Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent.
ID: 2771760 • Letter: B
Question
Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 6 percent.
If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amounts 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.)
What if rates suddenly fall by 2 percent instead? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amounts 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.)
Explanation / Answer
Suppose both bond is of face value of $ 100
Bond J:
Coupon rate=3%
Bond K=9%
Years to Maturity= 12 years
YTM=6%
Current Price of Bond J=Coupan Amount*cumulative discount factor upto 12 years+Maturity amount*discount factor of 12th Year
=3*8.384+100*.497
=$ 74.85
If Interest rate is rises by 2%,
Then Price =5*8.384+100*.497
=$ 91.62,
Bond K,
Current Price=9*8.384+100*.497
=$ 125.15
If interest rate is rise by 2%
Price=11*8.384+100*.497
=141.92
Bond J:
Price before interest rises=74.85
Price after interest rises=91.62
% Change in Price=(91.62-74.85/74.85)*100
=22.40%
Bond K,
Price Before Change=125.15
Price after change=141.92
% Change in price=(141.92-125.15/125.15)*100
=13.40%
In second part if Interest rate is fall by 2%
Bond J:
Price Before change of Price=74.84
Price after change of Price=58.08
Change in Price=(74.84-58.08/74.84)*100
=28.86%
Bond K:
Price Before=125.15
Price after=108.38
Change=15.47%