# After-Tax Cost of Debt

After-tax cost of debt is the net cost of debt determined by adjusting the gross cost of debt for its tax benefits. It equals pre-tax cost of debt multiplied by (1 – tax rate). It is the cost of debt that is included in calculation of weighted average cost of capital (WACC).

Tax laws in many countries allow deduction on account of interest expense. The effect of this deduction is a reduction in taxable income and resulting reduction in income tax. The reduction in income tax due to interest expense is called interest tax shield. Due to this tax benefit of interest, effective cost of debt is lower than the gross cost of debt.

## Formula

After-tax cost of debt can be determined using the following formula:

After-Tax Cost of Debt
= Pre-Tax Cost of Debt × (1 – Tax Rate)

The gross or pre-tax cost of debt equals yield to maturity of the debt. The applicable tax rate is the marginal tax rate. When the debt is not marketable, pre-tax cost of debt can be determined with comparison with yield on other debts with same credit quality.

## Example

iQ systems has earnings before interest and taxes of \$200 million. It has interest-bearing debt of \$50 million carrying 8% interest rate. The company's marginal tax rate is 35%. Find the after-tax cost of debt in dollar and in percentage.

Cost of debt (i.e. interest expense) is \$4 million [= \$50 million × 8%].

Earnings before taxes
= \$200 million – \$4 million
= \$196 million

Tax expense
= \$196 million × 35%
= \$68.6 million

Net income
= \$196 million × (1 – 35%)
= \$196 million – \$68.6 million
= \$127.4 million

If there were no debt, there would be no interest expense, and tax expense would be \$70 million [=\$200 million × 35%]

Existence of debt has reduced tax expense by \$1.4 million [= \$70 million – \$68.6 million] and this is the interest tax shield.

The true cost of debt i.e. the after-tax cost of debt is as follows

After-tax cost of debt
= total cost of debt – interest tax shield
= \$4 million – \$1.4 million
= \$2.6 million

In percentage terms, the after-tax cost of debt = 8% × (1 – 35%) = 5.2%. This precisely equals the ratio of after-tax interest expense in dollars to the principal balance of debt (i.e. \$2.6 million/\$50 million = 5.2%).