I just read the article at http://www.straightdope.com/mailbag/mlottery.html which asks, “If I win the lottery, should I ask for a lump sum or an annuity?”
In the answer, the basic idea is correct, that you need to apply calculations which take into account the time value of money. The math in the article, however, stinks. I’ll get to that in a minute. But first, I have to say that ignoring taxes (almost an afterthought in the article) is another very serious flaw.
Now back to the math. The article compares the 20-year annuity option on a $1,000,000 jackpot, to the offered $500,000 lump sum option. Ignoring taxes for the moment, it says that you would need a return of 8.92% on your $500k to have $1 million in twenty years. My calculations are very different. Even without compounding the interest (speding the $44,600 of interest each year), I make nearly $900,000 in interest alone over 20 years at that interest rate! Compounding it is even more drastic. At that interest rate, I come up with over $2.5 million in just 20 years.
No fancy financial calculator is needed - you can write out each payment period if you like. The first year is 500,000, and the second year is 500,000 * 1.0892. Then take that answer and multiply it by 1.0892.
Taxes complicate things more, and are essential to understanding why the annuity is not as big a rip-off as some people think (including some financial planners). The maximum federal tax rate is now at 35%. Most states have income tax around 5% or so (althout some have 0% and some are higher than 5%). Essentially, most people face a 40% tax bill on large payouts. The example used a $50,000 per year payout for the 20-year $1 million annuity. Most big jackpots are much larger, pushing people into the max tax bracket.
Let’s assume, therefore, a jackpot of $10,000,000, with a 20-year annuity of $500k per year. Cash value $5 million if taken in a lump sum. Mind you, the lump sum after taxes is just $3 million (60% left over). The annual payments would be $300,000 (60% of 500k) after tax if the annuity were taken. So after tax, the annual payments would equal a total of $6 million paid over 20 years.
Therefore, the real question should be this: can you invest your $3 million after-tax lump sum so that is equal to or greater than the $6 million (after tax) you receive over 20 years? (Plus any return on investments the annual payments might earn?) Remember, you also have to pay taxes each year on any interest you earn from your investments.
As it turns out, it is still only slightly better to take the lump sum. The is because the low rate of return on the annuity is augmented by the fact that it is tax-deferred year after year. (But introduces tax law risk.) Some financial planners have estimated that you need to make 4 percentage points more than the return on the annuity to compensate for this effect. So if the annuity pays 4% interest, you will need to make 8% per year or more with your investments with the lump sum to make it the wiser choice. This can be achieved, but you can see how the decision starts to be a close call.
Also consider that some or all of each annual payment can be invested too, making the total potentially larger than $6 million. Also consider that you will spend a lot or all of the income produced by the $3 million lump sum, lessening the effect of compounding. Both payouts end up about equal, taking all into consideration, unless you have a lot of discipline not to spend your windfall, and really good investments.
It ends up being more of a personal lifestyle choice than a math equation. Which would you rather have? (Figure life expectancy, risk tolerance, spending habits, self control, etc.) Would you spend half the lump sum right away instead of living off the interest?