An unlevered firm has a cost of capital of 13.8 percent and earnings before interest and taxes of $214,560.Assume the firm borrows $430,000 at an interest rate of 5.85 percent.The applicable tax rate is 35 percent.What is the value of the levered firm?
A)$1,209,518.70
B)$1,007,018.11
C)$1,161,108.70
D)$1,246,082.19
E)$1,105,018.11

Question

Quizplus · Accepted Answer

Step 1: Calculate the value of unlevered firm

Using WACC formula, WACC = E/V * Re + D/V * Rd * (1-T)
where 
E = Market value of equity = ?
D = Market value of debt = 0 (since it is an unlevered firm)
V = Total value of the firm = E + D
Re = Cost of equity = 13.8%
Rd = Cost of debt = 0 (since it is an unlevered firm)
T = Tax rate = 35%

WACC = Cost of capital = 13.8%
E/V = ?/V
1 - E/V = D/V = 0 (since it is an unlevered firm)
0.138 = E/V * 1 - 0 * (1 - 0.35)
E/V = 0.138 / 0.65 = 0.2123
V = E / 0.2123 = $1,011,688.31

Step 2: Calculate the value of levered firm

V'L = VU + T * D
where 
V'L = Total value of levered firm
VU = Total value of unlevered firm = $1,011,688.31
D = Market value of debt = $430,000
T = Tax rate = 35%

V'L = $1,011,688.31 + 0.35 * $430,000 = $1,161,108.70

Therefore, the value of the levered firm is $1,161,108.70, which is option C.

An Unlevered Firm Has a Cost of Capital of 13