The White Hills Co. has expected earnings before interest and taxes of $8,100, an unlevered cost of capital of 11%, and debt with both a book and market value of $12,000. The debt has an annual 8%
Coupon. The tax rate is 34%. What is the value of the ﬁrm?

Question

Quizplus · Accepted Answer

First, we need to calculate the weighted average cost of capital (WACC):

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)

Where:
E = market value of equity = total value of the firm - value of debt = V - D
V = total value of the firm = E + D
D = market value of debt = book value of debt = $12,000
Re = unlevered cost of equity = 11%
Rd = pretax cost of debt = 8%
Tc = tax rate = 34%

E/V = (V - D)/V = 1 - D/V = 1 - 12,000/(E + 12,000)
D/V = 12,000/(E + 12,000)

WACC = (1 - 12,000/(E + 12,000)) * 11% + 12,000/(E + 12,000) * 8% * (1 - 34%)
WACC = 10.52%

Next, we need to calculate the value of the firm using the perpetuity formula:

V = EBIT / WACC

V = $8,100 / 10.52% = $77,068.05

Finally, we need to subtract the value of the debt to get the value of the equity:

E = V - D = $77,068.05 - $12,000 = $65,068.05

Therefore, the value of the firm is C) $52,680.