Consider three bonds with 57% coupon rates, all selling at face value. The short
ID: 2782133 • Letter: C
Question
Consider three bonds with 57% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years a. what will be the price of each bond if their yields increase to 67%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 4 Years $L 8 Years 30 Years Bond price b. what will be the price of each bond if their yields decrease to 47%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 4 Years 8 Years 30 Years Bond priceExplanation / Answer
1-
present value annuity factor
1-(1+r)^-n / r
present value factor
1/(1+r)^n
when yield increases to 6.7%
PVAF at 6.7% for 4 years
1-(1.067)^-4 /.067
3.4102
PVF
1/1.067^4
0.771511
value of 4 year bond
interest*PVAF + Face value*PVF
57*3.4102 + 1000*.7715
965.88
when yield increases to 6.7%
PVAF at 6.7% for 8 years
1-(1.067)^-8 /.067
6.041
PVF
1/1.067^8
0.59523
value of 8 year bond
interest*PVAF + Face value*PVF
57*6.041 + 1000*.5952
939.54
when yield increases to 6.7%
PVAF at 6.7% for 30 years
1-(1.067)^-30 /.067
12.792
PVF
1/1.067^30
0.142912
value of 30 year bond
interest*PVAF + Face value*PVF
57*12.792 + 1000*.1429
872.04
2-
present value annuity factor
1-(1+r)^-n / r
present value factor
1/(1+r)^n
when yield increases to 4.7%
PVAF at 4.7% for 4 years
1-(1.047)^-4 /.047
3.57
PVF
1/1.047^4
0.832172
value of 4 year bond
interest*PVAF + Face value*PVF
57*3.57 + 1000*.8321
1035.59
when yield increases to 4.7%
PVAF at 4.7% for 8 years
1-(1.047)^-8 /.047
6.5423
PVF
1/1.047^8
0.692511
value of 8 year bond
interest*PVAF + Face value*PVF
57*6.5423 + 1000*.6925
1065.41
when yield decreases to 4.7%
PVAF at 4.7% for 30 years
1-(1.047)^-30 /.047
15.912
PVF
1/1.047^30
0.252116
value of 30 year bond
interest*PVAF + Face value*PVF
57*15.912 + 1000*.2521
1159.08
1-
present value annuity factor
1-(1+r)^-n / r
present value factor
1/(1+r)^n
when yield increases to 6.7%
PVAF at 6.7% for 4 years
1-(1.067)^-4 /.067
3.4102
PVF
1/1.067^4
0.771511
value of 4 year bond
interest*PVAF + Face value*PVF
57*3.4102 + 1000*.7715
965.88
when yield increases to 6.7%
PVAF at 6.7% for 8 years
1-(1.067)^-8 /.067
6.041
PVF
1/1.067^8
0.59523
value of 8 year bond
interest*PVAF + Face value*PVF
57*6.041 + 1000*.5952
939.54
when yield increases to 6.7%
PVAF at 6.7% for 30 years
1-(1.067)^-30 /.067
12.792
PVF
1/1.067^30
0.142912
value of 30 year bond
interest*PVAF + Face value*PVF
57*12.792 + 1000*.1429
872.04
2-
present value annuity factor
1-(1+r)^-n / r
present value factor
1/(1+r)^n
when yield increases to 4.7%
PVAF at 4.7% for 4 years
1-(1.047)^-4 /.047
3.57
PVF
1/1.047^4
0.832172
value of 4 year bond
interest*PVAF + Face value*PVF
57*3.57 + 1000*.8321
1035.59
when yield increases to 4.7%
PVAF at 4.7% for 8 years
1-(1.047)^-8 /.047
6.5423
PVF
1/1.047^8
0.692511
value of 8 year bond
interest*PVAF + Face value*PVF
57*6.5423 + 1000*.6925
1065.41
when yield decreases to 4.7%
PVAF at 4.7% for 30 years
1-(1.047)^-30 /.047
15.912
PVF
1/1.047^30
0.252116
value of 30 year bond
interest*PVAF + Face value*PVF
57*15.912 + 1000*.2521
1159.08