wants to have a weighted average cost of capital of 9.0 percent. The firm has an after-tax cost of debt of 6.0 percent and a cost of equity of 11.0 percent. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

33.33%

Explanation:

WACC can be calculated using the following formula:

WACC = Ke * (E/V) + Kd (1-T) * (D/V)

Here

V = Market Value of Equity + Market Value of Debt

Or simple we can write it as:

V = E + D

kd (1-T) is after tax cost of debt which is given in the question and is 6%.

Ke = 9% cost of equity

WACC = 9%

So by putting values we have:

9% = 11% * (E/V) + 6% * (D/V)

Which means:

0.09 = 0.11 (E/V) + 0.06 (D/V)

By multiplying by (V/E), we have:

0.09 (V/E) = 0.11 + 0.06 (D/E)

As we know that the V/E is just the equity multiplier, which is equal to:

V/E = 1 + D/E

So by putting value we have:

0.09 (D/E + 1) = 0.11 + 0.06 (D/E)

Now, we can solve for D/E as:

0.09 (D/E) + 0.09 = 0.11 + 0.06 (D/E)

0.09 (D/E) - 0.06 (D/E) = 0.11 - 0.09

0.03 (D/E) = 0.03

(D/E) = 0.02 / 0.03 = 33.33%