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If investors expect a return of 7.5 percent on the debt and 15 percent on the equity, then the expected return on the assets is

D E

rassets V rdebt V requity

a10030 7.5 b a10070 15 b 12.75%

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

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 return 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 securities. 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 return on assets

and solve for the return on equity

requity 16.0%

Increasing the amount of debt increased debtholder risk and led to a rise in the return that debtholders required (rdebt rose from 7.5 to 7.875 percent). The higher leverage also made the equity riskier and increased the return that shareholders re-

quired (requity rose from 15 to 16 percent). The weighted average return on debt and equity remained at 12.75 percent:

rassets 1.4 rdebt 2 1.6 requity 2

1.4 7.875 2 1.6 16 2 12.75%

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, rassets , would stay at 12.75 percent, and requity would also be 12.75 percent.

same beta as the firm’s overall assets, then rassets is the right discount rate for the project cash flows.

When the firm uses debt financing, the company cost of capital is not the same

as requity, the expected rate of return on the firm’s stock; requity is higher because of financial risk. However, the company cost of capital can be calculated as a

weighted average of the returns expected by investors on the various debt and equity securities issued by the firm. You can also calculate the firm’s asset beta as a weighted average of the betas of these securities.

When the firm changes its mix of debt and equity securities, the risk and expected returns of these securities change; however, the asset beta and the company cost of capital do not change.

Now, if you think all this is too neat and simple, you’re right. The complications are spelled out in great detail in Chapters 17 through 19. But we must note one complication here: Interest paid on a firm’s borrowing can be deducted from

taxable income. Thus the after-tax cost of debt is rdebt (l 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:

D E

WACC rdebt11 Tc 2V requity V

More—lots more—on this in Chapter 19.

Back to Union Pacific’s Cost of Capital

In the last section we estimated the return that investors required on Union Pacific’s common stock. If Union Pacific were wholly equity-financed, the company cost of capital would be the same as the expected return on its stock. But in mid2001 common stock accounted for only 60 percent of the market value of the company’s securities. Debt accounted for the remaining 40 percent.11 Union Pacific’s company cost of capital is a weighted average of the expected returns on the different securities.

We estimated the expected return from Union Pacific’s common stock at 7.5 percent. The yield on the company’s debt in 2001 was about 5.5 percent.12 Thus

D E

Company cost of capital rassets V rdebt V requity

a10040 5.5 b a10060 7.5 b 6.7%

Union Pacific’s WACC is calculated in the same fashion, but using the after-tax cost of debt.

11Union Pacific had also issued preferred stock. Preferred stock is discussed in Chapter 14. To keep matters simple here, we have lumped the preferred stock in with Union Pacific’s debt.

12This is a promised yield; that is, it is the yield if Union Pacific makes all the promised payments. Since there is some risk of default, the expected return is always less than the promised yield. Union Pacific debt has an investment-grade rating and the difference is small. But for a company that is hovering on the brink of bankruptcy, it can be important.

risk premium on the Swiss market index is 6 percent.13 Then Roche needs to discount the Swiss franc cash flows from its project at 1.1 6 6.6 percent above the Swiss franc interest rate.

That’s straightforward. But now suppose that Roche considers construction of a plant in the United States. Once again the financial manager measures the risk of this investment by its beta relative to the Swiss market index. But notice that the value of Roche’s business in the United States is likely to be much less closely tied to fluctuations in the Swiss market. So the beta of the U.S. project relative to the Swiss market is likely to be less than 1.1. How much less? One useful guide is the U.S. pharmaceutical industry beta calculated relative to the Swiss market index. It turns out that this beta has been .36.14 If the expected risk premium on the Swiss market index is 6 percent, Roche should be discounting the Swiss franc cash flows from its U.S. project at .36 6 2.2 percent above the Swiss franc interest rate.

Why does Roche’s manager measure the beta of its investments relative to the Swiss index, whereas her U.S. counterpart measures the beta relative to the U.S. index? The answer lies in Section 7.4, where we explained that risk cannot be considered in isolation; it depends on the other securities in the investor’s portfolio. Beta measures risk relative to the investor’s portfolio. If U.S. investors already hold the U.S. market, an additional dollar invested at home is just more of the same. But, if Swiss investors hold the Swiss market, an investment in the United States can reduce their risk. That explains why an investment in the United States is likely to have lower risk for Roche’s shareholders than it has for shareholders in Merck or Pfizer. It also explains why Roche’s shareholders are willing to accept a lower return from such an investment than would the shareholders in the U.S. companies.15

When Merck measures risk relative to the U.S. market and Roche measures risk relative to the Swiss market, their managers are implicitly assuming that the shareholders simply hold domestic stocks. That’s not a bad approximation, particularly in the case of the United States.16 Although investors in the United States can reduce their risk by holding an internationally diversified portfolio of shares, they generally invest only a small proportion of their money overseas. Why they are so shy is a puzzle.17 It looks as if they are worried about the costs of investing overseas, but we don’t understand what those costs include. Maybe it is more difficult to figure out which foreign shares to buy. Or perhaps investors are worried that a

13Figure 7.3 showed that this is the historical risk premium on the Swiss market. The fact that the realized premium has been lower in Switzerland than the United States may be just a coincidence and may not mean that Swiss investors expected the lower premium. On the other hand, if Swiss firms are generally less risky, then investors may have been content with a lower premium.

14This is the beta of the Standard and Poor’s pharmaceutical index calculated relative to the Swiss market for the period August 1996 to July 2001.

15When investors hold efficient portfolios, the expected reward for risk on each stock in the portfolio is proportional to its beta relative to the portfolio. So, if the Swiss market index is an efficient portfolio for Swiss investors, then Swiss investors will want Roche to invest in a new plant if the expected reward for risk is proportional to its beta relative to the Swiss market index.

16But it can be a bad assumption elsewhere. For small countries with open financial borders— Luxembourg, for example—a beta calculated relative to the local market has little value. Few investors in Luxembourg hold only local stocks.

17For 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 1995), pp. 95–102.

foreign government will expropriate their shares, restrict dividend payments, or catch them by a change in the tax law.

However, the world is getting smaller, and investors everywhere are increasing their holdings of foreign securities. Large American financial institutions have substantially increased their overseas investments, and literally dozens of funds have been set up for individuals who want to invest abroad. For example, you can now buy funds that specialize in investment in emerging capital markets such as Vietnam, Peru, or Hungary. As investors increase their holdings of overseas stocks, it becomes less appropriate to measure risk relative to the domestic market and more important to measure the risk of any investment relative to the portfolios that they actually hold.

Who knows? Perhaps in a few years investors will hold internationally diversified portfolios, and in later editions of this book we will recommend that firms calculate betas relative to the world market. If investors throughout the world held the world portfolio, then Roche and Merck would both demand the same return from an investment in the United States, in Switzerland, or in Egypt.

Do Some Countries Have a Lower Cost of Capital?

Some countries enjoy much lower rates of interest than others. For example, as we write this the interest rate in Japan is effectively zero; in the United States it is above 3 percent. People often conclude from this that Japanese companies enjoy a lower cost of capital.

This view is one part confusion and one part probable truth. The confusion arises because the interest rate in Japan is measured in yen and the rate in the United States is measured in dollars. You wouldn’t say that a 10-inch-high rabbit was taller than a 9-foot elephant. You would be comparing their height in different units. In the same way it makes no sense to compare an interest rate in yen with a rate in dollars. The units are different.

But suppose that in each case you measure the interest rate in real terms. Then you are comparing like with like, and it does make sense to ask whether the costs of overseas investment can cause the real cost of capital to be lower in Japan. Japanese citizens have for a long time been big savers, but as they moved into a new century they were very worried about the future and were saving more than ever. That money could not be absorbed by Japanese industry and therefore had to be invested overseas. Japanese investors were not compelled to invest overseas: They needed to be enticed to do so. So the expected real returns on Japanese investments fell to the point that Japanese investors were willing to incur the costs of buying foreign securities, and when a Japanese company wanted to finance a new project, it could tap into a pool of relatively low-cost funds.

9.5 SETTING DISCOUNT RATES WHEN YOU CAN’T CALCULATE BETA

Stock or industry betas provide a rough guide to the risk encountered in various lines of business. But an asset beta for, say, the steel industry can take us only so far. Not all investments made in the steel industry are typical. What other kinds of evidence about business risk might a financial manager examine?

In some cases the asset is publicly traded. If so, we can simply estimate its beta from past price data. For example, suppose a firm wants to analyze the risks of holding a large inventory of copper. Because copper is a standardized, widely traded commodity, it is possible to calculate rates of return from holding copper and to calculate a beta for copper.

What should a manager do if the asset has no such convenient price record? What if the proposed investment is not close enough to business as usual to justify using a company cost of capital?

These cases clearly call for judgment. For managers making that kind of judgment, we offer two pieces of advice.

1.Avoid fudge factors. Don’t give in to the temptation to add fudge factors to the discount rate to offset things that could go wrong with the proposed investment. Adjust cash-flow forecasts first.

2.Think about the determinants of asset betas. Often the characteristics of highand low-beta assets can be observed when the beta itself cannot be.

Let us expand on these two points.

Avoid Fudge Factors in Discount Rates

We have defined risk, from the investor’s viewpoint, as the standard deviation of portfolio return or the beta of a common stock or other security. But in everyday usage risk simply equals “bad outcome.” People think of the risks of a project as a list of things that can go wrong. For example,

•A geologist looking for oil worries about the risk of a dry hole.

•A pharmaceutical manufacturer worries about the risk that a new drug which cures baldness may not be approved by the Food and Drug Administration.

•The owner of a hotel in a politically unstable part of the world worries about the political risk of expropriation.

Managers often add fudge factors to discount rates to offset worries such as these. This sort of adjustment makes us nervous. First, the bad outcomes we cited appear to reflect unique (i.e., diversifiable) risks that would not affect the expected rate of return demanded by investors. Second, the need for a discount rate adjustment usually arises because managers fail to give bad outcomes their due weight in cash-flow forecasts. The managers then try to offset that mistake by adding a

fudge factor to the discount rate.

Example Project Z will produce just one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at a 10 percent company cost of capital:

But now you discover that the company’s engineers are behind schedule in developing the technology required for the project. They’re confident it will work, but they admit to a small chance that it won’t. You still see the most likely outcome as $1 million, but you also see some chance that project Z will generate zero cash flow next year.

Now the project’s prospects are clouded by your new worry about technology. It must be worth less than the $909,100 you calculated before that worry arose. But how much less? There is some discount rate (10 percent plus a fudge factor) that will give the right value, but we don’t know what that adjusted discount rate is.

We suggest you reconsider your original $1 million forecast for project Z’s cash flow. Project cash flows are supposed to be unbiased forecasts, which give due weight to all possible outcomes, favorable and unfavorable. Managers making unbiased forecasts are correct on average. Sometimes their forecasts will turn out high, other times low, but their errors will average out over many projects.

If you forecast cash flow of $1 million for projects like Z, you will overestimate the average cash flow, because every now and then you will hit a zero. Those zeros should be “averaged in” to your forecasts.

For many projects, the most likely cash flow is also the unbiased forecast. If there are three possible outcomes with the probabilities shown below, the unbiased forecast is $1 million. (The unbiased forecast is the sum of the probability-weighted cash flows.)

This might describe the initial prospects of project Z. But if technological uncertainty introduces a 10 percent chance of a zero cash flow, the unbiased forecast could drop to $900,000:

The present value is

PV .190.1 .818, or $818,000

Now, of course, you can figure out the right fudge factor to add to the discount rate to apply to the original $1 million forecast to get the correct answer. But you have to think through possible cash flows to get that fudge factor; and once you have thought through the cash flows, you don’t need the fudge factor.

Managers often work out a range of possible outcomes for major projects, sometimes with explicit probabilities attached. We give more elaborate examples and further discussion in Chapter 10. But even when a range of outcomes and probabilities is not explicitly written down, the manager can still consider the good and bad outcomes as well as the most likely one. When the bad outcomes outweigh the good, the cash-flow forecast should be reduced until balance is regained.