Chapter 11 The Opportunity Cost of Capital: The Cost of Equity Instructors: Please do not post raw PowerPoint files on public website. Thank you! 1

2 The Cost of Capital To value a company using enterprise DCF, we discount free cash flow by the weighted average cost of capital (WACC). The WACC represents the opportunity cost that investors face for investing their funds in one particular business instead of others with similar risk. In its simplest form, the weighted average cost of capital is the market-based weighted average of the after-tax cost of debt and cost of equity: To determine the weighted average cost of capital, we must calculate its three components: (1) the cost of equity, (2) the after-tax cost of debt, and (3) the company’s target capital structure.

3 Successful Implementation Requires Consistency The most important principle underlying successful implementation of the cost of capital is consistency between the components of WACC and free cash flow. To ensure consistency, –It must include the opportunity costs of all investors—debt, equity, and so on— since free cash flow is available to all investors, who expect compensation for the risks they take. –It must weight each security’s required return by its target market-based weight, not by its historical book value. –Any financing-related benefits or costs, such as interest tax shields, not included in free cash flow must be incorporated into the cost of capital or valued separately using adjusted present value. –It must be computed after corporate taxes (since free cash flow is calculated in after-tax terms), based on the same expectations of inflation, and match the duration of the cash flows.

4 The Cost of Capital: An Example The weighted average cost of capital at Home Depot equals 8.5 percent. The majority of enterprise value is held by equity holders (68.5 percent), whose CAPM-based required return equals 10.4 percent. The remaining capital is provided by debt holders at 4.2 percent of an after-tax basis. Let’s examine the components of WACC one by one, starting with the cost of equity… Home Depot: Weighted Average Cost of Capital

5 1. The Cost of Equity To estimate the cost of equity, we must determine the expected rate of return of the company’s stock. Since expected rates of return are unobservable, we rely on asset- pricing models that translate risk into expected return. The three most common asset-pricing models differ primarily in how they define risk. The capital asset pricing model (CAPM) states that a stock’s expected return is driven by how sensitive its returns are to the market portfolio. This sensitivity is measured using a term known as beta. The Fama-French three-factor model defines risk as a stock’s sensitivity to three portfolios: the stock market, a portfolio based on firm size, and a portfolio based on book-to-market ratios. The arbitrage pricing theory (APT) is a generalized multifactor model, but unfortunately provides no guidance on the appropriate factors that drive returns. The CAPM is the most common method for estimating expected returns, so we begin our analysis with that model.

Capital Asset Pricing Model A stock’s expected return is driven by three components: the risk-free rate, beta, and the expected market risk premium. Expected return of stock i Expected market risk premium Risk-free rate Stock’s beta 6 Estimating the Cost of Equity Using the CAPM Data requirementsConsiderations Risk-free rateUse a long-term government rate dominated in the same currency as cash flows. Market risk premiumThe market risk premium is difficult to measure. Various models point to a risk premium between 4.5 percent and 5.5 percent. Company betaTo estimate beta, lever the company's industry beta to the company's target debt-to- equity ratio.

Risk-Free Rate: 10-Year Local Treasury The cost of capital must be in the same currency as the company’s financials. Thus, use a risk-free rate posted by the local central bank of the company’s country/region. The cost of capital must match the duration of the cash flows in question. For long-term project valuation and company evaluation, use no less than the 10-year rate. 7 Government Zero Coupon Yields, May 2009

2. The Market Risk Premium Sizing the market risk premium—the difference between the market’s expected return and the risk-free rate—is arguably the most debated issue in finance. Methods to estimate the market risk premium fall into three general categories: 1.Estimating the future risk premium by measuring and extrapolating historical returns. 2.Using regression analysis to link current market variables, such as the aggregate dividend-to-price ratio, to project the expected market risk premium. 3.Using DCF valuation, along with estimates of return on investment and growth, to reverse engineer the market’s cost of capital. 8

9 Using Historical Excess Returns: Best Practices To best measure the risk premium using historical data, you should: –Calculate the premium over long-term government bonds. Use long-term government bonds, because they match the duration of a company’s cash flows better than do short-term rates. –Use the longest period possible. If the market risk premium is stable, a longer history will reduce estimation error. Since no statistically significant trend is observable, we recommend the longest period possible. –Use an arithmetic average of longer-dated intervals (such as five years). Although the arithmetic average of annual returns is the best predictor of future one-year returns, compounded averages will be upward biased (too high). Therefore, use longer- dated intervals to build discount rates. –Adjust the result for econometric issues, such as survivorship bias. Predictions based on U.S. data (a successful economy) are probably too high.

The Market Risk Premium for Holding Stocks Over the past 82 years, the S&P 500 index has earned on average a 11.1 percent annual return. The S&P 500 has earned 5.2 percent more than long-term government Treasuries (known as the market risk premium) % 15.1% 5.8% 5.9% 3.6% 3.0% Large Stocks Small Stocks Corporate Bonds Government Bonds Treasury Bills Inflation Average Annual Returns 1926−2008

11 When Possible, Use Long-Dated Holding Periods To correct for the bias caused by misestimation and/or negative autocorrelation in returns, we have two choices. First, we can calculate multiperiod holding returns directly from the data, rather than compound single-period averages. Alternatively, we can use an estimator proposed by Marshall Blume, one that blends the arithmetic and geometric averages.

Embedded Market Risk Premium Using the key value driver formula, we can reverse engineer the cost of equity. After inflation is stripped out, the expected market return (not excess return) is remarkably constant in the United States, averaging 7 percent. For the United Kingdom, the real market return is slightly more volatile, averaging 6 percent. To determine the market risk premium, subtract the real interest rate from the real cost of equity using Treasury inflation-protected securities (TIPS) Real and Nominal Expected Market Returns Implied k e inreal terms Implied k e innominal terms

3. Estimating Beta 13 According to the CAPM, a stock’s expected return is driven by beta, which measures how much the stock and market move together. Since beta cannot be observed directly, we must estimate its value. The most common regression used to estimate a company’s raw beta is the market model: Based on data from 1998 to 2003, Home Depot’s beta is estimated at Home Depot: Stock Returns, 2001–2006 Even though Home Depot matched the market in aggregate losses during 2007 and 2008 (37 percent for Home Depot versus 35 percent for the MSCI World Index), a slight difference in timing caused the two measures to be uncorrelated. Prior to 2007, Home Depot’s market beta was relatively stable. For this reason, we measure unlevered beta as of 2006.

Beta Varies over Time Between 1985 and 2008, IBM’s beta hovered near 0.7 in the 1980s but rose dramatically in the mid-1990s to a peak above 1.7 before falling back down. It now measures near 0.8. This rise in beta occurred during a period of great change for IBM, as the company moved from hardware (such as mainframes) to services (such as consulting). 14

15 Estimating Beta: Best Practices As can be seen on the previous slide, estimating beta is a noisy process. Based on certain market characteristics and a variety of empirical tests, we reach several conclusions about the regression process: –Raw regressions should use at least 60 data points (e.g., five years of monthly returns). Rolling betas should be graphed to examine any systematic changes in a stock’s risk. –Raw regressions should be based on monthly returns. Using shorter return periods, such as daily and weekly returns, leads to systematic biases. –Company stock returns should be regressed against a value-weighted, well- diversified portfolio, such as the S&P 500 or MSCI World Index. Next, recalling that raw regressions provide only estimates of a company’s true beta, we improve estimates of a company’s beta by deriving an unlevered industry beta and then relevering the industry beta to the company’s target capital structure.

Measuring Beta Using Peer Groups The Ibbotson “Beta Book” provides raw regression betas and peer group betas. To determine peer group betas, Ibbotson examines pure plays and conglomerates, using a methodology pioneered by Kaplan and Peterson…. such that x 1 is the “pure play” beta for industry 1, x 2 is the beta for industry 2… 16

Operating Risk across Industries A company’s beta represents the company’s exposure to changes in the overall stock market. Since the stock market is closely tied to the economy, a company’s beta represents its revenue and cash flow exposure to the economy’s strength Semiconductor Equipment Life Insurance Integrated Steel Specialty Retail Commodity Chemicals Information Services Retail Automotive Hotel/Gaming Aggregate Market Homebuilding Packaging & Container Property Management Water Utility Unlevered Beta by Sector Source: Aswath Damodaran,New York University.

Cost of Equity Using CAPM Base Return Long-Term Treasuries 4.0% Below Average Risk Above Average Risk 9.2% 14.4% Raytheon (7.8%) Cisco (10.4%) When the beta is high, the stock is considered more risky than the market. For instance, Cisco Systems moves more than the market, and has a beta of Thus, the company’s cost of equity is 10.4 percent. With a beta of 0.73, Raytheon’s cost of equity is estimated at 7.8 percent. Risk-free rate Expected market return 18

19 An Alternative Model: Fama & French In 1992, Eugene Fama and Kenneth French published a paper in the Journal of Finance that received a great deal of attention because they concluded, In short, our tests do not support the most basic prediction of the SLB [Sharpe-Lintner-Black] Capital Asset Pricing Model that average stock returns are positively related to market betas. Based on prior research and their own comprehensive regressions, Fama and French concluded that: Equity returns are inversely related to the size of a company (as measured by market capitalization). Equity returns are positively related to the ratio of the book value to market value of the company’s equity. With this model, a stock’s excess returns are regressed on three factors: excess market returns, the excess returns of small stocks over big stocks (SMB), and the excess returns of high book-to-market stocks over low book-to-market stocks (HML).

20 An Alternative Model: Fama & French Let’s use the Fama-French three-factor model to continue our Home Depot example. To determine the company’s three betas, Home Depot stock returns are regressed against the excess market portfolio, SMB, and HML (available from professional service providers). Home Depot: Fama-French Expected Returns For Home Depot, the Fama-French model leads to a slightly smaller cost of equity than the market model.

21 An Alternative Model: The Arbitrage Pricing Theory The arbitrage pricing theory (APT) can be thought of as a generalized version of the Fama-French three-factor model. In the APT, a security’s returns are fully specified by k factors and random noise: By creating well-diversified factor portfolios, it can be shown that a security’s expected return must equal the risk-free rate plus its exposure to each factor times the factor’s excess return (denoted by lambda): Implementation of the APT, however, has been elusive, as there is little agreement on either the number of factors, what the factors represent, or how to measure the factors.