about 6 months.
I probably spent about 5 grand more on the Model 3 LR than I would have on a comfortable sedan (read Toyota Avalon), so based on gas savings I should be net positive financially by year 3. Couple that with the fact that the 3 is super fun to drive (more so than a Toyota) and is basically a super fast super computer, I think it makes sense from both a financial and enjoyment standpoint.
Now granted the batteries will die in about 8 years but that is the typical life of a car anyway so I can either buy a new one then, or dump the money into replacing the batteries but either way, I'm probably looking at a major expense either way in 8 years. I'm also betting that the costs to replace the batteries in 8 years comes down from it's current costs.