Question

The following terms relate to independent bond issues:

1. 440 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments

2. 440 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments

3. 750 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments

4. 2,040 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

Price of bond = Coupen Amount * Present Value Annuity factor ( peroidic rate of interest, number of periods ) + Face value * Present Value Interest factor ( peroidic rate of interest, number of periods )

a) Price of bond = Coupen Amount * Present Value Annuity factor ( peroidic rate of interest, number of periods ) + Face value * Present Value Interest factor ( peroidic rate of interest, number of periods )

                           = ( 8 % * 1000 ) * PVAF (10%, 5 ) + 1000 * PVIF (10%, 5 )

                          = 80 * [ 1 / 1.10 + ..... + 1 / 1.10⁵ ] + 1000 * [ 1 / 1.10⁵ ]

                           = 80 * 3.7908 + 1000 * 0.6209

                           = 303.264 + 620.90

                           = 924.16

b) Price of bond = Coupen Amount * Present Value Annuity factor ( peroidic rate of interest, number of periods ) + Face value * Present Value Interest factor ( peroidic rate of interest, number of periods )

                           = ( 8 % * 1000 * 6/12 ) * PVAF (10%/2, 5*2 ) + 1000 * PVIF (10%/2, 5*2 )

                          = 40 * [ 1 / 1.05 + ..... + 1 / 1.05¹⁰ ] + 1000 * [ 1 / 1.05¹⁰ ]

                           = 40 * 7.7217 + 1000 * 0.6139

                           = 308.87 + 613.90

                           = 922.77

c) Price of bond = Coupen Amount * Present Value Annuity factor ( peroidic rate of interest, number of periods ) + Face value * Present Value Interest factor ( peroidic rate of interest, number of periods )

                           = ( 8 % * 1000 * 6/12 ) * PVAF (10%/2, 10*2 ) + 1000 * PVIF (10%/2, 10*2 )

                          = 40 * [ 1 / 1.05 + ..... + 1 / 1.05²⁰ ] + 1000 * [ 1 / 1.05²⁰ ]

                           = 40 * 12.4622 + 1000 * 0.3769

                           = 498.49 + 376.90

                           = 875.39

d) Price of bond = Coupen Amount * Present Value Annuity factor ( peroidic rate of interest, number of periods ) + Face value * Present Value Interest factor ( peroidic rate of interest, number of periods )

                           = ( 12 % * 1000 * 6/12 ) * PVAF (10%/2, 15*2 ) + 1000 * PVIF (10%/2, 15*2 )

                          = 60 * [ 1 / 1.05 + ..... + 1 / 1.05³⁰ ] + 1000 * [ 1 / 1.05³⁰ ]

                           = 25 * 15.3725 + 1000 * 0.2314

                           = 922.35 + 231.40

                           = 1153.75