Question

Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,850 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 9% per year, the winner would be better off accepting the , since that choice has the greater present value. At an interest rate of 11% per year, the winner would be better off accepting , since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend?

Answer 1

(1)

Present value (PV) of payments ($) = 1000 + [1000 / 1.06] + [1000 / (1.06)2] = 1000 + 943 + 890 = 2833

So, winner is better of accepting Payments over time since it has higher PV.

(2)

Present value (PV) of payments ($) = 1000 + [1000 / 1.09] + [1000 / (1.09)2] = 1000 + 917 + 842 = 2759

So, winner is better of accepting Lumpsum since it has higher PV.

(3)

Present value of future payments depend on interest rate and so cannot be advised one-off