Cash for Life, Right now?

Here’s a thought,

Consider the Ontario Lottery Corporation’s game “Cash for Life”. It’s the scratch and win game card where you hope to match up three identical “Cash for Life” symbols. If you do, you’ll receive $1000 every week for 20 years. Sounds good to me!

That adds up to a whopping total sum ($1000×52*20) $1,040,000 bucks over 20 years.

$1000 a week over time can buy you some fancy clothes or watches. Over some more time perhaps a decent used car. Or maybe you wait the long haul and save up for a child’s education. OR maybe you wait even looooonger and save up for a new home purchase. In that case lets say you want to buy a $250,000 home. That’s going to take (($250,000/$1,000)/52) 4.81 years to save up for.

So, what if we could determine how much the future sums of the cash flow is worth today and convince the lottery to pay that amount out to us in one lump sum of cash to do what ever we want with?

Here’s the numbers;

First, we’ll have to reference the trade-off between the sum of cash flows over the 20 years to the present sum of cash by the interest rate at which we will assume is constant. The Bank of Canada posts it’s 20 year government bond rate to be approx. 3.45% annually. I’ll choose 4% and imply that it would be more probable in a more stable less volatile interest rate environment. It’s an arguable assumption but that’s what were going to use. Don’t like it, tough! (There are several more robust ways to compute an interest rate assumption, but this is supposed to be quick and fun, not long and arduous)

Also, I have to set out the compounding frequency and number of periods. Given that we have 52 weeks in a year and the cash flows go on for 20 years, we have 1,040 compounding periods. Since were using weekly figures for the compounding period, we must do the same to the interest rate which will be used at 0.0769%.

So to make a long story short; the calculation’s using the inputs of 1040 cash flow periods (52*20), a weekly interest rate (4%/52) of 0.0769% and a cash flow amount of $1000.

Using my handy present value function on my calculator we find an answer that suggests that, given the inputs, a person is likely to accept $715,692.70 in lieu of $1000 a week for 20 years. In essence, the calculation says that based on a persons total risk aversion and opportunity cost of %4, one would accept $715,692.70 today in exchange for $1,040,000 over time.

Now maybe not all of you are agreeing; I’m not a surprised. Some people would prefer to live modestly and would be quite happy with $1,000 a week for 20 years. Some people may rather live dangerously and take that lump sum and invest it in high risk ventures or off track horse racing hoping to turn the $700,000 into much more. It’s all based on the person.

Since the chances of being one of the 4 people to win the jackpot each time OLG runs this game is 0.0000581% we won’t actually have to worry about having this problem. Interestingly enough, the OLG does give the winners the option of choosing a lump sum over a weekly payout. But it comes not without its penalties such as a cap on how long a term one can use to calculate the present value or the risk of the OLG using a discount rate below standard Bank of Canada rates. Not to mention, there are legal fees that have to be dealt with.

It’s an interesting thought though…

What would you do?

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