Final answer:
a) The value of the all-equity firm is $1.2 million. b) The value of the firm if it decides to borrow $1 million debt is $2.2 million. c) The WACC for the levered firm is 16.66%.
Step-by-step explanation:
a) To calculate the value of the all-equity firm, we need to use the formula for the present value of perpetuity: Value = Cash Flow / Cost of Equity. Plugging in the given values, we get: Value = $0.3 million / 0.15 = $2 million. However, since the firm has after-tax cash flows, we need to also take into account the corporate tax rate, which reduces the cash flows to $0.3 million * (1 - 0.4) = $0.18 million. Therefore, the value of the all-equity firm is $0.18 million / 0.15 = $1.2 million.
b) If the firm decides to borrow $1 million debt, the new value of the firm would be the sum of the value of the equity and the value of the debt. The value of the equity is still $1.2 million (as calculated in part a), and the value of the debt would be $1 million, since that is the amount borrowed. Therefore, the total value of the firm would be $1.2 million + $1 million = $2.2 million.
c) To calculate the Weighted Average Cost of Capital (WACC) for the levered firm, we need to weigh the cost of equity and the cost of debt by their respective proportions in the capital structure. The weight of equity is calculated as the market value of equity divided by the total market value of the firm, and the weight of debt is calculated as the market value of debt divided by the total market value of the firm. Since the firm is all-equity financed in the first case, the weight of equity is 100% and the weight of debt is 0%. Therefore, the WACC for the all-equity firm is the same as the cost of equity, which is 15%. If the firm goes ahead and borrows $1 million debt, the weight of equity would be $1.2 million / $2.2 million = 54.55% and the weight of debt would be $1 million / $2.2 million = 45.45%. The WACC for the levered firm can then be calculated as: WACC = (Weight of Equity * Cost of Equity) + (Weight of Debt * Cost of Debt) = (0.5455 * 0.15) + (0.4545 * 0.08) = 0.1302 + 0.0364 = 0.1666 or 16.66%.