Final answer:
To find Barton Industries' after-tax cost of debt, calculate the bond's yield to maturity (YTM) based on its current price and coupon rate, then adjust this rate for the firm's marginal tax rate. The final cost of debt represents the company's borrowing cost after accounting for the tax deductibility of interest expenses.
Step-by-step explanation:
The quantitative problem involves finding Barton Industries' after-tax cost of debt for a 25-year, noncallable, semiannual bond with a $1,000 face value and a 10% semiannual coupon ($50 payment every 6 months). Since the bonds are currently selling for $818.87 and the firm's marginal tax rate is 25%, we can calculate the before-tax cost of debt (YTM) and then adjust for taxes to find the after-tax cost of debt.
To calculate the yield to maturity (YTM), we would need to solve the present value of an annuity formula to find the semiannual discount rate that equates to the bond's price of $818.87. Afterwards, the semiannual rate is annualized by multiplying by 2 (as there are two periods per year). The resulting annual pre-tax YTM is then multiplied by (1 - tax rate) to determine the after-tax cost of debt. Using financial calculators or software to solve for YTM can streamline this process since it requires iterative calculation. However, for illustrative purposes, suppose the pre-tax semiannual YTM is found to be 6%, resulting in an annual pre-tax rate of 12%. Multiplying by (1 - 0.25) for the 25% tax rate, the after-tax cost of debt for Barton Industries is 9%.