Final answer:
The weighted average cost of capital (WACC) for the firm is approximately 13.65%, derived by multiplying the cost of each capital component by its respective weight, considering the tax shield benefits on debt.
Step-by-step explanation:
The question relates to the computation of the weighted average cost of capital (WACC), which represents the average rate of return a company is expected to pay to finance its assets. The WACC is a crucial component in financial decision-making and investments, and it includes the different costs associated with equity and debt.
To calculate the WACC, you multiply the cost of each capital component by its proportional weight and then summing these results. The formula for WACC is:
WACC = (E/V) * Re + (D/V) * Rd * (1-Tc)
- E is the market value of the equity.
- D is the market value of the debt.
- V is E + D, the total market value of the firm's financing (Equity and Debt).
- Re is the cost of equity.
- Rd is the cost of debt.
- Tc is the corporate tax rate.
In this question, a firm has $10 in equity and $9 in debt, the cost of equity (Re) is 0.2, and the pretax cost of debt (Rd) is 0.07. The firm's marginal tax rate (Tc) is 0.37.
Using these values:
- V = E + D = $10 + $9 = $19
- WACC = ($10/$19) * 0.2 + ($9/$19) * 0.07 * (1-0.37).
Therefore, the firm's WACC computation will be as follows:
WACC = (10/19) * 0.2 + (9/19) * 0.07 * (1-0.37) = 0.1052631579 + 0.0312163743 = 0.1364795322 or approximately 13.65%.
Thus, the weighted average cost of capital for the firm is roughly 13.65%.