So how does a private venture establish a colony on mars? Just one step at a time requiring only one assumption: entities exist that would pay $10m per month to lease 50 cubic meters of space in orbit to do research or just tourism. They would also have to pay their own $20m round trip cost to and from orbit transferring to a ship that never lands. Tourist have already paid about this price and governments have already paid exceedingly more.
You don't need the Raptor engine or the Falcon Heavy. It will be nice when they are available, but they are not required. This means we could start today rather than wait, assuming the initial funding of just $150m which is not out of range for a lot of potential investors.
A Sundancer class vehicle provides 60m3 for each of three people so a potential income of $30m per month. It can be launched into orbit on an existing F9 for a total cost to orbit of about $150m. The operating costs are included in the $20m travel expense so the entire $30m is profit giving us a 5 month return on investment. If the $150m is borrowed at 20% then you have an annual interest cost of $30m so let's make it a 6 month ROI. Everything after break even (regardless of how long it actually takes) is pure profit. A BA330 is actually better but requires the Falcon Heavy first. Either choice creates cash flow that enables everything else that follows.
The first ship that sends colonists to mars could be an Sundancer upgraded with life support for eight. This provides about 9m3 of private space and 108m3 of common space. It will have had shakedown cruises in Cislunar space to ensure reliability for the trip to mars orbit.
The more people sent the cheaper per colonist is will cost but first we have some more baby steps. We have to be able to land on mars. SpaceX has a lander designed for Mars One based on their current Dragon. It has to be tested again in steps. First the earth's upper atmosphere can be used to simulate propulsive landing in the martian atmosphere. Next is landing joint missions on mars to prove the lander. Then landing supplies on mars preposition for the first colonists (and proving we can do it within a small landing ellipse) safe for the colonists that follow.
It will take two landers for all eight colonists to get to the surface of mars. We should have supply ships in reserve in mars orbit in case either lands too far from prepositioned supplies (they will land with a vehicle that gives them 50 km range on each charge and the ability to recharge with solar panels.)
Total cost to put eight colonist on the surface of mars: less than $2b, possibly less than one. Certainly not the multi-billions you often read (which is based on doing it wrong.) The first landing will be more expensive because of prepositioned supplies (less than $200m for every 2500kg) which will not be required for subsequent landings.
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