the before-tax cost of debt will be 7.74%
the after-tax component cost of debt will be 6.12%
For businesses, governments, and many other types of organizations, bonds are a source of funding. Some bonds, known as coupon bonds, pay investors periodic coupon payments at the specified coupon rate in addition to being redeemable at face value at the time of maturity. The difference between the before-tax and after-tax cost of debt results from the fact that the issuing company's tax deduction for the coupon payments.
The interest rate used to determine the cost of a bond payment over the bond's lifetime is called the "cost of debt." This debt service charge is frequently contrasted with the risk-free rate of return.
Two measures can be taken to remedy this problem. The first step is to solve the cost of debt for the before-tax rate. To ascertain this, we must use the formula for calculating an annuity's future value:
FV of Annuity = PV + PMT (1+r)^n - (1 / r) ,
where PV = Present Value,
PMT = Annuity Payment,
r = rate, or cost of debt, and
n = number of periods
We will want to solve for r:
1000 = -1110 + 90 (1+r)^15 - 1 / r
2110 = 90 (1+r)^15 - 1 / r
23.4444 = (1+r)^15 - 1 / r
r = 7.74%
So the cost of debt before taxes is 7.74 percent.
After taxes, the debt's cost is calculated as follows:
Debt service charge: (1 - 0.21 = 7.74%
0.79 = 6.12%
∴ r = 6.12%
Therefore, the after-tax cost of debt is 6.12%
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