Recently I'm keeping an eye on lottery. I haven't bought a single ticket yet, but I may want to test water shortly. If I choose to do so, I will only allocate a small amount of money, say, $10 every month, to the games, and I will only focus on games with big jackpots, like Mega Millions and Lotto, both available in the State of Washington. The rationale will be simple: I can easily save $10 every 30 days, but if I am fortunately enough to become a jackpot winner, I can save more than ten years of financial heavylifting.

While I certainly recognize it is a wishful thinking, it does not hurt to do a mental exercise: if I win a jackpot, should I choose one-time payout, or annuity option?

Some background: in the case of Lotto, the minimal jackpot is $1 million. Jackpot winners can either choose one-time payout equal to 50% of the nominal jackpot size, or choose 25 equal annual installments with a total of the nominal amount. If the winner passes away before the 25 years, remaining winnings will go to his/her estate.

A simple way to calculate is the implied internal rate of return that makes both options indifferent to the winner. Assuming the jackpot is $1 million, a quick calculation in Microsoft Excel: RATE(25 - 1, -1,000,000 / 25, 1,000,000 * 50% - 1,000,000 / 25) will give out 6.97%, which means if the one-time payout can consistently grow at around 7% annually in the next 25 years, both options offers the same value for the winner. (If you have question about the formula: because the first installment is paid to the winner immediately, the comparison is essentially between $460,000 and 24 annual payout of $40,000.)

Income tax will add a little twist to this calculation. As you can reasonaly expect, gambling income is subject to income tax. If you file tax return by yourself and read the tax rate table, you surely know half-a-million will most likely push you to the top tax bracket of 35%. If you opt for annuity, an annual payout of $40,000 may well be taxed at much lower 25%. If we evaluate on an after-tax basis, the choice is now between $350,000 one-time payout and 25 annual payout of $30,000. The implied internal rate of return is 8.84% now.

Moreover, the 8.84% is an after-tax rate of return, which means if you take the one-time payout, your investment needs to turn in a before-tax return of 11.8% or more to come ahead of the game, assuming you are in the 25% tax bracket. Are you still confident you can do it?

Of course, this is only a math exercise. I can fully understand more often than not, people will choose the one-time payout for immediate gratification. What will I choose if I am so lucky? Who knows?