Weighted Average Cost of Capital(The WACC)

Capital Structure 33

Incorporating Interest Deductibility

:: NOPAT (part of FCF) ignores interest expense

:: So expected taxes in FCF is too large

:: As a fix, the Weighted Average Cost of Capital (WACC)lowers the discount rate to offset

Capital Structure 34

The Weighted-Average Cost of Capital (WACC)

rwacc = E (rd)(1− τ)D

V+ E (re)

E

V

:: E (rd) = Debt cost of capitalI Often assumed riskless, so that E (rd) = rf

:: τ = Corporate tax rate

:: E (rd)(1− τ) = After-tax cost of debt

:: E (re) = Equity cost of capitalI Expected return on equity (shareholders)

:: V = D + E

Capital Structure 35

Example: GPS Valuation (PS6, Q2)

rwacc = E (rd)(1− τ)D

V+ E (re)

E

V

Capital Structure 36

Changing The Capital Structure

We can only observe E (re) for the current capital structure.

:: If we want to consider a change, we need a model

:: Simplest model: “Miller-Modigliani (MM) Model”I (Expected) FCF is a constant perpetuity, cI Cost of capital = rI Debt is D: perpetual, riskless and constant. Cost of debt

capital is risk-free rate, rf .

:: First, what is the PV of the tax shields?

Net Income =(EBIT − rf D

)(1− τ

)= EBIT

(1− τ

)− rf D︸ ︷︷ ︸

Net Income, No Deduction

+ rf τ D︸ ︷︷ ︸Tax Shield

PV (Tax Shields) =rf τ D

rf= τ D

Capital Structure 37

Modigliani-Miller WACC Formula

Firm Value = Value(Unlevered Firm) + Value(Tax Shields)

Firm Value:

V =c

r+ τ D

Define L = D/V :

V =c

r+ τ LV

=c

r

( 1

1− τL

)=

c

r(1− τ DV )

Weighted-Average Cost of Capital:

rwacc = r(1− τ DV

)

Capital Structure 38

Calculating the Cost of Capital

:: WACC model requires estimate of the cost of capital, r .

:: We can obtain this by “unlevering” the equity beta:

AR, Inventory

Property, Plant& Equipment

(PPE)

AP

Debt

Equity

=

PV(tax shields)

Capital Structure 39

Un-Levering the Equity Beta

AR, Inventory

Property, Plant& Equipment

(PPE)

AP

Debt

Equity

=

PV(tax shields)

V = Vu + τD = D + E

=⇒ βuVu

V+ βtax

τD

V=

D

VβD +

E

VβE

=⇒ βu =E

V − τDβE =

1

1 + (1− τ)D/EβE

r = rf + βu(E (rm)− rf

)Capital Structure 40

Summary

Steps: Changing the leverage

:1: Current Firm Valuation. Estimate equity and debt cost of capital.Compute WACC. PV the FCF.

rwacc = E(rd)(1− τ)D

V+ E(re)

E

V

:2: Un-Lever. Purge equity beta of leverage effect, compute cost of capital of(hypothetical) 100% equity-financed firm:

βu =1

1 + (1− τ)D/EβE

r = rf + βu(E(rm)− rf

):3: Re-Lever. Compute WACC for new leverage, D∗

V∗ . PV the the FCF. Thisgives you the re-levered firm value, V ∗, and D∗, E∗.

rwacc = r(1− τ D∗

V ∗ )

Capital Structure 41

Problem Set 6, Q2. An LBO for GPS

Capital Structure 42

Problem Set 6, Q2. An LBO for GPS

Capital Structure 43