Q: You are looking at the valuation of some risk-free government bonds. It has been observed that the current 3-year discount factor for risk-free cash flows is 0.68. All bonds are assumed to have a par value of $100 and all cash flows occur at the end of the year.

(a) Propose the fair price for a zero-coupon bond that matures in exactly 3 years.

(b) Your friend makes the following comments about the above bond: "Since there is no risk of default and there are no coupons to reinvest, buying the 3-year zero-coupon bond today is a risk-free investment. In addition, the guaranteed risk-free annual rate of return is 13.72%." Analyse if you would agree entirely with this statement. (c) In addition to the bond observed in part (a), you also note the following:

• A 2-year coupon bond paying 10% annual coupons with a market price of $97.
• Two annuities that are priced exactly the same. 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 the above information, compute the term structure of interest rates and determine the 1-year and 2-year discount factors, d1 and d2 respectively. Also, calculate the price of each of the annuities. (d) Assume that the observed discount factors are such that d1 < d2 < d3. Analyse why it would be odd to observe such a situation in a competitive market.