In: Finance
A 16-year, 4.5 percent coupon bond pays interest annually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent?
a. |
0.21% increase |
|
b. |
2.14% decrease |
|
c. |
$19.19 increase |
|
d. |
1.97% increase |
Find the price of the bond when the yield to maturity is 5.5% and | ||||||||||||||||
then find the price of the bond when the yield to maturity is 5.7%. | ||||||||||||||||
Par/Face value | 1000 | |||||||||||||||
Annual Coupon rate | 0.045 | |||||||||||||||
Annual coupon | 45 | |||||||||||||||
Present Value = Future value/ ((1+r)^t) | ||||||||||||||||
where r is the interest rate that is .055 and t is the time period in years. | ||||||||||||||||
price of the bond = sum of present values of future cash flows | ||||||||||||||||
r | 0.055 | |||||||||||||||
mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
future cash flow | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 1045 |
present value | 42.65403 | 40.43036 | 38.32261 | 36.32475 | 34.43105 | 32.63606 | 30.93466 | 29.32195 | 27.79332 | 26.34438 | 24.97097 | 23.66917 | 22.43523 | 21.26562 | 20.15699 | 443.6872 |
sum of present values | 895.38 | |||||||||||||||
When the yield is 5.5% the price is $895.38. | ||||||||||||||||
r | 0.057 | |||||||||||||||
mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
future cash flow | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 45 | 1045 |
present value | 42.57332 | 40.2775 | 38.10549 | 36.05061 | 34.10653 | 32.2673 | 30.52724 | 28.88103 | 27.32358 | 25.85012 | 24.45613 | 23.1373 | 21.88959 | 20.70917 | 19.5924 | 430.4438 |
sum of present values | 876.19 | |||||||||||||||
When the yield is 5.7% the price is $876.19. | ||||||||||||||||
When the yield increases from 5.5% to 5.7%, the price of the bond decreases | ||||||||||||||||
from 895.38 to 876.19. | ||||||||||||||||
% change in price | (876.19 - 895.38)/895.38 | |||||||||||||||
% change in price | -2.14% | |||||||||||||||
b) 2.14% decrease. |