What is the formula for calculating the after-tax cost of debt, and how does it reflect the tax deductibility of interest?

The formula for calculating the after-tax cost of debt is rd(1 - T), where rd is the before-tax cost of debt and T is the firm's marginal tax rate. This formula reflects the tax deductibility of interest because it reduces the effective cost of debt by accounting for the tax savings that result from interest payments being tax-deductible.

The after-tax cost of debt is calculated by multiplying the before-tax cost of debt (rd) by (1 - T), where T represents the marginal tax rate. This adjustment is necessary because interest expenses on debt are tax-deductible, which effectively lowers the cost of borrowing for the firm. For example, if a firm has a before-tax cost of debt of 10% and a tax rate of 40%, the after-tax cost of debt would be 10% × (1 - 0.4) = 6%. This lower after-tax cost is used in the calculation of the weighted average cost of capital (WACC) to reflect the actual cost of financing after accounting for tax benefits.