Question

The following terms relate to independent bond issues:

620 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments

620 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments

790 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments

2,190 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

Use the appropriate present value table:

PV of $1 and PV of Annuity of $1

Required:

Assuming the market rate of interest is 10%, calculate the selling price for each bond issue. If required, round your intermediate calculations and final answers to the nearest dollar.

Situation	Selling Price of the Bond Issue
a.	$
b.	$
c.	$
d.	$

Answer 1

Situation a
Selling price of the bond = Present value of Face value of bond + Present Value of all future interest payment
Using present value of annuity formula we can calculate the present value of all future interest payments.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = present value of all future interest payments = ?
P = Annual Interest payment = $1000 *8% = $80
r = market rate of interest per annum = 10%
n = no.of compounding periods = 5 years
Present value of annuity = 80*{[1 - (1+0.10)^-5]/0.10} = 303.26
Present Value of all future interest payment = $303.26
Present value of face value of bond = Face value * discount factor at 10% at the end of 5th compounding period
Present value of face value of bond = $1000 * [1/1.10^5] = $620.92
Selling price of the bond = $620.92 + $303.26 = $924.18 i.e.$924 per bond
Situation b
Selling price of the bond = Present value of Face value of bond + Present Value of all future interest payment
Using present value of annuity formula we can calculate the present value of all future interest payments.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = present value of all future interest payments = ?
P = semi Annual Interest payment = $1000 *8% = $80/2 = $40
r = market rate of interest per semi annual period = 5%
n = no.of compounding periods = 5 years* 2 = 10
Present value of annuity = 40*{[1 - (1+0.05)^-10]/0.05} = 308.87
Present Value of all future interest payment = $308.87
Present value of face value of bond = Face value * discount factor at 5% at the end of 10th compounding period
Present value of face value of bond = $1000 * [1/1.05^10] = $613.91
Selling price of the bond = $308.87 + $613.91 = $922.78 i.e.$923 per bond
Situation c
Selling price of the bond = Present value of Face value of bond + Present Value of all future interest payment
Using present value of annuity formula we can calculate the present value of all future interest payments.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = present value of all future interest payments = ?
P = semi Annual Interest payment = $1000 *8% = $80/2 = $40
r = market rate of interest per semi annual period = 5%
n = no.of compounding periods = 10 years* 2 = 20
Present value of annuity = 40*{[1 - (1+0.05)^-20]/0.05} = 498.49
Present Value of all future interest payment = $498.49
Present value of face value of bond = Face value * discount factor at 5% at the end of 20th compounding period
Present value of face value of bond = $1000 * [1/1.05^20] = $376.89
Selling price of the bond = $498.49 + $376.89 = $875.38 i.e.$875 per bond
Situation d
Selling price of the bond = Present value of Face value of bond + Present Value of all future interest payment
Using present value of annuity formula we can calculate the present value of all future interest payments.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = present value of all future interest payments = ?
P = semi Annual Interest payment = [$500 *12%]/2 = $60/2 = $30
r = market rate of interest per semi annual period = 5%
n = no.of compounding periods = 15 years* 2 = 30
Present value of annuity = 30*{[1 - (1+0.05)^-30]/0.05} = 461.17
Present Value of all future interest payment = $461.17
Present value of face value of bond = Face value * discount factor at 5% at the end of 30th compounding period
Present value of face value of bond = $500 * [1/1.05^30] = $115.69
Selling price of the bond = $461.17 + $115.69 = $576.86 i.e.$577 per bond