A firm has a debt-to-equity ratio of 0.50. Its cost of debt is 10 percent. Its overall cost of capital is 14 percent. What is its cost of equity if there are no taxes?

Question

Quizplus · Accepted Answer

We can use the formula for WACC (weighted average cost of capital) to find the cost of equity:
WACC = (E/V) × Re + (D/V) × Rd × (1-Tc)
where E = market value of equity, V = total market value of the firm (E + D), Re = cost of equity, D = market value of debt, Rd = cost of debt, and Tc = corporate tax rate (assumed to be 0 in this case).
We are given D/E = 0.50, or D/V = 0.50/(1+0.50) = 0.33.
Solving for Re:
0.14 = (E/V) × Re + 0.33 × 0.10
(E/V) × Re = 0.11
(E/V) × Re = E/(E+D) × Re = cost of equity
Re = 0.11 × (1/0.50) = 0.22 = 22%
Therefore, the cost of equity is 22%. The only answer choice that is close to this is B, 16%.

A Firm Has a Debt-To-Equity Ratio of 0