QUESTION:

On January 1, 20X1, Company B issues a 5-year, 10% bond with a face value of $100,000. Interest is payable annually on December 31. What is the carrying amount of the bond liability on December 31, 20X2 if the market interest rate on similar bonds is now 12%?

ANSWER:

here are the calculations and journal entries for the carrying amount of the bond liability on December 31, 20X2:

To determine the carrying amount of the bond liability on December 31, 20X2, we first need to calculate the present value of the remaining cash flows using the market interest rate of 12%. We have three cash flows remaining - the annual interest payment of $10,000 for three years and the face value of $100,000 at maturity. Using the formula for the present value of an ordinary annuity and the present value of a lump sum, we get:

Present value of annuity of $10,000 for 3 years = $10,000 x ((1 - (1 / (1 + 0.12)^3)) / 0.12) = $25,852.49

Present value of lump sum of $100,000 in 3 years = $100,000 / (1 + 0.12)^3 = $71,107.68

The present value of the remaining cash flows is therefore $25,852.49 + $71,107.68 = $96,960.17. This is the present value of the bond on December 31, 20X2.

The carrying amount of the bond liability on December 31, 20X2 is calculated as follows:

• Carrying amount on January 1, 20X2: $100,000
• Add: Interest expense for the year ended December 31, 20X2: $90,909.09 x 0.12 = $10,909.09
• Carrying amount on December 31, 20X2: ($100,000 + $10,909.09) = $110,909.09
• Less: Present value of the remaining cash flows on December 31, 20X2: $96,960.17
• Carrying amount of the bond liability on December 31, 20X2: $110,909.09 - $96,960.17 = $94,548.92

Therefore, the carrying amount of the bond liability on December 31, 20X2 is $94,548.92.

To show the journal entries for the issuance of the bond and the interest payment on December 31, 20X2:

January 1, 20X1:

Debit Cash (asset) for $100,000

Credit Bonds payable (liability) for $100,000

To record the issuance of the bond.

December 31, 20X2:

Debit Interest expense (expense) for $10,909.09

Credit Cash (asset) for $10,000

Credit Discount on bonds payable (contra-liability) for $909.09