Answer:
To calculate the after-tax cost of debt, we need to first calculate the before-tax cost of debt, which is the yield to maturity (YTM) of the bond. We can use the bond pricing formula to find the YTM:
Bond Price = (Coupon Payment / YTM) x (1 - 1 / (1 + YTM)^n) + Face Value / (1 + YTM)^n
Where:
- Coupon Payment is the annual coupon payment
- YTM is the yield to maturity
- n is the number of years to maturity
We are given that the bond has a face value of $1,000, a coupon rate of 6%, and sells for $930. The annual coupon payment is:
Coupon Payment = Coupon Rate x Face Value = 0.06 x $1,000 = $60
The number of years to maturity is 22.
Substituting these values into the bond pricing formula, we get:
$930 = ($60 / YTM) x (1 - 1 / (1 + YTM)^22) + $1,000 / (1 + YTM)^22
We can use a financial calculator or spreadsheet software to solve for YTM. Doing so, we get YTM = 6.91%.
The before-tax cost of debt is the YTM of the bond, which is 6.91%.
To find the after-tax cost of debt, we need to adjust the before-tax cost of debt for the tax savings resulting from the tax-deductibility of interest payments. The after-tax cost of debt is given by the formula:
After-tax Cost of Debt = Before-tax Cost of Debt x (1 - Tax Rate)
where the tax rate is given as 34%.
Substituting the values, we get:
After-tax Cost of Debt = 6.91% x (1 - 0.34) = 4.56%
Therefore, the after-tax cost of debt is 4.56%.