Today's NASA has little in common with the organization that put men on the Moon, but they can put rovers on Mars so they have some ability to get stuff done.
Well...Elon has made guesses/estimates/given us lots of ideas about his monetization strategy. I think the most promising is to sell tickets at $500,000 apiece, which he thinks will be about the going market price to meet a demand of ~100,000 colonists.
Mars One thinks they can do it on a TV show (they'll fail, though, obviously).
My point is that your "nobody" comment is unfair and incorrect. Lots of intelligent, capable and experienced people have articulated a number of different business models around the colonization of Mars. None of them are proven, of course, but that will take time.
It's entirely possible that Elon Musk doesn't care about recouping his investment in SpaceX. It seems like the end goal of the company is to start a colony on Mars so he can go live there.
Curing malaria also doesn't have a return on investment to whoever is doing it. We're at the point where governments are doing the neccessary things, but private individuals are able to sponsor the visionary but less practical endeavors - simply because they believe that it's the right thing to do and don't have to answer to millions of voters who might quite rationally prefer more bread and circuses instead.
> So far nobody is able to come up with a way to recoup the many hundreds of millions of dollars it will cost to get humans to Mars and back.
Have you seen the price of "sovereign" islands lately? Say what you want about the validity and enforceability of the claim (and the sanity of the people who buy them), but land separated from any Earth government by ~55 million km+ doesn't seem like it would be a hard sell at any price.