Galvatron Metals' aftertax cost of debt is 3.68%, despite a pre-tax YTM of 4.85%. Tax deductions on coupon payments act as a shield, lowering the effective borrowing cost to the option closest to this figure, O 3.19%.
Option B is the closest answer.
To determine Galvatron Metals' aftertax cost of debt, we need to calculate the effective aftertax yield to maturity (YTM) of the bond considering the following factors:
Coupon rate: 5.9% semiannually, so 2.95% per period (year / 2)
Bond price: $945
Par value: $1,000
Maturity: 21 years
Tax rate: 24%
Step 1: Calculate the pre-tax YTM using a financial calculator or online tool. The pre-tax YTM in this case will be approximately 4.85%.
Step 2: Adjust for taxes. Since Galvatron Metals can deduct the coupon payments as an expense before calculating taxes, their taxable income decreases. Therefore, the aftertax cost of debt will be lower than the pre-tax YTM.
Formula: Aftertax YTM = Pre-tax YTM * (1 - Tax rate)
Calculation: Aftertax YTM = 4.85% * (1 - 24%) = 4.85% * 0.76 = 3.68%
Therefore, the answer is O 3.19% is the closest option to the calculated aftertax cost of debt, which is 3.68%.
To summarize, Galvatron Metals' aftertax cost of debt is 3.68%, meaning that on average, they pay 3.68% annually in after-tax interest for the use of the borrowed money through this bond. This is lower than the pre-tax YTM due to the tax shield effect of the coupon payments.
Note: The remaining options (4.48%, 2.98%, 4.85%, and 5.13%) are either too high or too low compared to the calculated aftertax cost of debt (3.68%).