Jeff, I will assume you are asking what the bottom line the bank will take is going to be. If not, then ignore the rest of this...
The bank will get between two to five opinions on the home's value. The listing agent will provide a good price opinion, and they will likely get one or two additional BPOs (Broker Price Opinions) and an appraisal.
Depending on how long it takes for an offer to come in and then get processed through the bank's loss mitigation department (weeks to months), the bank may make their sale price decision based on the initial price data or might order a newer appraisal or BPO. That will be one of the primary tools they use to set their "not lower than" price.
So, the current fair market value for the home will drive the bottom line they will accept, along with other possible conditions specific to that home's file such as other liens on it, whether or not there is mortgage insurance on the loan to soften the bank's exposure, and possibly other factors.
So, does this sound difficult to sort out? Well, it is, and isn't. As a Buyer, make your offer based on good data, have a strategy, and understand the probable outcomes.
Let me know if I can be of assistance.