THE COST OF CAPITAL AND ASSET BETAS Risk Asset Pricing and Discount Rates Discount rate rf adjustment for risk For what types of risk do investors require higher expected returns Financial markets only reward investors for taking risk that is correlated with the market or other priced factors i e systematic risk They don t reward idiosyncratic diversifiable risk Just as you ask this when buying and selling financial securities you also must do so when investing in projects Flashback to Investments No Arbitrage and the Risk Premium The risk premium of a security is determined only by its systematic risk The risk premium for diversifiable risk is zero so investors are not compensated for holding firm specific risk If the diversifiable risk of stocks were compensated with an additional risk premium then investors could buy the stocks earn the additional premium and simultaneously diversify and eliminate the risk By doing so investors could earn an additional premium without taking on additional risk This opportunity to earn something for nothing would quickly be exploited and eliminated Because investors can eliminate firm specific risk for free by diversifying their portfolios they will not require or earn a reward or risk premium for holding it Flashback to Investments CAPM The CAPM states ri rf i rm rf ri is the required asset return rf is today s risk free rate with same duration as the asset rm is the market return independent of the asset rm rf is the market risk premium i measures the sensitivity of the asset return to market movements Cov ri rm i Var rm EQUITY AND DEBT COST OF CAPITAL Estimating a firm s equity cost of capital E Ri rf i E RMkt rf o Cost of Equity Risk Free Rate Equity Beta Market Risk Premium Example o Assume the equity beta of DuPont is 1 37 the yield on long term Treasuries is 3 and you estimate the market risk premium to be 6 o Then DuPont s cost of equity is 3 1 37 6 11 22 CAPM inputs 1 Measuring Beta Estimated in a linear regression with respect to a market index return e g S P 500 usually with weekly or monthly data Can be difficult to measure beta accurately i e with a low standard error for individual firms so sometimes a portfolio of similar firms e g industry is used instead Betas with Respect to the S P 500 for Individual Stocks based on monthly data for 2004 2008 CAPM Inputs 2 Risk Free Rate U S Treasury securities are usually considered a risk free benchmark Surveys suggest most practitioners use 10 to 30 year treasuries Market Risk Premium We can estimate the risk premium E RMkt rf using the historical average excess return of the market over the risk free interest rate But what if the future premium is different from the past Estimating a firm s debt cost of capital Two ways to estimate the debt cost of capital i e the expected return on a firm s debt 1 Adjust the debt s yield for the risk of default 2 Estimate a beta for the debt and apply CAPM Debt cost of capital Adjusting yields for the risk of default If there is only a tiny risk the firm will default the yield to maturity is a reasonable estimate of investors expected return of holding the firm s debt If there is significant risk of default yield to maturity will overstate investors expected return Consider a one year bond with YTM of y For each 1 invested in the bond today the issuer promises to pay 1 y in one year Suppose the bond will default with probability p in which case bond holders receive only 1 y L where L is the expected loss per 1 of debt in the event of default So the expected return of the bond is rd 1 p y p y L y pL Yield to Maturity Prob default X Expected Loss Rate The size importance of this adjustment depends on the riskiness of the bond Example Adjusting yields for the risk of default We can use the bond s rating to estimate the probability of default that we can use for the adjustment Table Annual Default Rates by Debt Rating 1983 2008 Example During average times the annual default rate for B rated bonds is 5 2 from the Table The average loss rate for unsecured debt is 60 So the expected return to B rated bondholders during average times is 0 052X0 60 3 1 below the bond s quoted yield Debt cost of capital Debt beta and CAPM Alternatively we can estimate the debt cost of capital using the CAPM E Ri rf i E RMkt rf BUT debt betas are difficult to estimate because corporate bonds are traded infrequently One approximation is to use estimates of betas of bond indices by rating category Rating Category A and Above BBB BB B CCC Avg Beta 0 05 0 10 0 17 0 26 0 31 Source Schaefer and Strebulaev 2009 A PROJECT S COST OF CAPITAL A Project s Asset Beta We now know about equity beta E and debt beta D the sensitivity of a stock s or bond s return to the return on the market To evaluate an investment in a project a machine plant technology or a firm that produces cash flows we now seek a beta for the project We need a different kind of beta an asset beta A Idea is the same measures the sensitivity of the project to the return of the market as a whole Finding the Asset Beta How can we find an asset beta that is appropriate for the specific cash flows of the project under consideration One way is to find a traded firm with the same risk as our project and use its asset beta the Twin Method But we usually only see a firm s equity beta not its asset beta Solution we can calculate the asset beta from the equity beta by adjusting for the effect of leverage The Twin Method 1 Identify a comparable twin firm 2 3 4 Firm with activities that are equally risky to the activities of our project Look up or calculate its equity beta Unlever equity beta to get asset beta The asset beta goes into the CAPM formula to determine project s cost of capital Asset cost of capital Imagine a business as a portfolio of its liabilities The business total return rA is divided between equity E and debt holders D Equity holders receive rE Debt holders receive rD E and D are market values of equity and debt Because the return on a portfolio is the weighted average of the returns of the individual securities in the portfolio rA rE E D rD E D E D rA is the asset cost of capital Also called the unlevered cost of capital The correct discount rate for considering an all equity financed project We will make adjustments to this later if a project is not 100 equity financed Unlevering Formulas The beta of a …