Good luck and best regards.
There's actually a tremendous amount of information out there about the basics of making an offer to a bank, what to expect, how to price your offer, etc.
To make a long story short - you want to know as much about the property as humanly possible. You want to go back and pull up public records (your county recorder's office will have a wealth of info) - find out how much the house was originally purchased for, how much the owner still owed when the bank took it back, how long it's been in the bank's possession (sitting empty), how much it will require in repairs (if any) - and try to put all these things together.
Now - putting all that data together and using it to come up with a price to offer is where it gets tricky - and honestly is more then i'm even going to try to explain here. I think it's fairly obvious to say however that the more REO inventory on the market, the longer it's been sitting there, and the more the market would suggest it's going to be a long time before it sells - the lower you can make your offer. It still needs to be reasonable in terms of what your offer is in comparison to how much is owed on the property, and what fair market value for the home is. A lot of people make the mistake of expecting to be able to offer 20 cents on the dollar and get it just because it's bank owned. That's not the case.
Be aware that banks will negotiate with you - but it will be a much different process then negotiating with Joe down the street. Banks are interested solely in the numbers game, and will take much longer to get back to you. Don't expect a lot of incentives or extras thrown in. When you make your offer - be prepared to show that you have the ability to close quickly without issue - that will go a long way. A lot of banks are willing to forgo a couple thousand here or there if a seller is able to pay cash, or can show that they're capable of taking ownership very quickly. Banks are looking purely to minimize losses, and try to move the property as quickly as possible. The key is finding the right balance there. I would suggest making a strong, but low offer - be prepared to back it up - and be prepared to have it rejected once or twice.
You can get great deals on bank-owned property, but it may take some work and starting over from square one a couple times. You get rejected, go back to your data and try to figure out why (sometimes the bank will tell you, but don't count on it). Adjust your offer to compensate - and try again.
In Virginia we can actually look up what a Realtor (working for a bank) has accepted in their last 10 deals. This can give you a crystal ball into what they will accept. This one Realtor just dropped 9%. Well their last bank deal they also dropped.... 9%. Coincidence. I think not. We then saw that they accepted 4% under the new price, so we offered 5% under.
An agent's selling history is your best answer. (along with the traditional 101 stuff like CMAs)
If this doesn't get "best answer" I dunno what will. I will be blogging about this soon so sign up.
To add to the problem, there are so many qualified buyers and almost all are in the $225-250k price range, all looking for the same amenities in a home/area. Just to manage your expectations a little more, the listing agents are not taking the listings out of active status, even though the bank has an accepted offer. They like to wait until the seller has signed off on the paperwork, which usually takes weeks. This creates a lot of frustration after you get your hopes up, thinking you've put in a reasonable bid, only to find out the home was sold long before you ever saw it. I could go on with more stories and experiences, but the point is you want to find a Realtor who's experienced in the marketplace in Las Vegas now.
As far as the established listing price, as Damon answered below, it's based on what the home's value is based on comps in the immediate area. With so many REOs, the prices have been driven down, only to be brought back up by demand. What the bank is owed on the home isn't a criteria for its list price.
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Good luck in your search!
I'll send you some stats on bank owned list price to sale price ratios ;) As for the listing or asking price... it's usually based on one or more broker price opinions (BPO). Often it's actually less than what was owed by the former owner. Also, in my experience, it seems that there is more bargaining room as you go higher in price range. For example a bank owned home for $180k that hasn't been on the market long may actually sell for $180k or more, while a $500k home that's been on the market for weeks may have considerably more room for bargaining.