The OP focuses entirely on the time period where the revenue line finally catches up with the cost line, i.e. profitability has been reached. But guess what? See all the time periods before that, where the business is running at a loss? Where is the money coming from to fund those losses? That's the up-front investment required - VC, loans or digging into your own pocket.
So that's the first important yet unanswered question: what is the up-front investment before the business can sustain itself?
The second is to calculate the ROI for the above investment, but with a twist: calculate the average ROI at every time period, taking into account all periods before the period being calculated for, but ignoring all future periods. This will provide you with a very important result: you will see that the average ROI remains negative long after your business becomes profitable. You will also see in which time period your ROI reaches an acceptable level - a very important factor when risk is considered.
Yes, it's just a model driven by assumptions. But with the above metrics, you can play with the assumptions (worst, best case etc.) and get meaningful results for decision making.
Disclaimer: The above explanation has been simplified quite a bit. Liberties have been taken with definitions. All your base are belong to us.