Question

A bond was issued three years ago at a price of $1,050 with a maturity of six years, a yield-to-maturity (YTM) of 6.50% 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 7.75% compounded semi-annually

Answer 1

$967.20

Step-by-step explanation:

the YTM formula = {coupon + [(face value - present value)/time]} / [(face value + present value)/2]

to determine the coupon rate we fill the equation with the known factors:

0.065 = {coupon + [(1,000 - 1,050)/12]} / [(1,000 + 1,050)/2]

0.065 = (coupon - 41.67) / 1,025

66.625 = coupon - 4.167

coupon = 66.625 + 4.167 = $70.792

three years later, the YTM = 7.5%, what is the PV? Again we use the YTM formula:

0.0775 = {70.792 + [(1,000 - x)/6]} / [(1,000 + x)/2]

0.0775(500 + 0.5x) = 70.792 + 166.67 - 0.1667x

38.75 + 0.03875x = 237.462 - 0.1667x

0.20545x = 198.712

x = 198.712 / .20545

x = $967.20