Homework 20 Solution
1.
The corporate bond shown below was issued on July 2, 1967 with a face value of $1000. It has a
maturity date of July 1, 1992 and a coupon rate of 4½%. Coupons are payable on January 1 and July 1
of each year.
Assume I purchased this bond at par (i.e., “for face value”) on the day it was issued and held it to
maturity. Calculate (a) the coupon amount and (b) the yield to maturity.
o
r4
.
5
%
Coupon
B
$1000
$22.50
M2
To calculate the YTM, equate the $1000 purchase price to the $1000 redemption value plus the coupon
payments. The bond matures in 25 years, which is 50 coupon periods, so
$1000
$22.50 P  A,i%,50
$1000 P  F,i%,50
Rearranging:
$22.50 P  A,i%,50
$1000 P  F,i%,50
$1000
0
Let’s start at 2% per coupon period (the table in the back of the book closest to half the 4½ % coupon
rate) and work up from there:
31.4236
0.3715
$22.50 P  A,2%,50
$1000 P  F,2%,50
$1000
$78.53
This is too high, so we want to try a higher rate (remember, as i%
↑
PA and PF
↓
):
25.7298
.2281
$22.50 P  A,3%,50
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 Fall '08
 Moore,L
 coupon period

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