Chapter 14, Problem 7BP

1 (a)

To determine

Calculate the selling price of bonds where the market rate on the date of issuance is 8%.

Explanation of Solution

Selling price of bond:

Selling price of bond is the sum of present value of interest payments (annuity) and the principal amount (single sum). This is also known as issue price of bond.

Calculate the selling price of bonds:

Cash Flow	PV Factor (a)	Amount (b)	Present Value (a)×(b)
Par value	0.6139	$90,000	$55,251
Interest (annuity)	7.7217	(2) $5,400	$41,697
Price of bonds			$96,948
Bond premium			(3) $6,948

Table (1)

Therefore, the selling price of the bond is $96,948.

Note: Refer to Table B.1 from Appendix of textbook for Present value of $ 1 and refer to Table B.3 from Appendix of textbook for Present value of an annuity $ 1. . The discount rate is 5% and the periods are 10 (semi-annual).

Working notes:

Calculate the semi-annual face interest rate:

$\begin{array}{c}\text{Semiannual face interest rate }=\frac{\text{Face interest rate}}{\text{2}}\\ =\frac{12\%}{2}\\ =6\%\end{array}$ (1)

Calculate amount of interest payable.

$\begin{array}{c}\text{Interest payable }=\text{Face value of bonds }\times \text{ Semiannual}\text{face interest rate}\\ =\$90,000\times \frac{6(1)}{100}\\ =\$5,400\end{array}$ (2)

Calculate the value of bond premium:

$\begin{array}{c}\text{Bond}\text{premium}\text{=}\text{Selling}\text{price}\text{of}\text{bonds}-\text{par}\text{value}\text{of}\text{bonds}\\ \text{=}\text{\$96,948}-\text{\$90,000}\\ \text{=\$6,948}\end{array}$ (3)

1 (b)

To determine

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 8%.

Explanation of Solution

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 8%:

Date	Account Titles and Explanation	Debit ($)	Credit ($)
January 01	Cash	96,948
	Premium on bonds payable (3)		6,948
	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (4)

To record the sale of bonds on stated issue date:

• Cash is an asset and it is increased. Therefore cash is debited by $96,948.
• Premium on Bonds Payable is an adjunct liability account and it is increased. So, credit it by 6,948.
• Bonds payable is a liability and it is increased. Therefore credit bonds payable account by $90,000.

2 (a)

To determine

Calculate the selling price of bonds where the market rate on the date of issuance is 10%.

Explanation of Solution

Calculate the selling price of bonds:

Cash Flow	PV Factor (a)	Amount (b)	Present Value (a)×(b)
Par value	0.5584	$90,000	$50,256
Interest (annuity)	7.3601	(5) $5,400	$39,745
Price of bonds			$90,001

Table (2)

Therefore, the selling price of the bond is $90,001.

Note: Refer to Table B.1 from Appendix of textbook for Present value of $ 1 and refer to Table B.3 from Appendix of textbook for Present value of an annuity $ 1. The discount rate is 6% and the periods are 10 (semi-annual).

Working notes:

Calculate the semi-annual face interest rate:

$\begin{array}{c}\text{Semiannual face interest rate }=\frac{\text{Face interest rate}}{\text{2}}\\ =\frac{12\%}{2}\\ =6\%\end{array}$ (4)

Calculate amount of interest payable.

$\begin{array}{c}\text{Interest payable }=\text{Face value of bonds }\times \text{ Semiannual}\text{face interest rate}\\ =\$90,000\times \frac{6(4)}{100}\\ =\$5,400\end{array}$ (5)

2 (b)

To determine

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 10%.

Explanation of Solution

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 10%:

Date	Account Titles and Explanation	Debit ($)	Credit ($)
January 1	Cash	90,000
	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (5)

To record the sale of bonds on stated issue date:

• Cash is an asset and it is increased. Therefore cash is debited by $90,000.
• Bonds payable is a liability and it is increased. Therefore credit bonds payable account by $90,000.

3 (a)

To determine

Calculate the selling price of bonds where the market rate on the date of issuance is 12%.

Explanation of Solution

Calculate the selling price of bonds:

Cash Flow	PV Factor (a)	Amount (b)	Present Value (a)×(b)
Par value	0.5083	$90,000	$45,747
Interest (annuity)	7.0236	$5,400	$37,927
Price of bonds			$83,674
Bond discount			(8) $6,326

Table (3)

Therefore, the selling price of the bond is $83,674.

Note: Refer to Table B.1 from Appendix of textbook for Present value of $ 1 and refer to Table B.3 from Appendix of textbook for Present value of an annuity $ 1. . The discount rate is 7% and 10 periods (semi-annual).

Working notes:

Calculate the semi-annual face interest rate:

$\begin{array}{c}\text{Semiannual face interest rate }=\frac{\text{Face interest rate}}{\text{2}}\\ =\frac{12\%}{2}\\ =6\%\end{array}$ (6)

Calculate amount of interest payable.

$\begin{array}{c}\text{Interest payable }=\text{Face value of bonds }\times \text{ Semiannual}\text{face interest rate}\\ =\$90,000\times \frac{6(6)}{100}\\ =\$5,400\end{array}$ (7)

Calculate the value of bond premium:

$\begin{array}{c}\text{Bond}\text{discount}\text{=}\text{par}\text{value}\text{of}\text{bonds}-\text{Selling}\text{price}\text{of}\text{bonds}\\ \text{=}\text{\$90,000}-\text{\$83,674}\\ \text{=\$6,326}\end{array}$ (8)

(b) 3.

To determine

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 10%.

Explanation of Solution

Prepare journal entry to record issuance of bonds where the market rate at the date of issuance is 12%:

Date	Account Titles and Explanation	Debit ($)	Credit ($)
January 1	Cash	83,674
	Discount on bonds payable (8)	6,326
	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (6)

To record the sale of bonds on stated issue date:

• Cash is an asset and it is increased. Therefore cash is debited by $83,674.
• Discount on bonds payable is a contra liability and it is increased. Therefore debit discount on bonds payable by $6,326.
• Bonds payable is a liability and it is increased. Therefore credit bonds payable account by $90,000.