We don't know if it's a current "loss", but most likely it will break even in terms of box office. It will not lose any money.
I admire your enthusiasm, but that's wrong. This movie will lose money in terms of box office. Actually quite a lot, probably more than "Ghostbusters". As you put it yourself later, it's the secondary revenue that might take it into the black down the line.
Even if we say it lost $30-40 million in box office alone secondary revenue will be many times that..my updated guess, with the China merchandising deal already announced the other day(much bigger than any recent or current US deal) as well as the bluray already in the top 6 on Amazon, we'll see and eventual return of $120-200 million from Beyond in less than 2 years(and that is a conservative guess).
RAMA
At current state, the loss will be probably more than double the amount of what you said. I will wait for some official publication or expert guess from a credible source for that. No arms-chair experts here.
And where the hell did you get that 120 - 200 mio. number? That's not what you make selling DVDs nowadays! That might have been a few years ago, but the media landscape has changed during that. Please post sources when you claim such enormous (and quity frankly impossible) numbers. And I don't mean that funky "for beginners" graph you posted a while ago, but actual estimations of the secondary revenue sales for Paramount.
Also, the nuTrek franchise is amazingly bad at merchandise. I see a few nuTrek uniforms every now and then. But if I want to go out now to buy a Cpt. Kirk action figure, it will more than likely have William Shatners face on it.
1. Established franchise. $340-350 gross is better than any foreseeable replacement. It's potential $550+ revenue in 2 years makes it a viable franchise.
This! This right here. That's the one and only reason you will see another Kelvin Trek movie! They know it will make some money (compared to, say, Ben Hur or other remakes). It's not as much as they hoped or expected. But it's not nothing either. They will probably loose money with 'Beyond'. But they now know what margins to expect, and can adjust budget accordingly. It's not stellar, and if Paramount had any other franchises they would focus on them. But right now, they now a Trek movie (literally any Trek, when you look how bland and undistinguishable 'Beyond' looked in the marketing) generates some money. Not much. But still money. They would love having big, more profitable franchises. But a small-but-calculatable income is the second best thing to have. It allows for better income planning, and let's you rent money at lower interests.
2. It already has a production team, writers, a story and actors signed up for it.
5. They already announced the movie so it would look bad for investors if they back down.
6. Good reviews and good fan reaction. Not as important for business as the others, but at least it can be marketed as "successful" and popular.
Nothing from this has ever had any impact on studio decisions though. As long as production hasn't started nobody has seriously commited to anything.
3. It already has sets and therefore less overhead than for a new franchise.
Studio sets might be a big deal for television shows. In movie business they're peanuts. When they moved production from LA to Vancouver for Beyond they didn't shipped the Enterprise sets. They trashed them and built completely new ones over there. That's cheaper. You might not have noticed, but all the sets seen in Beyond were completely new ones.
4. It'll hope for a less "down" period to release it in, acknowledging that was the market force at work at the time of Beyond's release.
That, one the other hand, will be impossible to avoid. Beyond seriously underperformed and lost money. They need some down-time for analyzing the problems and overhaul the franchise. When a franchise is successfull they try to start a sequel as soon as possible to cash in on it while it's hot. If it's not, like Star Trek now, the "Go!" will only come at a point they are sure enough in it that it will make some money. So expect a lot of first drafts on complete story changes, and a longer waiting period, until you will see a sequel. Also, ST4 will be as much a sequel and storyline continuiation to "Beyond", as "Beyond" was a continuation of themes and story from "Into Darkness".