Chapter 10, Problem 1BP

(a)

To determine

Calculate the selling price of bonds for the given situations.

Explanation of Solution

1.

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			(7) $6,978

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.

Working notes:

Calculate the semiannual 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)

2.

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.

Working notes:

Calculate the semiannual 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)

3.

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.

Working notes:

Calculate the semiannual 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)

To determine

Prepare journal entry to record issuance of bonds for the three situations given.

Explanation of Solution

1.

Date	Account Titles and Explanation	Debit ($)	Credit ($)
2015	Cash	96,948
January 1	Premium on bonds payable (3)		6,948
	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (4)

• 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.

Date	Account Titles and Explanation	Debit ($)	Credit ($)
2015	Cash	90,000
January 1	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (5)

• 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.

Date	Account Titles and Explanation	Debit ($)	Credit ($)
2015	Cash	83,674
January 1	Discount on bonds payable (8)	6,326
	Bonds payable		90,000
	(To record the sale of bonds on stated issue date.)

Table (6)

• 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 decreased. 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.