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Q: Economics ( No Answer,   3 Comments )
Question  
Subject: Economics
Category: Business and Money > Accounting
Asked by: helpmequick-ga
List Price: $5.00
Posted: 26 Jan 2006 16:46 PST
Expires: 31 Jan 2006 10:45 PST
Question ID: 438116
Go to http://www.infospace.com/lycos.lotter/lotto/index.htm. Find the
most recent jackpot for the Lotto game (pick six numbers) for any
state. Assume you won that jackpot and will receive the payoff in
equal increments over the next 20 years. What is the present value of
your winnings (assume a discount rate of 10%)?
Answer  
There is no answer at this time.

Comments  
Subject: Re: Economics
From: sophrosune-ga on 27 Jan 2006 01:12 PST
 
Well, since no researcher has picked this up...

The Ohio Mega Millions (Pick six) jackpot is $40,000,000.  I will
assume you receive the 40,000,000 dollars divided into equal
$2,000,000 segments, one per year for 20 years.  Since the discount
rate, i,  is 10 percent per year, and the time, t, is 20 years, I'll
use them in the Present Worth formula:

PW = Annual Payment * ((1+i)^t-1)/(i*(1+i)^t)

PW = 2,000,000 (1+.1)^20  / (.1*(1+.1)^20)

PW = $17,027,124

In the accounting classes I've taken we usually refer to the discount
rate as the interest rate, and I understand there is some difference. 
Let me know if this helps.
Subject: Re: Economics
From: omnivorous-ga on 27 Jan 2006 07:22 PST
 
Helpmequick --

Sophrosune has handled the NPV calculations correctly but ignored
taxes, an important part of any discounted cash flow question.

Federal taxes alone on $2M would be $674,063 (married, filing jointly)
or 33.7%, reducing the NPV of the winnings.  Sorry, I don't have Ohio
state tax tables.  So, the annual payment should be adjusted to
$1,325,937.

To throw another cold dose of reality into this, I understand that
states typically withhold 25% of the winnings -- so you'd be receiving
$1,500,000 and then paying the extra taxes later in the year:
Washington State Lottery
"Cash Option Reference Table"
http://www.walottery.com/sections/LotteryGames/Lotto.aspx?Page=LottoChart

Best regards,

Omnivorous-GA
Subject: Re: Economics
From: antontodorov-ga on 27 Jan 2006 07:42 PST
 
Sophrosune,

I think that this question is quiete right. 
I mean - everything is fine with the formula itself. 
Yet, the final result in my opinion is 
Present Value = USD 18 729 840
----
The reason why this difference appears is that you are actually
estimating how much each dollar would cost, provided you receive it by
year-end (31.December)
However, if you receive it by the beginning of each year (01.jan) you
will not have to reduce the initial amount.
-----
Your formula should be PW = xxx ^19, not xxx ^20
You actually wrote it (t-1) but calculated differently.
---- 
Anyway, the final PRESENT VALUE of these money will be : 
18 729 840

If we consider taxes, and assume omnivorous is right about those taxes
reducing the 2 000 000 to 1 325 937,
then the final actual present value will be:

According to your formula: 
PV = 11 288 449
--
If we consider mine:
PV = 12 417 294

bet ?

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