Final answer:
The cost of equity for the firm can be calculated using the weighted average cost of capital (WACC) formula. In this case, the cost of equity is 24%.
Step-by-step explanation:
The cost of equity for the firm can be calculated using the weighted average cost of capital (WACC) formula. WACC is the average rate of return a company must earn to satisfy its shareholders and debt holders. The formula for WACC is: WACC = (Equity / Total Capital) * Cost of Equity + (Debt / Total Capital) * Cost of Debt
In this case, the firm is financed with $75 million of equity and $25 million of debt. The cost of debt capital is 7 percent. We are given that the WACC is 19.75 percent.
Plugging in the values, we can calculate the cost of equity as follows:
(75 / (75 + 25)) * Cost of Equity + (25 / (75 + 25)) * 7 = 19.75
Simplifying the equation, we get: 0.75 * Cost of Equity + 0.25 * 7 = 19.75
Which further simplifies to: 0.75 * Cost of Equity + 1.75 = 19.75
Then, we can solve for Cost of Equity:
0.75 * Cost of Equity = 19.75 - 1.75
0.75 * Cost of Equity = 18
Cost of Equity = 18 / 0.75
Cost of Equity = 24