The Lottery and Annuity Calculations

Cecil's Columns/Staff Reports
21

Back to the tax issue…

If you take the annuity option, does the state pay out taxes to the feds on the amount you haven’t yet collected? I would think not.

So, the amount you would pay in taxes, if you took the lump sum, is used by the annuity provider to build interest, if you take the annuity. Surely this has an effect on the interest rate used to figure NPV?

In other words, the annuity provider may be making 8% on the cash it’s holding (and paying you 7%) but, if you took the lump sum, in order to end up with an equal amount in 26 years, you might have to earn 12% on what’s left after the feds are done with you.

Does this have any real effect on the decision whether to take the annuity or lump sum? Is the annuity more attractive because of the tax deferment? Or is a matter of you get what you get, same thing either way?

22

The SD got this one wrong.

The correct evaluation of this problem considers the opportunity cost between the lump sum payment $500,000 vs. $1,000,000 received over a period of 20 years. In other words, what interest rate is required assuming that you invest the lump sum payment, $500,000, to generate $1,000,000 after 20 years.

Depending on when the interest is paid, beginning or end of period, the rate either 3.72% between 3.93%.

This is, (no big surprise), about the current rates available for commercial lending, which is what the lottery folks do with your winnings to generate the payments.

Take the lump sum.

23

Deferring taxes over the 26 years would definitely be advantageous. Also, unless you’re already earning in the highest tax bracket (probably not, if you’re buying lottery tickets), then the $1,000,000 upfront will largely be taxed at the highest rate, whereas $50,000 or $38,461 per year will likely not be taxed at such a high rate. So, there are two tax reasons to defer receipt of the full amount.

It would be tough for Dex to factor that in, since tax differences among people and also among states varies so greatly. If you win $1,000,000 or more, I would consult your tax advisor.

24

If you invest the $500,000 at 3.93%, you can get a payment of $35,180.59/year for 20 years. If the lottery commission is offering you $50,000/year, you should take that. Since $50,000/year implies a rate closer to 9%, that is your better option.

25

I’ll put what I’m thinking into smaller terms and see where it gets me.

Let’s say that you won a $20,000 jackpot in 1978. Taking the lump sum, you would have just enough cash to buy a new Corvette (and one of my favorite years, too). Taking the 20 annuities, investing in 6% savings, and planning to buy a new Corvette as soon as you have enough money, you might have:

$5,900 (annuities+interest) in 1983. Not enough to buy the $18K 82 Vette (there was no 83 vette).

$13,900 in 1988. Not enough to buy the $29.5K 88 Vette.

$24,500 in 1993. Not enough to buy the $34.6K 93 Vette.

$38,800 in 1998. Finally! After 20 years, you have enough to buy the $38K 98 Vette.

Meanwhile, you’ve missed out on 20 years of ownership of a vehicle that you could probably have sold in 1998 for what you paid in 1978.

Seems to me like inflation is most definitely a factor. Of course, I’m oversimplifying and 6% may be way off.

26

I’m not sure that Corvette pricing represents a good estimate of inflation, and I haven’t gone through your numbers to see if they are right. However, you could use computer pricing to come to the opposite conclusion. In 1978, $10,000 would buy around 8 1 MHz Apple ]['s with 16k of memory, no monitor, no disk drive. In 1998, $38,000 would buy you probably 8 300 MHz Pentium 2’s or 3’s, with probably 64 MB of memory, 20 GB HD, or the equivalent clock cycles of 2,400 Apple ]['s, equivalent storage space of 32,000 Apple ]['s, and so on.

27

I’m lousy with this kind of thing, but in this case:

… are you taking the interest plus withdrawing a certain amount to reach that $35K, thus depleting the original amount in 20 years? If so, here’s where the amount of the jackpot could make a difference. There is some amount of money, say $60,000, that I could live on annually for the rest of my life (accounting for inflation). So if I take the lump sum amount, subtract the cost of a new home (plus whatever celebratory purchases I’d want to make right away. like buying Mom a condo in Florida), invest the rest the rest, I’d want an annual return of $60K plus the current inflation rate X the balance (to reinvest as a hedge). That would last in perpetuity.

28

No one has addressed an issue I heard about years ago, and have wondered about e’er since. I doubt it’s true, but if it is, I need to know!

What I read was that if you win 100 mil, take an annuity at 4 million each year for 25 years, and die after the first payment, the IRS will tax your heirs for inheriting 96 million dollars immediately.

Doesn’t make much sense to me, but neither does people owing AMT on millions they’ve never received from stock options, and that happens.

Anyone care to calm my worries, or those of my childerkin?

29

For what it’s worth, I think that inflation risk is an important factor to consider.

If you take the lump sum, you can invest a decent chunk of the money in Swiss Francs and other investments outside of the United States. So that if the U.S. dollar is devalued and/or the U.S. hits a period of serious inflation, you’ll be hedged to a certain extent.

As another poster pointed out, there is also a default risk.

The lump sum means that you don’t have all your eggs in one basket. Granted, it’s probably a damn good basket. But with that kind of money, the sensible thing is to hedge yourself. I’d take the lump sum.

And with all due respect to Dex, the goal is not necessarily to maximize the expected return. Risk is an important thing to consider.

30

Dex:

All in all I think you made an excellent report, but it appears to me that you’ve made an error that’s pretty common in these kinds of things.

To answer the question: Which should I take, the lump sum of the annuity, there are actually two factors at play. The first as you correctly state is the interest rate the assumption is based on.

The second factor is the discount rate.

The annuity calculation is a simplistic model used simply to compare interest rate assumptions between annuitties.

In a bond calculation the discount rate is figured in seperately, in an annuity calculation you must interpolate it.

For example, you say:

Me neither, but you really aren’t guarranteed to make 8.9% in terms of actual value to you, are you?

What you will actually receive is a sum in dollars equal to an 8.9% interest rate.

If inflation runs at 10% for the next 20 years, in terms of actual value you are actually losing 1.1% annually in real terms, are you not?

So, clearly if you accept the annuity and lock in for the next 20 years you are accepting inflation risk. As we all know, if we are accepting a risk, we must get paid for it, right? Therefore, we would expect something that exposes us to inflation risk to pay us more than something that did not (like cash in hand, which we can spend.)

Similarly, we are losing use of the money that will not be paid to us until a future time, and there is an opportunity cost.

Since we will be paid in dollars we will have currency risk

Since we will be locked into an interest rate assumption we will have interest rate risk.

Depending on how confident we are in the ability of the annuity to keep its promises for the next 20 years and actually pay us, we are taking credit risk.

Finally, we have the nebulous quantity that cash in hand is inherently more valuable than cash down the road, since it can be spent now against need, and is readily exchangeable into goods and services. In short it is liquid. Liquidity is valuable. Nothing is more liquid than cash in hand.

So, in order to make a good comparison we either need to step of the value of a present sum based on these factors, or discount the annuity to compensate for them.

There’s a number of ways we can do this.

One way to do it is to close your eyes, squint really hard, concentrate and try to give birth to a discount rate that compensates you realistically for these risks. I know some professionals that do just this. “All that crap, right now? 20 years? That’s a 4% discount rate!” (This works surprisingly well)

If we accept that than your real interest rate discounted for the risk you are taking is only paying 4.9%. Because a discount rate is the cost of the risk taken.

The other way to do is to assign all these risks an individual value, and add them up.

A third way to do it is to try and see what everybody else is doing. For example, the annuity payments versus a string of consecutive zero coupon treasuries, and you can seperate out credit risk and portion of liquidity risk (Treasuries are more liquid than the assignment of an annuity.)

Since we know the treasuries contain interest rate risk, inflation risk, and currency risk we are left with the relative difference in liquidities and credit qualities.

By far the biggest component of discounting an annuity is the almost total loss of liquidity due to the difficulty in disposing of the asset. Five years down the road should you have a major liquidity need and seek to cash it in for it’s present value, you will be sorely disapointed. Neither the insurance company, nor the state will want to hear it or be willing to accomodate you. You will have great difficulty in finding somebody willing to buy the annuity from you because of the assignment problems of such a vehicle and they will want to buy it only at a very steep discount to it’s current present value.
Typically, this liquidity is very very highly valued and not given up lightly. This is why so few annuities actually annuitize, and why so few immediate annuities are sold.

Conversely this is also why lotteries are paid in this fashion. Since they are disadvantageous on so many levels, they are the vehicle that expands the present value of a current sum of money at the greatest rate, enabling those running the lottery to present the largest possible prize for the least amount of money.

This is why a 20 year treasury pays so much less than the 8.9% you get if you accept the annuity.

You are giving up a lot to get that 8.9% and taking a lot of risk to do so with very little recouse.

This is why most advisors and planners will recommend the lump sum option to lottery winners and why almost all lottery winners take the lump sum option. Undiscounted, that 8.9% is an illusion.

31

Trying to cover many issues here at once.

I used an interest rate to reflect the time-value of money. Presumably, this includes an inflation rate plus an earnings rate, so inflation is included in the calculation. And yes, I used an average rate over the 20 year period – the reality will be a different rate every year or every month or whatever.

I deliberately did not include taxes in the calculation for a number of reasons:
(1) My understanding is that if you have the choice between forms of payment,( lump sum or annuity), you are taxed on the lump sum value. U.S. Federal Tax is based on opportunity/ownership rather than cash-in-hand. Hence there is no tax advantage to an annuity over a lump sum. I’m trying to check this.
(2) IF tax rates remain where they are for the next 20 years, and IF the lottery winnings are your only source of income, then there is a tax advantage to taking an annuity – you’ll be at top marginal rates, but the effective rate will be lower. However, those are big if’s. And if the tax rates go up in the next 20 years, you could be screwed by taking the annuity. I didn’t want to get into that many what-if scenarios, so I ignored tax treatment.

I did say that anyone with a winning ticket for a millions-of-dollars jackpot should consult with a lawyer (and I implied with a tax-advisor) to figure best ways of structuring.

32

One problem with Scylla’s (terrific) post is that in purchasing a lottery ticket in the first place the winner has shown they are prepared to pay a premium to acquire risk.

A factor in favour of the annuity that was barely alluded to in Dex’s report is akrasia (incontinence or weakness of will). If you recognise that you might well “blow it all in a spree”, you would do well to have your hands tied. At the extreme end, Mike Tyson should have taken his money as an annuity even if the annuity was a pretty bad deal financially.

33

kapntoad,

I think that something similar happened in Massachusetts some years ago. A winner died shortly after winning, and the heirs were taxed based on inheriting the entire amount, despite the winner electing the annuity. The payments may even have been temporarily held up. There was a bit of a controversy before it was resolved.

To the best of my memory, the tax agencies had moved preemptively to assure their (future) payments. The heirs were required to sign agreements with the agencies, promising to pay their taxes on the money, before payments would be authorized.

One thing became very clear from all of this: the Lottery Commissions work VERY closely with the local and Federal tax agencies.

best to all,

plynck

34

I can’t tell you all how valuable your input has been to me.

In a few weeks, when the MegaMillions jackpot reaches some amount worth considering rather than the piddling $30 mil it’s currently at, I’m going to splurge one buck on a ticket. When the check comes in, I’ll buy you all lunch.

Thank you. Thank you.
:wink:

35

You are forgetting:
1 that you are investing the 500,000 so you get to keep it.
2 compound interest applies, so the interest changes over time.

For clarity, consider the following table, which assumes the interest is paid at the end of the period.

Year Rate Balance Interest
1 3.53% 500,000 17,632
2 3.53% 517,632 18,254
3 3.53% 535,887 18,898
4 3.53% 554,785 19,564
5 3.53% 574,349 20,254
6 3.53% 594,604 20,969
7 3.53% 615,572 21,708
8 3.53% 637,280 22,474
9 3.53% 659,754 23,266
10 3.53% 683,020 24,087
11 3.53% 707,107 24,936
12 3.53% 732,043 25,815
13 3.53% 757,858 26,726
14 3.53% 784,584 27,668
15 3.53% 812,252 28,644
16 3.53% 840,896 29,654
17 3.53% 870,551 30,700
18 3.53% 901,250 31,783
19 3.53% 933,033 32,903
20 3.53% 965,936 34,064
Final Balance 1,000,000
Try in on a financial calculator. Take the lump sum.

36

You are forgetting, you could take the $50k per year and invest it the same way as the $500k:

Interest rate 3.53%

Balance Additional Principal Interest
$- $50,000.00 $1,765.00
$51,765.00 $50,000.00 $3,592.30
$105,357.30 $50,000.00 $5,484.11
$160,841.42 $50,000.00 $7,442.70
$218,284.12 $50,000.00 $9,470.43
$277,754.55 $50,000.00 $11,569.74
$339,324.28 $50,000.00 $13,743.15
$403,067.43 $50,000.00 $15,993.28
$469,060.71 $50,000.00 $18,322.84
$537,383.56 $50,000.00 $20,734.64
$608,118.19 $50,000.00 $23,231.57
$681,349.77 $50,000.00 $25,816.65
$757,166.41 $50,000.00 $28,492.97
$835,659.39 $50,000.00 $31,263.78
$916,923.16 $50,000.00 $34,132.39
$1,001,055.55 $50,000.00 $37,102.26
$1,088,157.81 $50,000.00 $40,176.97
$1,178,334.78 $50,000.00 $43,360.22
$1,271,695.00 $50,000.00 $46,655.83
$1,368,350.84 $50,000.00 $50,067.78
$1,468,418.62

Take the payments.

37

Take the payments because the lump sum amount would NOT be $500,000. Federal taxes of approx. 35% would automatically reduce your lump sum to ‘only’ $325,000.

38

OK, so then the table created by owenscasper will have to be rejiggered with a starting point at $325,000 and a new interest rate so that the end point after 20 years will be $1,468,418.62.

But if you’re factoring taxes into it, then shouldn’t d511’s table be corrected as well? Let’s assume you’re filing jointly, and you make $30,000 a year to begin with, so you’re now at $80,000 income. According to grg88’s tax table, you’re now at 25%, so instead of getting $50,000 a year, you’re now at $37,500 a year . . . times 3.53% interest, compunded . . . carry the one . . . shit howdy, this is why I pay someone else to do my taxes.

39

Also, if anyone cares, the California lottery’s explanation of cash value vs. annual payments can be found here.

Some relevant quotes:

There’s a table that follows this second part explaining the $175,000/$357,000 thing.

So here’s a question: Given that the highest tax bracket cited above, by grg88, starts at $311,950, both for joint and single filers;

And assuming the prize is $14,000,000 or higher, and the first year payment rises proportionately so that it puts the winner into the highest bracket immediately;

And assuming said winner–let’s call him Airblairxxxx, with four 'x’s–stays in said highest bracket throughout the 25 year payment schedule;

THEN:

Aren’t taxes a wash when deciding between cash value and annual payments?

40

All you ever wanted to know about tax consequeces of lottery jackpots, but were afraid to ask (4 years out of date, rates have changed and who knows what else): 2021 | Williams Mullen

A simplified treatise onthe subject, dealing mostly with investment returns: http://www.washingtonpost.com/ac2/wp-dyn/A48910-2003Jul12?language=printer

In answer to your question: the taxes on $500,000 are less than half of the taxes on $1,000,000. Why? Because the tax rate you quote is the marginal tax rate, i.e. the tax you pay on the next $1 you make. So if you earn $500,000, you pay 10% on the first 14,500, 15% on the next $x thousand (sorry, too lazy to look it up), etc, etc, and then 35% on the final $188,050. Which works out to less than 35%, on average. Lets call it 30%, just for sake of argument. If you earn $1,000,000, you’ll pay the same as the dude making $500,000 on your first $500,000, then 35% on the final $500,000, yielding and average tax rate of 32.5%.

Based on my quick scan of the first cute, you will pay less taxes if you choose the annuity. However, if the jackpot is huge (say, $25M+), the differences are negligible. But, if you don’t have anywhere really good to invest the money, then the annuity is a good deal because taxes deferred are taxes saved.

All of this crap makes me want to move back to Canada, where the jackpot amount is the actual amount you win, in cash, on the day you claim it, and it is tax free (although I heard they were thinking of changing this). Of course I don’t play the lottery, so the point is moot.