Question

1. Rackawieca Corp. has issued a 7% annual coupon bond with a par of $1,000 and with 2 years to maturity.
   1. Find the value of this bond if the required rate of return is 7%.
   2. Say the price of this bond dropped by $50 later this afternoon. What is the YTM of this bond at the lower price?
   3. Calculate the duration and modified duration of this bond. Demonstrate that the modified duration is a reasonable measure of interest rate sensitivity of this bond.

Answer 1

1.
=Coupon rate*par value/yield*(1-1/(1+yield)^t)+par value/(1+yield)^t
=7%*1000/7%*(1-1/1.07^2)+1000/1.07^2=1000

2.
Using financial calculator
N=2
PMT=7%*1000=70
PV=-950
FV=1000
CPT I/Y=9.87617%

3.
Duration=Sum(t*Cash flow at time t/(1+yield)^t)/Price=(1*7%*1000/1.07+2*7%*1000/1.07^2+2*1000/1.07^2)/1000=1.934579439

Modified Duration=Duration/(1+yield)=1.934579439/1.07=1.8080182

Lets say rates rise by 1%,
Using Modified Duration: New Price=1000*(1-1.8080182*1%)=981.919818

Using exact formula: New Price=7%*1000/8%*(1-1/1.08^2)+1000/1.08^2=982.1673525

Price using both is very close and hence modified duration is a reasonable estimate of rate sensitivity of this bond