Question

Hilltop Paving has a levered equity cost of capital of 14.92 percent. The debt-to-value ratio is 0.4, the tax rate is 34 percent, and the pretax cost of debt is 7.2 percent. What is the estimated unlevered cost of equity?

a. 12.08%
b. 13.06%
c. 12.56%
d. 10.97%

Answer 1

Answer:

c. 12.56%

Explanation:

Debt-to-value=D/(D+E) =0.4=> D=0.4D + 0.4E => 0.6D = 0.4E => D/E=4/6=2/3

According to M&M proposition II with taxes,

re=r0+(D/E)(r0-rd)(1-Tax rate) . Where re= levered cost of equity(or cost of equity when the firm is levered)=.1492, r0 = unlevered cost of equity,Tax rate=34%=.34, rd=pretax cost of debt=7.2%=0.072,D/E=2/3

re = r0+(2/3) * (r0 - 0.072)*(1-.34)

=> 0.1492=r0(1+(2/3)*(1-.34)) -(2/3)*(.072)*(1-.34)

=> 0.1492 = r0(1+0.44) -0.03168

=> 0.1492 = 1.44*r0 -0.03168

r0 = (.1492+0.03168)/1.44

r0 =0.1256

r0 =12.56%

Thus, r0=unlevered cost of equity=12.56%

Answer 2

The estimated unlevered cost of equity is option c 12.56%.

• The calculation is as follows:

Debt-to-value = D ÷ (D+E)  = 0

D = 0.4D + 0.4E

0.6D = 0.4E

D ÷ E = 4 ÷ 6 = 2 ÷ 3

Now  

Levered cost of equity = unlevered cost of equity + (D ÷ E)(unlevered cost of equity - pretax cost of debt )(1-Tax rate)

Levered cost of equity  =  unlevered cost of equity+(2  ÷ 3) × ( unlevered cost of equity - 0.072) ×(1-.34)

0.1492 =  unlevered cost of equity (1+(2  ÷ 3) × (1 -.34)) - (2 ÷  3) × (.072) ×(1-.34)

0.1492 =  unlevered cost of equity  (1+0.44) -0.03168

0.1492 = 1.44 ×unlevered cost of equity -0.03168

unlevered cost of equity = (.1492+0.03168) ÷ 1.44

 =0.1256

=12.56%

Thus, we can conclude that the correct option is c.

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