Chapter 14, Problem 14.2E

(1)

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 Determine: The price of the bonds.

Explanation of Solution

Calculate the price of the bonds.

$\begin{array}{c}\text{Price of the bonds =}\left(\begin{array}{l}\text{Present value of the principal +}\\ \text{ Present value of the interest payments}\end{array}\right).\\ =\$321,970+\$565,022\\ =\$886,992\end{array}$

Working notes:

Calculate the present value of interest payments:

Particulars	Amount ($)
Interest payments amount (a)	$100,000
PV factor at an annual market rate of 12% for 10 periods (b)	$\times$5.65022
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$565,022

Table (1)

Note: The Present value of an ordinary annuity of $1 for 10 periods at 12% is 5.65022 (refer Table 4 in Appendix).

Hence, present value of interest payment is $565,022.

(1)

Calculate the present value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$1,000,000
PV factor at an annual market rate of 12% for 10 periods (b)	$\times$ 0.32197
Present value of face value of the bonds $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$321,970

Table (2)

Note: The present value of $1 for 8 periods at 12% is 0.32197 (refer Table 2 in Appendix).

Hence, present value of principal amount is $321,970.

(2)

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\\ =\$1,000,000\times \frac{10}{100}\\ =\$100,000\end{array}$

Hence, the interest payment amount is $100,000.

(3)

Conclusion

Therefore, price of the bonds is $886,992.

(2)

To determine

The price of the bonds.

Explanation of Solution

Calculate the price of the bonds.

$\begin{array}{c}\text{Price of the bonds =}\left(\begin{array}{l}\text{Present value of the principal +}\\ \text{ Present value of the interest payments}\end{array}\right).\\ =\$311,800+\$573,496\\ =\$885,296\end{array}$

Working notes:

Calculate the present value of interest payments:

Particulars	Amount ($)
Interest payments amount (a)	$50,000
PV factor at an annual market rate of 6% for 20 periods (b)	$\times$11.46992
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$573,496

Table (3)

Note: The Present value of an ordinary annuity of $1 for 20 periods at 6% is 11.46992 (refer Table 4 in Appendix).

Hence, present value of interest payment is $573,496.

(4)

Calculate the present value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$1,000,000
PV factor at an annual market rate of 6% for 20 periods (b)	$\times$ 0.31180
Present value of face value of the bonds $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$311,800

Table (4)

Note: The present value of $1 for 8 periods at 12% is 0.31180 (refer Table 2 in Appendix).

Hence, present value of principal amount is $311,800.

(5)

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$1,000,000\times \frac{10}{100}\times \frac{6}{12}\\ =\$50,000\end{array}$

Hence, the interest payment amount is $50,000.

(6)

Conclusion

Therefore, price of the bonds is $885,296.

(3)

To determine

The price of the bonds.

Explanation of Solution

Calculate the price of the bonds.

$\begin{array}{c}\text{Price of the bonds =}\left(\begin{array}{l}\text{Present value of the principal +}\\ \text{ Present value of the interest payments}\end{array}\right).\\ =\$376,890+\$747,733\\ =\$1,124,623\end{array}$

Working notes:

Calculate the present value of interest payments:

Particulars	Amount ($)
Interest payments amount (a)	$60,000
PV factor at an annual market rate of 5% for 20 periods (b)	$\times$12.46221
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$747,733

Table (5)

Note: The Present value of an ordinary annuity of $1 for 20 periods at 5% is 12.46221 (refer Table 4 in Appendix).

Hence, present value of interest payment is $573,496.

(7)

Calculate the present value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$1,000,000
PV factor at an annual market rate of 5% for 20 periods (b)	$\times$ 0.37689
Present value of face value of the bonds $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$376,890

Table (6)

Note: The present value of $1 for 8 periods at 6% is 0.37689 (refer Table 2 in Appendix).

Hence, present value of principal amount is $376,890.

(8)

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$1,000,000\times \frac{12}{100}\times \frac{6}{12}\\ =\$60,000\end{array}$

Hence, the interest payment amount is $60,000.

(9)

Conclusion

Therefore, price of the bonds is $1,124,623.

(4)

To determine

The price of the bonds.

Explanation of Solution

Calculate the price of the bonds.

$\begin{array}{c}\text{Price of the bonds =}\left(\begin{array}{l}\text{Present value of the principal +}\\ \text{ Present value of the interest payments}\end{array}\right).\\ =\$142,050+\$1,029,545\\ =\$1,171,595\end{array}$

Working notes:

Calculate the present value of interest payments:

Particulars	Amount ($)
Interest payments amount (a)	$60,000
PV factor at an annual market rate of 5% for 40 periods (b)	$\times$17.15909
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$1,029,545

Table (5)

Note: The Present value of an ordinary annuity of $1 for 40 periods at 5% is 17.15909 (refer Table 4 in Appendix).

Hence, present value of interest payment is $1,029,545.

(10)

Calculate the present value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$1,000,000
PV factor at an annual market rate of 5% for 40 periods (b)	$\times$ 0.14205
Present value of face value of the bonds $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$1,42,050

Table (6)

Note: The present value of $1 for 40 periods at 6% is 0.14205 (refer Table 2 in Appendix).

Hence, present value of principal amount is $142,050.

(11)

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$1,000,000\times \frac{12}{100}\times \frac{6}{12}\\ =\$60,000\end{array}$

Hence, the interest payment amount is $60,000.

(12)

Conclusion

Therefore, price of the bonds is $1,171,595.

(5)

To determine

The price of the bonds.

Explanation of Solution

Calculate the price of the bonds.

$\begin{array}{c}\text{Price of the bonds =}\left(\begin{array}{l}\text{Present value of the principal +}\\ \text{ Present value of the interest payments}\end{array}\right).\\ =\$97,220+\$902,778\\ =\$999,998\end{array}$

Working notes:

Calculate the present value of interest payments:

Particulars	Amount ($)
Interest payments amount (a)	$60,000
PV factor at an annual market rate of 6% for 40 periods (b)	$\times$15.04630
Present value of interest payments $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$902,778

Table (5)

Note: The Present value of an ordinary annuity of $1 for 40 periods at 6% is 15.04630 (refer Table 4 in Appendix).

Hence, present value of interest payment is $902,778.

(13)

Calculate the present value of principal.

Particulars	Amount ($)
Face value of bonds (a)	$1,000,000
PV factor at an annual market rate of 6% for 40 periods (b)	$\times$ 0.09722
Present value of face value of the bonds $\left(\text{a}\right)\text{×}\left(\text{b}\right)$	$97,220

Table (6)

Note: The present value of $1 for 40 periods at 6% is 0.09722 (refer Table 2 in Appendix).

Hence, present value of principal amount is $97,220.

(14)

Calculate the amount of interest payment.

$\begin{array}{c}\text{Interest payment}=\text{Face value of bonds}\times \text{ interest rate}\times \text{Time period}\\ =\$1,000,000\times \frac{12}{100}\times \frac{6}{12}\\ =\$60,000\end{array}$

Hence, the interest payment amount is $60,000.

(15)

Conclusion

Therefore, price of the bonds is $999,998