Chapter 9, Problem 14RQ

a.

To determine

Bonds

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.

To Calculate: The issue price of the bonds.

Answer to Problem 14RQ

The price of the bonds is $562,756.94

Explanation of Solution

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$186,215.31+\$376,541.63\\ =\$562,756.94\end{array}$

Working notes:

Calculate the present value of face value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$500,000
PV factor at an annual market rate of 2.5% for 40 periods (b)	$\times$ 0.37243
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$186,215.31

Note: The present value of $1 for 40 periods at 2.5% is 0.37243 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$15,000
PV factor at an annual market rate of 2.5% for 40 periods (b)	$\times$25.10278
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$376,541.63

Note: The Present value of an ordinary annuity of $1 for 40 periods at 2.5% is 25.10278 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{Stated interest rate}\times \text{Time period}\\ =\$500,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$15,000\end{array}$

Conclusion

Therefore, price of the bonds is $562,756.94.

b.

To determine

To Calculate: The issue price of the bonds.

Answer to Problem 14RQ

The price of the bonds is $500,000

Explanation of Solution

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$153,278.42+\$346,721.58\\ =\$500,000\end{array}$

Working notes:

Calculate the present value of face value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$500,000
PV factor at an annual market rate of 3% for 40 periods (b)	$\times$ 0.30656
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$153,278.42

Note: The present value of $1 for 40 periods at 3% is 0.30656 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$15,000
PV factor at an annual market rate of 3% for 40 periods (b)	$\times$23.11477
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$346,721.58

Note: The Present value of an ordinary annuity of $1 for 40 periods at 3% is 23.11477 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{Stated interest rate}\times \text{Time period}\\ =\$500,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$15,000\end{array}$

Conclusion

Therefore, price of the bonds is $500,000.

c.

To determine

To Calculate: The issue price of the bonds.

Answer to Problem 14RQ

The price of the bonds is $446,613.32.

Explanation of Solution

$\begin{array}{c}\text{Price of bonds}\}=\left\{\begin{array}{l}\text{Present value of principal}+\\ \text{Present value of interest payments}\end{array}\right\}\\ =\$126,286.23+\$320,326.09\\ =\$446,612.32\end{array}$

Working notes:

Calculate the present value of face value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$500,000
PV factor at an annual market rate of 3.5% for 40 periods (b)	$\times$ 0.25257
Present value of face value of principal $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$126,286.23

Note: The present value of $1 for 40 periods at 3.5% is 0.25257 (refer Table 2 in Appendix).

Calculate present value of interest payments.

Particulars	Amount ($)
Interest payments amount (a)	$15,000
PV factor at an annual market rate of 3.5% for 40 periods (b)	$\times$21.35507
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$320,326.09

Note: The Present value of an ordinary annuity of $1 for 40 periods at 3.5% is 21.35507 (refer Table 4 in Appendix).

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{Stated interest rate}\times \text{Time period}\\ =\$500,000\times \frac{6}{100}\times \frac{6}{12}\\ =\$15,000\end{array}$

Conclusion

Therefore, price of the bonds is $446.613.32.