If you're asking for my opinion--and it's just that, an opinion--even 54K for CPO (assuming Premium Sound, 19s, Sat, BMW Assist, PDC, e.g. loaded) is an overly generous offer. 52K is better. Here's why: Edmunds put the trade in at around 49K for "outstanding"; but I doubt the dealer gave that and they probably used "clean" and gave someone about 47K on the trade. In my experience dealers almost
never pay high Blue Book or Edmunds "Outstanding" values; often they give low BB or "Average". "Average" in this case is a little over 44K .
CPO costs them about 1.5K (we'll say 2K for an assumption) if I remember (and I think CPO is a good idea on this car).
So, let's assume they paid a "Clean" price for the car. That works out as follows: 55K (their offer to you "with supervisor approval BS") - 2K (CPO cost) - 47 (what they paid) =
6K profit for them. Plus you're going to pay tax, license, etc. so you're not walking out paying 55K.
What's a fair profit? That's a good question and one I can't answer. But a 5% profit would be ~51.5K (49K base * 1.05). 55K is over a 12% profit if the assumptions above are correct. That, IMO, is too much profit.
Other considerations: tires are going to cost you (unless they want to throw in new shoes). Tires on 19" wheels aren't cheap: replacing the PS2s will cost ~350 per tire front; 385 per tire rear: $1,470 not including tax and other fees. And that's not including balancing, alignment (if needed--at 18K miles a possibility), and mounting costs. I'd figure on 2K as a rule of thumb (other members can chime in here; I haven't replaced rubber yet). And that's not the only expense you're going to incur regarding tires....
You're also going to need winter wheels/tires. It's
must: you can't run the summer tires in your region in the cold, ice, snow or even wet. Take a look at the general forum--it's wreck o' rama due to folks having issues running summer tires in winter conditions. Not worth the risk. And a good winter set-up means less wide wheels and tires to match (wider is not better for snow); at the very least good winter tires if you want to keep the stock wheel setup. Check the wheel/tire section for recommendations-there's a
Tire Rack thread there (site sponsor) that's informative. If they want to throw a winter set of wheels/tires then you have to plug that into your cost/profit/offer scenarios.
If I were you I'd plug in various factors (similar to what I did above) and create scenarios, including winter tires/PS2 replacement, taxes, license etc. and see what this is really going to you before jumping in. Figure out what you can really afford to pay, what a reasonable profit for the dealer is, and work the deal from there. Doing your homework and being fully informed in terms of the numbers really pays off when shopping cars. Know your numbers inside out; it will pay off for you, and you'll be able to negotiate from a position of strength. Sales guys/dealers all count on this stuff being nebulous and on the buyer (us) not having a real idea of costs, plus the power of the emotion (buying a car is, let's face it, exciting), to take money from your pocket (at least that's my opinion).
Sorry if I'm being Mr. Negative on this deal and throwing out a lot of variables to consider....hopefully this is of some help and doesn't just add to the confusion.