Question

Sally has won the grand prize in a lottery and must choose between the following three options:


A. Receive a lump sum payment of $10,000,000

B. Receive annual end of year payments $2,000,000 for the next 8 years:

C. Receive annual end of the year payments of $1,500,000 for the next 20 years:

Which option should Sally chose based on annual investment of rate of 6%?

Answer 1

First -- there's no guarantee today that the investment rate is or will ever be 6% again.

Second, option C. is out if Sally is elderly.

What do you think?

Answer 2

Assume a constant investment rate of 6% indefinitely, and that Sally has a life expectancy of over 20 years.

Also, assume that the winnings are deposited the money in a trust fund independent of the lottery company.

A.
Future value at the end of 8 years
=10M*1.06^8
=15.938M$
Future value at the end of 20 years
=32.071M$

B. future value of 8 yearly payments
=2M$*(1.06^8-1)/(1.06-1)
=19.795M$ > 15.93 M$
i.e. better choice than A.

C. Future value of 20 yearly payments of 1.5M$
=1.5*(1.06^20-1)/(1.06-1)
=55.178M$ > 32.07M$
i.e. better choice than A.

Now compare B and C by investing the future value of B (after 8 years) for the following 12 years at 6%.

Future value of option B after 12 more years
= 19.795M$ * 1.06^12
= 39.831M$ < 55.178M$

Thus option C is by far the most advantageous, assuming all the pre-conditions are met.