# Reading: Lesson 4 - Using the Capital Asset Pricing Model

**8.4.A - Using the Capital Asset Pricing Model**

*1. Using the CAPM to Estimate the Cost of Common Stock*

- Before estimating the return required by MicroDrive’s shareholders, rs, it is worth considering the two ways that a company can raise common equity: (1) Sell newly issued shares to the public. (2) Reinvest (retain) earnings by not paying out all net income as dividends.
- Does new equity capital raised by reinvesting earnings have a cost? The answer is a resounding “yes!” If earnings are reinvested, then stockholders will incur an opportunity cost—the earnings could have been paid out as dividends or used to repurchase stock, and in either case stockholders would have received funds that they could reinvest in other securities. Thus, the firm should earn on its reinvested earnings at least as much as its stockholders could earn on alternative investments of equivalent risk.
- What rate of return could stockholders expect to earn on equivalent-risk investments? The answer is rs, because they could presumably earn that return by simply buying the stock of the firm in question or that of a similar firm. Therefore, rs is the cost of common equity raised internally as reinvested earnings. If a company can’t earn at least rs on reinvested earnings, then it should pass those earnings on to its stockholders as dividends and let them invest the money themselves in assets that do yield rs.

*2. The Capital Asset Pricing Model*

- To estimate the cost of common stock using the Capital Asset Pricing Model as discussed in an earlier unit, we proceed as follows. 1. Estimate the risk-free rate, rRF. 2. Estimate the current market risk premium, RPM, which is the required market return in excess of the risk-free rate. 3. Estimate the stock’s beta coefficient, bi, which measures the stock’s relative risk. The subscript i signifies Stock i’s beta. 4. Use these three values to estimate the stock’s required rate of return:
The Equation above shows that the CAPM estimate of rs begins with the risk-free rate, rRF. We then add a risk premium that is equal to the risk premium on the market, RPM, scaled up or down to reflect the particular stock’s risk as measured by its beta coefficient. The following sections explain how to implement this four-step process.

The starting point for the CAPM cost-of-equity estimate is rRF, the risk-free rate. There is no such thing as a truly riskless asset in the U.S. economy. Treasury securities are essentially free of default risk; however, nonindexed long-term T-bonds will suffer capital losses if interest rates rise, indexed long-term bonds will decline if the real rate rises, and a portfolio of short-term T-bills will provide a volatile earnings stream because the rate earned on T-bills varies over time.

Because we cannot, in practice, find a truly riskless rate upon which to base the CAPM, what rate should we use? Keep in mind that our objective is to estimate the cost of capital, which will be used to discount a company’s free cash flows or a project’s cash flows. Free cash flows occur over the life of the company and many projects last for many years.

Because the cost of capital will be used to discount relatively long-term cash flows, it seems appropriate to use a relatively long-term risk-free rate, such as the yield on a 10-year Treasury bond. Indeed, a survey of highly regarded companies shows that about two-thirds of them use the rate on 10-year Treasury bonds. T-bond rates can be found in The Wall Street Journal, the Federal Reserve Bulletin, or on the Internet. Although most analysts use the yield on a 10-year T-bond as a proxy for the risk-free rate, yields on 20- or 30-year T-bonds are also reasonable proxies.

We described three approaches for estimating the market risk premium, RPM: (1) use historical averages, (2) survey experts, and (3) estimate forward-looking expected market returns. All three approaches provide estimates in the same ballpark, around 3% to 7%. The final choice really boils down to judgment informed by the current state of the market and the estimates provided by the three approaches. We will use a market risk premium of 6% in this example.

Recall a stock’s beta, bi, can be estimated as:

Where ρiM is the correlation between Stock i’s return and the market return, σi is the standard deviation of Stock i’s return, and σM is the standard deviation of the market’s return. This definition is also equal to the estimated slope coefficient in a regression, with the company’s stock returns on the y-axis and market returns on the x-axis.

*3. An Illustration of the CAPM Approach*

- Following is an application of the CAPM approach to MicroDrive. As estimated earlier, MicroDrive’s beta, bi, is 1.43. We assume that the market risk premium, RPM, is about 6%. For this example, assume that the risk-free rate, rRF, is 5%. Using the Equation below, we estimate MicroDrive’s required return as about 13.6%:
This estimate of 13.6% is a required return from an investor’s point of view, but it is a cost of equity from a company’s perspective.

Always keep in mind that the estimated cost of equity is indeed an estimate, for several reasons. First, the yield on any long-term T-bond would be an appropriate estimate of the risk-free rate, and different yields would lead to different estimates of rs. Second, no one truly knows the correct market risk premium. We can narrow the estimated RPM down to a fairly small range, but different estimates in this range would lead to different estimates of rs. Third, estimates of beta are inexact. In addition to a large range of the confidence interval around an estimated beta, using slightly different time periods to estimate beta can lead to rather large differences in the estimated beta.

Still, in our judgment, it is possible to develop “reasonable” estimates of the required inputs, and we believe that the CAPM can be used to obtain reasonable estimates of the cost of equity. Indeed, despite the difficulties we have noted, surveys indicate that the CAPM is by far the most widely used method. Although most firms use more than one method, almost 74% of respondents in one survey (and 85% in another) used the CAPM. This is in sharp contrast to a 1982 survey, which found that only 30% of respondents used the CAPM.