Question

Bond J has a coupon rate of 7 percent and Bond K has a coupon rate of 13 percent. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 10 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.)

Percentage change in price of Bond J % ???

Percentage change in price of Bond K % ???

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.)

Percentage change in price of Bond J % ???

Percentage change in price of Bond K % ???

Answer 1

suppose the par value of bond J & K = 1000

now the value of bond J = 35*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 35*13.799+1000*0.310068

= 482.9525 + 310.068

= 793.02

value of bond K = 65*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 65*13.799+1000*0.310068

= 896.9117 + 310.068

= 1206.98

now calculation of value of bond when interest rates rise sudden by 2% -

now the interest rate of bond J & K will be 9% and 15% respectively.

now the value of bond J = 45*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 45*13.799+1000*0.310068

= 620.9389 + 310.068

= 931.0068

value of bond K = 75*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 75*13.799+1000*0.310068

= 1034.898 + 310.068

= 1344.966

% change in price of bond J = (931.0068 - 793.02)/793.02

= 137.9868/793.02

= 17.40%

% change in price of bond K = (1344.966 - 1206.98)/1206.98

= 137.986/1206.98

11.43%

now calculation of value of bond when interest rates decrease sudden by 2% -

now the interest rate of bond J & K will be 5% and 11% respectively.

now the value of bond J = 25*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 25*13.799+1000*0.310068

= 344.966 + 310.068

= 655.034

value of bond K = 55*PVIFA(5%, 24) +1000* PVIF(5%,24)

= 55*13.799+1000*0.310068

= 758.9253 + 310.068

= 1068.993

% change in price of bond J = (655.034 - 793.02)/793.02

= 137.986/793.02

= -17.40%

% change in price of bond K = ( 1068.993- 1206.98)/1206.98

= 137.986/1206.98

= -11.43%

Please comment in case of any clarification required.