Here's a formula, a variation of one used by investors:

(1) Determine the ARV (after repair value) of the property. What will it be worth in good condition? (Get your Realtor to do a CMA and explain that you want to know how much it'd be worth in good condition.

(2) Take 90% of the amount in (1) above. [That's to allow for any errors in the CMA and to allow for a continued soft market.]

(3) Determine the repair costs.

(4) Add 20% to the amount in (3) above. [That's because repair costs are almost always higher than the estimate. It's also to compensate you for your time and effort in managing any repairs.]

(5) Subtract the figure in (4) [the repair costs plus 20%] from the figure in (2) [90% of the ARV] This figure is the most you should pay for the home. Hopefully, this number is above the asking price of the bank. If so, pick a figure somewhere above the bank's asking price and below the figure you came up with in (5). The more you want the house, the higher the number should be. But don't offer more than the number you came up with in (5).

That's what you should offer.

Bank owned properties are usually already steeply discounted. Banks are only looking for the best price and so the closest you can offer to the asking price the better your chances of getting the property. Otherwise if you plan to low ball prepare to wait for a response for weeks (or sometimes not get one at all).

First you need to see the property to determine how much money you will have to put into it. Many bank owned properties come with no appliances and can be in need of repairs. You also need to know how long it has been on the market. If it is a recent listing, the bank will probably expect to get close to the listed price and might have it priced low enough to encourage multiple offers. The longer the property has been on the market, the more negotiable the bank will be. You need to see recent comps to see what the house is worth. Your REALTOR should be able to do a CMA to let you know the current market value. Not all the best deals are foreclosure properties. Good luck!