Final answer:
The before-tax cost of debt is calculated using the WACC formula, with the answer being approximately 8.16%, which is closest to option b (8.5%). This value is derived after several steps, adjusting for the firm's equity weight, cost of equity, and their corporate tax rate.
Step-by-step explanation:
The question involves calculating the firm's before-tax cost of debt using the given weight of equity, cost of equity, tax rate, and Weighted Average Cost of Capital (WACC).
The WACC formula is given by WACC = E/V * Re + D/V * Rd * (1-Tc), where E is the market value of the equity, V is the total market value of the firm's financing (Equity + Debt), Re is the cost of equity, D is the market value of the firm's debt, Rd is the cost of debt, and Tc is the corporate tax rate.
Step-by-step explanation:
- Let's first find out the weight of debt in the firm's capital structure. Since the weight of equity is 75%, the weight of debt will be 1 - 0.75 = 0.25 or 25%.
- Now, we can rearrange the formula to solve for Rd (before-tax cost of debt).
- Substitute the known values into the formula; 0.13 (WACC) = 0.75 (Equity weight) * 0.16 (Cost of equity) + 0.25 (Debt weight) * Rd * (1 - 0.30 (Tax rate)).
- We solve for Rd: 0.13 = 0.12 + 0.25 Rd * 0.7.
- Subtract 0.12 from both sides: Rd * 0.175 = 0.01.
- Finally, divide both sides by 0.175: Rd = 0.01 / 0.175.
- The result is Rd = 0.0571 or 5.71% as the after-tax cost of debt.
- To find the before-tax cost of debt, divide the after-tax cost by (1 - tax rate): Rd / (1 - 0.30).
- So, the before-tax cost of debt is 0.0571 / (1 - 0.30), which is approx 0.0816 or 8.16%.
This value is not an exact match to any of the options provided, which might indicate a rounding or input error in the question. However, the closest answer to our calculation is 8.5% (option b).