In the recent powerball lottery the prize money was 340 million, the
odds of winning is 1 in 146,107,962.00
http://www.powerball.com/powerball/pb_prizes.asp, suppose if i had
invested 146 million and change and bought all the lotteries and
guranteed a win and assuming that no other won, will i be still making
a profit if i would have choosen 30 year annuity payments or a single
cash payment ? if so how please provide  conservative estimate with
calculations. thanks

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Request for Question Clarification by pafalafa-ga on 21 Oct 2005 14:31 PDT

pb-ga,

You're getting a lot of info in the comments (below), but I'd suggest
taking a good deal of it with a few grains of salt.  You're not going
to double your money, but still -- the $146 million might be money
well-spent.

The current cash value of the $340 million jackpot -- according to the
Powerball folks themselves -- is $164 million.

That is, if you were the sole winner, you could collect a lump sum
payment of $164.4 million, rather than collecting $340 million over
the course of 30 years.

$164.4 million is not a bad return for a $146.1 million investment,
with a quick profit of $18.3 million.

In general, the lump sum payment is about half (give or take a few
million) of the total jackpot, but the proportion changes as interest
rates change.

As for calculations, I'm not sure just what you have in mind.  


Is the above enough info to answer your question?  If not, can be a
bit more specific about what you need?

Thanks,

pafalafa-ga

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Clarification of Question by powerball-ga on 21 Oct 2005 16:50 PDT

I was thinking in terms of net profit after federal & state tax
whether one lump-sum is better or annuities. Basically iam looking at
what sum amount will i have at the end of 30 years if i choose the
annuity option.

If you bought $146 million dollars in lottery tickets the odds for the
average person would have been approximately 1:292,107,962,000. Why?
Because the other 146,107,962,000 chances would still have been
purchased whether you bought $146M worth or not. By my calculations
the resulting edge for you would have been slightly less than 50:50.
Crappy odds for risking $146M.

tutuzdad-ga

The problem assummes no one else will win, so the odds of winning are
still 1:146,107,962,000. (I don't think this is realistic, but that's
what the problem says.)
But $340M future value converted to annuities based on 5%/year =
$408,526/month over 30 years.  $408,526 * 360 payments = $147M.  $340M
Future Value = 78M today if interest is 5%... So either way you look
at it, if I had 147M today, I'd rather invest it in treasury bonds
then put it in the lottery.

And if you had $147M I'd be your friend no matter how you decided to use it.  

:)

tutuzdad-ga

Yo, 146,107,962,000 is not 146 million. It's 146 billion.

leapinglizard

Darn. Now I can't be friends with him after all.

On the other hand, the page linked in the question does cite 1 in 146
million odds. If you could corner the market on tickets for a $340
million jackpot without spending more than $340 million, this would
indeed be a good investment. It would double your money on average. In
fact, if 146 million is the total number of powerball configurations,
it would be guaranteed to double your money.

leapinglizard

But think of the taxes!

Oh yeah, the taxes. Let's see...would I happily give away half of 340
million dollars for an opportunity to keep the rest for myself?
Hmmm...?

Don't rush me now, I'm thinking....

I mean no one will win the jackpot except me. IAm not sure why odds
will be 292million. can you clarify ? i don;t get it.

Hi There.

If you did buy 146 million tickets, then youre chances of winning
would be 146 million over 21347536559793444. An example would make it
easier to understand. Suppose I took part in a raffle. The chances of
winning were 1/10 and so I buy 10 tickets. This means that my chances
of winning are now 10/100 or still 1/10.

I am not improving my chances just my luck of winning. I got that
humungous number by timesing 146,107,962 by itself or squaring it.
Probability means that it is the number of tickets bought times the
chance of winning.

I am not even sure if this is right but then again, Maths was always
my worst subject. How did tutzdad get 292 million anyway???

The only way it works is if there is no other winner. Unfortunately
there is no way to ensure that.

I'm missing something 'cuz my estimates run around 120 million to one.
I hated statistics.

This is quite an interesting question.

By spending $146,107,962 to buy the tickets (assuming it's $1 a
piece), you are actually adding that to the jackpot... meaning the
jackpot will grow by $146,107,962.00 -- resulting in a jackpot at
$486.1 million...

And by spending that much money, you ensure that you will win... The
only question is, how many other winners there might be. If there is
one other winner, you will be splitting the $486 million - $243
million a piece.

Highest bracket federal tax rate is 40%, so you essentially gain
$145.8 million after taxes... a $300,000 loss.

If you are the sole winner, you will have huge gains. If there are 2
other winners, you are at a big loss. So the question is, are you
willing to take this kind of risk?

Wow.  To me the most interesting thing is that this question is most
interesting to the vistors to Google (TM) Answsers.

I'd like to know more psychology, but it appears that the chance of
receiving a thing perceived as really great is more interesting to us
than the certainty of having a merely good thing.

I think I'd put the $146 Million in debt securities from a variety of
nations and start giving away and spending the interest.