Chapter 9, Problem 7PA

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 7% and the bonds are issued at face amount.

Explanation of Solution

Bonds:

Bonds are long-term promissory notes that are issued by a company while borrowing money from investors to raise fund for financing the operations.

Amortization Schedule:

A schedule that gives the detail about each loan payment and shows the allocation of principal and interest over the life of the note, or bond is called amortization schedule.

Calculate the issue price of bonds:

Figure (1)

Working Note:

Determine the amount of Interest Payment (PMT).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Face value (FV)}\times \text{Stated rate of interest}\times \frac{1}{2}\\ =\$1,300,000\times \frac{7}{100}\times \frac{1}{2}\\ =\$45,500\end{array}$ (1)

Determine the amount of Market interest rate (I).

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

Determine the amount of periods to maturity (N).

$\begin{array}{c}\text{Periods to Maturity}=\text{Years}\times \left(\begin{array}{l}\text{Number of times interest}\\ \text{ payable annually}\end{array}\right)\\ =15\times 2\\ =30\end{array}$ (3)

Complete the first three rows of an amortization schedule for the issuance of bonds:

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Increase in carrying value (4)	Carrying value (5)
	$\begin{array}{l}\text{Face Amount}\times \\ \text{3}\text{.5\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ \text{3}\text{.5\% Market Rate}\end{array}$	$\left(3\right)-\left(2\right)$	$\text{Carrying value}+(4)$
January 01				$1,300,000
June 30	$45,500	$45,500	$0	$1,300,000
December 31	$45,500	$45,500	$0	$1,300,000

Table (1)

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 8% and the bonds are issued at a discount.

Explanation of Solution

Calculate the issue price of bonds:

Figure (2)

Working note:

Determine the amount of Market interest rate (I).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Stated rate of interest}\times \frac{1}{2}\\ =8\times \frac{1}{2}\\ =4.0\%\end{array}$ (4)

Complete the first three rows of an amortization schedule for the issuance of bonds:

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Increase in carrying value (4)	Carrying value (5)
	$\begin{array}{l}\text{Face Amount}\times \\ \text{3}\text{.5\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ 4.0\%\text{ Market Rate}\end{array}$	$\left(3\right)-\left(2\right)$	$\text{Carrying value}+(4)$
January 01				$1,187,602
June 30	$45,500	$47,504	$2,004	$1,189,606
December 31	$45,500	$47,584	$2,084	$1,191,690

Table (2)

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 6% and the bonds are issued at a premium.

Explanation of Solution

Calculate the issue price of bonds:

Figure (3)

Working note:

Determine the amount of Market interest rate (I).

$\begin{array}{c}\text{Interest Payment}\left(\text{PMT}\right)=\text{Stated rate of interest}\times \frac{1}{2}\\ =6\times \frac{1}{2}\\ =3.0\%\end{array}$ (5)

Complete the first three rows of an amortization schedule for the issuance of bonds:

Amortization Schedule
Date (1)	Cash paid (2)	Interest expense (3)	Decrease in carrying value (4)	Carrying value (5)
	$\begin{array}{l}\text{Face Amount}\times \\ \text{3}\text{.5\% Stated Rate}\end{array}$	$\begin{array}{l}\text{Carrying value}\times \\ \text{3}\text{.0\% Market Rate}\end{array}$	$\left(2\right)-\left(3\right)$	$\text{Carrying value}-(4)$
January 01				$1,427,403
June 30	$45,500	$42,822	$2,678	$1,424,725
December 31	$45,500	$42,742	$2,758	$1,421,967

Table (3)