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Friday, August 29, 2008

MM Cash or Annuity? The LPP Analysis of the Mega Millions Jackpot

Introduction
Mega Millions players are required to choose whether they wish to receive Cash or Annuity Option at the time of purchase. In most States, the players who choose the Annuity Option may opt to take the Cash Value within 60 days of winning, but those who originally chose the Cash Option may not change their mind. After asking around, we confirmed that most people select the Cash Option, believing this is the best choice. So, if you play Mega Millions, what do you choose:

The Cash or Annuity Option?

Since the beginning of 2002 through Aug 24 2008, seventy-five (75) jackpots have been won by individuals and groups. These are listed in the Mega Million Jackpot History of Winners page. However, the Mega Millions website does not indicate whether these winners had chosen the cash or annuity payouts. But, it does feature profiles of 19 winners in their Winners Gallery. Of these 19, three have chosen the Annuity, and the rest have taken the Cash Option.

This means that around 85%
of Mega Millions players
take the Cash Option.
Is this the best decision?

Or, would they have more money by taking the Annuity?


Real World Example
For purposes of this paper, we have chosen to analyze the Jul 25 2008 Mega Millions drawing. We believe this Jackpot Analysis is relevant because it represents the minimum jackpot payment as defined by the rules, and is current as of this writing.

Graph MM0808a illustrates the Jackpot Offerings for the Jul 25 2008 Mega Millions drawing.


In this drawing, Jackpot winners choosing to receive the Annuity option will be paid $12 million in 26 equal installments spread over a 25 year period. Those who elect the Cash option will receive only one lump sum payment of $7.1 million. Comparing the amounts of both options presented, the Cash to Annuity Ratio for this drawing is 59.2%.

Having little other information, most winners will elect to receive the Cash Option, believing that the $7.1 million is a fair amount within the current interest rate environment.

However, this Cash Option may not be fair.

Therefore, the purpose of this paper is to provide Mega Millions players with more information about their two options. In this, we shall examine both the tax implications of each, and explain how fluctuating interest rates influence the size of the offered Cash Option, and more. By

Analyzing and Comparing the
Cash and Annuity Mega Millions
Options

we believe both players and winners will have a better understanding of the fairness of the estimated cash option being offered in any particular Mega Millions drawing.


How the Cash and Annuity are Paid
In Mega Millions, a Jackpot annuity winner receives 26 equal payments over a 25 year period. This differs from Powerball whose payments are graduated over a 29 year period. Taxes are paid yearly on receipt of each payment, meaning that all accrued interest earned remains tax free until payment is made to the winner.

Conversely, players who choose to receive the Cash Option will receive a single lump sum payment whose estimated value is stated on their web site. Taxes on this full amount is payable in the year received.

Mega Millions describes these different payment options on their page: "Differences Between Cash Value and Annuity".


Mega Millions Annuity Yearly Cashflow Payments
Because each of the Mega Millions Annuity Payments is fixed, the amount of money that the Mega Millions organization must deposit varies, depending on the: length of time until payment is made, and interest rates earned on this money. However, the payments made to the winner is always fixed. This means that players who won $12 million and elected the annuity option, would receive an 26 annual payment of $462 thousand every year.

Assuming that the prevailing interest rates are at an even 4% per year, Graph MM0808b illustrates the 26 annuity cash deposits that would be required by Mega Millions in order to meet these payments.

We have chosen the 4.0% interest rate level because this is the rate that the competing Powerball assumes its reinvestment. By using this same rate, we can reliably compare the cash values of both of these lotteries.




Note: This graph is for an $12 M annuity, but is scalable. If the annuity is $30 M, multiply payments by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.

As shown, the blue horizontal line illustrates the constant payment of $462K made to the winner. The vertical green bars illustrate the money required to be deposited. Notice that as the time increases, the amount of money Mega Millions must deposit is reduced. This is because compound interest is being earned on each deposited cashflow. When interest rates are 4.0%, Mega Millions would need $462K for the first payment; $365K for the 5th year; $289K for year 10, ... and finally $143K for the 26th and final payment. The differences between the deposited amount and the $462K payment is the interest earned.

To be fair to the players, the total the 26 deposits should equal to the Cash Value Offered at the time the tickets are being sold. Since we are assuming 4.0% as a fair interest rate, Mega Millions must aside $7.672 Million in order to make these payments of $12 M to you.

We shall define this value of $7.672 million as Par.
The Par Cash to Annuity ratio is 63.9%.


Jul 25 2008 Jackpot Revised
Adding the $7.672 M Par Value to our Jackpot Graph (MM0808c) provides us with a relative measure by which to judge the fairness of the $7.1 million cash option offering. As shown, the Cash Option is $0.572 million below Par. This means that those who elect the Cash Offer immediately lose $0.572 of their winnings. In terms of ratios, we are offered 59.2% verses the par 63.9%, or a 4.7% loss.


Without knowing the prevailing interest rates by which to reinvest our Cash Option, we cannot yet say with certainty that the $7.1 offering is unfair.

But we know for sure that if we take the Annuity, $7.672 M will be set aside for our winnings. If we take the Cash Option, we immediately lose nearly $600,000. This comes out to losing $22 thousand per year.



Fair Value of Mega Millions Cash Option at Varying Interest Rates
Both the Mega Millions organization and us recognize that interest rates vary. Because of this, the value of the cash option will move in the opposite direction of interest rate movements. This means that if interest rates go up, the cash option goes down, and vice-versa. Knowing the fair value of the cash option at various interest rate levels further will help us to judge the fairness of the Cash Option being offered.



Graph MM0808d illustrates the fair value of the cash option value at interest rates varying from 2% to 10%. Note that when interest rates fall below 4%, the cash option increases above our $7.672 M Par Value (green line).

This graph tells us that when interest rates are at 2%, Mega Millions must invest $9.472 million to fund our $12 million annuity. At 3% interest, $8.498 must be deposited for funding. And, when interest rates rise to 10%, only $4.651 needs to be invested.

Referring to this graph, we observe that the July 25 2008 Cash Option of $7.1 M equates to an interest rate environment of slightly less than 5%. Considering that interest rates have fallen substantially during January 2008 and May 2008 (from 4.25% to 2.00%) and continue to remain low, this 5% investment level appears to be rather high.

Thus, the July 25 2008 $7.1 Million Cash Option begins to appear to be rather low.

Note: This graph is for an $12 M annuity, but is scalable. If the annuity is $30 M, multiply amounts by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.


Tax Implications
Regardless which option a winner selects, taxes represent a large portion of the income. Winners are automatically moved into the highest tax bracket, and both standard and itemized deductions become limited.

Because of this, we assume that Federal Taxes will consume 35% of one's winnings.

This means that those who elect the $12 million Annuity Option will pay a total of $4.2 million to the IRS. Without paying State taxes (many states do not tax those residents who win Mega Millions),

Annuity winners keep $7.8 million

to spend and invest. One important benefit of taking the annuity is that taxes will only be paid on the amount of money given to the winner each year. All other interest being earned will remain and grow tax free until it is paid out later.

Conversely, those who decide to take the Cash Option will be taxed immediately. In the case of the July 25 2008 cash jackpot, the winner will immediately fork over $2.5 million to the IRS. This means that the cash winner will only pocket $4.6 million. Typically, Mega Millions withholds only 25% of the jackpot winnings. This means that winners will be liable for the remaining 10% when they file their taxes. Most winners do not realize this and are unhappily shocked when they learn about the additional tax consequences.

The website USAMega.com provides excellent Mega Millions Jackpot Analysis pages that summarize both the Federal and State Tax implications on the Annuity and Cash Options.


Cash Value Implied Yield Curves
Knowing that $12 M annuity winners will retain $7.8 million of their winnings after taxes, it is possible to construct the associated Implied Yield Curves that will provide the cash option winners with the same amount of money. Using this $7.8 M value as a target, the Blue Curve displays the Tax Free Rates for varying cash offerings, meaning that the earned interest is not taxed until paid. Whereas, the Green Curve indicates the Taxable Equivalent Curve. The horizontal axis indicates the cash value offering in millions. The vertical axis indicates yield rates.


Note: These Cash Jackpot values are based on a $12 M annuity, and are scalable. If the annuity is $30 M, divide the offered amount by 2.5; if $84 M, divide by 7; if $240 M, divide by 20; etc.


Returning to the July 25 2008 drawing, the Cash Jackpot offering is $7.1 million.

Assuming that this is the fair value, it will be the same amount that Mega Millions will invest for the Annuity winners. From the graph MM0808e Blue Curve, we can guesstimate that Mega Millions will invest this money at approximately 5.0%. The interest earned on the annual payments will compound tax free at this rate and will generate a total of $12 M in payments to the winner. After paying taxes, the player will get to keep the $7.8 million.

However, if the player selects the cash option, he will receive $7.1 million, pay $2.5 M in taxes, and invest the remaining $4.6 million. The Green Curve in graph MM0808e already takes the reduction of taxes into account. So, to find the taxable equivalent yield the player must earn, we locate $7.1 M on the horizontal axis, then find the point on the Green Line above it. Doing this, we find that the cash option winner must receive approximately 6.5% on the remaining $4.6 M in order to earn $7.8 million.


Evaluating the July 25 2008 Cash Offering
Considering the Federal Reserve has reduced interest rates substantially, we know that short term rates are around 2.3%, 10-year Treasuries less than 4.0%, and 30-year treasuries below 4.5%. Thus, it is impossible for Mega Millions to earn an average rate of 5.0% on the annuity deposits at this time. Therefore, we conclude that:

The $7.1 million cash offering is extremely undervalued,
and should be at least $7.7 or more million.


Cash Loss per Million (Mar 14 - Aug 29 2008)
To test the correlation of the Mega Millions Cash Option Jackpot offering against actual changes in interest rates, we have constructed the Cash Loss per Annuity Million graph at right.


We define Cash Loss as the difference between the expected Cash Par Value and the Offered Cash Value, normalized to a single $1.0 million in annuity value.

As shown, the graph covered the 49 drawings beginning March 14 2008 and ending August 29 2008. The magnitude of the loss is displayed on the y-axis, and ranges from $10,000 to $60,000 per annuity equivalent million dollars. The vertical Green Lines indicate when a Mega Millions Jackpot was won and was reset to the minimum $12 M. The horizontal Blue Line indicates the average loss of $30,000 per million.

During this period, the FOMC reduced the Federal Funds Target rate twice:
  • Mar 18 2008 - from 3.00% to 2.25%, and
  • Apr 30 2008 - from 2.25% to 2.00%.
These are indicated by the magenta dots on the graph.

Because the interest rates were lowered, we would expect the Ratio of the Cash Offered Jackpot to Annuity to the closer to the Par Jackpot ratio of 63.9%, thus bringing the Loss per Million closer to zero.

But in reality, the Cash offering by Mega Millions appears to be random. During the period March 18 and April 30 when Fed Funds was 2.25%, the loss spiked to $60K, then dropped to $10K. After the April 30 cut, the losses remained constant, around $30K. Afterwards, the losses grew until the June 13th jackpot win, then fell. When the jackpot was reset on July 25th, the loss unexpectedly jumped to $47 K. Again in this cycle, as the Annuity jackpot has risen, the cash option loss has fallen to only $20 K per million.

Since players and winners had no basis to evaluate the fairness of the cash prize offering, complete trust was placed in the Mega Millions estimate, which appears to be arbitrary, and not really correlated to actual interest rates. Based on all of this, we believe that the:


Mega Millions Annuity Offer is Best!



Summary
To summarize, Mega Millions winners who elect to receive the Cash Option are usually penalized because: the Cash Option Value is under estimated; interest rates are typically lower than that offered by the Annuity; and, taxes erode the both the cash payment and interest earned.

MM Cash Option Breakdown
To visualize the July 25 2008 Cash Offering payout, Graph MM0808g illustrates the Cash breakdown against the comparative $12 million annuity prize. Notice that the player will retain a total of $6.7 million in winnings, consisting of the $4.6 M cash payment and $2.1 M of interest earned. A total of $3.6 million will be paid in taxes. And, $1.7 million will lost to Mega Millions .

Conversely, Mega Millions players who win $12M and elect to receive the Annuity payments will retain $7.8 million in cash, and will pay $4.2 million in taxes.

MM Annuity Breakdown
The net difference in money retained by the winner will be $1.1 million spread over the 26 payments.

This equates to approximately $42.3 thousand dollars per year. This is a lot of money.

Note: All amounts shown are based on a $12 M annuity at 4% interest. These values are scalable. Thus, if the annuity is $30 M, multiply amounts by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.



Conclusion
In this discussion, we have: illustrated how the Mega Millions Annuity payments are made; identified the fair cash value Par value of $7.672 million; described the fair cash jackpot offerings at varying interest rates; created the non-taxable and taxable implied break-even yield curves; shown the historical cash loss per million; and summarized the breakdowns of money retained, taxes paid, and money lost.

By focusing on the July 25 2008 cash and annuity jackpot offerings of $7.1 M and $12 M, we have concluded that winners in this drawing are far better off by receiving the Annuity Payments instead of the Cash Option.

Lastly, our advice with regard to this Mega Millions drawing (and most likely others) is to:

Take the Annuity,
You'll have alot More Money
Unless things change.

And remember, if you check the Annuity Option when you buy your tickets, you can change your mind and take the Cash Option (depending in which state you purchase the ticket). Those originally selecting the Cash Option cannot reverse that decision.

Learn More
We have not found many sites that provide detailed Mega Millions Jackpot information. However, you can learn more by visiting the following:
Focus for October: Florida Lotto Plus



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The purpose of this blog is to bring you a variety of articles focused on sharing Lottery Specific Topics that will better help you understand your chances of winning the large Mega Millions, Powerball, Lotto 649, Super 7, Euromillions, etc. jackpots.

We intend to post new articles on a Bimonthly (every 2 month) basis, but may add content more frequently. Examples of topics that we will address include: Do all combinations have an equal probability of winning?; Where does the money go?; What combinations occur most frequently and why? Should I take a lump sum payment or annuity?; and more.

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