You are the treasurer of a company and are obliged to arrange for a debt payment of $1 million that is due 3 years later. Assume annual compounding and annual coupon payment.

The term structure of interest rates is flat at r = 10%. In order to prepare for the debt you decide to invest in a portfolio of 1-year 10% coupon bond and 5-year 10% coupon bonds. Both bonds have a face value of $1000 per share. How many shares of each bond should you buy, not only to fund the obligation but also to insure against having to invest more in the future to make up for any shorfall if interest rates change?