A firm has a market value of assets of $50,000.It borrows $10,000 at 5%.If the unlevered cost of equity is 15%,what is the firm's cost of equity capital?
A)15%
B)17.5%
C)18.5%
D)19.2%
E)20.6%

Question

Quizplus · Accepted Answer

The firm's cost of equity capital can be calculated using the Modigliani-Miller Proposition II with taxes. The formula is: $r_E = r_0 + (r_0 - r_D) \times (D/E)$, where $r_E$ is the cost of equity, $r_0$ is the unlevered cost of equity, $r_D$ is the cost of debt, $D$ is the value of debt, and $E$ is the value of equity. Here, $r_0 = 15\%$, $r_D = 5\%$, $D = \$10,000$, and $E = \$50,000 - \$10,000 = \$40,000$. Plugging these values into the formula gives: $r_E = 15\% + (15\% - 5\%) \times (\$10,000/\$40,000) = 15\% + 10\% \times 0.25 = 15\% + 2.5\% = 17.5\%$.

A Firm Has a Market Value of Assets of $50,000