CAPM has an important application in corporate finance as well. In theory, the company must earn this cost on the equity-financed portion of its investments or its stock price will fall. If the company does not expect to earn at least the cost of equity, it should return the funds to the shareholders, who can earn this expected return on other securities at the same risk level in the financial marketplace. Since the cost of equity involves market expectations, it is very difficult to measure; few techniques are available.

This difficulty is unfortunate in view of the role of equity costs in vital tasks such as capital budgeting evaluation and the valuation of possible acquisitions. The cost of equity is one component of the weighted average cost of capital, which corporate executives often use as a hurdle rate in evaluating investments. Financial managers can employ CAPM to obtain an estimate of the cost of equity capital.

If CAPM correctly describes market behavior, the security market line gives the expected return on a stock. Over the past 50 years, the T-bill rate the risk-free rate has approximately equaled the annual inflation rate. In recent years, buffeted by short-term inflationary expectations, the T-bill rate has fluctuated widely. Estimating the expected return on the market is more difficult.

A common approach is to assume that investors anticipate about the same risk premium R m — R f in the future as in the past. This is substantially higher than the historical average of The future inflation rate is assumed to be 7. Expected returns in nominal terms should rise to compensate investors for the anticipated loss in purchasing power. Many brokerage firms and investment services also supply betas. Plugging the assumed values of the risk-free rate, the expected return on the market, and beta into the security market line generates estimates of the cost of equity capital.

In Exhibit IV I give the cost of equity estimates of three hypothetical companies. The betas in Exhibit IV are consistent with those of companies in the three industries represented. Many electric utilities have low levels of systematic risk and low betas because of relatively modest swings in their earnings and stock returns. Airline revenues are closely tied to passenger miles flown, a yardstick very sensitive to changes in economic activity. Amplifying this systematic variability in revenues is high operating and financial leverage.

The results are earnings and returns that vary widely and produce high betas in these stocks. Major chemical companies exhibit an intermediate degree of systematic risk. I should stress that the methodology illustrated in Exhibit IV yields only rough estimates of the cost of equity. Sophisticated refinements can help estimate each input. Sensitivity analyses employing various input values can produce a reasonably good range of estimates of the cost of equity. Nonetheless, the calculations in this exhibit demonstrate how the simple model can generate benchmark data.

The result is a pricing schedule for equity capital as a function of risk. Applications of these concepts are straightforward. The betas of these companies reflect the risk level of the industry. Of course, refinements may be necessary to adjust for differences in financial leverage and other factors. A second example concerns acquisitions. In discounted cash flow evaluations of acquisitions, the appropriate cost of equity should reflect the risks inherent in the cash flows that are discounted. Again, ignoring refinements required by changes in capital structure and the like, the cost of equity should reflect the risk level of the target company, not the acquiror.

But the true test of CAPM, naturally, is how well it works. There have been numerous empirical tests of CAPM. Most of these have examined the past to determine the extent to which stock returns and betas have corresponded in the manner predicted by the security market line. With few exceptions the major empirical studies in this field have concluded that:. Although these empirical tests do not unequivocally validate CAPM, they do support its main implications.

The contradictory finding concerning the slope of the SML is a subject of continuing research. Recent work in the investment management field has challenged the proposition that only systematic risk matters.

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In a complex world it would be unlikely to find only one relevant type of risk—market risk. Much progress has been made in the development of richer asset-pricing models. As of yet, however, none of these more sophisticated models has proved clearly superior to CAPM. This continues to be a fertile area of research, focused primarily on investment management applications.

In corporate finance applications of CAPM, several potential sources of error exist. First, the simple model may be an inadequate description of the behavior of financial markets. In attempts to improve its realism, researchers have developed a variety of extensions of the model. A second problem is that betas are unstable through time.

This fact creates difficulties when betas estimated from historical data are used to calculate costs of equity in evaluating future cash flows. Betas should change as both company fundamentals and capital structures change. In addition, betas estimated from past data are subject to statistical estimation error. Several techniques are available to help deal with these sources of instability.

## Capital Asset Pricing Model (CAPM)

The estimates of the future risk-free rate and the expected return on the market are also subject to error. Here too, research has focused on developing techniques to reduce the potential error associated with these inputs to the SML. A final set of problems is unique to corporate finance applications of CAPM. There are practical and theoretical problems associated with employing CAPM, or any financial market model, in capital budgeting decisions involving real assets.

These difficulties continue to be a fertile area of research. The deficiencies of CAPM may seem severe. They must be judged, however, relative to other approaches for estimating the cost of equity capital.

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The most commonly used of these is a simple discounted cash flow DCF technique, which is known as the dividend growth model or the Gordon-Shapiro model. With the assumption that future dividends per share are expected to grow at a constant rate and that this growth rate will persist forever, the general present value formula collapses to a simple expression.

If the market is pricing the stock in this manner, we can infer the cost of equity impounded in the stock price. Solving for the cost of equity yields:. The cost of equity implied by the current stock price and the assumptions of the model is simply the dividend yield plus the constant growth rate. One is the assumption of a constant, perpetual growth rate in dividends per share. If this is not the case, the equation is not valid.

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These two assumptions sharply limit the applicability of the dividend growth model. The model cannot be used in estimating costs of equity for companies with unstable dividend patterns or for rapidly growing companies where g is likely to be greater than k e. Obviously, the model also does not apply to companies paying no dividends. Unlike CAPM, the model is limited mainly to companies enjoying slow, steady growth in dividends.

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More complex DCF techniques can, however, handle a wider range of companies. Another problem with using the dividend growth model to estimate costs of equity is in gauging g. To derive a sound cost of equity figure, one must estimate the growth rate investors are using to value the stock. This is a major source of error in the dividend growth model. In contrast, the only company-specific input to the SML is the beta, which is derived by an objective statistical method. There is no reason, however, to consider CAPM and the dividend growth model as competitors.

Very few techniques are available for the difficult task of measuring the cost of equity. Investment managers have widely applied the simple CAPM and its more sophisticated extensions. Because of its shortcomings, financial executives should not rely on CAPM as a precise algorithm for estimating the cost of equity capital. Nevertheless, tests of the model confirm that it has much to say about the way returns are determined in financial markets. Its key advantage is that it quantifies risk and provides a widely applicable, relatively objective routine for translating risk measures into estimates of expected return.

CAPM represents a new and different approach to an important task. Financial decision makers can use the model in conjunction with traditional techniques and sound judgment to develop realistic, useful estimates of the costs of equity capital. See Marshall E. See Stephen A. See Roger G.

## Capital Asset Pricing Model (CAPM)

Ibbotson and Rex A. The rates I have used are arithmetic means. Arguments can be made that geometric mean rates are appropriate for discounting longer-term cash flows. For an exposition of the dividend growth model, see Thomas R. Piper and William E.

Fruhan, Jr. Mullins is associate professor of business administration at the Harvard Business School, where he teaches corporate financial management in the MBA and executive programs. He has spent the last several years developing material on modern financial theory for these courses and for the eighth edition of Case Problems in Finance for which he was a contributing editor , published this year by Richard D. Irwin, Inc. The deposit will be credited towards your total fee payment.

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## The Capital Asset Pricing Model: Theory and Evidence (Digest Summary)

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