Both bond A and bond B have 8.6 percent coupons and are priced at par value. Bon
ID: 2481765 • Letter: B
Question
Both bond A and bond B have 8.6 percent coupons and are priced at par value. Bond A has 8 years to maturity, while bond B has 18 years to maturity.
a. If interest rates suddenly rise by 1.2 percent, what is the percentage change in price of bond A and bond B? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Bond A %
Bond B %
b. If interest rates suddenly fall by 1.2 percent instead, what would be the percentage change in price of bond A and bond B? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Bond A %
Bond B %
Explanation / Answer
Answer: a)
Lets assume the par value of the bond is $1000
Annual payment of Bond A & B = 1000*0.086 = 86
New interest rate = 8.6 %+1.2 % = 9.8 %
Calculation of price of Each bond:
Bond A:
Price = 86*PVIFA(9.8%,8) + 1000*PVIF(9.8%,8)
= 86 *5.3736 +1000*0.4733
= 462.1292 + 473.3
= 935.43
% change in Price of Bond A = (935.43 - 1000)/1000 = - 6.46
Bond B:
Price = 86*PVIFA(9.8%,18) + 1000*PVIF(9.8%,18)
= 86 *8.30681 +1000*0.1858
= 714.385 + 185.8
= 900.185
% change in Price of Bond B = (900.185 - 1000)/1000 = - 9.98
Answer: b)
Lets assume the par value of the bond is $1000
Annual payment of Bond A & B = 1000*0.086 = 86
New interest rate = 8.6% - 1.2 % = 7.4%
Calculation of price of Each bond:
Bond A:
Price = 86*PVIFA(7.4%,8) + 1000*PVIF(7.4%,8)
= 86 *5.8793 +1000*0.5648
= 505.619 + 564.8
= 1070.419
% change in Price of Bond A = (1070.419 - 1000)/1000 =7.04
Bond B:
Price = 86*PVIFA(7.4%,18) + 1000*PVIF(7.4%,18)
= 86 *9.7741 +1000*0.2766
= 840.572 + 276.6
= 1117.1726
% change in Price of Bond B = (1117.1726 - 1000)/1000 = 11.72
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