Question

The Pumpkin Inc. has a cost of equity of 16.5 percent and a pre-tax cost of debt of 9.4 percent. The firm's target weighted average cost of capital is 12 percent and its tax rate is 20 percent. What is the firm's debt-equity ratio?

a) 0.89

b) 1.00

c) 1.26

d) 0.77

Answer 1

Let us say that the proportion of debt in the capital structure is D

Then, the proportion of equity in the capital structure = (1 -D)

after-tax cost of debt = before-tax cost of debt * (1 - tax rate) = 9.4% * (1 - 20%) = 7.52%

WACC = (weight of debt * after-tax cost of debt) + (weight of equity * cost of equity)

0.12 = (D * 0.0752) + ((1 - D) * 0.165)

0.12 = 0.0752D + 0.165 - 0.165D

0.165D - 0.0752D =  0.165 - 0.12

D = 0.5011

proportion of debt = 0.5011

proportion of equity = 1 - 0.5011 = 0.4989

debt-equity ratio =  0.5011 / 0.4989 = 1.00

debt-equity ratio = 1.00

Option (b) is correct