The after tax cost of debt is the interest a company paid minus the tax refund generated by deducting the interest on the company tax return.
Let’s say a company in the 33% tax bracket paid $18,000 of interest on a bank loan. The $18,000 is a tax deduction so the IRS would send the company a refund of $6000 (18,000 x .333). The $18,000 they paid minus the $6000 they received would be the true cost of the debt, $12,000. This is the after tax cost of debt.