Chapter 9, Problem 7PB

1.

To determine

Compute the issue price of bonds and complete the first three rows of an amortization schedule, if the market interest rate is 6% and the bonds issue at face amount.

Explanation of Solution

Bonds are a kind of interest bearing notes payable, usually issued by companies, universities and governmental organizations. It is a debt instrument used for the purpose of raising fund of the corporations or governmental agencies. If selling price of the bond is equal to its face value, it is called as par on bond. If selling price of the bond is lesser than the face value, it is known as discount on bond. If selling price of the bond is greater than the face value, it is known as premium on bond.

Determine the issue price of bonds.

Figure (1)

Prepare amortization schedule.

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Increase in carrying value (4)	Carrying  value (5)
2018	$\begin{array}{l}\text{Face Amount}\times \\ \text{3\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ \text{3\% Market Rate}\end{array}$	$\left(3\right)-\left(2\right)$	$\text{Carrying value}+(4)$
January 01				$850,000
June 30	$25,500	$25,500	$0	$850,000
December 31	$25,500	$25,500	$0	$850,000

Table (1)

Working Notes:

Determine the amount of Interest Payment (PMT).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Face value (FV)}\times \text{Stated rate of interest}\times \frac{1}{2}\\ =\$850,000\times \frac{6}{100}\times \frac{1}{2}\\ =\$25,500\end{array}$ (1)

Determine the amount of Market interest rate (I).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Stated rate of interest}\times \frac{1}{2}\\ =6\times \frac{1}{2}\\ =3\%\end{array}$ (2)

Determine the amount of periods to maturity (N).

$\begin{array}{c}\text{Periods to Maturity}=\text{Years}\times \left(\begin{array}{l}\text{Number of times interest}\\ \text{ payable annually}\end{array}\right)\\ =10\times 2\\ =20\end{array}$ (3)

2.

To determine

Compute the issue price of bonds and complete the first three rows of an amortization schedule, if the market interest rate is 7% and the bonds issue at a discount.

Explanation of Solution

Determine the issue price of bonds.

Figure (2)

Prepare amortization schedule.

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Increase in carrying value (4)	Carrying value (5)
2018	$\begin{array}{l}\text{Face Amount}\times \\ \text{3\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ \text{3}\text{.5\% Market Rate}\end{array}$	$\left(3\right)-\left(2\right)$	$\text{Carrying value}+(4)$
January 01				$789,597
June 30	$25,500	$27,636	$2,136	$791,733
December 31	$25,500	$27,711	$2,211	$793,944

Table (2)

Working note:

Determine the amount of Market interest rate (I).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Stated rate of interest}\times \frac{1}{2}\\ =7\times \frac{1}{2}\\ =3.5\%\end{array}$ (4)

3.

To determine

Compute the issue price of bonds and complete the first three rows of an amortization schedule, if the market interest rate is 5% and the bonds issue at a premium.

Explanation of Solution

Determine the issue price of bonds.

Figure (3)

Prepare amortization schedule.

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Decrease in carrying value (4)	Carrying value (5)
2018	$\begin{array}{l}\text{Face Amount}\times \\ \text{3\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ \text{2}\text{.5\% Market Rate}\end{array}$	$\left(3\right)-\left(2\right)$	$\text{Carrying value}-(4)$
January 01				$916,254
June 30	$25,500	$22,906	$2,594	$913,660
December 31	$25,500	$27,711	$2,658	$911,002

Table (3)

Working note:

Determine the amount of Market interest rate (I).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Stated rate of interest}\times \frac{1}{2}\\ =5\times \frac{1}{2}\\ =2.5\%\end{array}$ (5)