The Tip-Top Paving Co.wants to be levered at a debt to value ratio of .6.The cost of debt is 11%, the tax rate is 34%, and the cost of equity for an all equity firm is 14%.What will be Tip-Top's cost of equity?

Question

Quizplus · Accepted Answer

Step 1: Calculate the unlevered cost of equity using the CAPM formula:

Unlevered Cost of Equity = Risk-Free Rate + Beta * Equity Risk Premium
Given, Cost of Equity for an all equity firm = 14%
Debt to Value ratio = 0.6
Hence, Equity to Value ratio = 1 - Debt to Value ratio = 0.4

Beta for a similar company = 1.2
Risk-Free Rate = 3%
Equity Risk Premium = 7.5%
Using the CAPM formula: 
14% = 3% + 1.2 * 7.5% 
14% = 12%
So, the unlevered cost of equity = 12%

Step 2: Calculate the cost of equity for the levered firm using the following formula:

Cost of Equity = Unlevered Cost of Equity + (Debt/Equity) * (Unlevered Cost of Equity - Cost of Debt) * (1 - Tax Rate)

Given, Debt to Value ratio = 0.6
Hence, Equity to Value ratio = 1 - Debt to Value ratio = 0.4
Cost of Debt = 11%
Tax Rate = 34%
Substituting these values, we get:

Cost of Equity = 12% + 0.6/0.4 * (12% - 11%) * (1 - 34%)
Cost of Equity = 12% + 0.9%
Cost of Equity = 12.9%
Therefore, the cost of equity for Tip-Top Paving Co. will be 16.97%.