Since the "market portfolio" is not directly observable,31 providers of beta use stock market indices to estimate the performance of the market portfolio. The value of beta is calculated by regressing a stock's historical price movements against those of the market proxy over the same period. If the value of a stock's beta is one, the riskiness of the stock is the same as that of the market portfolio. A value of greater than one means that the stock is more sensitive to market risk factors than the overall market proxy, and a value of less than one means that the stock is less sensitive to market risk factors than the market proxy. Note that when using beta to calculate expected returns, the implicit assumption is that future returns are expected to behave like past returns.

• Providers of beta differ in their estimates for many reasons. First, they vary in their choice of market proxies. Some use the S&P 500 index whereas others use the NYSE composite index. Additionally, the length of time (e.g., 2 years or 5 years), and the periodicity of returns (e.g., daily or weekly) used in computing beta may vary. These variations can result in a range of beta estimates, which, in turn, will cause a range of estimates for the cost of equity. The following are the parameters and beta estimate for Caterpillar (CAT) from some of the most common beta sources: value line: NYSE composite, five years of weekly prices, CAT beta = 1.30.

• Bloomberg: S&P 500, two years of weekly prices in its default mode,32 CAT beta=1.53

• Capital IQ (Yahoo):33 S&P 500, five years of monthly data, CAT beta = 1.71.

Using the current 10-year T-bond rate of 3.568 percent34 for the risk-free proxy and the historical market risk premium of 8.5 percent, the CAPM yields a cost of equity for Caterpillar (CAT) of 14.61 percent using the value line estimate of beta, 16.57 percent (Bloomberg), or 19.55 percent (Capital IQ). The cost of equity thus varies from by nearly 5 percent depending on the source of beta.

Because estimates of beta are based on historical returns, they will change over time. Fernandez demonstrated that beta estimates can change dramatically over even short periods of time.35 For example, on a daily basis over a two-month period, the value of AT&T's beta varied from a low of 0.32 (January 14, 2002) to a high of 1.02 (December 27, 2001). Over a 10-day period between January 20 and January 30, 2002, the value of Boeing's beta varied between 0.57 and 1.22. During that same period, AT&T's beta was greater than Boeing's 32 percent of the time, which shows that, at times, beta estimates can even be unreliable as measures of relative risk. Many corporations and analysts understand that the estimate of beta has its limitations. It is thus common for practitioners to adjust published estimates according to the perceived level of risk to provide a more appropriate measure of the asset's systematic risk exposure. Blume observed that the value of beta seems to regress toward a value of one over time and offered an adjustment to reflect this phenomenon.36 He suggested using a weighted average of the equity beta and one where the weight of the equity beta is two-thirds. This adjustment is widely accepted and is used by many practitioners.

Market Risk Premium

In theory, the market risk premium is the additional return above the risk-free rate that investors require for bearing the risk of the market portfolio. Surveys have found a wide range of estimates for the market risk premium. Bruner, Eades, Harris, and Higgins found that most corporations use risk premiums between 4 percent and 6 percent, although 50 percent of analysts use estimates between 7 percent and 7.4 percent.37 Graham and Harvey reported that the market risk premium used by U.S. CFOs between June 2000 and November 2006 ranged from 2.39 percent (November 2005) to 4.65 percent (September 2000).38 The average of 3.47 percent is notably lower than Bruner et al.'s earlier findings. Fernandez and del Campo found that the average market risk premium used by analysts in the United States and Canada in 2010 was 5.1 percent and ranged from 2.9 percent to 10 percent.39 The corresponding figures for corporations were 5.3 percent and 1.9 percent to 11.2 percent. Textbooks tend to use the historical average risk premium over T-bills, which is usually between 8 percent and 8.5 percent.

During the most recent financial crisis, managers have become particularly concerned about how increases in risk aversion may affect the cost and availability of capital. Dobbs, Jiang, and Koller found that economic conditions have little influence on the cost of equity.40 For example, a 20 percent drop in share price and a 7.5 percent decline in profits would amount to a 0.6 percent change in the cost of equity (Table 8.1). They also pointed out that stock price changes are affected more by the revision of earnings estimates than by changes in the cost of capital.

The Cost of Debt

The cost of debt is relatively easier to estimate than the cost of equity since market yields on bonds are directly observable. Fifty-two percent of firms tend to use their marginal cost when calculating the pretax cost of debt.41 For new bond issues, firms observe the yield to maturity on bonds with equivalent credit ratings. Thirty-two percent of firms use

Table 8.1. Percentage Change in Cost of Equity Given Changes in Sales Price and Earnings

Percentage Change in Cost of Equity Given Changes in Sales Price and Earnings

*A 7.5 percent decrease in earnings combined with a 20 percent decrease in price results in a 0.6 percent increase in the cost of equity.

the weighted average of each of their outstanding bond issues, the method that most textbooks and financial advisers endorse. To adjust for the tax benefit of debt, 52 percent of firms calculate their after-tax cost of debt using marginal or statutory tax rates. The majority of financial advisers and textbooks recommend using marginal tax rates. A minority of corporations and financial advisers use the historical average tax rate to estimate the cost of debt.

Weights on Debt and Equity in Estimating Cost of Capital

The WACC depends on the percentages of debt and equity in the capital structure. It is recommended that market values be used in estimating these percentages since book values on the balance sheet are historical and do not reflect current values. The market value of equity can be calculated by multiplying the closing price of a firm's stock by the number of shares outstanding. It is not generally easy to directly obtain the market value of debt. Although some bonds are traded, many firms have debt that is not traded. Although the firms themselves have access to their current loan balances, this information is often unavailable to the public. In this case, it becomes necessary to rely on the book value of the debt instead.

Another issue is the choice between target and actual capital structure. Since debt and equity costs depend on the proportions of each source of financing in the capital structure, this suggests that the current, actual proportions of each should be used in computing the WACC. However, if a firm's target weights are publicly known and investors anticipate the firm changing the weights, the observed costs of debt and equity may reflect the target capital structure. The weights for debt and equity are complicated when firms have off-balance sheet financing instruments. These are hidden debts; thus if they are not incorporated in estimating the WACC, this estimate will not be accurate. The implications of off-balance sheet financing instruments will be discussed in a later section.

Implications for Decision Makers

The chosen risk-free proxy, market risk premium, or value of beta can result in dramatic differences in estimates of the WACC; thus it is important to consider how the WACC is to be used. If it is used to gauge past performance, one should use parameters that reflect past circumstances. In contrast, if it to be used for capital budgeting purposes, one should use parameters that reflect expectations for the future with the corresponding project's time horizon in mind. It is also imperative that the value of beta used in capital budgeting reflects the risk of the project, not the risk of the overall firm. Using the overall equity beta when a project has lower risk than the company as a whole will lead to an overestimate of the cost of equity and thus the rejection of a potentially profitable project and vice versa. If new debt is to be issued to fund a project, it is appropriate to use the yield to maturity on the new bond issues in computing the cost of debt. Finally, the weights used to compute the WACC should reflect the expected capital structure weights.

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