Why is the after-tax cost of debt the relevant cost of debt?

Explanation:

The after tax cost of debt is the tax-adjusted interest rate on a debt that a company borrows. Unlike dividends, debt has a tax shield which lowers the percentage rate paid on the debt.  When a levered firm wants to determine the appropriate discount rate for evaluating projects with similar risk as the firm, it would determine the weighted average cost of capital (WACC). In its calculation, the relevant cost of debt would be the after-tax cost of debt and not the pretax cost of debt.

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