Mastering Corporate Finance Essentials E-Book

Stuart A. McCrary

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Editions
• Sprache: Englisch

Seitenzahl: 234

Veröffentlichungsjahr: 2010

Beschreibung

An essential guide to corporate finance

Understanding corporate finance is a necessity for financial practitioners who struggle every day to find the right balance between maximizing corporate value and reducing a firm's financial risk.

Divided into two comprehensive parts, Mastering Corporate Finance Essentials presents the material by example, using an extended scenario involving a new business formation. In Part One, present and future value mathematics are introduced followed by a number of applications using the tools. In Part Two, statistics as applied to finance are examined, with detailed discussions of standard deviations, correlations, and how they impact diversification.

• Through theory and real-world examples this book provides a solid grounding in corporate finance
• Other titles by Stuart McCrary include: Mastering Financial Accounting Essentials, How to Create and Manage a Hedge Fund, and Hedge Fund Course
• Covers the essential elements of this field, from traditional capital budgeting concepts and methods of valuing investment projects under uncertainty to the importance of "real-options" in the decision-making process

This reliable resource offers a hands-on approach to corporate finance that will allow you to gain a solid understanding of this discipline.

Leseprobe

Table of Contents

Dedication

Title Page

Copyright Page

Preface

Acknowledgements

CHAPTER 1 - Time Value of Money Toolbox

INTRODUCTION

CASH FLOWS

FUTURE VALUE

THE IMPACT OF COMPOUNDING FREQUENCY ON FUTURE VALUE

EQUIVALENT INTEREST RATE

CONTINUOUSLY COMPOUNDED INTEREST

PRESENT VALUE

FORMULAS FOR PRESENT VALUE AND FUTURE VALUE

CONCLUSION

Questions

CHAPTER 2 - Statistics for Finance

INTRODUCTION

THE MEANING OF MEAN OR AVERAGE

MEDIAN AS A SUBSTITUTE FOR MEAN

STANDARD DEVIATION MEASURES THE NOISE

ANNUALIZING VARIANCE AND STANDARD DEVIATION ESTIMATES

THE NORMAL CURVE IS APROBABILITY DISTRIBUTION

THE CUMULATIVE DENSITY FUNCTION

MEASURES OF DEPENDENCY

MEASURING COVARIANCE AND CORRELATION

CALCULATING STATISTICS IN PRACTICE

COMBINING NORMAL DISTRIBUTIONS

CONCLUSION

Questions

CHAPTER 3 - Core Finance Theories and the Cost of Capital

INTRODUCTION

RISK REDUCTION FROM DIVERSIFICATION

SYSTEMATIC VERSUS UNSYSTEMATIC RISK

THE MARKET PORTFOLIO

THE CAPITAL ASSET PRICING MODEL

USING BETA TO DETERMINE THE REQUIRED RETURN FOR A STOCK

OTHER FACTOR MODELS

COST OF DEBT

WEIGHTED AVERAGE COST OF CAPITAL

MODIGLIANI AND MILLER

PATTERNS OF DEBT AND EQUITY IN CAPITAL STRUCTURES

CONCLUSION

Questions

CHAPTER 4 - Capital Budgeting Tools

INTRODUCTION

THREE WAYS TO EVALUATE INVESTMENTS

CALCULATING NET PRESENT VALUE

NET PRESENT VALUE EXAMPLE

CALCULATING INTERNAL RATE OF RETURN

CALCULATING YEARS TO PAYBACK

FINANCIAL DECISION MAKING

THE ANNUITY FORMULA

VALUING AN ANNUITY WITH MORE FREQUENT CASH FLOWS

USING THE PRESENT VALUE FORMULA AND THE ANNUITY FORMULA TO VALUE A BOND

USING THE ANNUITY FORMULA TO VALUE A MORTGAGE

NPV USING THE ANNUITY FORMULA

VALUING A PERPETUITY

VALUING A GROWTH PERPETUITY

INTRODUCTION TO UNCERTAINTY

CONCLUSION

Questions

CHAPTER 5 - Techniques for Handling Uncertainty

INTRODUCTION

USING SCENARIO ANALYSIS

USING MONTE CARLO SIMULATION

UNIFORM RANDOM NUMBERS

TRANSFORMING UNIFORM DISTRIBUTIONS

ADDING AND MULTIPLYING TWO RANDOM NUMBERS

USING RANDOM NUMBERS BUDGET IN ANALYSIS

USING RANDOM NUMBERS IN A CAPITAL BUDGETING ANALYSIS

CONCLUSION

Questions

CHAPTER 6 - Real Option Analysis of Capital Investments

INTRODUCTION

WHY STUDY OPTIONS?

WHAT IS A REAL OPTION?

TYPES OF REAL OPTIONS

METHODS FOR VALUING REAL OPTIONS

CONCLUSION

Questions

APPENDIX - Day Counting for Interest Rate Calculations

Questions and Answers

About the Author

Index

Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding.

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Copyright © 2010 by Stuart A. McCrary. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

McCrary, Stuart A.

Mastering corporate finance essentials : the critical quantitative methods and tools in finance / Stuart A. McCrary.

p. cm.—(Wiley finance series)

Includes index.

eISBN : 978-0-470-58893-2

1. Corporations—Finance. 2. Business enterprises—Finance. 3. Capital budget.

4. Capital investments. I. Title.

HG4026.M384 2010

658.15—dc22

2009033769

To my loving wife, Nancy

Preface

Mastering Corporate Finance Essentials is directed to corporate managers who work with their companies’ finance departments and need to understand their work, priorities, and methods. Since corporate finance is at the heart of many key issues, from performance evaluation to project funding, corporate managers must be able to discuss, assess, and contribute to the financial decision-making process to be successful.

The book is written as a text for an executive masters program in business school or as part of the business curriculum in a professional degree program (engineering, law, medicine, etc.). To respect the scarce time of the student, the most important material occupies the main text. Numerous stand-alone inserts, mostly in the detailed answers to review questions, dig into topics more deeply and may present some topics that are more quantitative. Although this text is designed as a concise book covering just the essentials, these inserts devote considerable attention to “quantitative finance,” including alternatives to discounted cash flow analysis.

The text is designed to permit the reader to quickly learn present value techniques in Chapter 1. Chapter 2 includes a review of statistics used in corporate finance. Chapter 3 summarizes the most important lessons in corporate finance. Chapter 4 synthesizes material in each earlier chapter to apply it to valuing projects and making investment decisions. Chapter 5 introduces additional tools to evaluate risk. Finally, Chapter 6 extends traditional financial tools to value risk and opportunities.

Each chapter builds a foundation for later chapters. The book ends with important topics in quantitative finance. However, readers can focus on traditional corporate finance and skip the later chapters.

Review questions follow each chapter. The book includes detailed answers to review questions that explore topics in greater depth. A short course can focus on the essential topics presented in the chapters. Instructors with more time can include the questions and answers to present practical, hands-on details. The detailed questions and answers work well for self-study.

This book is quantitative, because the field of finance is quantitative. Difficult topics are explained in clear and simple language. Numerous examples demonstrate how to perform each analysis and assist the reader to understand the material. The text also offers advice on how to use Excel for financial analysis.

A companion text on financial accounting, called Mastering Financial Accounting Essentials, presents key accounting concepts in a similarly condensed format. This book focuses on understanding accounting as a reader of financial statements or as a business manager. Mastering Financial Accounting Essentials is a great book to use to round out your understanding of business financial results.

Stuart A. McCrary August 2009

Acknowledgments

I would like to thank the many people at Chicago Partners LLC (a division of Navigant Consulting, Inc.) for their advice on presenting this corporate finance curriculum simply. In addition, I thank Paula Mikrut for making a careful reading of the text.

I also want to thank my students and the administration of Northwestern University, especially program directors Walter B. Herbst and Richard M. Lueptow. This book reflects my efforts to create an executive masters curriculum that covers topics in corporate finance in an incredibly short period. The class reflects our mutual efforts to present advanced financial information to nonfinance professionals so that these students can become more effective business leaders.

CHAPTER 1

Time Value of Money Toolbox

INTRODUCTION

One of the most important tools used in corporate finance is present value mathematics. These techniques are used to evaluate projects, make financial decisions, and evaluate investments. This chapter explains the time value of money, including present value (PV) and future value (FV), and how to adjust valuation formulas for various interest rate conventions. The chapter also presents several shortcuts to value a series of cash flows that fit a few standard patterns.

Readers should begin by developing an intuitive understanding of why it is necessary to incorporate interest rates into any analysis involving different periods of time. This understanding leads to a simple set of formulas expressing several time value relationships. After developing an intuitive understanding, readers will find it easy to incorporate interest rates by using the formulas for present value and/or future value in their analyses. Although this analysis shows up quite often, students will be relieved to find that its application is similar in most instances.

CASH FLOWS

Much of this text focuses on cash flows. Accountants realize the importance of cash; they devote an entire statement to the analysis of the sources and the uses of cash and cash balances. Accountants are interested in tracking cash flow in large measure because a company must have adequate cash to survive and prosper. Start-up companies may run out of cash before they have a chance to establish their businesses. Even established companies focus on both the profitability of the business and the flow of cash.

Corporate finance uses the same or similar measure of cash flow as accountants track in the statement of cash flows. However, this chapter and much of this book rely on cash flows for a completely different analysis and treat the cash flows from a project or even the cash flows of an entire corporation much like the cash flows of a bond. With a bond, investors transfer money today to borrowers, who in turn pay interest and eventually repay the loan. The size and timing of the cash payments and cash receipts determines the attractiveness of the bond investment. The techniques described herein will enable investors to evaluate the cash flows of any investment regardless of when the cash flows occur.

FUTURE VALUE

The future value of a cash flow is the value at some specified future time of a cash flow that occurs immediately. The concept of future value allows a company to decide whether cash flows that occur at two different times are equivalent. The way in which the two cash flows are equivalent is the subject of this chapter and will be explained subsequently.

Suppose that a company issues a bill that requires a customer to pay $100 upon receipt. The customer asks for extra time to pay. The company can borrow at an 8 percent interest rate. The company tells the customer that it will accept $102 instead in three months.

The company calculated the amount of cash it would accept that would be equivalent to getting $100 immediately. If the delay in receiving payment causes the company to borrow $100 for three months, the company must account for the interest on the loan. The formula for interest might look like Equation 1.1.

(1.1)

The immediate payment of $100 in the preceding example is called the present value. The later payment is called a future value. As has been demonstrated, the two amounts are linked by the interest rate and the amount of time between the two payment dates.

In the preceding example, an 8 percent interest rate was used to determine an equivalent future payment from a present value. The method relied on a bank rate of interest. In fact, the company may still prefer the immediate payment of $100 to a deferred payment of $102. The deferred payment exposes the company to the risk of nonpayment for a longer period of time. The delay increases the amount the company must record as an account receivable in its financial statements and requires the company to include a liability on the balance sheet for the bank loan.

To address these concerns, the company may increase the interest rate used in determining the future value it will accept in lieu of the immediate payment of $100. Later, this text will explore factors that affect the interest rate or return that links present values to future values. This chapter, however, generally assumes that the company knows the required rate that incorporates these factors.

A more general formula for interest appears in Equation 1.2.

(1.2)

where Time is the interval in years between the time of the present value and the time of the future value and Rate is the annual interest rate.

The value of a cash payment that occurs immediately is the present value. The future value of this cash flow is the present value plus interest, as set forth in Equation 1.3.

(1.3)

Substitute the formula for interest in Equation 1.2 into the formula for future value in Equation 1.3 to produce Equation 1.4.

(1.4)

Finally, simplify Equation 1.4 by collecting terms. The result is Equation 1.5, which shows that the future value is related to the present value by a rate of interest that applies to the time from the present payments to the future payments.

(1.5)

Compound Interest

The formula for future value in Equation 1.5 is correct for short intervals of time, but most investments pay interest every three months, every six months, or annually. When investments pay interest between the time of the present value and the time of the future value, the formula in Equation 1.5 is not correct. This section explains how these interim interest payments affect the calculation of the future value. First, it is necessary to explain the compounding process.

An old-fashioned passbook bank account illustrates the basic concepts of future value and compound interest. In the days before businesses had easy access to computers, banks used and reused a passbook as a simple ledger to account for customer deposits, withdrawals, and interest. Each time the customer deposited or withdrew funds, the new information was added to a running ledger. Modern monthly and quarterly statements work the same way, except that they include only a one-month or 3-month period of time. In contrast, the passbook included a running total of all deposits, withdrawals, and interest payments since the account was opened.

A customer could deposit an amount and see interest accumulate. Table 1.1 illustrates the process.

The investment of $1,000 on 3/14/20X1 grows to $1,040.28 by December 31, 20X1. In the absence of taxes, the cash amount on 3/14/20X1 is linked to the year-end balance of $1,040.28 by the amount of interest earned during the period.

The specific calculations in Table 1.1 require some explanation. In this example, interest is paid at the end of every calendar quarter. This example employs one commonly used method to calculate the number of days of interest—each month is assumed to have exactly 30 days and each year has 360 days. (See the appendix for a description of this method and other day-counting methods.) The first interest payment accumulates at 5 percent interest. If the rate applied for a full year (that is, the interest rate applied for a full year and was not compounded), the interest would be $50 ($1,000 times 5 percent). The interest for the 16-day period from March 14 to March 31 is a fraction of that annual amount equal to $50 * 16/360 or $2.22.

The period from March 31 to June 30 contains exactly 91 actual days but the counting convention used here assumes there are 30 days in each month or 90 in each quarter. The interest for this quarter is $1,002.22 * 5 percent * 90/360 or $12.53. Notice that this old-fashioned way to count days calls for an interest payment of $12.53, whereas a more precise method would calculate $1,002.22 * 91/365 or $12.49. The two values are generally fairly close, especially over a year or more. In some cases, the way interest is applied can have a big impact on the future value. It is important to understand the day-counting convention that is being used and to use the interest rate correctly.

TABLE 1.1Passbook Investment at 5 Percent Quarterly Interest

Suppose a business orders some goods and could either pay the supplier $1,000 on March 14 or pay $1,040.28 at the end of the year when the goods will be delivered. Because the company can invest the $1,000 deposit, the customer could pay $1,000 now or invest the funds at 5 percent and pay $1,040.28 at year-end. Because the bank account provides exactly enough interest to pay the higher amount at the end of the year, the company does not prefer one alternative to the other. (Eventually, the comparison must include taxes and the risk of loss on the investment.)

Alternatively, the company could borrow $1,000 on March 14 at 5 percent and pay the lower invoice amount. The interest would accumulate to $1,040.28 by year-end. The company would need to pay $1,040.28 to repay the loan, which exactly equals the amount of the delayed payment.

A company cannot both borrow at 5 percent and invest at 5 percent as implied by the foregoing description. It is not necessary to be able to borrow and lend at the same rate. Rather, it is important to determine the relevant interest rate that can link the value on March 14 and the value on December 31. The calculation of future value using the appropriate interest rate provides a way to compare two different cash flows at different points in time.

The passbook investment detailed in Table 1.1 includes compound interest. In other words, the interest paid on March 31 also earns interest following that payment date. The value of the account rises on each payment date, and the base used to determine the interest payment is larger in later quarters. As a result, the interest payments are larger than if the bank had paid simple interest.

In contrast, if the bank paid simple interest on $1,000 using Equation 1.5, the customer would not benefit from earning interest on the quarterly interest payments. The interest rate would apply for 286/360 years or .794 years, taking the fraction of the year using the 30/360 day counting method shown in Table 1.1. The future value using Equation 1.5 would be

(1.6)

Paying the customer quarterly (or even more frequent) interest has the effect of raising the return to the investor. It is important to follow the correct compounding assumption to determine the present or future value from a particular interest rate. This chapter will later address how to handle the difference in interest created by different compounding assumptions.

The formula for compound interest begins much like the formula for simple interest given in Equation 1.5. Suppose that the interest rate is 6 percent per year and an investment pays interest annually. The future value at the end of one year is shown in Equation 1.7.

(1.7)

After one year, a passbook would contain PV * (1 + Rate). This amount from Equation 1.7 appears in Equation 1.8 in square brackets and is reinvested for another year.

(1.8)

After two years, a passbook would contain PV * (1 + Rate)2. The amount from Equation 1.8 appears in Equation 1.9 in square brackets and is reinvested for another year.

(1.9)

Table 1.2 summarizes the growth in principal, now applying the specified rate of 6 percent and also showing the calculation of the interest generated in each period. In each case, the starting principal amount appears in the square brackets, and interest equals this updated principal amount times the annual interest rate.

The general formula for future value for an investment that pays annual interest appears in Equation 1.10.

(1.10)

where i equals the number of years between the present and the future.

TABLE 1.2 Passbook Investment at 6 Percent Annual Interest

TABLE 1.3 Passbook Investment at 6 Percent Annual Interest

Equation 1.10 makes it easy to calculate the future value for much longer periods without needing to calculate individual interest payments as was done in Table 1.2.

Some care should be exercised in using Equation 1.10 for fractional periods. For example, the future value after 3.5 years could be calculated successively, as in Table 1.3. In this case, the interest is prorated for half of a year.

Applying Equation 1.10 for the fractional period of 3.5 years yields approximately the same answer:

(1.11)

More Frequent Compounding

Equations 1.7 to 1.10 develop a general formula for compounding an investment that pays interest annually. Most U.S. bonds, along with many other instruments, pay interest twice each year. Equation 1.12 shows the future value of a cash flow one year in the future for investments that pay interest twice each year:

(1.12)

The term in the first set of parentheses adjusts the starting present value to the middle of the year using simple interest, much like the adjustment in Equation 1.5. Then the original amount plus the interest collected in six months is reinvested. The term in the second set of parentheses adjusts the starting present value plus interest from the first semiannual interest payment to the end of the year.

The future value one year in the future of a cash flow for investments that pay interest quarterly is presented in Equation 1.13.

(1.13)

Like Equation 1.12 for semiannual interest, the year is divided into subperiods. At the end of each subperiod, the investment pays interest and the interest is available to be reinvested. Equation 1.14 presents a more general formula that can account for rates that compound at difference frequencies.

(1.14)

where Years represents the time between the present and the future value date and Freq refers to the number of compounding periods per year.

For example, an annual bond has a frequency or Freq of one. In this case, Equation 1.14 simplifies to Equation 1.10. A semiannual bond would use 2 for Freq, and there would be twice as many semiannual periods and years between the present and the future value date. Two other common frequencies are quarterly for many money market instruments and monthly for mortgage investments. Banks may pay interest with daily compounding, in which case Freq would be 365 or 366. Finally, the shortest possible compounding period could be a tiny fraction of a year. Compounding over infinitesimally small compounding periods, called continuous compounding, is discussed further along in the text.

THE IMPACT OF COMPOUNDING FREQUENCY ON FUTURE VALUE

Interest on interest increases the effective interest rate. In other words, compound interest raises the future value compared to simple interest. In general, the more frequently interest is compounded, the higher the effective interest rate and the higher the resulting future value.

Table 1.4 begins with a present value of $1,000. The interest rate is 6 percent and the future value 10 years later is determined for simple interest (no compounding), and several commonly assumed compounding frequencies.

TABLE 1.4 Compounding Frequency at 6 Percent Interest

FrequencyDescriptionFuture Value0Simple1,600.001Annual1,790.852Semiannual1,806.114Quarterly1,814.0212Monthly1,819.40365Daily1,822.03∞Continuous1,822.12

FIGURE 1.1 Future Value versus Compounding Frequency

The data is presented visually in Figure 1.1, which plots the future value for simple interest and various compounding frequencies.

The important point to remember is that it is necessary to know what compounding assumptions are associated with the rate of interest used in present value and future value calculations and to develop a value using the correct assumption.

EQUIVALENT INTEREST RATE

More frequent compounding has the same effect as using a higher interest rate. That is, for a given present value, the future value increases as the assumed interest rate rises. The future value also increases as the compounding frequency rises.

Not surprisingly, market participants adjust downward the stated rates of frequently compounded interest rates to compensate for the larger amount of interest on interest earned with frequent compounding. It is often necessary to determine how much to adjust a particular rate to produce the same results as a different interest rate with a different compounding frequency.

Suppose a 10 percent quarterly-compounded interest rate is used—that is, the interest rate for one year is 10 percent so that interest of 2.5 percent is paid quarterly. By applying Equation 1.14, it is possible to determine the annually compounded rate that is equivalent.

Applying Equation 1.14 to a $100 present value for one year, the future value would be $110.38 as shown in Equation 1.15.

(1.15)

To determine the annual interest rate that produces the same result (i.e., produces in the same future value), set up Equation 1.14 again for an annually compounded rate.

(1.16)

It is easy to see that the annually-compounded rate of 10.38 percent would produce the same future value as a 10 percent rate compounded quarterly. The rate calculated from Equation 1.16 is called the equivalent annual rate or the effective annual rate. (Note that the “annual percentage rate” that mortgage lenders are required to disclose to borrowers is not the same. That rate includes the impact of certain loan origination costs not included here.)

To calculate an equivalent semiannual rate, set up Equation 1.14 again for two compounding periods per year.

(1.17)

This rate is a bit more challenging to calculate. By manipulating a few terms in Equation 1.17, it is possible to solve for the equivalent semiannual rate.

(1.18)

Simplify the right side with division and take the square root of both sides as shown in Equation 1.19.

(1.19)

Finally, rearrange with a little more algebra.

(1.20)

The equations in this book evaluated with more decimal points of accuracy than appear on the page. Equation 1.20 equals 10.124 percent using the values printed due to rounding.

This method converts a rate with one compounding frequency to an equivalent rate with a different compounding frequency by determining the rate that produces the same future value as the future value associated with the known beginning rate.

CONTINUOUSLY COMPOUNDED INTEREST

Figure 1.1 makes clear that more frequent compounding results in a higher future value (or equivalently, a higher effective interest rate). Figure 1.1 also suggests that the impact of more frequent compounding has a larger impact going from one to two to four compounding periods than the impact of compounding more frequently than monthly. Table 1.4 demonstrates that, for a given annual rate, daily compounding produces a higher future value than monthly compounding, but the impact is smaller. Compounding more frequently than daily produces very little difference in the future value or the effective interest rate.

Although the impact is small, many people use interest rates that are continuously compounded. Continuously compounded rates assume that interest is paid and reinvested after each infinitesimally small step in time. These rates are used not to raise the effective interest rate but instead to simplify the math. For example, option pricing formulas that use continuously compounded rates may be simpler or easier to apply than rates with other compounding frequencies.

The future value of a cash flow using continuous compounding is shown in Equation 1.21.

(1.21)

TABLE 1.5 Future Value at 6 Percent Continuous Compounding

TimeFuture ValueExcel Syntax0100.00=100*exp(6%*0)1106.18=100*exp(6%*1)2112.75=100*exp(6%*2)5134.99=100*exp(6%*5)10182.211001exp(6%110)

where Rate is a continuously compounded interest rate, Time again measures the difference in years between the future valuing date and the present, and e refers to the mathematical constant equal to 2.718.

Questions and answers that follow at the end of the chapter will use the continuously compounded rate and provide a more complete explanation of how to use continuous compounding. For a short explanation, refer to Table 1.5