Question

pr 11-2a bond premium, entries for bonds payable transactions continued
instructions

1. journalize the entry to record the amount of cash proceeds from the issuance of the bonds on july 1, 20y1.
2. journalize the entries to record the following:

a. the first semiannual interest payment on december 31, 20y1, and the amortization of the bond premium, using the straight-line method. round to the nearest dollar.
b. the interest payment on june 30, 20y2, and the amortization of the bond premium, using the straight-line method. round to the nearest dollar.

1. determine the total interest expense for 20y1.

issue date: jul 1, 20y1
face: $30,000,000
term: 10 years
contract rate: 10% ( % semiannual)
market rate: 9% ( % semiannual)
proceeds: $
premium: $
semiannual int: $
amortization of premium =

carrying value of bonds at december 31, 20y1:
bonds payable $30,000,000
add: premium on bp *
book value of bonds $

*remaining discount:
=

entry at issue date
jul 1

entry at 1st interest payment
dec 31

entry at 2nd interest payment
jun 30

Answer:

To solve this bond premium problem, we'll follow these steps:

Step 1: Calculate the semiannual contract rate and market rate

• Contract rate (annual): \( 10\% \), so semiannual contract rate: \( \frac{10\%}{2} = 5\% \)
• Market rate (annual): \( 9\% \), so semiannual market rate: \( \frac{9\%}{2} = 4.5\% \)

Step 2: Calculate the semiannual interest payment (based on face value and contract rate)

Face value of bonds: \( \$30,000,000 \)
Semiannual interest payment (\( I \)): \( 30,000,000 \times 5\% = 30,000,000 \times 0.05 = \$1,500,000 \)

Step 3: Calculate the present value of the bond (proceeds)

The bond has a 10 - year term, so there are \( 10\times2 = 20 \) semiannual periods.

• Present value of the face value (lump - sum) at the market rate: \( PV_{lump - sum}=30,000,000\times(1 + 0.045)^{-20}\)

Using the formula for present value of a lump - sum \( PV = FV\times(1 + r)^{-n}\), where \( FV = 30,000,000\), \( r=0.045\), \( n = 20\)
\( (1 + 0.045)^{-20}\approx0.414642869 \)
\( PV_{lump - sum}=30,000,000\times0.414642869\approx\$12,439,286.07 \)

• Present value of the semiannual interest payments (annuity) at the market rate:

The semiannual interest payment \( A=\$1,500,000 \), the number of periods \( n = 20\), and the interest rate per period \( r = 0.045\)
Using the present value of an annuity formula \( PV_{annuity}=A\times\frac{1-(1 + r)^{-n}}{r}\)
\( \frac{1-(1 + 0.045)^{-20}}{0.045}=\frac{1 - 0.414642869}{0.045}=\frac{0.585357131}{0.045}\approx13.00793624 \)
\( PV_{annuity}=1,500,000\times13.00793624\approx\$19,511,904.36 \)

• Proceeds from bond issuance (present value of bond) \( = PV_{lump - sum}+PV_{annuity}=12,439,286.07 + 19,511,904.36=\$31,951,190.43\approx\$31,951,190 \)

Step 4: Calculate the bond premium

Bond premium \( = \) Proceeds - Face value \( = 31,951,190-30,000,000=\$1,951,190 \)

Step 5: Calculate the amortization of premium per period (straight - line method)

Number of periods \( n = 20\)
Amortization of premium per period \(=\frac{1,951,190}{20}=\$97,559.5\approx\$97,560 \) (rounded to the nearest dollar)

1. Journal entry for bond issuance on July 1, 20Y1

• Debit Cash for the proceeds: \( \$31,951,190 \)
• Credit Bonds Payable for the face value: \( \$30,000,000 \)
• Credit Premium on Bonds Payable for the premium: \( \$1,951,190 \)

Journal Entry:

Date	Account Titles and Explanation	Debit (\$)	Credit (\$)
	Bonds Payable		30,000,000
	Premium on Bonds Payable		1,951,190
	(To record issuance of bonds at a premium)

2a. Journal entry for first semiannual interest payment and premium amortization on December 31, 20Y1

• Semiannual interest payment: \( \$1,500,000 \) (credit to Cash)
• Premium amortization: \( \$97,560 \) (debit to Premium on Bonds Payable)
• Interest expense \(=\) Interest payment - Premium amortization \( = 1,500,000-97,560=\$1,402,440 \) (debit to Interest Expense)

Journal Entry:

Date	Account Titles and Explanation	Debit (\$)	Credit (\$)
	Premium on Bonds Payable	97,560
	Cash		1,500,000
	(To record semiannual interest payment and premium amortization)

2b. Journal entry for second semiannual interest payment and premium amortization on June 30, 20Y2

• The interest payment, premium amortization, and interest expense amounts are the same as in the first semiannual period (straight - line method)
• Interest payment: \( \$1,500,000 \) (credit to Cash)
• Premium amortization: \( \$97,560 \) (debit to Premium on Bonds Payable)
• Interest expense \(=\$1,402,440 \) (debit to Interest Expense)

Journal Entry:

Date	Account Titles and Explanation	Debit (\$)	Credit (\$)
	Premium on Bonds Payable	97,560
	Cash		1,500,000
	(To record semiannual interest payment and premium amortization)

3. Total interest expense for 20Y1

Since the first interest payment is on December 31, 20Y1, the interest expense for 20Y1 is the interest expense for the first semiannual period, which is \( \$1,402,440 \)

Carrying Value of Bonds at December 31, 20Y1

• Bonds Payable: \( \$30,000,000 \)
• Premium on Bonds Payable: Initial premium - Amortized premium \( = 1,951,190-97,560=\$1,853,630 \)
• Book Value of Bonds \( = 30,000,000 + 1,853,630=\$31,853,630 \)

Final Answers (Key Figures)

• Proceeds from bond issuance: \( \boldsymbol{\$31,951,190} \)
• Bond premium: \( \boldsymbol{\$1,951,190} \)
• Amortization of premium per period: \( \boldsymbol{\$97,560} \)
• Interest expense per semiannual period: \( \boldsymbol{\$1,402,440} \)
• Total interest expense for 20Y1: \( \boldsymbol{\$1,402,440} \)
• Carrying value of bonds at Dec 31, 20Y1: \( \boldsymbol{\$31,853,630} \)