Question

A bond with a 7-year duration is worth $1,088, and its yield to maturity is 8.8%. If the yield to maturity falls to 8.56%, you would predict that the new value of the bond will be approximately $1,085.39 $1,088.00 $1,090.61 $1,104.76

Answer 1

"New value of the bond will be approximately=$1,104.76" is correct

Lets calculate the coupon amount first

Calculation of bond price with 7 year maturity no of period=7*2=14 as bonds making half yearly payment & YTM=(8.8/2)%=4.4% per period

Copon amount per period=1000*r%=x, face value of bond=$1,000

current price of bond=x*(PVIFA,4.4%,14)+ 1000*(PVIF,4.4%,14)

Formula to calculate

PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period

PVIF=1/(1+r)^n where r is the yield to maturity, n = period

Let put the value into above

PVIFA=((1-(1+4.4%)^(-14))/4.4%)

10.28957

PVIF=1/(1+4.4%)^14

0.54726

put this value into above equation

1088=x*(10.28957)+ 1000*(0.54726)

x=(1088- 1000*(0.54726))/10.28957

52.55

Half year coupon=$52.55

Now yield to maturity has been reduced to 8.56%, bond value will be

New price of bond=52.55*(PVIFA,4.28%,14)+ 1000*(PVIF,4.28%,14)

Formula to calculate

PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period

PVIF=1/(1+r)^n where r is the yield to maturity, n = period

Let put the value into above

PVIFA=((1-(1+4.28%)^(-14))/4.28%)

10.37051

PVIF=1/(1+4.28%)^14

0.55614

put this value into above equation

New price of bond=52.55*(10.37051)+ 1000*(0.55614)=$1,101.11