Final answer:
The initial cost of equity for the unlevered firm is 10%. After converting to 25% debt, the cost of equity becomes 11.7% and the WACC 9.275%; for 75% debt, the cost of equity rises to 15.4% and WACC decreases to 7.355%.
Step-by-step explanation:
To determine the cost of equity for an unlevered firm, we use the following formula:
Weighted Average Cost of Capital (WACC) = Cost of Equity (E/V) + Cost of Debt (D/V) * (1 - Tax Rate),
where E is the market value of the equity, D is the market value of the debt, and V is the total value of the firm (E + D). Since the firm is unlevered, the cost of equity is equal to the WACC, which is 10%.
When the firm converts to 25 percent debt, we would typically use the Modigliani-Miller theorem to adjust the cost of equity based on the new capital structure:
New Cost of Equity = Old Cost of Equity + (Old Cost of Equity - Cost of Debt) * (Debt/Equity) * (1 - Tax Rate).
However, we lack the old cost of equity explicitly; hence we must use the old WACC to represent it.
For 25 percent debt, the firm's new cost of equity will be:
10% + (10% - 6%) * (0.25/0.75) * (1 - 0.20) = 11.7%.
For 75 percent debt, it becomes:
10% + (10% - 6%) * (0.75/0.25) * (1 - 0.20) = 15.4%.
To calculate the WACC after the conversion to 25 percent debt:
WACC = (75% * Cost of Equity) + (25% * Cost of Debt) * (1 - Tax Rate);
WACC = (75% * 11.7%) + (25% * 6%) * (1 - 0.20) = 9.275%.
Similarly, for 75 percent debt:
WACC = (25% * Cost of Equity) + (75% * Cost of Debt) * (1 - Tax Rate);
WACC = (25% * 15.4%) + (75% * 6%) * (1 - 0.20) = 7.355%.