Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 16 years to maturity.

a.	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 9% for both

Part 1

Change in YTM =2

Bond Sam

K = Nx2

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

k=1

K =3x2

Bond Price =∑ [(9*1000/200)/(1 + 11/200)^k]     +   1000/(1 + 11/200)^3x2

k=1

Bond Price = 950.04

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

%age change in price = (950.04-1000)*100/1000

= -5%

Bond Dave

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(9*1000/200)/(1 + 11/200)^k]     +   1000/(1 + 11/200)^16x2

k=1

Bond Price = 850.96

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

%age change in price = (850.96-1000)*100/1000

= -14.9%

Part 2

Change in YTM =-2

Bond Sam

K = Nx2

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

k=1

K =3x2

Bond Price =∑ [(9*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^3x2

k=1

Bond Price = 1053.29

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

%age change in price = (1053.29-1000)*100/1000

= 5.33%

Bond Dave

K = Nx2

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

k=1

K =16x2

Bond Price =∑ [(9*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^16x2

k=1

Bond Price = 1190.69

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

%age change in price = (1190.69-1000)*100/1000

= 19.07%