Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 2 years to maturity, whereas Bond Dave has 12 years to maturity. (Do not round your intermediate calculations.)

Requirement 1: (a) If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Sam?

(b) If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Dave?

Requirement 2: (a) If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Sam be then?

(b) If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Dave be then?

Answer 1

Part 1

Change in YTM =5

Bond Sam

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(9*1000/200)/(1 + 14/200)^k]     +   1000/(1 + 14/200)^2x2

k=1

Bond Price = 915.32

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

%age change in price = (915.32-1000)*100/1000

= -8.47%

Bond Dave

K = Nx2

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

k=1

K =12x2

Bond Price =∑ [(9*1000/200)/(1 + 14/200)^k]     +   1000/(1 + 14/200)^12x2

k=1

Bond Price = 713.27

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

%age change in price = (713.27-1000)*100/1000

= -28.67%

Part 2

Change in YTM =-5

Bond Sam

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(9*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^2x2

k=1

Bond Price = 1095.19

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

%age change in price = (1095.19-1000)*100/1000

= 9.52%

Bond Dave

K = Nx2

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

k=1

K =12x2

Bond Price =∑ [(9*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^12x2

k=1

Bond Price = 1472.85

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

%age change in price = (1472.85-1000)*100/1000

= 47.29%