## Powerball Prize. Do you take the payout or the annuity?

In the US, this week’s Powerball prize is 1.5 billion, paid over 30 years, or a one-time payout of $930 million. Everyone takes the payout, but are they right to do so?

### The Value of an Analytical Approach

If everyone who wins the lottery gets professional investment advice, and everyone then takes the $930 million payout, the payout must be the best way to go. Or it is commonly thought. Should a winner follow the conventional wisdom? Of course the answer is: it depends. However, if we compare the two options equally (including risk and taxes) then a winner is far better to take the annuity.

If everyone who wins the lottery gets professional investment advice, and everyone then takes the $930 million payout, the payout must be the best way to go. Or is it? Should a winner follow the conventional wisdom? Of course the answer is: it depends. However, if we compare the two options equally (including risk and taxes) then a winner is far better to take the annuity.

### Here’s why.

The payout of $930 million is far less than the total of the 30 equal payments of $50 million that you would get with the annuity option. The lottery sponsors assume that they can invest their money at 3.57%, in order to grow the $930 million to make the needed annual payments of $50 million. Everyone thinks that they can beat 3.57%, so it is better to take the money, and then invest it. However, this forgets one very important item: risk. The annuity is absolutely risk free. If you die early, your estate still gets the cash. Where else in the world can you get a completely risk free investment that pays you 3.57%? The closest you might come is a US Government Treasury Bill, currently quoted at rates of less than 1%.

However, if you have a great stock broker, who can get you a good return of 5% with very low risk, should you still take the annuity, or should you opt for the payout?

Here is what the payout gets you: $930 million, invested at 5%, paying taxes at 40% on the returns and the initial winning, means you will have $1.314 billion at the end of 30 years.

Here is what the annuity gets you: $50 million year, invested at 5%, paying taxes at 40% on the returns and the winnings, mean you will have $1.427 billion at the end of 30 years. This is better than the payout by over $100 million.

The difference is taxes. In the payout option, you pay taxes on the initial winnings and the annual investment income. In the annuity option, the lottery sponsor shares in that tax burden.

However, if your genius stock broker can get you more than 6.17% (after investment fees) without exposing you to risk – you are better off to go with the payout.

### Does it ever make sense to buy a lottery ticket?

The answer is that it depends on the payout, the odds, and the top marginal tax rate when you live. It almost makes sense to buy a ticket in today’s (January 13th) PowerBall jackpot of $1.5B US. The odds of winning are 292,201,337 to one, but that is one huge payout. With the cost of a ticket being $2 US ($2.86 Cdn), and the prize being $1.5B US ($2.14B Cdn) the expected value is $7.33 Cdn– much higher than $2.86. Most people (wrongly) take the payout, rather than the 30 year annuity, which is $930M US (1.33B Cdn) which causes the expected value to decrease to $4.55 Cdn – again this is still more than the cost, so it is a good bet. However, that is before tax, and lottery winnings in the US are taxable, so with a marginal tax rate of 40% the expected value drops to $2.73, which is 9 cents below the cost. That’s right: even with a payout of $1.5B US, it is still not a good bet. However, 9 cents might be worth it for the 60 second fantasy about what you would do with the money.

Of course this assumes that no one else winning with the same numbers. There are an estimated 1 billion tickets being sold. With over 292,000,000 different possible combinations, and assuming every combination of numbers has an equal chance of being picked (which it doesn’t as people play their favourite numbers like birthdays, which only go up to 31 and not 69), there will likely be 3 to 4 winners sharing the prize – this makes it a bad bet (expected outcome of only 80 cents compared to a cost of $2.86).

If the top marginal tax rate where you live is less than 37% and if you don’t share the prize with anyone, then this is as close to a good bet / lottery ticket opportunity that we are likely to see. I know the winnings are not taxable in Canada, so the tax credit for the US tax bill means never having to pay tax again in Canada. And for $2.86 this is a relatively inexpensive fantasy.

Good luck!