Powerball math: annuity is better?

Questions on how we spend our money and our time - consumer goods and services, home and vehicle, leisure and recreational activities
letsgobobby
Posts: 10614
Joined: Fri Sep 18, 2009 1:10 am

Powerball math: annuity is better?

Post by letsgobobby » Tue Jan 12, 2016 2:00 pm

Apparently the Powerball annuity is paid out over 30 years, with each annual payment increasing by 5% for 'cost of living' raises.

Given this information, and with inflation currently between 1-2%, doesn't that make the annuity more attractive?

Ignore the possibility of not being paid (a risk with any annuity).

This NY Times article argues yes:

http://www.nytimes.com/2016/01/13/upsho ... v=top-news

His argument is that taking the annuity is like getting a 2.8xx% risk-free return on your money (why 2.8xx% and not the 5% that Powerball advertises?).

User avatar
greg24
Posts: 2869
Joined: Tue Feb 20, 2007 10:34 am

Re: Powerball math: annuity is better?

Post by greg24 » Tue Jan 12, 2016 2:27 pm

Best return is to not play.

westie
Posts: 374
Joined: Thu Jan 19, 2012 8:00 am

Re: Powerball math: annuity is better?

Post by westie » Tue Jan 12, 2016 2:32 pm

annuity is a bad idea in most cases....

http://finance.yahoo.com/news/taxes-1-4 ... 22750.html

southbay
Posts: 471
Joined: Thu Apr 16, 2015 2:40 pm

Re: Powerball math: annuity is better?

Post by southbay » Tue Jan 12, 2016 2:35 pm

Does it really matter?

Invest the $ instead of throwing it away on the lottery.

LearningtheRopes
Posts: 29
Joined: Sat Jun 06, 2015 4:34 pm

Re: Powerball math: annuity is better?

Post by LearningtheRopes » Tue Jan 12, 2016 2:37 pm

letsgobobby wrote:Ignore the possibility of not being paid (a risk with any annuity).



With all due respect, I'm not so sure this can or should be ignored (presuming for the sake of argument that hitting the lottery is a serious enough topic to have a serious discussion about). Illinois is already issuing IOUs for many of their lottery winners. I think some other state finances are only going to get worse. Plus, who knows what black swan events down the road are going to cause reallocation of spending priorities; my guess is that disgruntled lottery winners getting shafted (at least in part) on winnings won't make the loudest, largest or most effective constituency.

Also, tax rates on the high end could easily go up in the future.

There is always risk to any course of action, but I don't think the Times' analysis was as even-handed as it could have been.

Alex Frakt
Founder
Posts: 10730
Joined: Fri Feb 23, 2007 1:06 pm
Location: Chicago
Contact:

Re: Powerball math: annuity is better?

Post by Alex Frakt » Tue Jan 12, 2016 2:53 pm

Note - We've been locking Powerball speculation threads, but we'll let this thread run as long as it sticks to math issues.

greg24 wrote:Best return is to not play.

Normally true, but thanks to the rollover prizes, my rough estimate is that you now have a positive expected return even after taxes and the likelihood of a split pot.

[googles...]

Not quite. Someone has done the math: http://thefederalist.com/2016/01/12/wit ... ll-ticket/ . The break even point is around a $1.4 billion lump-sum payout (not the headline annuity payout). My mistake is that I thought a ticket cost $1, apparently it is $2.

mattshwink
Posts: 287
Joined: Mon Sep 21, 2015 10:01 am

Re: Powerball math: annuity is better?

Post by mattshwink » Tue Jan 12, 2016 2:58 pm

westie wrote:annuity is a bad idea in most cases....

http://finance.yahoo.com/news/taxes-1-4 ... 22750.html


Yahoo is mostly talking about estate taxes (and state taxes). Honestly, I don't care very much about those....

The "problem" with the lump sum is the amount of taxes paid (39.6% for most of it) plus probably the 3% medicare tax, and state/local taxes.

By taking the annuity you would shelter a small amount in taxes this year (my example, married filing jointly with 1 child) = $24,750
Taxed at 10%= Next $18,550
Taxed at 15%= Next $18,551<$75,300
...
Taxed at 35%= up to $466,950

So I would essentially pay less tax on $500,000 per year. So there is a return on this money. Could you do better yourself? Maybe....

letsgobobby
Posts: 10614
Joined: Fri Sep 18, 2009 1:10 am

Re: Powerball math: annuity is better?

Post by letsgobobby » Tue Jan 12, 2016 3:07 pm

so maybe a lower tax rate on $500k annually for 30 years is a pkus.

What of the core issues: that in a 1% inflation world, a 5% annual annuity increase is 4% real, about the same as the equity risk premium has been for some time? There's the risk that inflation increases substantially, but 5% is 5%. Is this not the same as buying a 15 year 5% CD (half the money paid out by 15 years, the other half over years 15-30)? This is 2%+ more than US 30 year bonds are yielding. It is backed by state governments, so not quite as safe, but again, we are trying to ignore the small risk of not being paid.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 3:07 pm

There's simply no way to answer the question because you don't know what inflation (or taxes, if you also consider taxes) are going to be, nor what interest rates are going to be.

Inflation doesn't actually come into it, because even though they say that the payment is "increased by 5% each year to keep up with the cost of living" it is not actually tied to the cost of living at all.

A straightforward answer to a not-very-interesting question is to calculate the net present value of the payouts assuming various interest rates.

In other words, let's suppose that you put the $930 million into a bank account that pays X% interest every year, and each year you withdraw from the bank account the exact number of dollars the annuity would pay. What interest rate does the bank account need to have in order for the money to last exactly 30 years, leave nothing at the end, and pay out exactly $1.5 billion?

When I fiddled with the figures in Excel, the answer I got is 2.84%.

In other words, if you know of an essentially-zero-risk investment, like a bank account or Treasury bills, that pays more than 2.84% per year for the next thirty years, then you will get more money by taking the $930 million lump sum and putting it into that account. If you can't get more than 2.84%, then you will get more money from the annuity.

Inflation doesn't come into it. In year Y, the lottery would have paid $X on the annuity, and you are taking the same $X out of the bank account. Inflation affects them both the same way. If inflation stays under 5%, either way, if inflation says less than 5% you enjoy a gradually increasing lottery-based-standard-of-living, if it doesn't you don't.

Taxes definitely come into account but I'm not enough of a tax expert to figure it out and I don't want to do that much work, but let's just say that unless you can somehow shelter the $930 million and only pay taxes on the money as you withdraw it, then taxation would weigh on the side of the annuity.

Here's what the drawdown looks like if you want to check my work. The interest rate is actually 2.84307453365% annual interest. The payouts ought to increase by 5% every year, ought to total exactly $1.5 billion, and in the "remaining" column I first subtracted the payout, assumed to occur at the beginning of the year, and then increased the remainder by 2.84307453365%, the earnings for the year.

Code: Select all

Year            Payout          Remaining
                                $930,000,000.00
2016            $22,577,152.62  $933,221,555.27
2017            $23,706,010.25  $935,373,749.85
2018            $24,891,310.76  $936,368,133.45
2019            $26,135,876.30  $936,110,838.65
2020            $27,442,670.12  $934,502,281.82
2021            $28,814,803.62  $931,436,848.25
2022            $30,255,543.80  $926,802,560.61
2023            $31,768,320.99  $920,480,730.15
2024            $33,356,737.04  $912,345,589.44
2025            $35,024,573.90  $902,263,905.91
2026            $36,775,802.59  $890,094,575.18
2027            $38,614,592.72  $875,688,193.00
2028            $40,545,322.36  $858,886,604.92
2029            $42,572,588.47  $839,522,432.36
2030            $44,701,217.90  $817,418,574.00
2031            $46,936,278.79  $792,387,681.12
2032            $49,283,092.73  $764,231,605.70
2033            $51,747,247.37  $732,740,819.68
2034            $54,334,609.74  $697,693,804.13
2035            $57,051,340.23  $658,856,406.65
2036            $59,903,907.24  $615,981,165.39
2037            $62,899,102.60  $568,806,598.07
2038            $66,044,057.73  $517,056,454.09
2039            $69,346,260.61  $460,438,927.97
2040            $72,813,573.65  $398,645,832.06
2041            $76,454,252.33  $331,351,726.49
2042            $80,276,964.94  $258,213,004.15
2043            $84,290,813.19  $178,866,928.48
2044            $88,505,353.85  $92,930,621.54
2045            $92,930,621.54  $0.00
                               
                $1,500,000,000.00
Last edited by nisiprius on Tue Jan 12, 2016 3:25 pm, edited 3 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

randomguy
Posts: 4884
Joined: Wed Sep 17, 2014 9:00 am

Re: Powerball math: annuity is better?

Post by randomguy » Tue Jan 12, 2016 3:15 pm

mattshwink wrote:
westie wrote:annuity is a bad idea in most cases....

http://finance.yahoo.com/news/taxes-1-4 ... 22750.html


Yahoo is mostly talking about estate taxes (and state taxes). Honestly, I don't care very much about those....

The "problem" with the lump sum is the amount of taxes paid (39.6% for most of it) plus probably the 3% medicare tax, and state/local taxes.

By taking the annuity you would shelter a small amount in taxes this year (my example, married filing jointly with 1 child) = $24,750
Taxed at 10%= Next $18,550
Taxed at 15%= Next $18,551<$75,300
...
Taxed at 35%= up to $466,950

So I would essentially pay less tax on $500,000 per year. So there is a return on this money. Could you do better yourself? Maybe....


The difference in tax percentage between 40 million/year and a lump sum of 600 million is pretty small. With a smaller winning (something like 10 million) your logic works a lot better.

If you take any sort of risk with the portfolio, you are likely to beat the annuity over 30 years. I would say the annuity might be safer (i.e. less chance to blow through it all in 6 years) but it is pretty easy to get advances against income streams. There is also some flexibility in the lump sum where you can avoid taxes on gains (i.e. you donate appreciated stock) and the use of munis (a 1.8% muni is giving you the same yield as a 3% taxable) which can also change the numbers. Getting the lump sum also gives you more time on working on getting the money out of your estate and into trusts to avoid the estate tax.

In the end this doesn't really matter. The difference isn't enough to change your life either way.

letsgobobby
Posts: 10614
Joined: Fri Sep 18, 2009 1:10 am

Re: Powerball math: annuity is better?

Post by letsgobobby » Tue Jan 12, 2016 3:21 pm

well done nisi, thank you for that explanation. not even as good as the 30 year paying 2.96%, and I wouldn't want a portfolio of 100% long bonds, anyway.

Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

Re: Powerball math: annuity is better?

Post by Rodc » Tue Jan 12, 2016 3:29 pm

It is really not a math problem, it is a behavioral problem.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 3:32 pm

Notice, by the way, that I'm just assuming that there's no difference in the date on which the lump sum or the first annuity payment would show up as "available funds" in your bank account.

I assume by the way--just my guess--is that the annuity payments are in fact calculated with the intention of being equitable and fair. It wouldn't surprise me if they are based on the actual yields available today for Treasuries maturing in 1, 2, 3, ... 30 years.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
Epsilon Delta
Posts: 6492
Joined: Thu Apr 28, 2011 7:00 pm

Re: Powerball math: annuity is better?

Post by Epsilon Delta » Tue Jan 12, 2016 3:34 pm

Alex Frakt wrote:Note - We've been locking Powerball speculation threads, but we'll let this thread run as long as it sticks to math issues.



Not quite. Someone has done the math: http://thefederalist.com/2016/01/12/wit ... ll-ticket/ . The break even point is around a $1.4 billion lump-sum payout (not the headline annuity payout). My mistake is that I thought a ticket cost $1, apparently it is $2.


If the lump sum cash payout (not the annuity value) increases to $1.4 billion, and the number of tickets sold hovers around 500 million, the total expected payout of a $2 Powerball ticket will be $2.01, making the purchase of a ticket a rational decision in pure mathematical terms.


I have highlighted the key part of this quote. With larger prizes the number of tickets sold increases in a way that makes it unlikely to every result in a positive expected value, unless the number of tickets sold is limited by the ability to sell them. But at that point you should look at the cost of standing in line to get some of the limited supply of tickets and the expected value still never goes positive.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 3:38 pm

Rodc wrote:It is really not a math problem, it is a behavioral problem.
I can think of so many things I could do with $930 million that I couldn't do with just $22 million. :(

Quite seriously, if I were running the lottery, I'd create a third option--one that pays out, oh, I dunno, 10% as a lump sum immediately and then the rest as an annuity. So you can buy the yacht right away, and then operate it later.

I assume the annual cost of operating a yacht is less than the cost of buying it? I wonder whether it is?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

rbaldini
Posts: 744
Joined: Mon Mar 23, 2015 3:20 pm

Re: Powerball math: annuity is better?

Post by rbaldini » Tue Jan 12, 2016 3:43 pm

Epsilon Delta wrote:
Alex Frakt wrote:Note - We've been locking Powerball speculation threads, but we'll let this thread run as long as it sticks to math issues.



Not quite. Someone has done the math: http://thefederalist.com/2016/01/12/wit ... ll-ticket/ . The break even point is around a $1.4 billion lump-sum payout (not the headline annuity payout). My mistake is that I thought a ticket cost $1, apparently it is $2.


If the lump sum cash payout (not the annuity value) increases to $1.4 billion, and the number of tickets sold hovers around 500 million, the total expected payout of a $2 Powerball ticket will be $2.01, making the purchase of a ticket a rational decision in pure mathematical terms.


I have highlighted the key part of this quote. With larger prizes the number of tickets sold increases in a way that makes it unlikely to every result in a positive expected value, unless the number of tickets sold is limited by the ability to sell them. But at that point you should look at the cost of standing in line to get some of the limited supply of tickets and the expected value still never goes positive.


Even if the expected value return were in fact positive, that doesn't necessarily mean playing is "rational". First, there are opportunity costs: if you can expect a better return elsewhere, it is irrational to play here. Second, there is no rule of human behavior that says playing to maximize expected payoff is necessarily rational. If the powerball were in fact the highest expected return on your investment of all choices, then you should presumably put all your money there - in which case, by far the most likely outcome is to lose all your money. Similarly, we don't put *all* our money in stocks just because their expected return is greater than bonds.

Sorry if that's a bit pedantic.
Last edited by rbaldini on Tue Jan 12, 2016 3:44 pm, edited 1 time in total.

westie
Posts: 374
Joined: Thu Jan 19, 2012 8:00 am

Re: Powerball math: annuity is better?

Post by westie » Tue Jan 12, 2016 3:44 pm

If you're over 40, you're making a bet on your mortality if you take the annuity.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 3:55 pm

westie wrote:If you're over 40, you're making a bet on your mortality if you take the annuity.
I don't think it's a life annuity (that is, one that stops with the death of the annuitant.) The word "annuity" is really confusing because it basically means any stream of annual payments. I think the Powerball annuity continues for 30 years no matter what. So you're only making a bet on your mortality in terms of your personal enjoyment of the money.

Yes, here it is, I'm right. It's not like an SPIA, and it's not like a variable annuity. It pays so many dollars each year for 30 years, period, no matter what. $22,577,152.62 the first year, $23,706,010.25, and on. It will always pay out $1.5 billion, total... you just can't be sure if it will pay it all to you.

http://www.powerball.com/pb_contact.asp
WHAT HAPPENS IF AN ANNUITY PRIZE WINNER DIES?

The estate will handle the lottery prize. A lottery annuity prize is just like any other asset. You can pass any remaining annuity payments on to your heirs or to anyone else. The Powerball game will even cash out an annuity prize for an estate. This may make it easier for the estate to distribute the prize. It also may be necessary to cash out the annuity to pay Federal estate taxes. We will sell some or all of the securities at competitive bid or will even just transfer the securities to the estate. We do not charge a fee of any kind. We often hear people complain that the jackpot should not go back to "the state" when a winner dies. It does not. I think that this misunderstanding may come from the response that the prize "goes to the Estate" and some people hear "goes to the State."
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
Epsilon Delta
Posts: 6492
Joined: Thu Apr 28, 2011 7:00 pm

Re: Powerball math: annuity is better?

Post by Epsilon Delta » Tue Jan 12, 2016 4:02 pm

rbaldini wrote:
Epsilon Delta wrote:
Alex Frakt wrote:Note - We've been locking Powerball speculation threads, but we'll let this thread run as long as it sticks to math issues.



Not quite. Someone has done the math: http://thefederalist.com/2016/01/12/wit ... ll-ticket/ . The break even point is around a $1.4 billion lump-sum payout (not the headline annuity payout). My mistake is that I thought a ticket cost $1, apparently it is $2.


If the lump sum cash payout (not the annuity value) increases to $1.4 billion, and the number of tickets sold hovers around 500 million, the total expected payout of a $2 Powerball ticket will be $2.01, making the purchase of a ticket a rational decision in pure mathematical terms.


I have highlighted the key part of this quote. With larger prizes the number of tickets sold increases in a way that makes it unlikely to every result in a positive expected value, unless the number of tickets sold is limited by the ability to sell them. But at that point you should look at the cost of standing in line to get some of the limited supply of tickets and the expected value still never goes positive.


Even if the expected value return were in fact positive, that doesn't necessarily mean playing is "rational". First, there are opportunity costs: if you can expect a better return elsewhere, it is irrational to play here. Second, there is no rule of human behavior that says playing to maximize expected payoff is necessarily rational. If the powerball were in fact the highest expected return on your investment of all choices, then you should presumably put all your money there - in which case, by far the most likely outcome is to lose all your money. Similarly, we don't put *all* our money in stocks just because their expected return is greater than bonds.

Sorry if that's a bit pedantic.


Not pedantic, that's why I never mentioned rational, just positive expected value. :twisted:

Pedantically, There are also cases where it is rational to accept a negative expected value, at least in dollar terms. You need a $1,000,000,000 surgery to save your life or similar. It's hard to envision in terms of the powerball lottery, but it's believed to be what happened in the case of the London whale.

Jags4186
Posts: 1374
Joined: Wed Jun 18, 2014 7:12 pm

Re: Powerball math: annuity is better?

Post by Jags4186 » Tue Jan 12, 2016 4:05 pm

I'd take the annuity.

Let's face it, if I won the powerball I'm most definitely NOT putting it in the stock market. I'm not going to buy bonds either. I'm probably going to buy TIPS. What do they pay, 2%-3%? A 0 risk guaranteed 5% sounds pretty good to me if I'm not looking to build my portfolio.

westie
Posts: 374
Joined: Thu Jan 19, 2012 8:00 am

Re: Powerball math: annuity is better?

Post by westie » Tue Jan 12, 2016 4:14 pm

nisiprius wrote:
westie wrote:If you're over 40, you're making a bet on your mortality if you take the annuity.
I don't think it's a life annuity (that is, one that stops with the death of the annuitant.) The word "annuity" is really confusing because it basically means any stream of annual payments. I think the Powerball annuity continues for 30 years no matter what. So you're only making a bet on your mortality in terms of your personal enjoyment of the money.

Yes, here it is, I'm right. It's not like an SPIA, and it's not like a variable annuity. It pays so many dollars each year for 30 years, period, no matter what. $22,577,152.62 the first year, $23,706,010.25, and on. It will always pay out $1.5 billion, total... you just can't be sure if it will pay it all to you.

http://www.powerball.com/pb_contact.asp
WHAT HAPPENS IF AN ANNUITY PRIZE WINNER DIES?

The estate will handle the lottery prize. A lottery annuity prize is just like any other asset. You can pass any remaining annuity payments on to your heirs or to anyone else. The Powerball game will even cash out an annuity prize for an estate. This may make it easier for the estate to distribute the prize. It also may be necessary to cash out the annuity to pay Federal estate taxes. We will sell some or all of the securities at competitive bid or will even just transfer the securities to the estate. We do not charge a fee of any kind. We often hear people complain that the jackpot should not go back to "the state" when a winner dies. It does not. I think that this misunderstanding may come from the response that the prize "goes to the Estate" and some people hear "goes to the State."


Maybe I misunderstood, referring to estate taxes, wouldn't your heir have to pay in taxes (40%) of the amount they received over the 5M+ threshold every year they collected it?

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 4:21 pm

With estate taxes, you might well be right.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Tue Jan 12, 2016 4:23 pm

Clearly we need to round up some small children and ask them to choose between getting 930 marshmallows today and getting a total of 1,500 marshmallows: 23 today, 24 tomorrow... 92 on day #30.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

rec7
Posts: 2185
Joined: Tue Oct 28, 2008 7:22 pm
Location: ST LOUIS

Re: Powerball math: annuity is better?

Post by rec7 » Tue Jan 12, 2016 4:28 pm

Rodc wrote:It is really not a math problem, it is a behavioral problem.


I think you hit the nail on the head. This would be the best choice for most people I don't know about Bogleheads. They are not the average bear. But 5% sounds good to this Boglehead.
Disclaimer: You might lose money doing anything I say. Although that was not my intent. | Favorite song: Sometimes He Whispers Jay Parrack

autolycus
Posts: 126
Joined: Thu Jul 31, 2014 3:01 pm

Re: Powerball math: annuity is better?

Post by autolycus » Tue Jan 12, 2016 4:45 pm

westie wrote:
nisiprius wrote:Maybe I misunderstood, referring to estate taxes, wouldn't your heir have to pay in taxes (40%) of the amount they received over the 5M+ threshold every year they collected it?

The estate would pay 40% on all assets over the 5M+ estate exemption ($10M+ for a couple). Those assets would include a right to a future income stream in the form of the remaining payments left on the lottery annuity. The remark about the lottery allowing an estate to cash out the annuity is basically saying that the lottery has a system in place to prevent an estate from being in an impossible situation. For purposes of illustration, I will use highly simplistic numbers that are not valid for Powerball or MegaMillions, but the estate tax issue is still covered validly:

AutoMillions jackpots are paid over 10 years
Linus wins a jackpot worth $1 billion, or $100 million/year for the 10 years, all after taxes (for simplification)
Linus dies after receiving just 1 payment
Linus is very cautious and has simply deposited all of the first payout into a money market fund that earned nothing yet
Remaining payouts are worth $900 million
At this point, the estate is liable for 40% of the assets minus the exemption, or $100 million + $900 million - $5 million-ish
Of course, the estate doesn't have anywhere near $400 million in liquid assets because Linus only actually got $100 million before he died

The IRS will still expect immediate payment on the estate tax liability. So what do the heirs do? There are usually several options:
Enter into a payment plan with the IRS with portions of each annual payout going to the IRS.
Borrow money against the future payments.
Sell the future payment stream for immediate cash.
"Cash out" the annuity with the lottery.

letsgobobby
Posts: 10614
Joined: Fri Sep 18, 2009 1:10 am

Re: Powerball math: annuity is better?

Post by letsgobobby » Tue Jan 12, 2016 5:32 pm

nisiprius wrote:Clearly we need to round up some small children and ask them to choose between getting 930 marshmallows today and getting a total of 1,500 marshmallows: 23 today, 24 tomorrow... 92 on day #30.

brilliant. Although in the original experiment the rate of growth was higher and faster: a starker choice.

User avatar
VictoriaF
Posts: 17491
Joined: Tue Feb 27, 2007 7:27 am
Location: Black Swan Lake

Re: Powerball math: annuity is better?

Post by VictoriaF » Tue Jan 12, 2016 5:50 pm

Annuity is better because it's 3 commas, and the lump sum is only 2.

Victoria
WINNER of the 2015 Boglehead Contest. | Every joke has a bit of a joke. ... The rest is the truth. (Marat F)

lee1026
Posts: 389
Joined: Sat Jun 21, 2014 7:47 pm

Re: Powerball math: annuity is better?

Post by lee1026 » Tue Jan 12, 2016 6:06 pm

Why is everyone using 5% as an interest rate? The payment will increase by 5% a year; that have nothing to do with the break even rate of return needed on the lump payment to come out ahead of the annuity.

User avatar
dm200
Posts: 13698
Joined: Mon Feb 26, 2007 2:21 pm
Location: Washington DC area

Re: Powerball math: annuity is better?

Post by dm200 » Tue Jan 12, 2016 6:09 pm

Apparently, whether you have to choose between lump sum and annuity differs in different states. Some states you can choos after you win; other states you must choose when you buy the ticket.

Also, in some states (not sure which) you can collect "anonymously" (which is what I would like to do). Have hundreds of millions of dollars - and just live my same old frugal life (in public anyway). I would probably set up a "business" to (legally of course) appear to be very successful in that business.

gvsucavie03
Posts: 1234
Joined: Sat Feb 16, 2013 8:30 am

Re: Powerball math: annuity is better?

Post by gvsucavie03 » Tue Jan 12, 2016 6:10 pm

greg24 wrote:Best return is to not play.


+1

YttriumNitrate
Posts: 1062
Joined: Tue Mar 26, 2013 12:13 pm

Re: Powerball math: annuity is better?

Post by YttriumNitrate » Tue Jan 12, 2016 6:23 pm

deleted.
Last edited by YttriumNitrate on Sat Mar 12, 2016 12:51 pm, edited 1 time in total.

User avatar
Epsilon Delta
Posts: 6492
Joined: Thu Apr 28, 2011 7:00 pm

Re: Powerball math: annuity is better?

Post by Epsilon Delta » Tue Jan 12, 2016 7:53 pm

VictoriaF wrote:Annuity is better because it's 3 commas, and the lump sum is only 2.

Victoria


If all you want is the commas move to India. You'll get an extra one for the crore and one more for the Rupee.

jjface
Posts: 2462
Joined: Thu Mar 19, 2015 6:18 pm

Re: Powerball math: annuity is better?

Post by jjface » Tue Jan 12, 2016 8:40 pm

lee1026 wrote:Why is everyone using 5% as an interest rate? The payment will increase by 5% a year; that have nothing to do with the break even rate of return needed on the lump payment to come out ahead of the annuity.


Yes I was thinking the same. They have just set the stream of income to rise by 5%. It is not as if you are getting more money by taking it as an annuity as the lump sum would take into account this increase. If they didn't have a payout pattern with a 5% increase you would simply have $50million throughout the 30 years (which would actually be worth more as a lump sum I reckon as you are getting more in earlier years - the 5% increases works to the lottery's advantage yet they spin it to make it sound good. I think anyway!). What you really need to compare to is the interest rate on the government securities they are using and factoring in the slight tax benefit to having it spread over 30 years.

Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

Re: Powerball math: annuity is better?

Post by Rodc » Tue Jan 12, 2016 8:55 pm

nisiprius wrote:
Rodc wrote:It is really not a math problem, it is a behavioral problem.
I can think of so many things I could do with $930 million that I couldn't do with just $22 million. :(

Quite seriously, if I were running the lottery, I'd create a third option--one that pays out, oh, I dunno, 10% as a lump sum immediately and then the rest as an annuity. So you can buy the yacht right away, and then operate it later.

I assume the annual cost of operating a yacht is less than the cost of buying it? I wonder whether it is?


Opens up a new line of thought: with a guaranteed income of $22M a year you could lease a yacht. And given interest rates, depreciation and such is it better to take lump sum and pay cash or annuity and lease? :happy

I have often thought some version of your new option would really be nice.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

mikep
Posts: 3596
Joined: Wed Apr 22, 2009 9:27 pm

Re: Powerball math: annuity is better?

Post by mikep » Tue Jan 12, 2016 11:50 pm

Maybe lump sum is better in CA, where as of today the lottery winnings are surprisingly state tax free. It would be a big mistake to take the annuity then CA changes their laws to charge the winner 13.3% tax on it for 30 years.

User avatar
walletless
Posts: 707
Joined: Fri Aug 15, 2014 4:55 pm

Re: Powerball math: annuity is better?

Post by walletless » Wed Jan 13, 2016 12:04 am

Considering the rule of 72, I would expect my money to double in approximately 14 years. At a 62% payout, the lumpsum is a no-brainer from a pure financial pov. You could easily expect to quadruple the money over 30 years with a 40/60 allocation or 5% annualized return and re-investing dividends.

If the reasons for choosing an annuity are non financial, such as needing more time to figure out a plan -- thats a different discussion altogether.

letsgobobby
Posts: 10614
Joined: Fri Sep 18, 2009 1:10 am

Re: Powerball math: annuity is better?

Post by letsgobobby » Wed Jan 13, 2016 12:12 am

In general it's not fair to compare risky with risk free investments.

lee1026
Posts: 389
Joined: Sat Jun 21, 2014 7:47 pm

Re: Powerball math: annuity is better?

Post by lee1026 » Wed Jan 13, 2016 1:23 am

And more importantly, you will be paying taxes on the earnings from the lump sum. Getting this kind of money into an IRA can be tricky.

Rodc
Posts: 13601
Joined: Tue Jun 26, 2007 9:46 am

Re: Powerball math: annuity is better?

Post by Rodc » Wed Jan 13, 2016 6:47 am

walletless wrote:Considering the rule of 72, I would expect my money to double in approximately 14 years. At a 62% payout, the lumpsum is a no-brainer from a pure financial pov. You could easily expect to quadruple the money over 30 years with a 40/60 allocation or 5% annualized return and re-investing dividends.

If the reasons for choosing an annuity are non financial, such as needing more time to figure out a plan -- thats a different discussion altogether.



Need to remember that compounding works on the annuity payments as well. First payment compounds for 30 years, next year for 29 years etc, if you want a fair comparison.

In both cases need to also account for any spending along the way.

Likely lump still wins.

On the other hand a fair comparison also equalizes risk and putting it all in the stock market is much more risky so of course the average result is higher.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Wed Jan 13, 2016 7:16 am

Epsilon Delta wrote:
VictoriaF wrote:Annuity is better because it's 3 commas, and the lump sum is only 2.

Victoria
If all you want is the commas move to India. You'll get an extra one for the crore and one more for the Rupee.
Wow! Thanks for making me Google that. Wikipedia:Indian Rupee, numeral system, Indian comma placement.

If I've got it right, USD $1.5 billion = 100,237,500,000 rupees which would be written ₹1,00,23,75,00,000.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
nisiprius
Advisory Board
Posts: 34135
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Powerball math: annuity is better?

Post by nisiprius » Wed Jan 13, 2016 7:29 am

lee1026 wrote:Why is everyone using 5% as an interest rate? The payment will increase by 5% a year; that have nothing to do with the break even rate of return needed on the lump payment to come out ahead of the annuity.
Everyone isn't using it, and the breakeven rate of return to match the annuity is 2.84% as I showed above.

The 5% rate of increase is some kind of arbitrary choice that someone pulled out of thin air, probably because it is easier and less risky to provide that then a true inflation-indexed increase; it seems like a pretty good one, but it's just someone's tasteful choice.

I think it's quite likely that the relationship between annuity and lump sum is calculated by actuaries in some way based on Treasury rates in a reasonably fair way; that is, in such a way that the Powerball people don't care which option the winner elects and have no motivation to "sell" one over the other.

But, yes, you are right, in some vague kind of way people seem to be thinking that the fact that the payments increase by 5%/year, and that the average rate of inflation--both since 1913 when they started to calculate it and over the last thirty years or so since Volcker got tough--has been in the general ballpark of 3%, that it somehow makes the annuity a good deal. It doesn't. It's not as if you had a choice between taking the Powerball annuity of about $23 million the first year, increasing 5% per year, versus buying one that starts at the same $23 million the first year and only increases according to the CPI.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

Dulocracy
Posts: 2253
Joined: Wed Feb 27, 2013 1:03 pm
Location: Atlanta, GA

Re: Powerball math: annuity is better?

Post by Dulocracy » Wed Jan 13, 2016 5:12 pm

greg24 wrote:Best return is to not play.


+1 I came here to say this.

To OP: I do not think you can ignore the risk that whatever entity is in charge might someday fail to pay. That is a part of the math one must do in consideration of this question.
I'm not a financial professional. Post is info only & not legal advice. No attorney-client relationship exists with reader. Scrutinize my ideas as if you spoke with a guy at a bar. I may be wrong.

User avatar
walletless
Posts: 707
Joined: Fri Aug 15, 2014 4:55 pm

Re: Powerball math: annuity is better?

Post by walletless » Wed Jan 13, 2016 5:16 pm

Dulocracy wrote:
greg24 wrote:Best return is to not play.


+1 I came here to say this.

To OP: I do not think you can ignore the risk that whatever entity is in charge might someday fail to pay. That is a part of the math one must do in consideration of this question.

Yes, additionally the state & localities that do not have tax currently, such as California, may start doing so. Annuity is not risk-free, like several folks on this thread seem to suggest. Is probably low-risk compared to investing in stock market, but not risk-free.

alex_686
Posts: 2545
Joined: Mon Feb 09, 2015 2:39 pm

Re: Powerball math: annuity is better?

Post by alex_686 » Wed Jan 13, 2016 5:29 pm

nisiprius wrote:
westie wrote:If you're over 40, you're making a bet on your mortality if you take the annuity.
I don't think it's a life annuity (that is, one that stops with the death of the annuitant.) The word "annuity" is really confusing because it basically means any stream of annual payments. I think the Powerball annuity continues for 30 years no matter what. So you're only making a bet on your mortality in terms of your personal enjoyment of the money.

Nisprius, first, +1 on the Excel work. I think you nailed the issue perfectly.

Second, the article refers to the payments as a "certainty annuity" - it pays for exactly 30 years and stops, even if you die the next day. So once again you have hit it on the noise.

FYI, I am playing the lotto because it is the rational thing to do. I would be very sad if the office pool won and I was the only one that showed up for work. A small insurance payment to avoid regret.

gvsucavie03
Posts: 1234
Joined: Sat Feb 16, 2013 8:30 am

Re: Powerball math: annuity is better?

Post by gvsucavie03 » Wed Jan 13, 2016 5:34 pm

FYI, I am playing the lotto because it is the rational thing to do. I would be very sad if the office pool won and I was the only one that showed up for work. A small insurance payment to avoid regret.


:confused the only assurance about playing the lotto is that you have a near 100% chance of not winning.

Twins Fan
Posts: 2775
Joined: Fri Mar 08, 2013 1:02 pm

Re: Powerball math: annuity is better?

Post by Twins Fan » Wed Jan 13, 2016 5:43 pm

I don't play the lotto, so....

But, I think I would take the annuity. Math and taxes and whatever be darned. You're getting a lot of money and paying a lot of taxes either way.

I would just get more of a kick out of becoming a $22 millionaire each and every year. That way just in case I were to go total Rock Star and blow it all in one year, there's always next year to get my head right. :D

Dick D
Posts: 114
Joined: Sat Jun 16, 2007 8:55 am
Location: Connecticut

Re: Powerball math: annuity is better?

Post by Dick D » Wed Jan 13, 2016 8:14 pm

My fantasy would be to take the annuity. I think that it would be easier to deal with a 23 million check annually than the big number all at once. Who cares if you could get more one what or another. So what if the whole system goes belly up after your first check. For a $2 investment, not bad. Just keep in mind that you are more likely to be struck by lightning and run over by a bus at the same time.

scotthal
Posts: 155
Joined: Wed Nov 06, 2013 9:20 pm
Location: Portland, Oregon

Re: Powerball math: annuity is better?

Post by scotthal » Wed Jan 13, 2016 9:47 pm

Heck - I'd go with the lump sum. Figure Oregon would collect it's 9.9% in either case (lump sum, or annuity); but I can change state of residence to minimize dings to investment returns & estate taxes.

Comic thought: Schrödinger's ticket - it could be a winner - I haven't checked the number, & nobody has (as yet) claimed the prize...
Growtch, grinch; paranoid contrarian

ponyboy
Posts: 484
Joined: Fri Feb 06, 2015 10:39 am

Re: Powerball math: annuity is better?

Post by ponyboy » Thu Jan 14, 2016 8:42 am

I just cant believe I didnt win the powerball. I was so certain that I was going to win. It appears 3 tickets were sold in different states. Im still in shock my numbers werent picked.

sesq
Posts: 544
Joined: Wed Jan 30, 2013 9:24 am

Re: Powerball math: annuity is better?

Post by sesq » Thu Jan 14, 2016 10:59 am

scotthal wrote:Comic thought: Schrödinger's ticket - it could be a winner - I haven't checked the number, & nobody has (as yet) claimed the prize...


Bravo. I buy a single ticket somewhat often. I usually don't check my tickets for a couple months unless there is a press report that says a winning ticket was sold in my state. Never thought of it that way, may need to borrow that.

Post Reply