Question

Consider two bonds, a 3-year bond paying an annual coupon of 6.60% and a 10-year bond also with an annual coupon of 6.60%. Both currently sell at a face value of $1,000. Now suppose interest rates rise to 10%. a. What is the new price of the 3-year bonds? b. What is the new price of the 10-year bonds?

Answer 1

Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 6.6% for both

Part 1

Change in YTM =3.4

Bond A

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(6.6*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^3x2

k=1

Bond Price = 913.71

%age change in price =(New price-Old price)*100/old price

%age change in price = (913.71-1000)*100/1000

= -8.63%

Bond B

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

Bond Price =∑ [(6.6*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^10x2

k=1

Bond Price = 788.14

%age change in price =(New price-Old price)*100/old price

%age change in price = (788.14-1000)*100/1000

= -21.19%