Chapter 9, Problem 9.8APEM

1.

To determine

The price of the bonds was issued on January 1, 2013 for $110,465,146.

Explanation of Solution

Calculate the issue price of the bonds.

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$47,674,268.52+\$62,790,877.78\\ =\$110,465,1146.30\end{array}$

Working notes:

Calculate the present value of face value of principal

Particulars	Amount ($)
Face value of bonds (a)	$100,000,000
PV factor at an annual market rate of 2.5% for 30 periods (b)	$\times$ 0.47674
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$47,674,268.52

Table (1)

Note: The present value of $1 for 30 periods at 2.5% is 0.47674 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$3,000,000
PV factor at an annual market rate of 2.5% for 30 periods (b)	$\times$20.93029
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$62,790,877.78

Table (2)

Note: The Present value of an ordinary annuity of $1 for 30 periods at 2.5% is 20.93029 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$100,000,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$3,000,000\end{array}$

2.

To determine

The carrying value of the bonds five years later on December 31, 2017.

Explanation of Solution

Calculate the issue price of the bonds.

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$61,027,094.29+\$46,767,486.86\\ =\$107,794,581.14\end{array}$

Working notes:

Calculate the present value of face value of principal

Particulars	Amount ($)
Face value of bonds (a)	$100,000,000
PV factor at an annual market rate of 2.5% for 20 periods (b)	$\times$ 0.61027
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$61,027,094.29

Table (3)

Note: The present value of $1 for 20 periods at 2.5% is 0.61027 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$3,000,000
PV factor at an annual market rate of 2.5% for 20 periods (b)	$\times$15.58916
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$46,767,486.86

Table (4)

Note: The Present value of an ordinary annuity of $1 for 20 periods at 2.5% is 15.58916 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$100,000,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$3,000,000\end{array}$

3.

To determine

The market value of the bonds five years later on December 31, 2017, when market interest rate is 4.5%.

Explanation of Solution

Calculate the issue price of the bonds.

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$41,464,285.97+\$39,023,809.35\\ =\$80,488,095.32\end{array}$

Working notes:

Calculate the present value of face value of principal

Particulars	Amount ($)
Face value of bonds (a)	$100,000,000
PV factor at an annual market rate of 4.5% for 20 periods (b)	$\times$ 0.41464
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$41,464,285.97

Table (5)

Note: The present value of $1 for 20 periods at 4.5% is 0.41464 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$3,000,000
PV factor at an annual market rate of 4.5% for 20 periods (b)	$\times$13.00794
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$39,023,809.35

Table (6)

Note: The Present value of an ordinary annuity of $1 for 20 periods at 4.5% is 13.00794 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$100,000,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$3,000,000\end{array}$

4.

To determine

To Prepare: The journal entry to record the early retirement of the bonds on December 31, 2017. Whether the transaction increase net income and how much amount would be increased.

Explanation of Solution

Redemption of Bonds

The process of repaying the sale amount of bonds to bondholders at the time of maturity or before the maturity period is called as redemption of bonds. It is otherwise called as retirement of bonds.

Prepare the journal entry to record early retirement of bonds as on 31^st December 2017.

Date	Account titles and Explanation	Debit	Credit
December 31, 2015	Bonds payable	$100,000,000
	Premium on bonds payable (1)	$7,794,581.14
	Gain on redemption of bonds (2)		$27,306,485.82
	Cash		$80,488,095.32
	(To record early retirement of bonds before the maturity period)

Table (7)

Working notes:

Calculate premium on bonds payable.

$\begin{array}{c}\text{Premium on bonds payable}\text{= Carrying value of the bonds }-\text{Face value of bonds}\\ \text{= \$107,794,581}\text{.14}-\$100,000,000\\ =\$7,794,581.14\end{array}$

(1)

Calculate gain on redemption of bonds.

$\begin{array}{c}\text{Gain on redemption of bonds =}\text{Bonds payable + premium on bonds payable }-\text{Cash}\\ \text{=}\text{\$100,000,000}\text{+}\text{\$7,794,581}\text{.14}-\$80,488,095.32\\ =\$27,306,485.82\end{array}$

(2)

Yes, this transaction surely, increase the net income $27,306,485.82.

5.

To determine

To Explain: Is DP plan is ethical or unethical, and Investors would agree with his plan.

Explanation of Solution

Yes, DP plan is ethical, the early retirement of bonds as on 31^st December 2017 of 6% bonds and company get a gain of $27,306,485.82 and he reissue of 9% bonds. According to the investor’s point of view, the gain amount of $27,306,485.82 needs to give a dividend. But DP plans to re-issue new bonds for 9%. Therefore, Investors would probably disagree with CFO plan.