Question

14. (Bonds) A bond with a $1,000 par, 6 years to maturity, a coupon rate of 5%, and annual payments has a yield to maturity of 4.3%. What will be the percentage change in the bond price if the yield changes instantaneously to 5%? (If your answer is, e.g., -1.123%, enter it as -1.123. If the sign of the price change is incorrect, no credit will be given.)

Answer 1

Solution:

We know that

Price of bond=Coupon/(1+r)^n+(Coupon+Face Value)^n

Coupon=$1000*.05=$50

r=YTM

Face Value=$1000

Calculaion of Price of bond when YTM is 4.3%

Let the Price of Bond be X

X=$50/(1+.043)+$50/(1+.043)^2+$50/(1+.043)^3+$50/(1+.043)^4+$50/(1+.043)^5+($50+$1000)/(1+.043)^6

=$1036.34

Price of Bond when YTM is 5%

Since the YTM is equal to Coupon rate,hence price of bond shall be equal to face value of bond.

X=$50/(1+.05)+$50/(1+.05)^2+$50/(1+.05)^3+$50/(1+.05)^4+$50/(1+.05)^5+($50+$1000)/(1+.05)^6

=$1000.00

% change in price=($1000-$1036.34)/$1036.34

=-3.51%

Thus, price of is decrease by 3.51% when yield change to 5%