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

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

What is the WACC? WACC = (D/D+E) r d (1-T c ) + (E/D+E) r eL D/D+E and E/D+E are capital structure weights evaluated at market value, based on the firm’s target capital structure T c is the firm’s marginal tax bracket, but the effective tax rate is often used as estimate r d is the cost of debt based on the risk of the debt (which depends on the debt ratio) r eL 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

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

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

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?

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, r f, plus a risk premium which is proportional to its beta risk Equation: r j = r f +  j (avg. risk prem.)

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?

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!

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

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 r m - r f is the risk premium on the market, so it is the risk premium for a beta of one Back to the equation

CAPM r j = r f +  j (r m - r f ) assets with betas less than one demand lower returns than r m assets with betas greater than one demand higher returns than r m

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) r f is long term government bond rate (forward looking, I.e., current long term T bond rate) r m - r f 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)

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

Estimating Charles Schwab beta

Regression for Charles Schwab SUMMARY OUTPUTCharles Schwab Regression Statistics Multiple R0.494088888 R Square0.24412383 Adjusted R Square0.231091482 Standard Error0.100953718 Observations60 ANOVA dfSSMSFSignificance F Regression10.1909115250.19091218.732156.02E-05 Residual580.5911158810.010192 Total590.782027406 CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept0.0062912720.0144648310.4349360.665223-0.022660.035246 Slope on market2.300.534.330.001.233.36

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

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

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 )

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.

Unlever the peer betas Peers have same business risk as project so back out the financial risk … How? First, estimate r eL for peers using CAPM Then use the unlevering formula: r eU = [r eL + (1-T)(D/E)(r d )]/[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)

Average the r eU ’s These are now estimates of required returns for business risk only! Average the r eU ’s This is your project’s r eU

The WACC needs r eL You are using WACC to value the project or division How do you get r eL for the WACC? Relevering formula: r eL = r eU + (1-T)(D/E)(r eU - r d )

Plug in your WACC Your r eL is now ready for your WACC Estimate T c, the capital structure weights and rd and you’re ready to go! Look at the lodging WACC Assignment: Bring back a restaurant division WACC!

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, r eu, r eL, etc. for Marriott as a whole!

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