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?

The lump sum is always better.

The payments over time are always better.

It will depend on the interest rate; advise her to get a calculator.

None of these answers is good advice.

Answer 1

(1) Interest rate = 9%

PV of installment payments = 1,000 + 1,000 x P/F(9%, 1) + 1,000 x P/F(9%, 2)

= 1,000 x (1 + 0.9174 + 0.8417) = 1,000 x 2.7591 = 2,759.1

The winner would be better off accepting the lump-sum payment, since that choice has the greater present value.

(2) Interest rate = 11%

PV of installment payments = 1,000 + 1,000 x P/F(11%, 1) + 1,000 x P/F(11%, 2)

= 1,000 x (1 + 0.9009 + 0.8116) = 1,000 x 2.7125 = 2,712.5

The winner would be better off accepting the lump-sum payment, since that choice has the greater present value.

(3) It will depend on the interest rate; advise her to get a calculator.