Why is the after-tax cost of debt lower than its before-tax cost according to the chapter?

The after-tax cost of debt is lower than its before-tax cost because interest payments on debt are tax deductible. This tax deductibility effectively reduces the overall cost of borrowing for the firm.

The after-tax cost of debt is calculated by taking the before-tax cost of debt and adjusting it for the tax savings that result from the deductibility of interest expenses. For example, if a firm has a before-tax cost of debt of 10% and a marginal tax rate of 40%, the after-tax cost of debt would be 10% multiplied by (1 - 0.4), resulting in an effective cost of 6%. This adjustment reflects the fact that the government effectively subsidizes part of the cost of debt, making it cheaper for firms to borrow.