Question

Solve for the bond/stock problem. Show all of your work and equations! Hint: The correct answer is $936.5 and n=Number of coupons remaining. PLEASE DO NOT USE EXCEL and SOLVE BY HAND!

1. A bond with a coupon rate of 7.30% has a price that today equals $868.92. The $1.000 face value bond pays coupon every 6 months, 30 coupons remain, and a coupon was paid yesterday. Suppose you buy this bond at today's price and hold it so that you receive 20 coupons. You sell the bond upon receiving that last coupon. Find the selling price if the bond's YTM remains constant. Note that the number of coupons left is the same as "n" at the time of pricing.

Answer 1

Bond price = coupon * (1 - (1 + YTM)^(-n))/YTM + face value/(1 + YTM)^n

868.92 = 36.5 * (1 - (1+YTM)^(-30))/YTM + 1000/(1 + YTM)^30

by solving trail and error we will get the value of YTM = 4.449%

If he wants to sell after receiving 20 coupons then we can find the value of the bond using following formula:

Bond price = coupon * (1 - (1 + YTM)^(-n))/YTM + face value/(1 + YTM)^n

Bond price = 36.5 * (1 - 1.0445^(-10))/.0445 + 1000/(1.0445)^10

= 36.5 * 7.9322 + 647.01

= 289.5 + 646.01

= $936.5