Bond X has a coupon of 52 percent Bond Z has a coupon of 92 percent. Both bonds have 15 years to maturity and have a YTM of 74 percent a. If interest rates suddenly rise by 1.6 percent, what is the percentage price change of these bonds? (A negative value should be indicated by a minus sign. Do not rod inte calculations. Enter your answers as a percent rounded to 2 decimal places) b. If interest rates suddenly fall by 1.6 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.) - What is your conclusion?

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a. Using the bond price formula:

Bond X price = (52/0.74)*(1 - 1/(1+0.74)^15) = $38.13
Bond Z price = (92/0.74)*(1 - 1/(1+0.74)^15) = $67.84

When interest rates rise by 1.6%, the new YTM is 0.74+0.016=0.756.

Bond X new price = (52/0.756)*(1 - 1/(1+0.756)^15) = $33.63
Bond Z new price = (92/0.756)*(1 - 1/(1+0.756)^15) = $59.91

The percentage price change for Bond X is (33.63-38.13)/38.13 = -11.79%
The percentage price change for Bond Z is (59.91-67.84)/67.84 = -11.71%

b. When interest rates fall by 1.6%, the new YTM is 0.74-0.016=0.724.

Bond X new price = (52/0.724)*(1 - 1/(1+0.724)^15) = $43.04
Bond Z new price = (92/0.724)*(1 - 1/(1+0.724)^15) = $77.72

The percentage price change for Bond X is (43.04-38.13)/38.13 = 12.88%
The percentage price change for Bond Z is (77.72-67.84)/67.84 = 14.55%

Conclusion: Bond Z has a higher percentage price change in both scenarios, indicating that it is more sensitive to changes in interest rates. This is because it has a higher coupon rate and longer maturity compared to Bond X.