Ok, I did the math for a smallish lottery. Here are my assumptions:
[*]When buying the ticket you choose the annuity if you want the annuity. Don't choose the annuity AFTER winning, choose before winning. This is an important key to saving tax money with the annuity.
[*]Assume the annuity pays a 6% return. This is reasonable, I think they are often 5%-9%.
[*]Assume you get 10% return if you take the cash option and invest it.
[*]Assume you have the standard tax deduction and no other deductions.
[*]Assume you have no job and plan to live off the lottery.
[*]Assume just income tax as other taxes will be constant for both cases.
[*]Since states vary so much, I'll just use a simplistic state income tax model where you are taxed 5% of whatever you earned that year no deductions.
[*]Assume tax laws don't change.
[*]Assume you don't blow any money and you ONLY live off of the (annuity money you get each year) or (cash out money + interest that you get each year).
[*]Assume it was a 30 year guaranteed annuity (varies by state, with some states you can't get the guaranteed annuity and you lose it when you die, but you are dead so why would you care).
[*]Assume annuity amount is $4.5 million (this is what is advertised on the billboards).
[*]Assume you don't do any retirement tax shelters as you want to be able to spend the cash out money each year (lets say you are young).
Results:
With the annuity.
[*]Collect $150,000/year.
[*]Pay $41,043/year in income tax.
[*]Spendable money: $108,957/year.
With the cash out.
[*]Cash out is $2,064,725 (the initial annuity value).
[*]After tax, you have $1,258,991 to invest.
[*]Lets have a $108,957/year spendable money.
[*]The cash balance drops each year because $108,957+tax on the interest is greater than the interest.
[*]Money runs out at the year 28 point.
In this example annuity lasts you 2 years more with the same spendable money.
Now lets pretend the cash out gives a net 11% return on investment.
[*]Same as above, but your money lasts 36 years.
Now lets pretend the cash out gives a net 12% return on investment.
[*]Same as above, but your money lasts infinitely long and in fact slightly grows.
So the key is, can you earn more than 10% guaranteed with that cash? Since you can estimate that you'll get 10% in stocks, this is basically a break even deal. If you do better, the cash is financially better. If you do worse than 10%, the annuity is financially better.
Note: as the lottery gets bigger, the advantage shifts towards the cash out option. But still, you need a guaranteed ~9% return to break even. And you have to have massive self control not to spend. If the lottery is smaller than $4.5M, then you need a bigger and bigger return on your investments for the cash out to be worth while.
Note: yes, changing an assumption can change the picture slightly.
What I'm saying is that the cash out option really isn't that much better than the annuity. That is, unless you are a stock genious and do far better than historical returns. Plus, you can essentially always switch from cash to an annuity with a little paperwork (with the realization that you probably shouldn't plan on the switch for tax reasons).