The aftertax cost of debt is the cost of debt after accounting for the tax savings due to the tax-deductibility of interest payments.
The annual coupon payment is calculated as follows:
Coupon payment = Coupon rate x Face value = 7% x $1,000 = $70
Since interest is paid semi-annually, the semi-annual coupon payment is:
Semi-annual coupon payment = $70 / 2 = $35
The bond matures in 20 years, so the total number of semi-annual periods is 20 years * 2 = 40.
The present value of the bond is $875, which is the price at which it was sold.
Using the present value formula and solving for the yield to maturity, we get:
$875 = $35 / (1 + r/2)^1 + $35 / (1 + r/2)^2 + ... + $35 / (1 + r/2)^40
where r is the semi-annual yield to maturity.
Using a financial calculator or spreadsheet, we can solve for r = 3.99%.
The before-tax cost of debt is 2 x 3.99% = 7.98%.
The tax rate is 35%, so the after-tax cost of debt is:
After-tax cost of debt = Before-tax cost of debt x (1 - Tax rate) = 7.98% x (1 - 0.35) = 5.19%.
Therefore, the aftertax cost of debt is 5.19%.