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Oftentimes, I will discuss “what if” scenarios that are not so pleasant (e.g., what if the investment goes belly-up? what if the market crashes? Etc.), in this blog entry, I am going to focus on a more upbeat “what if,” as in “what if you win the lottery?”  When someone wins the lottery, they are given the option of taking either a lump sum payout or a larger amount that is paid as an annuity over a period of time.

Of course the lump sum is smaller than the total amount paid out over years.  However, because of the time value of money, it is difficult to make an “apples to apples” comparison of the two.  As a refresher, the time value of money simply says that a dollar today is worth more than a dollar tomorrow, and much more than a dollar 20/30/40+ years from now because of the interest that can be earned on the dollar today that cannot be earned on those future dollars until they are in our possession.  BTW, this comparison that I am going to show you is not limited to lottery winners, but can also be applied to compare money today vs. a cash flow stream in the future.  (e.g., sell a property vs. keep and collect rent, etc)

Let’s put this into practice.  Let’s say Samantha won the lottery and the prize was \$500,000,000.  This could either be collected in an annuity that would pay Samantha the entire \$500,000,000 in monthly payments for the next 26 years (\$500,000,000 / 26 years or 312 months = approximately \$1,600,000/month) or the other option is to get an up-front lump sum payout of \$359,400,000. (note: these are all pre-tax numbers, so when you do win the lottery, please contact a tax professional to account for taxes;-)

So, how does Samantha pick which option offers a better return?  To answer this, she needs to find out if she invested the lump sum of \$359,400,000 today and received monthly payments over the next 26 years, how much interest would she have to earn to get the same \$1,600,000/month annuity payment?  To answer this, Samantha turns to her trusty HP10bii financial calculator for the answer:

N (Number of Months) = 312 (26 years for the annuity is equal to 312 months)

I/YR (Interest Rate/Year) = ????  (this is what we are solving)

PV (Present Value) = -\$359,400,000 (this is the amount that Samantha would get with the lump-sum payout up-front.  Samantha is going to determine how much interest she would have to earn on this lump sum payout to get a monthly payment that is equal to the annuity payment of \$1,600,000.  Also, this number is entered into the calculator as a negative as Samantha is going to act as if that entire sum was invested, therefore she loses access to the money as it earns interest.)

PMT (Payments) = \$1,600,000 (this is the amount that will earned every month in our scenario as this the amount equal to the monthly annuity payment.)

FV (Future value) = 0 (there is no lump sum balloon payment at the end of the 26 years)

After entering all of these numbers into the calculator, the interest rate comes out to 2.68%.  This means that if Samantha invested \$359,400,000 today, for her to receive \$1,600,000/month, her money would have to work at an interest rate of 2.68%.  So, if she can make her money earn more than 2.68% she may be better served taking the lump-sum payout.  Conversely, if she can’t earn more than 2.68% on her money, she may be better served to take the monthly annuity.

Thank you for your time.  Please feel free to respond to this post with any thoughts or questions as I would love to hear from you and I will respond.