Final answer:
Metra uses 30% debt and 70% equity to calculate its WACC. The cost of debt after tax is 5.25%, the cost of equity is 10.2%, and the resulting WACC is 8.61%.
Step-by-step explanation:
The weights of debt and equity used to calculate the Weighted Average Cost of Capital (WACC) are found by dividing the market value of each by the total market value of the firm's capital. Metra's debt is valued at $150 million, and the market value of equity is 14 million shares times $25 per share, or $350 million. Therefore, the weights are 30% for debt ($150 million / $500 million) and 70% for equity ($350 million / $500 million).
Metra's cost of debt before taxes is given as 7%. To find the after-tax cost of debt, we use the formula: after-tax cost of debt = yield to maturity × (1 - tax rate). Plugging in the numbers: 7% × (1 - 25%) = 5.25%.
The cost of common equity can be calculated using the Capital Asset Pricing Model (CAPM), which takes into account the risk-free rate, the beta of the stock, and the expected return on the market. The formula is: cost of equity = risk-free rate + (beta × (market return - risk-free rate)). So, Metra's cost of equity is 3% + (1.2 × (9% - 3%)) = 10.2%.
Finally, Metra's WACC can be determined using the formula: WACC = (weight of equity × cost of equity) + (weight of debt × cost of debt × (1 - tax rate)). After performing the calculations with the given weights and costs, Metra's WACC comes out to (70% × 10.2%) + (30% × 7% × (1 - 25%)) = 8.61%.