Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 CHAPTER NINE 220 C A P I T A L BUDGETING AND RISK Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 LONG BEFORE THE development of modern theories linking risk and expected return, smart financial managers adjusted for risk in capital budgeting. They realized intuitively that, other things being equal, risky projects are less desirable than safe ones. Therefore, financial managers demanded a higher rate of return from risky projects, or they based their decisions on conservative estimates of the cash flows. Various rules of thumb are often used to make these risk adjustments. For example, many com- panies estimate the rate of return required by investors in their securities and then use this company cost of capital to discount the cash flows on new projects. Our first task in this chapter is to explain when the company cost of capital can, and cannot, be used to discount a project’s cash flows. We shall see that it is the right hurdle rate for those projects that have the same risk as the firm’s exist- ing business; however, if a project is more risky than the firm as a whole, the cost of capital needs to be adjusted upward and the project’s cash flows discounted at this higher rate. Conversely, a lower discount rate is needed for projects that are safer than the firm as a whole. The capital asset pricing model is widely used to estimate the return that investors require. 1 It states We used this formula in the last chapter to figure out the return that investors expected from a sam- ple of common stocks but we did not explain how to estimate beta. It turns out that we can gain some insight into beta by looking at how the stock price has responded in the past to market fluctuations. Beta is difficult to measure accurately for an individual firm: Greater accuracy can be achieved by looking at an average of similar companies. We will also look at what features make some investments riskier than others. If you know why Exxon Mobil has less risk than, say, Dell Computer, you will be in a better position to judge the relative risks of different capital investment opportunities. Some companies are financed entirely by common stock. In these cases the company cost of cap- ital and the expected return on the stock are the same thing. However, most firms finance themselves partly by debt and the return that they earn on their investments must be sufficient to satisfy both the stockholders and the debtholders. We will show you how to calculate the company cost of capi- tal when the firm has more than one type of security outstanding. There is still another complication: Project betas can shift over time. Some projects are safer in youth than in old age; others are riskier. In this case, what do we mean by the project beta? There may be a separate beta for each year of the project’s life. To put it another way, can we jump from the capital asset pricing model, which looks one period into the future, to the discounted-cash-flow formula for valuing long-lived assets? Most of the time it is safe to do so, but you should be able to recognize and deal with the exceptions. We will use the capital asset pricing model, or CAPM, throughout this chapter. But don’t infer that it is therefore the last word on risk and return. The principles and procedures covered in this chapter work just as well with other models such as arbitrage pricing theory (APT). Expected return ϭ r ϭ r f ϩ 1beta2 1r m Ϫ r f 2 221 1 In a survey of financial practice, Graham and Harvey found that 74 percent of firms always, or almost always, used the capital as- set pricing model to estimate the cost of capital. See J. Graham and C. Harvey, “The Theory and Practice of Corporate Finance: Ev- idence from the Field,” Journal of Financial Economics 60 (May/June 2001), pp. 187–244. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 The company cost of capital is defined as the expected return on a portfolio of all the company’s existing securities. It is used to discount the cash flows on projects that have similar risk to that of the firm as a whole. For example, in Table 8.2 we estimated that investors require a return of 9.2 percent from Pfizer common stock. If Pfizer is contemplating an expansion of the firm’s existing business, it would make sense to discount the forecasted cash flows at 9.2 percent. 2 The company cost of capital is not the correct discount rate if the new projects are more or less risky than the firm’s existing business. Each project should in prin- ciple be evaluated at its own opportunity cost of capital. This is a clear implication of the value-additivity principle introduced in Chapter 7. For a firm composed of assets A and B, the firm value is Here PV(A) and PV(B) are valued just as if they were mini-firms in which stock- holders could invest directly. Investors would value A by discounting its fore- casted cash flows at a rate reflecting the risk of A. They would value B by dis- counting at a rate reflecting the risk of B. The two discount rates will, in general, be different. If the present value of an asset depended on the identity of the company that bought it, present values would not add up. Remember, a good project is a good project is a good project. If the firm considers investing in a third project C, it should also value C as if C were a mini-firm. That is, the firm should discount the cash flows of C at the ex- pected rate of return that investors would demand to make a separate investment in C. The true cost of capital depends on the use to which that capital is put. This means that Pfizer should accept any project that more than compensates for the project’s beta. In other words, Pfizer should accept any project lying above the upward-sloping line that links expected return to risk in Figure 9.1. If the project has a high risk, Pfizer needs a higher prospective return than if the project has a low risk. Now contrast this with the company cost of capital rule, which is to ac- cept any project regardless of its risk as long as it offers a higher return than the com- pany’s cost of capital. In terms of Figure 9.1, the rule tells Pfizer to accept any proj- ect above the horizontal cost of capital line, that is, any project offering a return of more than 9.2 percent. It is clearly silly to suggest that Pfizer should demand the same rate of return from a very safe project as from a very risky one. If Pfizer used the company cost of capital rule, it would reject many good low-risk projects and accept many poor high-risk projects. It is also silly to suggest that just because another company has a low company cost of capital, it is justified in accepting projects that Pfizer would reject. The notion that each company has some individual discount rate or cost of cap- ital is widespread, but far from universal. Many firms require different returns ϭ sum of separate asset values Firm value ϭ PV1AB2ϭ PV1A2ϩ PV1B2 222 PART II Risk 9.1 COMPANY AND PROJECT COSTS OF CAPITAL 2 Debt accounted for only about 0.3 percent of the total market value of Pfizer’s securities. Thus, its cost of capital is effectively identical to the rate of return investors expect on its common stock. The compli- cations caused by debt are discussed later in this chapter. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 from different categories of investment. For example, discount rates might be set as follows: CHAPTER 9 Capital Budgeting and Risk 223 Project beta Company cost of capital Security market line showing required return on project Average beta of the firm's assets = .71 r (required return) 3.5 9.2 FIGURE 9.1 A comparison between the company cost of capital rule and the required return under the capital asset pricing model. Pfizer’s company cost of capital is about 9.2 percent. This is the correct discount rate only if the project beta is .71. In general, the correct discount rate increases as project beta increases. Pfizer should accept projects with rates of return above the security market line relating required return to beta. Category Discount Rate Speculative ventures 30% New products 20 Expansion of existing business 15 (company cost of capital) Cost improvement, known technology 10 Perfect Pitch and the Cost of Capital The true cost of capital depends on project risk, not on the company undertaking the project. So why is so much time spent estimating the company cost of capital? There are two reasons. First, many (maybe, most) projects can be treated as av- erage risk, that is, no more or less risky than the average of the company’s other as- sets. For these projects the company cost of capital is the right discount rate. Sec- ond, the company cost of capital is a useful starting point for setting discount rates for unusually risky or safe projects. It is easier to add to, or subtract from, the com- pany cost of capital than to estimate each project’s cost of capital from scratch. There is a good musical analogy here. 3 Most of us, lacking perfect pitch, need a well-defined reference point, like middle C, before we can sing on key. But anyone who can carry a tune gets relative pitches right. Businesspeople have good intuition about relative risks, at least in industries they are used to, but not about absolute risk or required rates of return. Therefore, they set a companywide cost of capital as a benchmark. This is not the right hurdle rate for everything the company does, but adjustments can be made for more or less risky ventures. 3 The analogy is borrowed from S. C. Myers and L. S. Borucki, “Discounted Cash Flow Estimates of the Cost of Equity Capital—A Case Study,” Financial Markets, Institutions, and Investments 3 (August 1994), p. 18. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 Suppose that you are considering an across-the-board expansion by your firm. Such an investment would have about the same degree of risk as the existing business. Therefore you should discount the projected flows at the company cost of capital. Companies generally start by estimating the return that investors require from the company’s common stock. In Chapter 8 we used the capital asset pricing model to do this. This states An obvious way to measure the beta (␤) of a stock is to look at how its price has re- sponded in the past to market movements. For example, look at the three left-hand scatter diagrams in Figure 9.2. In the top-left diagram we have calculated monthly re- turns from Dell Computer stock in the period after it went public in 1988, and we have plotted these returns against the market returns for the same month. The second dia- gram on the left shows a similar plot for the returns on General Motors stock, and the third shows a plot for Exxon Mobil. In each case we have fitted a line through the points. The slope of this line is an estimate of beta. 4 It tells us how much on average the stock price changed for each additional 1 percent change in the market index. The right-hand diagrams show similar plots for the same three stocks during the subsequent period, February 1995 to July 2001. Although the slopes varied from the first period to the second, there is little doubt that Exxon Mobil’s beta is much less than Dell’s or that GM’s beta falls somewhere between the two. If you had used the past beta of each stock to predict its future beta, you wouldn’t have been too far off. Only a small portion of each stock’s total risk comes from movements in the mar- ket. The rest is unique risk, which shows up in the scatter of points around the fitted lines in Figure 9.2. R-squared (R 2 ) measures the proportion of the total variance in the stock’s returns that can be explained by market movements. For example, from 1995 to 2001, the R 2 for GM was .25. In other words, a quarter of GM’s risk was market risk and three-quarters was unique risk. The variance of the returns on GM stock was 964. 5 So we could say that the variance in stock returns that was due to the market was and the variance of unique returns was The estimates of beta shown in Figure 9.2 are just that. They are based on the stocks’ returns in 78 particular months. The noise in the returns can obscure the true beta. Therefore, statisticians calculate the standard error of the estimated beta to show the extent of possible mismeasurement. Then they set up a confidence interval of the estimated value plus or minus two standard errors. For example, the standard error of GM’s estimated beta in the most recent period is .20. Thus the confidence interval for GM’s beta is 1.00 plus or minus 2 ϫ .20. If you state that the true beta for GM is between .60 and 1.40, you have a 95 percent chance of being right. Notice that we can be more confident of our estimate of Exxon Mobil’s beta and less confident of Dell’s. Usually you will have more information (and thus more confidence) than this simple calculation suggests. For example, you know that Exxon Mobil’s estimated .75 ϫ 964 ϭ 723 25 ϫ 964 ϭ 241, Expected stock return ϭ r f ϩ␤1r m Ϫ r f 2 224 PART II Risk 9.2 MEASURING THE COST OF EQUITY 4 Notice that you must regress the returns on the stock on the market returns. You would get a very sim- ilar estimate if you simply used the percentage changes in the stock price and the market index. But sometimes analysts make the mistake of regressing the stock price level on the level of the index and ob- tain nonsense results. 5 This is an annual figure; we annualized the monthly variance by multiplying by 12 (see footnote 17 in Chapter 7). The standard deviation was percent.2964 ϭ 31.0 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 -10-20-30 0 10 20 30 -30 -40 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 -40 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -10 0 10 20 -30 -20 -10 0 10 20 30 -10 0 10 20 Dell Computer return % August 1988– January 1995 β = 1.62 (.52) R 2 = .11 Dell Computer return % February 1995– July 2001 Market return, % Market return, % β = 2.02 (.38) R 2 = .27 August 1988– January 1995 Market return, % Market return, % General Motors return % β = .8 (.24) R 2 = .13 February 1995– July 2001 General Motors return % β = 1.00 (.20) R 2 = .25 February 1995– July 2001 Exxon Mobil return % August 1988– January 1995 Market return, % Market return, % β = .52 (.10) R 2 = .28 Exxon Mobil return % β = .42 (.11) R 2 = .16 FIGURE 9.2 We have used past returns to estimate the betas of three stocks for the periods August 1988 to January 1995 (left- hand diagrams) and February 1995 to July 2001 (right-hand diagrams). Beta is the slope of the fitted line. Notice that in both periods Dell had the highest beta and Exxon Mobil the lowest. Standard errors are in parentheses below the betas. The standard error shows the range of possible error in the beta estimate. We also report the proportion of total risk that is due to market movements (R 2 ). 225 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 beta was well below 1 in the previous period, while Dell’s estimated beta was well above 1. Nevertheless, there is always a large margin for error when estimating the beta for individual stocks. Fortunately, the estimation errors tend to cancel out when you estimate betas of portfolios. 6 That is why financial managers often turn to industry betas. For example, Table 9.1 shows estimates of beta and the standard errors of these estimates for the common stocks of four large railroad companies. Most of the standard errors are above .2, large enough to preclude a precise estimate of any particular utility’s beta. However, the table also shows the estimated beta for a portfolio of all four railroad stocks. Notice that the estimated industry beta is more reliable. This shows up in the lower standard error. The Expected Return on Union Pacific Corporation’s Common Stock Suppose that in mid-2001 you had been asked to estimate the company cost of cap- ital of Union Pacific Corporation. Table 9.1 provides two clues about the true beta of Union Pacific’s stock: the direct estimate of .40 and the average estimate for the industry of .50. We will use the industry average of .50. 7 In mid-2001 the risk-free rate of interest r f was about 3.5 percent. Therefore, if you had used 8 percent for the risk premium on the market, you would have con- cluded that the expected return on Union Pacific’s stock was about 7.5 percent: 8 226 PART II Risk Standard ␤ equity Error Burlington Northern & Santa Fe .64 .20 CSX Transportation .46 .24 Norfolk Southern .52 .26 Union Pacific Corp. .40 .21 Industry portfolio .50 .17 TABLE 9.1 Estimated betas and costs of (equity) capital for a sample of large railroad companies and for a portfolio of these companies. The precision of the portfolio beta is much better than that of the betas of the individual companies—note the lower standard error for the portfolio. 6 If the observations are independent, the standard error of the estimated mean beta declines in propor- tion to the square root of the number of stocks in the portfolio. 7 Comparing the beta of Union Pacific with those of the other railroads would be misleading if Union Pacific had a materially higher or lower debt ratio. Fortunately, its debt ratio was about average for the sample in Table 9.1. 8 This is really a discount rate for near-term cash flows, since it rests on a risk-free rate measured by the yield on Treasury bills with maturities less than one year. Is this, you may ask, the right discount rate for cash flows from an asset with, say, a 10- or 20-year expected life? Well, now that you mention it, possibly not. In 2001 longer-term Treasury bonds yielded about 5.8 percent, that is, about 2.3 percent above the Treasury bill rate. The risk-free rate could be defined as a long-term Treasury bond yield. If you do this, however, you should subtract the risk premium of Treasury bonds over bills, which we gave as 1.8 percent in Table 7.1. This gives a rough-and-ready estimate of the expected yield on short-term Treasury bills over the life of the bond: The expected average future Treasury bill rate should be used in the CAPM if a discount rate is needed for an extended stream of cash flows. In 2001 this “long-term r f ” was a bit higher than the Treasury bill rate. ϭ .058 Ϫ .019 ϭ .039, or 3.9% Expected average T-bill rate ϭ T-bond yield Ϫ premium of bonds over bills Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 We have focused on using the capital asset pricing model to estimate the ex- pected returns on Union Pacific’s common stock. But it would be useful to get a check on this figure. For example, in Chapter 4 we used the constant-growth DCF formula to estimate the expected rate of return for a sample of utility stocks. 9 You could also use DCF models with varying future growth rates, or perhaps arbitrage pricing theory (APT). We showed in Section 8.4 how APT can be used to estimate expected returns. ϭ 3.5 ϩ .518.02ϭ 7.5% Expected stock return ϭ r f ϩ␤1r m Ϫ r f 2 CHAPTER 9 Capital Budgeting and Risk 227 9 The United States Surface Transportation Board uses the constant-growth model to estimate the cost of equity capital for railroad companies. We will review its findings in Chapter 19. 9.3 CAPITAL STRUCTURE AND THE COMPANY COST OF CAPITAL In the last section, we used the capital asset pricing model to estimate the return that investors require from Union Pacific’s common stock. Is this figure Union Pa- cific’s company cost of capital? Not if Union Pacific has other securities outstand- ing. The company cost of capital also needs to reflect the returns demanded by the owners of these securities. We will return shortly to the problem of Union Pacific’s cost of capital, but first we need to look at the relationship between the cost of capital and the mix of debt and equity used to finance the company. Think again of what the company cost of capital is and what it is used for. We define it as the opportunity cost of capital for the firm’s existing assets; we use it to value new assets that have the same risk as the old ones. If you owned a portfolio of all the firm’s securities—100 percent of the debt and 100 percent of the equity—you would own the firm’s assets lock, stock, and barrel. You wouldn’t share the cash flows with anyone; every dollar of cash the firm paid out would be paid to you. You can think of the company cost of capi- tal as the expected return on this hypothetical portfolio. To calculate it, you just take a weighted average of the expected returns on the debt and the equity: For example, suppose that the firm’s market-value balance sheet is as follows: Asset value 100 Debt value (D)30 Equity value (E)70 Asset value 100 Firm value (V) 100 Note that the values of debt and equity add up to the firm value (D ϩ E ϭ V) and that the firm value equals the asset value. (These figures are market values, not book values: The market value of the firm’s equity is often substantially different from its book value.) ϭ debt debt ϩ equity r debt ϩ equity debt ϩ equity r equity Company cost of capital ϭ r assets ϭ r portfolio Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 If investors expect a return of 7.5 percent on the debt and 15 percent on the eq- uity, then the expected return on the assets is If the firm is contemplating investment in a project that has the same risk as the firm’s existing business, the opportunity cost of capital for this project is the same as the firm’s cost of capital; in other words, it is 12.75 percent. What would happen if the firm issued an additional 10 of debt and used the cash to repurchase 10 of its equity? The revised market-value balance sheet is Asset value 100 Debt value (D)40 Equity value (E)60 Asset value 100 Firm value (V) 100 The change in financial structure does not affect the amount or risk of the cash flows on the total package of debt and equity. Therefore, if investors required a re- turn of 12.75 percent on the total package before the refinancing, they must require a 12.75 percent return on the firm’s assets afterward. Although the required return on the package of debt and equity is unaffected, the change in financial structure does affect the required return on the individual se- curities. Since the company has more debt than before, the debtholders are likely to demand a higher interest rate. We will suppose that the expected return on the debt rises to 7.875 percent. Now you can write down the basic equation for the re- turn on assets and solve for the return on equity Increasing the amount of debt increased debtholder risk and led to a rise in the return that debtholders required (r debt rose from 7.5 to 7.875 percent). The higher leverage also made the equity riskier and increased the return that shareholders re- quired (r equity rose from 15 to 16 percent). The weighted average return on debt and equity remained at 12.75 percent: Suppose that the company decided instead to repay all its debt and to replace it with equity. In that case all the cash flows would go to the equity holders. The com- pany cost of capital, r assets , would stay at 12.75 percent, and r equity would also be 12.75 percent. ϭ 1.4 ϫ 7.8752ϩ 1.6 ϫ 162ϭ 12.75% r assets ϭ 1.4 ϫ r debt 2ϩ 1.6 ϫ r equity 2 r equity ϭ 16.0% ϭ a 40 100 ϫ 7.875 bϩ a 60 100 ϫ r equity bϭ 12.75% r assets ϭ D V r debt ϩ E V r equity ϭ a 30 100 ϫ 7.5 bϩ a 70 100 ϫ 15 bϭ 12.75% r assets ϭ D V r debt ϩ E V r equity 228 PART II Risk Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 How Changing Capital Structure Affects Beta We have looked at how changes in financial structure affect expected return. Let us now look at the effect on beta. The stockholders and debtholders both receive a share of the firm’s cash flows, and both bear part of the risk. For example, if the firm’s assets turn out to be worth- less, there will be no cash to pay stockholders or debtholders. But debtholders usu- ally bear much less risk than stockholders. Debt betas of large blue-chip firms are typically in the range of .1 to .3. 10 If you owned a portfolio of all the firm’s securities, you wouldn’t share the cash flows with anyone. You wouldn’t share the risks with anyone either; you would bear them all. Thus the firm’s asset beta is equal to the beta of a portfolio of all the firm’s debt and its equity. The beta of this hypothetical portfolio is just a weighted average of the debt and equity betas: Think back to our example. If the debt before the refinancing has a beta of .1 and the equity has a beta of 1.1, then What happens after the refinancing? The risk of the total package is unaffected, but both the debt and the equity are now more risky. Suppose that the debt beta in- creases to .2. We can work out the new equity beta: You can see why borrowing is said to create financial leverage or gearing. Financial leverage does not affect the risk or the expected return on the firm’s assets, but it does push up the risk of the common stock. Shareholders demand a correspond- ingly higher return because of this financial risk. Figure 9.3 shows the expected return and beta of the firm’s assets. It also shows how expected return and risk are shared between the debtholders and equity hold- ers before the refinancing. Figure 9.4 shows what happens after the refinancing. Both debt and equity are now more risky, and therefore investors demand a higher return. But equity accounts for a smaller proportion of firm value than before. As a result, the weighted average of both the expected return and beta on the two components is unchanged. Now you can see how to unlever betas, that is, how to go from an observed ␤ equity to ␤ assets. You have the equity beta, say, 1.2. You also need the debt beta, say, .2, and the relative market values of debt (D/V) and equity (E/V). If debt accounts for 40 percent of overall value V, ␤ assets ϭ 1.4 ϫ .22ϩ 1.6 ϫ 1.22ϭ .8 ␤ equity ϭ 1.2 .8 ϭ 1.4 ϫ .22ϩ 1.6 ϫ␤ equity 2 ␤ assets ϭ␤ portfolio ϭ D V ␤ dept ϩ E V ␤ equity ␤ assets ϭ 1.3 ϫ .12ϩ 1.7 ϫ 1.12ϭ .8 ␤ assets ϭ␤ portfolio ϭ D V ␤ debt ϩ E V ␤ equity CHAPTER 9 Capital Budgeting and Risk 229 10 For example, in Table 7.1 we reported average returns on a portfolio of high-grade corporate bonds. In the 10 years ending December 2000 the estimated beta of this bond portfolio was .17. [...]... set dif- Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk CHAPTER 9 Capital Budgeting and Risk Construction Food Products Pharmaceuticals 47 792 8 39 1814 15 373 561 93 4 91 7 1 49 168 1083 1251 1271 227 Net working capital Fixed assets Total net assets Revenues Net profits Holiport Burchetts Green 251 TA B L E 9 3 Summary... 100 94 .6 89. 6 84.8 94 6 896 ϭ 94 62 848 ϭ 94 63 241 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 242 PART II II Risk 9 Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 Risk Our example illustrates that if we are to use the same discount rate for every future cash flow, then the certainty equivalents must decline steadily as a fraction of the cash flow There’s no law of nature... perimeter well Use a future oil price of $15 per barrel Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk CHAPTER 9 Capital Budgeting and Risk 2 49 b A geologist proposes to discount the cash flows of the new wells at 30 percent to offset the risk of dry holes The oil company’s normal cost of capital is 10 percent Does this... For an explanation of the cost of capital for international investments when there are costs to international diversification, see I A Cooper and E Kaplanis, “Home Bias in Equity Portfolios and the Cost of Capital for Multinational Firms,” Journal of Applied Corporate Finance 8 (Fall 199 5), pp 95 –102 233 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 234 II Risk 9 Capital Budgeting... to calculate its cost of equity based on its own beta estimate? EXCEL Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 248 PART II II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk Risk d Burlington’s cost of debt was 6 percent and its debt-to-value ratio, D/V, was 40 What was Burlington’s company cost of capital? Use the industry average beta 9 Amalgamated Products... There have been a number of studies of the relationship between accounting data and beta Many of these are reviewed in: G Foster: Financial Statement Analysis, 2nd ed., Prentice-Hall, Inc., Englewood Cliffs, N.J., 198 6 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk CHAPTER 9 Capital Budgeting and Risk 245 For... British Airways R2 Beta Standard Error of Beta 25 38 25 25 90 1.37 17 22 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk CHAPTER 9 Capital Budgeting and Risk 247 a What proportion of each stock’s risk was market risk, and what proportion was unique risk? b What is the variance of BP? What is the unique variance? c... is not a fudge factor introduced to offset optimistic cash-flow forecasts Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II Risk © The McGraw−Hill Companies, 2003 9 Capital Budgeting and Risk CHAPTER 9 Capital Budgeting and Risk 243 have the opportunity to invest in a project of normal risk, for which the normal discount rate of 10 percent would be appropriate Thus the firm has a 50... Thus the after-tax cost of debt is rdebt (l Ϫ Tc), where Tc is the marginal corporate tax rate When companies discount an average-risk project, they do not use the company cost of capital as we have computed it They use the after-tax cost of debt to compute the after-tax weighted-average cost of capital or WACC: WACC ϭ rdebt 11 Ϫ Tc 2 D E ϩ requity V V More—lots more—on this in Chapter 19 Back to Union... example, see W H Beaver and J Manegold, “The Association between Market-Determined and Accounting-Determined Measures of Systematic Risk: Some Further Evidence,” Journal of Financial and Quantitative Analysis 10 (June 197 9), pp 231–284 237 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 238 II Risk 9 Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 PART II Risk Those who receive . 20 30 -4 0 -3 0 -2 0 -1 0 0 10 20 30 40 50 -3 0 -2 0 -1 0 0 10 20 30 -3 0 -2 0 -1 0 0 10 20 30 -3 0 -2 0 -1 0 0 10 20 30 -3 0 -2 0 -1 0 0 10 20 30 -3 0 -2 0 -1 0 0 10 20 30 -1 0 0 10 20 -3 0 -2 0 -1 0 0 10 20 30 -1 0 0 10 20 Dell. 31.0 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital Budgeting and Risk © The McGraw−Hill Companies, 2003 -1 0-2 0-3 0 0 10 20 30 -3 0 -4 0 -2 0 -1 0 0 10 20 30 40 50 -3 0 -2 0 -1 0. the Cost of Capital for Multinational Firms,” Journal of Applied Corporate Finance 8 (Fall 199 5), pp. 95 –102. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition II. Risk 9. Capital