Chapter 9, Problem 19RQ

a.

To determine

Calculate the issue price of the bonds, if market rate is 5%.

Answer to Problem 19RQ

The price of the bonds is $562,756.94.

Explanation of Solution

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.

Calculate the issue price of the bonds, if market rate is 5%.

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

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

Calculate the issue price of the bonds, if market rate is 6%.

Answer to Problem 19RQ

The price of the bonds is $500,000

Explanation of Solution

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.

Calculate the issue price of the bonds, if market rate is 6%.

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

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

Calculate the issue price of the bonds, if market rate is 7%.

Answer to Problem 19RQ

The price of the bonds is $446,613.32.

Explanation of Solution

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.

Calculate the issue price of the bonds, if market rate is 7%.

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

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.