314  Estimating the Cost of Capital payments. The interim payments cause their effective maturity to be much shorter than their stated maturity. Using multiple discount rates is quite cumbersome. Therefore, few practi- tioners discount each cash flow using its matched bond maturity. Instead, most choose a single rate that best matches the cash flow stream being valued. For U.S.-based corporate valuations, we recommend ten-year government STRIPS (longer-dated bonds such as the 30-year Treasury bond might match the cash flow stream better, but they may not be liquid enough to correctly represent the risk-free rate). When valuing European companies, use ten-year German government bonds, because they trade more frequently and have lower credit risk than bonds of other European countries. Always use government bond yields denominated in the same currency as the company’s cash flow to esti- mate the risk-free rate. Also, make sure the inflation rate embedded in your cash flows is consistent with the inflation rate embedded in the government bond rate you are using. Do not use a short-term Treasury bill to determine the risk-free rate. When introductory finance textbooks calculate the CAPM, they typically use a short- term Treasury rate because they are estimating expected returns for the next month. Use longer-term bonds; they will be better in line with the time horizon of corporate cash flows. Closing Thoughts on Expected Market Returns  Although many in the fi- nance profession disagree about how to measure the market risk premium, we believe a number around 5 percent is appropriate. Historical estimates found in various textbooks (and locked in the minds of many), which often report numbers near 8 percent, are too high for valuation purposes, because they compare the market risk premium versus Treasury bills (very-short-term bonds) and are biased by the historical strength of the U.S. market. Adjust for Industry/Company Risk Once you’ve estimated the cost of equity for the market as a whole, adjust it for differences in risk across companies. Keep in mind the discussion from Chapter 4 about the difference between diversifiable and nondiversifiable risk. Only the nondiversifiable risk that investors cannot eliminate by holding a portfolio of stocks is incorporated into the cost of equity. The most common model used to adjust the cost of equity for differences in risk is the capital asset pricing model (CAPM). Other models include the Fama-French three-factor model and the arbitrage pricing theory (APT). The three models differ primarily in which factors are used to estimate the effect of compensated risk. Despite extensive criticism of the CAPM, we believe that it remains the best model to adjust for risk. Even so, significant judgment is required. A blind application of historical data may result in a cost of equity that is unrealistic. Estimating the Cost of Equity  315 Capital Asset Pricing Model  Because the CAPM is discussed at length in modern finance textbooks,15 we focus only on the key ideas. The CAPM pos- tulates that the expected rate of return on any security equals the risk-free rate plus the security’s beta times the market risk premium: E R r E R r i f i m f ( ) = + ( ) − β [ ] where E Ri ( ) = expected return of security i     rf = risk-free rate     βi = security i’s sensitivity to the market portfolio E Rm ( ) = expected return of the market portfolio In the CAPM, the risk-free rate and the market risk premium, which is defined as the difference between E(Rm) and rf, are common to all companies; only beta varies across companies. Beta represents a stock’s incremental risk to a diversified investor, where risk is defined as the extent to which the stock moves up and down in conjunction with the aggregate stock market. Consider General Mills, a manufacturer of cereals and snack foods, and Micron Technology, a semiconductor manufacturer that produces memory chips. Basic consumer foods purchases are relatively independent of the stock market’s value, so the beta for General Mills is low; we estimated it at 0.64.16 Based on a risk-free rate of 4.3 percent and a market risk premium of 5 percent, the cost of equity for General Mills equals 7.5 percent (see Exhibit 15.4). In contrast, technology companies tend to have high betas. When the economy struggles, the stock market drops, and companies stop purchasing new tech- nology. Thus, the value of Micron Technology is highly correlated with the market’s value, and its beta is high. Based on a beta of 1.68, Micron’s expected rate of return equals 12.7 percent. Since General Mills offers greater protection against market downturns than Micron Technology does, investors are will- ing to pay a premium for the stock, driving down the stock’s expected return. Conversely, since Micron offers little diversification in relation to the market portfolio, the company must earn a higher return to entice investors. To apply the CAPM in practice, you must estimate each component. The core question for a particular company’s cost of equity is its risk relative to the aggregate market and, consequently, beta. Keep in mind that when you are valuing a company, your objective is not to precisely measure the company’s historical beta. Rather, it is to estimate its future beta. Therefore, you must use judgment and common sense, not a purely mechanical approach. 15 For example, R. Brealey, S. Myers, and F. Allen, Principles of Corporate Finance, 11th ed. (New York: McGraw-Hill, 2014); and T. Copeland, F. Weston, and K. Shastri, Financial Theory and Corporate Policy (Boston: Pearson Education, 2013). 16 For the purpose of simple exposition, we regress 60 months of General Mills stock returns on the Morgan Stanley Capital International (MSCI) World Index to determine beta. Later, we use peer groups to estimate industry betas.