No, I'm not an aerospace engineer or a NASA/ESA project manager. But you don't need to be in order to a little skeptical (or a lot) here.
The cost of the Mars Exploration Rover mission was around $1b. Just for landing two robotic probes. Not humans and the supplies they'd need to survive on a brave new world. FYI... the Curiosity mission cost $2.5b
This project is much more ambitious -- can we at least agree on that? Probably more on the scale of the Apollo program, which cost upwards of $135b, adjusted for inflation (granted this counts the whole program, but they didn't go as far, plus, again, you'll need to land a lot more kilos on Mars to support people).
It's a case of too many impossible things before breakfast. It would be not only the most ambitious crewed space mission attempted by humankind, but one funded in a new, unproven, and unarguably less secure fashion. I have to ask: why do you find it credible?
It is more ambitious, of course. It doesn't remotely compare to Apollo, though - Apollo spent billions in research and development; this has the tech already. It has been sourced and priced. It could be done tomorrow.
Additionally, compared to NASA, costs can be remarkably low. Look how Elon Musk's capsules were sent to the ISS for a fraction of the price it would cost NASA. The private sector is (a) more efficient and (b) can take risks that would be completely uncceptable to a government agency. The savings on both fronts are immense.
I'd reiterate - it's been costed. I guess you can turn round and say "they're wrong; I know better", but you'll understand, I'm sure, when I consider their figures to be more reliable than yours.
