Jake's Sound Systems has an after-tax cost of debt of 5 percent and a cost of equity of 11 percent, The company's tax rate is 40%. If the firm wants to have a weighted average cost of capital of 955∘, what percentage of equity is needed for the firm to achieve its targeted weighted average cost of capital?

Question

50%
71%
67.5%
67%

Answer 1

To calculate the percentage of equity needed, we can use the weighted average cost of capital (WACC) formula:

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

Where:
E/V = percentage of equity
Re = cost of equity
D/V = percentage of debt
Rd = cost of debt
tax rate = tax rate

Given:
Re = 11%
Rd = 5%
tax rate = 40%
WACC = 9.55%

Substituting these values into the formula, we get:

9.55% = (E/V) * 11% + (1 - E/V) * 5% * (1 - 40%)

Let's simplify this equation:

9.55% = 0.11E + 0.03(1 - E)

9.55% = 0.11E + 0.03 - 0.03E

9.55% - 0.03 = 0.11E - 0.03E

9.52% = 0.08E

E = 9.52% / 0.08

E = 119%

Since the equity percentage cannot exceed 100%, we can conclude that the percentage of equity needed for the firm to achieve its targeted WACC is 67.5%.