Weighted average cost of capital

1. Weighted average cost of capital Timothy A. Thompson Executive Masters Program

2. What is the WACC? • WACC = (D/D+E) rd (1-Tc) + (E/D+E) reL • D/D+E and E/D+E are capital structure weights evaluated at market value, based on the firm’s target capital structure • Tc is the firm’s marginal tax bracket, but the effective tax rate is often used as estimate • rd is the cost of debt based on the risk of the debt (which depends on the debt ratio) • reL is the required rate of return on equity (I.e. the cost of equity) • the cost of equity depends on the business risk of the assets • and on the debt ratio

3. Why the WACC? • Measures the returns demanded by all providers of capital • Investments must offer this return to be worth using the capital providers’ money • As an opportunity cost • The rate of return investors could earn elsewhere on projects with the same risk and capital structure

4. WACC incorporates debt tax shields • The (1-T) term incorporates the fact that debt returns are tax deductible • Discounting project cash flows at WACC is an alternative to adding in the value of tax shields (ala AHP) • Key assumption: constant D/D+E ratio is reasonable as a target capital structure

5. Risk and return • It is reasonable to believe that the higher the risk of an investment, the higher its required return. But … • What is risk, and … • What is the relation between risk and required return?

6. Capital Asset Pricing Model • The result will be that risk of investment (stock j) is measured by its beta ( j) • Any risky security has a required return given by: • the risk free rate of return, rf, plus • a risk premium which is proportional to its beta risk • Equation: rj = rf + j (avg. risk prem.)

7. Diversification: roulette wheel • Fair roulette wheel • 40 slots, 20 black, 20 red (no house slots) • probability of red = 50% • Bet $10,000 on red, one spin • risky? • 50% prob of 100% loss • Bet $1 per spin on 10,000 spins: as risky? • Why is it less risky?

8. Diversification reduces risk • Investors don’t hold only one stock • Smart investors hold diversified portfolios • Why doesn’t risk go to zero as in the roulette wheel? • Because stocks are correlated with each other, with the market as a whole • This is risk you can not diversify away • For risk you must bear, you demand a premium!

9. What measures non-diversifiable risk? • Beta • Covariance measures the degree to which two things “move together” on average • The more a stock moves up and down with the market, the more non-diversifiable risk it has • How much “risk” is in the market portfolio itself? • The variance of the market • Beta = Covariance of stock with market/Variance of the market

10. What is the beta of the market? • Beta of market portfolio is one • Covariance of market with itself/Variance of market • Covariance of anything with itself is its own variance • The market risk premium • rm - rf is the risk premium on the market, so it is the risk premium for a beta of one • Back to the equation

11. CAPM • rj = rf + j (rm - rf) • assets with betas less than one demand lower returns than rm • assets with betas greater than one demand higher returns than rm

12. How do you apply CAPM? • Common assumption: discounting future,long term cash flows • so, you want a long term discount rate (forward looking if possible) • rf is long term government bond rate (forward looking, I.e., current long term T bond rate) • rm - rf is expected excess return on a very diversified portfolio of stocks (S&P500?) over long term government bonds (forward looking not available, so often use historical average)

13. How do you estimate beta? • Many services calculate beta estimates for stocks (some bonds) • Value Line, investment banks • The beta is a statistical estimate • Slope coefficient of a linear regression of the stock’s returns against the proxy for the market portfolio’s returns • A stock’s beta is a levered beta • Based on the debt ratio it has now

14. Estimating Charles Schwab beta

15. Regression for Charles Schwab 95% confidence interval Beta

16. Corporate WACC vs. Project WACC • The corporate WACC is not necessarily the cost of capital for a project within the firm: • The systematic risk of the project could differ from the average systematic risk of the firm’s projects • The target capital structure for the project (thought of as a mini-firm) could differ from the corporate target capital structure

17. Project-beta Adjusted Cost of capital Expected Rates Of Return Y Company-wide WACC X Avg. company Project beta Project Beta

18. How do you estimate the beta of a project or division? • Peer method • Collect a sample of publicly traded firms which are essentially like (you think they face the same systematic risk) the project or division being valued • Estimate (or look them up) the peer companies’ equity betas • Assuming they face the same business risk, not the same financial risk (I.e., different capital structures)

19. Equity risk • Equity beta risk has two sources: • Business risk (the risk of the asset cash flows) • which would equal the equity risk if the business were unlevered (I.e., if it had no debt) • Financial risk • The magnification of the business risk from the perspective of the equityholders because of the presence of debt in the capital structure.

20. Unlever the peer betas • Peers have same business risk as project • so back out the financial risk … How? • First, estimate reL for peers using CAPM • Then use the unlevering formula: • reU = [reL + (1-T)(D/E)(rd)]/[1 + (1-T)(D/E)] • For this formula, you technically need the peers’ costs of debt and marginal tax rates (for our assignment, assume the same as Marriott’s)

21. Average the reU’s • These are now estimates of required returns for business risk only! • Average the reU’s • This is your project’s reU

22. The WACC needs reL • You are using WACC to value the project or division • How do you get reL for the WACC? • Relevering formula: • reL = reU + (1-T)(D/E)(reU - rd)

23. Plug in your WACC • Your reL is now ready for your WACC • Estimate Tc, the capital structure weights and rd and you’re ready to go! • Look at the lodging WACC • Assignment: Bring back a restaurant division WACC!

24. Extra credit • For extra credit, bring back a contract services division WACC • There are no peers given for contract services • But you can estimate WACC, reu, reL, etc. for Marriott as a whole!