A ﬁrm has a debt-to-equity ratio of .60.Its cost of debt is 8%.Its overall cost of capital is 12%.What is its cost of equity if there are no taxes or other imperfections?
A)10.0%
B)13.5%
C)14.4%
D)18.0%
E)None of the above.

Question

Quizplus · Accepted Answer

First, we can use the debt-to-equity ratio to find the proportion of the total capital structure that is attributed to equity:

Equity proportion = 1 / (1 + debt-to-equity ratio) = 1 / (1 + 0.60) = 0.625

We also know that the overall cost of capital is a weighted average of the cost of debt and the cost of equity, where the weights are the proportions of each in the capital structure:

Overall cost of capital = (cost of debt) x (1 - equity proportion) + (cost of equity) x (equity proportion)

Plugging in the values we know, we get:

0.12 = 0.08 x 0.375 + (cost of equity) x 0.625

Solving for the cost of equity gives us:

(cost of equity) = (0.12 - 0.08 x 0.375) / 0.625 = 0.144 or 14.4%

Therefore, the correct answer is C) 14.4%.

A ﬁRm Has a Debt-To-Equity Ratio of