Final answer:
The net bond liability balance for Auerbach Incorporated after the first interest payment on March 31, 2025, would be $257,030,000. This figure is determined by adding the amortized discount to the initial bond liability, reflecting the difference between the coupon rate payment and the effective interest rate expense.
Step-by-step explanation:
To calculate the net bond liability balance of Auerbach Incorporated after its first interest payment on March 31, 2025, we need to consider both the interest payment made and the accruing interest expense at the market rate of 6%. The interest payment is based on the bond's coupon rate, which in this case is 4% of the $300 million face value, paid semiannually. Therefore, the first interest payment is: $300,000,000 × 4% × ½ = $6,000,000.
However, the interest expense that accrues is based on the effective market rate of 6% on the carrying value of the bond. Since the bonds were issued at $255,369,000, the first interest expense would calculate as: $255,369,000 × 6% × ½ = $7,661,070. This interest expense is higher than the actual payment, indicating a discount on the bonds that needs to be amortized over time. The difference of $1,661,070 ($7,661,070 - $6,000,000) is added to the bond liability.
Thus, the adjusted bond liability after the first interest payment will be: $255,369,000 (initial bond liability) + $1,661,070 (discount amortization) = $257,030,070, which rounded to the nearest thousand is $257,030,000. This aligns with the correct option provided in the question.