On 1/1/10, the following is observed for grade AAA (ìrisk-freeî) bonds: - A bond maturing on 12/31/12 with coupon 6.0% and face value $1000 is selling at $1112.80 - A bond maturing on 12/31/12 with coupon 5.0% and face value $1000 is selling at $1084.00 - A T-bill maturing on 12/31/10 is quoted with a yield to maturity of 2.0408%. Assume that bond coupons are paid annually on 12/31.
a) Find the price as of 1/1/10 of $1 delivered in one year (p1).
b) Find the prices as of 1/1/10 of $1 delivered in two years and three years (p2 and p3). (HINT: You may need to solve a system of equations)
c) Write down the cash áows of a three-year risk-free bond that has face value of $1,000 and pays coupon C each year-end.
d) What is the coupon rate (coupon divided by face value) which must be paid for a newly-issued (on 1/1/10) three-year risk-free bond with face value of $1000 to sell at par? (ìsell at Parî means market value = face (or principal) value.) Use your prices from a) and b).
e) What is the coupon rate which must be paid for a newly-issued (on 1/1/10) two-year risk-free bond to sell at par?