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There is a growing literature that uses either the above-mentioned dividend discount model, or an equity free cash flow model and observed stock prices, to impute the equity discount rate (and the market risk premium) as an internal rate of return. A typical example is the work of Gebhardt, Lee, and Swaminathan.13 They estimate the cost of equity at the individual company level using a residual income model to value the equity of a company (this is the same approach in principle as the economic profit model described in Chapter 8). Assume a flat term structure and that the firm uses clean surplus accounting (implying that all gains and losses affecting the book value of equity are also run through the income statement). Then the value of the stock, S,, is equal to the book value of equity, Bt, plus the discounted expected economic profit (defined as the spread between the return on equity, ROE, and the cost of equity, r, multiplied by the book value of equity). An ex ante estimate of the cost of equity for
a company is estimated through the following process: plug in the current stock price and the book value of equity; use I/B/E/S estimates of expected earnings per share to estimate net income as (ROE x Bw-1) for the next three years; implicitly forecast economic profit to year 12 by assuming that the company return on equity fades to equal the industry median return on equity by year 12; assume that economic profit during the terminal value period is a perpetuity, and then solve the above equation for the cost of equity.
Both the Gebhardt, Lee, and Swaminathan paper and a paper by Claus and Thomas find similar results.14 The ex-ante market risk premium
13 W. Gebhardt, C. Lee, and B. Swaminathan, ''Toward an Ex-Ante Cost of Capital," Working Paper (Ithaca,
NY: Cornell University, 1999).
14 J. Claus and J. Thomas, The Equity Risk Premium Is Much Lower than You Think It Is: Empirical Estimates from a New Approach, Working Paper (New York: Columbia University, 1998).
(estimated by subtracting the yield on 10-year U.S. Treasury bonds from the cost of equity) is in the two to three percent range while the historical risk premium is about 5 percent. We prefer not to use the ex ante approach because it always fits the data. Even if one makes an error forecasting future cash flows, the ex ante approach will produce an internal rate of return that is consistent with the observed stock price.
Exhibit 10.9 shows the valuation of 31 companies in August 1999. It duplicates the results of Exhibit 5.5, which showed a 92 percent r-squared between the market value and the DCF estimate of the value of these companies—except for one thing. In Exhibit 10.9, the free cash flows are discounted at a WACC that assumes a market risk premium of 3 percent (based on published ex ante estimates of the market risk premium). The results show that the r-squared falls to 79 percent, the slope of the line is significantly below unity, and so the DCF model vastly overvalues companies. Clearly, the 3-percent market risk premium assumption worsened the results. The higher market risk premium that we used in Exhibit 5.5 better fits the actual market values than the ex ante premium.
A number of investment banks have begun publishing estimates of the market risk premium, several using ex ante approaches. In early 2000, most of these estimates were 3 1/2 percent to 5 percent.
Estimating the Systematic Risk (Beta)
For listed companies, using published estimates of beta is the easiest approach. BARRA publishes betas for more than 10,000 companies around the world, but we recommend checking several reliable sources because beta estimates vary considerably. You should also compare the beta with the industry average beta. If the betas
Exhibit 10.9 Lower Risk Premium Distorts Value
from several sources vary by more than .2 or the beta for a company is more than .3 from the industry average, consider using the industry average. An industry average beta is typically more stable and reliable than an individual company beta because measurement errors tend to cancel out. When constructing the industry average, unlever the betas to estimate the average. The average unlevered beta can then be relevered using the company's capital structure.
For unlisted companies and business units, you should generally use industry averages as well. See Chapter 14 for a more detailed discussion.
Is Beta Dead? Criticism of the CAPM
In June 1992, Eugene Fama and Ken French of the University of Chicago published a paper in The Journal of Finance that received a great deal of attention because they concluded:
In short, our tests do not support the most basic prediction of the SLB model [The Sharpe-Lintner-Black Capital Asset Pricing Model] that average stock returns are positively related to market betas.15
At that time, theirs was the most recent in a long line of empirical studies that questioned the usefulness of measured betas in explaining the risk premium (above the riskless rate) on equities. Banz (1981) and Reinganum (1981) found a prominent size effect that added to the explanation of cross-sectional returns, in addition to beta. Basu (1983) found a seasonal (January) effect. Bhandari (1988) demonstrated that the degree of financial leverage was important. And Stattman (1980) as well as Rosenberg, Reid, and Lanstein (1985) found that average returns are positively related to the firm's equity book-to-market ratio.16