Bond J is a 5.8 percent coupon bond. Bond K is a 9.8 percent coupon bond. Both b
ID: 2761926 • Letter: B
Question
Bond J is a 5.8 percent coupon bond. Bond K is a 9.8 percent coupon bond. Both bonds have 15 years to maturity and have a YTM of 7.6 percent.
a. If interest rates suddenly rise by 2.2 percent, what is the percentage price change of these bonds? (Negative values 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 J % Bond K %
b. If interest rates suddenly fall by 2.2 percent, what is the percentage price change of these bonds? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
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Explanation / Answer
Solution:
Assumed the payments make in semiannual.
Currently, both bonds have the same YTM. Therefore, their current prices are:
Bond J: n = 30; I = 5.8; PMT = 29; FV = 1,000; YTM = 7.6
PV = 840.522
Bond K: n = 30; I = 9.8; PMT = 49; FV = 1,000; YTM = 7.6
PV = 1,194.918
a) If the YTM increases by 2.2% to 9.8%, the bond prices are:
Bond J: n = 30; I = 5.8; PMT = 29; FV = 1,000; YTM = 9.8
PV = 689.015
Bond K: n = 30; I = 9.8; PMT = 49; FV = 1,000; YTM = 9.8
PV = 1,000
The percentage change in price can be determined using the following equation:
Bond J = (689.015 – 840.522)/ 840.522 = -18.03%
Bond K = (1,000 – 1,194.918)/ 1,194.918 = -16.31%
b) If the YTM decline by 2.2% to 5.4%, the bond prices are:
Bond J: n = 30; I = 5.8; PMT = 29; FV = 1,000; YTM = 5.4
PV = 1,040.766
Bond K: n = 30; I = 9.8; PMT = 49; FV = 1,000; YTM = 5.4
PV = 1,448.423
The percentage change in price can be determined using the following equation:
Bond J = (1,040.766 – 840.522)/ 840.522 = +23.82%
Bond K = (1,448.423 – 1,194.918)/ 1,194.918 = +21.22%