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

F (face value) = 8,000; C (redemption value) = 9,000

N = 15; m (frequency of coupon payments) = 2; n (number of total coupon payments) = N*m = 15*2 = 30

a (annual coupon rate) = 7%, so r (coupon rate per period) = a/m = 7%/2 = 3.5%

Coupon per period = F*r = 8,000*3.5% = 280

Irene buys the bond just before the 18th coupon has to be paid (23 months + (7*12) months = 107 months or 8.92 years) holds the bond till maturity, so she gets 30-17 = 13 coupons.

The 18th coupon is to be paid one month after she buys the bond and she earns a yield of 3.6%/2 = 1.9% per period on the bond.

Price which she would have paid = (value of the bond at the time of the 18th coupon)*(1+yield per period)*(5/6)

Value of the bond at the time of the 18th coupon = PV of coupons + PV of redemption value

= 280*[(1 - (1+1.9%)^-13]/1.9% + 9,000/(1+1.9%)^13 = 3,198.59 + 7,046.58 = 10,245.17

Price = 10,245*(1+1.9%)^(5/6) = 10,407.13 (This is the common price for Pierre and Irene)

Eric has a yield per period of 3.6%/2 = 1.8%. He holds the bond for 23 months so he earns 3 coupons and the selling price of 10,407.13. Number of periods = 23/6

Price for Eric = PV of three coupons + PV of selling price

= 280*[(1 - (1+1.8%)^-3]/1.8% + 10,407.13/(1 + 1.8%)^(23/6)

= 810.64 + 9,719.21 = 10,529.85 (This is the price at issue for the bond.)