Question

you observe the following: a 2-year coupon bond

paying 10% annual coupons with a market price of $97, and two annuities that

are trading at the same market price as each other. The first annuity matures in 3

years and pays annual cash flows of $20, while the second annuity pays annual

cash flows of $28 and matures in 2 years. Using this information:

i. Complete the term structure of interest rates, i.e. determine the one- and

two-year discount factors, d1 and d2, respectively.

ii. Determine the price of the annuities.

Answer 1

First we find the YTM on 2-year coupon bond

Using a financial calculator

PV = -97

PMT = 10

N = 2

FV = 100

cpt I/Y, we get I/Y = 11.77

Hence, two year discount rate = 11.77%

i) One year discount factor = 1/(1+11.77%) = 0.8947

Two year discount factor = 1/((1+11.77%)^2) = 0.8005

ii) Price of the 2 year annuity is found out by multiplying the cash-flows by the discount factor

Price of the 2 year annuity = 28*0.8947 + 28*0.8005 = $47.4656

Hence, Price of the 3 year annuity =Price of the 2 year annuity = $47.4656