A firm has a market value of assets of $50 000. It borrows $10 000 at 3%. If the unlevered cost of equity is 15%, what is the firm's cost of equity capital?
A)16%
B)18%
C)19%
D)17%

Question

Quizplus · Accepted Answer

The cost of equity capital can be calculated using the Modigliani-Miller Proposition II with taxes, which states that the cost of equity increases with leverage because the risk to equity holders increases when debt is introduced. The formula to calculate the levered cost of equity (Re) is: Re = Ru + (Ru - Rd)(D/E), where Ru is the unlevered cost of equity, Rd is the cost of debt, D is the value of debt, and E is the value of equity. Here, Ru = 15%, Rd = 3%, D = $10,000, and E = $50,000 - $10,000 = $40,000. Plugging these values into the formula gives: Re = 15% + (15% - 3%)*($10,000/$40,000) = 15% + 12%*(1/4) = 15% + 3% = 18%.

A Firm Has a Market Value of Assets of $50