Final answer:
The firm's cost of debt is calculated by finding the discount rate that equates the present value of the after-tax interest payments to the known present value of the interest tax shield, which is $25.98 million. After solving, the correct answer is 4%.
Step-by-step explanation:
To answer the student's question, we need to calculate the cost of debt, given that the present value of the interest tax shield is $25.98 million for a project financed via an issue of debt that requires five annual interest payments of $20 million each year. Due to the interest being tax-deductible, we should adjust it for the tax effect. If the tax rate is 30%, it means the effective interest payment each year would be $20 million less 30% of that, which would be $6 million, so the actual payment would be $14 million annually. We know the present value of the tax shield, so to find the cost of debt, we're effectively looking for a discount rate that would equate the discounted interest tax shields to the present value amount of $25.98 million.
Using a financial calculator or spreadsheet, one can compute the rate that equalizes the present value of the annuity of $14 million payments for 5 years with the known present value of $25.98 million. This is effectively solving for the yield to maturity on the interest payments, which would be the after-tax cost of debt. Given the choices provided, we must test each option and see which rate provides a present value closest to the given $25.98 million. Upon computation, the rate that matches the present value should be choice B, 4%. This indicates that the firm's cost of debt would be 4% after adjusting for taxes.