Final answer:
The after-tax component cost of debt is calculated by first determining the yield to maturity (YTM) as the pre-tax cost of debt, then adjusting it by the tax rate to reflect the tax deductibility of interest expenses. This cost of debt is then used in computing the WACC.
Step-by-step explanation:
The student's question is about calculating the after-tax component cost of debt for a bond to be used in the firm's weighted average cost of capital (WACC). To calculate this, we need to consider the bond's yield to maturity (YTM) as the pre-tax cost of debt and then adjust it for taxes. Since the bond has a semiannual coupon, we have to double the number of periods and halve the coupon rate for the calculations.
Firstly, we calculate the YTM, which is essentially the internal rate of return of the bond. We do this by finding the rate at which the present values of all future cash flows (semiannual coupon payments and the par value at maturity) equal the current price of the bond, $586.13.
Once we have the YTM as the nominal pre-tax cost of debt, we calculate the after-tax cost of debt by multiplying the pre-tax cost of debt by (1 - tax rate), with the tax rate being 30%. This gives us the firm's after-tax component cost of debt, which is the figure adjusted for the benefit of being able to deduct interest expenses from taxable income.
Using financial calculators or spreadsheet software with built-in functions can assist in calculating the YTM more efficiently. However, the precise calculation requires iterative methods or financial calculators, and it involves setting up the present value equation of the bond's cash flows and solving for the discount rate that sets the present value equal to the bond's current price.