Textbook problem: David Ortiz Motors has a target capital structure of 40% debta

Question

Textbook problem: David Ortiz Motors has a target capital structure of 40% debtand 60% equity. The yield to maturity on the company'soutstanding bonds is 9% and the company's tax rate if 40%. Ortiz's CFO has calculated the company's WACC as 9.96%. Whatis the company's cost of equity capital? I have the WACC formula...however, am not seeing that I haveenough info to compute this. Can you help me set thisup? Textbook problem: David Ortiz Motors has a target capital structure of 40% debtand 60% equity. The yield to maturity on the company'soutstanding bonds is 9% and the company's tax rate if 40%. Ortiz's CFO has calculated the company's WACC as 9.96%. Whatis the company's cost of equity capital? I have the WACC formula...however, am not seeing that I haveenough info to compute this. Can you help me set thisup?

Explanation / Answer

Answer:

We know the formula for WACC asshown below:

WACC = [E * RE] + [P *RP] + [(D * RD) * (1 – TaxRate)]

But, in our example the company isfinanced by only debt and equity and not by preferred stock, so ourformula will become,

WACC = [E * RE] + [(D *RD) * (1 – Tax Rate)]

Here,

E = Ratio of Equity or Common StockOutstanding = 60% or 0.6

RE = Cost of Equity orRequired Rate of Return =?

D = Ratio of Debt = 40% or0.4

RD = Cost of Debt orYield to Maturity (YTM) = 9% or 0.09

WACC = Weighted Average Cost ofCapital = 9.96% or 0.0996

Tax Rate = 40% or 0.04

WACC = [E * RE] + [(D *RD) * (1 – Tax Rate)]

0.0996 = [0.6 * RE] +[(0.4 * 0.09) * (1 – 0.4)]

0.0996 = [0.6 * RE] +[(0.036) * (0.6)]

0.0996 = [0.6 * RE] +[0.0216]

0.0996 – [0.0216] = [0.6 *RE]

0.078 = [0.6 *RE]

RE = 0.078 /0.6

RE = 0.13 or13%

Let’s verify it as shownbelow:

WACC = [E * RE] + [(D *RD) * (1 – Tax Rate)]

WACC = [0.6 * 0.13] + [(0.4 * 0.09)* (1 – 0.4)]

WACC = [0.078] + [(0.036) *(0.6)]

WACC = [0.078] +[0.0216]

WACC = 0.0996 or 9.96%hence verified that all calculations arecorrect.

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