Question

Both Bond Bill and Bond Ted have 11.2 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 4 years to maturity, whereas Bond Ted has 21 years to maturity. Both bonds have a par value of 1,000. a. If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds? (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 3 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Bond Bill Bond Ted % % a. Percentage change in price b. Percentage change in price % %

Answer 1

When the bond is priced at par value = YTM = Coupon rate. Hence, YTM currently = 11.2%

Part (a)

Interest rate rises by 3% then YTM = 11.2% + 3% = 14.2%

Bond Bill price = - PV (Rate, Nper, PMT, FV) = - PV (14.2%/2, 4 x 2, 11.2%/2 x 1000, 1000) =  910.78

Hence, %age change =  910.78 /1,000 - 1 = -8.92%

Bond Ted price = - PV (Rate, Nper, PMT, FV) = - PV (14.2%/2, 21 x 2, 11.2%/2 x 1000, 1000) =   800.58

Hence, %age change =   800.58 /1,000 - 1 = -19.94%

Part (b)

Interest rate falls by 3% then YTM = 11.2% - 3% = 8.2%

Bond Bill price = - PV (Rate, Nper, PMT, FV) = - PV (8.2%/2, 4 x 2, 11.2%/2 x 1000, 1000) =   1,100.58  

Hence, %age change =   1,100.58/1,000 - 1 = 10.06%

Bond Ted price = - PV (Rate, Nper, PMT, FV) = - PV (8.2%/2, 21 x 2, 11.2%/2 x 1000, 1000) =  1,298.19

Hence, %age change = 1,298.19 /1,000 - 1 = 29.82%

Hence, your final answers:

	Bond Bill	Bond Ted
Part (a)	-8.92%	-19.94%
Part (b)	10.06%	29.82%