Tip-Top Paving has an equity cost of capital of 16.97%.The debt to value ratio is 0.6, the tax rate is 34%, and the cost of debt is 11%.What is the cost of equity if Tip-Top was unlevered?

Question

Quizplus · Accepted Answer

The cost of equity for an unlevered firm can be calculated using the Modigliani-Miller Proposition II without taxes. However, since there is a tax rate given, we adjust for the tax shield. The formula to adjust the cost of equity for leverage is $ r_E = r_0 + (r_0 - r_D)(1 - T_c)D/E $, where $ r_E $ is the levered cost of equity, $ r_0 $ is the unlevered cost of equity, $ r_D $ is the cost of debt, $ T_c $ is the corporate tax rate, and $ D/E $ is the debt-to-equity ratio. Given the debt to value ratio (D/V) is 0.6, we can find D/E as $ D/E = D/V / (1-D/V) = 0.6 / 0.4 = 1.5 $. Rearranging the formula to solve for $ r_0 $ and substituting the given values, we find that the unlevered cost of equity is approximately 14.0%.

Tip-Top Paving Has an Equity Cost of Capital of 16