Friday, June 27, 2008

PB Cash or Annuity? The LPP Analysis of the Powerball Jackpot

Playing Powerball requires players to make many immediate choices: What numbers to play? Buy the Powerplay? Play quick pick numbers? And, if the player is lucky enough to win the jackpot, the player must then choose whether to:

Take the Cash or Annuity Option?

Since the beginning of 2003 through Jun 18 2008, there have been 76 different winners (groups or individuals) that needed to make this choice (Powerball Winners). Of them, only three have opted for the Annuity; 70 have taken the cash option; 1 is still deciding; and 2 have mixed payments.

Since most players take the Cash Option,
they must be right.

Or, Are they wrong?

Real World Example
For purposes of this paper, we have chosen to analyze the May 31 2008 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 GR0606a illustrates the Jackpot Offerings for the May 31 2008 Powerball drawing.

In this drawing, Jackpot winners choosing to receive the Annuity option will be paid $15 million in 30 installments spread over a 29 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 47.3%.

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 players with more information about these 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
Powerball Options

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

How the Annuity is Paid
Beginning on October 9, 2002 (Colorado Lotto Powerball Information), Powerball made two significant changes to the annuity payout structure. First, the annuity period for paying the Jackpot was extended from 25 to 30 payments (paid over a 29 year period). Second, each payment (after the first) is gradually increased at a predetermined interest rate of 4%. Previously, each payment was in equal amounts.

The Powerball FAQS/Contact Us page explains the reason for these changes:

"Each payment is 4% higher than the previous year's payment to help keep up with inflation. The annuity prize used to be paid out in equal payments. Persons who elect to take the annuity prize do so because they don’t want to worry about investing the money. They want to maintain their lifestyle for the term of the annuity. In fact, our past practice of equal installments did not really meet the needs of these winners."

Changing the jackpot annuity payment structure to meet the needs of the winners sounds like a noble cause, but since few winners have ever elected this type of payment, this change has not benefited many players.

Other Powerball Rules
In addition to the above annuity payment schedule, Powerball has defined several rules of play. To summerize:
  1. The Minimum Annuity Jackpot is $15 Million. Payments to players will never be lower than this amount.
  2. The Minimum Increase in the Annuity Jackpot between Drawings will be $5 Million.
  3. Payment of the Annuity Option will be delivered in 30 unequal installments, spread over a 29 year period.
  4. Each Annuity Payment will be 4% higher than the previous.
  5. Amounts of both the Cash and Annuity Options are Estimated Values Only. Actual payments may be higher or lower than stated (with the exception of the minimum $15 M)
  6. $0.30 of every ticket sold goes to the Jackpot pool.
  7. Player has 60 days to decide which option to take. (This is important)
  8. The method of payment is binding. Once a winner as chosen, the option cannot be reversed.

Powerball Annuity Yearly Cashflow Payments
Using the above information, we have constructed a cashflow diagram of a $15 million annuity. Graph GR0806b illustrates the 30 annuity payments that would be made to the winner of this $15 million regardless of interest rates. While Powerball says they estimate the annuity, we know that the minimum jackpot annuity payment is $15 million. Thus, these payments are fixed.

Note: This graph is for an $15 M annuity, but is scalable. If the annuity is $30 M, multiply payments by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; etc.

The first payment is delivered immediately and those following increase by 4.0% each year. If we assume that the fair interest rate level was also 4.0% per year, then Powerball would need to create 30 buckets of $267 thousand each. The first $267,000 (rounded) would be paid to you when you were declared the winner, and all the rest would be invested in 4% annual paying interest Treasury Bonds or Strips. Looking at the above graph, the blue horizontal line illustrates the amount of money that was deposited. Everything above that line is interest earned. The total of all 30 payments, which include both the value of the cash deposited and the interest earned, will equal $15 Million (which is what you won).

But since Powerball only needs to allocate 30 $267 K buckets for payment, it only needs to aside $8.024 Million in order to make these payments (totaling $15 M) to you.

We shall define this value of $8.024 million as Par.
This has a Cash to Annuity ratio of 53.5%.

May 31 2008 Jackpot Revised
Adding the $8.024 M Par Value to our Jackpot Graph (GR0606c) provides us with a relative measure by which to judge the fairness of the $7.1 million cash option offering, which is $0.924 million below Par. In terms of ratios, we are offered 47.3% verses the par 53.5%, or a 5.2% 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, $8.024 M will be set aside for our winnings. If we take the Cash Option, we immediately lose nearly $1.0 million. This comes out to losing $61.6 thousand per annuity million won.

Fair Value of Cash Option at Varying Interest Rates
Both the Powerball 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. Thus, 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.

Graph GR0806d 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 $8.024 M Par Value (green line).

This graph tells us that when interest rates are at 2%, Powerball must invest $10.784 million to fund our $15 million annuity. At 3% interest, $9.262 must be deposited for funding. And, when interest rates rise to 10%, only $3.992 needs to be invested.

Referring to this graph, we observe that the May 31 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%), this 5% level appears to be rather high.

Thus, the May 31 2008 $7.1 Million Cash Option begins to appear to be extremely low.

Note: The Cash Fair Value amounts in the graph are based on a $15 M annuity, but these are scalable. If the annuity is $30 M, multiply amounts by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; 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 rates, and both standard and itemized deductions become limited.

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

This means that for those who elect the $15 million Annuity Option, they will pay a total of $5.25 million to the IRS. Without paying State taxes (many states do not tax those residents who win Powerball),

Annuity winners keep $9.75 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 May 31 2008 cash jackpot, the winner will fork over $2.5 million to the IRS. This means that the cash winner will only pocket $4.6 million. Typically, Powerball 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 Powerball 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 $15 M annuity winners will retain $9.75 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 $9.75 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 $15 M annuity, and are scalable. If the annuity is $30 M, divide the offered amount by 2; if $75 M, divide by 5; if $150 M, divide by 10; etc.

Returning to the May 31 2008 drawing, the Cash Jackpot offering is $7.1 million.

Assuming that this is the fair value, it will be the same amount that Powerball will invest for the Annuity winners. From the graph GR0806e Blue Curve, we can guesstimate that Powerball will invest this money at approximately 4.8%. The interest earned on the annual payments will compound tax free at this rate and will generate a total of $15 M in payments to the winner. After taxes, the player will get to keep the $9.75 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 GR0806e 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 6.2% on the remaining $4.6 M in order to earn $9.75 million.

Evaluating the May 31 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 4.1%, and 30-year treasuries below 4.7%. Thus, it is impossible for Powerball to earn an average rate of 4.8% on the annuity deposit at this time. Therefore, we conclude that:

The $7.1 million cash offering is extremely undervalued,
and should be at least $8 or more million.

Cash Loss per Million (Jan 2 - Jun 18 2008)
To test the correlation of the 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 January 2 2008 and ending June 18 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 Powerball Jackpot was won, and was reset to the minimum $15 M. The horizontal Blue Line indicates the average loss of $40,000 per million.

During this period, the FOMC reduced the Federal Funds Target rate:
  • Jan 22 2008 - from 4.25% to 3.50%
  • Jan 30 2008 - from 3.50% to 3.00%
  • 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 53.5%, thus bringing the Loss per Million closer to zero.

But in reality, the Cash offering by Powerball appears to be random. During the period January 30 and March 18 when Fed Funds was 3.00%, the loss became larger, and then smaller. After the March 18 cut, the loss narrowed, as expected. After the last lowering to 2.00% on April 30, the loss widened to a high of $60,000 per annuity million.

Since players and winners had no basis to evaluate the fairness of the cash prize offering, complete trust was placed in the Powerball estimate, which appears to be arbitrary.

Returning to our May 31 2008 example, we observe that the Jackpot Loss on that date was at its largest. Knowing that the interest rates had declined, we would have expected that the Cash Offering to increase. Because it decreased, we further believe that the:

Annuity Offer is Better!

To summarize, 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.

Sample chart
To visualize the May 31 2008 Cash Offering payout, Graph GR0806g illustrates the Cash breakdown against the comparitive $15 million annuity prize. The player will retain a total of $7.9 million in winnings, consisting of the $4.6 M cash payment and $3.3 M of interest earned. A total of $4.3 million will be paid in taxes. And, $2.8 million will lost to Powerball.

Conversely, winners who elect to receive the Annuity payments will retain $9.75 million in cash, and will pay $5.25 million in taxes.

Sample chart
The net difference in money retained by the winner will be $1.85 million spread over the 30 payments.

This equates to approximately $61.7 thousand dollars per year. This is a lot of money.

Note: All amounts shown are based on a $15 M annuity at 4% interest. These values are scalable. Thus, if the annuity is $30 M, multiply amounts by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; etc.

In this discussion, we have: illustrated how the Annuity payments are made; identified the fair cash value Par value or $8.024 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 May 31 2008 cash and annuity jackpot offerings of $7.1 M and $15 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 Powerball drawing (and most likely others) is to:

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

Learn More
We have not found many sites that provide detailed Powerball Jackpot information. However, you can learn more by visiting the following:
Focus for August: Analysis of the Mega Millions Jackpot

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