Until we see rocket fuel doubling in energy every eighteen months, any idea of a Mars mission (let alone colony) paid for with private money is wishful thinking.
Have you heard of the phrase "once you're in orbit, you're halfway to anywhere" (Robert Heinlein)?
The delta-v from LEO to mars is only ~4.6 km/s assuming you aerobrake once you're in orbit. Or 3.8 if you're doing aerocapture.
For comparison, it costs ~10 km/s just to get into LEO.
Remember the tyranny of the rocket equation. Saving the rocket fuel required to get into orbit drops the total fuel cost by an absurd proportion.
We already have the tech for being able to do at least an order-of-magnitude drop in price to orbit, if not more. Launch loop, etc. (With a launch loop you need ~120m/s additional to get into LEO, but that's peanuts comparatively.) The biggest issue currently is that it's a lot of money to potentially build. And the political components.
Yeah, it'd be a huge chunk of change to build. But it's potentially worth it.
As crackpot ideas go, the launch loop (or variants thereof), is the one that I am (still) most excited for.
s/is building/has built
> Nowhere in that endeavor is the technology to permanently move a sufficient number of people to some other planet.
Nowhere in 1999 Google was the technology to autonomously drive cars, either. Yet, Google's cofounders explained their vision in 1999 to collect and organize the world's information. Vision and leadership is an important part of predicting a company's future, and Elon is very clear about this: The purpose of SpaceX is Mars colonization.