Bond J is a 7.8 percent coupon bond. Bond K is a 11.8 percent coupon bond. Both
ID: 2767788 • Letter: B
Question
Bond J is a 7.8 percent coupon bond. Bond K is a 11.8 percent coupon bond. Both bonds have 12 years to maturity and have a YTM of 8.7 percent.
If interest rates suddenly rise by 2.4 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.)
If interest rates suddenly fall by 2.4 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.)
Bond J is a 7.8 percent coupon bond. Bond K is a 11.8 percent coupon bond. Both bonds have 12 years to maturity and have a YTM of 8.7 percent.
Explanation / Answer
Bond J:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 7.8%=$78
r=interest rate =8.7% or 0.087
n= 12 years
Bond Price = 78 x [1-{1(1 +0.087)12]/0.087 + 1,000/(1+0.087)12
=78 x [1-{1/(1.087)12}/0.087 + 1,000/(1.087)12
= 78 x [1- 1/2.721162824/]0.087 + 1,000/2.721162824
= 78 x (1- 0.367489954]0.087+367.49
=78 x [0.63251]/0.087+367.49
=78 x 7.27023 +367.49
=567.078+367.49
=$934.57
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Bond K:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 11.8%=118
r=interest rate =8.7% or 0.087
n= 12 years
Bond Price = 118 x [1-{1(1 +0.087)12]/0.087 + 1,000/(1+0.087)12
=118x [1-{1/(1.087)12}/0.087 + 1,000/(1.087)12
= 118x [1- 1/2.721162824/]0.087 + 1,000/2.721162824
= 118 x (1- 0.367489954]0.087+367.49
=118x [0.63251]/0.087+367.49
=118x 7.27023 +367.49
= 857.8871893+367.49
=$ 1,225.38
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If YTM raises from 8.7 to 11.1 (i.e 2.4 % increase)
Bond J:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 7.8%=$78
r=interest rate =11.1% or 0.111
n= 12 years
Bond Price = 78 x [1-{1(1 +0.111)12]/0.111 + 1,000/(1+0.111)12
=78 x [1-{1/(1.111)12}/0.111 + 1,000/(1.111)12
= 78 x [1- 1/ 3.53645965/]0.111 + 1,000/ 3.53645965
= 78 x (1- 0.282768672]0.111+ 282.7686723
=78 x [0.717231328]/0.111+ 282.7686723
=78 x 6.461543493 + 282.7686723
= 504.0003924+ 282.7686723
=$ 786.77
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Bond K:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 11.8%=118
r=interest rate =11.1% or 0.111
n= 12 years
Bond Price = 118 x [1-{1(1 +0.087)12]/0.111 + 1,000/(1+0.111)12
=118 x [1-{1/(1.111)12}/0.111 + 1,000/(1.111)12
= 118x [1- 1/ 3.53645965/]0.111 + 1,000/ 3.53645965
= 118 x (1- 0.282768672]0.111+ 282.7686723
=118 x [0.717231328]/0.111+ 282.7686723
= x 6.461543493 + 282.7686723
= 762.4621321+ 282.7686723
=$ 1,045.23
% Change in Bonds
Bond J:- [ 934.57-786.77 ]/ 934.57 x 100
= 147.80 / 934.57 x 100
=15.81%
Bond K:- [1,225.38 - 1,045.23 ]/ 1,225.38 x 100
= 180.15 / 1,225.38 x 100
=14.70%
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If YTM decreaes from 8.7 to 6.3 (i.e 2.4 % decrease)
Bond J:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 7.8%=$78
r=interest rate =6.3% or 0.063
n= 12 years
Bond Price = 78 x [1-{1(1 +0.063)12]/0.063 + 1,000/(1+0.063)12
=78 x [1-{1/(1.063)12}/0.063 + 1,000/(1.063)12
= 78 x [1- 1/ 2.081609083/]0.063 + 1,000/ 2.081609083
= 78 x (1- 0.480397596]0.063+ 480.3975963
=78 x [0.519602404]/0.063+480.3975963
=78 x 8.247657202 + 480.3975963
= 643.317+ 480.3975963
=$ 1,123.71
If YTM decreaes from 8.7 to 6.3 (i.e 2.4 % decrease)
Bond K:
Bond Price= C x [1-{1/(1+r)n}]/r + M/(1+r)n
M= Face Value=$1,000 assumed
C= Coupon Amount= 1,000 x 11.8%=$118
r=interest rate =6.3% or 0.063
n= 12 years
Bond Price = 118 x [1-{1(1 +0.063)12]/0.063 + 1,000/(1+0.063)12
=118x [1-{1/(1.063)12}/0.063 + 1,000/(1.063)12
= 118 x [1- 1/ 2.081609083/]0.063 + 1,000/ 2.081609083
= 118 x (1- 0.480397596]0.063+ 480.3975963
=118 x [0.519602404]/0.063+480.3975963
=118 x 8.247657202 + 480.3975963
= 973.2235498+ 480.3975963
=$ 1,453.62
% Change in Bonds
Bond J:- [ 934.57- 1,123.71 ]/ 934.57 x 100
= (189.15) / 934.57 x 100
=(20.24)%
Bond K:- [1,225.38 - 1,453.62 ]/ 1,225.38 x 100
= (228.24) / 1,225.38 x 100
= (18.63)%