MBA Finance

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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%?

  • MBA Finance -

    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?

  • MBA Finance -

    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.

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