# 3.3 The After-Tax Cost of Debt Capital

Interest on Debt is legally required to be paid first – before any dividends are paid on stock. It is also legally required to be paid. If the company does not pay its interest in full and on time, it has “defaulted” in its loan obligations; it has violated a legal contract called a “bond indenture.”

Moreover, we must consider the fact that bond interest, i.e., “interest expense,” is tax-deductible. Let’s see how this tax-deductibility affects taxes and company earnings by way of the following example.

Given:  In each of the following two scenarios assume that:

EBIT = \$500,000

T = .40

Scenario I:        No debt, no interest expense

Scenario II:       Debt of \$1,000,000 (Assume a par bond where i = YTM)

i = .10 (i = coupon rate of 10% per annum)

 Partial Income Statement Scenario 1 Scenario 2 Differences Operating Earnings: Earnings Before Interest and Taxes EBIT \$500,000 \$500,000 0 Interest Expense I 000 (100,000) 100,000 Earnings Before Taxes (after interest) EBT \$500,00 \$400,000 (100,000) Tax Expense T (200,00) (160,000) 40,000 Net Income NI \$300,000 \$240,000 (\$60,000) ΔNI-1 & NI-2= \$60,000

Because of the interest expense in “Scenario 2,” the company earned \$60,000 less, on an after-tax basis, than it would have under the no debt scenario (“Scenario 1”). That is a net cost of \$60,000 versus \$1,000,000 in debt, or 6%. This is equivalent to what we would have derived had we used the formula:

K d = i (1 – T) = .10 (1 – .40) = .06

Taxes paid are reduced by \$40,000 due to the lower taxable income (EBT). The lower EBT results in a reduction in net income of just \$60,000 rather than the full cost of \$100,000. (i.e., \$100,000 in interest paid less tax savings of \$40,000 = net income reduction of \$60,000).

Hence, .06 is the after-tax cost of (debt) capital on \$1,000,000 of debt in this case, or \$60,000. In practice, we may alternatively use the after-tax cost of debt as herein calculated, or some YTM-related, after-tax percent. Tax deductibility mitigates the cost of debt!

Note:

We have assumed in this example a “Par Bond,” i.e., one that was sold by the corporation for 100% of its Face Value. In the case where the bond was issued above or below Par, we must use the bond’s “Yield-to-Maturity” in order to calculate the expense.