Question

1. Consider the following two bonds.
   • Bond A: 10-year maturity, 4% coupon rate, $1,000 par value
   • Bond B: 5-year maturity, 4% coupon rate, $1,000 par value
     • Assuming that the YTM changes from 6% to 7%, calculate % change in each bond’s price.

Answer 1

Bond A

K = N

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

k=1

K =10

Bond Price =∑ [(4*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^10

k=1

Bond Price = 852.8

Bond B

K = N

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

k=1

K =5

Bond Price =∑ [(4*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^5

k=1

Bond Price = 915.75

Part 1

Change in YTM =1

Bond A

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(4*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^10x2

k=1

Bond Price = 786.81

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

%age change in price = (786.81-852.8)*100/852.8

= -7.74%

Bond B

K = Nx2

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

k=1

K =5x2

Bond Price =∑ [(4*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^5x2

k=1

Bond Price = 875.25

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

%age change in price = (875.25-915.75)*100/915.75

= -4.42%