I've never saw any official statement 

I wonder how many copies each Nintendo game need to sell in order to break even its costs

It will gave us the idea which franchises are truly profitable and are hard caring Nintendo financially 

Unlike movie industry, it's not common to show development costs of big productions. As far as the cinema goes, the box office performance each title must be sustainable. Meanwhile gaming studios are more likely to have some AAA games operating at loss as a proxy to building branding loyalty, while profiting a lot from cheap ports and remasters 

I recall them saying that BOTW needed to sell 2 million copies to break even: https://www.forbes.com/sites/olliebarder/2016/06/30/zelda-breath-of-the-wild-needs-to-sell-2-million-copies-to-break-even/?sh=2a751ec1615f

Not a lot of info out there...

It's been reported that Fire Emblem Awakening would have needed to sell 250K to continue the franchise.

So... 250K would have been just about 10million in revenue. About 1/5 of that would probably be gobbled up by retailers. Meaning 8 million would have been profitable. There's also other non-development costs like shipping/packaging, etc. Based on that, I'd guestimate the budget at somewhere around 3-5 million, but that's just speculation. And obviously games on Switch are generally going to be more expensive to develop.

Hope they can make back that investment...

250k does not seem enough pay all bills. I'm assuming with 250k was the minimum it needed to sell so they could try again, even with losses

I dunno about that. Fire Emblem doesn't seem like it would be that expensive. The gameplay is relatively simple, no physics, very little voice acting. 90% of the story is told through sprites and text. Characters didn't even have feet.  Seems like 10 million would be enough to pay everything off and have a little left over.

I recall hearing that Xenoblade Chronicles X (The Wii U game) was profitable. Don't have a source on that (years ago on IGN threads) but it's something that sticks with me. I think the general assumption is that the games tend to be profitable outside of specific exceptions even on the Wii U.

Yeah considering its team size, complexity, production values, and development time, it wouldn't surprise me if BOTW is the most expensive game they've made to date.

Marvel of its time is a bit of an overstatement. To be clear, I love me some Xenoblade Chronicles X, but while it was amazing for a Wii U game, it launched in the same year as Witcher 3. I actually like XBCX a lot better, but on a technical level it wasn't cutting edge outside of its console.

The team that made XCX was ridiculously small for a ridiculously huge and artistically beautiful game. It speaks volumes about the speed and skill of the team. There are mobile games supported by larger teams than the XCX dev team - granted, these are high profit games with frequent updates, so it’s more like a collection of 4-6 smaller dev teams working on the same project. The new Avatar mobile game has something like 200 employees mostly working on it. Supercell has 320 employees mainly across 2 games, and I’m not sure if those counts involve their QA staff which is often done by contracting other companies, but it’s not unusual for mobile companies to have several internal QA.

Takahashi has always been like that, though. He somehow made Xenogears in 2 years, and while the game was crunched down from what it was envisioned as, what remained was still one of the biggest RPGs made to that date.