Final answer:
The carrying value of Sharpsburg, Inc.'s bonds after the first interest payment on June 30, 2016, is $355,452. This includes the first interest payment and the amortization of the discount considering the market interest rate was higher than the bond's coupon rate.
Step-by-step explanation:
The question is essentially asking for the carrying value of a bond after the first interest payment. To answer this, we must update the carrying value of the bond by considering the first interest payment and the amortization of the discount. On January 1, 2016, Sharpsburg, Inc. issued $400,000, 10-year, 10% bonds for $354,200. The bond was issued at a discount because the market interest rate of 12% was higher than the coupon rate of 10%. The interest payment on June 30, 2016, would be $400,000 (the face value) × 10% (the coupon rate) × 1/2 (since interest is paid semi-annually), which totals $20,000.
The carrying value of the bond immediately after the first interest payment can be computed by adding the semiannual interest expense based on the market rate to the issue price and then subtracting the semiannual cash interest payment. The interest expense is calculated using the market rate of 12% per annum on the issue price: $354,200 × 12% × 1/2 = $21,252. Therefore, the carrying value after the first payment is $354,200 (issue price) plus $21,252 (interest expense) minus $20,000 (interest payment paid), which equals $355,452. This means the carrying value after the first payment is $355,452, aligning with option (a).