Phil's Carvings wants to have a weighted average cost of capital of 9%.The firm has an after-tax cost of debt of 5 %and a cost of equity of 11%.What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

Question

Quizplus · Accepted Answer

To calculate the weighted average cost of capital using a debt-equity ratio, we can use the following formula:

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

where:
E = market value of equity
D = market value of debt
V = E + D
Re = cost of equity
Rd = cost of debt
Tc = corporate tax rate

We know that WACC = 9%, Rd = 5%, and Re = 11%. We need to find the D/E ratio that will give us a WACC of 9%.

Let's assume that the market value of debt is D dollars and the market value of equity is E dollars. Then we have:

V = D + E

We can rewrite the formula as:

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

Plugging in the values we know, we get:

11% = (9% - (D/(D+E)) * 5% * (1 - 0.21)) / (E/(D+E))

where we assume a corporate tax rate of 21%.

Simplifying this equation yields:

0.02E = 0.04D

Or, put another way:

E/D = 2

So, the debt-equity ratio needed to achieve a WACC of 9% is:

D/E = 1/2 = 0.5

Therefore, the correct answer is C) 50%.

Phil's Carvings Wants to Have a Weighted Average Cost of Capital