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**Estimating the Cost of Capital**

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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.

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**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 assure consistency, It must include the opportunity costs from all sources of capital — debt, equity, and so on—since free cash flow is available to all investors. It must weight each security’s required return by its market-based target weight, not by its historical book value. It must be computed after corporate taxes (since free cash flow is calculated in after-tax terms). Any financing-related tax shields not included in free cash flow must be incorporated into the cost of capital or valued separately. It must be denominated in the same currency as free cash flow It must be denominated in nominal terms when cash flows are stated in nominal terms

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**The Cost of Capital: An Example**

LAN-ZWB ZWB The Cost of Capital: An Example The weighted average cost of capital at Home Depot equals 9.3%. The majority of enterprise value is held by equity holders (91.7%), whose CAPM-based required return equals 9.9%. The remaining capital is provided by debt holders at 2.9% of an after-tax basis. The Cost of Capital: Home Depot Proportion of total capital After-tax opportunity cost Contribution to weighted average Source of capital Cost of capital Marginal tax rate Debt Equity WACC 8.3% 91.7% 100.0% 4.7% 9.9% 38.2% 2.9% 9.9% 0.2% 9.1% 9.3% Let’s examine the components of WACC one-by-one, starting with the cost of equity…

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LAN-ZWB ZWB 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 assets 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 multi-factor 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.

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**The Capital Assets Pricing Model**

LAN-ZWB ZWB The Capital Assets Pricing Model The CAPM postulates that the expected rate of return on a company’s stock equals the risk-free rate plus the security’s beta times the market risk premium: Expected return Percent E[Ri] = rf + Bi (E[Rm] – rf) To estimate a stock’s expected return, you need to measure three inputs: The risk-free rate The market risk premium The stock’s beta Beta (systematic risk)

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**Component 1 of the CAPM: The Risk Free Rate**

LAN-ZWB ZWB Component 1 of the CAPM: The Risk Free Rate To estimate the risk-free rate, we look to government default-free bonds. For simplicity, most valuation analysts choose a single yield to maturity from one government bond that best matches the entire cash flow stream being valued. For U.S.-based corporate valuation, the most common proxy is the 10-year government bond rate. This rate can be found in any daily financial publication. Yield to Maturity on Government Bonds Ideally, each cash flow should be discounted using a government bond with a similar maturity. Percent Source: Bloomberg Years to maturity

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**Component 2 of the CAPM: 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 in three general categories: Extrapolate historical excess returns. If the risk premium is constant, we can use a historical average to estimate the future risk premium. Regression analysis. Using regression, we can link current market variables, such as the aggregate dividend-to-price ratio, to expected market returns. Use DCF to reverse engineer the risk premium. Using DCF, along with estimates of return on investment and growth, we can reverse engineer the market’s cost of capital – and subsequently the market risk premium. None of the methods precisely estimate the market risk premium. Still, based on evidence from each of these models, we believe the market risk premium as of year- end 2003 was approximately 5 percent.

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**Method 1: Use Historical Excess Returns**

Investors, being risk-averse, demand a premium for holding stocks rather than bonds. If the level of risk aversion hasn’t changed over the last 100 years, then historical excess returns are a reasonable proxy for future premiums. But many econometric issues quickly arise. For instance, Which risk free rate should be used to compute the excess return? Which method of averaging is better, arithmetic or geometric? Is a prediction based on U.S. data too high?

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**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.

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**Geometric Versus Arithmetic Average**

Annual returns can be calculated using either an arithmetic average or a geometric average. An arithmetic (simple) average sums each year’s observed premium and divides by the number of observations: A geometric (compounding) average compounds each year’s excess return and takes the root of the resulting product: Arithmetic averages always exceed geometric averages when returns are volatile. So which averaging method best estimates the expected future rate of return?

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**Problems with the Arithmetic Average**

LAN-ZWB ZWB Problems with the Arithmetic Average The arithmetic average of annual returns is the best predictor of future one year returns, but compounded averages will be biased upwards (i.e. too high). Consider a portfolio which can either grow by +20% or -10% in a given period. The arithmetic average equals 5%. If you invested $100 in this portfolio, what is the portfolio’s expected value after two years? Scenario 1 2 3 4 Current value 100 Return in period one 1.2 0.9 Return in period two Future value 144 108 81 Expected value when returns are independent 25% 100% 36.0 27.0 20.3 110.3 Expected value when returns are negatively autocorrelated 15% 35% 21.6 37.8 12.2 109.4 If returns are independent, the expected value is $110.3, the same as if $100 had grown consistently at the arithmetic average of 5% for two periods. If returns are negatively autocorrelated, i.e. high returns are more likely followed by low returns, a compounded arithmetic return is too high!

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**When Possible, Use Long-Dated Holding Periods**

LAN-ZWB ZWB When Possible, Use Long-Dated Holding Periods To correct for the bias caused negative autocorrelation in returns, we have two choices. First, we can calculate multi-period 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 & geometric averages. Arithmetic Returns for Various Intervals, Cumulative returns Annualized returns U.S. government bonds U.S. excess return U.S. excess returns Number of observations U.S. stocks Blume estimator Arithmetic mean of 1-year holding periods 2-year holding periods 4-year holding periods 5-year holding periods 10-year holding periods 100 50 25 20 10 11.3% 24.1 49.9 68.2 165.6 5.3% 10.9 23.1 29.5 72.1 6.2% 12.6 23.0 32.3 70.1 6.2% 6.1 5.3 5.8 5.5% 6.2% 6.1 6.0 5.9 5.6 Source: Ibbotson Associates; McKinsey analysis

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**Method 2: Regression Analysis**

LAN-ZWB ZWB Method 2: Regression Analysis Predicted Market Risk Premium based on the dividend to price ratio Using advanced regression techniques unavailable to earlier authors, Jonathan Lewellen of Dartmouth found that observable variables, such as dividend yields, do predict future market returns. Plotting the model’s predictions reveals one major drawback: the risk premium prediction can be negative! Other authors question the idea of using financial ratios, arguing unconditional historical averages predict better than more sophisticated regression techniques. -5 -3 -1 1 3 5 7 9 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Percent Source: Lewellen (2004); Goyal and Welch (2003); McKinsey analysis

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**Method 3: Reverse Engineer Discounted Cash Flow**

LAN-ZWB ZWB Method 3: Reverse Engineer Discounted Cash Flow Using the principles of discounted cash flow, along with estimates of growth, various authors have attempted to reverse engineer the market risk premium. We use the key value driver formula to reverse engineer the market risk premium. After stripping out inflation, the expected market return (not excess return) is remarkably constant, averaging 7.0%. 5 10 15 20 1962 1972 1982 1992 2002 Percent Predicted Market Risk Premium By reverse engineering market DCF Subtracting the real interest rate of 2.1% from our estimate of 7.0% leads to a risk premium just under 5%.

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**Component 3 of the CAPM: Measuring Beta**

LAN-ZWB ZWB Component 3 of the CAPM: Measuring Beta 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: The Beta for Home Depot Percent Home Depot monthly stock returns Based on data from , Home Depot’s beta is estimated at 1.37 S&P 500 monthly returns

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**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.

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**When Possible, Compute a Rolling Beta**

LAN-ZWB ZWB When Possible, Compute a Rolling Beta Because estimates of beta are imprecise, plot the company’s rolling 60-month beta to visually inspect for structural changes or short-term deviations. IBM’s beta hovered near 0.7 in the 1980s but rose dramatically in the mid-1990s and now measures near 1.3. This rise in beta occurred during a period of great change for IBM. IBM Market Beta, 0.00 0.40 0.80 1.20 1.60 1985 1988 1991 1994 1997 2000 2003 Beta

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**Levering and Unlevering Betas**

To improve the precision of beta estimation, use industry, rather than company-specific, betas. Companies in same industry face similar operating risks, so they should have similar operating betas. Simply using the median of an industry’s raw betas, however, overlooks an important factor: leverage. A company’s equity beta is a function of not only its operating risk, but also the financial risk it takes. The weighted average beta for operating assets (bu - which is called the unlevered beta) and financial assets (btxa) must equal the weighted average beta for debt (bd) and equity (be). Our goal is to use this to solve for bu: operating assets tax assets debt equity Because there are many unknowns and only one equation, we must impose additional assumptions to solve for bu…

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**Levering and Unlevering Betas**

Method 1: Assume btxa equals bu. If you believe the risk associated with tax shields (bu) equals the risk associated with operating assets (bu), the risk equation can be simplified dramatically. Specifically, if bd = 0 Method 2: Assume btxa equals bd. If you believe the risk associated with tax shields (btxa) is comparable to the risk of debt (bd), the equation can once again be arranged to solve for the unlevered cost of equity. If the dollar level of debt is constant and debt is risk free,

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**Determining the Industry Beta**

LAN-ZWB ZWB Determining the Industry Beta To estimate an industry-adjusted company beta: First, regress each company’s stock returns against the S&P 500 to determine raw beta. Next, to unlever each beta, calculate each company’s market-debt-to-equity ratio. Determine the industry unlevered beta by calculating the median (in this case, the median and average betas are the same). Relever the industry unlevered beta is to each company’s target debt-to-equity ratio Capital structure Home Depot Lowe’s Debt Operating leases Excess cash Total net debt Shares outstanding (Mil) Share price ($) Market value of equity Debt/equity Raw beta (step 1) Unlevered beta (step 2) Industry average (step 3) Relevered beta (step 4) 1,365 6,554 (1,609) 6,310 2,257 35.49 80,101 0.079 1.37 1.27 1.14 1.23 3,755 2,762 (948) 5,569 787 55.39 43,592 0.128 1.15 1.02 1.14 1.30 Beta calculations Home Depot Lowe’s

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**E[Ri] = rf + Bi (E[Rm] – rf)**

Applying the CAPM The CAPM postulates that the expected rate of return on a company’s stock equals the risk free rate plus the security’s beta times the market risk premium. To estimate the risk-free rate in developed economies, use highly liquid, long-term government securities, such as the 10-year zero-coupon strip. Based on historical averages and forward-looking estimates, the appropriate market risk premium is currently between 4.5 and 5.5 percent. To estimate a company’s beta, use industry derived betas levered to the company’s target capital structure. For Home Depot: E[Ri] = rf + Bi (E[Rm] – rf) E[Ri] = 4.34% (4.5%) = 9.9%

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**An Alternative Model: Fama & French**

LAN-ZWB ZWB 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 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).

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**An Alternative Model: Fama & French**

LAN-ZWB ZWB 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 0.25 0.36 Average monthly premium Percent 4.5% 3.0% 4.4% Average annual premium Percent Contribution to expected return 1.35 (0.04) (0.10) Regression beta Factor Market risk premium SMB premium HML premium Premium over risk free rate Risk free rate Cost of equity 6.1% (0.1) (0.5) 5.5 4.3 9.8% For HD, the F&F model leads to a slightly smaller cost of equity than the CAPM.

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**An Alternative Model: The Arbitrage Pricing Theory**

LAN-ZWB ZWB An Alternative Model: The Arbitrage Pricing Theory The Arbitrage Pricing Theory (APT) can be thought of as a generalized version of the Fama-French 3-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.

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The Cost of Debt The weighted average cost of capital represents the blended rate of return for a company’s investors, both debtholders and equity holders: To compute the WACC, we must estimate the cost of debt (kd). To do this we look to the yield to maturity (YTM). Although YTM represents a promised yield, it is a good approximation for expected return for investment grade companies. To compute yield-to-maturity, you have two options: Compute the yield-to-maturity on long-term bonds by reverse engineering the discount rate needed to set DCF equal to the price. Compute the yield-to-maturity indirectly by adding a default premium (based on the company’s rating) to the risk free rate. Let’s examine the indirect method…

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**Component 1 of YTM: The Risk Free Rate**

LAN-ZWB ZWB Component 1 of YTM: The Risk Free Rate The yield-to-matrurity can be estimated by adding a default premium (based on the company’s rating) to the risk free rate. The first component of yield-to-maturity is the risk free rate. Regardless of the maturity structure for the company’s debt, use a long-term risk free rate when estimating a company’s cost of capital. Using short-term debt yields to approximate the cost of debt ignores the fact that future debt will have different yields. Yield to Maturity on Government Bonds Percent In 2003, the 10-year yield to maturity was 4.3% in the U.S. and in Europe. Source: Bloomberg Years to maturity

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**S&P and Moody Ratings Classes**

In order to be compensated for default risk, lenders charge a premium over the default-free benchmark rate to risky customers. The higher the chance of default, the higher the premium will be. Professional firms, such as S&P and Moody’s, rate the default risk of most bonds. Let’s examine the ratings defined by Standard & Poors: S&P / Moody’s AAA / Aaa AA / Aa A/ A BBB / Baa EXTREMELY STRONG capacity to meet its financial commitments. ‘AAA’ is the highest Issuer Credit Rating assigned by Standard & Poor’s. VERY STRONG capacity to meet its financial commitments. It differs from the highest rated obligors only in small degree. STRONG capacity to meet its financial commitments but is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than obligors in higher-rated categories. ADEQUATE capacity to meet its financial commitments. However, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity of the obligor to meet its commitments. Speculative debt is rated BB, B, and CCC. In these case, YTM is a poor proxy for the cost of debt. Investment Grade

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**Component 2 of YTM: The Corporate Yield Spread**

LAN-ZWB ZWB Component 2 of YTM: The Corporate Yield Spread Once a bond rating has been identified, convert the rating into a yield to maturity. Let’s examine U.S. corporate yield spreads over U.S. government bonds. All quotes are presented in basis points, where 100 basis points equals 1%. Since Home Depot is rated Aa3 by Moody’s and AA by S&P, we estimate that the 10-year yield to maturity is between 34 and 37 basis points over the 10-year Treasury. Yield Spread in Basis Points, December 2003 Maturity in years Rating Aaa/AAA Aa1/AA+ Aa2/AA Aa3/AA– A2/A Baa2/BBB Ba2/BB B2/B 1 34 37 39 40 57 79 228 387 3 35 33 34 36 49 96 260 384 5 21 34 35 37 57 108 257 349 7 22 40 42 43 65 111 250 332 10 28 29 34 37 48 102 236 303 30 50 62 64 65 82 134 263 319 Source: Bloomberg

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**The Cost of Debt at Distressed Companies**

LAN-ZWB ZWB The Cost of Debt at Distressed Companies Yield to maturity is not an expected return. It is the return earned if the obligation is paid on time and in full. Since distressed company’s have a significant chance of default, the yield-to-maturity is a poor proxy for expected return. One alternative for computing expected return is the CAPM. Since most bonds don’t trade enough to generate a reliable beta, however, we compute index betas instead. Beta by Bond Rating High yield debt has only a slightly higher beta than investment grade debt. If the market risk premium equals 5%, this difference translates to only a 50 basis point differential in expected return! Asset class Treasury bonds Investment-grade corporate debt High-yield corporate debt Beta 0.19 0.27 0.37 Source: Lehman Brothers; “Global Family of Indices, Fixed Income Research”; Morgan Stanley Capital International; U.S. Treasury; Paul Sweeting

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**Use Market-Based Target Weights**

With our estimates of the cost of equity (ke) and cost of debt (kd), we can now blend the two expected returns into a single number. To do this, we use the target weights of debt (and equity) to enterprise value, on a market (not book) basis: D/V equals the company’s market-based, target debt-to-value ratio To develop a target capital structure for a company, Estimate the company’s current market-value-based capital structure. Review the capital structure of comparable companies. Review management’s implicit or explicit approach to financing the business and its implications for the target capital structure.

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**Typical Market Weights Across Industries**

LAN-ZWB ZWB Typical Market Weights Across Industries Median Debt-to-Value, 2003 To place the company’s current capital structure in the proper context, compare its capital structure with those of similar companies. Industries with heavy fixed investment in tangible assets tend to have higher debt levels. High-growth industries, especially those with intangible investments, tend to use very little debt. In percent Information technology Healthcare Aerospace and defence Industrial machinery Consumer discretionary Consumer staples Oil and gas Chemicals, paper, metals Telecommunications Airlines Utilities Note: Market value of debt proxied by book value. Enterprise value proxied by book value of debt plus market value of equity

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