Question 1.

As a financial advisor, you are consulting a client who has won the lottery. The prize for the competition can be paid in 4 different ways described below. The annual discount rate is 11%.

(1) $1,140,000 now

(2) A one-time payment of $1,000,000 in 5 years and an additional one-time payment of $1,100,000 in 10 years

(3) 5 consecutive annual payments of $400,000, with the first payment made at the end of year 3 (that is, at t=3) and the remaining payments made at the end of each of the four following years

(4) 25 consecutive annual payments, with the first payment of $270,000 made at the end of year 2 and the remaining payments (which occur at year end) declining by 10 % per year.

Questions:

(1a) What is the present value of each alternative and which option would you recommend?

(1b) Suppose that your client would like to replace alternative (1) with a perpetual stream of consecutive annual payments (made at year-end), which starts at the end of year 5 and grows by 6% per year forever. What should be the amount of the first payment at the end of year 5 so that you are indifferent between these two alternatives?

(1c) You are comparing alternative (2) to a stream of annual inflows of $160,000 each (payments occur at year-end), with the first payment made at the end of year 1. What is the minimum whole number of payments in this new income stream that would make it more valuable than alternative (2) in present value terms?