Question

Bond J has a coupon rate of 4.8 percent. Bond K has a coupon rate of 14.8 percent. Both bonds have eleven years to maturity, a par value of $1,000, and a YTM of 10.6 percent, and both make semiannual payments.

a.	If interest rates suddenly rise by 2 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 interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

a.Percentage change in price%%

Bond J Bond K

b.Percentage change in price%%

Bond J Bond K

Answer 1

Coupon of Bond J = 4.8%*1000/2 = 24
Number of Periods = 2*11 = 22
Semi annual YTM =10.6%/2 = 5.3%
Price of Bond J = PV of Coupons + PV of Par Value =24*((1-(1+5.3%)^-22)/5.3%) +1000/(1+5.3%)^22= 628.5003

Coupon of Bond K = 14.8%*1000/2 = 74
Price of Bond K = PV of Coupons + PV of Par Value =74*(1-(1+5.3%)^-22)/5.3%+1000/(1+5.3%)^22= 1269.0170

a) If interest rate increase by 2% then
Semi annual YTM = 12.6%/2 = 6.3%
Price of Bond J = PV of Coupons + PV of Par Value =24*((1-(1+6.3%)^-22)/6.3%) +1000/(1+6.3%)^22 = 542.3854
% Change in price of Bond J =(542.3854-628.5003)/628.5003=-13.70%

Price of Bond K = PV of Coupons + PV of Par Value =74*(1-(1+6.3%)^-22)/6.3%+1000/(1+6.3%)^22=1129.071
% Change in price of Bond J = (1129.071-1269.0170)/1269.0170= -11.03%

b) If interest rate decrease  by 2% then
Semi annual YTM = 8.6%/2 = 4.3%
Price of Bond J = PV of Coupons + PV of Par Value =24*((1-(1+4.3%)^-22)/4.3%) +1000/(1+4.3%)^22 = 733.1364
% Change in price of Bond J =(733.1364-628.5003)/628.5003=16.65%

Price of Bond K = PV of Coupons + PV of Par Value =74*(1-(1+4.3%)^-22)/4.3%+1000/(1+4.3%)^22=1435.4090
% Change in price of Bond J = (1435.4090-1249.95)/1249.95 =13.11%