Question

Eric purchases a $8,000 fifteen-year 7% bond with semiannual coupons and a redemption value of $9.000. After twenty-three months, he sells the bond to Pierre who holds the bond for seven years and then sells it to Irene for the same price at which he bought it. She holds the bond until maturity. The nominal yield rates convertible semiannually earned by Eric and Irene are 3.6% and 3.8% respectively. Find the price for the bond at issue and the price Pierre paid for it. The answers are: the price at issue = 10529. 86 The price Pierre paid=10407.13

Answer 1

Solutions:

The bond has

F= $8000

C = $9000

N = 15

m = 2

n= N m = 30

α = 7%

r = 7%/2 = 3.5%  &

coupon amount Fr= $280.

Pierre buys the bond at the end of 23 months and sells it 84(7 x 12) months later. i.e. at the end of the 107th month; this is 1 month before the 18^th coupon, since 107 = (6 x 18) - 1. Thus Irene, who purchases the bond from Pierre, is purchasing a level annuity with 30 - 17 = 13 payments of $280, the first of which will be paid in one month, along with the rights to a $9,000 redemption payment at the time of the last annuity payment. We were told that Irene's price P_Irene gave her a 3.8%/2 = 1.9% yield rate per coupon period. So,

Pirene = [s280a 731.9% + $9,000(1.019)-13] (1.01998 – ($10,245.16524)(1.015808447) – $10,407.1254.

Thus. Irene's and Pierre's common price was $10,407.13. To find Eric's price P_Eric. which was the price of the bond at issue, we use the fact that his yield per coupon period is 3.6%/2 = 1.8%. Since Eric held the bond for twenty three months (23/6 coupon periods) he received 3 semiannual $280 coupons and the $ 10,407.13 at the time of sale. Thus,

Plerie = $2804 71.8% + [$10,407.13(1.018)*] $10,529.85774 - $10,529.86.