Every time a big money contest or lottery is advertised, their big "jackpot" prize is always really a payment plan - something like $50,000 a year for the next twenty years. Is it ever preferable to wait the full twenty years for the full prize, or to take the reduced lump sum? Are the tax implications for doing so?
Setting aside for the moment the very relevant issue of whether you need the full amount quickly, I'll just tackle comparing which option gives you to maximum amount of money (in terms of real dollars).
The trick is, unless you think inflation will suddenly reverse itself or stop entirely (not likely), $50K today is worth a LOT more than $50K in 20 years. If you don't believe me, consider that just 30 years ago the average price for a mid-level new car was around $3k. When you grandfather says he got a burger for a nickel, he isn't talking about 2010 dollars.
So, how do you account for this? Well, the way financial people and project managers do it to estimate how much to pay today for $1 at some point in the future is through a net present value (NPV) calculation. You can find a calculator here.
In your question, you gave some numbers for the payout, but not the lump sum prize amount. Going solely on what you have provided, I calculate that you should take the lump sum if it is greater than $766,189.96 which is the net present value of 20 years of $50K Payments assuming 3% annual inflation, which is fairly a fairly reasonable number given history.
However, if you think the out-of-control Gov't spending is going to send inflation through the roof (possible, but not a given), then you almost certainly would want the lump sum. I suppose in that scenario you might want the lump sum anyway because if the Govt starts filching on their obligations, doing it to a small number of lottery winners might be politically more popular than cutting other programs that affect a large number of voters.
I'm going to offer a contrarian answer. Depending on how big the jackpot is, I would suggest that your best bet might be the annuity over the lump sum. Not because of math, but because of behavior.
Let's say that you are looking at a jackpot of hundreds of millions, and the annuity option is tens of millions each year. For me, even the annual payment of the annuity is more money than I can even comprehend. Do I trust myself to handle the lump sum? No. I have no experience with that kind of money, nor does anyone I know.
By taking the annuity option, I allow myself to figure it out a piece at a time. If I make a mistake by choosing the wrong advisor or spending more than I should, I can learn my lesson and do better with next year's payment.
There are too many stories of past lottery winners who blow it all early and end up broke. The annuity option protects you from yourself.
But, you don't have to take my word for it:
New York Times, Jan 12, 2016: Dear Powerball Winner: Take Our Advice and Take the Annuity
Looking at some large lotto games out there, it seems that the lump sum (cash) option comes in at anywhere from about 50 to 70 percent of the jackpot amount (sum of annual payouts, typically over 20 to 30 years).
I'm a fan of the phrase "money today is better than money tomorrow." There's no telling how laws will change, taxes will change, if inflation will skyrocket, if you'll die early, if you or a family member will encounter a life-changing event, etc. By taking the lump sum option you trade a percentage of the winnings for the risk of the future unknowns. How much are those unknowns worth to you?
The tax implications are something else to consider. In your example of a "small" jackpot with $50,000 annual payouts, it's likely that you could still avoid the highest tax bracket each year, whereas taking the lump sum would be taxed at the highest rate (35% of the amount above $373k, for a single filer in 2010). However, this might not make much of a difference for large jackpots with higher annual payouts.
With the lump sum option, you also have a greater potential of investment returns (and losses) since you can put all the money to work for you right away. It also allows you to purchase larger assets sooner, if that's something that interests you.
In the end, I'd say the reduced risk and the higher return potential of the lump sum option is well worth the reduced payout. I'd also suggest not playing the lottery :)
This is a bit pornographic, isn't it, in that we're looking at something we'd like to do (namely, "win the big lottery!") but probably won't ever have this happen to us. :)
Anyway. Ignoring the fact that this is kind of a hypothetical question...
Gotta go with The Straight Dope on this one, when deciding whether to take an annuity or a lump sum:
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.