If the pre-tax cost of debt is 6% and the tax rate is 30%, what is the after-tax cost of debt?

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Multiple Choice

If the pre-tax cost of debt is 6% and the tax rate is 30%, what is the after-tax cost of debt?

Explanation:
The key idea is that the after-tax cost of debt reflects the tax savings from the interest deduction. Since interest reduces taxable income, the effective cost to the firm is the pretax cost times (1 minus the tax rate). So with a pretax cost of 6% and a 30% tax rate, the after-tax cost is 6% × (1 − 0.30) = 6% × 0.70 = 4.2%. The other numbers come from misapplying the tax effect (for example, using the tax rate itself rather than its complement).

The key idea is that the after-tax cost of debt reflects the tax savings from the interest deduction. Since interest reduces taxable income, the effective cost to the firm is the pretax cost times (1 minus the tax rate). So with a pretax cost of 6% and a 30% tax rate, the after-tax cost is 6% × (1 − 0.30) = 6% × 0.70 = 4.2%. The other numbers come from misapplying the tax effect (for example, using the tax rate itself rather than its complement).

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