Final answer:
The after-tax cost of debt is relevant because it represents the actual, lowered expense a firm incurs for its debt due to the deductibility of interest expenses, making it the lowest possible cost.
Step-by-step explanation:
The after-tax cost of debt is the relevant cost of debt for a firm because it represents the actual expense the firm incurs for using debt as a source of financing, after considering the tax shield provided by interest expense deductions. Answer to the question is c. lowest.
This is the cost that the firm effectively pays, as interest payments on debt are tax-deductible, which reduces the firm's taxable income and, subsequently, its tax liabilities. As a result, the after-tax cost of debt is lower than the nominal rate of interest paid on the debt.