The future profits only need to be higher than the $5B plus whatever they can get today from liquidating their existing holding. Sunk cost fallacy, or "what is done is done".

Don't forget opportunity cost. The future profits need to be higher than the $5B plus liquidation value, PLUS the expected value of another investment at the margin.

Oh yeah you can use the yield curve to discount future flows, and then demand something extra on top of that (Graham's margin of safety).

There needs to be some kind of exit, because at some point the Vision Fund needs to return money to investors - and that's a lot sooner than "run WeWork to earn back $5b+ via dividends" would take.

As soon as it’s been transformed into a profitable business, the exit is going to become an option.

They could do a direct listing instead - it's like an IPO but without raising additional capital. Just put your existing shares on the market.

WeWork, though, needs a lot more than new capital.

True, but there's always the possibility of the Vision Fund selling WeWork to Softbank proper. And I don't think this round of investment is from the Vision Fund, so it appears that Softbank proper is going to end up with a larger stake than the Vision Fund already. I suppose there's also always the option of selling WeWork to Berkshire Hathaway or something if they can get it boring and profitable.