Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, an

Question

Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 3 years to maturity, whereas Bond Ted has 20 years to maturity.Requirement 1:If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)Requirement 2:If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Both Bond Bill and Bond Ted have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 3 years to maturity, whereas Bond Ted has 20 years to maturity.Requirement 1:If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?

Requirement 1

Bond Bill

Coupon 7/2= 5.5%

Assume FV= 1000

Assume YTM= 10% or 10/2= 5%

N= 3x2= 6 yrs

PV= 55PVIFA(5%,6)+1000PVIF(5%,6)= $1025.378

if nterest rates suddenly rise by 2 percent, YTm= 12% or 6%

PV= 55PVIFA(6%,6)+1000PVIF(6%,6)= $975.413

Therefore, percentage change in the price of these bonds= (975.413-1025.378)/1025.378= -4.961%

Bond Ted

Coupon 7/2= 5.5%

Assume FV= 1000

Assume YTM= 10% or 10/2= 5%

N= 20x2= 40 yrs

PV= 55PVIFA(5%,40)+1000PVIF(5%,40)= $1085.80

if nterest rates suddenly rise by 2 percent, YTm= 12% or 6%

PV= 55PVIFA(6%,40)+1000PVIF(6%,40)= $924.769

Therefore, percentage change in the price of these bonds= (924.769-1085.80)/1085.80= -14.83%

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