Question

The one-year forward rate 1 year from today is 5%; the one-year forward rate 2 years from today is 5.5%; the one-year forward rate 3 years from today is 6%; the one-year forward rate 4 year from today is 6.5%; and the one-year forward rate 5 years from today is 7%. What should the purchase price of a 2-year zero-coupon bond be if it is purchased at the beginning of year 2 and has face value of $1,000?

Answer 1

Given different forward rates at different year ends.

Since, as given in the question, the purchase price has to be arrived for the period 2 years ahead of 2 year beginning, which is nothing but 2 year ahead of end of year 1, the correct rate to be selected is one year forward rate of 2 years from now, which is 5.50%.

The purchase price = 1000 * PV factor discounted by the appropriate interest rate.

Therefore, the present value = 1000 * PV factor of 2 years @ 5.50%

= 1000 * (0.890 + 0.907) / 2 = 1000 * 0.8985 = $ 898.50