Moon Software Inc.is planning to issue two types of 25-year,noncallable bonds to raise a total of $6 million,$3 million from each type of bond.First,3,000 bonds with a 10% semiannual coupon will be sold at their $1,000 par value to raise $3,000,000.These are called "par" bonds.Second,Original Issue Discount (OID)bonds,also with a 25-year maturity and a $1,000 par value,will be sold,but these bonds will have a semiannual coupon of only 6.75%.The OID bonds must be offered at below par in order to provide investors with the same effective yield as the par bonds.How many OID bonds must the firm issue to raise $3,000,000? Disregard flotation costs,and round your final answer up to a whole number of bonds.

Question

Quizplus · Accepted Answer

The par bond has a coupon rate of 10% and a periodic rate of 5%,and it sells at par.Therefore,the going nominal rate must be 10% with an EFF% of 10.25%.The OID bond must provide the same EFF%,because it is equally risky.Therefore,it must be evaluated with the parameters shown below to find its price,which is then used to find the number of bonds to be issued.Note that if the OID bond is based on a 5% periodic rate,its EFF% will also be 10.25%.
Bond A: Issued at par:
Bond B: Issued at a discount (OID bonds):
Par value
$1,000
Par value
$1,000
Coupon rate
10.00%
Coupon rate
6.75%
Periods/year
2
Periods/year
2
Periodic rate
5.00%
Periodic rate
5.00%
Years to maturity
25
Years to maturity
25
Years 11ea856c_8bd3_d834_9aec_898faa34c184_TB1222_11 Periods/year = N
50
Years 11ea856c_8bd3_d835_9aec_21e4f170e6a2_TB1222_11 Period/year = N
50
PMT per period = Coupon 11ea856c_8bd3_ff46_9aec_69dea662b2a8_TB1222_11 Par/2 11ea856c_8bd3_ff47_9aec_b3be3cf97ce8_TB1222_00 $50.00
PMT per period = Coupon 11ea856c_8bd3_ff48_9aec_91275a902922_TB1222_11 Par/2
$33.75
PV = Price
$1,000
?
PV = Price
$703.3412
Funds needed from OID bonds
$3,000,000
Number of bonds = $3,000,000/OID price
4,265.36
Number of bonds,rounded up
4,266