You want to buy a 3 year bond with a coupon rate of 22%, annual coupons, and a face value of 1000. You know that 1 year zero coupon bonds (ZCBs) trade a yield to maturity of 12%, 2 year ZCBs trade at a yield to maturity of 9%, and 3 year ZCBs trade at a yield to maturity of 7.5%.
(a) What is the price of this 3 year 22% coupon rate bond?
(b) What is the yield to maturity on this 3 year 22% coupon rate bond?
(c) What does the market expect the rate on a 1-year zero coupon bond will be two years from now (what is the implied forward rate)?
(d) What does the market expect the rate on a 2-year zero coupon bond will be one year from now?
(e) Assume you buy the coupon bond and then you decide you do not need money until the end of three years. As a result, when you receive the coupons in years 1 and 2, you will reinvest them at the prevailing market rate (assume these will be the forward rates you calculated in parts c and d). How much money will you have at the end of the 3 years? What rate of return will you receive on your investment?