# After-Tax Cost of Debt

After-tax cost of debt is the cost of debt as adjusted for the effect of favorable treatment of interest expense for income tax purpose. Percentage after tax cost of debt equals pre-tax cost of debt multiplied by (1 – tax rate).

Majority of tax regimes 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. The true cost of debt accounts for this benefit of debt.

## Formula

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

## 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.

__Solution__

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 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 = 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%).

Written by Obaidullah Jan