Dear Straight Dope:

If I ever win the California lottery I'll have the option to receive the jackpot in either one lump sum or in 26 annual payments. Which is better? I figure it depends on the current jackpot. If the sum is below $26 million I choose cash value. If it is equal to or above $26 million I choose annual payments. My logic is this: If the jackpot is $26 million or above I'm guaranteed at least one million a year (before tax). If it's less than $26 million then I'll choose the lump sum and receive the cash value, which is estimated to be half of the jackpot. That way I'm sure to see some serious money. Make sense? Depending on the sum of the jackpot, which is better, cash value or annual payments? Also, could you advise me as to the best number combinations to pick (five numbers between 1 and 47 and one "mega" number between 1 and 27)? Thank you, Cecil - I'll be sure to cut you in on a piece of the swag if my winning numbers come up.

Dex replies:

If we knew how to pick winning numbers, kid, we wouldn’t be writing these reports, we’d be enjoying life on South Seas cruises. Cecil has already explained the problem.

The question of which is better, cash value or annual payments, doesn’t depend on the jackpot amount; it depends on the interest rate reflected in the annual payment. Since lottery rules are different in every state, I’m going to provide a general overview that works in every state, and caution you about what might be different in particular lotteries.

First some terms. An **annuity** is a series of annual payments (usually of equal size) over some period of time. There are different kinds of annuities, such as an **annuity certain** where the payments are made for a fixed number of years, or a **life annuity** where the payments are made for the lifetime of an individual. Most state lotteries offer an annuity certain.

The **face value** of an annuity is the payment amount times the number of payments. In a lottery, the face value is the amount advertised on the billboards – “this week’s jackpot is $X million!” — although nobody ever gets all the money at one time. The **cash value** or **present value** of an annuity is the amount of money, today, that is mathematically equivalent to the series of the payments, given a particular interest rate. By equivalent I mean that, if you deposited the cash value in an account bearing the agreed-upon interest rate for the term of the annuity, the accumulated amount would equal the face value.

In a typical state lottery, the cash value is roughly half the face value. Modern lotteries, you see, involve a bit of financial sleight of hand. You’ve “won” $X million only in the sense that you’ll receive that much if you’re willing to wait 20 years to collect it. What you’ve actually won is the cash value plus the interest that accumulates.

The assumption underlying most annuities is that money is constantly productive — that is, there is a time-value to money, represented mathematically as the interest rate. The interest rate is critical in determining whether a lump sum is a better deal than an annuity.

To put the matter in everyday terms, think of a standard U.S. mortgage. The bank loans you money today, say $100,000 (that’s the cash value), which you repay in fixed monthly installments for the next 20 years (that’s an annuity). The critical factors in determining your payment are the number of years for repayment and the interest rate being charged. At 5% annual interest, you would make monthly payments of $659.96 for the 20 years; at 3% annual interest, you would make $554.60 in monthly payments. It’s a fair deal in the sense that the two amounts — a payment of $100,000 or monthly payments of $659.96 — are mathematically equivalent given the agreed-upon rate of interest. The cash value amount doesn’t matter.

Let’s say you win a jackpot of $1,000,000 from the California lottery. The lottery rules say that total will be paid out to you in 20 equal annual payments of $50,000 each. Alternatively, you can take the lump sum cash value, which is about half the face amount, about $500,000. Which should you take? To find out, we need to determine what kind of interest rate you’ll be getting with the annuity. Punching a few numbers into my calculator, I find that if we start with a cash value of $500,000 and expect to wind up with $1,000,000 after 20 years (in other words, the equivalent of a $50,000 annuity), the underlying annual interest rate has to be 8.92%.

That tells me that in this case the annuity is a much better deal — I don’t know where I could find a guaranteed 8.9% annual interest rate for the next 20 years.

The biggest California jackpot is paid over 26 years, not 20 years, but the rules on the website were not clear. If they use the same process, that is, the cash value is half the face value, then the underlying interest rate is 6.68%, which makes the decision a little harder. It’s possible you could do better than that taking the cash value and investing the money on your own.

Caution: We’ve used the California lottery as an example, but the process and calculation for other states can be different. Basically, you want to calculate the interest rate that they’re using in converting from the face value to the cash value. Then ask yourself whether you can find investments that earn more than that. If you can, take the lump sum (if you have a choice). If you can’t, take the annuity and be happy.

For Illinois, the cash value is 51% of the face amount, and the annuity installments are paid annually over 26 years, so the underlying interest rate is 6.45% — tough call. New York forces a 26 year payment period but their website didn’t provide sufficient information for us to calculate the underlying interest rate. Not that it matters — winners don’t seem to have a choice anyway.

Real life, of course, is much more confusing than mathematics. That’s where the total amount and your personal circumstances and preferences come into play. For instance, if you win $1,000,000 at age 75, you may not want payments over 20 years; you might prefer to have the lower cash value of $500,000 to blow on a round-the-world-cruise or a gold-plated walker. On the other hand, if you win $100,000,000 at age 75, you might figure you can’t spend half the face value and your kids would blow it, so you might prefer the annuity. Your goal, Eggi, seem to be acquiring a big wad of cash, in which case your take-the-lump-sum-if-under-$26-milllion idea makes some sense. But stuffing $13 million in the mattress can be a little risky. Should you find yourself in that situation, I’d advise hiring an astute financial consultant, such as myself.

What happens if you die before the 20 or 26 years are up? The answer varies by state. In California, as in most states, the annual payments continue to your estate and heirs. But that’s worth checking. If the payments stop upon the death of the winner, then you are well advised to talk to a lawyer before you claim your winnings. A lawyer may suggest setting up a trust fund, so that payments will continue to the fund regardless of what happens to you – assuming, of course, that you want your heirs to get the remainder of the money rather than having the state keep it.

Then there’s the question of tax treatment. Normally, if you can choose the form of payment (i.e., lump sum vs. annuity), you’re taxed on the lump sum immediately. This is called the doctrine of “constructive receipt” — if you have any control whatsoever over the form of payment, the government taxes you all at once. Thus, the tax would be the same whether you chose a lump sum or an annuity.

However, the state lotteries have a way to circumvent this. When you purchase the ticket, you can sign an irrevocable agreement asking for an annuity. You no longer have a “choice” of how to take your winnings, so the tax treatment is different.

Normally, tax on an annuity will be less than that on a lump sum, because of the lower rates on lower income brackets. However, you’re also gambling on today’s tax rates being as high or higher than future tax rates — any future change in tax rates could screw up your calculations. If you’re already in the top bracket (and if you are, why are you buying lottery tickets?), then the tax treatment for the lottery would be the same, whether lump sum or annuity.

The bottom line, then, in deciding whether to take an annuity or a lump sum, includes the following considerations:

- What assumed interest rate is underlying the calculations? Do you think you can earn significantly more than that rate on your own? If so, take the lump sum cash value. If not, go with the annuity.
- What are your financial needs, both immediate and over the next twenty years? Do you need a steady flow of income? If you take the lump sum and invest it poorly or lose it, how much will it hurt you?
- If you give up your job to enjoy your wealth, what will happen if you’re still alive when the annuity payments stop? You don’t want to blow it all in a spree and then find yourself in poverty in your old age.
- What happens if you die before the annuity has been fully paid?
- As noted, there’s the question of whether to ask in advance for an annuity — the tax treatment alone could overwhelm any other considerations.

In short, you probably need to talk to a tax advisor and financial consultant … before you buy the winning ticket.

Send questions to Cecil via cecil@straightdope.com.

STAFF REPORTS ARE WRITTEN BY THE STRAIGHT DOPE SCIENCE ADVISORY BOARD, CECIL'S ONLINE AUXILIARY. THOUGH THE SDSAB DOES ITS BEST, THESE COLUMNS ARE EDITED BY ED ZOTTI, NOT CECIL, SO ACCURACYWISE YOU'D BETTER KEEP YOUR FINGERS CROSSED.