Question

Issue Price

The following terms relate to independent bond issues:

1. 460 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments
2. 460 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments
3. 890 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments
4. 1,830 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

Issue Price calculation

Issue price of bond = Present value of all interest plus Present value of Maturity repayment which is face value

Vb = Interest * PVIFA + Face value * PVIF

Where,

PVIFA = present value of interest factor annuity , r , n

PVIF = present value of interest factor , r , n

Interest = face value * stated rate

R = market interest rate = 10% for annual

So, semi annual period = 10% / 2 = 5%

If interest payment is for semi annual period, should covert annual interest to semi annual by dividing by 2

.

.

The following terms relate to independent bond issues:

a. 460 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments

.

Interest = 1000 * 8% = 80 for annual

n = number of interest payment period = 5

PVIFA,10%,5 = 3.7908

PVIF,10%,5 = 0.6209

Face value = 1000

.

Issue price = 80 * 3.7908 + 1000 * 0.6209

Issue price = 303.264 + 620.9 = $924 per bond

For 460 bonds = 460 * 924 = $425040

.

b. 460 bonds; $1,000 face value; 8% stated rate; 5 years; semiannual interest payments

.

Interest = 1000 * 8% = 80 for annual, for semi annual = 80 / 2 = 40

n = number of interest payment period = 5 * 2 = 10 semi annual period

PVIFA,5%,10 = 7.7217

PVIF,5%,10 = 0.6139

Face value = 1000

.

Issue price = 40 * 7.7217 + 1000 * 0.6139

Issue price = 308.87 + 613.9 = $923 per bond

For 460 bonds = 460 * 923 = $424580

.

c. 890 bonds; $1,000 face value; 8% stated rate; 10 years; semiannual interest payments

.

Interest = 1000 * 8% = 80 for annual, for semi annual = 80 / 2 = 40

n = number of interest payment period = 10 * 2 = 20 semi annual period

PVIFA,5%,20 = 12.4622

PVIF,5%,20 = 0.3769

Face value = 1000

.

Issue price = 40 * 12.4622 + 1000 * 0.3769

Issue price = 498.49 + 376.9 = $875 per bond

For 890 bonds = 890 * 875 = $778750

.

d. 1,830 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments

.

Interest = 500 * 12% = 60 for annual, for semi annual = 60 / 2 = 30

n = number of interest payment period = 15 * 2 = 30 semi annual period

PVIFA,5%,30 = 15.3725

PVIF,5%,30 = 0.2314

Face value = 500

.

Issue price = 30 * 15.3725 + 500 * 0.2314

Issue price = 461.175 + 115.7 = $577per bond

For 1830 bonds = 1830 * 577 = $1055910

.

Situation	Selling Price of the Bond Issue
a.	$425040
b.	$424580
c.	$778750
d.	$1055910