A finance lease is a long-term rental agreement that commits the firm to make regular payments. This commit- ment is just like the obligation to make payments on an outstanding loan.

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Chapter 4 Measuring Corporate Performance 101

Leverage may also be measured by the debt-equity ratio. For Home Depot,

Long-term debt–equity ratio = long-term debt ___________ equity = 24,267 _____ 1,454 = 16.69

For highly leveraged companies, the difference between these two ratios is large. Even a company financed two-thirds with debt and one-third with equity, a far- less-leveraged firm than Home Depot (at least based on book values), has a long-term debt ratio of 67% (2/3) and a debt-equity ratio of 2.

The long-term debt ratio for the average U.S. manufacturing company is about 33%, far less than the ratio for Home Depot. Some companies operate at intentionally high debt levels. For example, in Chapter 21 we will look at leveraged buyouts (LBOs). Firms that are acquired in a leveraged buyout usually issue large amounts of debt. When LBOs first became popular in the 1990s, these companies had average debt ratios of about 90%. Many of them flourished and paid back their debtholders in full; others were not so fortunate.

Notice that debt ratios make use of book (accounting) values rather than market val- ues.9 In principle, lenders should be more interested in the market value of the company, which reflects the actual value of the company’s assets and the actual cash flows those assets will produce. If the market value of the company covers its debts, then lenders should get their money back. Thus, you would expect to see the debt ratio computed using the market values of debt and equity. Yet book debt ratios are used almost universally.

Does use of book rather than market leverage ratios matter much? Perhaps not; after all, the market value of the firm includes the value of intangible assets generated by research and development, advertising, staff training, and so on. These assets are not easy to sell, and if the company falls on hard times, their value may disappear altogether. Thus, when banks demand that a borrower keep within a maximum debt ratio, they usu- ally define that ratio in terms of book values, and they ignore the intangible assets that contribute to the market value of the firm but are not shown on the balance sheet.

Notice also that these measures of leverage ignore short-term debt. That probably makes sense if the short-term debt is temporary or is matched by similar holdings of cash, but if the company is a regular short-term borrower, it may be preferable to widen the definition of debt to include all liabilities. In this case,

Total debt ratio = total liabilities __________ total assets = 43,075 _____ 44,529 = .97, or 97%

Therefore, Home Depot is financed 97% with long- and short-term debt and 3% with equity.10 We could also say that its ratio of total debt to equity is 43,075/1,454 = 29.6.

Managers sometimes refer loosely to a company’s debt ratio, but we have just seen that the debt ratio may be measured in several different ways. There is no law stating how a ratio should be defined. So be warned: Do not use a ratio without understanding how it has been calculated.

Times Interest Earned Ratio Another measure of financial leverage is the extent to which interest obligations are covered by earnings. Banks prefer to lend to firms with earnings that cover interest payments with room to spare. Interest coverage is measured by the ratio of earnings before interest and taxes (EBIT) to interest pay- ments. For Home Depot,

Times interest earned = EBIT _____________ interest payments = 14,681 _____ 983 = 14.9

By this measure, Home Depot is conservatively financed. Sometimes lenders are con- tent with coverage ratios as low as 2 or 3.

9 In the case of leased assets, accountants estimate the value of the lease commitments. In the case of long-term debt, they simply show the face value, which can be very different from market value. 10 In this case, the 97% of debt includes all liabilities, including accounts payable and other current liabilities.

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102 Part One Introduction

The regular interest payment is a hurdle that companies must keep jumping if they are to avoid default. The interest coverage ratio measures how much clear air there is between hurdle and hurdler. The ratio is only part of the story, however. For example, it doesn’t tell us whether Home Depot is generating enough cash to repay its debt as it becomes due.

Cash Coverage Ratio As we explained in Chapter 3, depreciation is not a cash expense. Depreciation is deducted when calculating the firm’s earnings, even though no cash goes out the door. Suppose we add back depreciation to EBIT in order to calculate operating cash flow. We then calculate a cash coverage ratio.11 For Home Depot,

Cash coverage ratio = EBIT + depreciation _______________ interest payments = 14,681 + 1,811 ___________ 983 = 16.8

11 Depreciation of intangible assets is called amortization and is therefore also added back to EBIT. This gives EBIT + depreciation + amortization = EBITDA. EBITDA coverage ratios are common. You may also encoun- ter still other ratios, in addition to the standard ratios covered here. 12 Again, we use after-tax operating income, which is the sum of net income and after-tax interest.

A firm repays $10 million face value of outstanding debt and issues $10 million of new debt with a lower rate of interest. What happens to its long-term debt ratio? What happens to its times interest earned and cash coverage ratios?

Self-Test4.7

Leverage and the Return on Equity When the firm raises cash by borrowing, it must make interest payments to its lenders. This reduces net profits. On the other hand, if a firm borrows instead of issuing equity, it has fewer equityholders to share the remaining profits. Which effect dominates? An extended version of the Du Pont formula helps us answer this question. It breaks down the return on equity (ROE) into four parts:

ROE = net income _________ equity = assets ______ equity ×

sales _____ assets × _____ sales ×

net income _________ (4.2)

Notice that the product of the two middle terms in Equation 4.2 is the return on assets. It depends on the firm’s production and marketing success and is unaffected by the firm’s financing mix.12 However, the first and fourth terms do depend on the debt- equity mix. The first term, assets/equity, which we call the leverage ratio, can be expressed as (equity + liabilities)/equity, which equals 1 + total-debt-to-equity ratio. The last term, which we call the “debt burden,” measures the proportion by which interest expense reduces profits.

Suppose that the firm is financed entirely by equity. In this case, both the leverage ratio and the debt burden are equal to 1, and the return on equity is identical to the return on assets. If the firm borrows, however, the leverage ratio is greater than 1 (assets are greater than equity) and the debt burden is less than 1 (part of the profits is absorbed by interest). Thus leverage can either increase or reduce return on equity. In fact, we will see in Chapter 16 that leverage increases ROE when the firm’s return on assets is higher than the interest rate it pays on its debt. Because Home Depot’s return on capital exceeds the interest rate on its debt, return on equity is higher than return on capital.

↑ leverage 

ratio

↑ asset

turnover

after-tax  operating income

after-tax  operating income↑

operating profit margin

↑ “debt burden”

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Chapter 4 Measuring Corporate Performance 103

Measuring Liquidity

If you are extending credit to a customer or making a short-term bank loan, you are interested in more than the borrower’s financial leverage. You want to know whether the company can lay its hands on the cash to repay you. That is why credit analysts and bankers look at several measures of liquidity. Liquid assets can be converted into cash quickly and cheaply.

Think, for example, what you would do to meet a large unexpected bill. You might have some money in the bank or some investments that are easily sold, but you would not find it so easy to turn your old sweaters into cash. Companies, likewise, own assets with different degrees of liquidity. For example, accounts receivable and inventories of finished goods are generally quite liquid. As inventories are sold off and customers pay their bills, money flows into the firm. At the other extreme, real estate may be quite illiquid. It can be hard to find a buyer, negotiate a fair price, and close a deal at short notice.

There is another reason to focus on liquid assets: Their book (balance sheet) values are usually reliable. The book value of a catalytic cracker may be a poor guide to its true value, but at least you know what cash in the bank is worth.

Liquidity ratios also have some less desirable characteristics. Because short-term assets and liabilities are easily changed, measures of liquidity can rapidly become out- dated. You might not know what the catalytic cracker is worth, but you can be fairly sure that it won’t disappear overnight. Cash in the bank can disappear in seconds.

Also, assets that seem liquid sometimes have a nasty habit of becoming illiquid. This happened during the subprime mortgage crisis in 2008. Some financial institutions had set up funds known as structured investment vehicles (SIVs) that issued short-term debt backed by residential mortgages. As mortgage default rates began to climb, the market in this debt dried up and dealers became very reluctant to quote a price.

Bankers and other short-term lenders applaud firms that have plenty of liquid assets. They know that when they are due to be repaid, the firm will be able to get its hands on the cash. But more liquidity is not always a good thing. For example, effi- cient firms do not leave excess cash in their bank accounts. They don’t allow custom- ers to postpone paying their bills, and they don’t leave stocks of raw materials and finished goods littering the warehouse floor. In other words, high levels of liquidity may indicate sloppy use of capital. Here, EVA can highlight the problem because it penalizes managers who keep more liquid assets than they really need.

Net Working Capital to Total Assets Ratio Current assets include cash, market- able securities, inventories, and accounts receivable. Current assets are mostly liquid. The difference between current assets and current liabilities is known as net working capital. It roughly measures the company’s potential net reservoir of cash. Because current assets usually exceed current liabilities, net working capital is usually positive. For Home Depot,

Net working capital = 18,933 − 16,194 = $2,739 million

4.7

liquidity The ability to sell an asset on short notice at close to the market value.

a. Sappy Syrup has a profit margin below the industry average, but its ROA equals the industry average. How is this possible?  

b. Sappy Syrup’s ROA equals the industry average, but its ROE exceeds the industry average. How is this possible?

Self-Test4.8

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104 Part One Introduction

Home Depot’s net working capital was 6.1% of total assets:

Net working capital ______________ Total assets = 2,739 _____ 44,529 = .061, or 6.1%

Current Ratio The current ratio is just the ratio of current assets to current liabilities:

Current ratio = current assets ____________ current liabilities = 18,933 _____ 16,194 = 1.17

Home Depot has $1.17 in current assets for every dollar in current liabilities. Changes in the current ratio can be misleading. For example, suppose that a com-

pany borrows a large sum from the bank and invests it in marketable securities. Current liabilities rise and so do current assets. If nothing else changes, net working capital is unaffected, but the current ratio changes. For this reason, it is sometimes preferable to net short-term investments against short-term debt when calculating the current ratio.

Quick (Acid-Test) Ratio Some current assets are closer to cash than others. If trou- ble comes, inventory may not sell at anything above fire-sale prices. (Trouble typically comes because the firm can’t sell its inventory of finished products for more than production cost.) Thus managers often exclude inventories and other less-liquid com- ponents of current assets when comparing current assets to current liabilities. They focus instead on cash, marketable securities, and bills that customers have not yet paid. This results in the quick ratio:

Quick ratio = cash + marketable securities + receivables _____________________________ current liabilities = 3,595 + 1,952 __________ 16,194 = .34

Cash Ratio A company’s most liquid assets are its holdings of cash and marketable securities. That is why analysts also look at the cash ratio:

Cash ratio = cash + marketable securities ____________________ current liabilities = 3,595 _____ 16,194 = .22

A low cash ratio may not matter if the firm can borrow on short notice. Who cares whether the firm has actually borrowed from the bank or whether it has a guaranteed line of credit that lets it borrow whenever it chooses? None of the standard measures of liquidity takes the firm’s “reserve borrowing power” into account.

a. A firm has $1.2 million in current assets and $1 million in current liabilities. If it uses $.5 million of cash to pay off some of its accounts payable, what will happen to the current ratio? What happens to net working capital?  

b. A firm uses cash on hand to pay for additional inventories. What will happen to the current ratio? To the quick ratio?  

Self-Test4.9

Interpreting Financial Ratios

We have shown how to calculate some common summary measures of Home Depot’s performance and financial condition. These are summarized in Table 4.6.

Now that you have calculated these measures, you need some way to judge whether they are a matter for concern or congratulation. In some cases, there may be a natural

4.8

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Chapter 4 Measuring Corporate Performance 105

Performance measures

Market value added ($ millions) market value of equity − book value of equity $221,092 Market-to-book ratio market value of equity ÷ book value of equity 153.0

Profitability Measures

Return on assets (ROA) after-tax operating income/total assets 21.6% Return on capital (ROC) after-tax operating income/(long-term debt + equity) 34.7% Return on equity (ROE) net income/equity 199.2% EVA ($ millions) after-tax operating income − (cost of capital × capital) $7,081

Efficiency Measures

Asset turnover sales/total assets at start of year 2.35 Receivables turnover sales/receivables at start of year 49.7 Average collection period (days) receivables at start of year/daily sales 7.3 Inventory turnover cost of goods sold/inventory at start of year 5.3 Days in inventory inventories at start of year/daily cost of goods sold 68.8 Profit margin net income/sales 8.6% Operating profit margin after-tax operating income/sales 9.2%

Leverage Measures

Long-term debt ratio long-term debt/(long-term debt + equity) 0.94 Long-term debt–equity ratio long-term debt/equity 16.69 Total debt ratio total liabilities/total assets 0.97 Times interest earned EBIT/interest payments 14.9 Cash coverage ratio (EBIT + depreciation)/interest payments 16.8

Liquidity Measures

Net working capital to assets net working capital/total assets 0.06 Current ratio current assets/current liabilities 1.17 Quick ratio (cash + marketable securities + receivables)/current liabilities 0.34 Cash ratio (cash + marketable securities)/current liabilities 0.22

TABLE 4.6 Summary of Home Depot’s performance measures

benchmark. For example, if a firm has negative value added or a return on capital that is less than the cost of that capital, it is not creating wealth for its shareholders.

But what about some of our other measures? There is no right level for, say, the asset turnover or profit margin, and if there were, it would almost certainly vary from year to year and industry to industry. When assessing company performance, managers usually look first at how the financial ratios have changed over time, and then they look at how their measures stack up in comparison with companies in the same line of business.

We will first compare Home Depot’s position in 2017 with its performance in ear- lier years. For example, Figure 4.3 plots Home Depot’s return on assets since 1996. We know that ROA = asset turnover × operating profit margin. Figure 4.3 shows that beginning in 1999 there was a steady decline in the company’s ability to generate sales from its assets, though for a while this effect was largely offset by a rise in the profit margin. When the downturn in the housing market in 2008 also led to a sharp decline in the profit margin, Home Depot’s ROA fell dramatically. The turnaround came under new management in 2009, and in each of the following years, the company was able to increase both the rate of asset turnover and the profit margin.

Managers also need to ask themselves how the company’s performance compares with that of its principal competitors. Table 4.7 sets out some key performance mea- sures for Home Depot and Lowe’s. Home Depot’s ROA is higher, due to its higher asset turnover ratio and its better operating profit margin. Home Depot has higher debt ratios, but, thanks to its greater profitability, it has the higher interest cover. Home Depot turns over its inventory more rapidly. However, its longer collection period seems to suggest that it is much less efficient in collecting its bills. This is actually an

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106 Part One Introduction

illusion. Lowe’s tends to sell its accounts receivable to other parties, and thus main- tains lower receivables on its balance sheet. The lesson? Ratios can tip you off to dif- ferences in strategy as well as to emerging business strengths or problems, but you will generally have to probe further to fully understand the implications of the numbers.

FIGURE 4.3 Home Depot’s financial ratios over time

P er

ce nt

10 x asset turnover

Operating profit margin (%) ROA (%)

0

5

10

15

20

25

19 9

6

19 9

8

20 0

0

20 0

2

20 0

4

20 0

6

20 0

8

20 10

20 12

20 14

20 16

20 18

Home Depot Lowe’s

Performance measures

Market value added ($ millions) $221,092 $62,677 Market-to-book ratio 153.0 11.7

Profitability Measures

Return on assets (ROA) 21.6% 11.2% Return on capital (ROC) 34.7% 18.5% Return on equity (ROE) 199.2% 53.6% EVA ($ millions) $7,081 $1,929

Efficiency Measures

Asset turnover 2.35 1.99 Receivables turnover 49.7 116.7 Average collection period (days) 7.3 3.1 Inventory turnover 5.3 4.3 Days in inventory 68.8 84.4 Profit margin 8.6% 5.0% Operating profit margin 9.2% 5.6%

Leverage Measures

Long-term debt ratio 0.94 0.73 Long-term debt–equity ratio 16.69 2.65 Total debt ratio 0.97 0.73 Times interest earned 14.9 10.4 Cash coverage ratio 16.8 12.7

Liquidity Measures

Net working capital to assets 0.06 0.02 Current ratio 1.17 1.06 Quick ratio 0.34 0.09 Cash ratio 0.22 0.06

TABLE 4.7 Selected financial measures for Home Depot and Lowe’s, 2017

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Chapter 4 Measuring Corporate Performance 107

Home Depot and Lowe’s are fairly close competitors, and it makes sense to com- pare their financial ratios. However, all financial ratios must be interpreted in the con- text of industry norms. For example, you would not expect a soft-drink manufacturer to have the same profit margin as a jeweler or the same leverage as a finance company. You can see this from Table 4.8, which presents some financial ratios for a sample of industry groups.

Notice the large variation across industries. Some of these differences, particularly in profitability measures, may arise from chance; in 2017 the sun shone more kindly on some industries than others. But other differences may reflect more fundamental factors. For example, you can see that computer companies turn over their assets slowly, but earn a relatively high profit margin on those sales. By contrast, retail firms turn over their assets rapidly. But competition ensures that retailers earn a correspondingly lower margin on their sales. The net effect is that the return on assets in the two industries is broadly similar.

Now that you know how to interpret financial ratios, you can use the nearby Beyond the Page feature to compare the ratios of other U.S. companies.

BEYOND THE PAGE

mhhe.com/brealey10e

Financial ratios for U.S. companies

Return on assets, %

Return on equity, %

Asset turnover

Receivables turnover

Inventory turnover

Operating profit

margin, % Long-term debt ratio

Times interest earned

Current ratio

Quick ratio

All manufacturing 6.54 13.82 0.64 9.17 8.34 10.16 0.38 3.75 1.25 0.64 Food products 7.54 15.32 0.86 12.64 10.05 8.82 0.40 5.00 1.50 0.67 Retail trade 7.55 19.04 2.06 38.11 10.17 3.67 0.46 5.48 1.27 0.54 Consultancy 4.13 8.96 0.72 6.09 92.09 5.78 0.34 2.59 0.88 0.63 Chemicals 5.54 11.79 0.40 6.74 7.81 13.97 0.45 2.73 1.08 0.52 Pharmaceuticals 4.67 9.43 0.32 6.16 7.36 14.68 0.50 2.74 1.06 0.54 Machinery 6.48 13.97 0.70 8.06 6.27 9.28 0.32 4.07 1.26 0.59 Electrical 1.67 2.33 0.54 7.19 5.84 3.08 0.35 3.97 1.23 0.63 Motor vehicles 4.64 11.02 1.18 14.31 13.43 3.92 0.27 4.90 1.02 0.54 Computer & electronics 7.80 15.47 0.39 8.27 10.64 20.00 0.37 2.86 1.22 0.77

TABLE 4.8 Financial ratios for major industry groups

Source: U.S. Census Bureau, Quarterly Financial Report for Manufacturing, Mining, Trade, and Selected Service Industries, second quarter 2018

Even within an industry, there can be a considerable difference in the type of business that companies do, and this shows up in their financial ratios. Here are some data on assets, sales, and income for two companies in 2017. Calculate for each company the asset turnover, the operating profit margin, and the return on assets. In each case, the values are expressed as a percentage of sales. One of these two companies is Walmart. The other is Tiffany. Which one is which? Explain.

Company A Company B

Sales 100 100 Assets 40.9 131.1 Net income + after-tax interest 4.25 19.41

Self-Test4.10

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108 Part One Introduction

The Role of Financial Ratios

Whenever two managers get together to talk business and finance, it’s a good bet that they will refer to financial ratios. Let’s drop in on two conversations.

Conversation 1 The CEO was musing out loud: “How are we going to finance this expansion? Would the banks be happy to lend us the $30 million that we need?”

“I’ve been looking into that,” the financial manager replies. “Our current debt ratio is 30%. If we borrow the full cost of the project, the ratio would be about 45%. When we took out our last loan from the bank, we agreed that we would not allow our debt ratio to get above 50%. So if we borrow to finance this project, we wouldn’t have much leeway to respond to possible emergencies. Also, the rating agencies currently give our bonds an investment-grade rating. They too look at a company’s leverage when they rate its bonds. I have a table here (Table 4.9) that shows that when firms are highly leveraged, their bonds receive a lower rating. I don’t know whether the rating agencies would downgrade our bonds if our debt ratio increased to 45%, but they might. That wouldn’t please our existing bondholders, and it could raise the cost of any new borrowing.

“We also need to think about our interest cover, which is beginning to look a bit thin. Debt interest is currently covered three times, and if we borrowed the entire $30 million, interest cover would fall to about two times. Sure, we expect to earn additional profits on the new investment, but it could be several years before they come through. If we run into a recession in the meantime, we could find ourselves short of cash.”

“Sounds to me as if we should be thinking about a possible equity issue,” concluded the CEO.

Conversation 2 The CEO was not in the best of moods after his humiliating defeat at the company golf tournament by the manager of the packaging division: “I see our stock was down again yesterday,” he growled. “It’s now selling below book value, and the stock price is only six times earnings. I work my socks off for this company; you would think that our stockholders would show a little more gratitude.”

“I think I can understand a little of our shareholders’ worries,” the financial man- ager replies. “Just look at our book rate of return on assets. It’s only 6%, well below the cost of capital. Sure we are making a profit, but that profit does not cover the cost of the funds that investors provide. Our economic value added is actually negative. Of course, this doesn’t necessarily mean that the assets could be used better elsewhere, but we should certainly be looking carefully at whether any of our divisions should be sold off or the assets redeployed.

4.9

Rating Category Operating

Margin (%)a EBITAb/Assets Long-Term

Debt Ratio (%)c Cash

Coverage Ratiod

Aaa 25.4 12.3 35.1 17.2 Aa 17.4 10.2 31.0 15.2 A 14.9 10.8 40.7 13.1 Baa 12.0 8.7 46.4 8.1 Ba 11.5 8.5 55.7 5.1 B 9.0 6.7 65.8 2.9 C 4.6 4.1 89.3 1.6

aOperating profit/net revenues bEBITA is earnings before interest, tax, and amortization cLong-term debt/book value of total capital dEBITA/Interest expense. (EBITA is earnings before interest, tax, and amortization.) Source: Moody’s Investor Service, “Moody’s Financial Metrics Key Ratios by Rating and Industry for Global Non- Financial Corporates: December 2016”.

TABLE 4.9 Median financial ratios by rating class for nonfinancial North American corporations

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Chapter 4 Measuring Corporate Performance 109

“In some ways we’re in good shape. We have very little short-term debt, and our current assets are three times our current liabilities. But that’s not altogether good news because it also suggests that we may have more working capital than we need. I’ve been looking at our main competitors. They turn over their inventory 12 times a year compared with our figure of just 8 times. Also, their customers take an average of 45 days to pay their bills. Ours take 67. If we could just match their performance on these two measures, we would release $300 million that could be paid out to shareholders.”

“Perhaps we could talk more about this tomorrow,” said the CEO. “In the meantime I intend to have a word with the production manager about our inventory levels and with the credit manager about our collections policy. You’ve also got me thinking about whether we should sell off our packaging division. I’ve always worried about the divisional manager there. Spends too much time practicing his backswing and not enough worrying about his return on assets.”

SUMMARY For a public corporation, this is relatively easy. Start with market capitalization, which equals price per share times the number of shares outstanding. The difference between market capitalization and the book value of equity measures the market value added by the firm’s investments and operations. The book value of equity is the cumulative invest- ment (including reinvested earnings) by shareholders in the company. The ratio of market value to book value is another way of expressing value added.

For private corporations, financial managers and analysts have to turn to other perfor- mance measures because stock prices are not available.

Financial managers and analysts track return on equity (ROE), which is the ratio of net income to shareholders’ equity. But net income is calculated after interest expense, so ROE depends on the debt ratio. The return on capital (ROC) and the return on assets (ROA) are better measures of operating performance. These are the ratios of after-tax operating income to total capitalization (long-term debt plus shareholders’ equity) and to total assets. ROC should be compared with the company’s cost of capital. EVA (economic value added or residual income) deducts the cost of capital from operating income. If EVA is positive, then the firm’s operations are adding value for shareholders.

Financial managers and analysts have to condense the enormous volume of information in a company’s financial statements. They rely on a handful of ratios to summarize financial performance, operating efficiency, and financial strength. Look back at Table 4.6, which summarizes the most important ratios. Remember that the ratios sometimes appear under different names and may be calculated differently.

Profitability ratios measure return on sales. Efficiency ratios measure how inten- sively the firm uses its assets. Leverage ratios measure how much the firm has borrowed and its obligations to pay interest. Liquidity ratios measure how easily the firm can obtain cash.

Financial ratios crop up repeatedly in financial discussions and contracts. For example, banks and bondholders usually demand limits on debt ratios or interest coverage.

The Du Pont system links financial ratios together to explain the return on assets and equity. Return on assets is the product of asset turnover and operating profit margin. Return on equity is the product of the leverage ratio, asset turnover, operating profit margin, and debt burden.

How do you measure whether a public corporation has delivered value for its shareholders? (LO4-1)

What measures are used to assess financial performance? (LO4-2)

What are the standard measures of profitability, efficiency, leverage, and liquidity? (LO4-3)

What determines the return on assets and equity? (LO4-4)

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110 Part One Introduction

Financial statement analysis will rarely be useful if done mechanically. Financial ratios do not provide final answers, although they should prompt the right questions. In addition, accounting entries do not always reflect current market values, and in rare cases account- ing is not transparent because unscrupulous managers make up good news and hide bad news in financial statements.

You will need a benchmark to assess a company’s financial condition. Therefore, ana- lysts usually compare financial ratios with the company’s ratios in earlier years and with ratios of other firms in the same business.

What are some potential pitfalls in financial statement analysis? (LO4-5)

LISTING OF EQUATIONS

4.1 Return on assets = after-tax operating income ____________________ assets

= sales _____ assets × after-tax operating income ______________________ sales

4.2 ROE = net income __________ equity = assets ______ equity ×

sales _____ assets × _____ sales ×

net income __________

↑ asset turnover

↑ operating

profit margin

↑ asset

turnover

↑ leverage 

ratio

↑ operating 

profit margin ↑

“debt burden”

after-tax  operating income

after-tax  operating income

QUESTIONS AND PROBLEMS 1. Market Value Added. Here is a simplified balance sheet for Locust Farming:

Current assets $42,524 Current liabilities $29,755 Long-term assets 46,832 Long-term debt 27,752

Other liabilities 14,317 Equity 17,532

Total $89,356 Total $89,356

Locust has 657 million shares outstanding with a market price of $83 a share. (LO4-1) a. Calculate the company’s market value added. b. Calculate the market-to-book ratio. c. How much value has the company created for its shareholders as a percent of shareholders’

equity, that is, as a percent of the net capital contributed by shareholders)?

2. Market Value Added. Suppose Home Depot’s Stock price falls by 10% in a given year. (LO4-1) a. Will the firm’s market value added increase or decrease? b. How will this change affect your assessment of the performance of the firm’s management? c. Now suppose that in the same year, the broad stock market fell by 20%, a lot more than the

decline in Home Depot’s stock. Would this cause you to rethink your assessment of the firm’s management?

d. Can you think of an improvement to the way in which we relate market value added to our evaluation of firm management?

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Chapter 4 Measuring Corporate Performance 111

3. Measuring Performance. Here are simplified financial statements for Watervan Corporation:

INCOME STATEMENT (Figures in $ millions)

Net sales $881 Cost of goods sold 741 Depreciation 31 Earnings before interest and taxes (EBIT) 109 Interest expense 12 Income before tax 97 Taxes 20 Net income 77

BALANCE SHEET (Figures in $ millions)

End of Year Start of Year

Assets Current assets $369 $312 Long-term assets 258 222 Total assets $627 $534 Liabilities and shareholders’ equity Current liabilities $194 $157 Long-term debt 108 121 Shareholders’ equity 325 256 Total liabilities and shareholders’ equity $627 $534

The company’s cost of capital is 8.5%. (LO4-2) a. Calculate Watervan’s economic value added (EVA). b. What is the company’s return on capital? (Use start-of-year rather than average capital.) c. What is its return on equity? (Use start-of-year rather than average equity.) d. Is the company creating value for its shareholders?

4. Measuring Performance. Recalculate Home Depot’s economic value added as we did in Section 4.3, but assuming its cost of capital is 10%. (LO4-2)

5. Economic Value Added. EVA will be positive whenever ROC is positive and greater than the cost of capital. Explain why this is so. (LO4-2)

6. Return on Capital. Microlimp does not raise any new finance during the year, but it generates a lot of earnings, which are immediately reinvested. If you were calculating the company’s return on capital, would it make more sense to use capital at the start of the year or an average of the starting and ending capital? Would your answer change if Microlimp made a large issue of debt early in the year? Illustrate your answer with simple examples. (LO4-2)

7. Financial Ratios. Here are simplified financial statements for Phone Corporation in 2017:

INCOME STATEMENT (Figures in $ millions)

Net sales $13,193 Cost of goods sold 4,060 Other expenses 4,049 Depreciation   2,518 Earnings before interest and taxes (EBIT) $ 2,566 Interest expense   685 Income before tax $ 1,881 Taxes (at 35%)   658 Net income $ 1,223 Dividends 856

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112 Part One Introduction

BALANCE SHEET (Figures in $ millions)

End of Year Start of Year

Assets Cash and marketable securities $ 89 $ 158 Receivables 2,382 2,490 Inventories 187 238 Other current assets 867 932 Total current assets $ 3,525 $ 3,818 Net property, plant, and equipment 19,973 19,915 Other long-term assets 4,216        3,770 Total assets $27,714 $27,503 Liabilities and shareholders’ equity Payables $ 2,564 $ 3,040 Short-term debt 1,419 1,573 Other current liabilities 811 787 Total current liabilities $ 4,794 $ 5,400 Long-term debt and leases 7,018 6,833 Other long-term liabilities 6,178 6,149 Shareholders’ equity 9,724 9,121 Total liabilities and shareholders’ equity $27,714 $27,503

Calculate the following financial ratios for Phone Corporation using the methodologies listed for each part: (LO4-3) a. Return on equity (use average balance sheet figures) b. Return on assets (use average balance sheet figures) c. Return on capital (use average balance sheet figures) d. Days in inventory (use start-of-year balance sheet figures) e. Inventory turnover (use start-of-year balance sheet figures) f. Average collection period (use start-of-year balance sheet figures) g. Operating profit margin h. Long-term debt ratio (use end-of-year balance sheet figures) i. Total debt ratio (use end-of-year balance sheet figures) j. Times interest earned k. Cash coverage ratio l. Current ratio (use end-of-year balance sheet figures) m. Quick ratio (use end-of-year balance sheet figures)

8. Financial Ratios. Consider this simplified balance sheet for Geomorph Trading: (LO4-3)

Current assets $100 Current liabilities $ 60 Long-term assets 500 Long-term debt 280

Other liabilities 70 Equity 190

$600 $600

a. What is the company’s debt-equity ratio? b. What is the ratio of total long-term debt to total long-term capital? c. What is its net working capital? d. What is its current ratio?

9. Receivables. Chik’s Chickens has accounts receivable of $6,333. Sales for the year were $9,800. What is its average collection period? (LO4-3)

10. Inventory. Salad Daze maintains an inventory of produce worth $400. Its total bill for produce over the course of the year was $73,000. How old on average is the lettuce it serves its customers? (LO4-3)

11. Times Interest Earned. In the past year, TVG had revenues of $3 million, cost of goods sold of $2.5 million, and depreciation expense of $200,000. The firm has a single issue of debt out- standing with book value of $1 million on which it pays an interest rate of 8%. What is the firm’s times interest earned ratio? (LO4-3)

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Chapter 4 Measuring Corporate Performance 113

12. Leverage Ratios. Lever Age pays an 8% rate of interest on $10 million of outstanding debt with face value $10 million. The firm’s EBIT was $1 million. (LO4-3) a. What is its times interest earned? b. If depreciation is $200,000, what is its cash coverage ratio?

13. Financial Ratios. There are no universally accepted definitions of financial ratios, but some of the following ratios make no sense at all. If the definition is incorrect, substitute a correct one. (LO4-3) a. Debt-equity ratio = long-term debt/(long-term debt + equity) b. Return on equity = net income/average equity c. Operating profit margin = after-tax operating income/sales d. Inventory turnover = total sales/average inventory e. Current ratio = current liabilities/current assets f. Average collection period = sales/(average receivables/365) g. Quick ratio = (cash + marketable securities + receivables)/current liabilities

14. Asset Turnover. In each case, choose the firm that you expect to have the higher asset turnover ratio. (Hint: think about the likely nature of each firm’s business model. For example, would the firm require a lot or a little capital? Would it strive for high sales or high profit margins?) (LO4-3) a. Economics Consulting Group or Home Depot b. Catalog Shopping Network or Gucci c. Electric Utility Co. or Standard Supermarkets

15. Inventory Turnover.  (LO4-3) a. If a firm’s inventory level of $10,000 represents 30 days’ sales, what is the annual cost of

goods sold? b. What is the inventory turnover ratio?

16. Leverage. A firm has a long-term debt–equity ratio of .4. Shareholders’ equity is $1 million. Current assets are $200,000, and the current ratio is 2. The only current liabilities are notes pay- able. What is the total debt ratio? (LO4-3)

17. Leverage Ratios. A firm has a debt-to-equity ratio of .5 and a market-to-book ratio of 2. What is the ratio of the book value of debt to the market value of equity? (LO4-3)

18. Liquidity Ratios. A firm uses $1 million in cash to purchase inventories. (LO4-3) a. Will its current ratio rise or fall? b. Will its quick ratio rise or fall?

19. Current Ratio. Would the following events increase or decrease a firm’s current ratio? (LO4-3) a. Inventory is sold. b. The firm takes out a bank loan to pay its suppliers. c. The firm arranges a line of credit with a bank that allows it to borrow at any time to pay its

suppliers. d. A customer pays its overdue bills. e. The firm uses cash to buy additional inventory.

20. Financial Ratios. True or false? (LO4-3) a. A company’s debt-equity ratio is always less than 1. b. The quick ratio is always less than the current ratio. c. For a profitable company, the return on equity is always less than the return on assets.

21. Interpreting Financial Ratios. In each of the following cases, state which of the two compa- nies is likely to be characterized by the higher ratio. (Hint: think about the likely nature of each firm’s business model. For example, would the firm require a lot or a little capital? Would it strive for high sales or high profit margins? Does it sell goods for cash or on credit?) (LO4-3) a. Debt-equity ratio: a shipping company or a computer software company b. Ratio of sales to assets: an integrated pulp and paper manufacturer or a paper mill c. Average collection period: Regional Electric Power Company or Z-Mart Discount Outlets

22. Financial Ratios. As you can see, someone has spilled ink over some of the entries in the bal- ance sheet and income statement of Transylvania Railroad. Use the information from the tables to work out the following missing entries, and then calculate the company’s return on equity. Note: Inventory turnover, average collection period, and return on equity are calculated using start-of-year, not average, values. (LO4-3)

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114 Part One Introduction

Long-term debt ratio 0.4 Times interest earned 8.0 Current ratio 1.4 Quick ratio 1.0 Cash ratio 0.2 Inventory turnover 5.0 Average collection period 73 days

INCOME STATEMENT (Figures in $ millions)

Net sales     Cost of goods sold     Selling, general, and administrative expenses 10 Depreciation 20 Earnings before interest and taxes (EBIT)     Interest expense     Income before tax     Tax (35% of income before tax)     Net income     

BALANCE SHEET (Figures in $ millions)

This Year Last Year

Assets Cash and marketable securities     20 Accounts receivable     34 Inventories     26 Total current assets     80 Net property, plant, and equipment     25 Total assets     105 Liabilities and shareholders’ equity Accounts payable 25 20 Notes payable 30 35 Total current liabilities     55 Long-term debt     20 Shareholders’ equity     30 Total liabilities and shareholders’ equity 115 105

a. Total assets b. Total current liabilities c. Total current assets d. Cash and marketable securities e. Accounts receivable f. Inventory g. Fixed assets h. Long-term debt i. Shareholders’ equity j. Net sales k. Cost of goods sold l. EBIT

m. Interest expense n. Income before tax o. Tax p. Net income

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Chapter 4 Measuring Corporate Performance 115

23. Interpreting Financial Ratios. (LO4-3) a. Turn back to Table 4.8. For the sample of industries in that table, plot operating profit mar-

gin against asset turnover in a scatter diagram. What is the apparent relationship between these two variables? Does this make sense to you?

b. Now plot a scatter diagram of the cash ratio versus quick ratio. Do these two measures of liquidity tend to move together? Would you conclude that once you know one of these ratios, there is little to be gained by calculating the other?

24. Du Pont Analysis. Last year Electric Autos had sales of $100 million and assets at the start of the year of $150 million. If its return on start-of-year assets was 15%, what was its operating profit margin? (LO4-4)

25. Du Pont Analysis. Torrid Romance Publishers has total receivables of $3,000, which repre- sents 20 days’ sales. Total assets are $75,000. The firm’s operating profit margin is 5%. Find: (a) the firm’s ROA and (b) its asset turnover ratio. (LO4-4)

26. Du Pont Analysis. Keller Cosmetics maintains an operating profit margin of 5% and asset turn- over ratio of 3. (LO4-4) a. What is its ROA? b. If its debt-equity ratio is 1, its interest payments and taxes are each $8,000, and EBIT is

$20,000, what is its ROE?

27. Interpreting Financial Ratios. CFA Corp. has a debt-equity ratio that is lower than the industry average, but its cash coverage ratio is also lower than the industry average. What might explain this seeming contradiction? (LO4-4)

28. Using Financial Ratios. For each category of financial ratios discussed in this chapter, give some examples of who would be likely to examine these ratios and why. (LO4-5)

WEB EXERCISE 1. Log on to finance.yahoo.com to find the latest simplified financial statements for The Home

Depot. Recalculate HD’s financial ratios. What have been the main changes from the financial statements shown in this chapter? If you owned some of HD’s debt, would these changes make you feel more or less happy?

SOLUTIONS TO SELF-TEST QUESTIONS 4.1 Market capitalization is $75 × 14.5 million = $1,087.5 million. Market value added is $1,087.5 −

$610 = $477.5 million. Market to book is 1,087.5/610 = 1.78. You can also calculate book value per share at $610/14.5 = $42.07, and use price per share to calculate market to book: $75/$42.07 = 1.78.

4.2 The cost of capital in dollars is .115 × $188 million = $21.62 million. EVA is $30 − $21.62 = $8.38 million.

4.3 After-tax operating income is calculated before interest expense. Net income is calculated after interest expense. Financial managers usually start with net income, so they add back after-tax interest to get after-tax operating income. After-tax operating income measures the profitability of the firm’s investment and operations. If properly calculated, it is not affected by financing.

4.4 ROE measures return to equity as net income divided by the book value of equity. ROC and ROA measure the return to all investors, including interest paid as well as net income to share- holders. ROC measures return versus long-term debt and equity. ROA measures return versus total assets.

4.5 Average daily expenses are 66,548/365 = $182.3 million. Accounts payable at the start of the year are $7,000 million. The average payment delay is therefore 7,000/182.3 = 38.4 days.

4.6 In industries with rapid asset turnover, competition forces prices down, reducing profit margins.

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116 Part One Introduction

4.7 Nothing will happen to the long-term debt ratio computed using book values because the face values of the old and new debt are equal. However, times interest earned and cash coverage will increase because the firm will reduce its interest expense.

4.8 a. The firm must compensate for its below-average profit margin with an above-average turn- over ratio. Remember that ROA is the product of operating margin × turnover.

b. If ROA equals the industry average but ROE exceeds the industry average, the firm must have above-average leverage. As long as ROA exceeds the borrowing rate, leverage will increase ROE.

4.9 a. The current ratio starts at 1.2/1.0 = 1.2. The transaction will reduce current assets to $.7 million and current liabilities to $.5 million. The current ratio increases to .7/.5 = 1.4. Net working capital is unaffected: Current assets and current liabilities fall by equal amounts.

b. The current ratio is unaffected because the firm merely exchanges one current asset (cash) for another (inventories). However, the quick ratio will fall because inventories are not included among the most liquid assets.

4.10 Company A Company B

1. Asset turnover 2.45 0.76 2. Operating profit margin (%) 4.25 19.41 3. Return on assets (%) (= 1 × 2) 10.4 14.8

Company A is Walmart; it generates a high volume of sales from its assets but earns a rela- tively low profit margin on these sales. The reverse is true of Tiffany (company B). The two companies differ enormously in their asset turnover and profit margin, but much less in their return on assets.

MINICASE Burchetts Green had enjoyed the bank training course, but it was good to be starting his first real job in the corporate lending group. Earlier that morning the boss had handed him a set of financial statements for The Hobby Horse Company Inc. (HH). “Hobby Horse,” she said, “has a $45 million loan from us due at the end of September, and it is likely to ask us to roll it over. The company seems to have run into some rough weather recently, and I have asked Furze Platt to go down there this afternoon and see what is happening. It might do you good to go along with her. Before you go, take a look at these financial statements and see what you think the problems are. Here’s a chance for you to use some of that stuff they taught you in the training course.”

Mr. Green was familiar with the HH story. Founded in 1990, it had rapidly built up a chain of discount stores selling materials for crafts and hobbies. However, last year a number of new store open- ings coinciding with a poor Christmas season had pushed the com- pany into loss. Management had halted all new construction and put 15 of its existing stores up for sale.

Mr. Green decided to start with the 6-year summary of HH’s balance sheet and income statement (Table 4.10). Then he turned to examine in more detail the latest position (Tables 4.11 and 4.12).

What appear to be the problem areas in HH? Do the financial ratios suggest questions that Ms. Platt and Mr. Green need to address?

2019 2018 2017 2016 2015 2014

Net sales 3,351 3,314 2,845 2,796 2,493 2,160 EBIT −9 312 256 243 212 156 Interest 37 63 65 58 48 46 Taxes 3 60 46 43 39 34 Net profit −49 189 145 142 125 76 Earnings per share −0.15 0.55 0.44 0.42 0.37 0.25 Current assets 669 469 491 435 392 423 Net fixed assets 923 780 753 680 610 536 Total assets 1,592 1,249 1,244 1,115 1,002 959 Current liabilities 680 365 348 302 276 320 Long-term debt 236 159 297 311 319 315 Stockholders’ equity 676 725 599 502 407 324 Number of stores 240 221 211 184 170 157 Employees 13,057 11,835 9,810 9,790 9,075 7,825

TABLE 4.10 Financial highlights for The Hobby Horse Company Inc., year ending March 31

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Chapter 4 Measuring Corporate Performance 117

Net sales $3,351 Cost of goods sold 1,990 Selling, general, and administrative expenses 1,211 Depreciation expense 159 Earnings before interest and taxes (EBIT) −$   9 Net interest expense 37 Taxable income −$  46 Income taxes   3 Net income −$  49 Allocation of net income Addition to retained earnings −$  49 Dividends 0

TABLE 4.11 Income statement for The Hobby Horse Company Inc., year ending March 31, 2019 (figures in $ millions)

Assets Mar. 31, 2019 Mar. 31, 2018

Current assets Cash and marketable securities $   14 $  72 Receivables 176 194 Inventories  479   203 Total current assets $ 669 $ 469 Fixed assets Property, plant, and equipment $1,077 $  910 Less accumulated depreciation  154    130 Net fixed assets $ 923 $  780 Total assets $1,592 $1,249

Liabilities and Shareholders’ Equity Mar. 31, 2019 Mar. 31, 2018

Current liabilities Debt due for repayment $ 484 $ 222 Accounts payable 94 58 Other current liabilities  102     85 Total current liabilities $ 680 $  365 Long-term debt $ 236 $  159 Stockholders’ equity Common stock and other paid-in capital $ 155 $ 155 Retained earnings    521  570 Total stockholders’ equity $   676 $   725 Total liabilities and stockholders’ equity $1,592 $1,249

Note: Column sums subject to rounding error.

TABLE 4.12 Consolidated balance sheet for The Hobby Horse Company Inc. (figures in $ millions)

bre13960_ch04_086-117.indd 117 1/28/19 5:40 PM

118

The Time Value of Money

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

5-1 Calculate the future value of money that is invested at a particular interest rate.

5-2 Calculate the present value of a future payment.

5-3 Calculate present and future values of a level stream of cash payments.

5-4 Compare interest rates quoted over different time intervals— for example, monthly versus annual rates.

5-5 Understand the difference between real and nominal cash flows and between real and nominal interest rates.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

5

bre13960_ch05_118-165.indd 118 1/26/19 11:27 AM

119

P A

R T

T W

O V

al ue

Time affects the value of a dollar. ©David Zalubowski/AP Images

Companies invest in lots of things. Some are tangible assets—that is, assets you can kick, like factories, machinery, and offices. Others are intangible assets, such as patents or trademarks. In each case the company lays out some money now in the hope of receiving even more money later.

Individuals also make investments. For example, your college education may cost you $30,000 per year. That is an investment you hope will pay off in the form of a higher salary later in life. You are sowing now and expecting to reap later.

Companies pay for their investments by raising money and, in the process, assuming liabilities. For example, they may borrow money from a bank and promise to repay it with interest later. You also may have financed your investment in a college education by borrowing money that you plan to pay back out of that fat salary.

All these financial decisions require comparisons of cash payments at different dates. Will your future salary be sufficient to justify the current expenditure on col- lege tuition? How much will you have to repay the bank if you borrow to finance your education?

In this chapter, we take the first steps toward under- standing the time value of money, that is, the relationship

between the values of dollars today and dollars in the future. We start by looking at how funds invested at a specific interest rate will grow over time. We next ask how much you would need to invest today to produce a specified future sum of money, and we describe some shortcuts for working out the value of a series of cash payments. Then we consider how inflation affects these financial calculations.

There is nothing complicated about the calculations, but if they are to become second nature, you should read the chapter thoroughly, work carefully through the exam- ples (we have provided plenty), and make sure you tackle the self-test questions. We are asking you to make an investment now in return for a payoff later. One of the pay- offs is that you will understand what is going on behind the screen when you value cash flows using a spreadsheet program or a financial calculator. We show how to use spreadsheets and financial calculators later in the chapter.

For simplicity, almost every example in this chapter is set out in dollars, but the concepts and calculations are identical in euros, yen, tugrik, or drams.1

1 The tugrik is the currency of Mongolia, and the dram is the cur- rency of Armenia.

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120 Part Two Value

Future Values and Compound Interest

You have $100 invested in a bank account. Suppose banks are currently paying an interest rate of 6% per year on deposits. So after a year, your account will earn interest of $6:

Interest = interest rate × initial investment = .06 × $100 = $6

You start the year with $100 and you earn interest of $6, so the value of your invest- ment will grow to $106 by the end of the year:

Value of investment after 1 year = $100 + $6 = $106

Notice that the $100 invested grows by the factor (1 + .06) = 1.06. In general, for any interest rate r, the value of the investment at the end of 1 year is (1 + r) times the initial investment:

Value after 1 year = initial investment × (1 + r) = $100 × (1.06) = $106

What if you leave this money in the bank for a second year? Your balance, now $106, will continue to earn interest of 6%. So

Interest in year 2 = .06 × $106 = $6.36

You start the second year with $106, on which you earn interest of $6.36. So by the end of the year the value of your account will grow to $106 + $6.36 = $112.36.

In the first year, your investment of $100 increases by a factor of 1.06 to $106; in the second year the $106 again increases by a factor of 1.06 to $112.36. Thus, the ini- tial $100 investment grows twice by a factor 1.06:

Value of investment after 2 years = $100 × 1.06 × 1.06 = $100 × (1.06)2 = $112.36

If you keep your money invested for a third year, your investment multiplies by 1.06 each year for 3 years. By the end of the third year it will total $100 × (1.06)3 = $119.10, scarcely enough to put you in the millionaire class, but even millionaires have to start somewhere.

Clearly, if you invest your $100 for t years, it will grow to $100 × (1.06)t. For an interest rate of r and a horizon of t years, the future value (FV) of your investment will be

Future value (FV) of $100 = $100 × (1 + r)t (5.1)

Notice in our example that your interest income in the first year is $6 (6% of $100) and in the second year is $6.36 (6% of $106). Your income in the second year is higher because you now earn interest on both the original $100 investment and the $6 of interest earned in the previous year. Earning interest on interest is called compounding or compound interest. In contrast, if the bank calculated the interest only on your original investment, you would be paid simple interest. With simple interest, the value of your investment would grow each year by .06 × $100 = $6.

Table 5.1 and Figure 5.1 illustrate the mechanics of compound interest. Table 5.1 shows that in each year, you start with a greater balance in your account—your savings have been increased by the previous year’s interest. As a result, your interest income also is higher.

5.1

future value (FV) Amount to which an investment will grow after earning interest.

compound interest Interest earned on interest.

simple interest Interest earned only on the original investment; no interest is earned on interest.

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Chapter 5 The Time Value of Money 121

Obviously, the higher the rate of interest, the faster your savings will grow. Figure 5.2 shows the balance in your savings account after a given number of years for several interest rates. Even a few percentage points added to the (compound) interest rate can dramatically affect the future balance. For example, after 10 years $100

Year Balance at 

Start of Year Interest Earned

during Year Balance at  End of Year

1 $100.00 0.06 × $100.00 = $6.00 $106.00 2 $106.00 0.06 × $106.00 = $6.36 $112.36 3 $112.36 0.06 × $112.36 = $6.74 $119.10 4 $119.10 0.06 × $119.10 = $7.15 $126.25 5 $126.25 0.06 × $126.25 = $7.57 $133.82

TABLE 5.1 How your savings grow; the future value of $100 invested to earn 6% with compound interest

FIGURE 5.1 A plot of the data in Table 5.1, showing the future values of an investment of $100 earning 6% with compound interest

Year

V al

ue in

y ou

r ac

co un

t ( $

)

140

120

100

80

60

40

20

0 1 2 3 4 5

This year’s interest

Interest from previous years

Original investment

FIGURE 5.2 How an investment of $100 grows with compound interest at different interest rates

2 4 6 8 10 12 14 16 18 20

Number of years

r = 0 r = 5% r = 10% r = 15%

Fu tu

re v

al ue

o f $

10 0

($ )

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

bre13960_ch05_118-165.indd 121 1/26/19 11:28 AM

122 Part Two Value

invested at 10% will grow to $100 × (1.10)10 = $259.37. If invested at 5%, it will grow to only $100 × (1.05)10 = $162.89.

Calculating future values is easy using almost any calculator. If you have the patience, you can multiply your initial investment by 1 + r (1.06 in our example) once for each year of your investment. A simpler procedure is to use the power key (the yx key) on your calculator. For example, to compute (1.06)10, enter 1.06, press the yx key, enter 10, press =, and discover that the answer is 1.7908. (Try this!)

If you don’t have a calculator, you can use a table of future values such as Table 5.2. Let’s use it to work out the future value of a 10-year investment at 6%. First, find the row corresponding to 10 years. Now work along that row until you reach the column for a 6% interest rate. The entry shows that $1 invested for 10 years at 6% grows to $1.7908.

Notice that as you move across each row in Table 5.2, the future value of a $1  investment increases, as your funds compound at a higher interest rate. As you move down any column, the future value also increases, as your funds compound for a longer period.

Now try one more example. If you invest $1 for 20 years at 10% and do not with- draw any money, what will you have at the end? Your answer should be $6.7275.

Table 5.2 gives future values for only a small selection of years and interest rates. Table A.1 at the end of the book is a bigger version of Table 5.2. It presents the future value of a $1 investment for a wide range of time periods and interest rates.

Future value tables are tedious, and as Table 5.2 demonstrates, they show future values only for a limited set of interest rates and time periods. For example, suppose that you want to calculate future values using an interest rate of 7.835%. The power key on your calculator will be faster and easier than future value tables.

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

  1  1.0500  1.0600  1.0700  1.0800  1.0900  1.1000    2  1.1025  1.1236  1.1449  1.1664  1.1881  1.2100    3  1.1576  1.1910  1.2250  1.2597  1.2950  1.3310    4  1.2155  1.2625  1.3108  1.3605  1.4116  1.4641    5  1.2763  1.3382  1.4026  1.4693  1.5386  1.6105  10 1.6289  1.7908  1.9672  2.1589  2.3674  2.5937  20 2.6533  3.2071  3.8697  4.6610  5.6044  6.7275  30 4.3219  5.7435  7.6123  10.0627  13.2677  17.4494 

TABLE 5.2 An example of a future value table, showing how an investment of $1 grows with compound interest

Manhattan Island

Almost everyone’s favorite example of the power of compound interest is the purchase of Manhattan Island for $24 in 1626 by Peter Minuit. Based on New York real estate prices today, it seems that Minuit got a great deal. But did he? Consider the future value of that $24 if it had been invested for 393 years (2019 minus 1626) at an interest rate of 8% per year:

$24 × (1.08)393 = $327,904,327,346,904 = $328 trillion

Perhaps the deal wasn’t as good as it appeared. The total value of land on Manhattan today is only a fraction of $328 trillion.

Though entertaining, this analysis is actually somewhat misleading. The 8% interest rate we’ve used to compute future values is high by historical standards. At a 3.5% interest rate,

Example 5.1 ⊲

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Chapter 5 The Time Value of Money 123

The power of compounding is not restricted to money. Foresters try to forecast the compound growth rate of trees, demographers the compound growth rate of popula- tions. A social commentator once observed that the number of lawyers in the United States is increasing at a higher compound rate than the population as a whole (3.6% versus .9% in the 1980s) and calculated that in about two centuries there will be more lawyers than people. In all these cases, the principle is the same: Compound growth means that value increases each period by the factor (1 + growth rate). The value after t periods will equal the initial value times (1 + growth rate)t. When money is invested at compound interest, the growth rate is the interest rate.

more consistent with historical experience, the future value of the $24 would be dramatically lower, only $24 × (1.035)393  = $17,855,364! On the other hand, we have understated the returns to Mr. Minuit and his successors: We have ignored all the rental income that the island’s land has generated over the last four centuries.

All things considered, if we had been around in 1626, we would have gladly paid $24 for the island. ■

Suppose that Peter Minuit did not become the first New York real estate tycoon but instead had invested his $24 at a 5% interest rate in New Amsterdam Savings Bank. What would have been the balance in his account after 5 years? 50 years?

Self-Test5.1

In 1973 Gordon Moore, one of Intel’s founders, predicted that the number of transistors that could be placed on a single silicon chip would double every 18 months, equivalent to an annual growth of 59% (i.e., 1.591.5 = 2.0). The first microprocessor was built in 1971 and had 2,250 transistors. By 2016, high-end Intel chips contained 7.2 billion transistors, 3.2 million times the number of tran- sistors 45 years earlier. What has been the annual compound rate of growth in processing power? How does it compare with the prediction of Moore’s law?  

Self-Test5.2

Present Values

Money can be invested to earn interest. If you are offered the choice between $100,000 now and $100,000 at the end of the year, you naturally take the money now to get a year’s interest. Financial managers make the same point when they say that money in hand today has a time value or when they quote perhaps the most basic financial prin- ciple: A dollar today is worth more than a dollar tomorrow.

We have seen that $100 invested for 1 year at 6% will grow to a future value of 100 × 1.06 = $106. Let’s turn this around: How much do we need to invest now in

5.2

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124 Part Two Value

order to produce $106 at the end of the year? In other words, what is the present value (PV) of the $106 payoff?

To calculate future value, we multiply today’s investment by 1 plus the interest rate, .06, or 1.06. To calculate present value, we simply reverse the process and divide the future value by 1.06:

Present value = PV =  future value __________ 1.06 =  $106 _____ 1.06  = $100

What is the present value of, say, $112.36 to be received 2 years from now? Again we ask, How much would we need to invest now to produce $112.36 after 2 years? The answer is obviously $100; we’ve already calculated that at 6% interest, $100 grows to $112.36:

$100 × (1.06)2 = $112.36

However, if we don’t know, or forgot the answer, we just divide future value by (1.06)2:

Present value = PV = $112.36 _______ (1.06)2

= $100

In general, for a future value or payment t periods away, present value is

Present value = future value after t periods ______________________ (1 + r)t   (5.2)

To calculate present value, we discounted the future value at the interest rate r. The calculation is therefore termed a discounted cash-flow (DCF) calculation, and the interest rate r is known as the discount rate.

In this chapter, we will be working through a number of more or less complicated DCF calculations. All of them involve a present value, a discount rate, and one or more future cash flows. If ever a DCF problem leaves you confused and flustered, just pause and write down which of these measures you know and which one you need to calculate.

present value (PV) Value today of a future cash flow.

discounted cash flow (DCF) Method of calculating present value by discounting future cash flows.

discount rate Interest rate used to compute present values of future cash flows.

Saving for a Future Purchase

Suppose you need $3,000 next year to buy a new computer. The interest rate is 8% per year. How much money must you set aside now in order to pay for the purchase? Just calculate the present value at an 8% interest rate of a $3,000 payment at the end of 1 year. To the near- est dollar, this value is

PV = $3,000 ______ 1.08 = $2,778

Notice that $2,778 invested for 1 year at 8% will prove just enough to buy your computer:

Future value = $2,778 × 1.08 = $3,000

The longer the time before you must make a payment, the less you need to invest today. For example, suppose that you can postpone buying that computer until the end of 2 years. In this case, we calculate the present value of the future payment by dividing $3,000 by (1.08)2:

PV = $3,000 ______ (1.08)2

= $2,572

Thus you need to invest $2,778 today to provide $3,000 in 1 year but only $2,572 to provide the same $3,000 in 2 years. ■

Example 5.2 ⊲

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Chapter 5 The Time Value of Money 125

You now know how to calculate future and present values: To work out how much you will have in the future if you invest for t years at an interest rate r, multiply the initial investment by (1 + r)t. To find the present value of a future payment, run the process in reverse and divide by (1 + r)t.

Present values are always calculated using compound interest. The ascending lines in Figure 5.2 showed the future value of $1 invested with compound interest. In con- trast, present values decline, other things equal, when future cash payments are delayed. The longer you have to wait for money, the less it’s worth today.

The descending line in Figure 5.3 shows the present value today of $100 to be received at some future date. Notice how even small variations in the interest rate can have a powerful effect on the value of distant cash flows. At an interest rate of 5%, a payment of $100 in year 20 is worth $37.69 today. If the interest rate increases to 10%, the value of the future payment falls by about 60% to $14.86.

The present value formula is sometimes written differently. Instead of dividing the future payment by (1 + r)t, we could equally well multiply it by 1/(1 + r)t:

PV = future payment _____________ (1 + r)t = future payment × 1 _______ (1 + r)t

The expression 1/(1 + r)t is called the discount factor. It measures the present value of $1 received in year t. For example, with an interest rate of 8%, the two-year discount factor is 1/1.082 = .8573. So we could equally well express the present value of the payment for a computer in year 2 as $3,000 × .8573 = $2,572.

The simplest way to find the discount factor is to use a calculator or spreadsheet, but financial managers sometimes find it convenient to use tables of discount factors. For example, Table 5.3 shows discount factors for a small range of years and interest rates. Table A.2 at the end of the book provides a set of discount factors for a wide range of years and interest rates.

Try using Table 5.3 to check our calculations of how much to put aside for that $3,000 computer purchase. If the interest rate is 8%, the present value of $1 paid at the end of 1 year is $.9259. So the present value of $3,000 is (to the nearest dollar)

PV = $3,000 × 1 ____ 1.08 = $3,000 × .9259 = $2,778

which matches the value we obtained in Example 5.2.

discount factor Present value of a $1 future payment.

FIGURE 5.3 Present value of a future cash flow of $100. Notice that the longer you have to wait for your money, the less it is worth today

2 4 6 8 10 12 14 16 18 20

Number of years

P re

se nt

v al

ue o

f $ 10

0 ($

)

100

80

90

70

60

50

40

30

20

10

0

r = 0% r = 5% r = 10% r = 15%

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126 Part Two Value

What if the computer purchase is postponed until the end of 2 years? Table 5.3 shows that the present value of $1 paid at the end of 2 years is .8573. So the present value of $3,000 is

PV = $3,000 × 1 ______ (1.08)2

 = $3,000 × .8573 = $2,572

as we found in Example 5.2. Notice that as you move along the rows in Table 5.3, moving to higher interest rates,

present values decline. As you move down the columns, moving to longer discounting periods, present values again decline. (Why does this make sense?)

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

  1  0.9524  0.9434  0.9346  0.9259  0.9174  0.9091    2  0.9070  0.8900  0.8734  0.8573  0.8417  0.8264    3  0.8638  0.8396  0.8163  0.7938  0.7722  0.7513    4  0.8227  0.7921  0.7629  0.7350  0.7084  0.6830    5  0.7835  0.7473  0.7130  0.6806  0.6499  0.6209  10  0.6139  0.5584  0.5083  0.4632  0.4224  0.3855  20  0.3769  0.3118  0.2584  0.2145  0.1784  0.1486  30  0.2314  0.1741  0.1314  0.0994  0.0754  0.0573 

TABLE 5.3 An example of a present value table, showing the value today of $1 received in the future

Finding the Value of Free Credit

Kangaroo Autos is offering free credit on a $20,000 car. You pay $8,000 up front and then the balance at the end of 2 years. Turtle Motors next door does not offer free credit but will give you $1,000 off the list price. If the interest rate is 10%, which company is offering the better deal?

Example 5.4 ⊲

A 10-Year Loan to the U.S. Government

A strip is a security issued by the U.S. government that promises to pay you $1,000 at some date in the future. In January 2018, investors demanded an interest rate of 2.55% to buy a 10-year strip. How much, therefore, were they prepared to pay for it? Easy! Because the strip matured in 10 years, we calculate its present value by multiplying the $1,000 future payment by the 10-year discount factor:

PV = $1,000 × 1 _________ (1.0255)10

= $1,000 × .7774 = $777.40 ■

strip A U.S. Treasury security that pays a single cash flow at a specified future date.

Example 5.3 ⊲

You could instead have bought a U.S. government strip that simply promised to pay $1,000 at the end of 5 years. If the 5-year interest rate was 2.35%, how much would investors have been prepared to pay for this strip?  

Self-Test5.3

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Chapter 5 The Time Value of Money 127

These calculations illustrate how important it is to use present values when compar- ing alternative patterns of cash payment. You should never compare cash flows occurring at different times without first discounting them to a common date. By calculating present values, we see how much cash must be set aside today to pay future bills.

Calculating present and future values can entail a considerable amount of tedious arithmetic. Fortunately, financial calculators and spreadsheets are designed with pres- ent value and future value formulas already programmed. They can make your work much easier. In Section 5.4, we will show how they do so.

Finding the Interest Rate When we looked at the U.S. government strip in Example 5.3, we used the current interest rate to compute a fair market price. Sometimes, however, you are given the price and have to calculate the interest rate that is being offered.

For example, suppose your financial advisor tells you that it costs $777.40 to buy the strip in Example 5.3. Thus, we know that

PV = $1,000 × 1 _______ (1 + r)10

= $777.40

What is the interest rate, r?

FIGURE 5.4 Drawing a time line can help us to calculate the present value of the payments to Kangaroo Autos

0 1 2

$12,000

$12,000 × $9,917.36

Present value today (time 0)

$17,917.36

$8,000.00

Year

Total

(1.10)2 1

$8,000

=

Notice that you pay more in total by buying through Kangaroo, but because part of the payment is postponed, you can keep this money in the bank where it will continue to earn interest. To compare the two offers, you need to calculate the present value of your pay- ments to Kangaroo. The time line in Figure 5.4 shows the cash payments. The first payment, $8,000, takes place today. The second payment, $12,000, takes place at the end of 2 years. To find its present value, we need to multiply by the 2-year discount factor. The total present value of the payments to Kangaroo is therefore

PV = $8,000 + $12,000 × 1 ______ (1.10)2

= $8,000 + $9,917.36 = $17,917.36

Suppose you start with $17,917.36. You make a down payment of $8,000 to Kangaroo Autos and invest the balance of $9,917.36. At an interest rate of 10%, this will grow over 2 years to $9,917.36 × 1.102 = $12,000, just enough to make the final payment on your automobile. The total cost of $17,917.36 is a better deal than the $19,000 charged by Turtle Motors. ■

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128 Part Two Value

To answer this question, you can rearrange the equation and use your calculator:

$777.40 × (1 + r)10 = $1,000

(1 + r)10 =  $1,000 _______ $777.40 = 1.2863

1 + r = 1.28631/10 = 1.0255

r = .0255, or 2.55%

Double Your Money

How many times have you heard of an investment adviser who promises to double your money? Is this really an amazing feat? That depends on how long it will take for your money to double. With enough patience, your funds eventually will double even if they earn only a very modest interest rate. Suppose your investment adviser promises to double your money in 8 years. What interest rate is implicitly being promised?

The adviser is promising a future value of $2 for every $1 invested today. Therefore, we find the interest rate by solving for r as follows:

Future value (FV) = PV × (1 + r)t

$2 = $1 × (1 + r)8

1 + r = 21/8 = 1.0905

r = .0905, or 9.05% ■

Example 5.5 ⊲

Multiple Cash Flows

So far, we have considered problems involving only a single cash flow. This is obviously limiting. Most real-world investments, after all, will involve many cash flows over time. When there are many payments, you’ll hear managers refer to a stream of cash flows.

Future Value of Multiple Cash Flows Recall the computer you hope to purchase in 2 years (see Example 5.2). Now suppose that instead of putting aside one sum in the bank to finance the purchase, you plan to save some amount of money each year. You might be able to put $1,200 in the bank now and another $1,400 in 1 year. If you earn an 8% rate of interest, how much will you be able to spend on a computer in 2 years?

The time line in Figure 5.5 shows how your savings grow. There are two cash inflows into the savings plan. The first inflow will have 2 years to earn interest and

5.3

FIGURE 5.5 Drawing a time line can help to calculate the future value of your savings.

0 1 2

$1,400

$1,399.68

$2,911.68

$1,512.00

$1,200 × (1.08)2 $1,400 × 1.08

Year

Future value in year 2

$1,200

=

=

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Chapter 5 The Time Value of Money 129

Our examples show that problems involving multiple cash flows are simple exten- sions of single cash-flow analysis. To find the value at some future date of a stream of cash flows, calculate the future value of each cash flow and then add up these future values.

As we will now see, a similar adding-up principle works for present value calculations.

Present Value of Multiple Cash Flows When we calculate the present value of a future cash flow, we are asking how much that cash flow would be worth today. If there is more than one future cash flow, we simply need to work out what each flow would be worth today and then add these present values.

Even More Savings

Suppose that the computer purchase can be put off for an additional year and that you can make a third deposit of $1,000 at the end of the second year. How much will be available to spend 3 years from now?

Again we organize our inputs using a time line as in Figure 5.6. The total cash available will be the sum of the future values of all three deposits. Notice that when we save for 3 years, the first two deposits each have an extra year for interest to compound:

$1,200 × (1.08)3 = $1,511.65

$1,400 × (1.08)2 = 1,632.96

$1,000 × (1.08) = 1,080.00 Total future value = $4,224.61 ■

Example 5.6 ⊲

Cash Up Front versus an Installment Plan

Suppose that your auto dealer gives you a choice between paying $15,500 for a used car or entering into an installment plan where you pay $8,000 today and make payments of $4,000 in each of the next 2 years. Which is the better deal? Before reading this chapter,

Example 5.7 ⊲

therefore will grow to $1,200 × (1.08)2 = $1,399.68, while the second inflow, which comes a year later, will be invested for only 1 year and will grow to $1,400 × (1.08) = $1,512. After 2 years, then, your total savings will be the sum of these two amounts, or $2,911.68.

FIGURE 5.6 To find the future value of a stream of cash flows, you just calculate the future value of each flow and then add them.

0 1 3

$1,400

$1,511.65

$4,224.61

$1,632.96

$1,200 × (1.08)3 $1,400 × (1.08)2

Year Future value in year 3 2

$1,200 $1,000

=

$1,080.00 $1,000 × 1.08=

=

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130 Part Two Value

FIGURE 5.7 To find the present value of a stream of cash flows, you just calculate the present value of each flow and then add them.

0 1 2

$8,000

Present value today (time 0)

Year

1.08 4,000

$4,000$4,000

(1.08)2 4,000

$3,703.70

$15,133.06Total

$8,000.00

$3,429.36

=

=

you might have compared the total payments under the two plans: $15,500 versus $16,000 in the installment plan. Now, however, you know that this comparison is wrong because it ignores the time value of money. For example, the last installment of $4,000 is less costly to you than paying out $4,000 now. The true cost of that last payment is the present value of $4,000.

Assume that the interest rate you can earn on safe investments is 8%. Suppose you choose the installment plan. As the time line in Figure 5.7 illustrates, the present value of the plan’s three cash flows is:

Present Value

Immediate payment $8,000 = $  8,000.00

Second payment $4,000/1.08 = 3,703.70

Third payment $4,000/(1.08)2 = 3,429.36

Total present value   = $15,133.06

Because the present value of the three payments is less than $15,500, the installment plan is in fact the cheaper alternative.

The installment plan’s present value is the amount that you would need to invest now to cover the three payments. Let’s check.

Here is how your bank balance would change as you make each payment:

Year Initial Balance − Payment = Remaining

Balance + Interest Earned =

Balance at Year-End

0 $15,133.06 $8,000 $7,133.06 $570.64 $7,703.70

1 7,703.70 4,000 3,703.70 296.30 4,000.00

2 4,000.00 4,000 0 0 0

If you start with the present value of $15,133.06 in the bank, you could make an immedi- ate $8,000 payment and be left with $7,133.06. After 1 year, your savings account would receive an interest payment of $7,133.06 × .08 = $570.64, bringing your account to $7,703.70. Similarly, you would make the second $4,000 payment and be left with $3,703.70. This sum left in the bank would grow with interest to $4,000, just enough to make the last payment. ■

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Chapter 5 The Time Value of Money 131

Reducing the Chore of the Calculations: Part 1

We have worked through a number of present value problems by hand because it is important that you understand how present values are calculated. But calculating values in this way can be laborious. Therefore, financial managers generally turn to financial calculators or computer spreadsheets to remove much of the tedium. In this section, we show how these calculators and spreadsheets are used to solve the future and present value problems that we have encountered so far. Later in the chapter, we will look at how they can also help to solve problems where there are recurring payments.

We start with an introduction to financial calculators and then look at spreadsheets.

Using Financial Calculators to Solve Simple Time-Value-of-Money Problems The basic financial calculator uses five keys that correspond to the inputs for common problems involving the time value of money:

FVPMTPVin

Each key represents the following input:

∙ n is the number of periods. (We have been using t to denote the length of time or the number of periods.)

∙ i is the interest rate, expressed as a percentage (not a decimal). For example, if the interest rate is 8%, you would enter 8, not .08. On some calculators, this key appears as I/YR, I/Y, or just i. (We have been using r to denote the interest rate.)

∙ PV is the present value. ∙ FV is the future value. ∙ PMT is the amount of any recurring payment, that is, any intermediate payments that

come before the date when future value, FV, is calculated. We will start with examples where there are no recurring payments, so for now we just set this key to zero.

Given any four of these inputs, the calculator will solve for the fifth. We can illustrate using Examples 5.1 and 5.2. In Example 5.1, we calculated the future value of Peter Minuit’s $24 investment if invested at 8% for 393 years. Our inputs would be as follows:

n i PV PMT FV

Inputs 393 8 24 0

5.4

Example 5.7 illustrates this general principle: The present value of a stream of future cash flows is the amount you need to invest today to generate that stream.

In order to avoid estate taxes, your rich aunt Frederica will pay you $10,000 per year for 4 years, starting 1 year from now. What is the present value of your benefactor’s planned gifts? The interest rate is 7%. How much will you have 4 years from now if you invest each gift at 7%?

Self-Test5.4

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132 Part Two Value

For example, to enter the number of periods, type 393 and then press the n key. Similarly, enter an interest rate of 8 and a present value of 24. There are no recurring cash flows, so you need to enter a value of 0 for PMT. You now wish to solve for the future value given the other four inputs. On some calculators, you do this by pressing FV. On others, you need to first press the compute key, which may be labeled CPT or COMP, and then press FV. Your calculator should show a value of −$327.90 trillion, which, except for the minus sign, is the future value of $24. Try it.

Why does the minus sign appear? Most calculators treat cash flows as either inflows (shown as positive numbers) or outflows (negative numbers). For example, if you bor- row $100 today at an interest rate of 12%, you receive money now (a positive cash flow), but you will have to pay back $112 in a year, a negative cash flow at that time. Therefore, the calculator displays FV as a negative number. The following time line of cash flows shows the reasoning employed. The final negative cash flow of $112 is the payment that you will need to make to clear your debt.

PV = $100

Year: 0 1

FV = $112

If, instead of borrowing, you were to invest $100 today to reap a future benefit, you would enter PV as a negative number (first press 100, then press the +/− key to change the value to negative, and finally press PV to enter the value into the PV register). In this case, FV would appear as a positive number, showing that you will reap a cash inflow when your investment comes to fruition.

In Example 5.2, we consider a simple savings problem. We need to solve for the amount that you must put aside today to produce $3,000 in 2 years. So our inputs look like this:

n i PV PMT FV

Inputs 2 8 0 3000

Now compute PV; you should get an answer of −2,572.02. Again the answer is displayed as a negative number because you need to make a cash outflow today (an investment) of $2,572.02 in order to reap a cash inflow of $3,000 in 2 years.

Using Spreadsheets to Solve Simple Time-Value-of-Money Problems Rather than using a financial calculator, an alternative is to use a computer spread- sheet. Spreadsheets have a particular advantage when a problem involves a number of uneven cash flows. Such problems can rapidly become tedious and prone to errors from “typos,” even if you use a financial calculator.

Like financial calculators, spreadsheets provide built-in functions that solve the equations linking the five variables in a time-value-of-money problem: the number of periods, the interest rate per period, the present value, the future value, and any recur- ring payment. For now we ignore recurring payments; later we will show you how to deal with them.

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Chapter 5 The Time Value of Money 133

Single Cash Flows We show first how spreadsheets, such as Microsoft Excel, can be used to solve the single cash-flow problems in Examples 5.1 and 5.2.

The two Excel functions for these single cash-flow problems are:

Future value = FV(rate, nper, pmt, PV) Present value = PV(rate, nper, pmt, FV)

As you can see, each spreadsheet formula requires four inputs—just as financial calculators require four inputs. The spreadsheet then provides the solution for the fifth variable. Also, as with most calculators, the spreadsheet functions interpret cash inflows as positive values and cash outflows as negative values. Unlike financial cal- culators, however, most spreadsheets require that interest rates be input as decimals rather than whole numbers (e.g., .06 rather than 6%). Note also the use of = in front of the formulas to alert Excel to the fact that these are predefined formulas.

Spreadsheet 5.1 solves for the future value of the $24 spent to acquire Manhattan Island (Example 5.1). The interest rate is entered as a decimal in cell B3. The number of periods is 393 (cell B4). We enter the recurring payment as zero in cell B5. The present value is entered as −24 (cell B6), representing the purchase price, and there- fore the future value, shown in cell B8, is a positive cash flow.2

Of course, memorizing Excel functions such as the one in cell B8 may not come eas- ily to everyone. (We admit that we’re still working on it.) But there is an easy cure for those of us with bad memories. You can pull down the appropriate function from Excel’s built-in functions (from the Formulas tab), and you will be prompted for the necessary inputs. Spreadsheet 5.2 illustrates. Go to the Formula tab, click Financial formulas, and then select FV. The “Function Arguments” screen shown in Spreadsheet 5.2 should now appear. At the bottom left of the function box, there is a Help facility with an example of how the function is used.

Now let’s solve Example 5.2 in a spreadsheet. We can type the Excel function = PV(rate, nper, pmt, FV) = PV(.08, 2, 0, 3000), or we can select the PV function from the pull-down menu of financial functions and fill in our inputs as shown in the dialog box below. Either way, you should get an answer of −$2,572. (Notice that you don’t type the comma in 3,000 when entering the number in the

SPREADSHEET 5.1 Using a spreadsheet to find the future value of $24

A B C 1 Finding the future value of $24 using a spreadsheet 2 INPUTS 3 Interest rate 0.08 4 Periods 393 5 Payment 0 6 Present value (PV) −24 7 Formula in cell B8

8 Future value $327,904,327,346,904 =FV(B3,B4,B5,B6) 9

10 Notice that we enter the present value in cell B6 as a negative number, 11 because the “purchase price” is a cash outflow. The interest rate in cell B3 12 is entered as a decimal, not a percentage. 13 14

2 Notice that, because the number is too big to display easily, the spreadsheet shows the answer as 3.27904E+14. This means that the number is 3.27904 × 1014.

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134 Part Two Value

SPREADSHEET 5.2 Using the financial function pull-down menu

A B C 1 Finding the future value of $24 using a spreadsheet 2 INPUTS 3 Interest rate 0.08 4 Periods 393 5 Payment 0 6 Present value (PV) −24 7 Formula in cell B8

8 Future value $327,904,327,346,904 = FV(B3,B4,B5,B6)

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

393 393

3.27904E+14

3.27904E+14

;

spreadsheet. If you did, Excel would interpret the entry as two different numbers, 3 followed by zero.)

Finding the present value of a future amount using the pull- down menu in Excel. This is the solution for the savings problem in Example 5.2.

Multiple Cash Flows Valuing multiple cash flows with a spreadsheet is no differ- ent from valuing single cash flows. You simply find the present value of each flow and then add them up. Spreadsheet 5.3 shows how to find the solution to Example 5.7.

The time until each payment is listed in column A. This value is then used to set the number of periods (nper) in the formula in column C. The values for the cash flow in each future period are entered as negative numbers in the PV formula. The present

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Source: Microsoft Excel

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Chapter 5 The Time Value of Money 135

values (column C) therefore appear as positive numbers. Column E shows an alterna- tive to the use of the PV function, where we calculate present values directly. This allows us to see exactly what we are doing.

The Beyond the Page icon will take you to an application that shows how each of the examples in this chapter can be solved using a spreadsheet.

Level Cash Flows: Perpetuities and Annuities

Frequently, you may need to value a stream of equal cash flows. For example, a home mortgage might require the homeowner to make equal monthly payments for the life of the loan. For a 30-year loan, this would result in 360 equal payments. A 4-year car loan might require 48 equal monthly payments. Any such sequence of equally spaced, level cash flows is called an annuity. If the payment stream lasts forever, it is called a perpetuity.

How to Value Perpetuities Some time ago, the British government borrowed by issuing loans known as consols. Consols are perpetuities. In other words, instead of repaying these loans, the British government pays the investors a fixed annual payment in perpetuity (forever).

How might we value such a security? Suppose that you could invest $100 at an interest rate of 10%. You would earn annual interest of .10 × $100 = $10 and could withdraw this amount from your investment account each year without ever running down your balance. In other words, a $100 investment could provide a perpetuity of $10 per year. In general,

Cash payment from perpetuity = interest rate × present value C = r × PV

We can rearrange this relationship to derive the present value of a perpetuity, given the interest rate r and the cash payment C:

PV of perpetuity = C __ r = cash payment ____________ interest rate (5.3)

Suppose some worthy person wishes to endow a chair in finance at your university. If the rate of interest is 10% and the aim is to provide $100,000 a year forever, the amount that must be set aside today is

Present value of perpetuity = C __ r = $100,000 ________ .10 = $1,000,000

5.5

annuity Level stream of cash flows at regular intervals with a finite maturity.

perpetuity Stream of level cash payments that never ends.

SPREADSHEET 5.3 Using a spreadsheet to find the present value of multiple cash flows

A B C D E 1 Finding the present value of multiple cash flows using a spreadsheet 2 3 Time until CF Cash flow Present value Formula in Col C Alternative formula for Col C 4 0 8000 $8,000.00 =PV($B$10, A4, 0, −B4) =B4/(1 + $B$10)^A4 5 1 4000 $3,703.70 =PV($B$10, A5, 0, −B5) =B5/(1 + $B$10)^A5 6 2 4000 $3,429.36 =PV($B$10, A6, 0, −B6) =B6/(1 + $B$10)^A6 7 8 SUM $15,133.06 =SUM(C4:C6) =SUM(C4:C6) 9

10 Discount rate: 0.08 11 12 Notice that the time until each payment is found in column A. 13 Once we enter the formula for present value in cell C4, we can copy it to cells C5 and C6. 14 The present value for other interest rates can be found by changing the entry in cell B10.

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136 Part Two Value

Two warnings about the perpetuity formula. First, at a quick glance you can easily confuse the formula with the present value of a single cash payment. A payment of $1 at the end of 1 year has a present value 1/(1 + r). The perpetuity has a value of 1/r. At a 10% interest rate, a perpetuity is 11 times more valuable than a single cash flow.

Second, the perpetuity formula tells us the value of a regular stream of payments starting one period from now. For example, our endowment of $1 million would pro- vide the university with its first payment of $100,000 at the end of the year. If the worthy donor wants to provide the university with an additional payment of $100,000 up front, he or she would need to put aside $1,100,000.

Sometimes you may need to calculate the value of a perpetuity that does not start to make payments for several years. For example, suppose that our philanthropist decides to provide $100,000 a year with the first payment 4 years from now. We know that in year 3, this endowment will be an ordinary perpetuity with payments starting at the end of 1 year. So our perpetuity formula tells us that in year 3 the endowment will be worth $100,000/r. But it is not worth that much now. To find today’s value, we need to multiply by the 3-year discount factor. Thus, at an interest rate of 10%, the “delayed” perpetuity is worth

$100,000 × 1 __ r × 1 _______

(1 + r)3 = $1,000,000 × 1 ______

(1.10)3 = $751,315

A British government perpetuity pays £4 a year forever and is selling for £48. What is the interest rate?

Self-Test5.5

How to Value Annuities Let us return to Kangaroo Autos for (almost) the last time. Most installment plans call for level streams of payments. So let us suppose that Kangaroo now offers an “easy payment” scheme of $8,000 at the end of each of the next 3 years.

The payments on the Kangaroo plan constitute a 3-year annuity. Figure 5.8 shows a time line of these cash flows and calculates the present value of each year’s flow assuming an interest rate of 10%. You can see that the total present value of the pay- ments is $19,894.82.

You can always value an annuity by calculating the present value of each cash flow and finding the total. However, it is usually quicker to use a simple formula that states

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FIGURE 5.8 To find the value of an annuity, you can calculate the value of each cash flow. It is usually quicker to use the annuity formula.

$6,611.57

$19,894.82

$7,272.73

$6,010.52

Total

(1.10)2 8,000

1.10 8,000

(1.10)3 8,000

0 21 3 Present value

Year

$8,000$8,000 $8,000

=

=

=

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Chapter 5 The Time Value of Money 137

that if the interest rate is r, then the present value of an annuity that pays C dollars a year for each of t periods is

Present value of t-year annuity = C [ 1 __ r − 1 ________ r (1 + r)t ] (5.4) The expression in brackets shows the present value of a t-year annuity of $1 starting in period 1. It is generally known as the t -year annuity factor. Therefore, another way to write the value of an annuity is

Present value of t-year annuity = payment × annuity factor

You can use this formula to calculate the present value of the payments to Kangaroo. The annual payment (C) is $8,000, the interest rate (r) is 10%, and the number of years (t) is 3. Therefore,

Present value = C [ 1 __ r − 1 ________ r (1 + r)t ] = 8,000 [ 1 ___ .10 − 1 _________ .10(1.10)3 ] = $19,894.82

This is exactly the same answer that we got by separately valuing each cash flow. If the number of periods is small, there is little to choose between the two methods, but when you are valuing long-term annuities, it is easier to use the formula.

If you are wondering where the annuity formula comes from, look at Figure 5.9. It shows the payments and values of three investments.

Row 1 The investment in the first row provides a perpetual stream of $1 starting at the end of the first year. We have already seen that this perpetuity has a present value of 1/r.

Row 2 Now look at the investment shown in the second row of Figure 5.9. It also provides a perpetual stream of $1 payments, but these payments don’t start until year 4. This stream of payments is identical to the payments in row 1, except that they are delayed for an additional 3 years. In year 3, the investment will be an ordinary perpetu- ity with payments starting in 1 year and will therefore be worth 1/r in year 3. To find the value today, we simply multiply this figure by the 3-year discount factor. Thus

PV = 1 __ r × 1 _______

(1 + r)3 = 1 ________

r(1 + r)3

Row 3 Finally, look at the investment shown in the third row of Figure 5.9. This provides a level payment of $1 a year for each of 3 years. In other words, it is a 3-year annuity. You can also see that, taken together, the investments in rows 2 and 3 provide exactly the same cash payments as the investment in row 1. Thus the value of our annuity (row 3) must be equal to the value of the row 1 perpetuity less the value of the delayed row 2 perpetuity:

Present value of a 3-year $1 annuity =  1 __ r − 1 ________

r (1 + r)3

annuity factor Present value of an annuity of $1 per period.

FIGURE 5.9 The value of an annuity is equal to the difference between the value of two perpetuities.

Cash Flow

Year: 1 2 3 4 5 6 . . . Present Value

1. Perpetuity A $1 $1 $1 $1 $1 $1 . . .

2. Perpetuity B $1 $1 $1 . . .

3. Three-year annuity $1 $1 $1

1 r

1 r (1 + r )3 1

- 1

r r (1 + r )3

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138 Part Two Value

Remembering formulas is about as difficult as remembering other people’s birth- days. But as long as you bear in mind that an annuity is equivalent to the difference between an immediate and a delayed perpetuity, you shouldn’t have any difficulty.

You can use a calculator or spreadsheet to work out annuity factors (we show you how momentarily), or you can use a set of annuity tables. Table 5.4 is an abridged annuity table (an extended version is shown in Table A.3 at the end of the book). Check that you can find the 3-year annuity factor for an interest rate of 10%.

Compare Table 5.4 with Table 5.3, which presented the present value of a single cash flow. In both tables, present values fall as we move across the rows to higher dis- count rates. But in contrast to those in Table 5.3, present values in Table 5.4 increase as we move down the columns, reflecting the greater number of payments made by longer annuities.

TABLE 5.4 An example of an annuity table, showing the present value today of $1 a year received for each of t years

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

 1 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091  2 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355  3 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869  4 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699  5 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908

10 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 20 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 30 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269

If the interest rate is 8%, what is the 4-year discount factor? What is the 4-year annuity factor? What is the relationship between these two numbers? Explain.

Self-Test5.6

Winning Big at the Lottery

In August 2017, a Massachusetts woman bought a Powerball lottery ticket and won a record $758.7 million. We suspect that she received unsolicited congratulations, good wishes, and requests for money from dozens of more or less worthy charities, relations, and newly devoted friends. In response, she could fairly point out that the prize wasn’t really worth $758.7 million. That sum was to be paid in 30 annual installments of about $23 million each. Assuming that the first payment occurred at the end of 1 year, what was the present value of the prize? The interest rate at the time was about 2.7%.

The present value of these payments is simply the sum of the present values of each annual payment. But rather than valuing the payments separately, it is much easier to treat them as a 30-year annuity. To value this annuity, we multiply $23 million by the 30-year annu- ity factor:

PV = 23 × 30-year annuity factor

= 23 × [ 1 __ r − 1 _______ r (1 + r)30 ] At an interest rate of 2.7%, the annuity factor is

[ 1 ____ .027 − 1 ___________ .027(1.027)30 ] = 20.3829

Example 5.8 ⊲

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Chapter 5 The Time Value of Money 139

Suppose you retire at age 70. You expect to live 20 more years and to spend $55,000 a year during your retirement. How much money do you need to save by age 70 to support this consumption plan? Assume an interest rate of 7%.

Self-Test5.7

The present value of the cash payments is 20.3829 × 23 = $468.8 million, much less than the much-advertised prize, but still not a bad day’s haul.

Lottery operators generally make arrangements for winners with big spending plans to take an equivalent lump sum. In our example, the winner could either take the $758.7 million spread over 30 years or receive $468.8 million up front. Both arrangements have the same present value.3 ■

How Much Luxury and Excitement Can $90 Billion Buy?

Bill Gates is one of the world’s richest persons, with wealth in 2018 reputed to be about $90 billion. Mr. Gates has devoted a large part of his fortune to the Bill and Melinda Gates Foun- dation; but suppose that he decided instead to allocate his entire wealth to a life of luxury and entertainment (L&E). What annual expenditures on L&E could $90 billion support over a 30-year period? Assume that Mr. Gates can invest his funds at 6%.

The 30-year, 6% annuity factor is 13.7648. We set the present value of Mr. Gates’s spend- ing stream equal to his total wealth:

Present value = annual spending × annuity factor 90,000,000,000 = annual spending × 13.7648 Annual spending = 6,538,000,000, or about $6.5 billion

Warning to Mr. Gates: We haven’t considered inflation. The cost of buying L&E will increase, so $6.5 billion won’t buy as much L&E in 30 years as it will today. More on that later. ■

Example 5.9 ⊲

Home Mortgages

Sometimes you may need to find the series of cash payments that would provide a given value today. For example, home purchasers typically borrow the bulk of the house price from a lender. The most common loan arrangement is a 30-year loan that is repaid in equal monthly installments. Suppose that a house costs $125,000 and that the buyer puts down 20% of the purchase price, or $25,000, in cash, borrowing the remaining $100,000 from a mortgage lender such as the local savings bank. What is the appropriate monthly mortgage payment?

The borrower repays the loan by making monthly payments over the next 30 years (360 months). The savings bank needs to set these monthly payments so that they have a present value of $100,000. Thus

Present value = mortgage payment × 360-month annuity factor

= $100,000

Mortgage payment = $100,000 ____________________ 360-month annuity factor

Example 5.10 ⊲

3 The lottery payoff is in fact more complicated than we describe. The amount paid in the first year is somewhat less than $23 million, but then increases in each subsequent year to give a present value of $468.8 million.

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140 Part Two Value

The mortgage loan in Example 5.10 is an example of an amortizing loan. “Amortiz- ing” means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan. Table 5.5 illustrates a 4-year amortizing loan of $1,000 with an interest rate of 10% and annual payments starting in 1 year. The annual payment (annuity) that would repay the loan is $315.47. (Confirm this for yourself.) At the end of the first year, the interest payment is 10% of $1,000, or $100. So $100 of your first payment is used to pay interest, and the remaining $215.47 is used to reduce (or “amortize”) the loan balance to $784.53.

Next year, the outstanding balance is lower, so the interest charge is only $78.45. Therefore, $315.47 − $78.45 = $237.02 can be applied to amortization. Amortization in the second year is higher than in the first because the amount of the loan has declined, and, therefore, less of the payment is taken up in interest. This procedure continues until the last year, when the amortization is just enough to reduce the out- standing balance on the loan to zero.

Because the loan is progressively paid off, the fraction of each payment devoted to interest steadily falls over time, while the fraction used to reduce the loan (the amorti- zation) steadily increases. Figure 5.10 illustrates the amortization of the mortgage loan in Example 5.10. In the early years, almost all of the mortgage payment is for interest. Even after 15 years, the bulk of the monthly payment is interest.

Suppose that the interest rate is 1% a month. Then

Mortgage payment = $100,000 ________________ [ 1 ___ .01 − 1 __________ .01(1.01)360 ] =

$100,000 ________ 97.218 = $1,028.61■

Year

Beginning- of-Year

Balance

Year-End Interest Due on Balance

Year-End Payment

Amortization of Loan

End-of-Year Balance

1 $1,000.00 $100.00 $315.47 $215.47 $784.53 2 784.53 78.45 315.47 237.02 547.51 3 547.51 54.75 315.47 260.72 286.79 4 286.79 28.68 315.47 286.79 0

TABLE 5.5 An example of an amortizing loan. If you borrow $1,000 at an interest rate of 10%, you would need to make an annual payment of $315.47 over 4 years to repay the loan with interest.

What will be the monthly payment if you take out a $100,000 15-year mortgage at an interest rate of 1% per month? How much of the first payment is interest, and how much is amortization?

Self-Test5.8

Future Value of an Annuity You are back in savings mode again. This time you are setting aside $3,000 at the end of every year. If your savings earn interest of 8% a year, how much will they be worth at the end of 4 years? We can answer this question with the help of the time line in Figure 5.11. Your first year’s savings will earn interest for 3 years, the second will earn interest for 2 years, the third will earn interest for 1 year, and the final savings in year 4 will earn no interest. The sum of the future values of the four payments is

($3,000 × 1.083) + ($3,000 × 1.082) + ($3,000 × 1.08) + $3,000 = $13,518

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Chapter 5 The Time Value of Money 141

But wait a minute! We are looking here at a level stream of cash flows—an annuity. We have seen that there is a shortcut formula to calculate the present value of an annu- ity. So there ought to be a similar formula for calculating the future value of a level stream of cash flows.

Think first how much your stream of savings is worth today. You are setting aside $3,000 in each of the next 4 years. The present value of this 4-year annuity is therefore equal to

PV = $3,000 × 4-year annuity factor

= $3,000 ×  [ 1 ___ .08 − 1 _________ .08(1.08)4 ] = $9,936 Now think how much you would have after 4 years if you invested $9,936 today. Sim- ple! Just multiply by (1.08)4:

Value at end of year 4 = $9,936 × 1.084 = $13,518

FIGURE 5.10 Mortgage amortization. This figure shows the breakdown of mortgage payments between interest and amortization. Monthly payments within each year are summed, so the figure shows the annual payment on the mortgage.

1 4 7 10 13 16 19 22 25 28

Year

D ol

la rs

14,000

10,000

12,000

8,000

6,000

4,000

2,000

0

Amortization Interest paid

FIGURE 5.11 Calculating the future value of an ordinary annuity of $3,000 a year for 4 years (interest rate = 8%)

$3,000

$3,499

$13,518

$3,240

3,000 × (1.08)2 3,000 × 1.08

Year

Future value in year 4

$3,000 $3,000$3,000

=

$3,779 3,000 × (1.08)3=

$3,000 3,000=

=

0 1 432

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The amortization schedule

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142 Part Two Value

We calculated the future value of the annuity by first calculating the present value and then multiplying by (1 + r)t. The general formula for the future value of a stream of cash flows of $1 a year for each of t years is therefore

= [ 1 __ r − 1 _______ r(1 + r)t ] × (1 + r)t = (1 + r)

t − 1 __________ r

If you need to find the future value of just four cash flows as in our example, it is a toss-up whether it is quicker to calculate the future value of each cash flow separately (as we did in Figure 5.11) or to use the annuity formula. If you are faced with a stream of 10 or 20 cash flows, there is no contest.

You can find the future value of an annuity in Table 5.6 or the more extensive Table A.4 at the end of the book. You can see that in the row corresponding to t = 4 and the column corresponding to r = 8%, the future value of an annuity of $1 a year is $4.5061. Therefore, the future value of the $3,000 annuity is $3,000 × 4.5061 = $13,518. In practice, you will tend to use a calculator or spreadsheet to find these values.

Future value (FV) of annuity of $1 a year =

present value of annuity of $1 a year × (1 + r)t

(5.5)

Number of Years

Interest Rate per Year

5% 6% 7% 8% 9% 10%

  1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000   2 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000   3 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100   4 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410   5 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 10 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 20 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 30 66.4388 79.0582 94.4608 113.2832 136.3075 164.4940

TABLE 5.6 An example of a table showing the future value of an investment of $1 a year for each of t years

Saving for Retirement

In only 50 more years, you will retire. (That’s right—by the time you retire, the retirement age will be around 70 years. Longevity is not an unmixed blessing.) Have you started saving yet? Suppose you believe you will need to accumulate $500,000 by your retirement date in order to support your desired standard of living. How much savings each year would be necessary to produce $500,000 at the end of 50 years? Let’s say that the interest rate is 10% per year. You need to find how large the annuity in the following figure must be to provide a future value of $500,000:

0 4948••••4321 •

$500,000

Level savings (cash outflows) in years 1–50 result in a future accumulated

value of $500,000

Example 5.11 ⊲

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Chapter 5 The Time Value of Money 143

Annuities Due Remember that our annuity formulas assume that the first cash flow does not occur until the end of the first period. The present value of an annuity is the value today of a stream of payments that starts in one period. Similarly, the future value of an annuity assumes that the first cash flow comes at the end of one period.

But in many cases, cash payments start immediately. For example, when Kangaroo Autos (see Figure 5.8) sells you a car on credit, it may insist that the first payment be made at the time of the sale. A level stream of payments starting immediately is known as an annuity due.

Figure 5.12 depicts the cash-flow streams of an ordinary annuity and an annuity due. Comparing panels a and b, you can see that each of the three cash flows in the annuity due comes one period earlier than the corresponding cash flow of the ordinary annuity. Therefore, each is discounted for one less period, and its present value increases by a factor of (1 + r). Therefore,

Present value of annuity due = present value of ordinary annuity × (1 + r) (5.6)

Figure 5.12 shows that bringing the Kangaroo loan payments forward by 1 year increases their present value from $19,894.82 (as an ordinary annuity) to $21,884.30 (as an annuity due). Notice that $21,884.30 = $19,894.82 × 1.10.

You may also want to calculate the future value of an annuity due. If the first cash flow comes immediately, the future value of the cash-flow stream is greater because each flow has an extra year to earn interest. For example, at an interest rate of 10%, the future value of an annuity due would be exactly 10% greater than the future value of an ordinary annuity. More generally, Future value of annuity due = future value of ordinary annuity × (1 + r) (5.7)

annuity due Level stream of cash flows starting immediately.

We know that if you were to save $1 each year, your funds would accumulate to

Future value (FV) of annuity of $1 a year = (1 + r)t – 1

_________ r = (1.10)50 – 1

__________ .10 = $1,163.91

We need to choose C to ensure that C × 1,163.91 = $500,000. Thus C = $500,000/1,163.91 = $429.59. This appears to be surprisingly good news. Saving $429.59 a year does not seem to be an extremely demanding savings program. Don’t celebrate yet, however. Your goal will appear far more daunting once we consider the impact of inflation. ■

In Example 5.11, we showed that an annual savings stream of $429.59 invested for 50 years at 10% a year would satisfy a savings goal of $500,000. Suppose instead that you made 50 annual investments, but you made these investments at the beginning of each year rather than at the end. How much would these savings amount to by the end of year 50?

Self-Test5.9

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144 Part Two Value

Reducing the Chore of the Calculations: Part 2

In Section 5.4, we showed how managers use financial calculators or spreadsheets to solve present value problems. At that point we had not encountered annuities, and we assumed that there were no recurring cash flows. We were simply concerned with the present value (PV) and the future value (FV). However, when we need to value an annuity, we are concerned with the present value, the future value, and the regular annuity payment (PMT). Here are some examples of how you can use a financial cal- culator and a spreadsheet to value annuities.

Using Financial Calculators to Solve Annuity Problems We looked earlier at the “easy payment” scheme offered by Kangaroo Autos. It called for a payment of $8,000 at the end of each of the next 3 years. What is the present value of these payments if the interest rate is 10%?

To find the answer on your financial calculator, you must enter the following numbers:

n i PV PMT FV

Inputs 3 10 −8000 0

5.6

FIGURE 5.12 The cash payments on the ordinary annuity in panel a start in year 1. The first payment on the annuity due in panel b occurs immediately. The annuity due is therefore more valuable.

3-year ordinary annuity

$6,611.57

$19,894.82

$7,272.73

$6,010.52

Total

(1.10)2 8,000

1.10 8,000

(1.10)3 8,000

0 21 3 Present value

Year

$8,000$8,000 $8,000

=

=

=

(a)

3-year annuity due

0 21 3

$7,272.73

Present value

$21,884.30

Year

Total

1.10 8,000

$8,000.00

$8,000 $8,000 $8,000

$6,611.57 (1.10)2 8,000

=

=

(b)

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Chapter 5 The Time Value of Money 145

Notice that PMT is no longer set at zero; instead, you need to enter the regular annuity payment (–8000). Note also that PMT is entered as a negative number; you are paying out $8,000 a year to Kangaroo Autos. There are no other payments involved, so FV is set at zero. (If, say, you were also required to pay an additional $5,000 in year 3, you would need to enter a future value, FV, of –5000.) Now compute PV; you should get an answer of 19,894.82.

Now let us use a financial calculator to solve Example 5.10. A savings bank needed to set the monthly payments on a mortgage so that they would have a present value, PV, of $100,000. There were 360 monthly payments, and the interest rate was 1% per month. To find the regular monthly payment (PMT), you need to enter the following data:

n i PV PMT FV

Inputs 360 1 100000 0

Notice that we enter PV as a positive number: You get a cash inflow when the bank lends you the money. When you press the PMT key, you should get the answer −1,028.61 because the payment is a cash outflow.

Suppose that the mortgage is an annuity due with the first monthly payment made immediately. You can solve for annuities due by pressing the begin key on your calcu- lator. The calculator will automatically interpret the cash-flow series as an annuity due with the cash flows coming at the beginning of each period. To return to the ordinary annuity mode, just press the begin key again.

Using Spreadsheets to Solve Annuity Problems Solving annuity problems with a spreadsheet involves exactly the same functions that we used to solve single cash-flow problems. However, with an annuity, the recurring payment (PMT) is no longer zero.

Think again of the “easy payment” scheme offered by Kangaroo Autos. This called for a payment of $8,000 at the end of each of the next 3 years. We need to calculate the present value of these payments at an interest rate of 10%. The following spreadsheet shows the solution to this problem.

A B C 1 Finding the present value of an annuity using a spreadsheet 2 3 Interest rate (i) 0.1 4 Number of periods (nper) 3 5 Payment per period (pmt) 8000 6 7 Formula in cell B8

8 Present value (PV) $19,894.82 =PV(B3,B4,−B5,0) 9 10 Notice that the interest rate is entered as a decimal, not a percentage.

Effective Annual Interest Rates

We realize that by this point in the chapter you probably feel overwhelmed by formu- las. We have, however, two more tasks; so, if your head is spinning, now might be a good time to take a break and drink a strong cup of coffee.

5.7

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146 Part Two Value

So far in this chapter we have mainly used annual interest rates to value a series of annual cash flows. But interest rates may be quoted for days, months, years, or any convenient interval. How should we compare rates when they are quoted for different periods, such as monthly versus annually?

Consider your credit card. Suppose you have to pay interest on any unpaid balances at the rate of 1% per month. What is it going to cost you if you neglect to pay off your unpaid balance for a year?

Don’t be put off because the interest rate is quoted per month rather than per year. The important thing is to maintain consistency between the interest rate and the number of periods. If the interest rate is quoted as a percent per month, then we must define the number of periods in our future value calculation as the number of months. So if you borrow $100 from the credit card company at 1% per month for 12 months, you will need to repay $100 × (1.01)12 = $112.68. Thus, your debt grows after 1 year to $112.68. Therefore, we can say that the interest rate of 1% a month is equivalent to an effective annual interest rate, or annually compounded rate, of 12.68%.

In general, the effective annual interest rate is defined as the rate at which your money grows, allowing for the effect of compounding. Therefore, for the credit card,

1 + effective annual rate = (1 + monthly rate)12

When comparing interest rates, it is best to use effective annual rates. This com- pares interest paid or received over a common period (1 year) and allows for possible compounding during the period. Unfortunately, short-term rates are sometimes annu- alized by multiplying the rate per period by the number of periods in a year. In fact, truth-in-lending laws in the United States require that rates be annualized in this man- ner. Such rates are called annual percentage rates (APRs).4 The interest rate on your credit card loan was 1% per month. Because there are 12 months in a year, the APR on the loan is 12 × 1% = 12%.5

If the credit card company quotes an APR of 12%, how can you find the effective annual interest rate? The solution is simple:

Step 1. Take the quoted APR and divide by the number of compounding periods in a year to recover the rate per period actually charged. In our example, the interest was calculated monthly. So we divide the APR by 12 to obtain the interest rate per month:

Monthly interest rate =  APR _____ 12 = 12% ____ 12 = 1%

Step 2. Now convert to an annually compounded interest rate:

1 + effective annual rate = (1 + monthly rate)12 = (1 + .01)12 = 1.1268

The effective annual interest rate is .1268, or 12.68%. In general, if an investment is quoted with a given APR and there are m compound-

ing periods in a year, then $1 will grow to $1 × (1 + APR/m)m after 1 year. The effec- tive annual interest rate is (1 + APR/m)m − 1. For example, a credit card loan that charges a monthly interest rate of 1% has an APR of 12% but an effective annual inter- est rate of (1.01)12 − 1 = .1268, or 12.68%. To summarize: The effective annual rate is the rate at which invested funds will grow over the course of a year. It equals the rate of interest per period compounded for the number of periods in a year.

effective annual interest rate Interest rate that is annualized using compound interest.

annual percentage rate (APR) Interest rate that is annualized using simple interest.

4 The truth-in-lending laws apply to credit card loans, auto loans, home improvement loans, and some loans to small businesses. The term “APR” is not commonly used or quoted in the big leagues of finance. 5 The rules for calculating the APR differ from one country to another. For example, in the EU, companies are obliged to quote the effective annual interest rate on most loans.

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Chapter 5 The Time Value of Money 147

Inflation and the Time Value of Money

When a bank offers to pay 6% on a savings account, it promises to pay interest of $60 for every $1,000 you deposit. The bank fixes the number of dollars that it pays, but it doesn’t provide any assurance of how much those dollars will buy. If the value of your investment increases by 6% while the prices of goods and services increase by 10%, you actually lose ground in terms of the goods you can buy.

Real versus Nominal Cash Flows Prices of goods and services continually change. Textbooks may become more expen- sive (sorry) while computers become cheaper. An overall general rise in prices is known as inflation. If the inflation rate is 5% per year, then goods that cost $1.00 a year ago typically cost $1.05 this year. The increase in the general level of prices means that the purchasing power of money has eroded. If a dollar bill bought one loaf of bread last year, the same dollar this year buys only part of a loaf.

5.8

inflation Rate at which prices as a whole are increasing.

The Effective Interest Rates on Bank Accounts

Back in the 1960s and 1970s, federal regulation limited the APR interest rates banks could pay on savings accounts. Banks were hungry for depositors, so to compete, they searched for ways to increase the effective rate of interest that could be paid within the rules. Their solution was to keep the same APR but to calculate the interest on deposits more frequently. As inter- est is compounded at shorter and shorter intervals, less time passes before interest can be earned on interest. Therefore, the effective annually compounded rate of interest increases. Table 5.7 shows the calculations assuming that the maximum APR that banks could pay was 6%. (Actually, it was a bit less than this, but 6% is a nice round number to use for illustration.)

You can see from Table 5.7 how banks were able to increase the effective interest rate simply by calculating interest at more frequent intervals.

The ultimate step was to assume that interest was paid in a continuous stream rather than at fixed intervals. With 1 year’s continuous compounding, $1 grows to eAPR, where e = 2.718 (a figure that may be familiar to you as the base for natural logarithms). Thus, if you deposited $1 with a bank that offered a continuously compounded rate of 6%, your investment would grow by the end of the year to (2.718).06 = $1.061837, just a hair’s breadth more than if interest were compounded daily. ■

Example 5.12 ⊲

Compounding Period

Periods per Year (m)

Per-Period Interest Rate

Growth Factor of Invested Funds

Effective Annual Rate

1 year 1 6% 1.06 6.0000% Semiannually 2 3 1.032 = 1.0609 6.0900 Quarterly 4 1.5 1.0154 = 1.061364 6.1364 Monthly 12 0.5 1.00512 = 1.061678 6.1678 Weekly 52 0.11538 1.001153852 = 1.061800 6.1800 Daily 365 0.01644 1.0001644365 = 1.061831 6.1831 Continuous e.06 = 1.061837 6.1837

TABLE 5.7 These investments all have an APR of 6%, but the more frequently interest is compounded, the higher is the effective annual rate of interest.

A car loan requiring quarterly payments carries an APR of 8%. What is the effec- tive annual rate of interest?  

Self-Test5.10

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148 Part Two Value

Economists track the general level of prices using several different price indexes. The best known of these is the consumer price index, or CPI. This measures the num- ber of dollars needed to buy a specified basket of goods and services that is supposed to represent the typical family’s purchases.6 Thus the percentage increase in the CPI from one year to the next measures the rate of inflation.

Table 5.8 shows the CPI for selected years. The base period for the index is 1982– 1984, so the index shows the price level in each year as a percentage of the average price level during these 3 years. For example, the index in 1950 was 25.0. This means that on average $25 in 1950 would have bought the same quantity of goods and ser- vices as $100 in 1982–1984. By the end of 2017, the index had risen to 246.5. In other words, prices in 2017 were 9.86 times their level in 1950 (246.5/25.0 = 9.86).7

It is interesting to look at annual inflation rates over a somewhat longer period. These are shown in Figure 5.13. The peak year for inflation was 1918, when prices rose by 20%, but you can see that there have also been a few years when prices have fallen quite sharply.

As we write this in 2018, all appears quiet on the inflation front. In the United States the inflation rate is close to zero and a few countries are even experiencing fall- ing prices, or deflation. This has led some economists to argue that inflation is dead; others are less sure.

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World inflation rates

6 Don’t ask how you buy a “basket” of services. 7 The choice by the Bureau of Labor Statistics of 1982–1984 as a base period is arbitrary. For example, it could have set December 1950 as the base period. In this case, the index would have been 100 in 1950 and 986.0 in 2017.

CPI Percent Change since 1950

1950   25.0 1960   29.8 +  19.2% 1970   39.8 +  59.2 1980   86.3 +245.2 1990 133.8 +435.2 2000 174.0 +596.0 2010 219.2 +776.8 2017 246.5 +886.0

TABLE 5.8 The consumer price index (CPI) shows how inflation has increased the cost of a typical family’s purchases.

The Price of Gasoline

Motorists in late 2017, who were paying about $2.50 for a gallon of gasoline, may have looked back longingly to 1980, when they were paying just $1.08 a gallon. But how much had the real price of gasoline changed over this period? Let’s check.

In 2017, the consumer price index was about 2.87 times its level in 1980. If the price of gasoline had risen in line with inflation, it would have cost 2.87 × $1.08 = $3.10 a gallon in 2017. That was the cost of gasoline in 1980 but measured in terms of 2017 dollars rather than 1980 dollars. Thus, the real price of gasoline had actually declined over the 37-year period. ■

Example 5.13 ⊲

Consider a telephone call to London that currently would cost $5. If the real price of telephone calls does not change in the future, how much will it cost you to make a call to London in 50 years if the inflation rate is 5% (roughly its aver- age over the past 30 years)? What if inflation is 10%?

Self-Test5.11

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Chapter 5 The Time Value of Money 149

Economists sometimes talk about current or nominal dollars versus constant or real dollars. Current or nominal dollars refer to the actual number of dollars of the day; constant or real dollars refer to the amount of purchasing power.

Some expenditures are fixed in nominal terms and therefore decline in real terms when the CPI increases. Suppose you took out a 30-year house mortgage in 1990. The monthly payment was $800. It was still $800 in 2017, even though the CPI increased by a factor of 246.5/133.8 = 1.84 over those years.

What’s the monthly payment for 2017 expressed in real 1990 dollars? The answer is $800/1.84, or $434 per month. The real burden of paying the mortgage was much less in 2017 than in 1990.

FIGURE 5.13 Annual rates of inflation in the United States from 1900 to 2017

In fla

tio n

ra te

(% )

19 00

19 05

19 10

19 15

19 20

19 25

19 30

19 35

19 40

19 45

19 50

19 55

19 60

19 65

19 70

19 75

19 80

19 85

19 90

19 95

20 00

20 05

20 10

20 15

20 20

-15

-10

-5

0

5

10

15

20

25

Source: Bureau of Labor Statistics.

If a family spent $250 a week on their typical purchases in 1950, how much would those purchases have cost in 1980? If your salary in 1980 was $30,000 a year, what would be the real value of that salary in terms of 1950 dollars? Use the data in Table 5.8.

Self-Test5.12

Inflation and Interest Rates Whenever anyone quotes an interest rate, you can be fairly sure that it is a nominal, not a real, rate. It sets the actual number of dollars you will be paid with no offset for future inflation.

If you deposit $1,000 in the bank at a nominal interest rate of 6%, you will have $1,060 at the end of the year. But this does not mean you are 6% better off. Suppose that the inflation rate during the year is also 6%. Then the goods that cost $1,000 last year will now cost $1,000 × 1.06 = $1,060, so you’ve gained nothing:

Real future value of investment = $1,000 × (1 + nominal interest rate) ______________________________ (1 + inflation rate)

= $1,000 × 1.06 ____________ 1.06 = $1,000

In this example, the nominal rate of interest is 6%, but the real interest rate is zero.

nominal interest rate Rate at which money invested grows.

real interest rate Rate at which the purchasing power of an investment increases.

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150 Part Two Value

The real rate of interest is calculated by

1 + real interest rate = 1 + nominal interest rate ____________________ 1 + inflation rate (5.8)

In our example, both the nominal interest rate and the inflation rate were 6%. So

1 + real interest rate =  1.06 ____ 1.06 = 1

Real interest rate = 0

What if the nominal interest rate is 6%, but the inflation rate is only 2%? In that case, the real interest rate is 1.06/1.02 − 1 = .039, or 3.9%. Imagine that the price of a loaf of bread is $1, so that $1,000 would buy 1,000 loaves today. If you invest that $1,000 at a nominal interest rate of 6%, you will have $1,060 at the end of the year. However, if the price of loaves has risen in the meantime to $1.02, then your money will buy you 1,060/1.02 = 1,039 loaves. The real rate of interest is 3.9%.

a. Suppose that you invest your funds at an interest rate of 8%. What will be your real rate of interest if the inflation rate is zero? What if it is 5%?  

b. Suppose that you demand a real rate of interest of 3% on your investments. What nominal interest rate do you need to earn if the inflation rate is zero? If it is 5%?

Self-Test5.13

Here is a useful approximation. The real rate approximately equals the difference between the nominal rate and the inflation rate:8

Real interest rate ≈ nominal interest rate − inflation rate (5.9)

Our example used a nominal interest rate of 6%, an inflation rate of 2%, and a real rate of 3.9%. If we round to 4%, the approximation gives the same answer:

Real interest rate ≈ nominal interest rate − inflation rate ≈ 6 − 2 = 4%

The approximation works best when both the inflation rate and the real rate are small. When they are not small, throw the approximation away and do it right.

8 The squiggle (≈) means “approximately equal to.”

Real and Nominal Rates

In the United States in early 2018, long-term high-grade corporate bonds offered a yield of 2.87%. If inflation in the coming year is expected to be about 1%, the real yield is

1 + real interest rate = 1 + nominal interest rate ____________________ 1 + inflation rate = 1.0287 ______ 1.01 1.0185

Real interest rate = .0185, or 1.85%

The approximation rule gives a similar value of 2.87 − 1.0 = 1.87%. But the approximation would not have worked in the German hyperinflation of 1922–1923, when the inflation rate was well over 100% per month (at one point you needed 1 million marks to mail a letter). ■

Example 5.14 ⊲

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German hyperinflation

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Chapter 5 The Time Value of Money 151

Valuing Real Cash Payments Think again about how to value future cash payments. Earlier in the chapter, you learned how to value payments in current dollars by discounting at the nominal inter- est rate. For example, suppose that the nominal interest rate is 10%. How much do you need to invest now to produce $100 in a year’s time? Easy! Calculate the present value of $100 by discounting by 10%:

PV = $100 _____ 1.10 = $90.91

You get exactly the same result if you discount the real payment by the real interest rate. For example, assume that you expect inflation of 7% over the next year. The real value of that $100 is therefore only $100/1.07 = $93.46. In one year’s time your $100 will buy only as much as $93.46 today. Also, with a 7% inflation rate, the real rate of interest is only about 3%. We can calculate it exactly from the formula:

1 + real interest rate = 1 + nominal interest rate ____________________ 1 + inflation rate = 1.10 ____ 1.07 = 1.028

Real interest rate = .028, or 2.8%

If we now discount the $93.46 real payment by the 2.8% real interest rate, we have a present value of $90.91, just as before:

PV = $93.46 ______ 1.028 = $90.91

The two methods should always give the same answer. Remember: Current dollar cash flows must be discounted by the nominal inter-

est rate; real cash flows must be discounted by the real interest rate. Mixing up nominal cash flows and real discount rates (or real rates and nominal

flows) is an unforgivable sin. It is surprising how many sinners one finds.

How Inflation Might Affect Bill Gates

We showed earlier (Example 5.9) that at an interest rate of 6%, Bill Gates could, if he wished, turn his $90 billion wealth into a 30-year annuity of $6.5 billion per year of luxury and excite- ment (L&E). Unfortunately, L&E expenses inflate just like gasoline and groceries. Thus, Mr. Gates would find the purchasing power of that $6.5 billion steadily declining. If he wants the same luxuries in 2048 as in 2018, he’ll have to spend less in 2018 and then increase expenditures in line with inflation. How much should he spend in 2018? Assume the long-run inflation rate is 3%.

Mr. Gates needs to calculate a 30-year real annuity. The real interest rate is a little less than 3%:

1 + real interest rate = 1 + nominal interest rate ____________________ 1 + inflation rate

= 1.06 ____ 1.03 = 1.029

Example 5.15 ⊲

You are owed $5,000 by a relative who will pay it back in 1 year. The nominal interest rate is 8%, and the inflation rate is 5%. What is the present value of your relative’s IOU? Show that you get the same answer (a) discounting the nominal payment at the nominal rate and (b) discounting the real payment at the real rate.

Self-Test5.14

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152 Part Two Value

Real or Nominal? Any present value calculation done in nominal terms can also be done in real terms, and vice versa. Most financial analysts forecast in nominal terms and discount at nom- inal rates. However, in some cases real cash flows are easier to deal with. In our exam- ple of Bill Gates, the real expenditures were fixed. In this case, it was easiest to use real quantities. On the other hand, if the cash-flow stream is fixed in nominal terms (for example, the payments on a loan), it is easiest to use all nominal quantities.

so the real rate is 2.9%. The 30-year annuity factor at 2.9% is 19.8562. Therefore, annual spending (in 2018 dollars) should be chosen so that

$90,000,000,000 = annual real spending × 19.8562 Annual real spending = $4,533,000,000

Mr. Gates could spend that amount on L&E in 1 year’s time and 3% more (in line with inflation) in each subsequent year. This is only about 70% of the value we calculated when we ignored inflation. Life has many disappointments, even for tycoons. ■

You have reached age 60 with a modest fortune of $3 million and are consider- ing early retirement. How much can you spend each year for the next 30 years? Assume that spending is stable in real terms. The nominal interest rate is 10%, and the inflation rate is 5%.

Self-Test5.15

SUMMARY An investment of $1 earning an interest rate of r will increase in value each period by the factor (1 + r). After t periods, its value will grow to $(1 + r)t. This is the future value of the $1 investment with compound interest.

The present value of a future cash payment is the amount that you would need to invest today to produce that future payment. To calculate present value, we divide the cash pay- ment by (1 + r)t or, equivalently, multiply by the discount factor 1/(1 + r)t. The discount factor measures the value today of $1 received in period t.

A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The present value of a stream of cash flows is simply the sum of the present value of each individual cash flow. Similarly, the future value of an annuity is the sum of the future value of each individual cash flow. Shortcut formulas make the calculations for perpetuities and annuities easy.

Interest rates for short time periods are often quoted as annual rates by multiplying the per- period rate by the number of periods in a year. These annual percentage rates (APRs) do not recognize the effect of compound interest; that is, they annualize assuming simple interest. The effective annual rate annualizes using compound interest. It equals the rate of interest per period compounded for the number of periods in a year.

If you invest money at a given interest rate, what will be the future value of your investment? (LO5-1)

What is the present value of a cash flow to be received in the future? (LO5-2)

How can we calculate present and future values of streams of cash payments? (LO5-3)

How should we compare interest rates quoted over different time intervals, for example, monthly versus annual rates? (LO5-4)

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Chapter 5 The Time Value of Money 153

A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress future cash flows in terms of real dollars—that is, dollars of constant purchasing power.

Be careful to distinguish the nominal interest rate and the real interest rate—that is, the rate at which the real value of the investment grows. Discount nominal cash flows (that is, cash flows measured in current dollars) at nominal interest rates. Dis- count real cash flows (cash flows measured in constant dollars) at real interest rates. Never mix and match nominal and real.

What is the difference between real and nominal cash flows and between real and nominal interest rates? (LO5-5)

LISTING OF EQUATIONS 5.1 Future value = present value × (1 + r)t

5.2 Present value =  future value after t periods ______________________ (1 + r)t

5.3 PV of perpetuity =  C __ r  =  cash payment ____________ interest rate

5.4 Present value of t-year annuity = C [ 1 __ r  −  1 _______ r(1 + r)t ] 5.5 Future value (FV) of annuity of $1 a year =  present value of annuity of

$1 a year × (1 + r)t 

= [ 1 __ r  −  1 _______

r(1 + r)t ] × (1 + r) t

=  (1 + r) t − 1 __________ r

5.6 Present value of annuity due = present value of ordinary annuity × (1 + r) 5.7 Future value of annuity due = future value of ordinary annuity × (1 + r)

5.8 1 + real interest rate =  1 + nominal interest rate ____________________ 1 + inflation rate

5.9 Real interest rate ≈ nominal interest rate − inflation rate

QUESTIONS AND PROBLEMS 1. Compound Interest. Old Time Savings Bank pays 4% interest on its savings accounts. If you

deposit $1,000 in the bank and leave it there: (LO5-1) a. How much interest will you earn in the first year? b. How much interest will you earn in the second year? c. How much interest will you earn in the 10th year?

2. Compound Interest. New Savings Bank pays 4% interest on its deposits. If you deposit $1,000 in the bank and leave it there, will it take more or less than 25 years for your money to double? You should be able to answer this without a calculator or interest rate tables. (LO5-1)

3. Compound Interest. Suppose that the value of an investment in the stock market has increased at an average compound rate of about 5% since 1900. It is now 2019. (LO5-1) a. If your great-grandfather invested $1,000 in 1900, how much would that investment be

worth today? b. If an investment in 1900 has grown to $1 million, how much was invested in 1900?

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154 Part Two Value

4. Future Values. Compute the future value of a $100 cash flow for the following combinations of rates and times. (LO5-1) a. r = 8%, t = 10 years b. r = 8%, t = 20 years c. r = 4%, t = 10 years d. r = 4%, t = 20 years

5. Future Values. You deposit $1,000 in your bank account. (LO5-1) a. If the bank pays 4% simple interest, how much will you accumulate in your account after

10 years? b. How much will you accumulate if the bank pays compound interest?

6. Future Values. If you earn 6% per year on your bank account, how long will it take an account with $100 to double to $200? (LO5-1)

7. Future Values. In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1993 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest. (LO5-1) a. How much was each granddaughter entitled to if the interest rate was 4%? b. How much was each entitled to if the interest rate was 8%?

8. Future Values. How long will it take for $400 to grow to $1,000 at the following interest rates? (LO5-1) a. 4% b. 8% c. 16%

9. Future Values. You invest $1,000 today and expect to sell your investment for $2,000 in 10 years. (LO5-1) a. Is this a good deal if the interest rate is 6%? b. What if the interest rate is 10%?

10. Future Values. Your wealthy uncle established a $1,000 bank account for you when you were born. For the first 8 years of your life, the interest rate earned on the account was 6%. Since then, rates have been only 4%. Now you are 21 years old and ready to cash in. How much is in your account? (LO5-1)

11. Present Values. You can buy property today for $3 million and sell it in 5 years for $4 million. (You earn no rental income on the property.) (LO5-2) a. If the interest rate is 8%, what is the present value of the sales price? b. Is the property investment attractive to you? c. Would your answer to part (b) change if you also could earn $200,000 per-year rent on the

property? The rent is paid at the end of each year.

12. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times. (LO5-2) a. r = 8%, t = 10 years b. r = 8%, t = 20 years c. r = 4%, t = 10 years d. r = 4%, t = 20 years

13. Present Values. You will require $700 in 5 years. If you earn 5% interest on your funds, how much will you need to invest today in order to reach your savings goal? (LO5-2)

14. Present Values. What is the present value of the following cash-flow stream if the interest rate is 6%? (LO5-2)

Year Cash Flow

1 $200 2 400 3 300

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Chapter 5 The Time Value of Money 155

15. Calculating the Interest Rate. Find the interest rate implied by the following combinations of present and future values. (LO5-2)

Present Value Years Future Value

$400 11 $684 183 4 249 300 7 300

16. Calculating the Interest Rate. Find the annual interest rate. (LO5-2)

Present Value Future Value Time Period

$100 $115.76 3 years 200 262.16 4 100 110.41 5

17. Calculating the Interest Rate. A U.S. Treasury strip that will pay $1,000 in 10 years is selling today for $422.41. What interest rate does the strip offer? (LO5-2)

18. Present Values. A factory costs $400,000. You forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. The discount rate is 12%. (LO5-2) a. What is the value of the factory? b. Is the factory a good investment?

19. Present Values. The 2-year discount factor is .92. What is the present value of $1 to be received in year 2? What is the present value of $2,000? (LO5-2)

20. Annuities. A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2 million a year for 5 years. The interest rate is 10%. Who is better paid? (LO5-3)

21. Annuities. Would you rather receive $1,000 a year for 10 years or $800 a year for 15 years if the interest rate is 5%? What if the interest rate is 20%? (LO5-3)

22. Perpetuities. A local bank advertises the following deal: “Pay us $100 a year for 10 years and then we will pay you (or your beneficiaries) $100 a year forever.” Is this a good deal if the inter- est rate is 6%? (LO5-3)

23. Perpetuities. A local bank will pay you $100 a year for your lifetime if you deposit $2,500 in the bank today. If you plan to live forever, what interest rate is the bank paying? (LO5-3)

24. Perpetuities. A property will provide $10,000 a year forever. If its value is $125,000, what must be the discount rate? (LO5-3)

25. Perpetuities. British government 4% perpetuities pay £4 interest each year forever. Another bond, 2.5% perpetuities, pays £2.50 a year forever. (LO5-3) a. What is the value of 4% perpetuities if the long-term interest rate is 6%? b. What is the value of 2.5% perpetuities?

26. Annuities. (LO5-3) a. What is the present value of a 3-year annuity of $100 if the discount rate is 6%? b. What is the present value of the annuity in part (a) if you have to wait 2 years instead of

1 year for the first payment? 27. Annuities. Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment

of $80,000 at age 65, the firm will pay the retiring professor $600 a month until death. (LO5-3) a. If the professor’s remaining life expectancy is 20 years, what is the monthly interest rate on

this annuity? b. What is the effective annual interest rate? c. If the monthly interest rate is .5%, what monthly annuity payment can the firm offer to the

retiring professor? 28. Annuities. You want to buy a new car, but you can make an initial payment of only $2,000 and

can afford monthly payments of at most $400. (LO5-3) a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the

maximum price you can pay for the car? b. How much can you afford if you finance the purchase over 60 months?

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156 Part Two Value

29. Annuities. You can buy a car that is advertised for $24,000 on the following terms: (a) pay $24,000 and receive a $2,000 rebate from the manufacturer; (b) pay $500 a month for 4 years for total payments of $24,000, implying zero percent financing. Which is the better deal if the inter- est rate is 1% per month? (LO5-3)

30. Annuities. You have just borrowed $100,000 to buy a condo. You will repay the loan in equal monthly payments of $804.62 over the next 30 years. (LO5-4) a. What monthly interest rate are you paying on the loan?  b. What is the APR? c. What is the effective annual rate on that loan? d. What rate is the lender more likely to quote on the loan?

31. Future Value of Annuities. I now have $20,000 in the bank earning interest of .5% per month. I need $30,000 to make a down payment on a house. I can save an additional $100 per month. How long will it take me to accumulate the $30,000? (LO5-3)

32. Real Annuities. A retiree wants level consumption in real terms over a 30-year retirement. If the inflation rate equals the interest rate she earns on her $450,000 of savings, how much can she spend in real terms each year over the rest of her life? (LO5-3)

33. Delayed Annuities. Suppose that you will receive annual payments of $10,000 for a period of 10 years. The first payment will be made 4 years from now. If the interest rate is 5%, what is the present value of this stream of payments? (LO5-3)

34. Annuity Due. Your landscaping company can lease a truck for $8,000 a year (paid at year-end) for 6 years. It can instead buy the truck for $40,000. The truck will be valueless after 6 years. The interest rate your company can earn on its funds is 7%. (LO5-3) a. What is the present value of the cost of leasing? b. Is it cheaper to buy or lease? c. What is the present value of the cost of leasing if the lease payments are an annuity due, so

the first payment comes immediately?  d. Is it now cheaper to buy or lease?

35. Annuity Due. Recall that an annuity due is like an ordinary annuity except that the first pay- ment is made immediately instead of at the end of the first period. (LO5-3) a. Why is the present value of an annuity due equal to (1 + r) times the present value of an

ordinary annuity? b. Why is the future value of an annuity due equal to (1 + r) times the future value of an ordi-

nary annuity?

36. Annuity Due. A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you can take a 10% discount from the purchase price. (LO5-3) a. Which is a better deal if you can borrow or lend funds at a 5% interest rate? b. How will your answer change if the payments on the 4-year installment plan do not start for

a full year?

37. Annuity Due. (LO5-3) a. If you borrow $1,000 and agree to repay the loan in five equal annual payments at an interest

rate of 12%, what will your payment be? b. What will your payment be if you make the first payment on the loan immediately instead of

at the end of the first year?

38. Annuity Due. The $40 million lottery payment that you have just won actually pays $2 million per year for 20 years. The interest rate is 8%. (LO5-3) a. If the first payment comes in 1 year, what is the present value of the winnings? b. What is the present value if the first payment comes immediately?

39. Amortizing Loan. You take out a 30-year $100,000 mortgage loan with an APR of 6% and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? (LO5-3)

40. Amortizing Loan. Consider a 4-year amortizing loan. You borrow $1,000 initially and repay it in four equal annual year-end payments. (LO5-3) a. If the interest rate is 8%, what is the annual payment? b. Fill in the following table, which shows how much of each payment is interest versus princi-

pal repayment (that is, amortization) and the outstanding balance on the loan at each date.

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Chapter 5 The Time Value of Money 157

Time Loan

Balance ($) Year-End Interest Due on

Loan Balance ($) Total Year-End

Payment ($) Amortization of

Loan ($)

0 1,000 _____ _____ _____ 1 _____ _____ _____ _____ 2 _____ _____ _____ _____ 3 _____ _____ _____ _____ 4 0 0

41. Retirement Savings. A couple will retire in 50 years; they plan to spend about $30,000 a year (in current dollars) in retirement, which should last about 25 years. They believe that they can earn a real interest rate of 8% on retirement savings. (LO5-3) a. If they make annual payments into a savings plan, how much will they need to save each

year? Assume the first payment comes in 1 year. b. How would the answer to part (a) change if the couple also realize that in 20 years they will

need to spend $60,000 in current dollars on their child’s college education?

42. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 6% per year, how much must you save each year to meet your retirement goal? (LO5-3)

43. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. You also believe that you will inherit $100,000 in 10 years. If the interest rate is 6% per year, how much must you save each year to meet your retirement goal? (LO5-3)

44. Retirement Savings. You believe you will spend $40,000 a year for 20 years once you retire in 40 years. If the interest rate is 6% per year, how much must you save each year until retirement to meet your retirement goal? (LO5-3)

45. Retirement Savings. A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $10,000 that also can be invested. (LO5-3) a. How much money will they have accumulated 30 years from now? b. If their goal is to retire with $800,000 of savings, how much extra do they need to save every

year?

46. Perpetuities and Effective Interest Rate. What is the value of a perpetuity that pays $100 every 3 months forever? The interest rate quoted on an APR basis is 6%. (LO5-3)

47. Amortizing Loans and Inflation. Suppose you take out a $100,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%. To keep things simple, we will assume you make payments on the loan annually at the end of each year. (LO5-3) a. What is your annual payment on the loan? b. Construct a mortgage amortization table in Excel similar to Table 5.5 in which you compute

the interest payment each year, the amortization of the loan, and the loan balance each year. (Allow the interest rate to be an input that the user of the spreadsheet can enter and change.)

c. What fraction of your initial loan payment is interest? d. What fraction of your initial loan payment is amortization? e. What fraction of the loan has been paid off after 10 years (halfway through the life of the

loan)? Why is the answer not 50%? f. If the inflation rate is 2%, what is the real value of the first (year-end) payment? g. If the inflation rate is 2%, what is the real value of the last (year-end) payment? h. Now assume the inflation rate is 8% and the real interest rate on the loan is unchanged. What

must be the new nominal interest rate? i. Recompute the amortization table. What is the real value of the first (year-end) payment in

this high-inflation scenario? j. What is the real value of the last payment in this high-inflation scenario?

48. Mortgage with Points. Home loans often involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $100,000 and 2 points are charged, the loan repayment schedule is calculated on a $100,000 loan but the net amount the borrower receives is only $98,000. Assume the interest rate is 1% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 360 months? (LO5-4)

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158 Part Two Value

49. Effective Interest Rate. A store will give you a 3% discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month? (LO5-4)

50. Effective Interest Rate. You’ve borrowed $4,248.68 and agreed to pay back the loan with monthly payments of $200. If the interest rate is 12% stated as an APR, how long will it take you to pay back the loan? What is the effective annual rate on the loan? (LO5-4)

51. Effective Interest Rate. You invest $1,000 at a 6% annual interest rate, stated as an APR. Inter- est is compounded monthly. How much will you have in 1 year? In 1.5 years? (LO5-4)

52. Effective Interest Rate. If a bank pays 6% interest with continuous compounding, what is the effective annual rate? (LO5-4)

53. Effective Interest Rate. In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as $10,000 and the interest rate is 10%, the borrower “pays” .10 × $10,000 = $1,000 immediately, thereby receiving net funds of $9,000 and repaying $10,000 in a year. (LO5-4) a. What is the effective interest rate on this loan? b. What is the effective annual rate on a 1-year loan with an interest rate quoted on a discount

basis of 20%?

54. Effective Interest Rate. Banks sometimes quote interest rates in the form of “add-on inter- est.” In this case, if a 1-year loan is quoted with a 20% interest rate and you borrow $1,000, then you pay back $1,200. But you make these payments in monthly installments of $100 each. (LO5-4) a. What is the true APR on this loan? b. What is the effective annual rate on the loan?

55. Effective Interest Rate. You borrow $1,000 from the bank and agree to repay the loan over the next year in 12 equal monthly payments of $90. However, the bank also charges you a loan initiation fee of $20, which is taken out of the initial proceeds of the loan. What is the effective annual interest rate on the loan, taking account of the impact of the initia- tion fee? (LO5-4)

56. Effective Interest Rate. First National Bank pays 6.2% interest compounded semiannually. Second National Bank pays 6% interest compounded monthly. Which bank offers the higher effective annual interest rate? (LO5-4)

57. Loan Payments. You take out an $8,000 car loan that calls for 48 monthly payments starting after 1 month at an APR of 10%. (LO5-4) a. What is your monthly payment? b. What is the effective annual interest rate on the loan? c. Now assume the payments are made in four annual year-end installments. What annual pay-

ment would have the same present value as the monthly payment you calculated?

58. Continuous Compounding. How much will $100 grow to if invested at a continuously com- pounded interest rate of 10% for 8 years? What if it is invested for 10 years at 8%? (LO5-4)

59. Effective Interest Rate. Find the effective annual interest rate for each case. (LO5-4)

APR Compounding Period

12% 1 month 8 3

10 6

60. Effective Interest Rate. Find the APR (the stated interest rate) for each case. (LO5-4)

Effective Annual Interest Rate

Compounding Period

10.00% 1 month 6.09 6 8.24 3

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Chapter 5 The Time Value of Money 159

61. Effective Interest Rate. Lenny Loanshark charges “1 point” per week (i.e., 1% per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate? (LO5-4)

62. Effective Interest Rate. Suppose you can borrow money at 8.6% per year (APR) compounded semiannually or 8.4% per year (APR) compounded monthly. Which is the better deal? (LO5-4)

63. Effective Interest Rate. If you take out an $8,000 car loan that calls for 48 monthly payments of $240 each, what is the APR of the loan? What is the effective annual interest rate on the loan? (LO5-4)

64. Real versus Nominal Perpetuities. If the interest rate is 6% per year, how long will it take for your money to quadruple in value? If the inflation rate is 4% per year, what will be the change in the purchasing power of your money over this period? (LO5-5)

65. Inflation. In October 2017 a pound of apples cost $1.32, while oranges cost $1.59. Three years earlier the price of apples was $1.36 a pound and that of oranges was $1.51 a pound. (LO5-5) a. What was the annual compound rate of growth in the price of apples? b. What was the annual compound rate of growth in the price of oranges? c. If the same rates of growth persist in the future, what will be the price of apples in 2030? d. What about the price of oranges?

66. Real versus Nominal Dollars. An engineer in 1950 was earning $6,000 a year. In 2017 she earned $80,000 a year. However, on average, prices in 2017 were higher than in 1950. What was her real income in 2017 in terms of constant 1950 dollars? Use the data in Table 5.8. (LO5-5)

67. Real versus Nominal Dollars. Your consulting firm will produce cash flows of $100,000 this year, and you expect cash flow thereafter to keep pace with any increase in the general level of prices. The interest rate currently is 6%, and you anticipate inflation of about 2%. (LO5-5) a. What is the present value of your firm’s cash flows for years 1 through 5? b. How would your answer to part (a) change if you anticipated no growth in cash flow?

68. Real versus Nominal Rates. If investors are to earn a 3% real interest rate, what nominal inter- est rate must they earn if the inflation rate is (a) zero? (b) 4%? (c) 6%? (LO5-5)

69. Real versus Nominal Rates. If investors receive a 6% interest rate on their bank deposits, what real interest rate will they earn if the inflation rate over the year is (a) zero? (b) 3%? (c) 6%? (LO5-5)

70. Real versus Nominal Annuities. Good news: You will almost certainly be a millionaire by the time you retire in 50 years. Bad news: The inflation rate over your lifetime will average about 3%. (LO5-5) a. What will be the real value of $1 million by the time you retire in terms of today’s dollars? b. What real annuity (in today’s dollars) will $1 million support if the real interest rate at retire-

ment is 2% and the annuity must last for 20 years?

71. Inflation.  According to the International Monetary Fund, the inflation rate in Argentina in 2017 was about 1.9% per month. What was the annual inflation rate? (LO5-5)

72. Real versus Nominal Annuities. You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $30,000 a year for 15 years. (LO5-5) a. If the interest rate is 10%, how much must you accumulate by the time you retire? b. How much must you save each year until retirement in order to finance your retirement

consumption? c. Now you remember that the annual inflation rate is 4%. If a loaf of bread costs $1 today,

what will it cost by the time you retire? d. You really want to consume $30,000 a year in real dollars during retirement and wish to save

an equal real amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire?

e. Calculate the required preretirement real annual savings necessary to meet your consump- tion goals.

f. What is the nominal value of the amount you need to save during the first year? (Assume the savings are put aside at the end of each year.)

g. What is the nominal value of the amount you need to save during the 30th year?

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160 Part Two Value

73. Retirement and Inflation. A couple will retire in 50 years; they plan to spend about $30,000 a year (in current dollars) in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. The inflation rate over the next 75 years is expected to average 5%. (LO5-5) a. What is the real annual savings the couple must set aside? b. How much do they need to save in nominal terms in the first year? c. How much do they need to save in nominal terms in the last year? d. What will be their nominal expenditures in the first year of retirement? e. What will be their nominal expenditures in the last year of retirement?

74. Real versus Nominal Cash Flows. (LO5-5) a. You’ve just graduated college, and you are contemplating your lifetime budget. You think

your general living expenses will average around $50,000 a year. For the next 8 years, you will rent an apartment for $16,000 a year. After that, you will want to buy a house that should cost around $250,000. In addition, you will need to buy a new car roughly once every 10 years, costing around $30,000 each. In 25 years, you will have to put aside around $150,000 to put a child through college, and in 30 years you’ll need to do the same for another child. In 50 years, you will retire and will need to have accumulated enough savings to support roughly 20 years of retirement spending of around $35,000 a year on top of your Social Security benefits. The interest rate is 5% per year. What average salary will you need to earn to support this lifetime consumption plan?

b. Whoops! You just realized that the inflation rate over your lifetime is likely to average about 3% per year, and you need to redo your calculations. As a rough cut, it seems reasonable to assume that all relevant prices and wages will increase at around the rate of inflation. What is your new estimate of the required salary (in today’s dollars)?

75. Real versus Nominal Rates. You will receive $100 from a savings bond in 3 years. The nomi- nal interest rate is 8%. (LO5-5) a. What is the present value of the proceeds from the bond? b. If the inflation rate over the next few years is expected to be 3%, what will the real value of

the $100 payoff be in terms of today’s dollars? c. What is the real interest rate? d. Show that the real payoff from the bond [from part (b)] discounted at the real interest rate

[from part (c)] gives the same present value for the bond as you found in part (a).

76. Time Value of Money. Solve the following crossword. (Round your final answers to the nearest dollar, but do not round intermediate calculations.)

1

11

15 16

20 21

22

18 19

12

10

8

13

17

14

23 24

2

9

3 4 5 6 7

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Chapter 5 The Time Value of Money 161

ACROSS 1. A rich uncle has promised to pay you $3,160 at the end of each of the next 25 years. If you

invest this money at 4.9%, how much will you have at the end of the 25 years?

5. Hepsibah Sloop put $10,000 under his mattress 20 years ago. Since then, inflation has averaged 1%. What is the real value of his savings?

9. A 20-year annuity has a present value of $42,419,233. If the interest rate is 15%, what is the annual cash flow?

10. A Treasury bond pays $1 million at the end of 20 years. What is its present value if the interest rate is 4%?

11. A project is forecast to produce a safe cash flow of $800,000 a year for 20 years. If the discount rate is 4%, what is the present value of the project?

12. If you invest $100,000 today, how much will your savings be worth at the end of 9 years if the interest rate is 10%?

15. An annuity due with 10 annual payments has a present value of 1,244,353. If the interest rate is 15%, what is the annual payment?

18. Investment in a Dustinbourne grinder is expected to produce cash flows over the following 7 years of $7 million, $8 million, $9 million, $10 million, $9 million, $8 million, and $7 million. What is the present value of the project if the discount rate is 5%?

20. You invest $95,525 for 20 years at 11.7%. Inflation over the same period is 4% a year. What is the real value of your savings at the end of that period?

22. You invest $1 million for 7 years at 5% and then for a further 7 years at 8%. How much will you have at the end of this time?

23. The discount factor is .8, and the present value of a cash flow is $2,703. What is the cash flow?

24. A deferred annuity makes four equal payments of $129,987 a year starting at the end of year 8. If the interest rate is 12%, what is its present value?

DOWN

2. The winning lottery ticket promises to make 30 payments of $30,000 a year starting immedi- ately. If the interest rate is 5.8%, what is the present value of these payments?

3. An investment in consol bonds promises to provide an interest payment of $2.5 million a year in perpetuity. If the interest rate is 3.3%, what is the value of this investment?

4. The discount factor is .9. What is the present value of $63,269?

6. If you pay the bank $50 a year for 10 years, it promises to pay you $100 a year forever starting in year 11. If the interest rate is 4.2%, what is the value of this proposal to you?

7. The nominal interest rate is 13% and inflation is 4%. If you invest $100,000 today, what will be the real value of your investment at the end of 20 years?

8. What is the value of a payment of $2,125,000 in year 30 if the interest rate is 3.8%?

13. What is the future value of an investment of $20 million at the end of 11 years if the interest rate is 9%?

14. Henry Hub will retire in 25 years and expects to spend a further 20 years in retirement (i.e., years 26–45). He lives an extravagant lifestyle and has drawn up a detailed spreadsheet that suggests he will spend $256,880 a year in real terms in retirement. If the real interest rate is 3%, how much does Henry need to save each year in real terms until retirement to attain his spending goal?

16. A factory is forecast to produce the following cash flows: year 1, $6,516; year 2, $7,000; year 3, $11,400; year 4 onward in perpetuity, $12,000. If the cost of capital is 6%, what is the factory’s present value?

17. What is the future value of $189,956 at the end of 7 years if the interest rate is 11%?

19. Natasha Petrov has savings of $78,780. If she invests the full amount in a bank at an interest rate of 4%, how much will she have after 4 years?

21. You plan to save $1,000 a year in each of years 1 through 5. If the interest rate is 8%, how much will you have saved by the end of year 5?

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162 Part Two Value

WEB EXERCISES 1. In Example 5.10, we showed you how to work out mortgage payments. Log on to the personal

finance page of www.bankrate.com and find the mortgage payment calculator. Assume a 20-year mortgage loan of $100,000 and an interest rate (APR) of 12%. What is the amount of the monthly payment? Check that you get the same answer when using the annuity formula. Now look at how much of the first month’s payment goes to reduce the size of the mortgage. How much of the payment is devoted to loan amortization 10 years later, i.e., what is the amor- tization on the 121st monthly payment? Can you explain why the figure changes? If the interest rate doubles, would you expect the mortgage payment to double? Check whether you are right.

2. You can find data on the consumer price index (CPI) on the Bureau of Labor Statistics website, www.bls.gov/cpi/home.htm. Tables of historical data can be formatted to provide either levels of the index or changes in the index (i.e., the rate of inflation). Construct a table of annual inflation rates since 1913. When did the USA last experience a year of deflation (i.e., falling prices)? Find the inflation rate in the latest year. Now log on to www.bloomberg.com, and on the first page find a measure of the short-term interest rate (e.g., the 2-year rate). Use the recent level of inflation to calculate the real interest rate. Consider the case of Herbert Prothe- roe, who in 1920 was an eligible bachelor with an income of $2,000 a year. What is that equivalent to today?

SOLUTIONS TO SELF-TEST QUESTIONS 5.1 Value after 5 years would have been 24 × (1.05)5 = $30.63; after 50 years, 24 × (1.05)50

= $275.22.

5.2 Call g the annual growth rate of transistors over the 45-year period between 1971 and 2016. Then

2,250 × (1 + g)45 = 7,200,000,000 (1 + g)45 = 3,200,000

1 + g = 3,200,000,0001/45 = 1.395

So the actual growth rate was g = .395, or 39.5%, not quite as high as Moore’s prediction, but not so shabby either.

5.3 Multiply the $1,000 payment by the 5-year discount factor:

PV = $1,000 ×  1 ________ (1.0235)5

= $890.35

5.4 Gift at Year Present Value

1 10,000/(1.07)   = $9,345.79 2 10,000/(1.07)2 =    8,734.39 3 10,000/(1.07)3 =    8,162.98 4 10,000/(1.07)4 =    7,628.95

$33,872.11

Gift at Year Future Value

1 10,000 × (1.07)3 = $12,250.43 2 10,000 × (1.07)2 =   11,449 3 10,000 × (1.07)   =    10,700 4 10,000  =   10,000

              $44,399.43

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Chapter 5 The Time Value of Money 163

5.5 The rate is 4/48 = .0833, about 8.3%.

5.6 The 4-year discount factor is 1/(1.08)4 = .7350. The 4-year annuity factor is [1/.08 − 1/(.08 × 1.084)] = 3.3121. This is the difference between the present value of a $1 perpetuity starting next year and the present value of a $1 perpetuity starting in year 5:

PV(perpetuity starting next year) =  1 ___ .08  = 12.50

− PV(perpetuity starting in year 5) =   1 ___ .08  ×   1 _______

(1.08)4   = 9.1879

= PV(4-year annuity) = 12.50 − 9.1879 = 3.3121

which matches the annuity factor.

5.7 You will need the present value at 7% of a 20-year annuity of $55,000:

Present value = annual spending × annuity factor

The annuity factor is [1/.07  − 1/(.07  × 1.0720)] = 10.5940. Thus, you need $55,000  × 10.594 = $582,670.

5.8 Fifteen years means 180 months.

Mortgage payment =  100,000 _____________________ 180-month annuity factor

=  100,000 _______ 83.32

= $1,200.17 per month

$1,000 of the first payment is interest. The remainder, $200.17, is amortization.

5.9 We know that the future value of an annuity due is equal to the future value of an ordinary annuity × (1 + r). Therefore, if you make the first of your 50 annual investments immediately, then by the end of the 50 years, your retirement savings will be 10% higher, $550,000.

5.10 The quarterly rate is 8/4 = 2%. The effective annual rate is (1.02)4 − 1 = .0824, or 8.24%.

5.11 The cost in dollars will increase by 5% each year, to a value of $5 × (1.05)50 = $57.34. If the inflation rate is 10%, the cost will be $5 × (1.10)50 = $586.95.

5.12 The CPI in 1980 was 3.452 times its value in 1950 (see Table 5.8). Therefore, purchases that cost $250 in 1950 would have cost $250 × 3.452 = $863 in 1980. The value of a 1980 salary of $30,000, expressed in real 1950 dollars, is $30,000 × (1/3.452) = $8,691.

5.13 a. If there’s no inflation, real and nominal rates are equal at 8%. With 5% inflation, the real rate is (1.08/1.05) − 1 = .02857, a bit less than 3%.

b. If you want a 3% real interest rate, you need a 3% nominal rate if inflation is zero and an 8.15% rate if inflation is 5%. Note that 1.03 × 1.05 = 1.0815.

5.14 The present value is

PV =  $5,000 ______ 1.08  = $4,629.63

The real interest rate is 2.857% (see Self-Test 5.13a). The real cash payment is $5,000/1.05 = $4,761.90. Thus,

PV =  $4,761.90 _________ 1.02857  = $4,629.63

5.15 Calculate the real annuity. The real interest rate is 1.10/1.05 − 1 = .0476. We’ll round to 4.8%. The real annuity is

Annual payment = $3,000,000 __________________ 30-year annuity factor  = $3,000,000 __________________

1 ____ .048  −  1 ___________

.048(1.048)30  =  $3,000,000 __________ 15.7292  = $190,728

You can spend this much each year in dollars of constant purchasing power. The purchasing power of each dollar will decline at 5% per year, so you’ll need to spend more in nominal dol- lars: $190,728 × 1.05 = $200,264 in the second year, $190,728 × 1.052 = $210,278 in the third year, and so on.

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164 Part Two Value

MINICASE Old Alfred Road, who is well-known to drivers on the Maine Turnpike, has reached his 70th birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully.

Mr. Road owns his home—the mortgage is paid off—and does not want to move. He is a widower, and he wants to bequeath the house and any remaining assets to his daughter.

He has accumulated savings of $180,000, conservatively invested. The investments are yielding 9% interest. Mr. Road also has $12,000 in a savings account at 5% interest. He wants to keep the savings account intact for unexpected expenses or emergencies.

Mr. Road’s basic living expenses now average about $1,500 per month, and he plans to spend $500 per month on travel and hob- bies. To maintain this planned standard of living, he will have to rely on his investment portfolio. The interest from the portfolio is $16,200 per year (9% of $180,000), or $1,350 per month.

Mr. Road will also receive $750 per month in Social Security payments for the rest of his life. These payments are indexed for

inflation. That is, they will be automatically increased in propor- tion to changes in the consumer price index.

Mr. Road’s main concern is with inflation. The inflation rate has been below 3% recently, but a 3% rate is unusually low by his- torical standards. His Social Security payments will increase with inflation, but the interest on his investment portfolio will not.

What advice do you have for Mr. Road? Can he safely spend all the interest from his investment portfolio? How much could he withdraw at year-end from that portfolio if he wants to keep its real value intact?

Suppose Mr. Road will live for 20 more years and is willing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase along with inflation over that period. In other words, he wants his monthly spending to stay the same in real terms. How much can he afford to spend per month?

Assume that the investment portfolio continues to yield a 9% rate of return and that the inflation rate will be 4%.

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166

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

6-1 Distinguish among a bond’s coupon rate, current yield, and yield to maturity.

6-2 Find the market price of a bond given its yield to maturity, find a bond’s yield given its price, and demonstrate why prices and yields move in opposite directions.

6-3 Show why bonds exhibit interest rate risk.

6-4 Understand why investors are interested in the plot of bond yields against time to maturity.

6-5 Understand why investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings.

C H A P T E R

6 Valuing Bonds

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

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167

P A

R T

T W

O V

al ue

Bondholders once received a beautifully engraved certificate like this one issued by a railroad. Nowadays their ownership is simply recorded on an electronic database. ©CPC Collection/Alamy

When a corporation needs external financing, it can borrow money. If it needs the money only for a month, quarter, or year, it will probably borrow from a bank. But if it needs to make a long-term investment, it may instead issue a bond, which is a debt security held by individual and institutional investors.

Companies are not the only bond issuers. State and local governments also raise money by selling bonds. So does the U.S. Treasury. Most investors would regard the risk of default on Treasury bonds as negligible, and, therefore, these issues offer a lower rate of interest than corporate bonds. Nevertheless, the interest rates on government bonds provide a benchmark for all interest rates. When government interest rates go up or down, corporate rates follow more or less proportionally. Thus, in the first part of this chapter, we focus on Treasury bonds and sidestep the issue of default.

We begin by showing you how to understand the bond pages in the financial press, and we explain what bond dealers mean when they quote yields to maturity. We look at why short-term rates are usually lower (but sometimes higher) than long-term rates and why the longest-term bond prices are most sensitive to fluctua- tions in interest rates. We distinguish real (inflation- adjusted) interest rates and nominal (money) rates and explain how future inflation can affect interest rates.

Toward the end of the chapter, we return to corporate bonds, which carry a possibility of default. We look at how bond ratings provide a guide to that default risk and how low-rated bonds offer higher promised yields. There is enormous variation in the design of corporate bonds. We introduce here some of the main ways in which they differ, but we will revisit the topic in Chapter 14.

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The Bond Market

Governments and corporations borrow money by selling bonds to investors. The mar- ket for these bonds is huge. At the start of 2018, public holdings of U.S. government bonds were more than $14 trillion ($14,000,000,000,000). Companies also raise very large sums of money by selling bonds. For example, in 2018, CVS borrowed $40 billion in one large issue of bonds. The market for bonds is sophisticated and active. Bond traders frequently make massive trades motivated by tiny price discrepancies.

Bonds sometimes go under different names. For example, Treasury bonds with maturities of 2 to 10 years at the time of issue are called “notes.” Some corporate bonds are called notes or “debentures.” In this chapter, we will simplify and just say “bonds.”

When governments or companies issue bonds, they promise to make a series of inter- est payments and then to repay the debt. But don’t get the idea that all bonds are alike. For example, most bonds make a fixed interest payment, but in other cases, the payment may go up or down as short-term interest rates change. Bonds may also have different maturities. Sometimes a company may borrow for only a few years, but there have been a few occasions when bonds have been issued with maturities of 100 years or more.

Bond Characteristics Several years ago, the U.S. government made a typical issue of a Treasury bond, in which it auctioned off 2.25% coupon bonds maturing in 2021. The bonds have a face value (also called the principal or par value) of $1,000. Each year until the bond matures, the bondholder receives interest of 2.25% of the face value, or $22.50. This 2.25% inter- est payment is called the bond’s coupon. (In the old days, most bonds used to have cou- pons that the investor clipped off and mailed to the bond issuer to claim the interest payment.) When the 2.25% coupon bond matures in 2021, the government must pay the $1,000 face value of the bond in addition to the final coupon payment.

At any moment, there are more than 300 different Treasury bonds outstanding. The prices at which you can buy and sell these bonds are shown each day in the financial press and on the web. Table 6.1, which is compiled from The Wall Street Journal’s web page, shows the prices for just a small sample of issues. The entry for the 2.25% bond maturing in February 2021 is highlighted.

Anyone buying the 2.25% bond would need to pay the asked price, which is given as 99.5938. This means that the price is 99.5938% of face value. Therefore, each bond costs $995.938. An investor who already owns the bond and wishes to sell it would receive the bid price, which is shown as 99.5781. Just as the used-car dealer earns a living by reselling cars at higher prices than he paid for them, so the bond dealer needs to charge a spread between the bid and the asked price. Notice that the spread for these 2.25% bonds is about .0157% of the bond’s value. Don’t you wish that used-car dealers charged similar spreads?

The final column in the table shows the asked yield to maturity. This measures the return to investors if they buy the bond at the asked price and hold it to maturity in 2021. You can see that the 2.25% coupon Treasury bond offers a yield to maturity of 2.391%. We will explain shortly how this figure was calculated.

6.1

bond Security that obligates the issuer to make specified payments to the bondholder.

face value Payment at the maturity of the bond. Also called principal or par value.

coupon The interest payments paid to the bondholder.

How much would an investor pay to buy one 7.625% Treasury bond of 2025 (see Table 6.1)? If a Treasury bond costs $1,106.25, how would this price be quoted? How much would the investor receive if he sold the 3% Treasury bond of 2048?

Self-Test6.1

168 Part Two Value

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You can’t buy Treasury bonds on the stock exchange. Instead, they are traded by a network of bond dealers, who quote bid and ask prices at which they are prepared to buy and sell. For example, suppose that in 2018 you decide to buy the “2.25s of 2021,” that is, the 2.25% coupon bonds maturing in 2021.1 You approach a broker who checks the current price on her screen. If you are happy to go ahead with the purchase, your broker will contact a bond dealer and the trade is done.

If you plan to hold your bond until maturity, you can look forward to the cash flows shown in Figure 6.1. For the first 2 years, the cash flows equal the 2.25% coupon pay- ment. Then, when the bond matures in 2021, you receive the $1,000 face value of the bond plus the final coupon payment.

Maturity Coupon Bid Asked

Change in

Asked Asked yield

to maturity (%)

15-Feb-2020 1.375 98.3281 98.3438 −0.0078 2.228

15-Feb-2021 2.25 99.5781 99.5938 0.0313 2.391

15-Feb-2025 7.625 130.6719 130.6875 0.1094 2.770

15-Feb-2029 5.25 121.8516 121.9141 0.2344 2.908

15-Feb-2036 4.5 120.9063 120.9688 0.5313 2.986

15-Feb-2041 4.75 127.2422 127.3047 0.6641 3.084

15-Feb-2048 3 97.2656 97.2969 0.7266 3.140

TABLE 6.1 Sample Treasury bond quotes in February 2018

Source: Wall Street Journal Online, February 15, 2018, www.wsj.com.

FIGURE 6.1 Cash flows to an investor in the 2.25% coupon bond maturing in 2021

$1,022.50

Year: 2018 2019 2020 2021

$22.50

$1,000

$22.50$22.50

-Price

Find the 5.25% coupon 2029 Treasury bond in Table 6.1.

a. How much does it cost to buy the bond?   b. If you already owned the bond, how much would a bond dealer pay you for it?   c. What annual interest payment does the bond make?   d. What is the bond’s yield to maturity?

Self-Test6.2

1 The ‘s’ after 2.25 is just a plural. This is how bond traders refer to bonds of any particular coupon.

Chapter 6 Valuing Bonds 169

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Interest Rates and Bond Prices

In Figure 6.1, we set out the cash flows from your 2.25% Treasury bond. The value of the bond is the present value of these cash flows. To find this value, you need to discount each future payment by the current interest rate.

The 2.25s were not the only Treasury bonds that matured in 2021. Almost identical bonds maturing at the same time offered an interest rate of just under 2.4%. If the 2.25s had offered a lower return than this, no one would have been willing to hold them. Equally, if they had offered a higher return, everyone would have rushed to sell their other bonds and buy the 2.25s. In other words, if investors were on their toes, the 2.25s had to offer the same rate of interest as similar Treasury bonds. You might recognize this as the opportunity cost of the funds invested in the bond, as we discussed in Chapter 1. This is the rate that investors could earn by placing their funds in similar securities rather than in this bond.

We can now calculate the present value of the 2.25s of 2021 by discounting the cash flows at 2.391%, or a shade under 2.4%:

PV = $22.50 _____ (1 + r) + $22.50 _____ (1 + r)2 +

$1,022.50 _______ (1 + r)3

= $22.50 _______ (1.02391) + $22.50 ________ (1.02391)2 +

$1,022.50 ________ (1.02391)3 = $995.96

Bond prices are usually expressed as a percentage of their face value. Thus, we can say that your 2.25% Treasury bond is worth 99.596% of face value.2

Did you notice that your bond is like a package of two investments? The first pro- vides a level stream of coupon payments of $22.50 a year for each of 3 years. The second consists of the final repayment of the $1,000 face value. Therefore, you can use the annuity formula to value the coupon payments and then add on the present value of the final payment of face value:

PV = PV(coupons) + PV(face value) (6.1) = (coupon × annuity factor) + (face value × discount factor)

= $22.50 × [ 1 _____ .02391 − 1 _____________ .02391(1.02391)3 ] + $1,000 × 1 _______ 1.023913 = $64.396 + $931.568 = $995.96

If you need to value a bond with many years to run before maturity, it is usually easiest to value the coupon payments as an annuity and then add on the present value of the final payment.

6.2

Calculate the present value of a 6-year bond with a 9% coupon. The interest rate is 12%.

Self-Test6.3

2 You will often find that your calculated value is slightly different from the asked price quoted in the financial press. For example, Table 6.1 shows that the actual price of the bond is $995.94. One reason is minor rounding error in the interest rate, which is reported to only three decimal places. Another is that the bond’s actual coupon is not $22.50 once per year, but $11.25 every 6 months. In the next example, we’ll show how to handle semian- nual coupons.

You can calculate bond prices easily using a financial calculator or spreadsheet. The trick is to recognize that the bond provides its owner both a recurring payment (the cou- pons) and an additional one-time cash flow (the face value). For the 2.25% bond, the time

170 Part Two Value

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to maturity is 3 years, the annual coupon payment is $22.50, and face value is $1,000. The interest rate is 2.391%. Therefore, the inputs for a financial calculator would be:

Inputs 3 2.391 22.50 1000 Compute –995.96

n i PV PMT FV

Bond Prices and Semiannual Coupon Payments

When we valued our Treasury bond, we assumed that interest payments occur annually. This is the case for bonds in many European countries, but in the United States, most bonds make coupon payments semiannually. So when you hear that a bond in the United States has a cou- pon rate of 2.25%, you can generally assume that the bond makes a payment of $22.50/2 = $11.25 every 6 months. Similarly, when investors in the United States refer to the bond’s inter- est rate, they usually mean the semiannual interest rate. Thus, an interest rate quoted at 2.391% really means that the 6-month rate is 2.391/2 = 1.1955%.3 The actual cash flows on the Treasury bond are illustrated in Figure 6.2. To value the bond a bit more precisely, we should have dis- counted the series of semiannual payments by the semiannual rate of interest as follows:

PV = $11.25 _______ (1.011955) + $11.25

________ (1.011955)2

+ $11.25 ________ (1.011955)3

+ $11.25 ________ (1.011955)4

+ $11.25 ________ (1.011955)5

+ $1,011.25 ________ (1.011955)6

= $995.94

Example 6.1 ⊲

Now compute PV, and you should get an answer of −995.96, which is the initial cash outflow required to purchase the bond.

For an introduction to bond pricing using Excel, turn to the box later in the chapter.

FIGURE 6.2 Cash flows to an investor in the 2.25% coupon bond maturing in 2021. The bond pays semiannual coupons, so there are two payments of $11.25 each year.

$1,011.25

Feb 2020

Aug 2020

Feb 2021

Feb 2018

$11.25

$1,000

$11.25

Aug 2019

$11.25 $11.25

Feb 2019

Aug 2018

$11.25

-Price

$11.25

3 You may have noticed that the quoted annual interest rate of 2.391% is also the bond’s APR, although this term is not generally used by bond investors. To find the effective annual rate, we can use a formula that we presented in Section 5.7:

Effective annual rate = (1 + APR/m)m − 1

where m is the number of payments each year. In the case of our Treasury bond,

Effective annual rate = (1 + .02391/2)2 − 1 = 1.0119552 − 1 = .02405, or 2.405%

When interest rates are low, there is negligible difference between the annually compounded interest rate and the APR. The difference is greater when rates are high.

Chapter 6 Valuing Bonds 171

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How Bond Prices Vary with Interest Rates Figure 6.3 plots the interest rate on 10-year maturity Treasury bonds from 1900 to 2018. Notice how much the interest rate fluctuates. For example, interest rates climbed steeply after 1979 when the Federal Reserve instituted a policy of tight money to rein in inflation. Within 2 years, the rate on 10-year government bonds rose from 10% to 14%. Contrast this with 2015, when long-term Treasuries offered a measly 1.9% rate of interest.

As interest rates change, so do bond prices. For example, suppose that investors demanded an interest rate of 2.25% on 3-year Treasury bonds. What would be the price of the Treasury 2.25s of 2021? Just repeat our PV calculation with a discount rate of r = .0225:

PV at 2.25% = $22.50 ______ (1.0225) + $22.50 _______ (1.0225)2 +

$1,022.50 _______ (1.0225)3 = $1,000.00

Thus, when the interest rate is the same as the coupon rate (2.25% in our example), the bond sells for its face value.

We first valued the Treasury bond using an interest rate of 2.391%, which is higher than the coupon rate. In that case, the price of the bond was lower than its face value. We then valued it using an interest rate that is equal to the coupon and found that the bond price equaled face value. You have probably already guessed that when the cash flows are discounted at a rate that is lower than the bond’s cou- pon rate, the bond is worth more than its face value. The following example con- firms that this is the case.

Thus, once we allow for the fact that coupon payments are semiannual, the value of the 2.25s is 99.594%, which precisely matches the actual price of the bond shown in Table 6.1. Still, the difference in value using semiannual versus annual payments is very small. Because semiannual coupon payments just add to the arithmetic, we will stick for the most part to our simplification and assume annual interest payments. ■

FIGURE 6.3 The interest rate on 10-year U.S. Treasury bonds, 1900–2018

Year

0

2

4

6

8

10

12

14

16

19 0

0

19 0

5

19 10

19 15

19 20

19 25

19 30

19 35

19 40

19 45

19 5

0

19 5

5

19 6

0

19 6

5

19 70

19 75

19 80

19 85

19 9

0

19 9

5

20 0

0

20 0

5

20 10

20 15

20 20

Y ie

ld (%

)

Source: www.econ.yale.edu/~shiller/data.htm.

172 Part Two Value

bre13960_ch06_166-195.indd 172 1/26/19 11:32 AM

This is a general result. When the market interest rate exceeds the coupon rate, bonds sell for less than face value. When the market interest rate is below the coupon rate, bonds sell for more than face value.

Suppose that interest rates rise. On hearing the news, bond investors appear discon- solate. Why? Don’t they like higher interest rates? If you are not sure of the answer, look at Figure 6.4, which shows the present value of the 2.25% Treasury bond for dif- ferent interest rates. For example, imagine yields soar from 2.391% to 10%. Our bond would then be worth only $807.27, creating a loss to bondholders of some 19%. Con- versely, bondholders have reason to celebrate when market interest rates fall. You can see this also from Figure 6.4. For instance, if interest rates fall to zero, the value of our 2.25% bond would increase to $1,067.50. That was just about the biggest profit that investors in the 2.25s could hope for.

Figure 6.4 illustrates a fundamental relationship between interest rates and bond prices: When the interest rate rises, the present value of the payments to be received by the bondholder falls and bond prices fall. Conversely, a decline in the interest rate increases the present value of those payments and the price of bonds.

A warning! People sometimes confuse the interest, or coupon, payment on the bond with the interest rate—that is, the return that investors require. The $22.50 coupon payments on our Treasury bond are fixed when the bond is issued. The coupon rate, 2.25%, measures the coupon payment ($22.50) as a percentage of the bond’s face value ($1,000) and is therefore also fixed. However, the interest rate changes from day to day. These changes affect the present value of the coupon payments but not the payments themselves.

coupon rate Annual interest payment as a percentage of face value.

Interest Rates and Bond Prices

Investors will pay $1,000 for a 2.25%, 3-year Treasury bond when the interest rate is 2.25%. Suppose that the interest rate is higher than the coupon rate at (say) 10%. Now what is the value of the bond? Simple! We just repeat our calculation but with r = .10:

PV at 10% = $22.50 ______ (1.10) + $22.50

______ (1.10)2 + $1,022.50

________ (1.10)3

= $807.27

The bond sells for 80.727% of face value. ■

Example 6.2 ⊲

FIGURE 6.4 The value of the 2.25% bond falls as interest rates rise

600

700

800

900

1,000

1,100

0 2 4 6 8 10 12 14 16

B on

d pr

ic e

($ )

Interest rate (%)

Price = $807.27

Interest rate = 10%

Chapter 6 Valuing Bonds 173

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Interest Rate Risk We have just seen that bond prices fluctuate as interest rates change. In other words, bonds are subject to interest rate risk. Bond investors cross their fingers that market interest rates will fall, so that the price of their bond will rise. If they are unlucky and the market interest rate rises, the value of their investment falls.

A change in interest rates has only a modest impact on the present value of near-term cash flows but a much greater impact on the value of distant cash flows. Therefore, any change has a greater impact on the price of long-term bonds than the price of short- term bonds. For example, compare the two curves in Figure 6.5. The blue line shows how the value of the 3-year, 2.25% coupon bond varies with the interest rate. The green line shows how the price of a 30-year, 2.25% bond varies. You can see that the 30-year bond is more sensitive to interest rate fluctuations than the 3-year bond. This should not surprise you. If you buy a 3-year bond and rates then rise, you will be stuck with a bad deal—you could have got a better interest rate if you had waited. However, think how much worse it would be if the loan had been for 30 years rather than 3 years. The longer the loan, the more you have lost by accepting what turns out to be a low interest rate. This shows up in a bigger decline in the price of the longer-term bond. Of course, there is a flip side to this effect, which you can also see from Figure 6.5. When interest rates fall, the longer-term bond responds with a greater increase in price.

interest rate risk The risk in bond prices due to fluctuations in interest rates.

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How changes in interest rates affect long- and short-term bonds

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Which is the longer-term bond?

FIGURE 6.5 Plot of bond prices as a function of the interest rate. The price of long- term bonds is more sensitive to changes in the interest rate than is the price of short-term bonds.

B on

d pr

ic e

($ )

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Interest rate (%)

3-year bond

When the interest rate equals the 2.25% coupon rate, both bonds sell for face value.

30-year bond

Suppose that the market interest rate is 4% and then drops overnight to 2%. Calculate the present values of the 2.25%, 3-year bond and of the 2.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5. Use your financial calculator or a spreadsheet. You can find a box on bond pricing using Excel later in this chapter.

Self-Test6.4

Yield to Maturity

Suppose you are considering the purchase of a 3-year bond with a coupon rate of 10%. Your investment adviser quotes a price for the bond. How do you calculate the rate of return the bond offers?

6.3

174 Part Two Value

bre13960_ch06_166-195.indd 174 1/26/19 11:32 AM

For bonds priced at face value the answer is easy. The rate of return is the coupon rate. We can check this by setting out the cash flows on your investment:

Notice that you are paying out $1,200 and receiving an annual income of $100. So your income as a proportion of the initial outlay is $100/$1,200 = .083, or 8.3%. This is sometimes called the bond’s current yield.

However, your total return depends on both interest income and any capital gains or losses. A current yield of 8.3% may sound attractive until you realize that the bond’s price must fall. The price today is $1,200, but when the bond matures 3 years from now, the bond will sell for its face value, or $1,000. A price decline (i.e., a capital loss) of $200 is guaranteed, so the overall return over the next 3 years must be less than the 8.3% current yield.

Let us generalize. A bond that is priced above its face value is said to sell at a pre- mium. Investors who buy a bond at a premium must absorb a capital loss over the life of the bond, so the return on these bonds is always less than the bond’s current yield. A bond priced below face value sells at a discount. Investors in discount bonds receive a capital gain over the life of the bond; the return on these bonds is greater than the current yield: Because it focuses only on current income and ignores prospective price increases or decreases, the current yield does not measure the bond’s total rate of return. It overstates the return of premium bonds and understates that of discount bonds.

We need a measure of return that takes account of both coupon payments and the change in a bond’s value over its life. The standard measure is called yield to matu- rity. The yield to maturity is the answer to the following question: At what interest rate would the bond be correctly priced? The yield to maturity is defined as the discount rate that makes the present value of the bond’s payments equal to its price.

If you can buy the 3-year bond at face value, the yield to maturity is the coupon rate, 10%. We can check this by noting that when we discount the cash flows at 10%, the present value of the bond is equal to its $1,000 face value:

PV at 10% = $100 _____ (1.10) + $100 _____ (1.10)2 +

$1,100 _____ (1.10)3 = $1,000.00

But what if our 3-year bond is priced at $1,200? In this case, the yield to maturity is only 2.94%. At that discount rate, the bond’s present value equals its actual market price, $1,200:

PV at 2.94% = $100 ______ (1.0294) + $100 _______ (1.0294)2 +

$1,100 _______ (1.0294)3 = $1,200

The yield to maturity is a measure of a bond’s total return, including both coupon income and capital gain. If you buy the bond today and hold it to maturity, your return

current yield Annual coupon payment divided by bond price.

yield to maturity Discount rate at which the present value of the bond’s payments equals the price.

Cash Paid to You in Year:

You Pay 1 2 3 Rate of Return

$1,000 $100 $100 $1,100 10%

Notice that in each year you earn 10% on your money ($100/$1,000). In the final year, you also get back your original investment of $1,000. Therefore, your total return is 10%, the same as the coupon rate.

Now suppose that the market price of the 3-year bond rises to $1,200. Your cash flows are as follows:

Cash Paid to You in Year:

You Pay 1 2 3 Rate of Return

$1,200 $100 $100 $1,100 ?

Chapter 6 Valuing Bonds 175

bre13960_ch06_166-195.indd 175 1/26/19 11:32 AM

A 4-year maturity bond with a 14% coupon rate can be bought for $1,200. What is the yield to maturity if the coupon is paid annually? What if it is paid semiannu- ally? You will need a spreadsheet or a financial calculator to answer this question.

Self-Test6.5

Rate of Return versus Yield to Maturity

On May 15, 2008, the U.S. Treasury sold $9 billion of 4.375% bonds maturing in February 2038. The bonds were issued at a price of 96.38% and offered a yield to maturity of 4.60%. This was the return to anyone buying at the issue price and holding the bonds to maturity. In the months following the issue, the financial crisis reached its peak. Lehman Brothers filed for bankruptcy with assets of $691 billion, and the government poured money into rescuing Fannie Mae, Freddie Mac, AIG, and a host of banks. As investors rushed to the safety of Treasury bonds, their prices soared. By mid-December, the price of the 4.375s of 2038

Example 6.3 ⊲

176 Part Two Value

will be the yield to maturity. Bond investors often refer loosely to a bond’s “yield.” It’s a safe bet that they are talking about its yield to maturity rather than its current yield.

Calculating the Yield to Maturity To find the price of the 2.25% Treasury bond, we discounted the cash payments at the interest rate r. If r = 2.391%, then the value of the bond is $995.96:

Price = $22.50 _____ (1 + r) + $22.50 ______ (1 + r)2 +

$1,022.50 _______ (1 + r)3

= $22.50 _______ (1.02391) + $22.50 ________ (1.02391)2 +

$1,022.50 ________ (1.02391)3 = $995.96

We could have phrased the question the other way round and asked, “If the price of the bond is $995.96, what is the bond’s yield to maturity?”

To calculate yield, we need to find the discount rate, r, for which the present value equals the actual bond price. The only general procedure for doing this is trial and error. You guess at an interest rate and calculate the present value of the bond’s pay- ments. If the present value is greater than the actual price, your discount rate must have been too low, so you try a higher interest rate (because a higher rate results in a lower PV). Conversely, if PV is less than price, you must reduce the interest rate. Of course, this would be a mind-numbing procedure to do by hand. Fortunately, financial calculators or spreadsheet programs can rapidly find a bond’s yield to maturity, using a similar trial-and-error process. We give examples in the nearby boxes.

Bond Rates of Return

The yield to maturity is defined as the discount rate that equates the bond’s price to the present value of all its promised future cash flows. It measures the rate of return that you will earn if you buy the bond today and hold it to maturity. However, as interest rates fluctuate, the return that you earn in the interim may be very different from the yield to maturity. If interest rates rise in a particular week, month, or year, the price of your bond will fall and your return for that period will be lower than the yield to matu- rity. Conversely, if rates fall, the price of your bond will rise and your return will be higher. This is emphasized in the following example.

6.4

bre13960_ch06_166-195.indd 176 1/26/19 11:32 AM

had reached 138.05% of face value and the yield had fallen to 2.5%. Anyone fortunate enough to have bought the bond at the issue price would have made a capital gain of $1,380.50 − $963.80 = $416.70. In addition, on August 15 the bond made its first coupon payment of $21.875 (this is the semiannual payment on the 4.375% coupon bond with a face value of $1,000). Our lucky investor would therefore have earned a 7-month rate of return of 45.5%:

Rate of return = coupon income + price change

_____________________ investment (6.2)

= $21.875 + $416.70 ______________ $963.80

= .455 = 45.5%

Suddenly, government bonds did not seem quite so boring as before. ■

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Bond pricing using financial calculators

rate of return Total income per period per dollar invested.

Suppose that you purchased 8% coupon, 10-year bonds for $1,324.44 when they were yielding 4% (we assume annual coupon payments). One year later, you receive the annual coupon payment of $80, but the yield to maturity has risen to 6%. Confirm that the rate of return on your bond over the year is less than the original 4% yield to maturity.

Self-Test6.6

Suppose that you buy 8%, 2-year bonds for $1,036.67 when they yield 6%. At the end of the year, they still yield 6%. Show that if you continue to hold the bond until maturity, your return in each of the two years will also be 6%.

Self-Test6.7

177

payments of $11.25. Therefore, we can find the semiannual yield as follows:

This yield to maturity, of course, is a 6-month yield, not an annual one. Bond dealers would typically annualize the semi- annual rate by doubling it, so the yield to maturity would be quoted as 1.19556 × 2 = 2.391%, which exactly matches the value in Table 6.1.

You can use a financial calculator to calculate the yield to maturity on our 2.25% Treasury bond. The inputs are:

Now compute i and you should get an answer of 2.392%, which is just a tick above the yield reported in Table 6.1.

Let’s now redo this calculation but recognize that the cou- pons are paid semiannually. Instead of three annual coupon payments of $22.50, the bond makes six semiannual

Financial Calculator Using a Financial Calculator to Compute Bond Yield

Inputs 3 995.938 22.5 1000 Compute 2.392

n i PV PMT FV

Inputs 6 995.938 11.25 1000 Compute 1.19556

n i PV PMT FV

Is there any connection between the yield to maturity and the rate of return during a particular period? Yes: If the bond’s yield to maturity remains unchanged during the period, the bond price changes with time so that the total return on the bond is equal to the yield to maturity. The rate of return will be less than the yield to maturity if interest rates rise, and it will be greater than the yield to maturity if interest rates fall.

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Bond prices and approaching maturity

bre13960_ch06_166-195.indd 177 1/26/19 11:32 AM

178

Alternatively, we could simply enter the following function in Excel:

=PRICE(DATE(2018,2,15), DATE(2021,2,15), .0225, .02391, 100, 1)

The DATE function in Excel, which we use for both the set- tlement and maturity dates, uses the format DATE(year,month,day).

Notice that the coupon rate and yield to maturity are expressed as decimals, not percentages. In most cases, redemption value will be 100 (i.e., 100% of face value), and the resulting price will be expressed as a percent of face value. Occasionally, however, you may encounter bonds that pay off at a premium or discount to face value. One example would be callable bonds, which give the company the right to buy back the bonds at a premium before maturity.

Excel and most other spreadsheet programs provide built- in functions to compute bond values and yields. They typi- cally ask you to input both the date you buy the bond (called the settlement date) and the maturity date of the bond.

The Excel function for bond value is:

=PRICE(settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of face value, number of coupon payments per year)

(If you can’t remember the formula, just remember that you can go to the Formulas tab in Excel, and from the Financial tab pull down the PRICE function, which will prompt you for the necessary inputs.) For our 2.25% coupon bond, we would enter the values shown in the spreadsheet below.

Spreadsheet Solutions Bond Valuation

A B C D E F 1 2.25% annual 2.25% semiannual 6% annual 2 coupon bond, coupon bond, coupon bond, 3 maturing Feb 2021 Formula in column B maturing Feb 2021 30-year maturity 4 5 Settlement date 15-Feb-2018 =DATE(2018,2,15) 15-Feb-2018 15-Feb-2018 6 Maturity date 15-Feb-2021 =DATE(2021,2,15) 15-Feb-2021 15-Feb-2021 7 Annual coupon rate 0.0225 0.0225 0.06 8 Yield to maturity 0.02391 0.02391 0.07 9 Redemption value

(% of face value) 100 100 100

10 Coupon payments per year

1 2 1

11 12 13 Bond price (% of par) 99.596 =PRICE(B5,B6,B7,B8,B9,B10) 99.594 87.591

The solid curve in Figure 6.6 plots the price of a 30-year maturity, 6% coupon bond over time assuming that its yield to maturity is currently 4% and does not change. The price declines gradually until the maturity date, when it finally reaches face value. In each period, the price decline offsets the coupon income by just enough to reduce total return to 4%. The dashed curve in Figure 6.6 shows the corresponding price path for a bond with a 2% coupon that sells at a discount to face value. In this case, the coupon income would provide less than a competitive rate of return, so the bond sells below face value. Its price gradually approaches face value, however, and the price gain each year brings its total return up to the market interest rate.

The Yield Curve

When you buy a bond, you buy a package of coupon payments plus the final repay- ment of face value. But sometimes it is inconvenient to buy things in packages. For example, perhaps you do not need a regular income and would prefer to buy just the final repayment. That’s not a problem. The Treasury is prepared to split its bonds into

6.5

bre13960_ch06_166-195.indd 178 1/26/19 11:32 AM

179

a series of mini-bonds, each of which makes a single payment. These single-payment bonds are called strips.

The prices of strips are shown regularly in the financial press or on the web. For example, in February 2018 it would have cost you $931.87 to buy a strip that would

The value of the bond assuming annual coupon payments is 99.596% of face value, or $995.96. If we wanted to assume semiannual coupon payments, as in Example 6.1, we would simply change the entry in cell B10 to 2 (see cell D10), and the bond value would change to 99.594% of face value, as we found in that example.

We have also assumed that the first coupon payment comes in exactly one period (either a year or a half-year). In other words, the settlement date is precisely at the beginning of the period. However, the PRICE function will make the nec- essary adjustments for intraperiod purchase dates.

Suppose now that you wish to find the price of a 30-year maturity bond with a coupon rate of 6% (paid annually) selling at a yield to maturity of 7%. You are not given a specific settle- ment or maturity date. You can still use the PRICE function to

value the bond. Simply choose an arbitrary settlement date (January 1, 2000, is convenient) and let the maturity date be 30 years hence. The appropriate inputs appear in column F of the preceding spreadsheet, with the resulting price, 87.591% of face value, appearing in cell F13.

Excel also provides a function for yield to maturity. It is:

=YIELD(settlement date, maturity date, annual coupon rate, bond price, redemption value as percent of face value, number of coupon payments per year)

For example, to find the yield to maturity of our 2.25% bond, we would use column B of the following spreadsheet if the coupons were paid annually. If the coupons were paid semi- annually, we would change the entry for payments per year to 2 (see cell D8), and the yield would change very slightly.

A B C D E 1 Annual coupons Semiannual coupons 2 3 Settlement date 15-Feb-2018 15-Feb-2018 4 Maturity date 15-Feb-2021 15-Feb-2021 5 Annual coupon rate 0.0225 0.0225 6 Bond price (from Table 6.1) 99.5938 99.5938 7 Redemption value (% of face value) 100 100 8 Coupon payments per year 1 2 9

10 Yield to maturity (decimal) 0.02392 0.02391 11 12 13 The formula entered here is =YIELD(B3,B4,B5,B6,B7,B8) 14

FIGURE 6.6 How bond prices change as they approach maturity, assuming an unchanged yield to maturity of 4%. Prices of both premium and discount bonds approach face value as their maturity date approaches.

262830 24 20 16 12 8 4 022 18 14 10 6 2

Years to maturity

Maturity date Today

B on

d pr

ic e

($ )

1,400

1,300

1,200

1,100

1,000

900

800

700

600

Price path for the 2% coupon discount bond

Price path for 6% coupon bond selling at a premium to face value

bre13960_ch06_166-195.indd 179 1/26/19 11:32 AM

One-year Treasury bonds yield 5%, while 2-year bonds yield 6%. You are quite confident that in 1 year’s time 1-year bonds will yield 8%. Would you buy the 2-year bond today? Show that there is a better strategy.

Self-Test6.8

FIGURE 6.7 Treasury strips are bonds that make a single payment. The yields on Treasury strips in December 2017 show that investors received a higher yield to maturity on longer-term bonds.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Y ie

ld to

m at

ur ity

(% )

Maturity (years)

4 Coupon bonds are like packages of strips. Investors often plot the yield curve using the yields on these pack- ages. For example, you could plot the yields on the small sample of bonds in Table 6.1 against their maturity.

180 Part Two Value

pay out $1,000 in February 2021. The yield on this 3-year mini-bond was 2.38%. In other words, $931.87 × 1.02383 = $1,000.

Bond investors often draw a plot of the relationship between bond yields and matu- rity. This is known as the yield curve. Treasury strips provide a convenient way to measure this yield curve. For example, if you look at Figure 6.7, you will see that in February 2018 one-year strips offered a yield to maturity of just 1.92%; those with 20 or more years to run provided a yield above 3%. In this case, the yield curve sloped upward.4 This is usually the case, though long-term bonds occasionally offer lower yields, in which case the yield curve slopes downward.

But that raises a question. If long-term bonds offered much higher yields, why didn’t everyone buy them? Who were the (foolish?) investors who put their money into short-term Treasuries at such low yields?

Even when the yield curve is upward-sloping, investors might rationally stay away from long-term bonds for two reasons. First, the prices of long-term bonds fluctuate much more than prices of short-term bonds. We saw in Figure 6.5 that long-term bond prices are more sensitive to shifting interest rates. A sharp increase in interest rates could easily knock 20% or 30% off long-term bond prices. If investors don’t like price fluctuations, they will invest their funds in short-term bonds unless they receive a higher yield to maturity on long-term bonds.

Second, short-term investors can profit if interest rates rise. Suppose you hold a 1-year bond. A year from now, when the bond matures, you can reinvest the proceeds and enjoy whatever rates the bond market offers then. These rates may be high enough to offset the first year’s relatively low yield on the 1-year bond. Thus, you are more likely to see an upward-sloping yield curve when future interest rates are expected to rise.

yield curve Plot of relationship between bond yields to maturity and time to maturity.

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Chapter 6 Valuing Bonds 181

Nominal and Real Rates of Interest In Chapter 5, we drew a distinction between nominal and real rates of interest. The cash flows on the Treasury bonds that we have been discussing are fixed in nominal terms. Investors are sure to receive a fixed interest payment each year, but they do not know what that money will buy. The real interest rate on the Treasury bonds depends on the rate of inflation. For example, if the nominal rate of interest is 8% and the infla- tion rate is 4%, then the real interest rate is calculated as follows:

1 + real interest rate = 1 + nominal interest rate _________________ 1 + inflation rate = 1.08 ____ 1.04 = 1.0385

Real interest rate = .0385 = 3.85%

Because the inflation rate is uncertain, so is the real rate of interest on the Treasury bonds.

You can nail down a real rate of interest by buying an indexed bond, whose pay- ments are linked to inflation. Indexed bonds have been available in some countries for many years, but they were almost unknown in the United States until 1997, when the U.S. Treasury began to issue inflation-indexed bonds known as Treasury Inflation- Protected Securities, or TIPS.5 The real cash flows on TIPS are fixed, but the nominal cash flows (interest and principal) are increased as the consumer price index increases. For example, suppose the U.S. Treasury issues 3% coupon, 2-year TIPS. The real cash flows on the 2-year TIPS are therefore:

These cash payments are just sufficient to provide the holder with a 3% real rate of interest.

As we write this in late-2018, 10-year TIPS offer a yield of about 1.1%. This yield is a real interest rate. It measures the amount of extra goods your investment will allow you to buy. The 1.1% real yield on TIPS was 2.1% less than the 3.2% nominal yield on nominal 10-year Treasury bonds at the time. If the annual inflation rate proves to be higher than 2.1%, you will earn a higher real return by holding TIPS; if the inflation rate is lower than 2.1%, the reverse will be true.

Figure 6.8 shows the history of both real and nominal rates of interest in the United States since 2003. During this period, the two rates have moved pretty much together and inflation has been quite moderate, so it is primarily variations in the real rate that have caused the nominal rate to move. Notice that in 2012 and 2013, real rates were negative. This means that your savings in these bonds would buy less and less each year. 

Since 2003, the outlook for inflation has been benign, but when inflation is expected to be high, investors demand a higher nominal interest rate to compensate for the declining purchasing power of each dollar. For example, suppose that investors revise

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Inflation and nominal interest rates

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How to make a certain loss 

Year 1 Year 2

Real cash flows $30 $1,030

The nominal cash flows on TIPS depend on the inflation rate. For example, assume that inflation turns out to be 5% in year 1 and a further 4% in year 2. Then the nominal cash flows would be:

Year 1 Year 2

Nominal cash flows $30 × 1.05 = $31.50 $1,030 × 1.05 × 1.04 = $1,124.76

5 Indexed bonds were not completely unknown in the United States before 1997. For example, in 1780 American Revolution soldiers were compensated with indexed bonds that paid the value of “five bushels of corn, 68 pounds and four-sevenths part of a pound of beef, ten pounds of sheep’s wool, and sixteen pounds of sole leather.”

bre13960_ch06_166-195.indd 181 1/26/19 11:32 AM

Notice from Figure 6.8 that the yield on nominal bonds was less  than that on TIPS bonds in late 2008. What does that signify about expected inflation at the time? What was the state of the economy in late 2008?

Self-Test6.9

182 Part Two Value

upward their forecast of inflation by 1%. If investors demand the same real rate of interest on their savings, the nominal interest rate must rise by 1% to compensate for the higher inflation prospects. Therefore, in periods of high and variable inflation, we would expect to see much more variation in the nominal rate than the real rate. For example, in 1980 U.S. inflation rose to greater than 14%. The interest rate on Treasury bills rose correspondingly to top 15%; the real rate remained at a relatively modest value of about 1%.

FIGURE 6.8 The bottom line shows the real yield on 7-year indexed bonds issued by the U.S. government. The top line shows the yield on 7-year U.S. government nominal bonds.

-2

-1

0

1

2

3

4

5

6

20 0

3

20 0

5

20 0

7

20 0

9

20 11

20 13

20 15

20 17

20 19

Y ie

ld (%

)

Yield on 7-year TIPS

Yield on 7-year nominal T-bonds

Corporate Bonds and the Risk of Default

Our focus so far has been on U.S. Treasury bonds. But the federal government is not the only issuer of bonds. State and local governments borrow by selling bonds.6 So do corporations. Many foreign governments and corporations also borrow in the United States. At the same time, U.S. corporations may borrow dollars or other currencies by issuing their bonds in other countries. For example, they may issue dollar bonds in London that are then sold to investors throughout the world.

6.6

6 These municipal bonds enjoy a special tax advantage; investors are exempt from federal income tax on the coupon payments on state and local government bonds. As a result, investors are prepared to accept lower yields on this debt.

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Chapter 6 Valuing Bonds 183

Investors usually regard bonds issued by the U.S. Treasury as completely safe. They know that the government can always print the money needed to pay off the debt. But when a foreign government borrows dollars, investors do worry that in some future crisis the government may not be able to come up with enough dollars to repay the debt. This worry shows up in bond prices and yields to maturity. For example, in 2001 the Argentinian government defaulted on $95 billion of dollar-denominated loans. As the prospect of default loomed, the price of Argentinian bonds slumped and the promised yield climbed to more than 40 percentage points above the yield on U.S. Treasuries.

Unlike governments, corporations cannot print their own money, and the specter of default is always lurking in the shadows. The payments promised to the bondholders, therefore, represent a best-case scenario: The firm will never pay more than the prom- ised cash flows, but in hard times it may pay less.7

The risk that a bond issuer may default on its obligations is called default risk (or credit risk). Companies need to compensate for this default risk by promising a higher rate of interest on their bonds. The difference between the promised yield on a corpo- rate bond and the yield on a U.S. Treasury bond with the same coupon and maturity is called the default premium. The greater the chance that the company will get into trouble, the higher the default premium demanded by investors.

The safety of most corporate bonds can be judged from bond ratings provided by Moody’s, Standard & Poor’s, or other bond rating firms. Table 6.2 lists the possible bond ratings in declining order of quality. For example, the bonds that receive the highest Moody’s rating are known as Aaa (or “triple A”) bonds. Then come Aa (“double A”), A, Baa bonds, and so on. Bonds rated Baa and above are called investment grade, while those with a rating of Ba or below are referred to as speculative grade, high yield, or junk bonds.8

Table 6.2 shows how the chances of default vary by Moody’s bond rating. You can see that it is rare for highly rated bonds to default. Since 1983, only 1 in 1,000 triple-A

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Sovereign defaults

default risk The risk that a bond issuer may default on its bonds. Also called credit risk.

credit risk See default risk.

default premium The additional yield on a bond that investors require for bearing credit risk.

investment grade Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s or Fitch.

junk bond Bond with a rating below Baa or BBB.

7 Municipalities also cannot print their own money, and they too are liable to default. This was brought home to investors in 2013 when the city of Detroit, with $18.5 billion of debt outstanding, stopped making payments on some of its bonds. In 2017, Puerto Rico, with outstanding debt of over $70 billion, similarly failed to make its required payments. 8 Rating agencies also distinguish between bonds in the same class. For example, the most secure A-rated bonds would be rated A1 by Moody’s and A+ by Standard & Poor’s. The least secure bonds in this risk class would be rated A3 by Moody’s and A− by Standard & Poor’s.

TABLE 6.2 Key to Moody’s and Standard & Poor’s bond ratings. The highest-quality bonds are rated triple A, then come double-A bonds, and so on.

Moody’s Standard & Poor’s

Percent of Bonds Defaulting within 10 Years of Issue Safety

Investment-Grade Bonds Aaa AAA 0.1% The strongest rating; ability to repay interest

and principal is very strong. Aa AA 0.7 Very strong likelihood that interest and

principal will be repaid. A A 2.2 Strong ability to repay, but some vulnerability to

changes in circumstances. Baa BBB 3.5 Adequate capacity to repay; more vulnerability

to changes in economic circumstances. High-Yield Bonds Ba BB 15.7 Considerable uncertainty about ability to repay. B B 35.5 Likelihood of interest and principal payments

over sustained periods is questionable. Caa Ca

CCC CC

48.9 Bonds that may already be in default or in danger of imminent default.

C C — Little prospect for interest or principal on the debt ever to be repaid.

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184 Part Two Value

U.S. corporate bonds have defaulted within 10 years of issue. However, when an investment-grade bond is downgraded or defaults, the shock waves can be consider- able. For example, in May 2001 WorldCom sold $11.8 billion of bonds with an invest- ment-grade rating. Within little more than a year, WorldCom filed for bankruptcy, and its bondholders lost more than 80% of their investment. For low-grade issues, defaults are more common. For example, nearly 50% of the bonds that were rated CCC or below by Moody’s at issue have defaulted within 10 years.9

Table 6.3 shows prices and yields to maturity in March 2018 for a sample of corpo- rate bonds. As you would expect, corporate bonds offer higher yields than U.S. Trea- suries. You can see that the yield differential generally rises as safety falls off.

Investors also prefer liquid bonds that they can easily buy and sell. So, additionally we find that the heavily traded bonds are more highly prized and offer lower yields than their less-liquid brethren. This became important during the banking crisis of 2007–2009 when the market for many corporate bonds effectively dried up and inves- tors found it almost impossible to sell their holdings.

Figure 6.9 shows the yield spread between corporate bonds and Treasuries since 1953. During periods of uncertainty, the spread shoots up. For example, as worries about the economy intensified at the end of 2008, the promised yield on Baa bonds climbed to 6% above the yield on Treasuries. You might have been tempted by the higher promised yields on the lower-grade bonds. But remember, these bonds do not always keep their promises.

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Bond rating definitions

FIGURE 6.9 Yield spreads between corporate and 10-year Treasury bonds

-1

0

1

2

3

4

5

6

7

19 70

19 74

19 78

19 82

19 86

19 9

0

19 9

4

19 9

8

20 0

2

20 0

6

20 10

20 14

20 18

Y ie

ld s

pr ea

d (%

)

Aaa-rated

Baa-rated

9 Moody’s Investor Service, “Annual Default Study: Corporate Default and Recovery Rates, 1920–2017.”

TABLE 6.3 Prices and yields of a sample of senior corporate bonds, March 2018

Issuer Name Ticker Coupon (%) Maturity Rating Yield (%)

Microsoft MSFT 2.40 2022 AAA 2.89 Walmart WMT 6.75 2023 AA 2.92 Bristol Myers BMY 6.80 2023 A 3.43 Corning GLW 7.73 2024 BBB 4.00 Southwestern Energy SWN 4.10 2022 BB 4.80 AMD AMD 7.00 2024 B 5.28

Source: FINRA.

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Chapter 6 Valuing Bonds 185

You can find considerable information about most corporate bonds, including their rating, at the website of the Financial Industry Regulatory Authority (FINRA). See the nearby box for more information.

Promised versus Expected Yield to Maturity

Bad Bet Inc. issued bonds several years ago with a coupon rate (paid annually) of 10% and face value of $1,000. The bonds are due to mature in 6 years. However, the firm is currently in bankruptcy proceedings, the firm has ceased to pay interest, and the bonds sell for only $200. Based on promised cash flow, the yield to maturity on the bond is 63.9%. (On your calculator, set PV = −200, FV = 1000, PMT = 100, n = 6, and compute i.) But this calculation is based on the very unlikely possibility that the firm will resume paying interest and come out of bankruptcy. Suppose that the most likely outcome is that after 3 years of litigation, during which no interest will be paid, debtholders will receive 27 cents on the dollar—that is, they will receive $270 for each bond with $1,000 face value. In this case, the expected yield on the bond is 10.5%. (On your calculator, set PV = −200, FV = 270, PMT = 0, n = 3, and compute i.) When default is a real possibility, the promised yield can depart considerably from the expected return. ■

Example 6.4 ⊲

Protecting against Default Risk Corporate debt can be dependable or as risky as a dizzy tightrope walker—it depends on the value and the risk of the firm’s assets. Bondholders can never eliminate default risk, but they can take steps to minimize it. Here are some of the ways that they do so.

Seniority Some debts are subordinated. In the event of default, the subordinated lender gets in line behind the firm’s general creditors. The subordinated lender holds a junior claim and is paid only after all senior creditors are satisfied. Therefore, investors who want to limit their risk will hold senior claims. 

When you lend money to a firm, you can assume that you hold a senior claim unless the debt agreement says otherwise. However, this does not always put you at the front of the line because the firm may have set aside some of its assets specifically for the protection of other lenders. That brings us to our next classification.

Security When you borrow to buy your home, the lender will take out a mortgage on the house. The mortgage acts as security for the loan. If you default on the loan pay- ments, the lender can seize your home.

When companies borrow, they also may set aside some assets as security for the loan. These assets are termed collateral, and the debt is said to be secured. In the event of default, the secured lender has first claim on the collateral but has the same claim as other lenders on the rest of the firm’s assets.

Protective Covenants When investors lend to a company, they know that they might not get their money back. But they expect that the company will use the money well and not take unreasonable risks. To help ensure this, lenders usually impose a number of conditions, or protective covenants, on companies that borrow from them. An honest firm is willing to accept these conditions because it knows that they allow the firm to borrow at a reasonable rate of interest.

Companies that borrow in moderation are less likely to get into difficulties than those that are up to the gunwales in debt. So lenders usually restrict the amount of extra debt that the firm can issue. Lenders are also eager to prevent others from push- ing ahead of them in the queue if trouble occurs. So they may not allow the company to create new debt that is senior to theirs or to set aside assets for other lenders.

secured debt Debt that, in the event of a default, has first claim on specified assets.

protective covenants Conditions imposed on borrowers to protect lenders from unreasonable risks.

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and securities firms making markets in bonds and other secu- rities. One of its goals has been to foster transparency. To this end, its website makes it far easier for individuals to obtain up-to-date information on bonds.

Go to finra-markets.morningstar.com/BondCenter, click on the Bonds tab on the left side of the page, click on the Search tab, and enter a company ticker symbol, e.g., FDX for FedEx. When you submit your request, you will be given a list of all bonds issued by FedEx. Click on any bond, and you will find a page like the one in this box. The page contains infor- mation about the bond’s coupon, yield, issue size, and the price and date of its most recent trade.

A firm may sell many, even dozens, of issues of bonds to the public. For example, there are currently around 25 FedEx bond issues outstanding with various maturity dates and cou- pon rates. Because of the plethora of bonds, many issues do not trade on any particular day, so pricing information can be, at best, irregular. Moreover, most bonds do not trade on pub- lic exchanges. Instead, they trade through an electronic net- work linking together bond dealers. It can be quite difficult for individual investors to find current information on any particu- lar bond. 

The Financial Industry Regulatory Authority (FINRA) is a so- called self-regulatory organization that oversees brokerage

Bond detail for FedEx

Finance in Practice Finding bond information on the web

Source: http://finra-markets.morningstar.com/BondCenter, February 28, 2018.

Classification ElementsPrice/Yield Chart

Price $

Price

04/16/2003 02/22/2018-

Yield ChartPrice Chart

140.00

120.00

100.00

80.00 2015 201720132011200920072005

US Corporate Debentures

Industrial

Senior Unsecured Note

Transportation

CORP Corporate Bond

N

— —

— —

—

— —

— —

—

—

07/07/1997

07/01/1997

01/01/1998

$250,000.00

$250,000.00 Credit and Rating Elements Moody’s® Rating Standard & Poor’s Rating

Baa2 (03/15/2016) BBB (07/09/1997)

Investment GradeTRACE Grade Default Bankruptcy

Insurance Mortgage Insurer

Pre-Refunded/Escrowed

Last Trade Price Last Trade Yield Last Trade Date

5.262%$143.69 02/22/2018

O�ering Date

Medium Term Note

Special Characteristics

Issue Elements

Security Code

Use of Proceeds

State

Sub-Product Asset Type Sub-Product Asset

Industry Sub Group

Industry Group

Debt Type

Bond Type

Dated Date

First Coupon Date

Original O�ering*

Amount Outstanding* Series

Issue Description Project Name

Day Count Form

Depository/Registration

Security Level Collateral Pledge

Payment Frequency Semi-Annual

N 30/360

Book Entry

Depository Trust Company

Senior

Zoom: 5D 1M 3M YTD 1Y 3Y 5Y 10Y Max

FDX.GD Symbol CUSIP Next Call Date

313309AP1 —

US Treasury Yield

—

Callable

—

Bond Detail

Maturity Date

07/01/2097 Coupon Rate

7.600%

Last Updated: 02/28/2018

FEDERAL EXPRESS CORP

Trade History

FDX.GDLookup Symbol: GO

+ ADD TO WATCHLIST

186

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In 1987 RJR Nabisco, the food and tobacco giant, had $5 billion of A-rated debt outstanding. In that year, the company was taken over, and $19 billion of debt was issued and used to buy back equity. The debt ratio skyrocketed, and the debt was downgraded to a BB rating. The holders of the previously issued debt were furious, and one filed a lawsuit claiming that RJR had violated an implicit obligation not to undertake major financing changes at the expense of existing bondholders. Why did these bondholders believe they had been harmed by the massive issue of new debt? What type of explicit restriction would you have wanted if you had been one of the original bondholders?

Self-Test6.10

SUMMARY A bond is a long-term debt of a government or corporation. When you own a bond, you receive a fixed interest payment each year until the bond matures. This payment is known as the coupon. The coupon rate is the annual coupon payment expressed as a fraction of the bond’s face value. At maturity the bond’s face value is repaid. In the United States most bonds have a face value of $1,000. The current yield is the annual coupon payment expressed as a percentage of the bond price. The yield to maturity measures the rate of return to an investor who purchases the bond and holds it until maturity, accounting for coupon income as well as the difference between purchase price and face value.

Bonds are valued by discounting the coupon payments and the final repayment by the yield to maturity on comparable bonds. The bond payments discounted at the bond’s yield to maturity equal the bond price. You may also start with the bond price and ask what interest rate the bond offers. The interest rate that equates the present value of bond payments to the bond price is the yield to maturity. Because present values are lower when discount rates are higher, price and yield to maturity vary inversely.

Bond prices are subject to interest rate risk, rising when market interest rates fall and falling when market rates rise. Long-term bonds exhibit greater interest rate risk than short-term bonds.

The yield curve plots the relationship between bond yields and maturity. Yields on long- term bonds are usually higher than those on short-term bonds. These higher yields com- pensate holders for the fact that prices of long-term bonds are more sensitive to changes in

What are the differences between the bond’s coupon rate, current yield, and yield to maturity? (LO6-1)

How can one find the market price of a bond given its yield to maturity or find a bond’s yield given its price? Why do prices and yields vary inversely? (LO6-2)

Why do bonds exhibit interest rate risk? (LO6-3)

What is the yield curve and why do investors pay attention to it? (LO6-4)

Chapter 6 Valuing Bonds 187

Not All Corporate Bonds Are Plain Vanilla In finance, “plain vanilla” means simple, standard, and common. In this chapter, we have stuck with plain-vanilla bonds. In Chapter 14, we will introduce bonds and other ways of borrowing money that are not plain vanilla, but here are just a few examples:

∙ Zero-coupon bonds repay principal at maturity but do not have coupon payments along the way. (Zero-coupon Treasuries are called “strips” because coupons are stripped away from the bonds and sold separately.)

∙ Floating-rate bonds  have coupon payments that are not fixed but fluctuate with short-term interest rates.

∙ Convertible bonds can be exchanged for a specified number of shares of the issuing corporation’s common stock.

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188 Part Two Value

interest rates. Investors may also be prepared to accept a lower interest rate on short-term bonds when they expect interest rates to rise.

Investors demand higher promised yields if there is a high probability that the borrower will run into trouble and default. Credit risk implies that the promised yield to maturity on the bond is higher than the expected yield. The additional yield investors require for bearing credit risk is called the default premium. Bond ratings measure the bond’s credit risk.

Why do investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings? (LO6-5)

LISTING OF EQUATIONS

6.1 Bond price = PV(coupons) + PV(face value) = (coupon × annuity factor) + (face value × discount factor)

6.2 Bond rate of return = coupon income + price change ______________________ investment

QUESTIONS AND PROBLEMS 1. Financial Pages. Turn back to Table 6.1. (LO6-1)

a. What is the current yield of the 4.75% 2041 maturity bond? What is its yield to maturity? b. “The current yield is less than the yield to maturity whenever the bond price is greater than

the face value.” True or false?

2. Bond Yields. A 30-year Treasury bond is issued with face value of $1,000, paying interest of $60 per year. If market yields increase shortly after the T-bond is issued, what happens to the bond’s: (LO6-1) a. coupon rate? b. price? c. yield to maturity? d. current yield?

3. Bond Yields. If a bond with face value of $1,000 and a coupon rate of 8% is selling at a price of $970, is the bond’s yield to maturity more or less than 8%? (LO6-1)

4. Bond Yields. A bond with face value $1,000 has a current yield of 6% and a coupon rate of 8%. (LO6-1) a. If interest is paid annually, what is the bond’s price? b. Is the bond’s yield to maturity more or less than 8%?

5. Bond Pricing. A General Power bond carries a coupon rate of 8%, has 9 years until maturity, and sells at a yield to maturity of 7%. (Assume annual interest payments.) (LO6-1 and LO6-2) a. What interest payments do bondholders receive each year? b. At what price does the bond sell? c. What will happen to the bond price if the yield to maturity falls to 6%? d. If the yield to maturity falls to 6%, will the current yield be less, or more, than the yield to

maturity?

6. Bond Yields. A bond has 8 years until maturity, has a coupon rate of 8%, and sells for $1,100. (LO6-1 and LO6-2) a. What is the current yield on the bond? b. What is the yield to maturity if interest is paid once a year? c. What is the yield to maturity if interest is paid semiannually?

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Chapter 6 Valuing Bonds 189

7. Bond Prices and Returns. One bond has a coupon rate of 8%, another a coupon rate of 12%. Both bonds pay interest annually, have 10-year maturities, and sell at a yield to maturity of 10%. (LO6-2) a. If their yields to maturity next year are still 10%, what is the rate of return on each

bond? b. Does the higher-coupon bond give a higher rate of return over this period?

8. Bond Pricing. A 6-year Circular File bond with face value $1,000 pays interest once a year of $80 and sells for $950. (LO6-2) a. What is its coupon rate? b. What is its yield to maturity? c. If Circular wants to issue a new 6-year bond at face value, what coupon rate must the bond

offer?

9. Coupon Rate. General Matter’s outstanding bond issue has a coupon rate of 10%, and it sells at a yield to maturity of 9.25%. The firm wishes to issue additional bonds to the public. What coupon rate must the new bonds offer in order to sell at face value? (LO6-2)

10. Bond Pricing. A 30-year-maturity bond with face value of $1,000 makes annual coupon payments and has a coupon rate of 8%. What is the bond’s yield to maturity if the bond is selling for: (LO6-2) a. $900? b. $1,000? c. $1,100?

11. Bond Pricing. A 30-year-maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 8%. What is the bond’s yield to maturity if the bond is selling for: (LO6-2) a. $900? b. $1,000? c. $1,100?

12. Bond Pricing. The following table shows some data for three zero-coupon bonds. The face value of each bond is $1,000. (LO6-2)

Bond Price Maturity (years) Yield to Maturity

A $300 30 — B 300 — 8% C — 10 10

a. What is the yield to maturity of bond A? (Express your answer as a percentage rather than a decimal.)

b. What is the maturity of B? c. What is the price of C?

13. Pricing Consol Bonds. Perpetual Life Corp. has issued consol bonds with coupon payments of $60. (Consols pay interest forever and never mature. They are perpetuities.) (LO6-2) a. If the required rate of return on these bonds at the time they were issued was 6%, at what

price were they sold to the public? b. If the required return today is 10%, at what price do the consols sell?

14. Bond Pricing. Sure Tea Co. has issued 9% annual coupon bonds that are now selling at a yield to maturity of 10% and current yield of 9.8375%. What is the remaining maturity of these bonds? (LO6-2)

15. Bond Pricing. Maxcorp’s bonds sell for $1,065.15. The bond life is 9 years, and the yield to matu- rity is 7%. What is the coupon rate on the bonds? (Assume annual coupon payments.) (LO6-2)

16. Bond Returns. You buy an 8% coupon, 10-year-maturity bond for $980. A year later, the bond price is $1,200. (Assume annual coupon payments.) (LO6-2) a. What is the new yield to maturity on the bond? b. What is your rate of return over the year?

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190 Part Two Value

17. Bond Returns. A bond has 10 years until maturity, a coupon rate of 9%, and sells for $1,100. Interest is paid annually. (LO6-2 and LO6-3) a. If the bond has a yield to maturity of 9% 1 year from now, what will its price be at that

time? b. What will be the rate of return on the bond? c. If the inflation rate during the year is 3%, what is the real rate of return on the bond?

18. Bond Returns. You buy an 8% coupon, 20-year-maturity bond when its yield to maturity is 9%. (Assume semiannual coupon payments.) Six months later, the yield to maturity is 10%. What is your return over the 6 months? (LO6-3)

19. Interest Rate Risk. Consider three bonds with 8% coupon rates, all making annual coupon pay- ments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate- term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years. (LO6-3) a. What will be the price of the 4-year bond if its yield increases to 9%? b. What will be the price of the 8-year bond if its yield increases to 9%? c. What will be the price of the 30-year bond if its yield increases to 9%? d. What will be the price of the 4-year bond if its yield decreases to 7%? e. What will be the price of the 8-year bond if its yield decreases to 7%? f. What will be the price of the 30-year bond if its yield decreases to 7%? g. Comparing your answers to parts (a), (b), and (c), are long-term bonds more or less affected

than short-term bonds by a rise in interest rates? h. Comparing your answers to parts (d), (e), and (f), are long-term bonds more or less affected

than short-term bonds by a decline in interest rates?

20. Rate of Return. A 2-year-maturity bond with face value of $1,000 makes annual coupon pay- ments of $80 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is: (a) 6%? (b) 8%? (c) 10%? (LO6-3)

21. Rate of Return. A bond is issued with a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 8%? (LO6-3)

22. Real Returns. Suppose that you buy a 1-year-maturity bond with a coupon of 7% paid annually. If you buy the bond at its face value, what real rate of return will you earn if the inflation rate is: (a) 4%? (b) 6%? (c) 8%? (LO6-3)

23. Real Returns. Suppose that you buy a TIPS (inflation-indexed) bond with a 1-year maturity and a (real) coupon of 4% paid annually. If you buy the bond at its face value of $1,000, and the inflation rate is 8%: (LO6-3) a. What will be your cash flow at the end of the year? b. What will be your nominal rate of return? Interest rates during the year are unchanged. c. What will be your real rate of return?

24. Real Returns. Suppose that you buy a TIPS (inflation-indexed) bond with a 2-year maturity and a (real) coupon of 4% paid annually. If you buy the bond at its face value of $1,000, and the inflation rate is 8% in each year: (LO6-3) a. What will be your cash flow in year 1? b. What will be your cash flow in year 2? c. What will be your real rate of return over the two-year period?

25. Interest Rate Risk. Consider two bonds, a 3-year bond paying an annual coupon of 5% and a 10-year bond also with an annual coupon of 5%. Both currently sell at face value. Now suppose that the market interest rate rises to 10%. (LO6-3) a. What is the new price of the 3-year bond? b. What is the new price of the 10-year bond? c. Do you conclude that long-term or short-term bonds are more sensitive to a change in inter-

est rates?

26. Interest Rate Risk. Suppose interest rates increase from 8% to 9%. Which bond will suffer the greater percentage decline in price: a 30-year bond paying annual coupons of 8% or a 30-year zero-coupon bond? (LO6-3)

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Chapter 6 Valuing Bonds 191

27. Interest Rate Risk. Look again at the previous question. Can you explain intuitively why the zero exhibits greater interest rate risk even though it has the same maturity as the coupon bond? (LO6-3)

28. Interest Rate Risk. Consider two 30-year-maturity bonds. Bond A has a coupon rate of 4%, while bond B has a coupon rate of 12%. Both bonds pay their coupons semiannually. (LO6-3) a. Construct an Excel spreadsheet showing the prices of each of these bonds for yields to matu-

rity ranging from 2% to 15% at intervals of 1%. Column A should show the yield to maturity (ranging from 2% to 15%), and columns B and C should compute the prices of the two bonds (using Excel’s bond price function) at each interest rate.

b. Suppose Bond A is currently priced to offer a yield to maturity of 8%. Calculate the (per- centage) capital gain or loss on the bond if its yield immediately changes to each value in column A. Report the capital gain or loss corresponding to the new yield in column D.

c. Now repeat part (b) for Bond B. Show the capital gain or loss corresponding to each yield to maturity in column E.

d. Plot the values in columns D and E as a function of the yield to maturity. Which bond’s price exhibits greater proportional sensitivity to changes in its yield? In other words, which bond has greater interest rate risk?

e. Can you explain the result you found in part (d)? (Hint: Is there any sense in which a bond that pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate?)

29. The Yield Curve. Suppose that investors expect interest rates to fall sharply. Would you expect short-term bonds to offer higher or lower yields than long-term bonds? (LO6-4)

30. Yield Curve. The following table shows the prices of a sample of Treasury strips. Each strip makes a single payment at maturity. (LO6-4)

Years to Maturity Price (% of face value)

1 96.852% 2 93.351 3 89.544 4 85.480

a. What is the 1-year interest rate? b. What is the 2-year interest rate? c. What is the 3-year interest rate? d. What is the 4-year interest rate? e. Is the yield curve upward-sloping, downward-sloping, or flat? f. Is this the usual shape of the yield curve?

31. Yield Curve. In Figure 6.7, we saw a plot of the yield curve on stripped Treasury bonds and pointed out that bonds of different maturities may sell at different yields to maturity. In princi- ple, when we are valuing a stream of cash flows, each cash flow should be discounted by the yield appropriate to its particular maturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows: (LO6-4)

Years to Maturity Yield to Maturity

1 4.0% 2 5.0

3–5 5.5 6–10 6.0

You wish to value a 10-year bond with a coupon rate of 10%, paid annually. a. Set up an Excel spreadsheet to value each of the bond’s annual cash flows using this table of

yields. Add up the present values of the bond’s 10 cash flows to obtain the bond price. b. What is the bond’s yield to maturity? c. Compare the yield to maturity of the 10-year, 10% coupon bond with that of a 10-year zero-

coupon bond or Treasury strip. Which is higher? Why does this result make sense given this yield curve?

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192 Part Two Value

32. Credit Risk. (LO6-5) a. Many years ago, Castles in the Sand Inc. issued bonds at face value at a yield to maturity of

7%. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is now the price of the bond? (Assume semiannual coupon payments.)

b. Suppose that investors believe that Castles can make good on the promised coupon pay- ments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

33. Credit Risk. Suppose that Casino Royale has issued bonds that mature in 1 year. They currently offer a yield of 20%. However, there is a 50% chance that Casino will default and bondholders will receive nothing. What is the expected yield on the bonds? (LO6-5)

34. Credit Risk. Bond A is a 10-year U.S. Treasury bond. Bond B is a 10-year corporate bond. True or false? (LO6-3 and LO6-5) a. If you hold bond A to maturity, your return will be equal to the yield to maturity. b. If you hold bond B to maturity, your return will be equal to or less than the yield to

maturity. c. If you hold bond A for 5 years and then sell it, your return could be greater than the yield to

maturity.

35. Credit Risk. A bond’s credit rating provides a guide to its risk. Suppose that long-term bonds rated Aa currently offer yields to maturity of 7.5%. A-rated bonds sell at yields of 7.8%. Sup- pose that a 10-year bond with a coupon rate of 7.6% is downgraded by Moody’s from an Aa to A rating. (LO6-5) a. Is the bond likely to sell above or below par value before the downgrade? b. Is the bond likely to sell above or below par value after the downgrade?

36. Credit Risk. Sludge Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is a senior bond; bond B is subordinated. Sludge has suffered a severe downturn in demand, and its assets are now worth only $3 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

37. Credit Risk. Slush Corporation has two bonds outstanding, each with a face value of $2 mil- lion. Bond A is secured on the company’s head office building; bond B is unsecured. Slush has suffered a severe downturn in demand. Its head office building is worth $1 million, but its remaining assets are now worth only $2 million. If the company defaults, what payoff can the holders of bond B expect? (LO6-5)

WEB EXERCISES 1. Log on to www.investopedia.com to find a simple calculator for working out bond prices.

(Start by clicking the Investing link and then look for another link to Calculators.) Check whether a change in yield has a greater effect on the price of a long-term or a short-term bond.

2. When we plotted the yield curve in Figure 6.7, we used the prices of Treasury strips. You can find current prices of strips by logging on to The Wall Street Journal website (www.wsj.com) and clicking on Markets, Market Data, and then Rates. Try plotting the yields on stripped cou- pons against maturity. Do they currently increase or decline with maturity? Can you explain why? You can also use The Wall Street Journal site to compare the yields on nominal Treasury bonds with those on TIPS. Suppose that you are confident that inflation will be 3% per year. Which bonds are the better buy?

3. In Figure 6.9, we showed how bonds with greater credit risk have promised higher yields to maturity. This yield spread goes up when the economic outlook is particularly uncertain. You can check how much extra yield lower-grade bonds offer today by logging on to the Federal Reserve Economic Database (FRED) at the St. Louis Fed website (fred.stlouisfed.org). Search for Corporate Bonds and compare the yields on Aaa and Baa bonds. How does the current spread in yields compare with the spread in November 2008 at the height of the financial crisis?

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Chapter 6 Valuing Bonds 193

SOLUTIONS TO SELF-TEST QUESTIONS 6.1 The asked price of the 7.625s is 130.6875. So one bond would cost $1,306.875. A bond sell-

ing for $1,106.25 would be quoted at 110.625. The bid price of the 3% bond of 2048 is 97.2656. So you would receive $972.656.

6.2 a The asked price is 121.9141% of face value, or $1,219.141. b. The bid price is 121.8516% of face value, or $1,218.516. c. The annual coupon is 5.25% of face value, or $52.50, a year. d. The yield to maturity, based on the asked price, is given as 2.908%.

6.3 The coupon is 9% of $1,000, or $90 a year. First value the 6-year annuity of coupons:

PV = $90 × (6-year annuity factor)

= $90 × [ 1 ___ .12 − 1 _______ .12(1.12)6 ] = $90 × 4.1114 = $370.03

Then value the final payment and add:

PV = $1,000 _____ (1.12)6 = $506.63

PV of bond = $370.03 + $506.63 = $876.66

Using a financial calculator, your inputs would be: n = 6; i = 12; PMT = 90; FV = 1000. Now compute PV.

6.4 At an interest rate of 4%, the 3-year bond sells for $951.44. If the interest rate drops to 2%, the bond price rises to $1,007.21, an increase of 5.9%. The 30-year bond sells for $697.39 when the interest rate is 4%, but its price rises to $1,055.99 at an interest rate of 2%, a much larger percentage increase of 51.4%.

6.5 The yield to maturity assuming annual coupons is about 8% because the present value of the bond’s cash returns is $1,199, almost exactly $1,200, when discounted at 8%:

PV = PV(coupons) + PV(final payment) = (coupon × annuity factor) + (face value × discount factor)

= $140 × [ 1 ___ .08 − 1 _______ .08(1.08)4 ] + $1,000 × 1 ____ 1.084 = $463.70 + $735.03 = $1,199

To obtain a more precise solution on your calculator, these would be your inputs:

Annual Payments Semiannual Payments

n 4 8 PV −1200 −1200 FV 1000 1000 PMT 140 70

Compute i to find yield to maturity (annual payments) = 7.97%. Yield to maturity (semi- annual payments) = 4.026% per 6 months, which would be reported in the financial press as 8.052% annual yield.

6.6 With a yield of 4%, the 8% coupon, 10-year bond sells for $1,324.44. At the end of the year, the bond has only 9 years to maturity and investors demand an interest rate of 6%. Therefore, the value of the bond becomes $1,136.03. (On your calculator, input n = 9; i = 6; PMT = 8; FV = 1000; compute PV.) Thus, you have received a coupon payment of $80 but have a capital loss of 1,324.44 − 1,136.03 = $188.41. Your total return is therefore (80 − 188.41)/1,324.44 = −.082, or −8.2%. Because interest rates rose over the year, your return was less than the yield to maturity.

6.7 By the end of the year, the bond will have only 1 year left until maturity. So its price will be $1,080/1.06 = $1,018.87. You will therefore receive a coupon payment of $80 and make a capital loss of $1,036.67 − $1,018.87 = $17.80. Your total return over the year is

bre13960_ch06_166-195.indd 193 1/26/19 11:32 AM

194 Part Two Value

(80 − 17.80)/1,036.67 = .060, or 6.0%. When the bond matures, you receive the face value of $1,000. So, in the final year, you receive a coupon payment of $80 and make a capital loss of $18.87. Your total return over this year is (80 − 18.87)/1,018.87 = .060, or 6.0%. When the yield to maturity does not change, your return is equal to the yield to maturity.

6.8 If you invest in a 2-year bond, you will have $1,000 × 1.062 = $1,123.60. If you are right in your forecast about 1-year rates, then an investment in 1-year bonds will produce $1,000 × 1.05 × 1.08 = $1,134.00 by the end of 2 years. You would do better to invest in the 1-year bond.

6.9 The difference between the nominal yield and the real yield is a rough guide to inflation expectations. That difference turned negative in late 2008, signifying that prices were gener- ally expected to decrease, or, equivalently, that inflation would be negative. This was the beginning of the so-called Great Recession resulting from the financial crisis. In deep reces- sions like that one, inflationary pressures can disappear, and prices are more prone to actually decline.

6.10 The extra debt makes it more likely that the firm will not be able to make good on its promised payments to its creditors. If the new debt is not junior to the already-issued debt, then the original bondholders suffer a loss when their bonds become more susceptible to default risk. A protective covenant limiting the amount of new debt that the firm can issue would have prevented this problem. Investors, having witnessed the problems of the RJR bondholders, generally demanded the covenant on later debt issues.

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196

Valuing Stocks

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

7-1 Understand the stock trading reports on the Internet or in the financial pages of the newspaper.

7-2 Calculate the present value of a stock given forecasts of future dividends and show how growth opportunities are reflected in stock prices and price-earnings ratios.

7-3 Apply valuation models to an entire business.

7-4 Understand what professionals mean when they say that there are no free lunches on Wall Street.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

7

bre13960_ch07_196-237.indd 196 1/29/19 5:40 PM

197

P A

R T

T W

O V

al ue

A corporation can raise cash for investment either by borrowing or by selling new shares of com-mon stock to investors. If it borrows, it has a fixed obligation to repay the lender. If it issues shares, there is no fixed obligation, but the new stockholders become part-owners of the firm. All old and new stock- holders share in its fortunes, in proportion to the number of shares that they hold. In this chapter, we take a first look at common stocks, the stock market, and the prin- ciples of stock valuation.

We start by looking at how stocks are bought and sold. Then we look at what determines stock prices and how stock valuation formulas can be used to value indi- vidual stocks as well as entire businesses. We will see how the firm’s investment opportunities are reflected in its stock price and why stock market analysts focus so much attention on the price-earnings, or P/E, ratio of the company.

Why should you care how stocks are valued? After all, if you want to know the value of a firm’s stock, you

can look up the stock price on the Internet or in The Wall Street Journal. But you need to know what deter- mines prices for at least two reasons. First, you may need to value the common stock of a business that is not traded on a stock exchange. For example, you may be the founder of a successful business that plans to sell stock to the public for the first time. You and your advisers need to estimate the price at which those shares can be sold.

Second, in order to make good capital budgeting decisions, corporations need to have some understand- ing of how the market values firms. A project is attractive if it increases shareholders’ wealth. But you can’t judge that unless you know how their shares are valued.

There may be a third reason that you would like to know how stocks are valued. You may be hoping that the knowledge will allow you to make a killing on Wall Street. It’s a pleasant thought, but we will see that even professional investors find it difficult to outsmart the competition and to earn consistently superior returns.

Charts of stock prices. Looking at past fluctuations in stock prices can be mesmerizing, but what determines those prices? ©woraput chawalitphon/Getty Images

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198 Part Two Value

Stocks and the Stock Market

In Chapter 1, we saw how FedEx was founded and how it then grew and prospered. To fund this growth, FedEx needed capital. Initially, that capital came largely from bor- rowing, but in 1978 FedEx sold shares of common stock to the public for the first time. Those investors who bought shares in the initial public offering, or IPO, became part-owners of the business, and as shareholders they shared in the company’s future successes and setbacks.1

A company’s initial public offering is rarely its last, and since 1978 FedEx has raised more capital by selling additional shares. These sales of shares by the company are called primary offerings and are said to be made in the primary market.

Owning shares is a risky occupation. For example, if at the start of 2017 you had the misfortune to buy shares in General Electric, you would have lost almost half of your money by the year-end. You can understand, therefore, why investors would be reluctant to buy shares if they were forced to tie the knot with a particular company forever. So large companies usually arrange for their common stock to be listed on a stock exchange so that investors can trade shares among themselves. Exchanges are really markets for secondhand stocks, but they prefer to describe themselves as secondary markets, which sounds more important.

The two principal stock markets in the United States are the New York Stock Exchange (NYSE) and NASDAQ.2 In addition, there are many computer networks called electronic communication networks (ECNs) that connect traders with each other. All of these markets compete vigorously for the business of traders and just as vigorously tout the advantages of their own trading venue. The volume of trades in these markets is immense. For example, every day the NYSE alone trades around 1.5 billion shares with market value exceeding $60 billion.

Of course, there are stock exchanges in many other countries. Some are tiny, such as the stock exchange in the Maldives, which trades shares in just eight companies. Oth- ers, such as the London, Tokyo, Frankfurt, and pan-European Euronext exchanges, trade the shares of thousands of firms.

Suppose that Ms. Jones, a longtime FedEx shareholder, no longer wishes to hold her shares in the company. She can sell them via a stock exchange to Mr. Brown, who wishes to increase his stake in the firm. The transaction merely transfers (par- tial) ownership of the firm from one investor to another. No new shares are created, and FedEx usually will neither care nor even be aware that such a trade has taken place.3

Ms. Jones and Mr. Brown do not buy or sell FedEx shares themselves. Instead, each must hire a brokerage firm with trading privileges on an exchange to arrange the transaction for them. Not so long ago, such trades would have involved hands-on negotiation. The broker would have had to agree on an acceptable price with a dealer in the stock or would have brought the trade to the floor of an exchange where a specialist in FedEx would have coordinated the transaction. But today, the vast major- ity of trades are executed automatically and electronically, even on the more traditional exchanges.

When Ms. Jones and Mr. Brown decide to buy or sell FedEx stock, they need to give their brokers instructions about the price at which they are prepared to transact. Ms. Jones, who is anxious to sell quickly, might give her broker a market order to sell

7.1

secondary market Market in which previously issued securities are traded among investors.

1 We use the terms “shares,” “stock,” and “common stock” interchangeably, as we do “shareholders” and “stockholders.” 2 This originally was an acronym for National Association of Security Dealers Automated Quotation system, but now is simply known as the NASDAQ market. 3 Eventually, FedEx must know to whom it should send dividend checks, but this information is needed only when such payments are being prepared. In some cases, FedEx might care about a stock transaction, for exam- ple, if a large investor is building a big stake in the firm. But this is the exception.

BEYOND THE PAGE

mhhe.com/brealey10e

The world’s stock exchanges

common stock Ownership shares in a publicly held corporation.

initial public offering (IPO) First offering of stock to the general public.

primary offering The corporation sells shares in the firm.

primary market Market for the sale of new securities by corporations.

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Chapter 7 Valuing Stocks 199

stock at the best available price. On the other hand, Mr. Brown might give his broker a price limit at which he is willing to buy FedEx stock. If his order cannot be executed immediately, it is recorded in the exchange’s limit order book until it can be executed.

Figure 7.1 shows a portion of the limit order book for FedEx from the BATS Exchange, one of the largest electronic markets. The bid prices on the left are the prices (and numbers of shares) at which investors are currently willing to buy. The Ask column presents offers to sell. The prices are arranged from best to worst, so the high- est bids and lowest asks are at the top of the list. The broker might electronically enter Ms. Jones’s market order to sell 100 shares on the BATS Exchange, where it would be automatically matched or crossed with the best offer to buy, which at that moment was $239.81 a share. Similarly, a market order to buy would be crossed with the best ask price, $240.06. The bid-ask spread at that moment was therefore 25 cents per share.

Reading Stock Market Listings If you are thinking about buying shares in FedEx, you will wish to see its current price. Until recently, you probably would have looked for that information in The Wall Street Journal or the financial pages of your local newspaper. But those pages contain less and less information about individual stocks, and most investors today turn to the Internet for their information. For example, go to finance.yahoo.com; enter FedEx’s ticker symbol, FDX, under Quote Lookup; and you will find recent trading data such as those presented in Figure 7.2.4

The most recent price at which the stock traded on March 22, 2018, was $239.98 per share, which was $9.04 lower than the previous day’s closing price. The range of prices at which the stock traded that day, as well as over the previous 52 weeks, is provided in the set of columns on the right. Yahoo! also tells us that the average daily trading volume over the last 3 months was 1,866,076 shares. Trading volume on this day was heavy, however, and by 1:02 p.m., 2,359,358 shares already had traded. FedEx’s market cap (shorthand for market capitalization) is the total value of its out- standing shares of stock, $64.32 billion. You will frequently hear traders referring to large-cap or small-cap firms, which is a convenient way to summarize the size of the company.

FedEx earned $10.86 per share in the past year. (The abbreviation “TTM” in the parentheses stands for trailing 12 months.) Therefore, the ratio of price per share to earnings per share, known as the price-earnings multiple or, equivalently, P/E ratio, is 239.98/10.86 = 22.1. The P/E ratio is a key tool of stock market analysts, and we will have much to say about it later in the chapter.

P/E ratio Ratio of stock price to earnings per share.

FIGURE 7.1 A portion of the limit order book for FedEx on the BATS Exchange, March 22, 2018

Price

239.81

239.80

239.70

239.33

230.03

100

400

100

100

100

Size Price

240.06

240.16

241.02

241.14

241.23

100

100

100

100

500

Size

Bid Ask

Top of Order Book, 1:04 PM EST

FedEx Corporation (FDX) - NYSE

Source: BATS, accessed from markets.cboe.com/us/equities/overview.

4 Other good sources of trading data are moneycentral.msn.com/investor/home.asp or the online edition of The Wall Street Journal at www.wsj.com (look for the Market and then Market Data tabs).

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200 Part Two Value

The dividend yield tells you how much dividend income you would receive for every $100 invested in the stock. FedEx paid annual dividends of $2.00 per share, so its yield was (based on yesterday’s closing price of $249.02) was $2.00/$249.02 = .0080, or .80%. For every $100 invested in the stock, you would have received $.80 in dividends. Of course, this would not be the total rate of return on your investment, as you would also hope for some increase in the stock price. The dividend yield is thus much like the current yield of a bond. Both measures ignore prospective capital gains or losses.

The price at which you can buy shares in FedEx changes day to day and minute to minute as investors change their estimates of the company’s prospects. Figure 7.3 shows the share price of FedEx over several months in 2018. The price fell by 10% in just one week at the start of February. Why would the price that investors were willing to pay for each share change so suddenly? And, for that matter, why were they willing that month to pay $240 a share for FedEx but only $90 a share for Microsoft? To answer these questions, we need to look at what determines value.

FIGURE 7.2 Trading information for FedEx

Prev Close:

Summary Chart Conversations Statistics Profile Final

Add to watchlist

Open:

Bid:

Ask:

Day’s Range:

52wk Range:

Volume:

Avg. Volume:

249.02

246.00

239.98 × 100

240.10 × 100

236.00–246.00

182.89–274.66

2,359,358

1,866,076

239.98 -9.04 (-3.63%) As of 1:02PM EDT. Market open.

FedEx Corporation (FDX) NYSE - Nasdaq Real Time Price. Currency in USD

Market Cap:

Beta:

PE Ratio (TTM):

EPS (TTM):

Earnings Date:

Forward Dividend & Yield:

Ex-Dividend Date:

64.318B

1.57

22.11

10.86

Mar 19, 2018–Mar 23, 2018

2.00 (0.80%)

N/A

284.691y Target Est:

Source: Yahoo! Finance, March 22, 2018.

FIGURE 7.3 Share price history for FedEx

230

235

240

245

250

255

260

265

270

275

280

20 -J

an

25 -J

an

30 -J

an

4- Fe

b

9 -F

eb

14 -F

eb

19 -F

eb

24 -F

eb

1- M

ar

6 -M

ar

11 -M

ar

16 -M

ar

21 -M

ar

S ha

re p

ri ce

($ )

Source: Yahoo! Finance, downloaded March 22, 2018.

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Chapter 7 Valuing Stocks 201

Market Values, Book Values, and Liquidation Values

Finding the value of FedEx stock may sound like a simple problem. Each quarter, the company publishes a balance sheet, which lists the value of the firm’s assets and liabil- ities. The simplified balance sheet in Table 7.1 shows that in May 2017, the book value of all FedEx’s assets—plant and machinery, inventories of materials, cash in the bank, and so on—was $48,552 million. FedEx’s debt and other liabilities—money that it owes the banks, taxes that are due to be paid, and the like—amounted to $32,479 mil- lion. The difference between the value of the assets and the liabilities was $16,073 million. This was the book value of the firm’s equity.5 Book value records all the money that FedEx has raised from its shareholders plus all the earnings that have been plowed back on their behalf.

Book value is a reassuringly definite number. But does the stock price equal book value? FedEx shares in March 2018 were selling at around $240, but as Table 7.2 shows, its book value per share was only $63.68. So the shares were worth about 3.8 times book value. This and the other cases shown in Table 7.2 tell us that investors in the stock market do not just buy and sell at book value per share.

Accountants don’t even try to estimate market values. The value of the assets reported on the firm’s balance sheet is equal to their original (or “historical”) cost less an allowance for depreciation. But that may not be a good guide to what the firm could sell its assets for today.

Well, maybe stock price equals liquidation value per share, that is, the amount of cash per share a company could raise if it sold off all its assets in secondhand markets and paid off all its debts. Wrong again. A successful company ought to be worth more than liquidation value. After all, that’s the goal of bringing all those assets together in the first place.

7.2

book value Value shown in the firm’s balance sheet.

liquidation value Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.

Assets Liabilities and shareholders’ equity

Current assets 12,628 Current liabilities 7,918 Plant, equipment, and other long-term assets

35,924 Debt and other long-term liabilities

24,561

Shareholders’ equity 16,073 Total assets  48,552 Total liabilities and equity 48,552

Note: Shares of stock outstanding = 252.4 million. Book value of equity (per share) : $16,073/252.4 = $63.68.

TABLE 7.1 Simplified balance sheet for FedEx, May 30, 2017 (figures in $ millions)

Ticker Stock Price Book Value per Share

Market-to-Book- Value Ratio

FedEx FDX 240.00 63.68 3.8

Johnson & Johnson JNJ 138.83 22.41 6.2 Campbell Soup CPB 47.76 6.47 7.4 PepsiCo PEP 119.93 7.78 15.4 Walmart WMT 98.75 25.67 3.8 Microsoft MSFT 85.14 10.17 8.4 Amazon AMZN 1,169.47 57.24 20.4 DowDuPont DWDP 67.43 43.22 1.6 American Electric Power AEP 72.86 37.29 2.0 US Steel X 40.24 18.91 2.1

TABLE 7.2 Market values versus book values, March 2018

Source: Yahoo! Finance, finance.yahoo.com.

5 “Equity” is still another word for stock. Thus, stockholders are often referred to as equity investors.

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202 Part Two Value

The difference between a company’s actual value and its book or liquidation value is often attributed to going-concern value, which refers to three factors:

1. Extra earning power. A company may have the ability to earn more than an adequate rate of return on assets. In this case the value of those assets will be higher than their book value or secondhand value.

2. Intangible assets. There are many assets that accountants don’t put on the balance sheet. Some of these assets are extremely valuable. Take Johnson & Johnson, a health care product and pharmaceutical company. As you can see from Table 7.2, it sells at 6.2 times book value per share. Where did all that extra value come from? Largely from the cash flow generated by the drugs it has developed, patented, and marketed. These drugs are the fruits of a research and development (R&D) program that has grown to more than $10 billion per year. But U.S. accountants don’t recognize R&D as an investment and don’t put it on the company’s balance sheet. Nevertheless, expertise, experience, and knowledge are crucial assets, and their values do show up in stock prices.

3. Value of future investments. If investors believe a company will have the opportunity to make very profitable investments in the future, they will pay more for the company’s stock today. When eBay, the Internet auction house, first sold its stock to investors in 1998, the book value of shareholders’ equity was about $100 million. Yet 1 day after the issue investors valued the equity at more than $6 billion. In part, this difference reflected an intangible asset, eBay’s unique platform for trading a wide range of goods over the Internet. But investors also judged that eBay was a growth company. In other words, they were betting that the company’s know-how and brand name would allow it to expand internationally and make it easier for customers to trade and pay online. By 2018, eBay had operating income of more than $2 billion and a market capitalization of $42 billion.

Market price is not the same as book value or liquidation value. Market value, unlike book value and liquidation value, treats the firm as a going concern.

It is not surprising that stocks virtually never sell at book or liquidation values. Investors buy shares on the basis of present and future earning power. Two key fea- tures determine the profits the firm will be able to produce: first, the earnings that can be generated by the firm’s tangible and intangible assets, and second, the oppor- tunities the firm has to invest in lucrative projects that will increase future earnings.

Amazon and Consolidated Edison

Amazon is a growth company. As recently as 2014, its profit was actually negative, −$241 mil- lion. Yet investors in March 2018 were prepared to pay about $760 billion for Amazon’s com- mon stock. The value of the stock came from the company’s market position, its highly regarded distribution system, and the promise of new related products that will generate increased future earnings. Amazon was a growth firm because its market value depended so heavily on intangible assets and the anticipated profitability of new investments.

Contrast this with Consolidated Edison (Con Ed), the electric utility servicing the New York City area. Con Ed is not a growth company. Its market is limited, and it is expanding capacity at a very deliberate pace. More important, it is a regulated utility, so its returns on present and future investments are constrained. Con Ed’s value derives mostly from the stream of income generated by its existing assets. Therefore, while Amazon shares sold for 27 times book value in 2018, Con Ed shares sold at only about 1.5 times book value. ■

Example 7.1 ⊲

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Chapter 7 Valuing Stocks 203

Investors refer to Amazon as a growth stock and Con Ed as an income stock. A few stocks, like Alphabet (the parent company of Google), offer both income and growth. Alphabet earns plenty from its current products, such as the Google search engine. These earnings are part of what makes the stock attractive to investors. In addition, investors are willing to pay for the company’s ability to invest profitably in new ven- tures that will increase future earnings.

Let’s summarize. Just remember:

∙ Book value records what a company has paid for its assets, less a deduction for depreciation. It does not capture the true value of a business.

∙ Liquidation value is what the company could net by selling its assets and repaying its debts. It does not capture the value of a successful going concern.

∙ Market value is the amount that investors are willing to pay for the shares of the firm. This depends on the earning power of today’s assets and the expected profitability of future investments.

The next question is, What determines market value?

In the 1970s, the computer industry was growing rapidly. In the 1980s, many new competitors entered the market, and computer prices fell. Since then, com- puter makers have struggled with thinning profit margins and intense competi- tion. How has the industry’s market-value balance sheet changed over time? Have assets in place become proportionately more or less important? Do you think this progression is unique to the computer industry?

Self-Test7.1

Valuing Common Stocks

Valuation by Comparables When financial analysts need to value a business, they often start by identifying a sample of similar firms. They then examine how much investors in these companies are prepared to pay for each dollar of assets or earnings. This is often called valuation by comparables. Look, for example, at Table 7.3. The first column of numbers shows, for some well-known companies, the ratio of the market value of the equity to the book value. Notice that in each case market value is higher than book value.

The second column of numbers shows the market-to-book ratio for competing firms. For example, you can see from the second row of the table that the stock of the typical large retailing firm against which Walmart competes sells for 4.0 times its book value. If you did not have a market price for the stock of Walmart, you might estimate that it would also sell at 4.0 times book value. In this case, your estimate of Walmart’s market price would have been a bit high.

An alternative would be to look at how much investors in other retail stocks are prepared to pay for each dollar of earnings. The final column of Table 7.3 shows that the typical price-earnings (P/E) ratio for retail stocks in 2018 was 19.6. If you assumed that Walmart should sell at a similar multiple of earnings, you would have gotten a value for the stock of $102, somewhat higher than its actual price of $88.18 in March 2018.

7.3

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204 Part Two Value

Market-to-book and price-earnings ratios are the most popular rules of thumb for valuing common stocks, but financial analysts sometimes look at other multiples. For example, infant firms often do not have any earnings. So, rather than calculate a price- earnings ratio, analysts may look at the price-to-sales ratio for these firms. In the late 1990s, when dot-com companies were growing rapidly and losing lots of money, mul- tiples were often based on the number of subscribers or website visits.

There is nothing wrong with such rules of thumb if intelligently applied. For example, you can see that valuation by comparables would have worked fairly well for American Electric Power and Walmart in 2018. However, that is not the case for all the companies shown in Table 7.3. For example, if you had naively assumed that Amazon stock would sell at similar ratios to comparable Internet retail stocks, you would have been out by a wide margin. Both the market-to-book ratio and the price-earnings ratio can vary considerably from stock to stock even for firms that are in the same line of business. To understand why this is so, we need to dig deeper and look at what deter- mines a stock’s market value.

Price and Intrinsic Value In the previous chapter, we saw that the value of a bond is the present value of its cou- pon payments plus the present value of its final payment of face value. You can think of stocks in a similar way. Instead of receiving coupon payments, investors may receive dividends, and instead of receiving the bond’s face value, they will receive the stock price at the time they sell their shares.

Consider, for example, an investor who buys a share of Blue Skies Inc. today and plans to sell it in 1 year. Call the predicted stock price in 1 year P1, the expected divi- dend per share DIV1, and the discount rate for the stock’s expected cash flows r.6 Remember, the discount rate reflects the risk of the stock. Riskier firms will have higher discount rates. Then the present value of the cash flows the investor will receive from Blue Skies is

V0 = DIV1 + P1 _________ 1 + r (7.1)

We call V0 the intrinsic value of the share. Intrinsic value is just the present value of the cash payoffs anticipated by the investor in the stock.

To illustrate, suppose investors expect a cash dividend next year of $3 (DIV1 = $3) and expect the stock to sell for $81 a year hence (P1 = $81). If the discount rate is 12%, then intrinsic value is $75:

V0 = 3 + 81 _____ 1.12 = $75

intrinsic value Present value of future cash payoffs from a stock or other security.

Market-to-Book Value Ratio Price-Earnings Ratio

Company Industry Company* Industry

FedEx 3.8 7.3 14.4 22.6 Johnson & Johnson 6.2 4.9 14.9 23.9 Campbell Soup 7.4 2.9 13.4 27.0 PepsiCo 15.4 10.0 17.6 27.3 Walmart 3.8 4.0 16.9 19.6 Microsoft 8.4 6.6 23.7 60.8 Amazon 20.4 9.4 97.2 46.6 DowDuPont 1.6 3.5 13.7 13.5 American Electric Power 2.0 1.9 15.9 21.0 US Steel 2.1 2.3 8.2 27.8

* Price divided by forecasted earnings in the coming year.

TABLE 7.3 Market-to-book- value ratios and price-earnings ratios for selected companies and their principal competitors, March 2018

6 For simplicity we assume that the dividend is paid at the end of the year.

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Chapter 7 Valuing Stocks 205

You can think of intrinsic value as the “fair” price for the stock. If investors buy the stock for $75, their expected rate of return will precisely equal the discount rate—in other words, they can expect their investment return to just compensate them for the opportunity cost of their money.

To confirm this, note that the expected rate of return over the next year is the expected dividend plus the expected increase in price, P1 − P0, all divided by price at the start of the year, P0. If the investor buys the shares for intrinsic value, then P0 = $75 and

Expected return = DIV1 + P1 − P0 _____________ P0

 =  3 + 81 − 75 __________ 75  = .12, or 12%

Notice that this expected return comes in two parts, the dividend yield and the capital gain:

Expected rate of return = expected dividend yield + expected capital gain

=  DIV1 _____ P0

 +  P1 − P0 _______ P0

=  3 ___ 75  +  81 − 75 _______ 75

= .04 + .08 = .12, or 12%

Of course, the actual return for Blue Skies may turn out to be more or less than investors expect. For example, in 2018, information technology stocks were one of the best performing sectors with an average return of more than 35%. This was almost certainly better than investors expected at the start of the year. At the other extreme, the share prices of energy service firms actually declined a bit. No investor at the start of the year would have purchased these shares anticipating a loss. Never confuse the actual outcome with the expected outcome.

The dream of every investor is to buy shares at a bargain price—that is, a price less than intrinsic value. But in competitive markets, no price other than intrinsic value could survive for long. To see why, imagine that Blue Skies’ current price was above $75. Then the expected rate of return on Blue Skies stock would be lower than that on other securities of equivalent risk. (Check this!) Investors would bail out of Blue Skies stock and move into other securities. In the process, they would force down the price of Blue Skies stock. If P0 were less than $75, Blue Skies stock would offer a higher expected rate of return than equivalent-risk securities. (Check this, too.) Everyone would rush to buy, forcing the price up to $75. When the stock is priced correctly (that is, price equals present value), the expected rate of return on Blue Skies stock is also the rate of return that investors require to hold the stock. In a well-functioning mar- ket, all equally risky securities are priced to offer the same expected rate of return. This is a fundamental characteristic of prices in competitive markets. It is also common sense.

Equation 7.1 is just a definition of intrinsic value, which works for any discount rate r. Now we can go beyond that definition and identify r as the expected rate of return on all securities with a particular level of risk. If a stock is priced correctly, it will offer an expected rate of return equal to that of other equally risky stocks and price will equal intrinsic value:

P0 = DIV1 + P1 _________ 1 + r

Thus, today’s price will equal the present value of dividend payments plus the present value of future price. But now we need to take a further step: How do we estimate the future price P1?

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206 Part Two Value

Of course, many corporations do not currently pay cash dividends. Investors in a young, growing company may have to wait a decade or more before the firm matures and starts paying out cash to shareholders. Our formula for P0 still applies to such firms if we set the immediate dividend DIV1 equal to zero. In this case value depends on the subsequent dividends. But let’s begin with a mature firm that is paying divi- dends now. We will say more about growth firms later.

The Dividend Discount Model Our equation for stock price depends on DIV1 + P1, that is, next period’s dividend and next period’s price. Suppose you have forecast the dividend. How do you forecast the price P1? We can answer this question by moving our stock price equation forward one period and applying it in period 1. The equation then says that P1 depends on the sec- ond period’s dividend DIV2 and the second-period price P2. The second-period price P2 in turn depends on the third period’s dividend DIV3 and the third-period price P3, which depends on DIV4 … you can see where this logic is going.

As it turns out, we can express a stock’s intrinsic value (and, therefore, price) as the present value of all the forecasted future dividends paid by the company to its sharehold- ers without referring to the future stock price. This is the dividend discount model:

P0 = present value of (DIV1, DIV2, DIV3, . . . , DIVt , . . .)

=  DIV1 _____ 1 + r  +  DIV2 _______

(1 + r)2  +  DIV3 _______

(1 + r)3  + . . . +  DIVt _______ (1 + r)t  + 

. . .

How far out in the future could we look? In principle, 40, 60, or 100 years or more—corporations are potentially immortal. However, far-distant dividends will not have significant present values. For example, the present value of $1 received in 30 years using a 10% discount rate is only $.057. Most of the value of established compa- nies comes from dividends to be paid within a person’s working lifetime.

How do we get from the one-period formula P0 = (DIV1 + P1)/(1 + r) to the divi- dend discount model? We look at increasingly long investment horizons.

Let’s consider investors with different investment horizons. Each investor will value the share of stock as the present value of the dividends that she or he expects to receive plus the present value of the price at which the stock is eventually sold. Unlike bonds, however, the final horizon date for stocks is not specified—stocks do not “mature.” More- over, both dividends and final sales price can only be estimated. But the general valuation approach is the same. For a one-period investor, the valuation formula looks like this:

P0 = DIV1 + P1 _________ 1 + r

A 2-year investor would value the stock as

P0 = DIV1 _____ 1 + r

+ DIV2 + P2 _________ (1 + r)2

and a 3-year investor would use the formula

P0 = DIV1 _____ 1 + r

+ DIV2 _______ (1 + r)2

+ DIV3 + P3 _________ (1 + r)3

dividend discount model Discounted cash-flow model that states that today’s stock price equals the present value of all expected future dividends.

Androscoggin Copper is increasing next year’s dividend to $5 per share. The forecast stock price next year is $105. Equally risky stocks of other companies offer expected rates of return of 10%. What should Androscoggin common stock sell for?

Self-Test7.2

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Chapter 7 Valuing Stocks 207

In fact, we can look as far out into the future as we like. Suppose we call our hori- zon date H. Then the stock valuation formula would be

P0 = DIV1 _____ 1 + r

+ DIV2 _______ (1 + r)2

+ . . . + DIVH + PH __________ (1 + r)H

(7.2)

In words, the value of a stock is the present value of the dividends it will pay over the investor’s horizon plus the present value of the expected stock price at the end of that horizon.

Does this mean that investors with different horizons will come to different conclu- sions about the value of the stock? No! Regardless of the investment horizon, the stock value will be the same. This is because the stock price at the horizon date is deter- mined by expectations of dividends from that date forward. Therefore, as long as investors agree about a firm’s prospects, they will also agree on its present value. Let’s confirm this with an example.

Valuing Blue Skies Stock

Take Blue Skies. The firm is growing steadily, and investors expect both the stock price and the dividend to increase at 8% per year. Now consider three investors, Erste, Zweiter, and Dritter. Erste plans to hold Blue Skies for 1 year, Zweiter for 2, and Dritter for 3. Compare their payoffs:

Year 1 Year 2 Year 3

Erste DIV1 = 3 P1 = 81

Zweiter DIV1 = 3 DIV2 = 3.24 P2 = 87.48

Dritter DIV1 = 3 DIV2 = 3.24 DIV3 = 3.50 P3 = 94.48

Remember, we assumed that dividends and stock prices for Blue Skies are expected to grow at a steady 8%. Thus, DIV2 = $3 × 1.08 = $3.24, DIV3 = $3.24 × 1.08 = $3.50, and so on.

Each investor requires the same 12% expected return. So we can calculate present value over Erste’s 1-year horizon:

PV = DIV1 + P1 ________ 1 + r =

$3 + $81 ________ 1.12 = $75

or Zweiter’s 2-year horizon:

PV = DIV1 ____ 1 + r +

DIV2 + P2 ________ (1 + r)2

= $3 ____ 1.12

+ $3.24 + $87.48 _____________ (1.12)2

= $2.68 + $72.32 = $75

or Dritter’s 3-year horizon:

PV = DIV1 ____ 1 + r +

DIV2 ______ (1 + r)2 +

DIV3 + P3 ________ (1 + r)3

= $3 ____ 1.12

+ $3.24 ______ (1.12)2

+ $3.50 + $94.48 _____________ (1.12)3

= $2.68 + $2.58 + $69.74 = $75

Example 7.2 ⊲

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208 Part Two Value

Look at Table 7.4, which continues the Blue Skies example for various time hori- zons, still assuming that the dividends are expected to increase at a steady 8% com- pound rate. The expected price increases at the same 8% rate. Each row in the table represents a present value calculation for a different horizon year. Note that total pres- ent value does not depend on the investment horizon. Figure 7.4 presents the same data in a graph. Each column shows the present value of the dividends up to the hori- zon and the present value of the price at the horizon. As the horizon recedes, the divi- dend stream accounts for an increasing proportion of present value, but the total present value of dividends plus terminal price always equals $75.

All agree the stock is worth $75 per share. This illustrates our basic principle: The value of a common stock equals the present value of dividends received out to the investment hori- zon plus the present value of the forecast stock price at the horizon. Moreover, when you move the horizon date, the stock’s present value should not change. The principle holds for horizons of 1, 3, 10, 20, and 50 years or more. ■

Refer to Self-Test 7.2. Assume that Androscoggin Copper’s dividend and share price are expected to grow at a constant 5% per year. Calculate the current value of Androscoggin stock with the dividend discount model using a 3-year horizon. You should get the same answer as in Self-Test 7.2.

Self-Test7.3

Horizon (years) PV (dividends) + PV (terminal price) = Value per Share 1 $ 2.68 $72.32 $75

2 5.26 69.74 75 3 7.75 67.25 75

10 22.87 52.13 75 20 38.76 36.24 75 30 49.81 25.19 75 50 62.83 12.17 75

100 73.02 1.98 75

TABLE 7.4 Value of Blue Skies

FIGURE 7.4 Value of Blue Skies for different horizons

V al

ue p

er s

ha re

($ )

1 2 3 10 20 30 50 100

Investment horizon (years)

70

80

50

60

40

30

20

10

0

PV (terminal price)

PV (dividends)

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Chapter 7 Valuing Stocks 209

If the horizon is infinitely far away, then we can forget about the final horizon price—it has almost no present value—and simply say,

Stock price = PV(all future dividends per share)

This is the dividend discount model.

Simplifying the Dividend Discount Model

The dividend discount model requires a forecast of dividends for every year into the future, which poses a bit of a problem for stocks with potentially infinite lives. If the model is to be of practical use, we need some simplifying assumptions. We will look at three cases, beginning with the most basic and ending with the most general.

Case 1: The Dividend Discount Model with No Growth Consider a company that pays out all its earnings to its common shareholders. Such a company does not grow because it does not reinvest.7 Stockholders might enjoy a generous immediate dividend, but they could not look forward to higher future divi- dends. The company’s stock would offer a perpetual stream of equal cash payments, DIV1 = DIV2 = ⋅ ⋅ ⋅ = DIVt = ⋅ ⋅ ⋅.

The dividend discount model says that these no-growth shares should sell for the present value of a constant, perpetual stream of dividends. We learned how to do that calculation when we valued perpetuities in Chapter 5. Just divide the annual cash pay- ment by the discount rate. The discount rate is the rate of return demanded by investors in other stocks with the same risk:

Value of a no-growth stock = P0 = DIV1 _____ r

Because our company pays out all its earnings as dividends, dividends and earnings are the same, and we could just as well calculate stock value by

Value of a no-growth stock = P0 = EPS1 _____ r

where EPS1 represents next year’s earnings per share of stock. Thus some people loosely say, “Stock price is the present value of future earnings,” and calculate value by this formula. Be careful—this is a special case.

7.4

BEYOND THE PAGE

mhhe.com/brealey10e

Value and the investor’s horizon

7 We assume it does not raise money by issuing new shares.

Moonshine Industries has produced a barrel per week for the past 20 years but cannot grow because of certain legal hazards. It earns $25 per share per year and pays it all out to stockholders. The stockholders have alternative, equiva- lent-risk ventures yielding 20% per year on average. How much is one share of Moonshine worth? Assume the company can keep going indefinitely.

Self-Test7.4

Case 2: The Dividend Discount Model with Constant Growth Here’s another simplification that finds a good deal of practical use. Suppose forecast dividends grow at a constant rate into the indefinite future. Then instead of forecasting an infinite number of dividends, we need to forecast only the next dividend and the dividend growth rate.

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210 Part Two Value

Suppose that a stock is expected to pay a dividend of DIV1 next year, and thereafter, the dividend is expected to grow each year by the rate g. Thus the expected dividend in year 2 is DIV1 × (1 + g), the dividend in year 3 is DIV1 × (1 + g)2, and so on. The present value of this stock is, therefore:

P0 = DIV1 _____ 1 + r +

DIV1(1 + g) ___________ (1 + r)2

+ DIV1(1 + g) 2 ___________

(1 + r)3 + DIV1(1 + g)

3 ___________

(1 + r)4 + ⋅ ⋅ ⋅

Although there are an infinite number of terms, each of them is proportionately smaller than the preceding one as long as the dividend growth rate g is less than the discount rate r. Because the present value of distant dividends will be ever closer to zero, the sum of all of these terms is finite despite the fact that an infinite number of dividends will be paid. The sum can be shown to equal

P0 = DIV1 _____ r − g (7.3)

This equation is called the constant-growth dividend discount model, or the Gordon growth model after Myron Gordon, who did much to popularize it.8

The formula for the present value of a no-growth perpetuity (our first case) is sim- ply a special case of this constant-growth formula. Suppose you forecast no growth in dividends (g = 0). Then the dividend stream is a simple perpetuity, and the valuation formula reduces to P0 = DIV1/r. This is precisely the formula you used in Self-Test 7.4 to value Moonshine, a no-growth common stock.

Our task in this section is to show how the constant-growth model can be used to estimate P0, the value of a common stock. But sometimes managers find it useful to rearrange the constant-growth formula as:

r = DIV1 _____ P0

+ g (7.4)

= dividend yield + growth rate Thus, if you know a stock’s dividend yield and the expected growth rate, you

can deduce its expected return. We will come back to this version of the formula in Chapter 13, when we look at how managers estimate the cost of equity capital.

constant-growth dividend discount model Version of the dividend discount model in which expected dividends grow at a constant rate.

8 Notice that the first dividend is assumed to come at the end of the first period and is discounted for a full period. If the stock has just paid a dividend DIV0, then next year’s dividend will be (1 + g) times the dividend just paid. So another way to write the valuation formula is

P0 = DIV1 _____ r − g  = 

DIV0 × (1 + g) _____________ r − g

Using the Constant-Growth Model to Value the Stock of Aqua America

Aqua America (ticker symbol WTR) is a water utility serving parts of 14 states from Maine to Texas. In early 2018, its stock was selling for $38.65 a share. Because there were 178 million shares outstanding, investors were placing a total value on the stock of 178 million × $38.65 = $6.9 billion. Can we explain this valuation?

In 2018 Aqua America could point to a remarkably consistent growth record. For each of the past two decades, it had steadily increased its dividend payment (see Figure 7.5), and, with one minor hiccup, earnings had also grown steadily. The constant-growth model, there- fore, seems tailor-made for valuing Aqua America’s stock.

In 2018 investors were forecasting that, in the coming year, Aqua America would pay a dividend of $.86 (DIV1 = $.86). The forecast growth in dividend (g) was about 4.75% a year over the foreseeable future (we explain in a moment where this figure comes from). If inves- tors required a return of 7.0% from Aqua America’s stock, then the constant-growth model predicts a current share value (P0) of $38.22, almost identical to the market price:

P0 = DIV1 ____ r − g =

$.86 ___________ .070 − .0475 = $38.22 ■

Example 7.3 ⊲

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Chapter 7 Valuing Stocks 211

Estimating the Growth Rate for Aqua America The constant-growth model generalizes the perpetuity formula to allow for constant growth in dividends. But how do we estimate that growth rate? Mature companies grow mainly by reinvesting earn- ings. How rapidly they grow depends on both the proportion of earnings reinvested into the business and the profits generated by those new investments. The firm’s sustainable growth rate is the rate at which the firm can grow by reinvesting earnings, keeping its long-term debt ratio constant.

Aqua America has a book value per share of $11.10 at the start of 2018. Suppose that it will generate a return on this book value of 12.5%.9 Then in 2018 earnings per share will be

EPS = book value per share × ROE = $11.10 × .125 = $1.3875

Over the next several years, the firm is expected to maintain a payout ratio (the proportion of earnings to be paid out as dividends) of 62%, so next year’s dividend will be .62 × 1.3875 = .86. The plowback ratio (the fraction of earnings reinvested in the firm) is 1 − .62 = .38. Therefore, in the first year, Aqua America will plow back .38 × $1.3875 = $.527 a share into new plant and equipment. Book value per share will increase by $.527 to $11.10 + $.527 = $11.627. The growth rate of equity generated by reinvesting earnings is

Growth rate in book equity = plowed-back earnings __________________ initial equity = $.527 ______ $11.10 = .0475, or 4.75%

To see how growth depends on plowback and ROE, we can rewrite this equation as follows:

Growth rate = plowed-back earnings __________________ initial equity = plowed-back earnings __________________ total earnings ×

total earnings ____________ initial equity

= plowback ratio × ROE

= .38 × .125 = .0475, or 4.75%

This is the growth rate of the book value of equity. What about dividends and earn- ings? If ROE is constant, then earnings per share will grow in direct proportion to equity (remember that EPS = ROE × book equity), so earnings also will grow at 4.75%.

payout ratio Fraction of earnings paid out as dividends.

plowback ratio Fraction of earnings retained by the firm.

FIGURE 7.5 Aqua America’s dividends have grown steadily

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1999 2001 2003 2005 2007 2009 2011 2013 2015 2017

D iv

id en

ds p

er s

ha re

($ )

sustainable growth rate The firm’s growth rate if it plows back a constant fraction of earnings, maintains a constant return on equity, and keeps its debt ratio constant.

9 We construct estimates of trend earnings and dividends using data from the Value Line Investment Survey, January 12, 2018.

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212 Part Two Value

And if the payout ratio is constant, dividends will be a fixed proportion of earnings, so they too will grow at that rate. Therefore, if ROE and plowback are stable, book equity, earnings, and dividends will all increase at the sustainable growth rate. The sustainable growth rate, therefore, is the natural choice for g in the constant-growth dividend dis- count model. This is the value we used for Aqua America in Example 7.3.

If a company earns a constant return on equity and plows back a constant pro- portion of earnings, then its growth rate, g, is

g = sustainable growth rate = ROE × plowback ratio (7.5)

The sustainable growth rate assumes that the firm’s long-term debt ratio is constant so that debt and total capital also increase at the sustainable growth rate. Aqua Amer- ica could grow its assets at a faster rate by borrowing more and more, but such a strat- egy, entailing ever-higher debt ratios, would not be sustainable.

A Caveat The sustainable growth rate that we found for Aqua America is moderate, and it is plausible that the firm can continue to grow at a trend rate of nearly 5% for the indefinite future. But sometimes you will find that the formula for sustainable growth, ROE × plowback, results in crazy values—for example, growth rates of 20% or even more. No company could expect to maintain growth rates like these forever. After all, the (real) growth rate of the economy as a whole is only around 2.5%. If a firm or industry grew indefinitely at 20%, it eventually would outgrow the entire economy and then move on to take over the galaxy!

Other things equal, the constant-growth formula implies that the stock price will be higher when the dividend growth rate, g, is higher. But the formula is valid only if the growth rate is sustainable and is less than the discount rate. If you forecast perpetual dividend growth at a rate higher than investors’ required return, r, then two things happen:

1. The formula explodes and gives nutty values. (For example, what would be the “value” of Aqua America in Example 7.3 if you assumed a growth rate of 10%?)

2. You know your forecasts must be wrong because the present value of far-distant dividends would be incredibly high. If projected dividends grow at a higher rate than the discount rate, the present value of each successive dividend will grow without limit. (Again, try a numerical example using Aqua America. Calculate the present value of a dividend paid after 100 years, assuming DIV1 = $.86, r = .07, and g = .10.)

Clearly, the constant-growth model cannot handle cases where there is temporary rapid growth. We will show you how to deal with this situation shortly.

Aqua America Gets a Windfall

Suppose that a shift in water usage allows Aqua America to generate 5% per year expected future growth without sacrificing immediate dividends. Will that increase r, the expected rate of return?

This is good news for the firm’s stockholders. The stock price will jump to

P0 = DIV1 ____ r − g =

$.86 ________ .07 − .05 = $43.00

Aqua America’s good news is reflected in a higher stock price today. But the good news does not imply a higher expected rate of return in the future. At this price, Aqua’s expected rate of return is unchanged at 7%, consistent with its unchanged risk. ■

Example 7.4 ⊲

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Chapter 7 Valuing Stocks 213

The Sources of Aqua America’s Value We often hear investors speak of growth stocks and income stocks. They buy growth stocks primarily in the expectation of capi- tal gains, and they are interested in the future growth of earnings rather than in next year’s dividends. On the other hand, they buy income stocks principally for the cash dividends. Let us see whether these distinctions make sense, and what we can learn about the sources of Aqua America’s value.

Aqua America is expected to pay a dividend in 2018 of $.86 (DIV1 = .86), and this dividend is expected to grow at a steady rate of 4.75% a year (g = .0475). If investors require a return of 7.0% (r = .070), then the price of Aqua America should be

P0 = DIV1 _____ r − g =

$.86 ___________ .070 − .0475 = $38.22

What if Aqua America did not plow back any of its earnings into new plant and equipment? In that case, it would pay out all of its earnings, $1.3875 a share, but would forgo any further growth in earnings and dividends:

g = sustainable growth rate = return on equity × plowback ratio = .125 × 0 = 0

We could recalculate the value of Aqua America assuming it paid out all its forecast earnings and forwent any growth:

P0 = DIV1 _____ r − g =

EPS1 _____ r = $1.3875 _______ .070 = $19.82

Thus, if Aqua America did not reinvest any of its earnings, its stock price would not be $38.22, but instead it would be only $19.82. The $19.82 represents the value of earnings from assets that are already in place. The rest of the stock price ($38.22 − $19.82 = $18.40) is the net present value of the future investments that Aqua America is expected to make.

What if the company kept to its policy of reinvesting 38% of its profits, but the fore- cast return on new investments was only 7.0%, just equal to the required rate of return? In that case, the sustainable growth rate would also be lower:

g = sustainable growth rate = return on equity × plowback ratio = .07 × .38 = .0266, or 2.66%

If we plug this new figure into our valuation formula, we come up again with a value of $19.82 for Aqua America stock, no different from the value if it had chosen not to grow at all:

P0 = DIV1 _____ r − g =

.86 ___________ .070 − .0266 = $19.82

Plowing earnings back into new investments may result in growth in earnings and dividends, but it does not add to the current stock price if that money is expected to earn only the return that investors require. Plowing earnings back

Androscoggin Copper can grow at 5% per year for the indefinite future. It’s sell- ing at $100, and next year’s dividend is $5. What is the expected rate of return from investing in Carrabasset Mining common stock? Carrabasset and Andro- scoggin shares are equally risky.

Self-Test7.5

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Estimating stock value with non- constant growth

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214 Part Two Value

does add value if investors believe that the reinvested earnings will earn a higher rate of return.

To repeat, if Aqua America did not reinvest any of its earnings, the value of its stock would simply derive from the stream of earnings from the existing assets. The price of its stock would be $19.82. If the company did reinvest each year but earned only the return that investors require, then those new investments would not add any value, and, therefore, the price of the stock would still be $19.82. In this case, both dividends and earnings are expected to grow, but this growth makes no contribution to firm value. Be careful not to equate firm performance with the growth in earnings per share.

Fortunately, investors believe that Aqua America has the opportunity to earn 12.5% on its new investments, somewhat above the 7.0% return that investors require. This is reflected in the $38.22 that investors are prepared to pay for the stock. The total value of Aqua America stock is equal to the value of its assets in place plus the present value of its growth opportunities, or PVGO:

Value of assets in place $19.82 + Present value of growth opportunities (PVGO) 18.40

= Total value of Aqua America’s stock $38.22

A true “growth stock” is one where the net present value of its future investments accounts for a significant fraction of the stock’s price.

The investment prospects of Aqua America are reflected in its price-earnings ratio. With a stock price of $38.22 and forecast earnings of $1.3875, the P/E ratio is $38.22/$1.3875 = 27.5. If the company had no growth opportunities, its stock price would be only $19.82 and its P/E would be $19.82/$1.3875 = 14.3. The P/E ratio is, therefore, an indicator of Aqua America’s prospects and the profitability of its growth opportunities.

Does this mean that the financial manager should celebrate if the firm’s stock sells at a high P/E? The answer is usually yes. The high P/E suggests that investors think that the firm has good growth opportunities. However, firms can have high P/E ratios not because the price is high but because earnings are temporarily depressed. A firm that earns nothing in a particular period will have an infinite P/E.

present value of growth opportunities (PVGO) Net present value of a firm’s future investments.

Suppose that instead of plowing money back into lucrative ventures, Aqua America’s management is investing at an expected return on equity of 5%, which is below the return of 7% that investors could expect to get from comparable securities.

a. Find the sustainable growth rate of dividends and earnings in these circum- stances. Continue to assume a 38% plowback ratio.

b. Find the new value of its investment opportunities. Explain why this value is negative despite the positive growth rate of earnings and dividends.

c. If you were a corporate raider, would Aqua America be a good candidate for an attempted takeover?

Self-Test7.6

Case 3: The Dividend Discount Model with Nonconstant Growth Water companies and other utilities tend to have steady rates of growth and are, there- fore, natural candidates for application of the constant-growth model. But many com- panies grow at rapid or irregular rates for several years before settling down.

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Chapter 7 Valuing Stocks 215

Obviously, in such cases, we can’t use the constant-growth model to estimate value. However, there is an alternative approach. It involves three steps:

Step 1: Set the investment horizon (year H) as the future year after which you expect the company’s growth to settle down to a stable rate. Then calculate the present value of dividends from now to this horizon year.

Step 2: Forecast the stock price at the horizon, and discount it also to give its pres- ent value today. That price can be estimated using the constant-growth for- mula to value the dividends that will be paid after the horizon date because by then they will be growing at a sustainable rate.

Step 3: Finally, sum the total present value of dividends plus the present value of the ending stock price.

The formula is

P0 =  DIV1 _____ 1 + r  + 

DIV2 _______ (1 + r)2

 + . . . +  DIVH _______ (1 + r)H

  +   PH _______ (1 + r)H

PV of dividends from year 1 to horizon PV of stock price at horizon

Estimating the Value of Walmart Stock

In early 2018, the price of Walmart stock was just a shade below $100 (see Table 7.2). The company was expected to earn about $5.14 a share in the coming year and was projected to pay out about 43% of earnings as dividends. Let’s see how we might use the dividend dis- count model to estimate Walmart’s intrinsic value.

Investors in 2018 were optimistic about the prospects for Walmart and were forecasting that earnings would grow over the next 5 years by just under 6.5% a year.10 This growth rate is almost certainly higher than the return, r, that investors required from Walmart stock, and it is implausible to suppose that this growth could continue indefinitely. Therefore, we cannot use the simple constant-growth formula to value the shares. Instead, we will break the prob- lem down into our three steps:

Step 1: Our first task is to value Walmart’s dividends over the next 5 years. If dividends keep pace with the growth in earnings, then forecast earnings and dividends are as follows:

Year 1 2 3 4 5 Earnings 5.14 5.48 5.83 6.21 6.61 Dividends (43% of earnings) 2.21 2.36 2.51 2.67 2.85

In 2018, investors required a return of about 5.6% from Walmart stock.11 There- fore, the present value of the forecast dividends for years 1 to 5 was:

PV of dividends years 1–5 = $2.21 _____ 1.056 + $2.36

_______ (1.056)2

+ $2.51 _______ (1.056)3

+ $2.67 _______ (1.056)4

+ $2.85 _______ (1.056)5

= $10.66

Step 2: The trickier task is to estimate the price of Walmart stock in the horizon year 5. The most likely scenario is that after year 5 growth will gradually settle down to

Example 7.5 ⊲

10 Consensus analysts’ forecasts are collected by Zack’s, First Call, and IBES. They are available on the web at moneycentral.com and finance.yahoo.com. 11 For now, you can take this value purely as an assumption. In Chapter 12 we will show you how to estimate required returns. The estimate of 5.6% for Walmart is taken from Table 12.2.

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216 Part Two Value

a sustainable rate, but to keep life simple, we will assume that in year 6 the growth rate falls immediately to 3% a year. Thus, the forecast dividend in year 6 is

DIV6 = 1.03 × DIV5 = 1.03 × $2.85 = $2.94

and the expected price at the end of year 5 is

P5 = DIV6 ____ r − g =

$2.94 _________ .056 − .03 = $113.08

Step 3: Remember, the value of Walmart today is equal to the present value of forecast dividends up to the horizon date plus the present value of the price at the hori- zon. Thus,

P0 = PV(dividends years 1−5) + PV(price in year 5)

= $10.66 + $113.08 _______ 1.0565

= $96.77 ■

A Reality Check Our estimate of Walmart value looks reasonable and almost matches the actual market price. But does it make you nervous to note that your esti- mate of the terminal price accounts for such a large proportion of the stock’s value? It should. Only very minor changes in your assumptions about growth beyond year 5 could change your estimate of this terminal price by 10%, 20%, or 30%. In other words, it’s easy for a discounted-cash-flow business valuation to be mechanically perfect and practically wrong.

In the case of Walmart, we know what the market price really was, but suppose that you are using the dividend discount model to value a company going public for the first time or that you are wondering whether to buy Blue Skies’ concatenator division. In such cases you do not have the luxury of looking up the market price in The Wall Street Journal. A valuation error of 30% could amount to serious money. Wise manag- ers, therefore, check that their estimate of value is in the right ballpark by looking at what the market is prepared to pay for similar businesses. For example, suppose you can find mature, public companies whose scale, risk, and growth prospects today roughly match those projected for Walmart at the investment horizon. You look back at Table 7.3 and discover that the stocks in Walmart’s industry group typically sell at 19.6 times recent earnings. Then you can reasonably guess that Walmart’s value in year 5 will be about 19.6 times the earnings forecast for that year, that is, 19.6 × 6.61 = $129.56, somewhat higher than the $113.08 horizon value that we obtained in Step 2 of the dividend discount model.

In total, over the next 5 years Walmart is forecast to earn $29.27 a share (see the assumptions for earnings and dividends in Step 1 of the Example). If it continues to plow back 57% of these earnings, then book value per share will increase from $25.67 to $25.67 + .57 × $29.27 = $42.35 by the end of year 5. If Walmart’s market–book ratio is still 3.8 in year 5, then

Forecasted horizon value = 3.8 × $42.35 = $160.93,

which is considerably higher than our other estimates. It’s easy to poke holes in our last two calculations. Book value, for example, is often

a poor measure of the true value of a company’s assets. It can fall far behind actual asset values when there is rapid inflation, and it often entirely misses important intan- gible assets. Earnings may also be biased by inflation and a long list of arbitrary accounting choices. Finally, you never know when you have found a sample of truly

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217

similar companies to use as comparables. But remember, the purpose of discounted cash flow is to estimate market value—to estimate what investors would pay for a stock or business. When you can observe what they actually pay for similar compa- nies, that’s valuable evidence. Try to figure out a way to use it. One way to use it is through valuation by comparables, based on price-earnings or market–book ratios. Valuation rules of thumb, artfully employed, sometimes beat a complex discounted- cash-flow calculation hands down.

Valuing stocks is always harder in practice than in principle. Forecasting cash flows and settling on an appropriate discount rate require skill and judgment. The difficulties are often greatest in the case of young companies such as Facebook or Twitter, whose value comes largely from growth opportunities rather than assets that are already in place. These companies usually pay no cash dividends, and their current growth rates cannot be sustained for the longer run. Here, the dividend discount model still works logically—we could project dividends as zero out to some distant date when the firm matures and payout commences. But forecasting far-off dividends is easier said than done. In these cases, it’s more helpful to think about the value of a stock as the sum of the value of assets in place plus PVGO, the present value of growth opportunities. As the nearby box shows, in these cases there is plenty of room for disagreement about value.

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Valuing Google

Facebook at around half of Google’s value at the time, even though Google’s profits that year were 10 times Facebook’s. But optimists argued that Facebook could generate much higher growth than Google in its advertising revenue, which would justify higher earnings multiples. Clearly, valuation by comparables was tricky given the difficulties in projecting and comparing growth opportunities.

In the end, investors were overly optimistic. Facebook’s closing stock price on the day of its IPO was $38 per share, implying total market capitalization of just over $100 billion. But the stock price almost immediately fell, bottoming out at $18 by September 2012; the price did not again reach $38 for about another year.

Does this mean that Facebook’s IPO was a failure? While some firms seem to covet an “IPO pop”—that is, a stock price run-up on the day of the IPO—it is hard to see why a pop is in their interest. A pop signifies that investors would have been willing to pay more for the shares or, in other words, that the IPO was underpriced and the issuing firm “left money on the table.” In contrast, Facebook seems to have received all it could from its IPO.

What is Facebook worth? This was the question that con- fronted investors as the company’s highly anticipated initial public offering approached in May 2012. Estimates of value in the months before the IPO ranged from as little as $50 billion to as much as $125 billion. The difference in these estimates turned on questions of growth.

Facebook’s revenue grew by 88% in 2011, and net income grew by 65%. Such growth was impressive but was sharply lower than in the previous few years. From 2009 to 2010, for example, revenue had increased by around 150%. What was a reasonable projection of growth in the years following the IPO?

It is notoriously difficult to guess what future opportunities may be available to a high-tech company. Rather than attempting to make detailed growth forecasts, many inves- tors used valuation by comparables, comparing Facebook to rival companies with similar business models.

Facebook’s reported profits in 2011 were around $1 billion. Even at the low range for the IPO of $50 billion, this would imply a P/E ratio of 50, well above even successful Internet firms such as Google. At the higher end of the valuation estimates—say, $100 billion—investors would be valuing

Finance in Practice Facebook’s IPO

Suppose that on further analysis you decide that after year 5 Walmart’s earnings and dividends will grow by a constant 2.5% a year. How does this affect your estimate of the value of Walmart stock at year 0?

Self-Test7.7

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218 Part Two Value

Valuing a Business by Discounted Cash Flow

Investors buy or sell shares of common stock. Companies often buy or sell entire busi- nesses. For example, in 2012, McGraw-Hill, the publisher of this textbook, sold its education division to the private equity firm Apollo Global Management for $2.5 bil- lion. The business was not a public company, and, therefore, there was no stock price to look at. It’s a safe bet that before the sale, Apollo was doing its best to value that business by discounted cash flow. You can be equally sure that it was endeavoring to identify the most appropriate comparables for the business and checking what it would be worth if it traded at similar P/E and P/B ratios to these other firms.

One more example should help you to understand how DCF models work in such cases. It doesn’t matter whether you forecast dividends per share or the total free cash flow of a business. Value today always equals future cash flow discounted at the opportunity cost of capital.

Valuing the Concatenator Business Blue Skies is interested in selling its concatena tor manufacturing operation. Its prob- lem is to figure out what the business is worth.

Table 7.5 gives a forecast of free cash flow (FCF) for the concatenator business. Free cash flow is the amount of cash that a firm can pay out to investors after paying for all investments necessary for growth. As we will see, free cash flow can be zero or negative for rapidly growing businesses. Growth for the concatenator business starts out at a rapid 12% per year, then falls in two steps to a moderate 6% rate for the long run. The growth rate determines the net additional investment required, and the return on equity determines the earnings thrown off by the business.

Free cash flow, the fourth line in Table 7.5, is equal to the firm’s earnings less the new investment expenditures. Free cash flow is zero in years 1 to 3, even though the parent com pany is earning more than $3 million during this period.

Are the early zeros for free cash flow a bad sign? No: Free cash flow is zero because the business is growing rapidly, not because it is unprofitable. Rapid growth is good news, not bad, because the business is earning a return of 12%, 2 percentage points over the 10% cost of capital.

7.5

free cash flow (FCF) Cash flow available for distribution to investors after firm pays for new investments or additions to working capital.

Year

l 2 3 4 5 6 7 8 9 10

Asset value 10.00 11.20 12.54 14.05 15.31 16.69 18.19 19.29 20.44 21.67

Earnings 1.20 1.34 1.51 1.69 1.84 2.00 2.18 2.31 2.45 2.60 Net investment 1.20 1.34 1.51 1.26 1.38 1.50 1.09 1.16 1.23 1.30 Free cash flow (FCF) 0.00 0.00 0.00 0.42 0.46 0.50 1.09 1.16 1.23 1.30 Return on equity (ROE) 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 Asset growth rate 0.12 0.12 0.12 0.09 0.09 0.09 0.06 0.06 0.06 0.06 Earnings growth rate 0.12 0.12 0.12 0.09 0.09 0.09 0.06 0.06 0.06

TABLE 7.5 Forecasts of free cash flow in $ millions for the concatenator division, with input assumptions given in the footnotes to the table. Free cash flow is zero for periods 1 to 3 because investment absorbs all of net income. Free cash flow turns positive when growth slows down after period 3.

Notes: 1. Starting asset value is $10 million. Assets grow at 12% to start, then at 9%, and finally at 6% in perpetuity. Profitability (ROE) is assumed constant at 12%. 2. Free cash flow equals earnings minus net investment. Net investment equals total capital outlays minus depreciation. We assume that investment for replace- ment of existing assets is covered by depreciation and that net investment is devoted to growth. Earnings are also net of depreciation.

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Chapter 7 Valuing Stocks 219

The value of a business is usually computed as the discounted value of free cash flows out to a valuation horizon (H), plus the forecasted value of the business at the horizon, also dis counted back to present value. That is,

PV =  FCF1 _____ 1 + r  +  FCF2 _______

(1 + r)2  + . . . +  FCFH _______

(1 + r)H   +   PVH _______

(1 + r)H

PV(free cash flow) PV(horizon value)

Of course, the concatenator business will continue after the horizon, but it’s not practical to forecast free cash flow year-by-year to infinity. PVH stands in for the total present value of the project’s free cash flows in periods H + 1, H + 2, and so on.

Valuation horizons are often chosen arbitrarily. Sometimes the boss tells everybody to use 10 years because that’s a round number. We will try year 6 because growth of the concatena tor business seems to settle down to a long-run trend after year 7.

There are several common formulas or rules of thumb for estimating horizon value. We will just use the constant-growth DCF formula. This requires free cash flow for year 7, which we have from Table 7.5; a long-run growth rate, which is projected at 6%; and a discount rate, which some high-priced consultant has told us is 10%. 

Horizon value (i.e., PV as of period 6) = PVH = 1.09 ________ .10 − .06 = $27.3 million

PV of Horizon value (discounted back to today, time 0) = 27.3 _____ (1.10)6

= $15.4 million

Given the forecasts in Table 7.5, the PV of the near-term free cash flows is $.9 mil- lion. Thus, the present value of the concatenator division is

PV(business) = PV(free cash flow) + PV(horizon value)

= .9 + 15.4 = $16.3 million

Repurchases and the Dividend Discount Model We assumed that the concatenator business was a division of Blue Skies, not a free- standing corporation. But suppose it was a separate corporation with 1 million shares outstanding. How would we calculate price per share? Simple: Calculate the PV of the busi ness and divide by 1 million. If we decide that the business is worth $16.3 million, the price per share is $16.30.

If the concatenator business were a public Concatenator Corp. with no other assets and operations, it could pay out its free cash flow as dividends. Dividends per share would be the free cash flow shown in Table 7.5 divided by 1 million shares: $0 in peri- ods 1 to 3, then $.42 per share in period 4, $.46 per share in period 5, and so forth.

Dividends are not the only way that firms can return cash to their equity investors. They also can, and commonly do, engage in stock repurchases. In a repurchase, the firm buys back a small fraction of the outstanding shares of its shareholders. In some years, repurchases may exceed dividend payouts. Repurchases are attractive to firms that wish to distribute cash to equityholders but do not want to signal to them, even informally, that they should expect to receive such distributions on a regular basis in the future. In contrast, investors (rightly) interpret dividends as a repeated cash distri- bution that the firm will, in most circumstances, try to maintain or even increase. We discuss repurchases in some detail in Chapter 17.

When we use the dividend discount model, we should recognize that repurchases act much like dividends. For example, if the firm buys back 1% of all the shares of each of its shareholders, that action is very similar to paying a dividend equal to 1% of the share price.

Repurchases do not invalidate the dividend discount model. The value of any share is still the present value of the dividends that the holder will receive. But

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Valuing the concatenator business

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Try It! Table 7.5: Valuing the concatenator division

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220 Part Two Value

repurchases do complicate the implementation of the model because, as the number of shares changes, it can be hard to forecast dividends on a “per share” basis. This can lead to difficult bookkeeping and complications working out the correct value for sustainable growth. Here is our suggestion: When repurchases are important, it is usually simpler to value the firm’s total free cash flow, as we did for the concatena- tor division, rather than just per share dividends. By free cash flow, we mean the cash the firm has available to distribute after paying for all investments necessary for its growth. 

In a sense, imagine that you own all the shares in the firm. Free cash flow is what you could receive as the single shareholder in the firm; importantly, it will not depend on the breakdown between dividends and repurchases. After all, as the sole share- holder, you won’t care whether you get free cash flow by receiving dividends or by selling some of your shares back to the firm. If you value the whole firm by applying the dividend discount model to free cash flow, then you can find the share price by dividing the value of the firm by the current number of shares outstanding.

There Are No Free Lunches on Wall Street

Corporations rely on both comparables and the dividend discount model to value entire businesses. Investors in the stock market regularly use comparables in their quest for undervalued stocks. For example, an investor might judge that Kappa Phar- maceuticals is undervalued because it is selling at a lower P/E than Omicron and Upsi- lon despite the potential profits from its new carboglutin drug. Major investment management companies also use dividend discount models to estimate the value of common stocks and to compare those estimates with stock market prices. In each case, the investor is betting that once others have realized that a stock is undervalued, its price will shoot up and earn her juicy profits.

We will look shortly at how challenging it is for investors to find undervalued stocks. But before we do so, we should explain why a corporate financial manager, who is more concerned with issuing or purchasing securities, should care whether investors can “beat the market.” The reason is that, if even professional investors can- not consistently find undervalued stocks, then financial managers should generally assume that market prices provide a good estimate of intrinsic value. A similar mes- sage applies to the financial manager when setting the firm’s exchange rate policy or deciding on an issue of debt. If it is impossible to identify when a currency or a bond is wrongly valued, then the financial manager should trust market prices rather than engage in risky attempts to “beat the market.”

Let’s start with a quick look at the performance of amateur investors. Brad Barber and Terrance Odean examined the common stock investments of more than 66,000 households during the period 1991 to 1996.12 After controlling for differences in risk, they found that the average household underperformed the market by about 1.8% a year before trading costs and by 3.7% after costs.

It may not be surprising that the amateurs don’t beat the market, but what about the pros? Presumably, if the amateurs lose before trading costs, the professional investors must gain. Figure 7.6 provides some evidence on the matter. It shows the average per- formance of equity mutual funds over 3 decades. You can see that in some years, these mutual funds did beat the market, but more often than not (in fact, in 28 of the 47 years since 1970), it was the other way around. On average, these funds underperformed the market by about 1% a year. It looks as if any gains that the professionals made at the expense of the amateurs were more than eaten up by expenses.

Of course, it would be surprising if some managers were not smarter than others and able to earn superior returns. Unfortunately, it seems difficult to spot the smart ones. For

7.6

12 B.M. Barber and T. Odean, “Trading Is Hazardous to Your Wealth: The Stock Market Investment Perfor- mance of Individual Investors,” Journal of Finance 55 (2000), pp. 773–806.

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Chapter 7 Valuing Stocks 221

example, a top-quartile fund in one year has no more than an average chance of being in the top quartile the following year. It seems that the top-performing managers in one period have about an average chance of falling on their faces in the next period.

As this kind of discouraging evidence has accumulated, many investors have given up the search for superior investment returns. Instead, they simply buy and hold index funds or exchange-traded portfolios (ETFs) that track the entire stock market. We dis- cussed index funds and ETFs in Chapter 2. Recall that they provide maximum diversi- fication, with very low management fees. Why pay higher fees to managers who attempt to “beat the market” but can’t do so consistently? Corporate pension funds now invest over one-quarter of their U.S. equity holdings in index funds.

Random Walks and Efficient Markets Why is it so difficult to earn superior returns? Suppose that you manage a portfolio of common stocks. You try to gauge the business prospects of each firm by studying the financial and trade press, the company’s financial accounts, the president’s annual statements, and other items of news. You attend company presentations and speak to financial analysts who specialize in a particular industry. Your aim is to uncover undervalued stocks that will offer a superior expected return. But what happens if there are many other talented and industrious analysts trying to find undervalued stocks? If you uncover a stock that appears to be a bargain, it stands to reason that oth- ers will also do so, and there will be a wave of buying that pushes up its price. This buying pressure will eliminate the original bargain opportunity.

Suppose some new information becomes available—perhaps Kappa announces that it has obtained FDA approval for its new drug. You rush to buy. The chances are that you will be too late. New information is typically incorporated into stock prices in seconds or minutes. For example, every day the cable television news provider CNBC features a Morning and Midday Call that summarizes the opinions of secu- rity analysts and provides information about individual stocks. A study of 322 stocks that were discussed on these calls in 2000 found that positive reports resulted in a significant price impact beginning seconds after the stock is first mentioned and lasting approximately 1 minute. Investors could have earned a small profit after expenses only if they were able to buy within about 15 seconds of the report.13

FIGURE 7.6 Annual returns on the Wilshire 5000 Market Index and equity mutual funds, 1971–2017. The market index provided a higher return than the average mutual fund in 28 of the 47 years.

R at

e of

r et

ur n

(% )

-40

-30

-20

-10

0

10

20

30

40

19 71

19 73

19 75

19 77

19 79

19 81

19 83

19 85

19 87

19 89

19 9

1

19 9

3

19 9

5

19 9

7

19 9

9

20 0

1

20 0

3

20 0

5

20 0

7

20 0

9

20 11

20 13

20 15

20 17

Active funds Wilshire 5000

13 The price response to negative reports was more gradual, lasting 15 minutes, perhaps due to the higher costs of short selling. See J. A. Busse and T. C. Green, “Market Efficiency in Real Time,” Journal of Financial Eco- nomics 65 (2002), pp. 415–437.

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222 Part Two Value

The price that emerges from this competition is likely to reflect the information and views of all the market participants. In this case, it is not enough to have better infor- mation than any one of your competitors; to earn superior returns, you need to have better information than all of them combined. This is a tall order.

If a stock is fairly priced, it will reflect all existing information and respond only to new information. But new information is necessarily unanticipated. Therefore, the resulting change in the stock price must be a surprise and cannot be predicted from earlier changes in the stock price. So in a market where stocks are fairly valued, their prices will wander randomly. Stocks will be equally likely to offer a high or low return on any particular day, regardless of what occurred on previous days. In other words, prices will follow a random walk.

If you are not sure what we mean by “random walk,” consider the following exam- ple: You are given $100 to play a game. At the end of each week, a coin is tossed. If it comes up heads, you win 3% of your investment; if it is tails, you lose 2.5%. Therefore, your payoff at the end of the first week is either $103 or $97.50. At the end of the sec- ond week, the coin is tossed again. Now the possible outcomes are as follows:

Heads $106.09 Heads $103.00 Tails $100.43

$100 Tails $97.50 Heads $100.43

Tails $95.06

This process is a random walk because successive changes in the value of your stake are independent and determined by the flip of a fair coin. That is, the odds of making money each week are the same, regardless of the value at the start of the week or the pattern of heads or tails in the previous weeks. If a stock’s price follows a ran- dom walk, the odds of an increase or decrease during any day, month, or year do not depend at all on the stock’s previous price moves. In this case, the patterns that investors sometimes see in stock prices are a mirage, and the historical path of prices gives no useful information about the future—just as a long series of recorded heads and tails gives no information about the next toss.

The notion that successive stock prices follow something close to a random walk has been confirmed in countless ways. Look, for example, at Figure 7.7a. The horizon- tal axis shows the return on the New York Composite Index in 1 week (5 business days), while the vertical axis shows the return in the following week. Each point in the chart represents a different week over a 40-year period. If a market rise one week tended to be followed by a rise the next week, the points in the chart would plot along an upward-sloping line. But you can see that there was no such tendency; the points are scattered randomly across the chart. Statisticians sometimes measure the relation- ship between these changes by the correlation coefficient. In our example, the correla- tion between the market movements in successive weeks is −.022, in other words, effectively zero. Figure 7.7b shows a similar plot for monthly (20-business-day) moves. Again, you can see that this month’s change in the index gives you almost no clue as to the likely change next month. The correlation between successive monthly changes is −.004. This is almost exactly what we would expect in a market where new information is rapidly impounded in stock prices.

Does it surprise you that stocks seem to follow a random walk? If so, imagine that it was not the case and that changes in stock prices were expected to persist for several months. Figure 7.8 provides a hypothetical example of such a predictable cycle. You can see that an upswing in the market started when the index was 1,600 and is expected to carry the price to 1,800 next month. What will happen when investors perceive this bonanza? Because stocks are a bargain at their current level, investors will rush to buy and, in so doing, will push up prices. They will stop buying only when stocks are fairly priced. Thus, as soon as a cycle becomes apparent to investors, they immediately elim- inate it by their trading.

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Chapter 7 Valuing Stocks 223

Economists often refer to the stock market as an efficient market. By this they mean that the competition to find misvalued stocks is intense. So when new information comes out, investors rush to take advantage of it and thereby eliminate any profit opportunities. As a result, each new change in the price of a stock is independent of earlier changes. Professional investors express the same idea when they say that there are no free lunches on Wall Street. It is very difficult to detect undervalued stocks and to beat the market consistently. Of course, this does not mean that investors have perfect foresight and never

efficient market Market in which prices reflect all available information.

FIGURE 7.7a Each dot shows the returns on the New York Composite Index on two successive weeks over a 40-year period. The circled dot shows a weekly return of +3.1%, followed by +5.2% in the next week. The scatter diagram shows no significant relationship between returns on successive weeks.

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FIGURE 7.7b This scatter diagram shows that there is also no relationship between market returns in successive months.

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224 Part Two Value

make mistakes. The large fluctuations in stock market prices suggest that investors are being caught by surprise every day, and that with the benefit of hindsight (but only with that benefit) wonderful profit opportunities were dangling from every tree.

FIGURE 7.8 Cycles self- destruct as soon as they are recognized by investors. The stock price instantaneously jumps to the present value of the expected future price.

M ar

ke t i

nd ex

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1,600

1,700

Last month

This month

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Actual price as soon as upswing is recognized

Next month

1,800

True or false: If stock prices follow a random walk,

a. successive stock prices are not related. b. successive stock price changes are not related. c. stock prices fluctuate above and below a normal long-run price. d. the history of stock prices cannot be used to predict future returns to

investors.

Self-Test7.8

Market Anomalies and Behavioral Finance

Market Anomalies Almost without exception, early researchers concluded that the efficient-market hypothesis was a remarkably good description of reality. They tested three versions of the hypothesis. The weak form of the hypothesis maintains that stock prices follow a random walk, so that it is impossible to make superior returns just from a study of past price changes. Figure 7.7, which shows that price changes are essentially independent from one period to the next, provides just one example of a test of the weak-form hypothesis. The semi-strong form of the hypothesis maintains that public information is impounded in the stock price, so that it is impossible to earn superior returns by a study of information that is also available to other investors. Researchers have tested this hypothesis by looking at how rapidly prices incorporate different types of news such as our example of the CNBC Morning and Midday Calls. The strong form of the hypothesis holds that no group of investors with whatever information and skill-sets that they possess can earn consistently superior returns. Figure 7.6, which shows that

7.7

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Chapter 7 Valuing Stocks 225

even professional managers do not generally outperform the market, offers some evi- dence that the market is strong-form efficient.

But eventually, cracks in the evidence began to appear, and soon the finance jour- nals were packed with examples of anomalies, or seeming profit opportunities, that investors have apparently failed to exploit. Some of these concern very short-term stock returns. To have any chance of making money from anomalies that may last for only a few seconds, you need to be a high-frequency trader with one eye on the com- puter screen and the other on your annual bonus. If you are a corporate financial man- ager, these patterns may be intriguing conundrums, but they are unlikely to change major financial decisions about which projects to invest in and how they should be financed. Corporate managers should be more concerned about possible mispricing that lasts months or years.

Economists have unearthed a number of these longer-term anomalies. Here are a couple examples.

The Momentum Factor We said earlier that stock prices follow something close to a random walk. That is true, but there do appear to be some exceptions. For example, researchers who have looked at stock market returns over long periods have found a tendency for price rises to persist for some 6 to 9 months and then to revert.14 Investors refer to this persistence of returns as momentum.

The Book-to-Market Factor Now look at Figure 7.9, which shows the cumulative difference between the returns on value stocks and growth stocks. Value stocks are defined as those with a high ratio of book to market value. Growth stocks are those with low ratios of book to market.15 Notice that value stocks have provided a higher return than growth stocks. Between 1926 and 2017 the average annual difference between the returns on the two sets of stocks was 4.9%.

Is this pattern another exception to the efficient-market theory, an exception that gave investors the opportunity to earn exceptional returns over many decades simply by investing in low book-to-market stocks? Perhaps. But it also could be that value stocks have extra risks that we have not yet identified or learned how to measure. If so, investors may have demanded the higher returns as compensation for these risks.

14 See, for example, N. Jegadeesh, “Evidence of Predictable Behavior of Stock Returns,” Journal of Finance 45, (1990), pp. 881–898; and T. J. Moskowitz, Y. H. Ooi, and L. H. Pedersen, “Time Series Momentum,” Journal of Financial Economics 104, no. 2 (2012), pp. 228–250. 15 They are called growth stocks because a high expected rate of growth would justify their high price relative to book value.

FIGURE 7.9 Difference in the cumulative values of $1 investments in stocks with low versus high ratios of book value to market value. 1926 = $0.

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226 Part Two Value

Market anomalies such as the momentum factor suggest that there may be occa- sions when prices of individual stocks can get out of line. But are there also cases in which prices as a whole can no longer be justified by fundamentals? We will look at the evidence in a moment, but first we should note how difficult it is to value common stocks and to determine whether their prices are irrational.

For example, imagine that in December 2017 you wanted to check whether the stocks forming Standard & Poor’s Composite Index were fairly valued. As a first stab, you might use the constant-growth formula that we introduced earlier. In 2018, the annual dividends paid by the companies in the index totaled around $460 billion. Sup- pose that these dividends were expected to grow at a steady rate of 4.0% and that investors required a return of 6.0%. Then the constant-growth formula gives a value for the common stocks of

PV = DIV1 _____ r − g = $460 billion __________ .06 − .04 = $23,000 billion

which was slightly less than their actual value of $24,000 billion in December 2017. But how confident could you be about these figures? Perhaps the likely dividend growth was only 3.5% per year. In that case, your estimate of the value of the common stocks would decline to

PV = DIV1 _____ r − g = $460 billion __________ .06 − .035 = $18,400 billion

In other words, a reduction of just half a percentage point in the expected rate of dividend growth would reduce the value of common stocks by 20%. The extreme sensitivity of price to even minor changes in assumptions tells us that valuing common stocks from scratch is always going to be very imprecise. This conclusion has two important consequences.

First, investors find it easier to price a common stock relative to yesterday’s price or relative to today’s price of comparable securities. In other words, they generally take yesterday’s price as correct, adjusting upward or downward on the basis of today’s information. If information arrives smoothly, then, as time passes, investors become increasingly confident that today’s price level is correct. But when investors lose con- fidence in the benchmark of yesterday’s price, there may be a period of confused trad- ing and volatile prices before a new benchmark is established.

Second, most of the tests of market efficiency are concerned with relative prices and focus on whether there are easy profits to be made. It is almost impossible to test whether stocks are correctly valued because no one can measure true value with any precision.

Bubbles and Market Efficiency It may be impossible to prove that market levels are, or are not, consistent with funda- mentals. However, every now and again investors seem to be caught up in a specula- tive frenzy, and asset prices then reach levels that (at least with hindsight) cannot easily be justified by the outlook for profits and dividends. Investors refer to such occasions as bubbles.

The Japanese bubble is a good example. Between 1985 and 1989, the Japanese Nik- kei index roughly quadrupled. But in 1990, interest rates rose and stock prices started to fall. By October the Nikkei had sunk to about half its peak, and by March 2009 it was down 80% from its peak value 19 years earlier.

The boom in Japanese stock prices was matched by an even greater explosion in land prices. For example, Ziemba and Schwartz document that the few hundred acres of land under the Emperor’s Palace in Tokyo, evaluated at neighborhood land prices, was worth as much as all the land in Canada or California.16 But then the real estate bubble also burst. By 2005 land prices in the six major Japanese cities had slumped to just 13% of their peak.

16 See W. T. Ziemba and S. L. Schwartz, Invest Japan (Chicago: Probus Publishing, 1992), p. 109.

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Chapter 7 Valuing Stocks 227

The dot-com bubble in the United States was almost as dramatic. The technology- heavy NASDAQ stock index rose 580% from the start of 1995 to its eventual high in March 2000. But then, as rapidly as it began, the boom ended, and by October 2002 the index had fallen 78% from its peak.

Looking back at these episodes, it seems difficult to believe that expected future cash flows could ever have been sufficient to justify the initial price run-ups. If that is the case, we have two important exceptions to the theory of efficient markets.

But beware of jumping to the conclusion that prices are always arbitrary and capri- cious. First, most bubbles become obvious only after they have burst. At the time, there often seems to be a plausible explanation for the price run-up. In the dot-com boom, for example, many contemporary observers rationalized stock price gains as justified by the prospect of a new and more profitable economy, driven by technological advances.

Behavioral Finance Why might prices depart from fundamental values? Some scholars believe that the answer to this question lies in behavioral psychology. People are not 100% rational 100% of the time. This shows up in three broad areas—their attitudes to risk, the way that they assess probabilities, and their sentiment about the economy:

1. Attitudes toward risk. Psychologists have observed that, when making risky decisions, people are particularly loath to incur losses, even if those losses are small. Losers are liable to regret their actions and kick themselves for having been so foolish. To avoid this unpleasant possibility, individuals will tend to shun those actions that may result in loss.

The pain of a loss seems to depend on whether it comes on the heels of earlier losses. Once investors have suffered a loss, they may be even more cautious not to risk a further loss. Conversely, just as gamblers are known to be more willing to take large bets when they are ahead, so investors may be more prepared to run the risk of a stock market dip after they have experienced a period of substantial gains. If they do then suffer a small loss, they at least have the consolation of being up on the year.

You can see how this sort of behavior could lead to a stock price bubble. For example, early investors in the technology firms that boomed during the dot-com bubble were big winners. They may have stopped worrying about the risk of loss. They may have thrown caution to the winds and piled even more investment into these companies, driving stock prices far above fundamental values. The day of reckoning came when investors woke up and realized how far above fundamental value prices had soared.

2. Beliefs about probabilities. Most investors do not have a Ph.D. in probability theory and may make common errors in assessing the probability of uncertain outcomes. Psychologists have found that, when judging the possible future outcomes, individuals commonly look back to what has happened in recent periods and then assume that this is representative of what may occur in the future. The temptation is to project recent experience into the future and to forget the lessons learned from the more distant past. For example, an investor who places too much weight on recent events may judge that glamorous growth companies are very likely to continue to grow rapidly, even though very high rates of growth cannot persist indefinitely.

A second common bias is overconfidence. Most of us believe that we are better- than-average drivers, and most investors think that they are better-than-average stock pickers. We know that two speculators who trade with one another cannot both make money from the deal; for every winner there must be a loser. But presumably investors are prepared to continue trading because each is confident that it is the other one who is the patsy.

You can see how such characteristics may have reinforced the dot-com boom. As the bull market developed, it generated increased optimism about the future and stimulated demand for shares. The more that investors racked up profits on their

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228 Part Two Value

stocks, the more confident they became in their views and the more willing they became to bear the risk that the next month might not be so good.

3. Sentiment. Efficient markets bring to mind absolutely rational investors on the lookout for every possible profit opportunity. But real investors are people, and people are subject to emotion. Sentiment may be interpreted as their general level of optimism or pessimism about the economy. If the sentiment of large groups of investors varies in tandem, it potentially could have a noticeable impact on security pricing.

Sentiment is offered as another reason that stock market bubbles might develop. An improvement in sentiment can lead to an increase in stock prices. That increase can feed on itself, with investors extrapolating recent performance into the future and deciding that it is a good time to buy, thus pushing prices up even further.

Now it is not difficult to believe that your uncle Harry or aunt Hetty may become caught up in a scatty whirl of irrational exuberance,17 but why don’t hardheaded professional investors bail out of the overpriced stocks and force their prices down to fair value? Perhaps they feel that it is too difficult to predict when the boom will end and that their jobs will be at risk if they move aggressively into cash when others are raking up profits. In this case, sales of stock by the pros are simply not large enough to stem the tide of optimism sweeping the market.

It is too early to say how far behavioral finance scholars can help to sort out some of the puzzles and explain events like the dot-com boom. One thing, however, seems clear: It is relatively easy for statisticians to spot anomalies with the benefit of hind- sight and for psychologists to provide an explanation for them. It is much more diffi- cult for investment managers who are at the sharp end to spot and invest in mispriced securities in real time. And that is the basic message of the efficient-market theory. For corporate financial managers there is a clear lesson: Trust market prices unless you have a clear advantage that ensures the odds are in your favor.

SUMMARY Large companies usually arrange for their stocks to be traded on a stock exchange. The stock listings report the stock’s price, price change, volume, dividend yield, and price- earnings (P/E) ratio.

To value a stock, financial analysts often start by identifying similar firms and looking at how much investors in these companies are prepared to pay for each dollar of earnings or book assets.

Stockholders generally expect to receive (1) cash dividends and (2) capital gains or losses. The rate of return that they expect over the next year is defined as the expected dividend per share DIV1 plus the expected increase in price P1 − P0, all divided by the price at the start of the year P0.

Unlike the fixed interest payments that the firm promises to bondholders, the divi- dends that are paid to stockholders depend on the fortunes of the firm. That’s why a company’s common stock is riskier than its debt. The return that investors expect on any one stock is also the return that they demand on all stocks subject to the same degree of risk.

The present value of a share is equal to the stream of expected dividends per share up to some horizon date plus the expected price at this date, all discounted at the return

What information is included in stock trading reports, and how can stock- price information about other firms be used to help you value a particular firm? (LO7-1)

17 The term “irrational exuberance” was coined by Alan Greenspan, former chairman of the Federal Reserve Board, to describe the dot-com boom. It was also the title of a book by Robert Shiller that examined the boom. See R. Shiller, Irrational Exuberance (New York City: Broadway Books, 2001).

How can one calculate the present value of a stock given forecasts of future dividends and future stock price, and how do a company’s growth opportunities show up in its stock price and price- earnings ratio? (LO7-2)

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Chapter 7 Valuing Stocks 229

How does competition among investors lead to efficient markets? (LO7-4)

that investors require. If the horizon date is far away, we simply say that stock price equals the present value of all future dividends per share. This is the dividend discount model.

If forecast dividends grow at a constant rate, g, then the value of a stock is P0 = DIV1/(r − g). This is the constant-growth dividend discount model. Sometimes, it is feasible to discount forecasted dividends for the next few years and then to discount the expected price at the end of this period. The expected price is often estimated using the constant-growth model.

You can think of a share’s value as the sum of two parts—the value of the assets in place and the present value of growth opportunities, that is, of future opportunities for the firm to invest in high-return projects. The price-earnings (P/E) ratio reflects the market’s assess- ment of the firm’s growth opportunities.

Similar valuation methods can be used to estimate the value of an entire business. In this case, you need to forecast and discount the free cash flows provided by the business. These are the cash flows that are not plowed back into the business but can be used to pay divi- dends or repurchase stock.

Competition between investors will tend to produce an efficient market—that is, a market in which prices rapidly reflect new information and investors have difficulty making con- sistently superior returns. Of course, we all hope to beat the market, but if the market is efficient, all we can rationally expect is a return that is sufficient on average to compensate for the time value of money and for the risks we bear.

The evidence for market efficiency is voluminous, and there is little doubt that skilled professional investors find it difficult to win consistently. Nevertheless, there remain some puzzling instances where markets do not seem to be efficient. Some financial economists attribute these apparent anomalies to behavioral foibles.

How can these stock valuation formulas be used to infer the value of an entire business? (LO7-3)

LISTING OF EQUATIONS

7.1 V0 = DIV1 + P1 _________ 1 + r

7.2 P0 = DIV1 _____ 1 + r +

DIV2 _______ (1 + r)2

+ . . .  + DIVH + PH __________ (1 + r)H

7.3 P0 = DIV1 _____ r − g (Constant-growth dividend discount model)

7.4 r = DIV1 ______ P0

+ g = dividend yield + growth rate

7.5 sustainable growth rate = return on equity × plowback ratio

QUESTIONS AND PROBLEMS 1. Stock Markets. True or false? (LO7-1)

a. The bid price is always greater than the ask price. b. An investor who wants to sell his stock immediately should enter a limit order. c. The sale of shares by a large investor is usually termed a “primary offering.” d. Electronic Communications Network refers to the automated ticker tape on the New York

Stock Exchange.

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230 Part Two Value

2. Stock Quotes. Go to finance.yahoo.com and get trading quotes for IBM. (LO7-1) a. What are the latest stock price and market cap? b. What is the bid-ask spread? c. What are IBM’s dividend payment and dividend yield? d. What is IBM’s P/E ratio?

3. Stock Quotes. Here is a small part of the order book for Mesquite Foods: (LO7-1)

Bid Ask

Price Size Price Size

103 100 103.5 200 102.5 200 103.8 200 101 400 104 300 99.8 300 104.5 400

a. Georgina Sloberg submits a market order to sell 100 shares. What price will she receive? b. Norman Pilbarra submits a market order to buy 400 shares.  What is the maximum price that

he will pay? c. Carlos Ramirez submits a limit bid order at 105. Will it execute immediately?

4. P/E Ratios. Favorita Candy’s stock is expected to earn $2.40 per share this year. Its P/E ratio is 18. What is the stock price? (LO7-1)

5. Dividend Yield. BMM Industries pays a dividend of $2 per quarter. The dividend yield on its stock is reported at 4.8%. What is the stock price? (LO7-1)

6. Valuation by Comparables. Look up the P/E and P/B ratios for American Electric Power (ticker symbol AEP), using Yahoo! Finance or another online source. Calculate the same ratios for the following potential comparables: Duke Energy (DUK), FirstEnergy Corporation (FE), PG&E Corporation (PCG), CenterPoint Energy (CNP), and Southern Company (SO). Are the ratios for these electric companies tightly grouped or scattered? If you didn’t know AEP’s stock price, would the comparables give a good estimate? (LO7-2)

7. Valuation by Comparables. Valuation by comparables worked much better for some of the companies in Table 7.3 than for others. Choose four electric utilities, for example, ED, DUK, ES, and FE, and four computer software firms, for example, INTU, MSFT, ADBE, and ORCL. Collect both P/E and market-to-book value ratios of each firm from Yahoo! Finance. For which industry will valuation by comparables work better? Does this make sense to you? (LO7-2)

8. Dividend Discount Model.  Rework Table 7.4 for horizon years 1, 2, 3, and 10, assuming that investors expect the dividend and the stock price to increase at only 6% a year and that each investor requires the same 12% expected return. (LO7-2) a. What value would Dritter place on the stock? b. Add a new row to Table 7.4 for a new investor, Zehnte, who has a 10-year horizon.

9. Dividend Discount Model. Amazon has never paid a dividend, but in March 2018, the market value of its stock was greater than $760 billion. Does this invalidate the dividend discount model? (LO7-2)

10. Dividend Discount Model. How can we say that price equals the present value of all future dividends when many actual investors may be seeking capital gains and planning to hold their shares for only a year or two? Explain. (LO7-2)

11. Dividend Discount Model. True or False? (LO7-2) a. Investors will invest in a stock only if it gives a higher return than they could get elsewhere.

Therefore, if a stock is fairly priced, its expected return will be greater than the cost of equity capital.

b. A stock that is expected to pay a level dividend in perpetuity has a value of P0 = DIV1/r.  Any company that can reinvest to grow its earnings will have a greater value. 

c. The dividend discount model is still logically correct even for stocks that do not currently pay a dividend.

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Chapter 7 Valuing Stocks 231

12. Dividend Discount Model. Integrated Potato Chips just paid a $1 per share dividend. You expect the dividend to grow steadily at a rate of 4% per year. (LO7-2) a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 12%, at what price will the stock sell? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to sell it 3 years from now, what are your expected cash flows

in (i) year 1; (ii) year 2; (iii) year 3?  e. What is the present value of the stream of payments you found in part (d)? Compare your

answer to part (b).

13. Preferred Stock. Preferred Products has issued preferred stock with an $8 annual dividend that will be paid in perpetuity. (LO7-2) a. If the discount rate is 12%, at what price should the preferred sell? b. At what price should the stock sell 1 year from now? c. What are (i) the dividend yield; (ii) the capital gains yield; (iii) the expected rate of return of

the stock?

14. Constant-Growth Model. Arts and Crafts Inc. will pay a dividend of $5 per share in 1 year. It sells at $50 a share, and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company’s dividends? (LO7-2)

15. Constant-Growth Model. A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is a constant 15% and the company reinvests a constant 40% of earnings in the firm, what must be the discount rate? (LO7-2)

16. Constant-Growth Model. Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely. (LO7-2) a. What price should the stock sell at? The discount rate is 15%. b. How would your answer change if the discount rate was only 12%? Why does the answer

change?

17. Constant-Growth Model. Eastern Electric currently pays a dividend of $1.64 per share and sells for $27 a share. (LO7-2) a. If investors believe the growth rate of dividends is 3% per year, what rate of return do they

expect to earn on the stock? b. If investors’ required rate of return is 10%, what must be the growth rate they expect of the

firm? c. If the sustainable growth rate is 5% and the plowback ratio is .4, what must be the rate of

return earned by the firm on its new investments?

18. Constant-Growth Model. You believe that the Non-Stick Gum Factory will pay a dividend of $2 on its common stock next year. Thereafter, you expect dividends to grow at a rate of 6% a year in perpetuity. If you require a return of 12% on your investment, how much should you be prepared to pay for the stock? (LO7-2)

19. Constant-Growth Model. Horse and Buggy Inc. is in a declining industry. Sales, earnings, and dividends are all shrinking at a rate of 10% per year. (LO7-2) a. If r = 15% and DIV1 = $3, what is the value of a share? b. What price do you forecast for the stock next year? c. What is the expected rate of return on the stock? d. Can you distinguish between “bad stocks” and “bad companies”? Does the fact that the

industry is declining mean that the stock is a bad buy?

20. Constant-Growth Model. Metatrend’s stock will generate earnings of $6 per share this year. The discount rate for the stock is 15%, and the rate of return on reinvested earnings also is 15%. (LO7-2) a. Find both the growth rate of dividends and the price of the stock if the company reinvests the

following fraction of its earnings in the firm: (i) 0%; (ii) 40%; (iii) 60%. b. Redo part (a) now assuming that the rate of return on reinvested earnings is 20%. What is the

present value of growth opportunities for each reinvestment rate? c. Considering your answers to parts (a) and (b), can you briefly state the difference between

companies experiencing growth and companies with growth opportunities?

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232 Part Two Value

21. Constant-Growth Model. Here are data on two stocks, both of which have discount rates of 15%: (LO7-2)

Stock A Stock B

Return on equity 15% 10% Earnings per share $2.00 $1.50 Dividends per share $1.00 $1.00

a. What is the dividend payout ratio for each firm? b. What is the expected dividend growth rate for each stock? c. What is the value of each stock?

22. Constant-Growth Model. Fincorp will pay a year-end dividend of $2.40 per share, which is expected to grow at a 4% rate for the indefinite future. The discount rate is 12%. (LO7-2) a. What is the stock selling for? b. If earnings are $3.10 a share, what is the implied value of the firm’s growth opportunities?

23. Dividend Discount Model. Consider the following three stocks: a. Stock A is expected to provide a dividend of $10 a share forever. b. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected

to be 4% a year forever. c. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected

to be 20% a year for 5 years (i.e., years 2 through 6) and zero thereafter.

If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%? (LO7-2)

24. Rate of Return. Steady As She Goes Inc. will pay a year-end dividend of $3 per share. Inves- tors expect the dividend to grow at a rate of 4% indefinitely. (LO7-2) a. If the stock currently sells for $30 per share, what is the expected rate of return on the stock? b. If the expected rate of return on the stock is 16.5%, what is the stock price?

25. Dividend Growth. Grandiose Growth has a dividend growth rate of 20%. The discount rate is 10%. The end-of-year dividend will be $2 per share. (LO7-2) a. What is the present value of the dividend to be paid in: (i) Year 1? (ii) Year 2? (iii) Year 3? b. Could anyone rationally expect this growth rate to continue indefinitely?

26. Valuing Businesses. Start-Up Industries is a new firm that has raised $200 million by selling shares of stock. Management plans to earn a 24% rate of return on equity, which is more than the 15% rate of return available on comparable-risk investments. Half of all earnings will be reinvested in the firm. (LO7-3) a. What will be Start-Up’s ratio of market value to book value? b. How would that ratio change if the firm can earn only a 10% rate of return on its

investments?

27. Nonconstant Growth. You expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 in each of the next 3 years. You believe the stock will sell for $20 at the end of the third year. (LO7-2) a. What is the stock price if the discount rate for the stock is 10%? b. What is the dividend yield for year 1?   c. What will be the dividend yield at the start of year 2?

28. Nonconstant Growth. Planned Obsolescence has a product that will be in vogue for 3 years, at which point the firm will close up shop and liquidate the assets. As a result, forecast dividends are DIV1 = $2, DIV2 = $2.50, and DIV3 = $18. What is the stock price if the discount rate is 12%? (LO7-2)

29. Nonconstant Growth. Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. (LO7-2) a. If the last dividend paid was $2, what will the next dividend be? b. If the discount rate is 15% and the steady growth rate after 3 years is 4%, what should the

stock price be today?

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Chapter 7 Valuing Stocks 233

30. Nonconstant Growth. Reconsider Tattletale News from the previous problem. (LO7-2) a. What is your prediction for the stock price in 1 year? b. Show that the expected rate of return equals the discount rate.

31. Nonconstant Growth. Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $3 per share), dividend growth is expected to settle down to a more moderate long-term growth rate of 6%. If the firm’s investors expect to earn a return of 14% on this stock, what must be its price? (LO7-2)

32. Nonconstant Growth. A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be $4 per share, and it is expected that dividends will grow at 5% per year thereafter. The expected rate of return on the stock is 12%. (LO7-2) a. What is the current price of the stock? b. What is the expected price of the stock in a year? c. Show that the expected return, 12%, equals dividend yield plus capital appreciation.

33. Nonconstant Growth. Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 20% per year for 4 years. By then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth rate will fall to 5%. The most recent annual dividend was DIV0 = $1 per share. (LO7-2) a. What are the expected values of: (i) DIV1, (ii) DIV2, (iii) DIV3, and (iv) DIV4? b. What is the expected stock price 4 years from now? The discount rate is 10%. c. What is the stock price today? d. Find the dividend yield, DIV1/P0. e. What will next year’s stock price, P1, be? f. What is the expected rate of return to an investor who buys the stock now and sells it in

1 year?

34. Nonconstant Growth. (LO7-2) a. Return to the previous problem, and compute the value of Better Mousetraps for assumed

sustainable growth rates of 6% through 9%, in increments of .5%. b. Compute the percentage change in the value of the firm for each 1 percentage point increase

in the assumed final growth rate, g. c. What happens to the sensitivity of intrinsic value to changes in g? What do you conclude

about the reliability of estimates based on the dividend growth model when the assumed sustainable growth rate begins to approach the discount rate?

35. Valuing Businesses. Construct a new version of Table 7.5, assuming that competition drives down profitability (on existing assets as well as new investment) to 11.5% in year 6, 11% in year 7, 10.5% in year 8, and 8% in year 9 and all later years. What is the value of the concatenator business? (L07-3)

36. P/E Ratios. No-Growth Industries pays out all of its earnings as dividends. It will pay its next $4 per share dividend in a year. The discount rate is 12%. (LO7-2) a. What is the price-earnings ratio of the company? b. What would the P/E ratio be if the discount rate were 10%?

37. P/E Ratios. Castles in the Sand generates a rate of return of 20% on its investments and main- tains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock. (LO7-2) a. Find the price and P/E ratio of the firm. b. What happens to the P/E ratio if the plowback ratio is reduced to .20? Why? c. Show that if plowback equals zero, the earnings-price ratio, E/P, equals the expected rate of

return on the stock.

38. P/E Ratios. Web Cites Research projects a rate of return of 20% on new projects. Management plans to plow back 30% of all earnings into the firm. Earnings this year will be $3 per share, and investors expect a 12% rate of return on stocks facing the same risks as Web Cites. (LO7-2) a. What is the sustainable growth rate? b. What is the stock price?

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234 Part Two Value

c. What is the present value of growth opportunities? d. What is the P/E ratio? e. What would the price and P/E ratio be if the firm paid out all earnings as dividends? f. What do you conclude about the relationship between growth opportunities and P/E ratios?

39. P/E Ratios. Investors in Rance Electric’s stock require a return of 8%. If the company simply earns the cost of capital on its new investments, what is the stock’s P/E? (LO7-2)

40. Growth Opportunities. Stormy Weather has no attractive investment opportunities. Its return on equity equals the discount rate, which is 10%. Its expected earnings this year are $4 per share. Fill in the following table. (LO7-2)

Plowback Ratio Growth Rate Stock Price P/E Ratio

0 a. b. c. 0.4 d. e. f. 0.8 g. h. i.

41. Growth Opportunities. Trend-Line Inc. has been growing at a rate of 6% per year and is expected to continue to do so indefinitely. The next dividend is expected to be $5 per share. (LO7-2) a. If the market expects a 10% rate of return on Trend-Line, at what price must it be selling? b. If Trend-Line’s earnings per share will be $8 next year, what part of its value is due to assets

in place? c. What part of its value is due to growth opportunities?

42. Efficient Markets. Which if any of these statements are true? Stock prices appear to behave as though successive values (LO7-4) a. are random numbers. b. follow regular cycles. c. differ by a random number.

43. Forms of Efficient Markets. Fill in the missing words from the following list:  semi-strong, strong, weak. (LO7-4)

There are three forms of the efficient-market theory. Tests that have found there are no patterns in share price changes provide evidence for the (a) form of the theory. Evidence for the (b) form of the theory is provided by tests that look at how rapidly markets respond to new public information, and evidence for the (c) form of the theory is provided by tests that look at the performance of professionally managed portfolios. 

44. Information and Efficient Markets. “It’s competition for information that makes securities markets efficient.” Is this statement correct? Explain. (LO7-4)

45. Behavioral Finance. Some finance scholars cite well-documented behavioral biases to explain apparent cases of market inefficiency. Describe two of these biases. (LO7-4)

46. Interpreting the Efficient-Market Theory. How would you respond to the following com- ments? (LO7-4) a. “Efficient market, my eye! I know lots of investors who do crazy things.” b. “Efficient market? Balderdash! I know at least a dozen people who have made a bundle in

the stock market.” c. “The trouble with the efficient-market theory is that it ignores investors’ psychology.”

47. Real versus Financial Investments. Why do investments in financial markets almost always have zero NPVs, whereas firms can find many investments in their product markets with posi- tive NPVs? (LO7-4)

48. Investment Performance. It seems that every month we read an article in The Wall Street Jour- nal about a stock picker with a marvelous track record. Do these examples mean that financial markets are not efficient? (LO7-4)

49. Implications of Efficient Markets. The president of Good Fortunes Inc. states at a press con- ference that the company has a 30-year history of ever-increasing dividend payments. Good Fortunes is widely regarded as one of the best-run firms in its industry. Does this make the firm’s stock a good buy? Explain. (LO7-4)

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Chapter 7 Valuing Stocks 235

50. Implications of Efficient Markets. “Long-term interest rates are at record highs. Most compa- nies, therefore, find it cheaper to finance with common stock or relatively inexpensive short- term bank loans.” Discuss. (LO7-4)

51. Expectations and Efficient Markets. Geothermal Corp. just announced good news: Its earn- ings have increased by 20%. Most investors had anticipated an increase of 25%. Will Geother- mal’s stock price increase or decrease when the announcement is made? (LO7-4)

52. Behavioral Finance. True or false? (LO7-4) a. Most managers tend to be overconfident. b. Psychologists have found that, once people have suffered a loss, they are more relaxed about

the possibility of incurring further losses. c. Psychologists have observed that people tend to put too much weight on recent events when

forecasting. d. Behavioral biases open up the opportunity for easy arbitrage profits.

WEB EXERCISES 1. Review Table 7.2, which lists the market values of several stocks. Update the table. Which

stock’s value has changed by the greatest percentage since 2018, when the table was created? Now recalculate book value per share. Have the book values for any firm changed? Which seems to be more stable, book or market value? Why?

2. From finance.yahoo.com, obtain the price-earnings ratios of Adobe Systems (ADBE) and American Electric Power (AEP). Which of these two firms seems to be more of a “growth stock”? Now obtain a forecast of each firm’s expected earnings per share in the coming year. You can find earnings forecasts on yahoo.com under “Analysts Estimates.” What is the present value of growth opportunities for each firm as a fraction of the stock price? (Assume, for sim- plicity, that the required rate of return on the stocks is r = 8%.) Are the relative values you obtain for PVGO consistent with the P/E ratios?

SOLUTIONS TO SELF-TEST QUESTIONS 7.1 Expected industry profitability has fallen. Thus, the value of future investment opportunities

has fallen relative to the value of assets in place. This happens in all growth industries sooner or later, as competition increases and profitable new investment opportunities shrink.

7.2 P0 = DIV1 + P1 _________ 1 + r =

$5 + $105 _________ 1.10 = $100

7.3 Because dividends and share price grow at 5%,

DIV2 = $5 × 1.05 = $5.25, DIV3 = $5 × 1.052 = $5.51

P3 = $100 × 1.053 = $115.76

P0 = DIV1 _____ 1 + r

+ DIV2 _______ (1 + r)2

+ DIV3 + P3 _________ (1 + r)3

= $5.00 _____ 1.10

+ $5.25 ______ (1.10)2

+ $5.51 + $115.76 ______________ (1.10)3

= $100

7.4 P0 = DIV ____

r = $25 ____ .20 = $125

7.5 The two firms have equal risk, so we can use the data for Androscoggin to find the expected return on either stock:

r = DIV1 _____ P0

+ g = $5 _____ $100 + .05 = .10, or 10%

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236 Part Two Value

7.6 a. The sustainable growth rate is

g = return on equity × plowback ratio = .05 × .38 = .019, or 1.9%

b. First value the company. At a 62% payout ratio, DIV1 = $.86 as before. Using the constant- growth model,

P0 = $.86 _________ .07 − .019 = $16.86

which is $2.96 per share less than the company’s no-growth value of $19.82. In this exam- ple, Aqua America would be throwing away $2.96 of potential value by investing in proj- ects with unattractive rates of return.

c. Sure. A raider could take over the company and generate a profit of $2.96 per share just by halting all investments offering less than the 7.0% rate of return demanded by investors. This assumes the raider could buy the shares for $16.86.

7.7 The present value of dividends in years 1 to 5 is still $10.66. However, with a lower terminal growth rate after year 5, the stock price in year 5 will be lower. If we assume a 2.5% growth rate, then the forecast dividend in year 6 is

DIV6 = 1.025 × DIV5 = 1.025 × $2.85 = $2.92

and the expected price at the end of year 5 is

P5 = DIV6 _____ r − g =

$2.92 _________ .056 − .025 = $94.19

Therefore, present value is

P0 = PV(dividends years 1−5) + PV(price in year 5)

= $10.66 + $94.19 _______ 1.0565

= $82.39

7.8 a. False. The levels of successive stock prices are related. If a stock is selling for $100 per share today, the best guess of its price tomorrow is about $100.

b. True. Changes in stock prices are unrelated. Whether a stock price increases or decreases today has no bearing on whether it will do so tomorrow.

c. False. There is no such thing as a “normal” price. If there were, you could make easy prof- its by buying shares selling below their normal prices (which would tend to be rising back toward those normal levels) and selling shares currently selling above their normal prices. Under a random walk, prices are equally likely to rise or fall.

d. True. Under a random walk, prices are equally likely to over- or underperform regardless of their past history.

MINICASE Terence Breezeway, the CEO of Prairie Home Stores, wondered what retirement would be like. It was almost 20 years to the day since his uncle Jacob Breezeway, Prairie Home’s founder, had asked him to take responsibility for managing the company. Now it was time to spend more time riding and fishing on the old Lazy Beta Ranch.

Under Mr. Breezeway’s leadership, Prairie Home had grown slowly but steadily and was solidly profitable. (Table 7.6 shows earnings, dividends, and book asset values for the last 5 years.) Most of the company’s supermarkets had been modernized, and its brand name was well known.

Mr. Breezeway was proud of this record, although he wished that Prairie Home could have grown more rapidly. He had passed up several opportunities to build new stores in adjacent counties. Prairie Home was still just a family company. Its common stock was distributed among 15 grandchildren and nephews of Jacob Breezeway, most of whom had come to depend on generous regular dividends. The commitment to high dividend payout18 had reduced the earnings available for reinvestment and thereby constrained growth.

Mr. Breezeway believed the time had come to take Prairie Home public. Once its shares were traded in the public market, the

18 The company traditionally paid out cash dividends equal to 10% of start-of-period book value. See Table 7.6.

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Chapter 7 Valuing Stocks 237

Breezeway descendants who needed (or just wanted) more cash to spend could sell off part of their holdings. Others with more inter- est in the business could hold on to their shares and be rewarded by higher future earnings and stock prices.

But if Prairie Home did go public, what should its shares sell for? Mr. Breezeway worried that shares would be sold, either by Breezeway family members or by the company itself, at too low a price. One relative was about to accept a private offer for $200, the current book value per share, but Mr. Breezeway had intervened and convinced the would-be seller to wait.

Prairie Home’s value depended not just on its current book value or earnings but on its future prospects, which were good. One financial projection (shown in the top panel of Table 7.7) called for growth in earnings of more than 100% by 2030. Unfortunately, this plan would require reinvestment of all of Prairie Home’s earnings from 2024–2027. After that, the company could resume its normal dividend payout and growth rate. Mr. Breezeway believed this plan was feasible.

He was determined to step aside for the next generation of top management. But before retiring, he had to decide whether to

recommend that Prairie Home Stores “go public”—and before that decision he had to know what the company was worth.

The next morning, he rode thoughtfully to work. He left his horse at the south corral and ambled down the dusty street to Mike Gordon’s Saloon, where Francine Firewater, the company’s CFO, was having her usual steak-and-beans breakfast. He asked Ms. Fire- water to prepare a formal report to Prairie Home stockholders, valuing the company on the assumption that its shares were pub- licly traded.

Ms. Firewater asked two questions immediately. First, what should she assume about investment and growth? Mr. Breezeway suggested two valuations, one assuming more rapid expansion (as in the top panel of Table 7.7) and another just projecting past growth (as in the bottom panel of Table 7.7).

Second, what rate of return should she use? Mr. Breezeway said that 15%, Prairie Home’s usual return on book equity, sounded right to him, but he referred her to an article in the Journal of Finance indicating that investors in rural supermarket chains, with risks similar to Prairie Home Stores, expected to earn about 11% on average.

2019 2020 2021 2022 2023

Book value, start of year $62.7 $66.1 $69.0 $73.9 $76.5 Earnings 9.7 9.5 11.8 11.0 11.2 Dividends 6.3 6.6 6.9 7.4 7.7 Retained earnings 3.4 2.9 4.9 2.6 3.5 Book value, end of year 66.1 69.0 73.9 76.5 80.0

Notes: 1. Prairie Home Stores has 400,000 common shares. 2. The company’s policy is to pay cash dividends equal to 10% of start-of-year book value.

TABLE 7.6 Financial data for Prairie Home Stores, 2019–2023 (figures in millions)

Notes: 1. Both panels assume earnings equal to 15% of start-of-year book value. This profitability rate is constant. 2. The top panel assumes all earnings are reinvested from 2024–2027. In 2028 and later years, two-thirds of earnings

are paid out as dividends and one-third reinvested. 3. The bottom panel assumes two-thirds of earnings are paid out as dividends in all years. 4. Columns may not add up because of rounding.

2024 2025 2026 2027 2028 2029

Rapid-Growth Scenario

Book value, start of year $80 $ 92.0 $105.8 $121.7 $139.9 $146.9 Earnings 12 13.8 15.9 18.3 21.0 22.0 Dividends 0 0 0 0 14.0 14.7 Retained earnings 12 13.8 15.9 18.3 7.0 7.4 Book value, end of year 92 105.8 121.7 139.9 146.9 154.3

Constant-Growth Scenario

Book value, start of year $80 $84.0 $88.2 $92.6 $  97.2 $102.1 Earnings 12 12.6 13.2 13.9 14.6 15.3 Dividends 8 8.4 8.8 9.3 9.7 10.2 Retained earnings 4 4.2 4.4 4.6 4.9 5.1 Book value, end of year 84 88.2 92.6 97.2 102.1 107.2

TABLE 7.7 Financial projections for Prairie Home Stores, 2024–2029 (figures in millions)

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238

Net Present Value and Other Investment Criteria

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

8-1 Calculate the net present value of a project.

8-2 Calculate the internal rate of return of a project and know what to look out for when using the internal rate of return rule.

8-3 Calculate the profitability index and use it to choose between projects when funds are limited.

8-4 Understand the payback rule and explain why it doesn’t always make shareholders better off.

8-5 Use the net present value rule to analyze three common prob- lems that involve competing projects: (a) when to postpone an investment expenditure, (b) how to choose between projects with unequal lives, and (c) when to replace equipment.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

8

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239

P A

R T

T W

O V

al ue

The investment decision, also known as the capital budgeting decision, is central to the success of the company. We have already seen that capital investments can sometimes absorb substantial amounts of cash; they also have very long-term consequences. The assets you buy today may determine the business you are in many years hence.

For some investment projects, “substantial” is an understatement. Consider the following examples:

■ Verizon spent $23 billion rolling out its fiber-optic network.

■ The cost of bringing one new prescription drug to mar- ket has been estimated to be as high as $2.6 billion.

■ The eventual cost of the Gorgon natural gas project in Western Australia is forecast at $54 billion.

■ General Motors’ research and development costs for the Chevrolet Volt have been about $1.2 billion.

■ Estimated production costs for the most recent Star Wars movie (Solo) were over $250 million.

■ The development costs of the Boeing 787 Dream- liner jet were over $30 billion.

Notice that many of these big capital projects require heavy investment in intangible assets. For example, almost all the cost of drug development is for research and testing. So is much of the cost of developing the electric auto. Any expenditure made in the hope of gen- erating more cash later can be called a capital invest- ment project, regardless of whether the cash outlay goes to tangible or intangible assets.

A company’s shareholders prefer to be rich rather than poor. Therefore, they want the firm to invest in every proj- ect that is worth more than it costs. The difference between a project’s value and its cost is termed the net present value. Companies can best help their shareholders by investing in projects with a positive net present value.

We start this chapter by showing how to calculate the net present value of some simple investment projects. We then examine three other criteria that companies sometimes use to evaluate investments. Often, they com- pare the expected rate of return offered by a project to the return that their shareholders could earn on equiva- lent-risk investments in the capital market. They accept only projects that provide a higher return than sharehold- ers could earn for themselves. Generally, this rule will

High-tech businesses often require huge investments. How do companies decide which investments are worth pursuing? ©Shutterstock/science photo

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240

Net Present Value

In Chapters 6 and 7, you learned how to value bonds and stocks by adding up the pres- ent values of the cash flows that they are expected to provide to their investors. Now we will do the same for investment projects.

Suppose that you are in the real estate business. You are considering construction of an office block. The land would cost $50,000, and construction would cost a further $300,000. You foresee a shortage of office space and predict that a year from now you will be able to sell the building for $400,000. Thus, you would be investing $350,000 now in the expectation of realizing $400,000 at the end of the year. The projected cash flows may be summarized in a simple time line as follows:

8.1

give the same guidance as the net present value rule, but, as we shall see, it presents some pitfalls, especially when choosing between alternative projects. We explore the key pitfalls of the rate of return rule, and in the appendix we show you some tricks for avoiding them.

Another measure of project worth is the profitability index, which is net present value per dollar invested. This can be a handy tool when the company does not have enough money to take on every project with a posi- tive net present value.

The third measure, the payback rule, is a simple rule of thumb that companies may use to separate the no- brainers from more marginal cases. But we shall see that

this rule is an unreliable guide to project viability and is even more unreliable when used to choose between com- peting projects. We will spend relatively little time on it.

We start the chapter by looking at some simple take- it-or-leave-it decisions. However, in practice, projects can rarely be considered in isolation. Usually, there are sev- eral alternatives, only one of which can be chosen. For example, suppose you are considering whether to build a new factory. Should you build a 100,000-square-foot factory or 150,000? Should you design it to last 20 years or 30? Should it be built today, or should you wait a year? Later in the chapter we explain how to make such choices.

$400,000

0 Year

1

-$350,000

You should go ahead if the present value of the $400,000 payoff is greater than the investment of $350,000.

Assume for the moment that the $400,000 payoff is certain. The office building is not the only way to obtain a sure-fire $400,000 a year from now. You could instead invest in 1-year U.S. Treasury securities. Suppose Treasury securities offer interest of 7%. How much would you have to invest in them in order to receive $400,000 at the end of the year? That’s easy: You would have to invest

$400,000 × 1 ____ 1.07 = $400,000 × .9346 = $373,832

Let’s assume that as soon as you have purchased the land and laid out the money for construction, you decide to cash in on your project. How much could you sell it for? Because the property will be worth $400,000 in a year, investors would be willing to pay, at most, $373,832 for it now. That’s the amount it would cost them to get precisely the same $400,000 payoff by investing in government securities. Of course, you could always sell your property for less, but why sell for less than the market will bear?

Therefore, at an interest rate of 7%, the present value of the $400,000 payoff from the office building is $373,832. The $373,832 present value is the only price that satis- fies both buyer and seller. In general, the present value is the only feasible price, and the present value of the property is also its market price or market value.

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Chapter 8 Net Present Value and Other Investment Criteria 241

To calculate present value, we discounted the expected future payoff by the rate of return offered by comparable investment alternatives. The discount rate—7% in our example—is often known as the opportunity cost of capital. It is called the opportu- nity cost because if you decide to invest in this project, you will forgo other similar investment opportunities such as the purchase of Treasury securities.

The building is worth $373,832, but this does not mean that you are $373,832 better off. You committed $350,000, and therefore your net present value (NPV) is $23,832. Net present value is found by subtracting the required initial investment from the pres- ent value of the project cash flows:1

NPV = PV − required investment (8.1) = $373,832 − $350,000 = $23,832

In other words, your office development is worth more than it costs—it makes a net contribution to value. The net present value rule states that managers increase shareholders’ wealth by accepting projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value.

A Comment on Risk and Present Value In our discussion of the office development, we assumed that we knew the value of the completed project. In practice, you will never be certain about the future values of office buildings. The $400,000 represents the best forecast, but it is not a sure thing.

In this case, our initial conclusion about how much investors would pay for the building is premature. Because they could achieve $400,000 risklessly by investing in $373,832 worth of U.S. Treasury bills, they would not buy your risky project for that amount. You would have to cut your asking price to attract investors’ interest.

Here we can invoke a basic financial principle: A risky dollar is worth less than a safe one.

Most investors avoid risk when they can do so without sacrificing return. However, the concepts of present value and the opportunity cost of capital still apply to risky investments. It is still proper to discount the payoff by the rate of return offered by a comparable investment. But we have to think of expected payoffs and the expected rates of return on other investments. And we need to make sure that those other invest- ments have comparable risk.

Not all investments are equally risky. The office development is riskier than a Trea- sury bill but is probably less risky than investing in a start-up biotech company. Sup- pose you believe the office development is as risky as an investment in the stock market and that you forecast a 12% rate of return for stock market investments. Then 12% would be the appropriate opportunity cost of capital. That is what you are giving up by not investing in securities with similar risk. You can now recompute NPV:

PV = $400,000 × 1 ____ 1.12 = $400,000 × .8929 = $357,143

NPV = PV − $350,000 = $7,143

If other investors agree with your forecast of a $400,000 expected payoff and with your assessment of a 12% opportunity cost of capital, then the property ought to be worth $357,143 once construction is under way. If you tried to sell for more than that, there would be no takers because the property would then offer a lower expected rate of return than the 12% available in the stock market. Even at a discount rate of 12%, the office building still makes a net contribution to value, but it is much smaller than our earlier calculations indicated.

opportunity cost of capital Expected rate of return given up by investing in a project rather than in the capital market.

net present value (NPV) Present value of project cash flows minus investment.

1 You often hear financial innocents talk about net present value when they really mean present value. Remem- ber, the present value measures what a project is worth. Net present value deducts the cost of the investment.

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242 Part Two Value

Valuing Long-Lived Projects The net present value rule works for projects of any length. For example, suppose that you are approached by a possible tenant who is prepared to rent your office block for 3 years at a fixed annual rent of $25,000. You would need to expand the reception area and add some other tailor-made features. This would increase the initial investment to $375,000, but you forecast that after you have collected the third year’s rent, the build- ing could be sold for $450,000. The projected cash flow (denoted C) in each year is shown here (the final cash flow is the sum of the third year’s rental income plus the proceeds from selling the building).

What is the NPV of the office development if construction costs increase to $355,000? Assume the opportunity cost of capital is 12%. Is the development still a worthwhile investment? How high can development costs be before the project is no longer attractive? Now suppose that the opportunity cost of capital is 20% with construction costs of $355,000. Why is the office development no longer an attractive investment?

Self-Test8.1

C1 = $25,000 C2 = $25,000 C3 = $475,000

0 Year

1 2 3

C0 = -$375,000

Notice that the initial investment shows up as a negative cash flow. That first cash flow, C0, is −$375,000. For simplicity, we will again assume that these cash flows are certain and that the opportunity cost of capital is r = 7%.

Figure 8.1 shows a time line of the cash inflows and their present values. To find the present value of the project, we discount these cash inflows at the 7% opportunity cost of capital:

PV = C1 _____ 1 + r

+ C2 _______ (1 + r)2

+ C3 _______ (1 + r)3

= $25,000 _______ 1.07

+ $25,000 _______ 1.072

+ $475,000 ________ 1.073

= $432,942

The net present value of the revised project is NPV = $432,942 − $375,000 = $57,942. Constructing the office block and renting it for 3 years makes a greater addition to your wealth than selling it at the end of the first year.

Of course, rather than subtracting the initial investment from the project’s present value, you could calculate NPV directly, as in the following equation, where C0 denotes the initial cash outflow required to build the office block.

NPV = C0 + C1 _____

1 + r + C2 _______

(1 + r)2 + C3 _______

(1 + r)3

= −$375,000 + $25,000 _______ 1.07

+ $25,000 _______ 1.072

+ $475,000 ________ 1.073

= $57,942

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The revised office project

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Chapter 8 Net Present Value and Other Investment Criteria 243

Let’s check that the owners of this project really are better off. Suppose you put up $375,000 of your own money, commit to build the office building, and sign a lease that will bring in $25,000 a year for 3 years. Now you can cash in by selling the project to other investors.

Suppose you sell 1,000 shares in the project. Each share represents a claim to 1/1,000 of the future cash flows. Because the cash flows are certain, and the interest rate offered by other certain investments is 7%, investors will value each share at

Price per share = $25 ____ 1.07

+ $25 _____ 1.072

+ $475 _____ 1.073

= $432.94

Thus, you can sell the project to outside investors for 1,000 × $432.94 = $432,940, which, save for rounding, is exactly the present value we calculated earlier. Your net gain is

Net gain = $432,942 − $375,000 = $57,942

which is the project’s NPV. This equivalence should be no surprise because the present value calculation is designed to calculate the value of future cash flows to investors in the capital markets.

Notice that, in principle, there could be a different opportunity cost of capital for each period’s cash flow. In that case, we would discount C1 by r1, the discount rate for 1-year cash flows; C2 would be discounted by r2; and so on. However, here we assume that the cost of capital is the same regardless of the date of the cash flow. We do this for one reason only—simplicity. But we are in good company: With only rare excep- tions, firms decide on an appropriate discount rate and then use it to discount all cash flows from the project.

FIGURE 8.1 Cash flows and their present values for the office-block project. Final cash flow of $475,000 is the sum of the rental income in year 3 plus the forecast sales price for the building.

0

= 21,836

Present value

432,942

1.072 25,000

= 23,364 1.07

25,000

= 387,741 1.073

475,000

2 31

$450,000

$25,000

$25,000 $25,000

$475,000

Valuing a New Computer System

Obsolete Technologies is considering the purchase of a new computer system to help han- dle its warehouse inventories. The system costs $50,000 and is expected to last 4 years and to reduce the cost of managing inventories by $22,000 a year. The opportunity cost of capi- tal is 10%. Should Obsolete go ahead?

Don’t be put off by the fact that the computer system does not generate any sales. If the expected cost savings are realized, the company’s cash flows will be $22,000 a year higher

Example 8.1 ⊲

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244 Part Two Value

The first two steps in calculating NPVs—forecasting the cash flows and estimating the opportunity cost of capital—are tricky, and we will have a lot more to say about them in later chapters. But once you have assembled the data, the calculation of pres- ent value and net present value should be routine.

Spreadsheets are ideal for taking the drudgery out of these calculations. The nearby box provides guidance on how they are used to calculate NPVs.

Choosing between Alternative Projects So far, the simple projects that we have considered all involved take-it-or-leave-it deci- sions. But real-world decisions are rarely straightforward go-or-no-go choices; rather, you will almost always be forced to choose between several alternatives. In these cases, you need to rank your alternatives and select the most attractive one. In principle, the decision rule is easy:

When choosing between mutually exclusive projects, choose the one that offers the highest net present value.

In reality, however, it can be surprisingly tricky to compare projects properly. We treat some of the challenging cases later in the chapter, in Section 8.5. For now, we illustrate the general rule with a simple example.

as a result of buying the computer. Thus, we can say that the computer increases cash flows by $22,000 a year for each of 4 years. To calculate present value, you can discount each of these cash flows by 10%. However, it is smarter to recognize that the cash flows are level, and therefore, you can use the annuity formula to calculate the present value:

PV = cash flow × annuity factor = $22,000 × [ 1 ___ .10 − 1 ________ .10(1.10)4 ] = $22,000 × 3.1699 = $69,738

The net present value is

NPV = −$50,000 + $69,738 = $19,738

The project has a positive NPV of $19,738. Undertaking it would increase the value of the firm by that amount. ■

Choosing between Two Projects

It has been several years since your office last upgraded its office networking software. Two competing systems have been proposed. Both have an expected useful life of 3 years, at which point it will be time for another upgrade. One proposal is for an expensive, cutting- edge system, which will cost $800,000 and increase firm cash flows by $350,000 a year through increased productivity. The other proposal is for a cheaper, somewhat slower sys- tem. This system would cost only $700,000 but would increase cash flows by only $300,000 a year. If the cost of capital is 7%, which is the better option?

The following table summarizes the cash flows and the NPVs of the two proposals:

Cash Flows (thousands of dollars)

System C0 C1 C2 C3 NPV at 7%

Faster −800 +350 +350 +350 118.5

Slower −700 +300 +300 +300     87.3

In both cases, the software systems are worth more than they cost, but the faster system would make the greater contribution to value and, therefore, should be your preferred choice. ■

Example 8.2 ⊲

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245

The formulas used in column C (specifically, in cells C3 through C7) and spelled out in column D all contain 1.07. What if you want to see how the PVs change at a different discount rate, say, 9%? You would have to change each of the formulas manually. However, there is an easier way. Instead of repeat- edly replacing 1.07 with 1.09 in each of those cells, first enter the appropriate discount rate in cell B1, and then replace every incidence of 1.07 with (1 + $B$1) in column C. This tells Excel that the discount factor is 1 plus the number in cell B1, where the discount rate resides. (The dollar signs in $B$1 ensure that the Excel formula always refers to exactly that cell, regardless of where the formula is located in the spreadsheet.) Now you can easily experiment with different discount rates by chang- ing just one number, the rate entered in cell B1; Excel will recal- culate the PVs and NPV automatically using that rate.

For example, the formula used in cell C4 and displayed in D4 becomes =C4/(1 + $B$1)^A4. The NPV formula becomes =NPV($B$1,B4:B6) + B3. The “live” version of Spreadsheet 8.1, which is available in Connect, is set up in this way.

Spreadsheet Questions 1. Go to the spreadsheet version of Spreadsheet 8.1. How

does NPV change if the discount rate increases? What dis- count rate would drive NPV down to zero?

2. Try calculating the office project’s NPV using the formula =NPV($B$1,B3:B6), using a discount rate of 7%. You should find that NPV decreases by a multiple of exactly 1/1.07. Why?

Brief solutions appear at the end of the chapter.

Computer spreadsheets are tailor-made to calculate the pres- ent value of a series of cash flows. Spreadsheet 8.1 is an Excel spreadsheet for the revised office project (see Figure 8.1). Cells C3 through C6 calculate the PV of each year’s cash flow by discounting at 7% for the length of time given in column A. Cell C7 calculates NPV as the sum of the PVs of all years’ cash flows. Column D shows the Excel formulas used to calculate the results in column C.

Excel also provides a built-in function to calculate NPVs. The formula is =NPV(discount rate, list of cash flows). So, instead of calculating the PV of each cash flow and summing up, we can use the NPV function in cell C9. (The formula used in that cell is shown in D9.) The first entry in the function is the discount rate expressed as a decimal, in this case .07. That is followed by B4:B6, which tells Excel to discount all cash flows in column B from cells B4 to B6.

Why is the first cash flow in the NPV formula from cell B4, which contains the cash flow for year 1, rather than B3, which contains the immediate investment in year 0? It turns out that Excel always assumes that the first cash flow comes after one period, the next after two periods, and so on. If the first cash flow actually comes at year 0, we do not want it discounted, nor do we want later cash flows discounted for an extra period. Therefore, we don’t include the immediate cash flow in the NPV function. Instead, we add it undis- counted to the NPV of other cash flows. See cell D9 for the formula.

Be careful with the timing of cash flows when you use the NPV function. If in doubt, discount each cash flow and add them up, as in cell C7.

Spreadsheet Solutions Present Values

A B C D 1 Cost of Capital: 0.07

2 Year Cash Flow ($ millions) PV Formula for Column C

(Note the = sign before formula)

3 0 −375 −375.0 =B3 4 1      25   23.4 =B4/1.07^A4 5 2       25   21.8 =B5/1.07^A5 6 3    475 387.7 =B6/1.07^A6 7 Sum (NPV):   57.9 =SUM(C3:C6) 8 9 Using Excel’s NPV function:   57.9 =NPV(.07,B4:B6) + B3

SPREADSHEET 8.1 Forecast cash flows and present values for the revised office project

The Internal Rate of Return Rule

Instead of calculating a project’s net present value, companies often prefer to ask whether the project’s return is higher or lower than the opportunity cost of capital. For example, think back to the original proposal to build an office block. You planned to invest $350,000 to get back a cash flow of C1 = $400,000 in 1 year. Therefore, you forecast a profit on the venture of $400,000 – $350,000 = $50,000. In a one-period

8.2

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246 Part Two Value

project like this one, it is easy to calculate the rate of return. Simply compute end-of- year profit per dollar invested in the project:

Rate of return = profit _________ investment = C1 − investment ______________ investment =

$400,000 − $350,000 __________________ $350,000

= .1429, or about 14.3%

The alternative of investing in a U.S. Treasury bill would provide a return of only 7%. Thus, the return on your office building is higher than the opportunity cost of capital.2

This suggests two rules for deciding whether to go ahead with an investment project:

1. The NPV rule. Invest in any project that has a positive NPV when its cash flows are discounted at the opportunity cost of capital.

2. The rate of return rule. Invest in any project offering a rate of return that is higher than the opportunity cost of capital.

Both rules set the same cutoff point. An investment that is on the knife edge with an NPV of zero will also have a rate of return that is just equal to the cost of capital.

Suppose that the rate of interest on Treasury securities is not 7% but 14.3%. Because your office project also offers a return of 14.3%, the rate of return rule suggests that you will be indifferent between taking the project and leaving your money in Treasury securities.

The NPV rule likewise tells you that if the interest rate is 14.3%, the project is evenly balanced with an NPV of zero:

NPV = C0 + C1 _____ 1 + r = −$350,000 +

$400,000 ________ 1.143 = 0

The project would make you neither richer nor poorer; it is worth just what it costs. Thus, the NPV rule and the rate of return rule both give the same decision on accept- ing the project.

A Closer Look at the Rate of Return Rule We know that if the office project’s cash flows are discounted at a rate of 7%, the proj- ect has a net present value of $23,832. If they are discounted at a rate of 14.3%, it has an NPV of zero. Figure 8.2 plots the project’s NPV for a variety of discount rates. This is often called the NPV profile of the project. Notice two important things about Figure 8.2:

1. The project rate of return (in our example, 14.3%) is also the discount rate that would give the project a zero NPV. This gives us a useful definition: The rate of return is the discount rate at which NPV equals zero.

2. If the opportunity cost of capital is less than the project rate of return, then the NPV of your project is positive. If the cost of capital is greater than the project rate of return, then NPV is negative. Thus, for this accept-or-reject decision, the rate of return rule and the NPV rule are equivalent.

Calculating the Rate of Return for Long-Lived Projects There is no ambiguity in calculating the rate of return for an investment that generates a single payoff after one period. But how do we calculate return when the project pro- duces cash flows in several periods? Just think back to the definition that we intro- duced above—the project rate of return is also the discount rate that gives the project

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IRR is the discount rate at which NPV = 0

2 Recall that we are assuming the profit on the office building is risk-free. Therefore, the opportunity cost of capital is the rate of return on other risk-free investments.

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Chapter 8 Net Present Value and Other Investment Criteria 247

a zero NPV. We can use this idea to find the return on a project that has many cash flows. The discount rate that gives the project a zero NPV is known as the proj- ect’s internal rate of return, or IRR. It is also called the discounted cash-flow (DCF) rate of return.

Let’s calculate the IRR for the revised office project. If you rent out the office block for 3 years, the cash flows are as follows:

FIGURE 8.2 The value of the office project is lower when the discount rate is higher. The project has a positive NPV if the discount rate is less than 14.3%.

N et

p re

se nt

v al

ue ($

th ou

sa nd

s)

Discount rate (%)

-80

-60

-40

-20

0

20

40

60

120 4 8 2016

Rate of return = 14.3%

NPV profile

24 32 3628 40

Year: 0 1 2 3

Cash flows –$375,000 +$25,000 +$25,000 +$475,000

The IRR is the discount rate at which these cash flows would have zero NPV. Thus,

NPV = −$375,000 + $25,000 _______ 1 + IRR

+ $25,000 _________ (1 + IRR)2

+ $475,000 _________ (1 + IRR)3

= 0

There is no simple general method for solving this equation to find the IRR. You have to rely on a little trial and error. Let us arbitrarily try a zero discount rate. This gives an NPV of $150,000:

NPV = −$375,000 + $25,000 _______ 1.0

+ $25,000 _______ (1.0)2

+ $475,000 ________ (1.0)3

= $150,000

With a zero discount rate, the NPV is positive. So it looks as if the IRR is greater than zero.

The next step might be to try a discount rate of 50%. In this case, NPV is –$206,481:

NPV = −$375,000 + $25,000 _______ 1.50

+ $25,000 _______ (1.50)2

+ $475,000 ________ (1.50)3

= −$206,481

At this higher discount rate, NPV turns negative. So the IRR should lie somewhere between zero and 50%. In Figure 8.3, we have plotted the net present values for a range of discount rates. You can see that a discount rate of 12.56% gives an NPV of zero. Therefore, the IRR is 12.56%. You can always find the IRR by plotting an NPV pro- file, as in Figure 8.3, but it is quicker and more accurate to let a spreadsheet or spe- cially programmed financial calculator do the trial and error for you. The nearby Spreadsheet Solution and Financial Calculator boxes illustrate how to do so.

The rate of return rule tells you to accept a project if the rate of return exceeds the opportunity cost of capital. You can see from Figure 8.3 why this makes sense. Because the NPV profile is downward-sloping, the project has a positive NPV as long as the opportunity cost of capital is less than the project’s 12.56% IRR. If the opportunity

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248 Part Two Value

cost of capital is higher than the 12.56% IRR, NPV is negative. Therefore, when we compare the project IRR with the opportunity cost of capital, we are effectively asking whether the project has a positive NPV. This was true for our one-period office proj- ect. It is also true for our three-period office project. Thus, the rate of return rule will give the same answer as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases.3

The usual agreement between the net present value and internal rate of return rules should not be a surprise. Both are discounted cash-flow methods of choosing between projects. Both are concerned with identifying those projects that make shareholders better off, and both recognize that companies always have a choice: They can invest in a project, or if the project is not sufficiently attractive, they can give the money back to shareholders and let them invest it for themselves in the capital market.

FIGURE 8.3 The internal rate of return is the discount rate at which NPV equals zero.

N et

p re

se nt

v al

ue ($

th ou

sa nd

s)

Discount rate (%)

-100

-150

-50

0

50

100

150

12 140 4 62 8 10 20 2216 18 24 26 28 30

NPV profile

IRR = 12.56%

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Interpreting the IRR

Suppose the cash flow in year 3 is only $420,000. Redraw Figure 8.3. How would the IRR change?

Self-Test8.2

A Word of Caution Some people confuse the internal rate of return on a project with the opportunity cost of capital. Remember that the project IRR measures the profitability of the project. It is an internal rate of return in the sense that it depends only on the project’s own cash flows. The opportunity cost of capital is the standard for deciding whether to accept the project. It is equal to the return offered by equivalent-risk investments in the capital market.

Some Pitfalls with the Internal Rate of Return Rule Many firms use the internal rate of return rule instead of net present value. We think that this is a pity. When used properly, the two rules lead to the same decision, but the rate of return rule has several pitfalls that can trap the unwary. In particular, it is poorly suited to choosing between two (or more) competing proposals. Here are three examples.

3 In Chapter 6, we showed how to calculate the yield to maturity on a bond. A bond’s yield to maturity is simply its IRR by another name.

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249

Pitfall 1: Mutually Exclusive Projects We have seen that firms are seldom faced with take-it-or-leave-it projects. Usually, they need to choose from a number of mutu- ally exclusive alternatives. Given a choice between several competing projects, you should accept the one that adds most to shareholder wealth. This is the one with the highest NPV.

But what about the rate of return rule? Would it make sense just to choose the proj- ect with the highest internal rate of return? Unfortunately, no. Mutually exclusive proj- ects involve a dangerous pitfall for users of the IRR rule.

Consider once more the two office-block proposals from Section 8.1. You initially intended to invest $350,000 in the building and then sell it at the end of the year for $400,000. Under the revised proposal, you planned to invest $375,000, rent out the offices for 3 years at a fixed annual rent of $25,000, and then sell the building for $450,000. The following table shows the cash flows, IRRs, and NPVs for the two projects:

Calculating internal rate of return in Excel is as easy as listing the project cash flows. For example, to calculate the IRR of the office-block project, you could simply type in its cash flows as in the spreadsheet shown here, and then calculate IRR as we do in cell E4. As always, the interest rate is returned as a decimal.

Spreadsheet Solutions Internal Rate of Return

A B C D E F

1 Calculating IRR by using a spreadsheet 2 3 Year Cash Flow Formula 4 0 –375,000 IRR= 0.1256 =IRR(B4:B7) 5 1 25,000 6 2 25,000 7 3 475,000

Year: 0 1 2 3 IRR NPV at 7%

Initial proposal –350,000 +400,000 14.29% +$23,832 Revised proposal –375,000 +25,000 +25,000 +475,000 12.56% +$57,942

Both projects are good investments; both offer a positive NPV. But the revised proposal has the higher net present value and, therefore, is the better choice. Unfortunately, the superiority of the revised proposal doesn’t show up as a higher rate of return. The IRR rule seems to say you should go for the initial proposal because it has the higher IRR. If you follow the IRR rule, you have the satisfaction of earning a 14.29% rate of return; if you use NPV, you are nearly $58,000 richer.

Figure 8.4 shows why the IRR rule gives the wrong signal. The figure plots the NPV of each project for different discount rates. These two NPV profiles cross at an interest rate of 11.72%. So if the opportunity cost of capital is higher than 11.72%, the initial proposal, with its rapid cash inflow, is the superior investment. If the cost of capital is lower than 11.72%, then the revised proposal dominates. Depending on the discount rate, either proposal may be superior. For the 7% cost of capital that we have assumed, the revised proposal is the better choice.

Now consider the IRR of each proposal. The IRR is simply the discount rate at which NPV equals zero, that is, the discount rate at which the NPV profile crosses the horizontal axis in Figure 8.4. As noted, these rates are 14.29% for the initial proposal and 12.56% for the revised proposal. However, as you can see from Figure 8.4, the higher IRR for the initial proposal does not mean that it has a higher NPV.

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250

In our example, both projects involved the same outlay, but the revised proposal had the longer life. The IRR rule mistakenly favored the quick payback project with the high percentage return but the lower NPV. Remember, a high IRR is not an end in itself. You want projects that increase the value of the firm. Projects that earn a good rate of return for a long time often have higher NPVs than those that offer high percentage rates of return but die young.

FIGURE 8.4 The initial proposal offers a higher IRR than the revised proposal, but its NPV is lower if the discount rate is less than 11.72%

The calculator should display the value 12.56%, the project’s internal rate of return.

To calculate project NPV, the procedure is similar. You need to enter the discount rate in addition to the project cash flows, and then simply press the NPV key. Here is the specific sequence of keystrokes, assuming that the opportunity cost of capital is 7%:

–375,000 CFj 25,000 CFj

25,000 CFj

475,000 CFj

7 I/YR

{NPV}

The calculator should display the value 57,942, the project’s NPV when the discount rate is 7%.

By the way, you can check that NPV = 0 when the dis- count rate equals the IRR. Enter 12.56 (the project’s IRR) as the interest rate, and you will find that NPV is just about zero (it is not exactly zero because we are rounding off the IRR to only two decimal places).

We saw in Chapter 5 that the formulas for the present and future values of level annuities and one-time cash flows are built into financial calculators. However, as the example of the office block illustrates, most investment projects entail multi- ple cash flows that cannot be expected to remain level over time. Fortunately, many calculators are equipped to handle problems involving a sequence of uneven cash flows. In gen- eral, the procedure is quite simple. You enter the cash flows one by one into the calculator, and then you press the IRR key to find the project’s internal rate of return. The first cash flow you enter is interpreted as coming immediately, the next cash flow is interpreted as coming at the end of one period, and so on. We can illustrate using the office block as an example. To find the project IRR, you would use the following sequence of keystrokes:*

Financial Calculator Using Financial Calculators to Find NPV and IRR

* Various calculators entail minor variations on these key strokes. For example, on the HP12C, the first cash flow is entered using the CF0 key, to signify that the cash flow comes immediately and not after 1 year. The other cash flows are entered using the CFj key. On the Texas Instruments BAII Plus calculator, you would begin by hitting the CF key to signify that the following entries should be interpreted as cash flows. Each cash flow entry is then followed by the down arrow, rather than the CFj key. After hitting the IRR key, you would then hit CPT (the compute key). If you don’t have your own financial calculator, you can download an emulator onto your computer or phone and practice using that. See the nearby Beyond the Page icon.

–375,000 CFj 25,000 CFj

25,000 CFj

475,000 CFj

{IRR/YR}

Finding NPV and IRR on financial calculators

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N P

V ($

t ho

us an

ds )

Discount rate (%)

-75

-50

-25

0

25

50

75

150

125

100

10860 2 4 1814 1612 20

IRR = 12.56%

IRR = 14.29%

Revised proposal

Initial proposal

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Chapter 8 Net Present Value and Other Investment Criteria 251

Pitfall 1a: Mutually Exclusive Projects Involving Different Outlays A similar misranking also may occur when comparing projects with the same lives but different outlays. In this case, the IRR may mistakenly favor small projects with high rates of return but low NPVs. When you are faced with a straightforward either-or choice, the simple solution is to compare their NPVs. However, if you are determined to use the IRR rule, there is a way to do so. We explain how in the appendix.

A rich, friendly, and probably slightly unbalanced benefactor offers you the opportunity to invest $1 million in two mutually exclusive ways. The payoffs are:

a. $2 million after 1 year, a 100% return. b. $300,000 a year forever.

Neither investment is risky, and safe securities are yielding 7%. Which invest- ment will you take? You can’t take both, so the choices are mutually exclusive. Do you want to earn a high percentage return, or do you want to be rich?

Self-Test8.3

Your wacky benefactor (see Self-Test 8.3) now offers you the choice of two opportunities:

a. Invest $1,000 today and quadruple your money—a 300% return—in 1 year with no risk.

b. Invest $1 million for 1 year at a guaranteed 50% return.

Which will you take? Do you want to earn a wonderful rate of return (300%), or do you want to be rich? Safe securities still yield 7%.

Self-Test8.4

Pitfall 2: Lending or Borrowing? Remember our condition for the IRR rule to work: The project’s NPV must fall as the discount rate increases. Now consider the following projects:

Cash Flows (dollars)

Project C0 C1 IRR (%) NPV at 10%

A −100 +150 +50 +$36.4 B +100 –150 +50 –36.4

Each project has an IRR of 50%. In other words, if you discount the cash flows at 50%, both projects would have zero NPV.

Does this mean that the two projects are equally attractive? Clearly not. In the case of project A we are paying out $100 now and getting $150 back at the end of the year. That is better than any bank account. But what about project B? Here we are getting paid $100 now, but we have to pay out $150 at the end of the year. That is equivalent to borrowing money at 50%.

If someone asked you whether 50% was a good rate of interest, you could not answer unless you also knew whether that person was proposing to lend or borrow at

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252 Part Two Value

that rate. Lending money at 50% is great (as long as the borrower does not flee the country), but borrowing at 50% is not usually a good deal (unless, of course, you plan to flee the country). When you lend money, you want a high rate of return; when you borrow, you want a low rate of return.

If you plot a graph like Figure 8.2 for project B, you will find the NPV increases as the discount rate increases. (Try it!) Obviously, the rate of return rule will not work in this case.

Project B is a fairly obvious trap, but if you want to make sure you don’t fall into it, calculate the project’s NPV. For example, suppose that the cost of capital is 10%. Then the NPV of project A is +$36.4 and the NPV of project B is –$36.4. The NPV rule correctly warns us away from a project that is equivalent to borrowing money at 50%.

When NPV rises as the interest rate rises, the rate of return rule is reversed: A project is acceptable only if its internal rate of return is less than the opportunity cost of capital.

Pitfall 3: Multiple Rates of Return Here is a tricky problem: King Coal Corpora- tion is considering a project to strip-mine coal. The project requires an investment of $210 million and is expected to produce a cash inflow of $125 million in the first 2 years, building up to $175 million in years 3 and 4. However, the company is obliged in year 5 to reclaim the land at a cost of $400 million. At a 20% opportunity cost of capital, the project has an NPV of $5.9 million.

To find the IRR of King Coal’s project, we have calculated the NPV for various discount rates and plotted the results in Figure 8.5. You can see that there are two dis- count rates at which NPV = 0. That is, each of the following statements holds:

NPV = −210 + $125 _____ 1.03

+ 125 _____ 1.032

+ 175 _____ 1.033

+ 175 _____ 1.034

− 400 _____ 1.035

= 0

and

NPV = −210 + $125 _____ 1.25

+ 125 _____ 1.252

+ 175 _____ 1.253

+ 175 _____ 1.254

− 400 _____ 1.255

= 0

In other words, the investment has an IRR of both 3% and 25%. The reason for this is the double change in the sign of the cash flows. There can be as many different inter- nal rates of return as there are changes in the sign of the cash-flow stream.4

FIGURE 8.5 King Coal’s project has two internal rates of return. NPV = 0 when the discount rate is either 3% or 25%.

N et

p re

se nt

v al

ue ($

m ill

io ns

)

Discount rate (%)

-10

-15

-5

0

5

10

15

13 150 5 71 3 9 11 21 2317 19 25 27 29 3331 35

IRR = 25% IRR = 3%

4 There may be fewer IRRs than the number of sign changes. You may even encounter projects for which there is no IRR. For example, there is no IRR for a project that has cash flows of +$1,000 in year 0, −$3,000 in year 1, and +$2,500 in year 2. If you don’t believe us, try plotting NPV for different discount rates. Can such a project ever have a negative NPV?

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Chapter 8 Net Present Value and Other Investment Criteria 253

Is the coal mine worth developing? The simple IRR rule—accept if the IRR is greater than the cost of capital—won’t help. For example, you can see from Figure 8.5 that with a low cost of capital (less than 3%) the project has a negative NPV. It has a positive NPV only if the cost of capital is between 3% and 25%.

Decommissioning and clean-up costs, which make King Coal’s final cash flow neg- ative, can sometimes be huge. For example, the ultimate cost of removing North Sea oil platforms in the United Kingdom has been estimated at $75 billion. It can cost $500 million to decommission a nuclear power plant. These are obvious examples where cash flows go from positive to negative, but you can probably think of a number of other cases where the company needs to plan for later expenditures. Ships periodi- cally need to go into dry dock for a refit, hotels may receive a major facelift, machine parts may need replacement, and so on.

Whenever the cash-flow stream is expected to change sign more than once, the proj- ect typically has more than one IRR and there is no simple IRR rule. It is possible to get around the problem of multiple rates of return by calculating a modified internal rate of return (MIRR). We explain how to do so in the appendix to this chapter. However, it is much easier in such cases to abandon the IRR rule and just calculate project NPV.

The Profitability Index

The profitability index measures the net present value of a project per dollar of investment:

Profitability index = net present value ______________ initial investment (8.2)

For example, our initial proposal to construct an office building involved an invest- ment of $350,000 and had an NPV of $23,832. Its profitability index5 was

23,832 _______ 350,000 = .068

The profitability index is also known as the benefit-cost ratio. The “benefit” of the project is its net present value. The “cost” is the required investment. The index mea- sures the benefit realized per dollar of cost.

Any project with a positive profitability index must also have a positive NPV, so it would seem that either criterion must result in identical decisions. Why go to the trou- ble of calculating the profitability index? The answer is that whenever there is a limit on the amount the company can spend, it makes sense to concentrate on getting the biggest bang for each investment buck. In other words, when there is a shortage of funds, the firm needs to pick those projects that have the highest profitability index.

Let us illustrate. Assume that you are faced with the following investment opportunities:

8.3

profitability index Ratio of net present value to initial investment.

Cash Flows ($ millions)

Project C0 C1 C2 NPV at 10% Profitability Index

C −10 +30 +5 21 21/10 = 2.1 D −5 +5 +20 16 16/5 = 3.2 E −5 +5 +15 12 12/5 = 2.4

5 Sometimes the profitability index is defined as the ratio of total present value (rather than net present value) to required investment. By this definition, all the profitability indexes calculated below are increased by 1. For example, the office building’s profitability index would be PV/investment = 373,832/350,000 = 1.068. Note that project rankings under either definition are identical.

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254 Part Two Value

All three projects are attractive, but suppose that the firm is limited to spending $10 million. In that case, you can invest either in project C or in projects D and E, but you can’t invest in all three. The solution is to start with the project that has the highest profitability index and continue until you run out of money. In our example, D provides the highest NPV per dollar invested, followed by E. These two projects exactly use up the $10 million budget. Between them they add $28 million to shareholder wealth. The alternative of investing in C would have added only $21 million.

Capital Rationing Economists use the term capital rationing to refer to a shortage of funds available for investment. In simple cases of capital rationing, the profitability index can measure which projects to accept.6 But that raises a question. Most large corporations can obtain very large sums of money on fair terms and at short notice. So why does top management sometimes tell subordinates that capital is limited and that they may not exceed a specified amount of capital spending? There are two reasons.

Soft Rationing For many firms, the limits on capital funds are “soft.” By this we mean that the capital rationing is not imposed by investors. Instead, the limits are imposed by top management. For example, suppose that you are an ambitious, upwardly mobile junior manager. You are keen to expand your part of the business, and as a result you tend to overstate the investment opportunities. Rather than trying to determine which of your many bright ideas are truly worthwhile, senior management may find it simpler to impose a limit on the amount that you and other junior managers can spend. This limit forces you to set your own priorities.

Even if capital is not rationed, other resources may be. For example, very rapid growth can place considerable strains on management and the organization. A some- what rough-and-ready response to this problem is to ration the amount of capital that the firm spends.

Hard Rationing Soft rationing should never cost the firm anything. If the limits on investment become so tight that truly good projects are being passed up, then manage- ment should raise more money and relax the limits it has imposed on capital spending. But what if there is “hard rationing,” meaning that the firm actually cannot raise the money it needs? This may not be a common problem for large, publicly owned corpo- rations, but in many countries some of the largest businesses are owned by the govern- ment. Suppose that you are the manager of a state-owned enterprise, where you do not have the freedom to raise new capital. In that case, you may be forced to pass up positive-NPV projects. You may still be interested in net present value, but you now need to select the package of projects that is within the company’s resources and yet gives the highest net present value. This is when the profitability index can be useful.

Pitfalls of the Profitability Index The profitability index is sometimes used to rank projects even when there is neither soft nor hard capital rationing. In this case the unwary user may be led to favor small projects over larger projects that have higher NPVs. The profitability index was designed to select projects with the most bang per buck—the greatest NPV per dollar spent. That’s the right objective when bucks are limited. When they are not, a bigger bang is always better than a smaller one, even when more bucks are spent. This is another case where project comparisons can go awry once we abandon the NPV rule. Self-Test 8.5 is a numerical example.

capital rationing Limit set on the amount of funds available for investment.

6 Unfortunately, when capital is rationed in more than one period, or when personnel, production capacity, or other resources are rationed in addition to capital, it isn’t always possible to get the NPV-maximizing package just by ranking projects on their profitability index. Tedious trial and error may be called for, or linear program- ming methods may be used.

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Chapter 8 Net Present Value and Other Investment Criteria 255

The Payback Rule

A project with a positive net present value is worth more than it costs. So whenever a firm invests in such a project, it is making its shareholders better off.

These days almost every large corporation calculates the NPV of proposed invest- ments, but management may also consider other criteria when making investment decisions. When properly used, the internal rate of return and profitability index lead to the same decisions as net present value. However, payback is no better than a very rough guide to an investment’s worth.

We suspect that you have often heard conversations that go something like this: “A washing machine costs about $800. But we are currently spending $6 a week, or around $300 a year, at the Laundromat. So the washing machine should pay for itself in less than 3 years.” You have just encountered the payback rule.

A project’s payback period is the length of time before you recover your initial investment. For the washing machine the payback period was just under 3 years. The payback rule states that a project should be accepted if its payback period is less than a specified cutoff period. For example, if the cutoff period is 4 years, the wash- ing machine makes the grade; if the cutoff is 2 years, it doesn’t.

As a rough rule of thumb, the payback rule may be adequate, but it is easy to see that it can lead to nonsensical decisions, especially when used to compare projects. For example, compare projects F and G. Project F has a 2-year payback and a large posi- tive NPV. Project G also has a 2-year payback but a negative NPV. Project F is clearly superior, but the payback rule ranks both equally. This is because payback does not consider any cash flows that arrive after the payback period. A firm that uses the pay- back criterion with a cutoff of 2 or more years would accept both F and G despite the fact that only F would increase shareholder wealth.

Cash Flows (dollars) Payback Period (years)

NPV at 10%Project C0 C1 C2 C3

F –2,000 +1,000 +1,000 +10,000 2 $7,249 G –2,000 +1,000 +1,000 0 2 –264 H –2,000 0 +2,000 0 2 –347

A second problem with payback is that it gives equal weight to all cash flows arriv- ing before the cutoff period, despite the fact that the more distant flows are less valu- able. For example, look at project H. It also has a payback period of 2 years, but it has an even lower NPV than project G. Why? Because its cash flows arrive later within the payback period.

To use the payback rule, a firm has to decide on an appropriate cutoff period. If it uses the same cutoff regardless of project life, it will tend to accept too many short- lived projects and reject too many long-lived ones. The payback rule will bias the firm against accepting long-term projects because cash flows that arrive after the payback period are ignored.

8.4

payback period Time until cash flows recover the initial investment in the project.

Calculate the profitability indexes of the two pairs of mutually exclusive invest- ments in Self-Tests 8.3 and 8.4. Use a 7% discount rate. Does the profitability index give the right ranking in each case?

Self-Test8.5

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256 Part Two Value

The primary attraction of the payback criterion is its simplicity. But remember that the hard part of project evaluation is forecasting the cash flows, not doing the arithme- tic. Today’s spreadsheets make discounting a trivial exercise. Therefore, the payback rule saves you only the easy part of the analysis.

We have had little good to say about payback. So why do many companies continue to use it? Senior managers don’t truly believe that all cash flows after the payback period are irrelevant. It seems more likely (and more charitable to those managers) that payback survives because there are some offsetting benefits. Thus, managers may point out that payback is the simplest way to communicate an idea of project desirabil- ity. Investment decisions require discussion and negotiation between people from all parts of the firm, and it is important to have a measure that everyone can understand. Perhaps, also, managers favor quick payback projects even when the projects have lower NPVs because they believe that quicker profits mean quicker promotion. That takes us back to Chapter 1, where we discussed the need to align the objectives of managers with those of the shareholders.

In practice, payback is most commonly used when the capital investment is small or when the merits of the project are so obvious that more formal analysis is unnecessary. For example, if a project is expected to produce constant cash flows for 10 years and the payback period is only 2 years, the project in all likelihood has a positive NPV.

Discounted Payback Sometimes managers calculate the discounted-payback period. This is the number of periods before the present value of prospective cash flows equals or exceeds the initial investment. The discounted-payback measure asks, How long must the project last in order to offer a positive net present value? If the discounted payback meets the com- pany’s cutoff period, the project is accepted; if not, it is rejected. The discounted- payback rule has the advantage that it will never accept a negative-NPV project. On the other hand, it still takes no account of cash flows after the cutoff date, so a com- pany that uses the discounted-payback rule risks rejecting good long-term projects and can easily misrank competing projects.

Rather than automatically rejecting any project with a long discounted-payback period, many managers simply use the measure as a warning signal. These managers don’t unthinkingly reject a project with a long discounted-payback period. Instead, they check that the proposer is not unduly optimistic about the project’s ability to gen- erate cash flows into the distant future. They satisfy themselves that the equipment truly has a long life or that competitors will not enter the market and eat into the proj- ect’s cash flows.

A machine costs $700 and will generate annual cash flows of $100 for 20 years. What is the payback period? If the interest rate is 7.1%, what is the discounted payback period? What is the project NPV? Should the project be accepted?

Self-Test8.6

More Mutually Exclusive Projects

We’ve seen that almost all real-world decisions entail either-or choices between com- peting alternatives. A real estate developer can build an apartment block or an office block on an available lot. Either can be heated with oil or with natural gas. Building

8.5

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Chapter 8 Net Present Value and Other Investment Criteria 257

can start today or a year from now. All of these choices are said to be mutually exclu- sive. When choosing between mutually exclusive projects, we must calculate the NPV of each alternative and choose the one with the highest positive NPV.

Sometimes, it is enough simply to compare the NPV of two or more projects. But in other cases, the choices you make today will affect your future investment opportuni- ties. In that case, choosing between competing projects can be trickier. Here are three important, but often challenging, problems:

∙ The investment timing problem. Should you buy a computer now or wait and think about it again next year? (Here, today’s investment is competing with possible future investments.)

∙ The choice between long- and short-lived equipment. Should the company save money today by installing cheaper machinery that will not last as long? (Here, today’s decision would accelerate a later investment in machine replacement.)

∙ The replacement problem. When should existing machinery be replaced? (Using it another year could delay investment in more modern equipment.)

We will look at each of these problems in turn.

Problem 1: The Investment Timing Decision In Example 8.1, Obsolete Technologies is contemplating the purchase of a new com- puter system. The proposed investment has a net present value of almost $20,000, so it appears that the cost savings would easily justify the expense of the system. However, the financial manager is not persuaded. She reasons that the price of computers is con- tinually falling and, therefore, suggests postponing the purchase, arguing that the NPV of the system will be even higher if the firm waits until the following year. Unfortu- nately, she has been making the same argument for 10 years, and the company is steadily losing business to competitors with more efficient systems. Is there a flaw in her reasoning?

This is a problem in investment timing. When is it best to commit to a positive-NPV investment? Investment timing problems all involve choices between mutually exclu- sive investments. You can either proceed with the project now or do so later. You can’t do both.

Table 8.1 lays out the basic data for Obsolete. You can see that the cost of the com- puter is expected to decline from $50,000 today to $45,000 next year, and so on. The new computer system is expected to last for 4 years from the time it is installed. The present value of the savings at the time of installation is expected to be $70,000. Thus, if Obsolete invests today, it achieves an NPV of $70,000 – $50,000 = $20,000; if it invests next year, it will have an NPV of $70,000 – $45,000 = $25,000.

Isn’t a gain of $25,000 better than one of $20,000? Well, not necessarily—you may prefer to be $20,000 richer today than $25,000 richer next year. Your decision should depend on the cost of capital. The final column of Table 8.1 shows the value today (year 0) of those net present values at a 10% cost of capital. For example, you can see

Year of Purchase

Cost of Computer PV Savings

NPV at Year of Purchase (r = 10%) NPV Today

0 $50 $70 $20 $20.0 1   45   70   25   22.7 2   40   70   30   24.8 3   36   70   34   25.5 ⟵ optimal purchase date 4   33   70   37   25.3 5   31   70   39   24.2

TABLE 8.1 Obsolete Technologies: The gain from purchase of a computer is rising, but the NPV today is highest if the computer is purchased in year 3 (dollar values in thousands)

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258 Part Two Value

that the discounted value of that $25,000 gain is $25,000/1.10 = $22,700. The finan- cial manager has a point. It is worth postponing investment in the computer: Today’s NPV is higher if she waits a year. But the investment should not be postponed indefi- nitely. You maximize net present value today by buying the computer in year 3.

Notice that you are involved in a trade-off. The sooner you can capture the $70,000 savings the better, but if it costs you less to realize those savings by postponing the investment, it may pay for you to wait. If you postpone purchase by 1 year, the gain from buying a computer rises from $20,000 to $25,000, an increase of 25%. Because the cost of capital is only 10%, it pays to postpone at least until year 1. If you postpone from year 3 to year 4, the gain rises from $34,000 to $37,000, a rise of just under 9%. Because this is less than the cost of capital, this postponement would not make sense. The decision rule for investment timing is to choose the investment date that pro- duces the highest net present value today.

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Investment timing decisions

Unfortunately, Obsolete Technologies’ business is shrinking as the company dithers and dawdles. Its chief financial officer realizes that the savings from installing the new computer will likewise shrink by $4,000 per year, from a pres- ent value of $70,000 now, to $66,000 next year, then to $62,000, and so on. Redo Table 8.1 with this new information. When should Obsolete buy the new computer?

Self-Test8.7

Problem 2: The Choice between Long- and Short-Lived Equipment Suppose the firm is forced to choose between two machines, I and J. The machines are designed differently but have identical capacity and do exactly the same job. Machine I costs $15,000 and will last 3 years. It costs $4,000 per year to run. Machine J is an “economy” model, costing only $10,000, but it will last only 2 years and costs $6,000 per year to run.

Because the two machines produce exactly the same product, the only way to choose between them is on the basis of cost. Suppose we compute the present value of the costs:

Costs (thousands of dollars)

Year: 0 1 2 3 PV at 6%

Machine I 15 4 4 4 $25.69 Machine J 10 6 6 —   21.00

Should we take machine J, the one with the lower present value of costs? Not neces- sarily. All we have shown is that machine J offers 2 years of service for a lower total cost than 3 years of service from machine I. But is the annual cost of using J lower than that of I?

Suppose the financial manager in corporate headquarters agrees to buy machine I and pay for its operating costs out of her budget. She then charges the plant manager an annual amount for use of the machine. There will be three equal payments starting in year 1. Obviously, the financial manager has to make sure that the present value of these payments equals the present value of the costs of machine I, $25,690. When the

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Chapter 8 Net Present Value and Other Investment Criteria 259

discount rate is 6%, the payment stream with such a present value turns out to be $9,610 a year. In other words, the cost of buying and operating machine I over its 3-year life is equivalent to an annual charge of $9,610 a year for 3 years. This figure is therefore termed the equivalent annual annuity of operating machine I.

Costs (thousands of dollars)

Year: 0 1 2 3 PV at 6%

Machine I 15 4 4 4 $25.69 Equivalent annual annuity 9.61 9.61 9.61   25.69

How did we know that an annual charge of $9,610 has a present value of $25,690? The annual charge is a 3-year annuity. So we calculate the value of this annuity and set it equal to $25,690:

Equivalent annual annuity × 3-year annuity factor = PV of costs = $25,690

If the cost of capital is 6%, the 3-year annuity factor is 2.6730. So

Equivalent annual annuity = PV of costs _________________ 3-year annuity factor (8.3)

= $25,690 _________________ 3-year annuity factor = $25,690 _______ 2.6730 = $9,610

If we make a similar calculation of costs for machine J, we get:

Costs (thousands of dollars)

Year: 0 1 2 PV at 6%

Machine J 10 6 6 $21.00 Equivalent annual annuity 11.45 11.45   21.00

We see now that machine I is better because its equivalent annual cost is less ($9,610 for I versus $11,450 for J). In other words, the financial manager could afford to set a lower annual charge for the use of I. We thus have a rule for comparing assets with different lives: Select the machine that has the lowest equivalent annual annuity.

Think of the equivalent annual annuity as the level annual charge that is necessary to recover the present value of investment outlays and operating costs.7 The annual charge continues for the life of the equipment. Calculate the equivalent annual annuity by dividing the present value by the annuity factor.

equivalent annual annuity The cash flow per period with the same present value as the cost of buying and operating a machine.

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Equivalent annual annuities

7 We have implicitly assumed that inflation is zero. If that is not the case, it would be better to calculate the equivalent annual annuities for machines I and J in real terms, using the real rate of interest to calculate the annuity factor.

Equivalent Annual Annuity

You need a car for at least 7 years. You can purchase one outright for $15,000 and sell it in 7 years for $500. The auto dealer also offers 7-year leases. If the discount rate is 10%, what is the maximum lease payment you would be willing to pay?

The present value of the cost of purchasing is

PV = $15,000 − $500 ______ (1.10)7

= $14,743

Example 8.3 ⊲

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260 Part Two Value

Problem 3: When to Replace an Old Machine Our earlier comparison of machines I and J took the life of each machine as fixed. In practice, the point at which equipment is replaced reflects economics, not physical collapse. We, rather than nature, usually decide when to replace. For example, we usu- ally replace a car not when it finally breaks down but when it becomes more expensive and troublesome to maintain than a replacement.

Here is an example of a replacement problem: You are operating an old machine that will last 2 more years before it gives up the ghost. It costs $12,000 per year to operate. You can replace it now with a new machine that costs $25,000 but is much more efficient (only $8,000 per year in operating costs) and will last for 5 years. Should you replace the machine now or stick with it for a while longer? The opportunity cost of capital is 6%.

We calculate the NPV of the new machine and its equivalent annual annuity in the following table:

Thus, the equivalent annual cost of purchasing the car is the annuity with this present value:

Equivalent annual annuity × 7-year annuity factor at 10% = PV costs of buying = $14,743

Equivalent annual annuity = $14,743 _________________ 7-year annuity factor = $14,743

_______ 4.8684 = $3,028

Therefore, purchasing the car and eventually selling it after 7 years would entail the same present value as paying $3,028 annually for each of those 7 years. You should be willing to pay up to $3,028 annually to lease. ■

Another Equivalent Annual Annuity

Low-energy light bulbs typically cost $3.50, have a life of 9 years, and use about $3.19 of electricity a year. Conventional light bulbs are cheaper to buy because they cost only $.50. On the other hand, they last only about a year and use about $11.25 of energy. If the discount rate is 5%, which product is cheaper to use?

To answer this question, you need first to convert the initial cost of each bulb to an annual figure and then to add in the annual energy cost.8 The following table sets out the calculations:

Example 8.4 ⊲

It seems that a low-energy bulb provides an annual saving of about $11.77 − $3.68 = $8.09. ■

Low-Energy Bulb Conventional Bulb

1. Initial cost ($) 3.50 0.50 2. Estimated life (years) 9 1 3. Annuity factor at 5% 7.1078 0.9524 4. Equivalent annual annuity ($) = (1)/(3) 0.49 0.52 5. Annual energy cost ($) 3.19 11.25 6. Total annual cost ($) = (4) + (5) 3.68 11.77 Assumption: Energy costs are incurred at the end of each year.

Costs (thousands of dollars)

Year: 0 1 2 3 4 5 PV at 6%

New machine 25 8 8 8 8 8 $58.70 Equivalent annual annuity 13.93 13.93 13.93 13.93 13.93 58.70

8 Our calculations ignore any environmental costs.

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Chapter 8 Net Present Value and Other Investment Criteria 261

The cash flows of the new machine are equivalent to an annuity of $13,930 per year. So we can equally well ask whether you would want to replace your old machine, which costs $12,000 a year to run, with a new one costing $13,930 a year. When the question is posed this way, the answer is obvious. As long as your old machine costs only $12,000 a year, why replace it with a new machine that costs $1,930 a year more?

A Last Look

We’ve covered several investment criteria, each with its own nuances. If your head is spinning, you might want to take a look at Table 8.2, which gives an overview and summary of these decision rules.

8.6

Machines K and L are mutually exclusive and have the following investment and operating costs. Note that machine K lasts for only 2 years.

Year: 0 1 2 3

K $10,000 $1,100 $1,200 — L 12,000 1,100 1,200 $1,300

a. Calculate the equivalent annual annuity of each investment by using a dis- count rate of 10%. Which machine is the better buy?

b. Now suppose you have an existing machine. You can keep it going for 1 more year only, but it will cost $2,500 in repairs and $1,800 in operating costs. Is it worth replacing now with either K or L?

Self-Test8.8

Criterion Definition Investment Rule Comments

Net present value (NPV)

Present value of cash flows minus initial investment

Accept project if NPV is positive. For mutually exclusive projects, choose the one with the highest (positive) NPV.

The “gold standard” of investment criteria. Only criterion necessarily consistent with maximizing the value of the firm. Provides appropriate rule for choosing between mutually exclusive investments. Only pitfall involves capital rationing, when one cannot accept all positive-NPV projects.

Internal rate of return (IRR)

The discount rate at which project NPV equals zero

Accept project if IRR is greater than opportunity cost of capital.

If used properly, results in same accept-reject decision as NPV in the absence of project interactions. However, beware of the following pitfalls: IRR cannot rank mutually exclusive projects—the project with higher IRR may have lower NPV. The simple IRR rule cannot be used in cases of multiple IRRs or an upward- sloping NPV profile.

Profitability index Ratio of net present value to initial investment

Accept project if profitability index is greater than 0. In case of capital rationing, accept projects with highest profitability index.

Results in same accept-reject decision as NPV in the absence of project interactions. Useful for ranking projects in case of capital rationing, but potentially misleading in the presence of interactions or in comparing projects of different size.

Payback period Time until the sum of project cash flows equals the initial investment

Accept project if payback period is less than some specified number of years.

A quick and dirty rule of thumb, with several critical pitfalls. Ignores cash flows beyond the acceptable payback period. Ignores discounting. Tends to improperly reject long-lived projects.

TABLE 8.2 A comparison of investment decision rules

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262 Part Two Value

Clearly, NPV is the gold standard. It is designed to tell you whether an investment will increase the value of the firm and by how much it will do so. It is the only rule that can always be used to rank and choose between mutually exclusive investments. The time that you need to be careful when applying the NPV rule occurs when the firm faces capital rationing. In this case, there may not be enough cash to take every project with a positive NPV, and the firm must then rank projects by the profitability index, that is, net present value per dollar invested.

For managers in the field, discounted cash-flow analysis is in fact the dominant tool for project evaluation. Table 8.3 provides a sample of the results of a large survey of chief financial officers (CFOs). Notice that 75% of firms either always or almost always use NPV or IRR to evaluate projects. The dominance of these criteria is even stronger in larger, presumably more sophisticated, firms. Despite the clear advantages of discounted cash-flow methods, however, firms do use other investment criteria to evaluate projects. For example, just over half of corporations always or almost always compute a project’s payback period. The profitability index is routinely computed by about 12% of firms.

What explains such wide use of presumably inferior decision rules? To some extent, these rules present rough reality checks on the project. As we noted in Section 8.4, managers might want to consider some simple ways to describe project profitability, even if they present obvious pitfalls. For example, managers talk casually about quick- payback projects in the same way that investors talk about high-P/E stocks. The fact that they talk about payback does not mean that the payback rule governs their deci- sions. Shortcuts like payback may work for very simple go-or-no-go decisions, but they are dangerous when used to compare projects.

Investment Criterion

Percentage of Firms That Always or Almost Always Use Criterion

Average Score on 0–4 Scale (0 = never use; 4 = always use)

All Firms Small Firms Large Firms

Internal rate of return 76 3.1 2.9 3.4 Net present value 75 3.1 2.8 3.4 Payback period 57 2.5 2.7 2.3 Profitability index 12 0.8 0.9 0.8

TABLE 8.3 Capital budgeting techniques used in practice

Source: J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” from Journal of Financial Economics, Vol. 60, Issue 2–3, May 2001, pp. 187–243. Copyright © 2001 Elsevier Science.

SUMMARY The net present value of a project measures the difference between its value and cost. NPV is, therefore, the amount that the project will add to shareholder wealth. A company maximizes shareholder wealth by accepting all projects that have a positive NPV.

Instead of asking whether a project has a positive NPV, many businesses prefer to ask whether it offers a higher return than shareholders could expect to get by investing in the capital market. Return is usually defined as the discount rate that would result in a zero NPV. This is known as the internal rate of return, or IRR. The project is attractive if the IRR exceeds the opportunity cost of capital.

There are some pitfalls in using the internal rate of return rule. Be careful about using the IRR when (1) you need to choose between two mutually exclusive projects, (2) there is more than one change in the sign of the cash flows, or (3) the early cash flows are positive.

How is the internal rate of return of a project calculated, and what must one look out for when using the internal rate of return rule? (LO8-2)

What is the net present value of an investment, and how do you calculate it? (LO8-1)

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Chapter 8 Net Present Value and Other Investment Criteria 263

If there is a shortage of capital, companies need to choose projects that offer the highest net present value per dollar of investment. This measure is known as the profitability index.

The net present value rule and the rate of return rule both properly reflect the time value of money. But companies sometimes use rules of thumb to judge projects. One is the payback rule, which states that a project is acceptable if you get your money back within a specified period. The payback rule takes no account of any cash flows that arrive after the payback period and fails to discount cash flows within the payback period.

Sometimes, a project may have a positive NPV if undertaken today but an even higher NPV if the investment is delayed. Choose between these alternatives by comparing their NPVs today.

When you have to choose between projects with different lives, you should put them on an equal footing by comparing the equivalent annual annuity of the two projects. When you are considering whether to replace an aging machine with a new one, you should com- pare the annual cost of operating the old one with the equivalent annual annuity of the new one.

Why doesn’t the payback rule always make shareholders better off? (LO8-4)

How can the net present value rule be used to analyze three common problems that involve competing projects: when to postpone an investment expenditure, how to choose between projects with unequal lives, and when to replace equipment? (LO8-5)

How is the profitability index calculated, and how can it be used to choose between projects when funds are limited? (LO8-3)

LISTING OF EQUATIONS

8.1 NPV = PV − required investment

8.2 Profitability index = net present value ______________ initial investment

8.3 Equivalent annual annuity = present value of costs __________________ annuity factor

QUESTIONS AND PROBLEMS Problems 1–9 refer to two projects with the following cash flows:

Year Project A Project B

0 −$200 −$200 1 80 100 2 80 100 3 80 100 4 80

1. IRR/NPV. If the opportunity cost of capital is 11%, which of these projects is worth pursuing? (LO8-1)

2. Mutually Exclusive Investments. Suppose that you can choose only one of these projects. Which would you choose? The discount rate is still 11%. (LO8-1)

3. IRR/NPV. Which project would you choose if the opportunity cost of capital is 16%? (LO8-1) 4. IRR. What are the internal rates of return on projects A and B? (LO8-2) 5. Investment Criteria. In light of your answers to Problems 2, 3, and 4, is the project with the

higher IRR the better project? (LO8-2)

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264 Part Two Value

6. Profitability Index. If the opportunity cost of capital is 11%, what is the profitability index for each project? (LO8-3)

7. Profitability Index. Is the project with the highest profitability index also the one with the highest NPV?  (LO8-3)

8. Payback. What is the payback period of each project? (LO8-4) 9. Investment Criteria. Is the project with the shortest payback period also the one with the high-

est NPV? (LO8-4)

10. NPV and IRR. A project that costs $3,000 to install will provide annual cash flows of $800 for each of the next 6 years. (LO8-1 and LO8-2) a. What is NPV if the discount rate is 10%?  b. How high can the discount rate be before you would reject the project? 

11. NPV. A proposed nuclear power plant will cost $2.2 billion to build and then will produce cash flows of $300 million a year for 15 years. After that period (in year 15), it must be decommis- sioned at a cost of $900 million. (LO8-1 and LO8-2) a. What is project NPV if the discount rate is 5%?  b. What if the discount rate is 18%? 

12. NPV/IRR. A new computer system will require an initial outlay of $20,000, but it will increase the firm’s cash flows by $4,000 a year for each of the next 8 years. (LO8-1) a. Is the system worth installing if the required rate of return is 9%? b. What if the required return is 14%? c. How high can the discount rate be before you would reject the project?

13. NPV/IRR. Here are the cash flows for a project under consideration: (LO8-1 and LO8-2)

C0 C1 C2

−$6,750 +$4,500 +$18,000

a. Calculate the project’s net present value for discount rates of 0, 50%, and 100%. b. What is the IRR of the project?

14. NPV versus IRR. Here are the cash flows for two mutually exclusive projects: (LO8-1 and LO8-2)

Project C0 C1 C2 C3 A −$20,000 +$8,000 +$8,000 +$ 8,000 B −20,000 0 0 +25,000

a. At what interest rates would you prefer project A to B? (Hint: Try drawing the NPV profile of each project.)

b. What is the IRR of each project?

15. NPV/IRR. Growth Enterprises believes its latest project, which will cost $80,000 to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of the first year will be $5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%. (LO8-1 and LO8-2) a. If the discount rate for this project is 10%, what is the project NPV? b. What is the project IRR?

16. IRR/NPV. Consider the following project with an internal rate of return of 13.1%. (LO8-2)

Year Cash Flow

0 +$100 1 −60 2 −60

a. Should you accept or reject the project if the discount rate is 12%? b. What is project NPV?

17. Multiple IRRs. Strip Mining Inc. can develop a new mine at an initial cost of $5 million. The mine will provide a cash flow of $30 million in 1 year. The land then must be reclaimed at a cost of $28 million in the second year. (LO8-2)

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Chapter 8 Net Present Value and Other Investment Criteria 265

a. What are the IRRs of this project? b. Should the firm develop the mine if the discount rate is 10%?  c. What if it is 20%?  d. What if it is 350%?  e. What if it is 400%?

18. IRR. Marielle Machinery Works forecasts the following cash flows on a project under consid- eration. It uses the internal rate of return rule to accept or reject projects. (LO8-2)

C0 C1 C2 C3

−$10,000 0 +$7,500 +$8,500

a. What is the project’s IRR?  b. Should this project be accepted if the required return is 12%?

19. NPV/IRR. Consider projects A and B: (LO8-2)

Cash Flows (dollars)

Project C0 C1 C2 NPV at 10%

A −30,000 21,000 21,000 +$6,446 B −50,000 33,000 33,000 +7,273

a. Calculate IRRs for A and B. b. Which project does the IRR rule suggest is better? c. Which project is really better?

20. IRR. You are offered the chance to participate in a project that produces the following cash flows:

C0 C1 C2 +$5,000 +$4,000 −$11,000

The internal rate of return is 13.6%. If the opportunity cost of capital is 12%, would you accept the offer? (What is the net present value of the project?) (LO8-2)

21. Multiple IRRs. Consider the following cash flows: (LO8-2)

C0 C1 C2 C3 C4

−$22 +$20 +$20 +$20 −$40

a. Which two of the following rates are the IRRs of this project: 2.5%, 7.2%. 14.3%, 33.7%, 40.0%?

b. What is project NPV if the discount rate is 5%? c. What if it is 20%? d. What if it is 40%?

22. Profitability Index. What is the profitability index of a project that costs $10,000 and provides cash flows of $3,000 in years 1 and 2 and $5,000 in years 3 and 4? The discount rate is 9%. (LO8-3)

23 Profitability Index. Consider the following projects: (LO8-3)

Project C0 C1 C2 A −$2,100 +$2,000 +$1,200 B −2,100 +1,440 +1,728

a. Calculate the profitability index for A and B assuming a 22% opportunity cost of capital. b. According to the profitability index rule, which project(s) should you accept?

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266 Part Two Value

24. Capital Rationing. You are a manager with an investment budget of $8 million. You may invest in the following projects. Investment and cash-flow figures are in millions of dollars. (LO8-3)

Project Discount Rate (%) Investment

Annual Cash Flow

Project Life (years)

A 10 3 1 5 B 12 4 1 8 C 8 5 2 4 D 8 3 1.5 3 E 12 3 1 6

a. Which projects should the manager choose? b. Which projects will be chosen if there is no capital rationing?

25. Profitability Index versus NPV. Consider projects A and B with the following cash flows: (LO8-3)

C0 C1 C2 C3

A −$36 +$20 +$20 +$20 B −50 +25 +25 +25

a. Which project has the higher NPV if the discount rate is 10%? b. Which has the higher profitability index? c. Which project is most attractive to a firm that can raise an unlimited amount of funds to pay

for its investment projects?  d. Which project is most attractive to a firm that is limited in the funds it can raise?

26. Investment Criteria. If you insulate your office for $10,000, you will save $1,000 a year in heating expenses. These savings will last forever. (LO8-1, LO8-2, and LO8-4) a. What is the NPV of the investment when the cost of capital is 8%? b. What if it is 10%? c. What is the IRR of the investment? d. What is the payback period on this investment?

27. Payback. A project that costs $2,500 to install will provide annual cash flows of $600 for the next 6 years. (LO8-4) a. The firm accepts projects with payback periods of less than 5 years. What is this project’s

payback period?  b. Will it be accepted? c. Should this project be pursued if the discount rate is 2%? (What is its NPV?)  d. What if the discount rate is 12%?  e. Will the firm’s decision change as the discount rate changes?

28. Payback and NPV. A project has a life of 10 years and a payback period of 10 years. Is the project NPV positive or negative? (LO8-4)

29. Payback and NPV. Here are the expected cash flows for three projects: (LO8-4)

Cash Flows (dollars)

Project Year: 0 1 2 3 4

A −5,000 +1,000 +1,000 +3,000 0 B −1,000 0 +1,000 +2,000 +3,000 C −5,000 +1,000 +1,000 +3,000 +5,000

a. What is the payback period on each of the projects? b. If you use the payback rule with a cutoff period of 2 years, which projects will you accept?

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Chapter 8 Net Present Value and Other Investment Criteria 267

c. If you use a cutoff period of 3 years, which projects will you accept? d. If the opportunity cost of capital is 10%, which projects have positive NPVs? e. “Payback gives too much weight to cash flows that occur after the cutoff date.” True or

false?

30. Investment Criteria. A new furnace for your small factory will cost $27,000 to install and will require ongoing maintenance expenditures of $1,500 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 2,400 gallons per year. Heating oil this year will cost $3 a gallon; the price per gallon is expected to increase by $.50 a year for the next 3 years and then to stabilize for the foreseeable future. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value. The discount rate is 8%. (LO8-1, LO8-2, LO8-4, and LO8-5) a. What is the net present value of the investment in the furnace? b. What is the IRR? c. What is the payback period? d. What is the equivalent annual cost of the furnace? e. What are the equivalent annual savings derived from the furnace? f. Compare the PV of the difference between the equivalent annual cost and savings over the

life of the furnace. Show that it equals the NPV of the investment in the furnace.

31. Mutually Exclusive Investments. Here are the cash-flow forecasts for two mutually exclusive projects: (LO8-5)

Cash Flows (dollars)

Year Project A Project B

0 −100 −100 1 30 49 2 50 49 3 70 49

a. Which project would you choose if the opportunity cost of capital is 2%? b. Which would you choose if the opportunity cost of capital is 12%?

32. Equivalent Annual Annuity. A precision lathe costs $10,000 and will cost $20,000 a year to operate and maintain. If the discount rate is 10% and the lathe will last for 5 years, what is the equivalent annual cost of the tool? (LO8-5)

33. Equivalent Annual Annuity. A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for $20,000. (LO8-5) a. What is the equivalent annual cost of buying and maintaining the truck if the discount rate is

10%? b. Which is the better option: leasing or buying?

34. Equivalent Annual Annuity. Econo-Cool air conditioners cost $300 to purchase, result in elec- tricity bills of $150 per year, and last for 5 years. Luxury Air models cost $500, result in elec- tricity bills of $100 per year, and last for 8 years. The discount rate is 21%. (LO8-5) a. What is the equivalent annual cost of the Econo-Cool model? b. What is the equivalent annual cost of the Luxury Air model? c. Which model is more cost-effective? d. Now you remember that the inflation rate is expected to be 10% per year for the foreseeable

future. Redo parts (a) and (b).

35. Investment Timing. You can purchase an optical scanner today for $400. The scanner provides benefits worth $60 a year. The expected life of the scanner is 10 years. Scanners are expected to decrease in price by 20% per year. Suppose the discount rate is 10%.  (LO8-5) a. Should you purchase the scanner today or wait to purchase? b. When is the best purchase time? 

36. Replacement Decision. You are operating an old machine that is expected to produce a cash inflow of $5,000 in each of the next 3 years before it fails. You can replace it now with a new machine that costs $20,000 but is much more efficient and will provide a cash flow of $10,000 a year for 4 years. Should you replace your equipment now? The discount rate is 15%. (LO8-5)

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268 Part Two Value

37. Investment Timing. A classic problem in management of forests is determining when it is most economically advantageous to cut a tree for lumber. When the tree is young, it grows very rap- idly. As it ages, its growth slows down. Why is NPV maximized if you cut the tree when its growth rate equals the discount rate? (LO8-5)

38. Replacement Decision. A forklift will last for only 2 more years. It costs $5,000 a year to main- tain. For $20,000 you can buy a new lift that can last for 10 years and should require mainte- nance costs of only $2,000 a year. (LO8-5) a. If the discount rate is 4% per year, should you replace the forklift? b. What if the discount rate is 12% per year? 

SOLUTIONS TO SELF-TEST QUESTIONS 8.1 Even if construction costs are $355,000, NPV is still positive:

NPV = PV − $355,000 = $357,143 − $355,000 = $2,143

Therefore, the project is still worth pursuing. The project is viable as long as construction costs are less than the PV of the future cash flow, that is, as long as construction costs are less than $357,143. However, if the opportunity cost of capital is 20%, the PV of the $400,000 sales price is lower and NPV is negative:

PV = $400,000 × 1 ____ 1.20 = $333,333

NPV = PV − $355,000 = −$21,667

The present value of the future cash flow is not as high when the opportunity cost of capital is higher. The project would need to provide a higher payoff in order to be viable in the face of the higher opportunity cost of capital.

8.2 The IRR is now about 8.3% because

NPV = −$375,000 + $25,000 _______ 1.083

+ $25,000 _______ (1.083)2

+ $420,000 ________ (1.083)3

= 0

Note in Figure 8.6 that NPV falls to zero as the discount rate reaches 8.3%.

8.3 You want to be rich. The NPV of the long-lived investment is much larger.

Short: NPV = −$1 + $2 ____ 1.07 = +$.869 million

Long: NPV = −$1 + $.3 ___ .07 = +$3.286 million

FIGURE 8.6 NPV falls to zero at an interest rate of 8.3%.

N et

p re

se nt

v al

ue ($

th ou

sa nd

s)

Discount rate (%)

-250

-200

-150

-100

-50

0

50

100

120 4 8 2016 24 32 36 40 4428 48

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Chapter 8 Net Present Value and Other Investment Criteria 269

8.4 You want to be richer. The second alternative generates greater value at any reasonable dis- count rate. Other risk-free investments offer 7%. Therefore,

NPV = −$1,000 + $4,000 ______ 1.07 = +$2,738

NPV = −$1,000,000 + $1,500,000 __________ 1.07 = +$401,869

8.5 The profitability index gives the correct ranking for the first pair, but the incorrect ranking for the second:

Project PV Investment NPV Profitability Index (NPV/ Investment)

Short $1,869,159 $1,000,000 $ 869,159 0.869 Long 4,285,714 1,000,000 3,285,714 3.286 Small 3,738 1,000 2,738 2.738 Large 1,401,869 1,000,000 401,869 0.402

8.6 The payback period is $700/$100 = 7 years. Discounted payback is 10 years. (We need to find how long an annuity of $100 a year must last to provide a present value of $700. On your calcu- lator, set PV = (−)700, PMT = 100, i = 7.1%, FV = 0, and solve for n. You should find that n = 10.) Calculate NPV as follows. The present value of a $700 annuity for 20 years at 7.1% is

PV annuity = $1,051 NPV = −$700 + $1,051 = +$351

The project should be accepted.

8.7 Year of

Purchase Cost of

Computer PV Savings NPV at Year of Purchase NPV Today

0 $50 $70 $20 $20 1 45 66 21 19.1 2 40 62 22 18.2 3 36 58 22 16.5 4 33 54 21 14.3 5 31 50 19 11.8

Purchase the new computer now.

8.8 Year: 0 1 2 3 PV of Costs

K Cash flows $10,000 $1,100 $1,200 $11,992

          Equivalent annual annuity 6,910 6,910 11,992

L Cash flows 12,000 1,100 1,200 $1,300 14,968          Equivalent annual annuity 6,019 6,019 6,019   14,968

Machine L is the better buy. However, it’s even better to keep the old machine going for 1 more year. That costs $4,300, which is less than L’s equivalent annual cost, $6,019.

SOLUTIONS TO SPREADSHEET QUESTIONS 1. NPV is zero at .1256, or 12.56%. This is the office project’s IRR.

2. The answer is 54.2. The correct NPV of 57.9 is 7% higher. The Excel function treats the initial cash flow as if it occurs at the end of 1 year, and discounts each successive cash flow by an extra year.

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270 Part Two Value

MINICASE Flowton Products enjoys a steady demand for stainless steel infil- trators used in a number of chemical processes. Revenues from the infiltrator division are $50 million a year, and production costs are $47.5 million. However, the 10 high-precision Munster stamping machines that are used in the production process are coming to the end of their useful life. One possibility is simply to replace each existing machine with a new Munster. These machines would cost $800,000 each and would not involve any additional operating costs. The alternative is to buy 10 centrally controlled Skilboro stampers. Skilboros cost $1.25 million each, but compared with the Munster, they would produce a total saving in operator and mate- rial costs of $500,000 a year. Moreover, the Skilboro is sturdily built and would last 10 years, compared with an estimated 7-year life for the Munster.

Analysts in the infiltrator division have produced the accompa- nying summary table, which shows the forecast total cash flows from the infiltrator business over the life of each machine. Flowton’s standard procedures for appraising capital investments

involve calculating net present value, internal rate of return, and payback, and these measures are also shown in the table.

As usual, Emily Balsam arrived early at Flowton’s head office. She had never regretted joining Flowton. Everything about the place, from the mirror windows to the bell fountain in the atrium, suggested a classy outfit. Ms. Balsam sighed happily and reached for the envelope at the top of her in-tray. It was an analysis from the infiltrator division of the replacement options for the stamper machines. Pinned to the paper was the summary table of cash flows and a note from the CFO, which read, “Emily, I have read through 20 pages of excruciating detail and I still don’t know which of these machines we should buy. The NPV calculation seems to indicate that the Skilboro is better, while IRR and payback suggest the opposite. Would you take a look and tell me what we should do and why. You also might check that the calculations are OK.”

Can you help Ms. Balsam by writing a memo to the CFO? You need to justify your solution and also to explain why some or all of the measures in the summary table are inappropriate.

Cash Flows (millions of dollars)

Year: 0 1–7 8 9 10

Munster Investment –8.0 Revenues 50.0 0 0 0 Costs 47.5 0 0 0 Net cash flow –8.0 2.5 0 0 0 NPV at 15% $2.40 million IRR 24.5% Payback period 3.2 years Skilboro Investment –12.5 Revenues 50.0 50.0 50.0 50.0 Costs 47.0 47.0 47.0 47.0 Net cash flow –12.5 3.0 3.0 3.0 3.0 NPV at 15% $2.56 million IRR 20.2% Payback period 4.2 years

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Chapter 8 Net Present Value and Other Investment Criteria 271

APPENDIX More on the IRR Rule

In Section 8.2, we described several pitfalls that lie in wait for users of the IRR rule. However, there are some tricks that users of the rule may use to circumvent these hazards. In this appendix, we show how you can adapt the IRR rule when you need to choose between competing projects or when there are multiple IRRs.

Using the IRR to Choose between Mutually Exclusive Projects When you need to choose between mutually exclusive projects, a simple comparison of internal rates of return is liable to lead to poor decisions. We illustrated this by looking at our two office building projects. Your initial proposal involved constructing the office building and then selling it. Under the revised proposal you would construct a more expensive building and rent it out before selling it at the end of 3 years. The cash flows from the two projects were as follows:

Cash Flows

C0 C1 C2 C3 IRR NPV at 7%

Initial proposal −350,000 +400,000 14.29% +$23,832 Revised proposal −375,000 +25,000 +25,000 +475,000 12.56% +$57,942

Although the initial proposal has the higher IRR, it has the lower net present value. If you were mis- led into choosing the initial rather than the revised proposal, you would have been more than $30,000 poorer.

You can salvage the IRR rule in these cases; you do so by calculating the IRR on the incremental cash flows, that is, the difference in cash flows between the two projects. Start with the project with the smaller initial investment, where you plan to invest $350,000 and sell the office building after 1 year. It has an IRR of 14.29%, which is well in excess of the 7% cost of capital. So you know that it is worthwhile. You now ask yourself whether it is worth investing the additional $25,000 and renting out the building for 3 years. Here are the incremental cash flows from doing so, together with their IRR and NPV:

Cash Flows: C0 C1 C2 C3 IRR NPV at 7%

Incremental cash flows −25,000 −375,000 +25,000 +475,000 11.72% +$34,110

The IRR on the incremental cash flows is 11.72%. Because this is greater than the opportunity cost of capital, you should prefer the revised proposal.

Using the Modified Internal Rate of Return When There Are Multiple IRRs Whenever there is more than one change in the sign of the cash flows, there is generally more than one internal rate of return and, therefore, no simple IRR rule. Companies sometimes get around this problem by calculating a modified IRR (MIRR), which can then be compared with the cost of capital.

Think back to King Coal’s strip-mining project. Its cash flows are as follows:

BEYOND THE PAGE

mhhe.com/brealey10e

Calculate the MIRR

Cash Flows: C0 C1 C2 C3 C4 C5

Cash flows ($ millions) –210 +125 +125 +175 +175 −400

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272 Part Two Value

The problem with the IRR rule arises because the cash flow in year 5 is negative. So let us try replac- ing the last two cash flows with a single year 4 cash flow that has the same present value. If the cost of capital is 20%, then we can replace the cash flows in years 4 and 5 with a single cash flow in year 4 of

+175 − 400 ____ 1.20 = −158

This figure is also negative. So we still have a problem. Therefore, we need to step back a further year and combine the last three cash flows into a single year 3 cash flow with the same present value:

+175 + 175 ____ 1.20

− 400 _____ 1.202

= +43

This value is positive, so if we use it in place of the last three cash flows, we will have only one change of sign. Now we can compute IRR using the modified cash-flow sequence:

Year: 0 1 2 3 4 5

Cash flows ($ millions) −210 +125 +125 +43 — —

The modified IRR (MIRR) is the discount rate at which the net present value of these cash flows is zero:

−210 + 125 _________ 1 + MIRR

+ 125 ___________ (1 + MIRR)2

+ 43 ___________ (1 + MIRR)3

= 0

We solve to find that MIRR = .22, or 22%, which is greater than the cost of capital of 20%. If the modified IRR is greater than the cost of capital, then the project must have a positive NPV.

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274

Using Discounted Cash-Flow Analysis to Make Investment Decisions

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

9-1 Identify the cash flows from a proposed new project.

9-2 Calculate the cash flows of a project from standard financial statements.

9-3 Understand how the company’s tax bill is affected by depreci- ation and how this affects project value.

9-4 Understand how changes in working capital affect project cash flows.

C H A P T E R

R E L AT E D W E B S I T E S F O R T H I S C H A P T E R C A N B E F O U N D I N C O N N E C T.

9

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275

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A working magnoosium mine. But how do you find its net present value? ©Andrey Rudakov/Bloomberg/Getty Images

Think of the problems that Toyota’s managers face when considering whether to introduce a new model. What investment must be made in new plant and equipment? What will it cost to market and promote the new car? How soon can the car be put into production? What is the likely production cost? How much must be invested in inventories of raw materials and finished cars? How many cars can be sold each year and at what price? What credit arrangements should be given to dealers? How long will the model stay in pro- duction? When production comes to an end, can the plant and equipment be used elsewhere in the com- pany? All of these issues affect the level and timing of project cash flows. In this chapter we continue our analy- sis of the capital budgeting decision by turning our focus to how the financial manager should prepare cash-flow estimates for use in net present value analysis.

In Chapter 8, you used the net present value rule to make a simple capital budgeting decision. You tackled the problem in four steps:

Step 1. Forecast the project cash flows.

Step 2. Estimate the opportunity cost of capital— that is, the rate of return that your share- holders could expect to earn if they invested their money in the capital market.

Step 3. Use the opportunity cost of capital to dis- count the future cash flows. The project’s present value (PV) is equal to the sum of the discounted future cash flows.

Step 4. Net present value (NPV) measures whether the project is worth more than it costs. To calculate NPV, you need to subtract the required investment from the present value of the future payoffs: NPV = PV − required investment

If NPV is positive, you should go ahead with the project.

We now need to consider how to apply the net pres- ent value rule to practical investment problems. The first step is to decide what to discount. We know the answer in principle: Discount cash flows. This is why capital bud- geting is often referred to as discounted cash-flow, or DCF, analysis. But useful forecasts of cash flows do not arrive on a silver platter. Often, the financial manager has to make do with raw data supplied by specialists in design, production, marketing, and so on. In addition, most financial forecasts are prepared in accordance with accounting principles that do not necessarily rec- ognize cash flows when they occur. These forecasts must also be adjusted.

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276

We look first at what cash flows should be discounted. We then present an example that shows how cash flows can be derived from standard accounting information and why cash flows and accounting income usually

differ. The example will lead us to various further points, including the links between depreciation and taxes and the importance of tracking investments in working capital.

Identifying Cash Flows

Discount Cash Flows, Not Profits Up to this point we have been concerned mainly with the mechanics of discounting and with the various methods of project appraisal. We have had almost nothing to say about the problem of what you should discount. The first and most important point is this: To calculate net present value, you need to discount cash flows, not accounting profits.

We stressed the difference between cash flows and profits in Chapter 3. Here we stress it again. Income statements are intended to show how well the firm has per- formed. They are not designed to track cash flows.

If the firm lays out a large amount of money on a big capital project, you do not conclude that the firm performed poorly that year, even though a lot of cash is going out the door. Therefore, the accountant does not deduct capital expenditure when cal- culating the year’s income but, instead, depreciates it over several years.

That is fine for computing year-by-year profits, but it could get you into trouble when working out net present value. For example, suppose that you are analyzing an investment proposal. It costs $2,000 and is expected to bring in a cash flow of $1,500 in the first year and $500 in the second. You think that the opportunity cost of capital is 10% and so calculate the present value of the cash flows as follows:

PV = $1,500 _____ 1.10 + $500 _____

(1.10 ) 2 = $1,776.86

The project is worth less than it costs; it has a negative NPV: NPV = $1,776.86 − $2,000 = −$223.14

The project costs $2,000 today, but accountants would not treat that outlay as an immediate expense. They would depreciate that $2,000 over 2 years and deduct the depreciation from the cash flow to obtain accounting income:1

Year 1 Year 2

Cash inflow +$1,500 +$ 500 Less depreciation − 1,000 −  1,000 Accounting income + 500 −    500

Thus, an accountant would forecast income of $500 in year 1 and an accounting loss of $500 in year 2.

Suppose you were given this forecast income and loss and naively discounted them. Now NPV looks positive:

Apparent NPV = $500 ____ 1.10 + − $500 _____ (1.10 ) 2

= $41.32

Of course we know that this is nonsense. The project is obviously a loser; we are spending money today ($2,000 cash outflow), and we are simply getting our money back later ($1,500 in year 1 and $500 in year 2). We are earning a zero return when we could get a 10% return by investing our money in the capital market.

The message of the example is this: When calculating NPV, recognize invest- ment expenditures when they occur, not later when they show up as depreciation.

9.1

1 For reporting purposes, firms typically spread depreciation evenly over the life of the project, as we assume here. This figure may differ from the depreciation allowed for tax purposes. We discuss this issue in more detail later in the chapter.

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 277

Projects are financially attractive because of the cash they generate, either for distribution to shareholders or for reinvestment in the firm. Therefore, the focus of capital budgeting must be on cash flow, not profits.

We saw another example of the distinction between cash flow and accounting prof- its in Chapter 3. Accountants try to show profit as it is earned, rather than when the company and the customer get around to paying their bills. For example, an income statement will recognize revenue when the sale is made, even if the bill is not paid for months. This practice also results in a difference between accounting profits and cash flow. The sale generates immediate profits, but the cash flow comes later.

When Cash Flow Comes Later Than Sales

Your firm’s ace computer salesman closed a $500,000 sale on December 15, just in time to count it toward his annual bonus. How did he do it? Well, for one thing he gave the customer 180 days to pay. The income statement will recognize the sale in December, even though cash will not arrive until June.

To take care of this timing difference, the accountant adds $500,000 to accounts receiv- able in December and then reduces accounts receivable when the money arrives in June. (The total of accounts receivable is just the sum of all cash due from customers.)

You can think of the increase in accounts receivable as an investment—it’s effectively a 180-day loan to the customer—and, therefore, a cash outflow. That investment is recovered when the customer pays. Thus, financial analysts often find it convenient to calculate cash flow as follows:

December June

Sales $500,000 Sales 0 Less investment in accounts receivable −500,000

Plus recovery of accounts receivable +$500,000

Cash flow 0 Cash flow $500,000

Note that this procedure gives the correct cash flow of $500,000 in June. ■

Example 9.1 ⊲

It is not always easy to translate accounting data back into actual dollars. If you are in doubt about what is a cash flow, simply count the dollars coming in and take away the dollars going out.

A regional supermarket chain is deciding whether to install a tewgit machine in each of its stores. Each machine costs $250,000. Projected income per machine is as follows:

Year: 1 2 3 4 5

Sales $250,000 $300,000 $300,000 $250,000 $250,000 Operating expenses 200,000 200,000 200,000 200,000 200,000 Depreciation   50,000   50,000   50,000   50,000   50,000 Accounting income 0 50,000 50,000 0 0

Why would a store continue to operate a machine in years 4 and 5 if it produces no profits? What are the cash flows from investing in a machine? Assume each tewgit machine has no salvage value at the end of its 5-year life. Ignore taxes.

Self-Test9.1

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278 Part Two Value

Discount Incremental Cash Flows A project’s present value depends on the extra cash flows that it produces. So you need to forecast first the firm’s cash flows if you go ahead with the project. Then forecast the cash flows if you don’t accept the project. Take the difference and you have the extra (or incremental) cash flows produced by the project:

Incremental cash flow = cash flow with project − cash flow without project

Launching a New Product

Consider the decision by Apple to develop an iPhone 11. If successful, the 11 could lead to several billion dollars in profits.

But would these profits all be incremental cash flows? Certainly not. Our with-versus-without principle reminds us that we need also to think about what the cash flows would be without the new phone. By launching the iPhone 11, Apple will reduce demand for the iPhone 10. The incre- mental cash flows therefore are

Cash flow with 11 (including lower cash flow

from iPhone 10)  − 

cash flow without 11 (with higher cash flow

from iPhone 10) ■

Example 9.2 ⊲

The trick in capital budgeting is to trace all the incremental flows from a proposed project. Here are some things to look out for.

Include All Indirect Effects The decision to launch a new smartphone illustrates a common indirect effect. New products often damage sales of an existing product. Of course, companies frequently introduce new products anyway, usually because they believe that their existing product line is under threat from competition. Even if Apple doesn’t go ahead with a new product, Samsung and other competitors will surely con- tinue to improve their Android phones, so there is no guarantee that sales of the exist- ing product line will continue at their present level. Sooner or later they will decline.

Sometimes, a new project will help the firm’s existing business. Suppose that you are the financial manager of an airline that is considering opening a new short-haul route from Peoria, Illinois, to Chicago’s O’Hare Airport. When considered in isola- tion, the new route may have a negative NPV. But once you allow for the additional business that the new route brings to your other traffic out of O’Hare, it may be a worthwhile investment. To forecast incremental cash flow, you must trace out all indirect effects of accepting the project.

Some capital investments have very long lives once all indirect effects are recog- nized. Consider the introduction of a new jet engine. Engine manufacturers often offer attractive pricing to achieve early sales because, once an engine is installed, 15 years’ sales of replacement parts are almost ensured. Also, because airlines prefer to limit the number of different engines in their fleet, selling jet engines today improves sales tomorrow as well. Later sales will generate further demands for replacement parts. Thus, the string of incremental effects from the first sales of a new-model engine can run for 20 years or more.

Forget Sunk Costs Sunk costs are like spilled milk: They are past and irreversible outflows. Sunk costs remain the same whether or not you accept the project. Therefore, they do not affect project NPV.

Take the case of the James Webb Space Telescope. It was originally supposed to launch in 2011 and cost $1.6 billion. But the project became progressively more expensive and further behind schedule. Latest estimates put the cost at $8.8 billion and a launch date of 2019. When Congress debated whether to cancel the program,

[ [[ [

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 279

supporters of the project argued that it would be foolish to abandon a project on which so much had already been spent. Others countered that it would be even more foolish to continue with a project that had proved so costly. Both groups were guilty of the sunk-cost fallacy; the money that had already been spent by NASA was irrecoverable and, therefore, irrelevant to the decision to terminate the project.

Include Opportunity Costs Resources are almost never free, even when no cash changes hands. For example, suppose a new manufacturing operation uses land that could otherwise be sold for $100,000. This resource is costly; by using the land, you pass up the opportunity to sell it. There is no out-of-pocket cost, but there is an opportunity cost, that is, the value of the forgone alternative use of the land.

This example prompts us to warn you against judging projects “before versus after” rather than “with versus without.” A manager comparing before versus after might not assign any value to the land because the firm owns it both before and after:

Before Take Project After Cash Flow,

Before versus After

Firm owns land Firm still owns land 0

The proper comparison, with versus without, is as follows:

Before Take Project After Cash Flow, with Project

Firm owns land Firm still owns land 0

Before Do Not Take

Project After Cash Flow,

without Project

Firm owns land Firm sells land for $100,000 $100,000

If you compare the cash flows with and without the project, you see that $100,000 is given up by undertaking the project. The original cost of purchasing the land is irrelevant—that cost is sunk. The opportunity cost equals the cash that could be realized from selling the land now; you lose that cash if you take the project.

When the resource can be freely traded, its opportunity cost is simply the market price.2 However, sometimes opportunity costs are difficult to estimate. Suppose that you go ahead with a project to develop Computer Nouveau, pulling your software team off their work on a new operating system that some existing customers are not- so-patiently awaiting. The exact cost of infuriating those customers may be impossible to calculate, but you’ll think twice about the opportunity cost of moving the software team to Computer Nouveau.

Recognize the Investment in Working Capital Net working capital (often referred to simply as working capital) is the difference between a company’s short- term assets and its liabilities. The principal short-term assets that you need to consider are accounts receivable (customers’ unpaid bills) and inventories of raw materials and finished goods, and the principal short-term liabilities are accounts payable (bills that you have not paid) and accruals (liabilities for items such as wages or taxes that have recently been incurred but have not yet been paid).

Most projects entail an additional investment in working capital. For example, before you can start production, you need to invest in inventories of raw materials. Then, when you deliver the finished product, customers may be slow to pay and accounts receivable

opportunity cost Benefit or cash flow forgone as a result of an action.

net working capital Current assets minus current liabilities. Often called working capital.

2 If the value of the land to the firm were less than the market price, the firm would sell it. On the other hand, the opportunity cost of using land in a particular project cannot exceed the cost of buying an equivalent parcel to replace it.

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280 Part Two Value

will increase. (Remember the computer sale described in Example 9.1. It required a $500,000, 6-month investment in accounts receivable.) Next year, as business builds up, you may need a larger stock of raw materials and you may have even more unpaid bills. Investments in working capital, just like investments in plant and equipment, result in cash outflows.

Working capital is one of the most common sources of confusion in forecasting project cash flows.3 Here are the most common mistakes:

1. Forgetting about working capital entirely. We hope that you never fall into that trap. 2. Forgetting that working capital may change during the life of the project. Imagine

that you sell $100,000 of goods per year and customers pay on average 6 months late. You will, therefore, have $50,000 of unpaid bills. Now you increase prices by 10%, so revenues increase to $110,000. If customers continue to pay 6 months late, unpaid bills increase to $55,000, and therefore, you need to make an additional investment in working capital of $5,000.

3. Forgetting that working capital is recovered at the end of the project. When the project comes to an end, inventories are run down, any unpaid bills are (you hope) paid off, and you can recover your investment in working capital. This generates a cash inflow.

Remember Terminal Cash Flows The end of a project almost always brings addi- tional cash flows. For example, you might be able to sell some of the plant, equipment, or real estate that was dedicated to it. Also, as we just mentioned, you may recover some of your investment in working capital as you sell off inventories of finished goods and collect on outstanding accounts receivable.

Sometimes, there may be costs to shutting down a project. For example, the decom- missioning costs of nuclear power plants can soak up several hundred million dollars. Similarly, when a mine is exhausted, the surrounding environment may need rehabili- tation. The mining company FCX has earmarked $451 million to cover the future closure and reclamation costs of its New Mexico mines. Don’t forget to include these terminal cash flows.

Beware of Allocated Overhead Costs We have already mentioned that the accountant’s objective in gathering data is not always the same as the project analyst’s. A case in point is the allocation of overhead costs such as rent, heat, or electricity. These overhead costs may not be related to a particular project, but they must be paid for nevertheless. Therefore, when the accountant assigns costs to the firm’s projects, a charge for overhead is usually made. But our principle of incremental cash flows says that in investment appraisal we should include only the extra expenses of the project.

A project may generate extra overhead costs, but then again it may not. We should be cautious about assuming that the accountant’s allocation of overhead costs represents the incremental cash flow that would be incurred by accepting the project.

3 If you are not clear why working capital affects cash flow, look back to Chapter 3, where we gave a primer on working capital and a couple of simple examples.

A firm is considering an investment in a new manufacturing plant. The site already is owned by the company, but existing buildings would need to be demolished. Which of the following should be treated as incremental cash flows?

Self-Test9.2

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 281

Discount Nominal Cash Flows by the Nominal Cost of Capital Interest rates are usually quoted in nominal terms. If you invest $100 in a bank deposit offering 6% interest, then the bank promises to pay you $106 at the end of the year. It makes no promises about what that $106 will buy. The real rate of interest on the bank deposit depends on inflation. If inflation is 2%, that $106 will buy you only 4% more goods at the end of the year than your $100 could buy today. The nominal rate of inter- est is 6%, but the real rate is about 4%.4

If the discount rate is nominal, consistency requires that cash flows be estimated in nominal terms as well, taking account of trends in selling price, labor and materials costs, and so on. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Some costs or prices increase faster than inflation, some slower. For example, perhaps you have entered into a 5-year fixed-price contract with a supplier. No matter what happens to inflation over this period, this part of your costs is fixed in nominal terms.

Of course, there is nothing wrong with discounting real cash flows at the real inter- est rate, although this is not commonly done. We saw in Chapter 5 that real cash flows discounted at the real discount rate give exactly the same present values as nominal cash flows discounted at the nominal rate.

While the need to maintain consistency may seem like an obvious point, analysts sometimes forget to account for the effects of inflation when forecasting future cash flows. As a result, they end up discounting real cash flows at a nominal discount rate. This can grossly understate project values.

It should go without saying that you cannot mix and match real and nominal quantities. Real cash flows must be discounted at a real discount rate, nominal cash flows at a nominal rate. Discounting real cash flows at a nominal rate is a big mistake.

a. The market value of the site. b. The market value of the existing buildings. c. Demolition costs and site clearance. d. The cost of a new access road put in last year. e. Lost cash flows on other projects due to executive time spent on the new

facility. f. Future depreciation of the new plant.

g. The reduction in the firm’s tax bill resulting from depreciation of the new plant. h. The initial investment in inventories of raw materials. i. Money already spent on engineering design of the new plant.

4 Remember from Chapter 5, Real rate of interest ≈ nominal rate of interest − inflation rate

The exact formula is

1 + real rate of interest = 1 + nominal rate of interest _______________________ 1 + inflation rate = 1.06 ____ 1.02 = 1.0392

Therefore, the real interest rate is .0392, or 3.92%.

Cash Flows and Inflation

City Consulting Services is considering moving into a new office building. The cost of a 1-year lease is $8,000, paid immediately. This cost will increase in future years at the annual infla- tion rate of 3%. The firm believes that it will remain in the building for 4 years. What is the present value of its rental costs if the discount rate is 10%?

Example 9.3 ⊲

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282 Part Two Value

Separate Investment and Financing Decisions Suppose you finance a project partly with debt. How should you treat the proceeds from the debt issue and the interest and principal payments on the debt? The answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments on the debt as cash outflows. Regardless of the actual financing, you should view the project as if it were all-equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them.6

This procedure focuses exclusively on the project cash flows, not the cash flows associated with alternative financing schemes. It, therefore, allows you to separate the analysis of the investment decision from that of the financing decision. First, you ask whether the project has a positive net present value, assuming all-equity financing.

The present value can be obtained by discounting the nominal cash flows at the 10% dis- count rate as follows:

Year Cash Flow Present Value at

10% Discount Rate

0 8,000 8,000 1 8,000 × 1.03   = 8,240 8,240/1.10   =  7,491 2 8,000 × 1.032 = 8,487 8,487/(1.10)2 =  7,014 3 8,000 × 1.033 = 8,742 8,742/(1.10)3 =    6,568

$29,073

Alternatively, the real discount rate can be calculated as 1.10/1.03 − 1 = .06796 = 6.796%.5 The present value can then be computed by discounting the real cash flows at the real dis- count rate as follows:

Year Real Cash Flow Present Value at

6.796% Discount Rate

0 8,000 8,000 1 8,000 8,000/1.06796   =   7,491 2 8,000 8,000/(1.06796)2 =   7,014 3 8,000 8,000/(1.06796)3 =      6,568

$29,073

Notice the real cash flow is a constant because the lease payment increases at the rate of inflation. The present value of each cash flow is the same regardless of the method used to discount it. The sum of the present values is, of course, also identical. ■

Nasty Industries is closing down an outmoded factory and throwing all of its work- ers out on the street. Nasty’s CEO is enraged to learn that the firm must continue to pay for workers’ health insurance for 4 years. The cost per worker next year will be $2,400 per year, but the inflation rate is 4%, and health costs have been increas- ing at 3 percentage points faster than inflation. What is the present value of this obligation? The (nominal) discount rate is 10%. The company does not pay taxes.

Self-Test9.3

5 We calculate the real discount rate to three decimal places to avoid confusion from rounding. Such precision is rarely necessary in practice. 6 Notice that this means that when you calculate the working capital associated with the project, you should assume zero short-term debt or holdings of cash.

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Chapter 9 Using Discounted Cash-Flow Analysis to Make Investment Decisions 283

Then you can undertake a separate analysis of any potential impact of your financing strategy. Financing decisions are considered later in the text.

Corporate Income Taxes

When valuing a project, you need to discount after-tax cash flows. Occasionally you come across firms that forecast pretax cash flows and discount them at a higher “pre- tax” discount rate. This does not work; there is no simple adjustment to the discount rate that will lead to the correct NPV.