Question

A bond was issued three years ago at a price of $1,060 with a maturity of six years, a yield-to-maturity (YTM) of 7.75% compounded semi-annually, and a face value of $1,000 with semi-annualy coupons. What is the price of this bond today immediately after the receipt of today's coupon if the YTM has risen to 9.00% compounded semi-annually?

Answer 1

Price of the bond = Coupon * [ 1 - ( 1 + periodic ytm ) ^ - no of periods ] / periodic ytm + principal value * 1/ ( 1+ periodic ytm )^ no of periods

no of periods = 6*2 = 12

periodic ytm = 7.75/2 = 3.875

Coupon = missing = C

1060 = C * [ 1 - 1.03875^-12] /0.03875 + 1000 * 1 / 1.03875^12

1060 = C * 9.4535 + 1000 * 0.633676

C = ( 1060- 633.68 ) / 9.4535

= $45.10

Now after 3 years

no of periods = 3*2 = 6

periodic ytm = 9/2 = 4.50

Coupon = 45.10

Price of bond = 45.10 * [ 1 - 1.045^-6 ] / 0.045 - 1000 * 1/1.045^6

= 45.10 * 5.1579 + 1000 * 0.7679

= $1000.51