Weighted average cost of capital

Timothy A. ThompsonExecutive Masters Program

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

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 costThe 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 deductibleDiscounting 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 returnIt 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, rf, plus

a risk premium which is proportional to its beta risk

Equation: rj = rf + 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 spinrisky?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 stockSmart investors hold diversified portfoliosWhy 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• rm - rf is the risk premium on the market,

so it is the risk premium for a beta of one

Back to the equation

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

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)

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

Schwab's returns vs. Market returns

-0.4

-0.2

0

0.2

0.4

-0.10 -0.05 0.00 0.05 0.10

Returns on Market

Sc

hw

ab

R

etu

rns

Regression for Charles SchwabSUMMARY OUTPUT Charles Schwab

Regression Statistics

Multiple R 0.494088888

R Square 0.24412383

Adjusted R Square 0.231091482

Standard Error 0.100953718

Observations 60

ANOVA

  df SS MS F Significance F

Regression 1 0.190911525 0.190912 18.73215 6.02E-05

Residual 58 0.591115881 0.010192

Total 59 0.782027406      

  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 0.006291272 0.014464831 0.434936 0.665223 -0.02266 0.035246

Slope on market 2.30 0.53 4.33 0.00 1.23 3.36

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 projectsThe target capital structure for the project (thought of as a mini-firm) could differ from the corporate target capital structure

ExpectedRatesOfReturn

Company-wideWACC

Project-betaAdjustedCost of capital

Avg. companyProject beta Project Beta

X

Y

How do you estimate the beta of a project or division?

Peer methodCollect a sample of publicly traded firms which are essentially like (you think they face the same systematic risk) the project or division being valuedEstimate (or look them up) the peer companies’ equity betasAssuming 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 reL for peers using CAPMThen 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)

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

The WACC needs reL

You are using WACC to value the project or divisionHow do you get reL for the WACC?

Relevering formula:reL = reU + (1-T)(D/E)(reU - rd)

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 WACCAssignment: 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 servicesBut you can estimate WACC, reu, reL, etc. for Marriott as a whole!