Cost Benefit Analysis? I can give it to you. Payback time is well over a century. When I was a practicing Professional Engineer, our cost estimate times generally used a seven year payback as the maximum acceptable figure. On that scale, Mars colonization cannot be economically justified presently.Ultimately, this renders to a cost/benefit analysis. What is there to Mars that would be ultimately valuable to us?
Research? As noted, this can be adequately done using purpose-built rovers.
Living space? That's an awful difficult thing to justify, given the sheer distance, small amounts of material we could send and the limited number of people as well.
Terraforming, Doctor Forward and such notwithstanding, is a hugely difficult thing to pull off.
And really, if we can build the proper and in-depth infrastructure with which to even manage limited landings on Mars, there are far better targets to apply this to. The Asteroid Belt is chock-full of resources and, if we can get to Mars in any meaningful way, then we can get to the Belt as well - where there's a real economic incentive to do so.
All this IMO, of course.
Hey, it only just became possible for less cost than a global war.
Simple living space isn't a reason to colonize Mars. There are other, better ways to get that. O'Niel Cylinders or Bernal Spheres can be built with Lunar processed materials to give us room for many times more people than currently exist.
True Terraforming isn't possible on Mars. There isn't enough atmosphere and without a magnetic field there can't be. So the farms on Mars won't be outside. They will be inside. Maybe in large domes, maybe underground and artificially lit. Maybe even growing crops in plastic roofed river valleys with big dams at both ends.
We're already growing some crops indoors commercially in New York and Tokyo. The technology exists and is slowly growing more economical. Farmers are already a skilled trade here on Earth, just like plumbers or electricians are. This will just move them indoors like the other trades already are.
So no, those aren't the reason to go to Mars. The reason for Mars is simple, really. Mars has nitrogen. We can't live without it. After Earth, the next closest source of nitrogen is the moons of Jupiter. Mars we can do now. Jupiter and the asteroid belt we can't yet. For either of those, we'll need fusion.
Venus is easier to reach, but over an order of magnitude harder. Jupiter is easier than Venus.
After we have fusion, and after that becomes more economical, then there will probably be colonies on the asteroids and nearly all the planets as well.
But we can't do those yet. We can do the Moon and Mars.
The Moon however will never be able to exist without Earth. Mars can. Not well at present, but easily if we build it up over a century or so.
BTW, Terraforming plans that I have seen all require a working time of several centuries to a couple of millennia before anyone could go outside without a special suit. So it's still not an economical sort of thing. Recall that seven year rule.