Great comment!
As your link shows, when both annual payout and lump sum are taxed at the same rate (the maximum in PowerBall’s case), the NPV of the annualized payout is less than the lump sum (working backwards) or the FV of the annual payout invested conservatively and compounded is less than the FV of the lump sum invested on the same terms.
But if we’re talking about $25,000 a year for forty years versus a lump sum,
it’s considerably more complicated when dealing with a sliding tax rate. $25,000 is taxed at far less of a rate than some huge lump sum, and if it’s invested and compounded yearly, the tax rate on the interest is not going to hit the max for quite a while.
Whereas if the lump sum is something like $500,000, the tax rate on the lump sum is at the max, and within a decade the interest on whatever’s left will hit the max too.
I should set up a spreadsheet. It may still be true for the 40x$25,000 example we’re discussing, but I need to run the numbers against a specific tax scale.