Question

Vamos, Inc. 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?

Group of answer choices

0.353

0.667

0.859

0.545

0.471

Answer 1

Option 0.667 is correct

Let Weight of Debt = wd = x

Weight of equity = we = 1-x

after tax cost of debt = rd(1-t) = 6%

cost of equity = re = 11%

Weighted Average Cost of Capital = 9%

Weighted Average Cost of Capital = [(wd * rd (1-t))] + [we * re]

9% = [x * 6%] + [(1-x) * 11%]

9% = 6% x + 11% - 11%x

5% x = 2%

x = 0.4

Weight of Debt = 0.4

Weight of Equity = 1-x = 1 - 0.4 = 0.6

Debt Equity ratio = Debt / Equity = Weight of Debt / Weight of Equity = 0.4 / 0.6 = 0.667

Therefore, Debt Equity ratio = 0.667