Final answer:
The weighted average cost of capital (WACC) for the firm is calculated by determining the weights for each source of capital, adjusting the cost of debt for tax benefits, and summing the weighted costs of debt, preferred stock, and equity. The calculated WACC is 7.8346%, which can be rounded to 7.83%.
Step-by-step explanation:
To calculate the weighted average cost of capital (WACC), we need to consider the proportion of each source of capital (debt, preferred stock, and equity) and their respective costs, adjusting for the tax benefits of debt. Given that the firm has $10 million in debt at a 4% rate, $1 million in preferred stock at a 3% rate, and $26 million in equity at a 10% rate and a corporate tax rate of 33%, we can calculate each component's weight and cost.
First, we calculate the weights for each component:
- Debt: $10 million / ($10 million + $1 million + $26 million) = 0.270
- Preferred Stock: $1 million / ($10 million + $1 million + $26 million) = 0.027
- Equity: $26 million / ($10 million + $1 million + $26 million) = 0.703
Next, we calculate the after-tax cost of debt because interest on debt is tax-deductible:
After-tax cost of debt = Interest rate on debt * (1 - Corporate tax rate) = 4% * (1 - 33%) = 2.68%
Then we compute the WACC using the weights and costs:
WACC = (Weight of debt * After-tax cost of debt) + (Weight of preferred stock * Cost of preferred stock) + (Weight of equity * Cost of equity)
WACC = (0.270 * 2.68%) + (0.027 * 3%) + (0.703 * 10%)
WACC = 0.7236% + 0.081% + 7.03%
WACC = 7.8346% or approximately 7.83%