Bond J has a coupon rate of 5.8 percent. Bond S has a coupon rate of 15.8 percen
ID: 2786166 • Letter: B
Question
Bond J has a coupon rate of 5.8 percent. Bond S has a coupon rate of 15.8 percent. Both bonds have eleven years to maturity, make semiannual payments, a par value of $1,000, and have a YTM of 12.6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (A negative answer 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 Bond J % Bond S % If interest rates suddenly fall by 2 percent instead, what is the percentage price change of these bonds?
Explanation / Answer
(A) Bond J:-
Coupon Rate = 5.8%
Maturity Period = 11 years
Payments = Semi annually
Value at Par = $1000
Ytm =12.6%
Solve:-
1. Calculation of price of bond when coupon rate is 5.8%.
Bo= 29/(1+.063)^1+..............+29(1+.063)^22+1000(1+.063)^22
=29*pvaf(6.3%,22years)+1000*pvf(6.3%,22years)
=29*11.73+1000*.261
=340.17+261
=$601.17
2. If the interest rate rise by 2%
Revised Coupon rate = 5.8% +2%=7.8%
caalcuulation of value of bond:
Bo=39/(1+.063)^1+................+39(1+.063)^22+1000(1+.063)^22
=39*Pvaf(6.3%,22 years)+1000(6.3%,22years)
=39*11.73+1000*.261
=457.47+261
=$718.47
3.If the interest rate fall by 2%.
Revised Coupon Rate= 5.8%-2%=3.8%
Calculation of value of bond:
Bo=19*pvaf(6.3%,22years)+1000pvf(6.3%,22years)
=19*11.73+1000*261
=222.87+261
=$483.87
4.calcculation of % change in price due to incrrease in interest rate:
=$718.47-$601.17/$601.17
=19.51%
5. Calculation of % change in price due to faall in inteereest rate:
=$483.87-$601.17/$601.17
=19.51%
(B) Bond S:-
Coupon Rate = 15.8%
Maturity Period = 11 years
Payments = Semi annually
Value at Par = $1000
Ytm =12.6%
Solve:-
1. Calculation of price of bond when coupon rate is 15.8%.
Bo= 79/(1+.063)^1+..............+79(1+.063)^22+1000(1+.063)^22
=79*pvaf(6.3%,22years)+1000*pvf(6.3%,22years)
=79*11.73+1000*.261
=926.67+261
=$1187.67
2. If the interest raate rise by 2%
Revised Coupon rate = 15.8% +2%=17.8%
caalcuulation of value of bond:
Bo=89/(1+.063)^1+................+89(1+.063)^22+1000(1+.063)^22
=89*Pvaf(6.3%,22 years)+1000(6.3%,22years)
=89*11.73+1000*.261
=1043.97+261
=$1304.97
3.If the interest rate fall by 2%.
Revised Coupon Rate=1 5.8%-2%=13.8%
Calculation of value of bond:
Bo=69*pvaf(6.3%,22years)+1000pvf(6.3%,22years)
=69*11.73+1000*261
=692.07+261
=$953.07
4.calcculation of % change in price due to incrrease in interest rate:
=$1304.97-$1187.67/$1187.67
=9.88%
5. Calculation of % change in price due to fall in interest rate:
=$953.07-$1187.67/$1187.67
=19.75%