Keep in mind that this is not 100% confirmed officially. It is believable though, so I'll assume it is true for this thread.
Anyways, Ken Levine has said several times that they've made enough raw content for this game to fill four or five games with how much they have cut from the game over the five years of development. Considering that and the fact that they've spent nearly 5 years in full development, it's actually surprising that the pricetag for development wasn't much higher than $100 million.
Aside from so much content being thrown out or redone, the development of this game actually seems to have been pretty well-managed financially. The big issue seems to be that so much content was replaced or trashed, which is extremely costly.
Plus, on a purely audiovisual level, it looks and sounds amazing from what I've seen. Compared to Dead Space 3 (which is another long SP-only game with a massive budget), Bioshock Infinite looks and sounds better.
I have no idea how marketing budgets have gotten so massive so quickly this generation. I honestly have no idea how you spend $100 million on marketing a game unless you buy tons of TV ads and billboards and buy a bunch of tie-in sponsorships alongside the internet marketing and posters that accompany most games these days. It seems to me that they want to get the Bioshock name on the same level as GTA, Halo, or CoD, because that's the only way I could see justifying such a huge ad budget.
If making bets of this magnitude are required for AAA success (which I doubt for several reasons, but that's another topic), then the industry is well and truly messed up in some massive ways. If the industry does crash in some way, I hope that we still get deep and intense SP-only games. System Shock 2 still holds up in a lot of ways today, and making an equivalent game today couldn't cost much more than $10 million. Publishers need to stop spending hundreds of millions to aim their games at everyone (which is a self-perpetuating cycle: game budget is too big so we have to make the game appeal to as many people as possible and then spend more on marketing to reach them) and instead budget appropriately for a known audience.
Ah, that explains the ridiculous level of preorder bullshit going on.
Part of it is ensuring a huge launch, but part of it is raising awareness for future 2K products. XCOM is being given away free to many Infinite preorders, and Bioshock is a bigger brand than XCOM is. 2K is clearly hoping that offering XCOM to hundreds of thousands that don't know much about XCOM will make them more likely to buy the XCOM shooter whenever it comes out. That game has probably racked up a pretty big development cost by now too!