ABC Corp. expects to make payment of one time lump sum cash flow of $10 million in 10 years. The firm would like to immunize its liability by investing in two different securities: an annuity paying $1 million for the next 5 years annually and a perpetuity paying $50,000 annually forever. Each of the securities has a 5% yield.

1. (15 points) Find the Macaulay's duration for (i) the lump sum liability, (ii) the 5-year annuity and, (iii) the perpetuity. Show calculations.

2. (15 points) Calculate the convexity for each of the three securities. Show calculations.