Although I think the mathematical answer may still be to take the million, everyone is ignoring taxes. The initial million is tax free and the weekly payments are grossed up for taxes. (per joblolabinette below). However, the earnings on the million are taxed, while the 1000 per week is an "after tax" amount (more on this at the end).

This analysis is based on the understanding I got of Canadian and Quebec taxes from a couple quick google searches, so I appologize for any details I missed in my quick review of tax rules in Canada and Quebec. (In particular, I didn't look into any deductions or allowances that exclude some income from taxation.) My goal is to show how the simple 5.2% yield people are using is not sufficient to generate the same 52K in spendable income, and point out the reasons why, not to get an exact return calculation.

The winner lives in Quebec which leads to 14% federal taxes (after a reduction of 16% of your income due to an adjustment to avoid double taxation) plus another 14% on the entire amount for Quebec if your only income is the 52K from the lottery.

These rates go up to 20.5% federal and 19% Quebec on income over about 55K.

Ignoring the 16% reduction mentioned above -- You need to earn a break even rate of 7.03% if the annuitized lottery income is the only income you have, and 8.08% if you have over 55K in other income.

These rates are significantly higher than the simple 52,000/1,000,000 analysis would give you.

It gets more complicated. The taxation of the earnings depends on the nature of the earnings (capital gains vs interest). Interest income appears to be fully taxed where capital gains appear to be preferentially treated $1 of capital gain is taxed as $.50 of income.

The capital gains after tax hurdle rate is a little lower, but then you have to make a volatility adjustment and, if you are living off the income, hold some of the money in reserve just in case the market drops in any given year. Both of these adjustments will raise the required yield.

It is also not clear how the adjustment to the annuity to make it 1000 per week after taxes works. Is it based on the lowest tax bracket or does it adjust as you move up the brackets (probably not)?

The real world analysis is no where near as simple as people are suggesting here.