James Bay Water Park operates in a world with zero taxes and no financial distress.The firm has a debt/equity ratio of 1.The cost of equity is 15% and the cost of debt is 8%.The only difference between Whispering Pines Resort and James Bay Water Park is that Whispering Pines Resort has a debt/equity ratio of 3.What is the cost of equity for Whispering Pines Resort?
A)11.5%
B)12.67%
C)15.0%
D)22.0%

Question

Quizplus · Accepted Answer

Given the zero-tax environment and no financial distress, the cost of equity can be calculated using the Modigliani-Miller Proposition II without taxes. The formula is:$$ r_E = r_0 + (r_0 - r_D) \times \frac{D}{E} $$where $ r_E $ is the cost of equity, $ r_0 $ is the unlevered cost of capital, $ r_D $ is the cost of debt, and $ \frac{D}{E} $ is the debt-to-equity ratio.For James Bay Water Park, we have:- Debt/Equity = 1- Cost of Equity ($ r_E $) = 15%- Cost of Debt ($ r_D $) = 8%First, we need to find the unlevered cost of capital ($ r_0 $) for James Bay, which is the same for Whispering Pines Resort since they are otherwise identical.$$ 15\% = r_0 + (r_0 - 8\%) \times 1 $$Solving for $ r_0 $, we get $ r_0 = 11.5\% $.For Whispering Pines Resort with a Debt/Equity ratio of 3:$$ r_E = 11.5\% + (11.5\% - 8\%) \times 3 $$$$ r_E = 11.5\% + 3.5\% \times 3 $$$$ r_E = 11.5\% + 10.5\% $$$$ r_E = 22\% $$Therefore, the cost of equity for Whispering Pines Resort is 22%.

James Bay Water Park Operates in a World with Zero