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• The short-term real interest rate, measured by the difference between the yield on Treasury bills and the Consumer Price Index.
• Short-term inflation, measured by unexpected changes in the Consumer Price Index.
• Long-term inflation, measured as the difference between the yield to maturity on long- and shortterm U.S. government bonds.
• Default risk, measured by the difference between the yield to maturity on Aaa- and Baa-rated long-term corporate bonds.
Empirical evidence also confirms that the APM explains expected returns better than the singlefactor CAPM (for example, see Chen 1983; Chen, Ross, and Roll 1986; or Berry, Burmeister, and McElroy 1988).18 In addition, the APM can add insight into the type of risk that is relevant. This is illustrated in Exhibit 10.10. The axes are two of the fundamental factors, the industrial production index and short-term inflation. The diagonal dotted lines
18 N. Chen, R. Roll, and S. Ross, ''Economic Forces and the Stock Market," Journal of Business (July 1986), pp. 383-403; and M. Berry, E. Burmeister, and M. McElroy, "Sorting Out Risks Using Known APT Factors," Financial Analysts Journal, vol. 44 (March/April 1988), pp. 29-42.
Exhibit 10.10 The Arbitrage Pricing Model
k, = r, + [E(F,)-r,] beta, + [E(F2)-rf] beta2...
represent constant returns with different combinations of risk. Any portfolio at the origin (point F) has no exposure to either factor, and therefore earns the riskless rate, r.
For a portfolio at point G, exposure to the systematic risk of unexpected inflation has increased but is offset by decreased risk relative to the industrial production index. The net result is that point G earns the riskless rate, just like point F, but is exposed to a different bundle of risks. A similar story can be told about points A, M, and B. All earn the same expected return as the CAPM market portfolio, E(rm), but have varying exposures to the risk of unexpected inflation and changes in the industrial production index.
Exhibit 10.11 shows the difference in risk premiums as calculated by the APM and the CAPM for five industries. Oil and money center banks are riskier in every dimension. Forest products are less risky, and electric utilities have much less default risk. A larger risk premium means that the industry is more sensitive to a given type of risk than would be predicted by the CAPM. Banks and other financial institutions are more sensitive to unexpected changes in long-term inflation, and the market charges a risk premium—that is, it requires a higher cost of equity.
Exhibit 10.12 shows the net effect of using the CAPM versus the APM to estimate the cost of equity for nine industries. The importance of these differences for valuation of an all-equity perpetual stream of cash flows is reflected in the last column. The 4.7 percent higher APM cost-of-equity estimate in the oil industry means that equity cash flows discounted using the CAPM would be overvalued by 25 percent. Cost-of-equity estimates using the APM are significantly lower for forest products and electric utilities and significantly higher for money center banks and for oil companies with more than 50 percent of their assets in oil reserves.
Exhibit 10.11 Differences in Risk Premiums between APM and CAPM
Exhibit 10.12 Comparison of CAPM and APM Cost of Equity Estimates
Industry Number of companies Cost-of-equity estimate CAPM APM Difference (percent) (percent) (percent) Change in value (percent)
Brokerage 10 17.1 17.4 -0.3 -1.7
Electric utilities 39 12,7 11.8 0.9 7,6
Food and beverage 11 14 4 14,3 0.1 0.7
Forest products 7 16.8 15.0 1.S1 12.0
Large savings and loans 13 15.8 19.6 -3.8' -17,7
Mining IS 14,7 14.2 0,5 3,5
Money center banks 12 15.9 16.9 -1.01 -5.9
Oil with large reserves 12 14 4 19.1 -4.7' -24 6
Property and casualty insurance 13 14,6 13.7 0,9 6,6
1 Statistically significant at the 5% confidence level.
Source: Akar's APT'. Me Kinsey analysis.
We estimated Heineken's WACC as 6.7 percent, as of December 31, 1998, calculated as shown on Exhibit 10.13. We assumed that Heineken would maintain its capital structure at 1998 levels, so the target weights are based on the market values on December 31, 1998 (Exhibit 10.14). The following sections describe how we estimated the cost of each capital source and its market value.
Short-term debt matures within one year, so in most cases book value approximates market value. The cost of Heineken's debt was assumed to equal the cost of its long-term debt, 4.3 percent, since the short-term debt is most likely a revolving loan that will be continuously rolled over. Applying Heineken's marginal tax rate of 35 percent resulted in an after-tax cost of 2.8 percent.