Question

legacy issues $630,000 of 9.0%, four - year bonds dated january 1, 2021, that pay interest semiannually on june 30 and december 31. they are issued at $571,310 when the market rate is 12%.
required:

1. prepare the january 1 journal entry to record the bonds issuance.
2. complete the below table to calculate the total bond interest expense to be recognized over the bonds life.
3. prepare an effective interest amortization table for the bonds first two years.
4. prepare the journal entries to record the first two interest payments.

complete this question by entering your answers in the tabs below.
prepare an effective interest amortization table for the bonds first two years.
note: round your intermediate and final answers to the nearest whole dollar.
semiannual interest period - end cash interest paid bond interest expense discount amortization unamortized discount carrying value
01/01/2021 $571,310
06/30/2021
12/31/2021
06/30/2022
12/31/2022

Explanation:

Step1: Calculate cash interest paid

The cash interest paid is calculated as \(Face\ value\times Stated\ rate\times Time\).
The face value of the bonds is \(F = \$630,000\), the stated annual rate \(r=9\%\), and the time \(t = 0.5\) (since interest is paid semiannually).

$$Cash\ interest\ paid=\$630,000\times9\%\times0.5=\$28,350$$

This amount is the same for each semiannual period.

Step2: Calculate bond interest expense (using effective - interest method)

The bond interest expense is calculated as \(Carrying\ value\times Market\ rate\times Time\).

• For the period 06/30/2021:

The carrying value on 01/01/2021 is \(CV_1=\$571,310\), the market annual rate \(i = 12\%\), and \(t=0.5\)

$$Bond\ interest\ expense_1=\$571,310\times12\%\times0.5=\$34,279$$

• For the period 12/31/2021:

The carrying value after 06/30/2021 is \(CV_2=\$571,310+(34,279 - 28,350)=\$577,239\)

$$Bond\ interest\ expense_2=\$577,239\times12\%\times0.5=\$34,634$$

• For the period 06/30/2022:

The carrying value after 12/31/2021 is \(CV_3=\$577,239+(34,634 - 28,350)=\$583,523\)

$$Bond\ interest\ expense_3=\$583,523\times12\%\times0.5=\$35,011$$

• For the period 12/31/2022:

The carrying value after 06/30/2022 is \(CV_4=\$583,523+(35,011 - 28,350)=\$589,184\)

$$Bond\ interest\ expense_4=\$589,184\times12\%\times0.5=\$35,351$$

Step3: Calculate discount amortization

Discount amortization is \(Bond\ interest\ expense - Cash\ interest\ paid\)

• For 06/30/2021: \(34,279 - 28,350=\$5,929\)
• For 12/31/2021: \(34,634 - 28,350=\$6,284\)
• For 06/30/2022: \(35,011 - 28,350=\$6,661\)
• For 12/31/2022: \(35,351 - 28,350=\$7,001\)

Step4: Calculate unamortized discount

The initial unamortized discount on 01/01/2021 is \(630,000 - 571,310=\$58,690\)

• After 06/30/2021: \(58,690-5,929 = \$52,761\)
• After 12/31/2021: \(52,761-6,284=\$46,477\)
• After 06/30/2022: \(46,477-6,661=\$39,816\)
• After 12/31/2022: \(39,816-7,001=\$32,815\)

Step5: Calculate carrying value

The carrying value is \(Face\ value - Unamortized\ discount\)

• 06/30/2021: \(630,000 - 52,761=\$577,239\)
• 12/31/2021: \(630,000 - 46,477=\$583,523\)
• 06/30/2022: \(630,000 - 39,816=\$589,184\)
• 12/31/2022: \(630,000 - 32,815=\$597,185\) (rounded to the nearest whole dollar)

Answer:

Semiannual Interest Period - End	Cash Interest Paid	Bond Interest Expense	Discount Amortization	Unamortized Discount	Carrying Value
06/30/2021	\(28,350\)	\(34,279\)	\(5,929\)	\(52,761\)	\(577,239\)
12/31/2021	\(28,350\)	\(34,634\)	\(6,284\)	\(46,477\)	\(583,523\)
06/30/2022	\(28,350\)	\(35,011\)	\(6,661\)	\(39,816\)	\(589,184\)
12/31/2022	\(28,350\)	\(35,351\)	\(7,001\)	\(32,815\)	\(597,185\)