Bond J is a 6 percent coupon bond. Bond K is a 12 percent coupon bond. Both bond
ID: 2627713 • Letter: B
Question
Bond J is a 6 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have 20 years to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))) Percentage change in price of Bond J % Percentage change in price of Bond K % What if rates suddenly fall by 2 percent instead? (Round your answers to 2 decimal places. (e.g., 32.16)) Percentage change in price of Bond J % Percentage change in price of Bond K %
Explanation / Answer
Current Prices:
Bond J:
Nper = 20*2 = 40 (indicates the period over which the payments are made)
PMT = 1000*6%*1/2 = 30 (indicates interest payment)
Rate = 9%/2 = 4.5% (indicates YTM semiannual)
FV = 1000 (indicates par value)
Current Price = PV(Rate,Nper,PMT,FV) = PV(4.5%,40,30,1000) = 723.98
Bond K:
Nper = 20*2 = 40 (indicates the period over which the payments are made)
PMT = 1000*12%*1/2 = 60 (indicates interest payment)
Rate = 9%/2 = 4.5% (indicates YTM semiannual)
FV = 1000 (indicates par value)
Current Price = PV(Rate,Nper,PMT,FV) = PV(4.5%,40,60,1000) = 1276.02
Part A:
Bond J (Revised Prices) = PV(Rate,Nper,PMT,FV) = PV(5.5%,40,30,1000) = 598.85
Bond K (Revised Prices) = PV(Rate,Nper,PMT,FV) = PV(5.5%,40,60,1000) = 1080.23
% Change in Price (Bond J) = (598.85 - 723.98)/723.98*100 = -17.28%
% Change in Price (Bond K) = (1080.23 - 1276.02)/1276.02*100 = -15.34%
Part B:
Bond J (Revised Prices) = PV(Rate,Nper,PMT,FV) = PV(3.5%,40,30,1000) = 893.22
Bond K (Revised Prices) = PV(Rate,Nper,PMT,FV) = PV(3.5%,40,60,1000) = 1533.88
% Change in Price (Bond J) = (893.22 - 723.98)/723.98*100 = 23.38%
% Change in Price (Bond K) = (1533.88 - 1276.02)/1276.02*100 = 20.21%