I strongly doubt they would shoot for an asteroid belt operation.
The energy cost of sending something out there, let alone bringing anything back, would be obscene enough to make it unrealistic.
This post does some basic maths on the energetics of shifting something from the asteroid belt to earth orbit. Critical section;
The asteroid belt is over 20 km/s away in terms of velocity impulse. If the goal is to use the raw materials for production on Earth or in Earth orbit, we have to supply about 10 km/s of impulse. We would probably try to get lucky and find a nickel-metal asteroid in an unusual orbit requiring substantially less energy to reel it in. So let’s say we can find something requiring only 5 km/s of delta-v. Our imagined prize will be a cube 1 km on a side, having a mass around 10^13 kg. This is very small for an asteroid, but we need to moderate our ambitions. From a resource point of view, it’s still a lot.
To get this asteroid moving at 5 km/s with conventional rocket fuel (or any “fuel” that involves spitting the mass elements/ions out at high speed) would require a mass of fuel approximately twice that of the asteroid. As an example, using methane and oxygen, (4 kg of O2 for every 1 kg of CH4), we would require two years’ of global natural gas production to be delivered to the asteroid (now multiply this by a large factor for the fuel to actually deliver it from Earth’s potential well). The point is that we would be crazy to elect to push the asteroid our way with conventional rockets.
He then dismisses solar sails (unrealistic for the mass of material needed and the time of travel involved - unless your business doesn't need the materials this or next century). The only remaining option is ion engines, which have some of the flaws of each (still requires fuel which would become significant over the power levels and times required, very low thrust to date would mean excessive transport time).
Very simply, I don't see the energetics working out. And as that link says, if the energetics don't work then the economics aren't even an issue.
Near earth objects are another matter, but again delays and arguably less economical. You can't really pick your rock; there are very few candidates. You still have to wait an extended period to get it locked in; the best method would be attaching ion engines during one pass to push it into earth orbit on the next. And you still need to make the investments in zero gravity mining technology.
I'd still be in favour of this though, even if it wasn't economically viable. While some materials might have value on earth they are worth far more in space. Let's imagine we could get a significant chunk of iron (preferably a large nickel/iron rock, similar to the larger objects in the belt, but realistically not anywhere near that magnitude of size) rich material in earth orbit. Even a small asteroid would be worth a few hundred rocket launches. If we could capture and develop with just one or two launches it would be a significant return on investment. Use it as raw materials to do further captures or go straight to deeper exploration and remote bases. You are instantly making future operations significantly cheaper. If there was then a significant shortage of a specific material on earth you could target and fill that need. But in the meantime keep whatever we can in orbit to save the costs of lifting things out of our gravity well in the future.
You could make a few million selling the materials back on earth. I doubt you would seriously recoup your entire investment. It just seems to me that dumping such significant amounts into the economy would depress the price too far too quickly, and earth based mining would be remain far cheaper until supplies are actually exhausted. The only real advantage such resources would have, other than their potential abundance, would be their altitude. Selling on earth would lose that advantage, trading billions in future potential (and potential energy) to trade in materials at around cost.