THE COST OF CAPITALAND ASSET BETASRisk, Asset Pricing, and Discount Rate s• 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 projectsFlashback 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: CAPMThe CAPM states :*if i mfrr r r• riis the required asset return• rfis today’s risk free rate with same duration as the asset• rmis the market return (independent of the asset)• (rm-rf) is the market risk premium• βimeasures the sensitivity of the asset return to market movements:(, )()imimCov r rVar rEQUITY AND DEBT COST OF CAPITALEstimating a firm’s equity cost of capital• E[Ri] = rf+ βi(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 insteadBetas 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 sug gest 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 inter est 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 CAPMDebt 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 bondExample: 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+ βi(E[RMkt] –rf)• BUT, debt betas are difficult to estimate because corporate bonds are traded infrequently!• One approximation is to use estimates of bet as of bond indices by rating category:RatingCategoryA and AboveBBB BB B CCCAvg. Beta <0.05 0.10 0.17 0.26 0.31Source: Schaefer and Strebulaev (2009)A PROJECT’S COST OF CAPITALA Project’s Asset Bet a•