Question

Bond J has a coupon of 7.2 percent. Bond K has a coupon of 11.2 percent. Both bonds have 12 years to maturity and have a YTM of 8.4 percent.

a. If interest rates suddenly rise by 1.8 percent, what is the percentage price change of these bonds? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

%Δ in Price

Bond J: %

Bond K:   %

b. If interest rates suddenly fall by 1.8 percent, what is the percentage price change of these bonds? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

%Δ in Price

Bond J: %

Bond K:   %

Answer 1

Bond J

K = N

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

k=1

K =12

Bond Price =∑ [(7.2*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^12

k=1

Bond Price = 911.41

Bond K

K = N

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

k=1

K =12

Bond Price =∑ [(11.2*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^12

k=1

Bond Price = 1206.71

a

b

Change in YTM =-1.8

Bond J

K = Nx2

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

k=1

K =12x2

Bond Price =∑ [(7.2*1000/200)/(1 + 6.6/200)^k]     +   1000/(1 + 6.6/200)^12x2

k=1

Bond Price = 1049.2

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

%age change in price = (1049.2-911.41)*100/911.41

= 15.12%

Bond K

K = Nx2

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

k=1

K =12x2

Bond Price =∑ [(11.2*1000/200)/(1 + 6.6/200)^k]     +   1000/(1 + 6.6/200)^12x2

k=1

Bond Price = 1377.22

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

%age change in price = (1377.22-1206.71)*100/1206.71

= 14.13%