I get that but we are speculating in the dark. We need some data. Since we don't have any, let's make some up.
Suppose that you have the choice between $20,000,000 lump sum or $750,000 per year for 20 years. And suppose that the tax on each is 50%. Then taking the first option, you would get $10,000,000 in hand which you decide to invest. A reasonable rate of return might be 5% per annum or $500,000 which, after tax would be $250,000 pa (I suspect that your rate of return will be a lot lower if you invest in "municipal bonds, T-bills, and other things that generate income which is not fully taxable").
The second option would return after taxes $375,000 per year.
Of course, this is not the whole story. Your investments may generate income for a lot longer than 20 years or the income may increase with inflation.
Uhm ... okay ... not okay!
For starters: 20 * 750,000 = 15 million.
That's 5 million less than the lump sum you propose.
Doesn't make an aweful lot of sense, does it? At least I don't get it.
The least I would expect would be a payout of 1 million for each of the next 20 years.
And so, assuming 50% flat tax rate, 500,000 into your bank account.
The question is then: Do you spend the full 500,000, or spend less and invest the balance?
Let's say you spend it all:
Then after 20 years, you are left with - nothing. And need to dratically revert your lifestyle back to where you came from.
Now, lump sum: You get 20 million, you pay 10 million in taxes right away so you are left with 10 million, you blow 500,000, invest 9.5 million at 5% per annum, on which you again pay 50% taxes immediately, so effective interest rate is 2.5% per annum: 237,500 is added to your wealth; you now have 9,737,500. Next year, you take out 500,000, and invest 9,237,500 at 2.5% net interest rate... and so forth...
...*creates a spreadsheet*...
...then after 20 years have completed, and you have taken out half a million 20 times, and earned 2.5% interest on the remainder, you still have about 3.3 million left.
So taking the lump sum is, to no-one's surprise, superior to an annual payment that does NOT earn you any interest.
(But you are still blowing through your money that way: In year 28, you'll have spent all your money)
A better strategy of course would be to NOT spend 1/20th of your wealth every year. Or your entire annual payout, when payouts end after 20 years.
The smart way would be to take out a little less than your interest after taxes. So, say, spend only 225,000 per year, if you earn 237,500 in interest in year 1.
That way, your lump sum of 10 million will have grown to about 10.5 million after 20 years.
But now, if you take the payout plan, you'll have cash left after the end of every year that you can invest!
After the first year, you have 275,000 left, on which you earn only 6,875 after another year. But as your depot grows in value, so does the value of your interest, and after 20 years, you have 7.25 million left.
Again, that's (of course) less than what the lump sum gave you.
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But NOW let's modify the payout plan such that it implies a 5% guaranteed interest rate on the original 20 million which the lottery parks with an insurance company. This happens when the annual payout is about 1.25 million (my spreadsheet thinks: 1,251,652), and the 20 annual rates sum up to 25 million! Then, after paying 50% tax on each rate and cashing in 625,826 per year, you can blow 625,826 each year and end up with nothing when the 20 years are history.
Do the same with 20 million lump sum, earn 2.5% interest after tax, take out 625,826 every year, and you will also end up with zero after 20 years.
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Now, the math of course gets a little more complicated when you want to factor in inflation / increased spending, and also want to end up with enough money after 20 years that it lasts you for the rest of your life. Which has two variants:
A) You die with the equivalent of 10 million plus accrued inflation
B) You die with nothing
Strategy A) is more or less straightforward: You spend only the money from interests earned that exceeds the inflation rate. (Which may be difficult to do in some years if indeed you only earn 2.5% after taxes!)
Strategy B) can only, or best, be done by puting the remainder of your money in a life insurance kind of investment plan: The insurance knows your life expectancy, and its standard variation, and can compute at which payout rates the expected value of the investment at the time of your death is zero.
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And a further complication is indeed that perhaps you want to spend a lot of the windfall on luxury early, so you enjoy it the longest time. So, buy that fancy mansion in Southern France, plus the super sports car that best matches the color of the car port, plus the yacht, in year one. That leaves you with a lot less to invest. Ooooooor are you of the type that you think you may resist the urge to do all that, and settle for a smaller mansion, or one in a less fancy region, and wait with the sports car another year, and with the yacht until after you had the time to get your own high seas sailing license so you can additionally save on the skipper the first three years? Then the annual payout rates may help your discipline to stick with that plan.
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Long story short:
It's complicated, really.
And, as someone said in a quote that I read, when you are really stinking filthy rich al of a sudden, perhaps it doesn't matter so very much if you totally optimize your finances. Enjoy life!
And see a pro once a year to check if you are not on a course already to blow it all through the pipe.
I mean, 20 million, whether in lump or in 20 rates of a million, should see you through easily. And if 15 mio go to waste and you find yourself left with only 5 million, you should still be able to live comfortably till you die. Especially if you do something, anything, to earn an ordinary living on the side.