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USING THE CAPM TO ESTIMATE EXPECTED RETURNS

To calculate the returns that investors are expecting from particular stocks, we need three numbers ¤the risk-free interest rate, the expected market risk premium, and beta. In mid-1999, the interest rate on Treasury bills was about 4.8 percent. Assume that the market risk premium is about 9 percent. Finally, look back to Table 4.9, where we gave you betas of several stocks. Table 4.10 puts these numbers together to give an estimate of the expected return from each stock. Let`s take Exxon as an example: Expected return on Exxon = risk-free interest rate + (beta ГЧ expected market ) risk premium

r = 4.8% + (.61 ГЧ 9%) = 10.3%

You can also use the capital asset pricing model to find the discount rate for a new capital investment. For example, suppose you are asked to analyze a proposal by Merck to expand its operations. At what rate should you discount the forecast cash flows? According to Table 4.10 investors are looking for a return of 13.1 percent from investments with the risk of Merck stock. That is the opportunity cost of capital for Merck`s expansion project.

In practice, choosing a discount rate is seldom this easy. (After all, you can`t expect to become a captain of finance simply by plugging numbers into a formula.) For example, you must learn how to estimate the return demanded by the company`s investors when the company has issued both equity and debt securities.7We will come to such refinements later.

Comparing Project Returns and the Opportunity Cost of Capital

You have forecast the cash flows on a project and calculated that its internal rate of return is 15.0 percent. Suppose that Treasury bills offer a return of 5 percent and the expected market risk premium is 9 percent. Should you go ahead with the project? To answer this question you need to figure out the opportunity cost of capital r. This depends on the project`s beta. For example, if the project is a sure thing, the beta is zero and the cost of capital equals the interest rate on Treasury bills:

r = 5 + (0 ГЧ 9) = 5%

If your project offers a return of 15.0 percent when the cost of capital is 5 percent, you should obviously go ahead.8 Sure-fire projects rarely occur outside finance texts. So let`s think about the cost of capital if the project has the same risk as the market portfolio. In this case beta is 1.0 and the cost of capital is the expected return on the market: r = 5 + (1.0 ГЧ 9) = 14%

The project appears less attractive than before but still worth doing. But what if the project has even higher risk? Suppose, for example, that it has a beta of 1.5. What is the cost of capital in this case? To find the answer, we plug a beta of 1.5 into our formula for r: r = 5 + (1.5 ГЧ 9) = 18.5%

A project this risky would need a return of at least 18.5 percent to justify going ahead. The 15 percent project should be rejected. This rejection occurs because, as Figure 4.13 shows, the project`s expected rate of return plots below the security market line. The project offers a lower return than investors can get elsewhere, so it is a negative-NPV investment.

The security market line provides a standard for project acceptance. If the project`s return lies above the security market line, then the return is higher than investors could expect to get by investing their funds in the capital market and therefore is an attractive investment opportunity.

The expected return of this project is less than the expected return one could earn on stock market investments with the same market risk (beta). Therefore, the project`s expected return Јrisk combination lies below the security market line, and the project should be rejected.

7We could ignore this complication in the case of Merck, because Merck is financed almost entirely by common stock. Therefore, the risk of its assets equals the risk of its stock. But most companies issue a mix of debt and common stock.

8 Earlier we described some special cases where you should prefer projects that offer a lower internal rate of return than the cost of capital. We assume here that your project is a ¬normal ­ one, and that you prefer high IRRs to low ones.