Question

Issue Price

The following terms relate to independent bond issues:

1. 610 bonds; $1,000 face value; 8% stated rate; 5 years; annual interest payments
2. 610 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. 1,850 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

(a) -- 610 bonds; $1000 face value; 8% stated rate; 5 years; annual interest payments, market rate of interest is 10%.

Answer -

	Particulars	Cash Flow ($)	Calculation	Amount ($)
I.	Face Value of Bond	$610000 [$1000 * 610 bonds]	= Cash Flow * PVIF of $1 (i%, n) = $610000 * $1(10%,5 years) = $610000 * 0.62092 = $378761	378761
II.	Interest Payments of Bond	$48800 [($1000 * 8%) * 610 bonds]	= Cash Flow * PVAF of $1 (i%, n) = $48800 * $1(10%,5 years) = $48800 * 3.79079 = $184991	184991
Selling Price of the Bond Issue			I + II	563752

.

(b) -- 610 bonds; $1000 face value; 8% stated rate; 5 years; semiannual interest payments, market rate of interest is 10%.

Answer -

Note -

	Particulars	Cash Flow ($)	Calculation	Amount ($)
I.	Face Value of Bond	$610000 [$1000 * 610 bonds]	= Cash Flow * PVIF of $1 (i%, n) = $610000 * $1(5%,10 years) = $610000 * 0.61391 = $374485	374485
II.	Interest Payments of Bond	$24400 [($1000 * 8%) / 2] * 610 bonds]	= Cash Flow * PVAF of $1 (i%, n) = $24400 * $1(5%,10 years) = $24400 * 7.72173 = $188410	188410
Selling Price of the Bond Issue			I + II	562895

.

(c) -- 750 bonds; $1000 face value; 8% stated rate; 10 years; semiannual interest payments, market rate of interest is 10%.

Answer -

	Particulars	Cash Flow ($)	Calculation	Amount ($)
I.	Face Value of Bond	$750000 [$1000 * 750 bonds]	= Cash Flow * PVIF of $1 (i%, n) = $750000 * $1(5%,20 years) = $750000 * 0.37689 = $282668	282668
II.	Interest Payments of Bond	$30000 [($1000 * 8%) / 2] * 750 bonds]	= Cash Flow * PVAF of $1 (i%, n) = $30000 * $1(5%,20 years) = $30000 * 12.46221 = $373866	373866
Selling Price of the Bond Issue			I + II	656534

.

(d) -- 1850 bonds; $500 face value; 12% stated rate; 15 years; semiannual interest payments, market rate of interest is 10%.

Answer -

	Particulars	Cash Flow ($)	Calculation	Amount ($)
I.	Face Value of Bond	$925000 [$500 * 1850 bonds]	= Cash Flow * PVIF of $1 (i%, n) = $925000 * $1(5%,30 years) = $925000 * 0.23138 = $214027	214027
II.	Interest Payments of Bond	$55500 [($500 * 12%) / 2] * 1850 bonds]	= Cash Flow * PVAF of $1 (i%, n) = $55500 * $1(5%,30 years) = $55500 * 15.37245 = $853171	853171
Selling Price of the Bond Issue			I + II	1067198