Principles of Corporate Finance_ 12th Edition

Chapter 9 Risk and the Cost of Capital 225

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corporations, so the after-tax cost of debt is (1 – Tc)rD, where Tc is the marginal corporate tax

rate. Suppose Tc = 35%. Then after-tax WACC is

After-tax WACC = (1 − Tc)rDD/V + rEE/V

= (1 − .35) × 7.5 × .30 + 15 × .70 = 12.0%

We give another example of the after-tax WACC later in this chapter, and we cover the

topic in much more detail in Chapter 19. But now we turn to the hardest part of calculating

WACC, estimating the cost of equity.

9-2 Measuring the Cost of Equity

To calculate the weighted-average cost of capital, you need an estimate of the cost of equity.

You decide to use the capital asset pricing model (CAPM). Here you are in good company: As

we saw in the last chapter, most large U.S. companies do use the CAPM to estimate the cost of

equity, which is the expected rate of return on the firm’s common stock.^4 The CAPM says that

Expected stock return = rf + β(rm − rf)

Now you have to estimate beta. Let us see how that is done in practice.

Estimating Beta

In principle we are interested in the future beta of the company’s stock, but lacking a crystal

ball, we turn first to historical evidence. For example, look at the scatter diagram at the top

left of Figure 9.2. Each dot represents the return on Dow Chemical stock and the return on the

market in a particular month. The plot starts in November 2004 and runs to October 2009, so

there are 60 dots in all.

The second diagram on the left shows a similar plot for the returns on Microsoft stock, and

the third shows a plot for Campbell Soup. In each case we have fitted a line through the points.

The slope of this line is an estimate of beta. It tells us how much on average the stock price

changed when the market return was 1% higher or lower.

The right-hand diagrams show similar plots for the same three stocks during the subse-

quent period ending in October 2014. Betas do change. For example, Dow’s beta leapt up in

the financial crisis. You would have been well off target if you had blindly used its beta dur-

ing this period to predict its beta in more normal times. However, you could have been pretty

confident that Campbell Soup’s beta was much less than Dow’s and that Microsoft’s beta was

somewhere between the two.^5

Only a small portion of each stock’s total risk comes from movements in the market. The

rest is firm-specific, diversifiable 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 2009 to 2014, the R^2

for Microsoft was .37. In other words, 37% of Microsoft’s risk was market risk and 63% was

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How to estimate

beta

(^4) The CAPM is not the last word on risk and return, of course, but the principles and procedures covered in this chapter work just as
well with other models such as the Fama–French three-factor model. See Section 8-4.
(^5) Notice that to estimate beta you must regress the returns on the stock on the market returns. You would get a very similar estimate if
you simply used the percentage changes in the stock price and the market index. But sometimes people make the mistake of regressing
the stock price level on the level of the index and obtain nonsense results.
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Try It! Comparing
beta estimates
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Try It! Fama-
French 3-factor
betas