Refer to figure 2.3 and look at the treasury bond maturing in february 2036.

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Fundamentals of

Corporate Finance

Eighth EDITION

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Fundamentals of

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

Eighth EDITION

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THE McGRAW-HILL/IRWIN SERIES IN FINANCE, INSURANCE, AND REAL ESTATE

Stephen A. Ross, Franco Modigliani Professor of Financial Economics Sloan School of Management, Massachusetts Institute of Technology Consulting Editor

Financial Management

Block, Hirt, and Danielsen Foundations of Financial Management Fifteenth Edition

Brealey, Myers, and Allen Principles of Corporate Finance Eleventh Edition

Brealey, Myers, and Allen Principles of Corporate Finance, Concise Second Edition

Brealey, Myers, and Marcus Fundamentals of Corporate Finance Eighth Edition

Brooks FinGame Online 5.0

Bruner Case Studies in Finance: Managing for Corporate Value Creation Seventh Edition

Cornett, Adair, and Nofsinger Finance: Applications and Theory Third Edition

Cornett, Adair, and Nofsinger M: Finance Second Edition

DeMello Cases in Finance Second Edition

Grinblatt (editor) Stephen A. Ross, Mentor: Influence through Generations

Grinblatt and Titman Financial Markets and Corporate Strategy Second Edition

Higgins Analysis for Financial Management Tenth Edition

Kellison Theory of Interest Third Edition

Ross, Westerfield, and Jaffe Corporate Finance Tenth Edition

Ross, Westerfield, Jaffe, and Jordan Corporate Finance: Core Principles and Applications Fourth Edition

Ross, Westerfield, and Jordan Essentials of Corporate Finance Eighth Edition

Ross, Westerfield, and Jordan Fundamentals of Corporate Finance Tenth Edition

Shefrin Behavioral Corporate Finance: Decisions That Create Value First Edition

White Financial Analysis with an Electronic Calculator Sixth Edition

Investments

Bodie, Kane, and Marcus Essentials of Investments Ninth Edition

Bodie, Kane, and Marcus Investments Tenth Edition

Hirt and Block Fundamentals of Investment Management Tenth Edition

Hirschey and Nofsinger Investments: Analysis and Behavior Second Edition

Jordan, Miller, and Dolvin Fundamentals of Investments: Valuation and Management Seventh Edition

Stewart, Piros, and Heisler Running Money: Professional Portfolio Management First Edition

Sundaram and Das Derivatives: Principles and Practice First Edition

Financial Institutions and Markets

Rose and Hudgins Bank Management and Financial Services Ninth Edition

Rose and Marquis Financial Institutions and Markets Eleventh Edition

Saunders and Cornett Financial Institutions Management: A Risk Management Approach Eighth Edition

Saunders and Cornett Financial Markets and Institutions Sixth Edition

International Finance

Eun and Resnick International Financial Management Seventh Edition

Real Estate

Brueggeman and Fisher Real Estate Finance and Investments Fourteenth Edition

Ling and Archer Real Estate Principles: A Value Approach Fourth Edition

Financial Planning and Insurance

Allen, Melone, Rosenbloom, and Mahoney Retirement Plans: 401(k)s, IRAs, and Other Deferred Compensation Approaches Eleventh Edition

Altfest Personal Financial Planning First Edition

Harrington and Niehaus Risk Management and Insurance Second Edition

Kapoor, Dlabay, and Hughes Focus on Personal Finance: An Active Approach to Help You Develop Successful Financial Skills Fourth Edition

Kapoor, Dlabay, and Hughes Personal Finance Eleventh Edition

Walker and Walker Personal Finance: Building Your Future First Edition

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Dedication To Our Wives

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FUNDAMENTALS OF CORPORATE FINANCE, EIGHTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2015 by McGraw- Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2012, 2009, 2007, 2004, 2001, 1999, and 1995. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

This book is printed on acid-free paper.

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ISBN 978-0-07-786162-9 MHID 0-07-786162-0

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Library of Congress Cataloging-in-Publication Data

Brealey, Richard A. Fundamentals of 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.—Eighth edition.

pages cm.—(The McGraw-Hill/Irwin series in finance, insurance and real estate) Includes index. ISBN-13: 978-0-07-786162-9 (alk. paper) ISBN-10: 0-07-338230-2 (alk. paper) 1. Corporations–Finance. I. Myers, Stewart C. II. Marcus, Alan J. III. Title. HG4026.B6668 2014 658.15–dc23 2014018986

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

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vi

the Authors About

Richard A. Brealey Professor of Finance at the London Business School He 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 a 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.

Stewart C. Myers Gordon Y Billard Professor of Finance at MIT’s Sloan School of Management He 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.

Alan J. Marcus Mario Gabelli Professor of Finance in the Carroll School of Management at Boston College His 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 Invest- ments. 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.

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vii

Preface

This book is about corporate finance. It focuses on how companies invest in real assets, how they raise the money to pay for these investments, and how those assets ulti- mately affect the value of the firm. It also provides a broad introduction to 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. Also, a firm’s success or failure depends in large part on its ability to find the capital that it needs.

Finance is interesting for several reasons. Financial decisions often involve huge sums of money. Large investment projects or acquisitions may involve billions of dollars. 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 why the firm’s own- ers would like the manager to increase firm value and shows how managers choose 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, interesting, and fun for the beginning student. We set out to show that modern finance and good finan- cial 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.

First, we provide much more detailed discussion of the principles 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.

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viii Preface

Second, we use numerical examples in this text to a greater degree than in Prin- ciples. 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 pos- sible. Even when we present an equation, we usually write it in words rather than sym- bols. 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 chapter we discuss how businesses are organized, the role of the financial manager, and the financial markets in which the manager operates. We explain how shareholders 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 mecha- nisms 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, and so the firm produces financial statements to help the players monitor its progress. Chapter 3 provides a brief overview of these finan- cial statements and introduces two key distinctions—between market and book values and between cash flows and profits. This chapter also discusses some of the shortcom- ings in accounting practice. The chapter concludes with a summary of federal 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, since 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 streams of cash flows and work through the valuation of perpetuities and annui- ties. 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 students 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

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Preface ix

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 com- plex investment proposals, including choices between alternative projects, machine replacement decisions, and decisions of when to invest. We also look at other mea- sures of an investment’s attractiveness—its internal rate of return, payback period, and profitability index. We show how the profitability index can be used to choose between investment 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 dis- tinction between accounting break-even and NPV break-even. We conclude the chap- ter by describing how managers try to build future flexibility into projects so that they can capitalize on good luck and mitigate the consequences 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 financing decisions. In Chapter 16 we ask how much the firm should borrow, and we summa- rize bankruptcy procedures that occur when firms can’t pay their debts. In 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 observation 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 combined 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, and describes the principal sources of short-term borrowing. Chapter 20 addresses working capital management. It describes the basic steps of credit management, the principles of inventory management, and how firms handle payments efficiently and put cash to work as quickly as possible.

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x Preface

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 projects. How- ever, 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 financial systems are scattered throughout the book. However, Chapter 22 tackles the specific problems that arise when a corpora- tion 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 interest- ing questions that either were unanswered in the text or are still puzzles to the finance profession. 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 topics 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 Finan- cial 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 after the student is familiar with the basic principles of valuation and financing, but we recognize that here also 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 Eighth 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 biggest change in this edition is the introduction of Beyond the Page digital extensions and applications. These digital extensions are not, as they may sound, false fingernails; they are additional examples, spreadsheet programs, and opportunities to explore topics in more depth. This material is very easily accessed on the web. For example, it is seamlessly available with a click on the e-versions of the book, but it is also readily accessible in the traditional hard copy of the text using either QR codes from a smartphone or shortcut URLs, both provided in the margins of relevant pages.

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Preface xi

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. Consider, for example, Chapter 1, where we have made three significant changes. First, we have included a completely rewritten section on corporate governance and agency issues. We empha- size that you need a good system of corporate governance to ensure that managers maximize value. Second, discussions of ethical issues often focus on the egregiously improper and illegal actions, but for honest financial managers the important problems are the gray areas. We have therefore addressed three topics for which there are no easy answers—the role of corporate raiders, short-selling, and tax avoidance. Finally, students tackling finance for the first time need some broad understanding of what the subject is all about. We therefore conclude Chapter 1 with a review of the big themes.

Updating Of course, in each new edition we try to ensure that any statistics are as up to date as possible. For example, since the previous edition, we have available an extra 3 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.

Recent Events We discussed the financial crisis of 2007–2009 in the previous edi- tion, but we have now been able to expand the discussion to include the spillover to the crisis in the eurozone and to introduce the Dodd-Frank Act. The eurozone crisis was also a reminder that government debt is not risk-free. We come back to that issue in Chapter 6 when we discuss default risk.

Concepts There are several places where we have introduced new conceptual mate- rial. For example, students who have learned about the dividend discount model are often confused about how to value the many companies that also repurchase their stock. We introduce the issue in Chapter 13, and in Chapter 17 we explain how to value these companies. The growth in repurchases has also changed the way that we think about the dividend controversy. We have therefore substantially rewritten Chapter 17 to focus on the trade-off between dividends and repurchases. We have also added a final section that discusses how the payout decision changes over the life cycle of the firm.

New Illustrative Boxes The text contains a number of boxes with illustrative real- world examples. Many of these are new. Look, for example, at the box in Chapter 15 that discusses the Facebook IPO or the box about how WobbleWorks used crowd- funding to finance its 3Doodler project.

More Worked Examples We have added more worked examples in the text, many of them taken from real companies. For instance, when we discuss company valuation in Chapter 7, we show how to value the Cape Wind power project in Nantucket Sound.

New Calculator and Spreadsheet Boxes We have reworked the explanations of how to use calculators or spreadsheets to solve financial problems. We now have separate subsections that show how they can be used to solve single-cash-flow and multiple-cash-flow problems. We think that this better integrates the material into the rest of the chapter and is easier for the student to follow.

Specific Chapter Changes in the Eighth Edition Chapter 1 contains an expanded discussion of agency issues, including additions

on corporate raiders, creative accounting, tax avoidance, and “say on pay.”

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xii Preface

Chapter 2 includes an additional discussion of the fi nancial crisis and its spillover to the sovereign debt crisis in the eurozone.

Chapter 3 introduces free cash fl ow in the discussion of accounting and fi nance and includes updated discussions of accounting malfeasance and the conver- gence of GAAP and IFRS accounting standards.

Chapter 5 has a reorganized and integrated discussion of calculators and spread- sheets.

Chapter 6 now includes an overview of the determinants of bond default risk in the discussion of credit spreads.

Chapter 7 contains an integrated discussion of sustainable growth in the develop- ment of the dividend growth model, includes a new box on Facebook’s IPO, and explains how to best deal with stock repurchases when using the dividend discount model.

Chapter 8 features an enhanced explanation of why mutually exclusive invest- ments are central to almost all real-life investment decisions and how that affects the capital budgeting decision.

Chapter 10 includes updated examples of real options and explains how those op- tions are integrated into a fi rm’s longer-term strategic considerations.

Chapter 11 introduces a simple derivation of the investment opportunity frontier and demonstrates the role of correlation in assessing the potential for an invest- ment to reduce risk through portfolio diversifi cation.

Chapter 12 contains a new discussion of how the index model can be used to measure and distinguish between systematic and diversifi able risks using an ex- tended example comparing the risks of mutual funds and individual stocks. The discussion also introduces key issues in performance evaluation, for example, the appropriate way to trade off average return versus risk.

Chapter 13 includes clarifi cations on real-world procedures used when computing the weighted-average cost of capital.

Chapter 14 features an extended treatment of corporate governance, particularly the composition of the board of directors.

Chapter 15 introduces alternative fundraising methods for start-ups, such as crowdsourcing.

Chapter 16 clarifi es the practical implications of Miller and Modigliani for debt policy and introduces new material on assessing the present value of tax shields associated with debt.

Chapter 17 contains a fully revamped treatment of the information content of div- idends as well the trade-offs governing the use of dividends versus repurchases.

Chapter 19 includes a closer integration of the analysis of sources and uses of funds with the fi rm’s statement of cash fl ows.

Chapter 21 features numerous updates to refl ect mergers that have taken place in recent years.

Chapter 23 presents a new treatment of the VIX contract and its use as a “fear index.”

Chapter 24 includes a new discussion of a practical issue in risk management— banks that have lost hundreds of millions after “rogue traders” made large but unauthorized trades.

Assurance of Learning Assurance of learning is an important element of many accreditation standards. Fun- damentals of Corporate Finance, Eighth Edition, is designed specifically to support 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-chapter 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

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Preface xiii

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, Eighth 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.

The statements contained in Fundamentals of Corporate Finance, Eighth 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, Eighth Edition, and the teaching package make no claim of any specific AACSB qualification or eval- uation, we have, within the test bank, labeled selected questions according to the six general knowledge and skills areas.

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O RG

A N

IZ A

TI O

N Key Features

New and Enhanced Pedagogy A great deal of effort has gone into expanding and enhancing the features in Fundamentals of Corporate Finance.

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Chapter Opener Each chapter begins with a chapter narrative to help set the tone for the material that follows. Learn- ing Objectives are also included to provide a quick introduction to the material students will learn and should understand fully before mov- ing to the next chapter.

Brealey / Myers / Marcus Your guide through the challenging landscape of corporate finance

The Time Value of Money 5 CHAPTE

R

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5.5 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 per year and

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

perpetuity Stream of level cash payments that never ends.

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Key Terms in the Margin Key terms are presented in bold and defined in the margin as they are introduced. A glossary is also avail- able at the back of the book.

Example 5.8 Winning Big at the Lottery In May 2013 an 84-year-old Florida woman invested $10 in five Powerball lottery tickets and won a record $590.5 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 $590.5 million. That sum was to be paid in 30 equal annual installments of $19.683 million each. Assuming that the first pay- ment occurred at the end of 1 year, what was the present value of the prize? The interest rate at the time was about 3.6%.

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 simply multiply $19.683 million by the 30-year annuity factor:

PV = 19.683 × 30-year annuity factor

= 19.683 × c1 r -

1 r (1 + r)30

d At an interest rate of 3.6%, the annuity factor is

c 1 .036

- 1

.036(1.036)30 d = 18.1638

▲

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Numbered 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 they are applied to answer concrete questions and scenarios.

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PE D

A G

O G

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

Spreadsheet Solutions Boxes These boxes provide the student with detailed examples of how to use Excel spreadsheets when applying financial con- cepts. The boxes include questions that apply to the spreadsheet, and their solutions are given at the end of the applicable chapter. Denoted by an icon, these spreadsheets are available in Connect.

The DATE function in Excel, which we use for both the settlement 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.

The value of the bond assuming annual coupon payments is 120.556% of face value, or $1,205.56. 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 col- umn D), and the bond value would change to 120.574% of face value, as we found in that example.

Excel and most other spreadsheet programs provide built-in functions to compute bond values and yields. They typically 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 7.25% coupon bond, we would enter the values shown in the spreadsheet below. Alterna- tively, we could simply enter the following function in Excel:

= PRICE(DATE(2013,5,15),DATE(2016,5,15),.0725, .0035,100,1)

Solutions Spreadsheet Bond Valuation

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Finance in Practice Boxes These are excerpts that appear in most chapters, usually from the financial press, providing real-life illustrations of the chap- ter’s topics, such as ethi- cal choices in finance, disputes about stock valuation, financial plan- ning, and credit analysis.

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 busi- nesses was unfocused 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 fi nancial engineering.” But Timken’s stock price rose at the prospect of a breakup, and a nonbinding share- holder vote on Relational’s proposal attracted a 53% majority.

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

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 profi t of $1 billion for his fund. †

Was Paulson’s trade unethical? Some believe not only that he was profi ting from the misery that resulted from the crash in mortgage-backed securities but that his short trades accen- tuated 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 ghoulishness of “creatures who, at all great earthquakes and fi res, 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

Finance in Practice Ethical Disputes in Finance

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Excel Exhibits Selected exhibits are set as Excel spreadsheets. They are also available in Connect.

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

SPREADSHEET 5.1 Using a spreadsheet to find the future value of $24