Maybe? But what if it cost way, way more? You actually have to look at the time value of money for anything that takes more than a year or two to pay off to be sure that there isn't some kind of false economy.

If you assume that the thing lasts forever, well, you divide $x/infinity so it's free. EXCEPT that you've got $x tied up that could be earning interest instead. So it's not $x/infinity, it's the opportunity cost on $x versus anything else out there like batteries, the grid, etc.