Question

In: Finance

A 16-year, 4.5 percent coupon bond pays interest annually. The bond has a face value of...

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

Solutions

Expert Solution

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.

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