Question

A bond with a 8-year duration is worth $1,077, and its yield to maturity is 7.7%. If the yield to maturity falls to 7.57%, you would predict that the new value of the bond will be approximately _________.

Answer 1

$1,085.35

Step-by-step explanation:

we can use the approximate yield to maturity formula to determine the market price of the bond if the interest rate falls to 7.57%

but first we need to calculate the coupon:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

0.077 = {coupon + [(1,000 - 1,077)/8]} / [(1,000 + 1,077)/2]

0.077 = {coupon - 9.625} / 1,038.50

0.077 x 1,038.50 = coupon - 9.625

79.9645 = coupon - 9.625

coupon = 79.9645 + 9.625 = $89.5895 ≈ $89.60

now we can calculate the new market price for the bond:

YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]

0.0757 = {89.60 + [(1,000 - MV)/8]} /

0.0757 x [(1,000 + MV)/2] = 89.60 + [(1,000 - MV)/8]

0.0757 x (500 + 0.5MV) = 89.60 + 125 - 0.125MV

37.85 + 0.03785MV = 214.60 - 0.125MV

0.16285MV = 176.75

MV = 176.75 / 0.16285 = $1,085.35