Final answer:
Auerbach Incorporated's net bond liability as of December 31, 2024, is $448,631,000 after accounting for interest expense using the effective interest rate. This figure is obtained by adding the three-month prorated interest expense to the initial carrying value of the bonds, rounded to the nearest thousand.
Step-by-step explanation:
To calculate Auerbach Incorporated's net bond liability balance on December 31, 2024, after issuing bonds at a discount, we need to consider the effective interest method for amortizing the bond discount. Since the bonds were issued for $437,689,200 but have a face value of $500 million, there is a discount of $62,310,800. No interest payment occurs in 2024 since the bonds were issued on October 1, 2024, and the first interest payment is on March 31, 2025. However, we need to account for the interest expense incurred from the issue date to the end of the year based on the effective interest rate of 10%.
The interest expense for the three months from October 1, 2024, to December 31, 2024, would be calculated as the carrying amount of the bonds ($437,689,200) multiplied by the effective interest rate (10% per annum) prorated for the three-month period. The computation would be:
Interest Expense = $437,689,200 × 10% × (3/12) = $10,942,230
This interest expense would be added to the carrying value of the bonds to find the net bond liability on December 31, 2024. Therefore, we have:
Net Bond Liability = Carrying Value of Bonds + Interest Expense = $437,689,200 + $10,942,230 = $448,631,430
After rounding the net bond liability balance to the nearest thousand, we get $448,631,000 as the net bond liability balance on December 31, 2024, which corresponds to option (d).