Cosmic Communications Inc. is planning two new issues of 25-year bonds. Bond Par
ID: 2697734 • Letter: C
Question
Cosmic Communications Inc. is planning two new issues of 25-year bonds. Bond Par will be sold
at its $1,000 par value, and it will have a 10% semiannual coupon. Bond OID will be an Original
Issue Discount bond, and it will also have a 25-year maturity and a $1,000 par value, but its
semiannual coupon will be only 6.25%. If both bonds are to provide investors with the same
effective yield, how many of the OID bonds must Cosmic issue to raise $3,000,000? Disregard
flotation costs, and round your final answer up to a whole number of bonds.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
a. 4,228
b. 4,337
c. 4,448
d. 4,562
e. 4,676
Explanation / Answer
Bond Par
semiannual coupon payment = 10% *$1,000/2 = 50
Price of Bond Par =$1,000
$1,000 = $50/(1+r/2) + $50/(1+r/2)^2 + $50/(1+r/2)^3 ....................1050/(1+r/2)^50
r = 10%
Bond OID
semiannual coupon payment = 6.25%*$1,000/2 =$31.25
Price of Bond OID = $31.25/(1+r/2) + $31.25/(1+r/2)^2 + $31.25/(1+r/2)^3 ....................$1031.25/(1+r/2)^50
Price = $657.70
No of OID bonds Cosmic issue to raise $3,000,000 =$3,000,000/657.70
=4561.35016
Answer d. 4,562