Question

Bond Jay has a coupon rate of 7 percent and bond k has a coupon rate of 13 percent. Both barns have 16 years to maturity, makes semi annual payments, and have a YRM of 10 percent.

if interest rates suddenly rise to percent, what is the percentage price change of these bonds?

If the rates suddenly fall by 2percent instead?

Answer 1

Bond jay

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(7*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^16x2

k=1

Bond Price = 762.96

bond k

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(13*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^16x2

k=1

Bond Price = 1237.04

Change in YTM =2

Bond Jay

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(7*1000/200)/(1 + 12/200)^k]     +   1000/(1 + 12/200)^16x2

k=1

Bond Price = 647.9

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

%age change in price = (647.9-762.96)*100/762.96

= -15.08%

Bond k

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(13*1000/200)/(1 + 12/200)^k]     +   1000/(1 + 12/200)^16x2

k=1

Bond Price = 1070.42

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

%age change in price = (1070.42-1237.04)*100/1237.04

= -13.47%

Change in YTM =-2

Bond Jay

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(7*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^16x2

k=1

Bond Price = 910.63

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

%age change in price = (910.63-762.96)*100/762.96

= 19.35%

Bond k

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(13*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^16x2

k=1

Bond Price = 1446.84

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

%age change in price = (1446.84-1237.04)*100/1237.04

= 16.96%