Central Systems desires a weighted average cost of capital of 12.7 percent. The firm has an aftertax cost of debt of 4.8 percent and a cost of equity of 15.4 percent. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

Question

Quizplus · Accepted Answer

To find the debt-equity ratio, we need to use the weighted average cost of capital formula:

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

Where: 
E = Market value of equity
D = Market value of debt
V = Total value of firm (E + D)
Re = Cost of equity
Rd = Cost of debt
Tc = Corporate tax rate

We know that:
WACC = 12.7%
Rd = 4.8%
Re = 15.4%

Let x be the debt-equity ratio:

x = D/E

1 + x = V/D

Substituting the known values in the WACC equation:

0.127 = [(E/V) * 0.154] + [(D/V) * 0.048 * (1-0.3)]

0.127 = [(1/(1+x)) * 0.154] + [(x/(1+x)) * 0.048 * 0.7]

Solving for x:
x = 0.34 or 34%

Therefore, Central Systems needs a debt-equity ratio of 34% to achieve its targeted weighted average cost of capital of 12.7%. 
The answer is D.

Central Systems Desires a Weighted Average Cost of Capital of 12.7