Question

Both Bond A and Bond B have 7.2 percent coupons and are priced at par value. Bond A has 6 years to maturity, while Bond B has 16 years to maturity.

a. If interest rates suddenly rise by 1.6 percent, what is the percentage change in price of Bond A and Bond B? (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.)

b. If interest rates suddenly fall by 1.6 percent instead, what would be the percentage change in price of Bond A and Bond B?

Answer 1

Because bonds are priced at par that means original price = 1000 and YTM =coupon rate = 7.2% for both

Part 1

Change in YTM =1.6

Bond A

K = N

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

k=1

K =6

Bond Price =∑ [(7.2*1000/100)/(1 + 8.8/100)^k]     +   1000/(1 + 8.8/100)^6

k=1

Bond Price = 927.8

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

%age change in price = (927.8-1000)*100/1000

= -7.22%

Bond B

K = N

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

k=1

K =16

Bond Price =∑ [(7.2*1000/100)/(1 + 8.8/100)^k]     +   1000/(1 + 8.8/100)^16

k=1

Bond Price = 865.34

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

%age change in price = (865.34-1000)*100/1000

= -13.47%

Part 2

Change in YTM =-1.6

Bond A

K = N

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

k=1

K =6

Bond Price =∑ [(7.2*1000/100)/(1 + 5.6/100)^k]     +   1000/(1 + 5.6/100)^6

k=1

Bond Price = 1079.68

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

%age change in price = (1079.68-1000)*100/1000

= 7.97%

Bond B

K = N

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

k=1

K =16

Bond Price =∑ [(7.2*1000/100)/(1 + 5.6/100)^k]     +   1000/(1 + 5.6/100)^16

k=1

Bond Price = 1166.23

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

%age change in price = (1166.23-1000)*100/1000

= 16.62%