When it comes to making offers on bank owned property I always like to mention that since you are dealing with a bank, the transaction is not an emotional one. This is important to keep in mind because when you throw out low offers on someones personal property, as opposed to a banks or larger investment companies property, you can truly upset them. A home is someones haven, the biggest and often times most important purchase they probably have ever made, and where they dwell with their most prized possessions; family.
When dealing with a bank however there is no emotion tied to the property, its a number-so making a low offer wont likely truly hurt anyone in the process. I am always more willing to make low ball offers on bank owned properties for my buyers because of this. The worst thatusually happens is they ignor the offer and you have to come up until you get a response.
However when dealing with personal property it becomes more important to treat the home you are making an offer on with a more gentle and thoughtful approach. Doing your research and making sure that you have legitimate case for presenting a certain price is more important because if you present a low offer, without solid grounds, you could offend the seller and they may not be willing to counter or sell to you period.
Banks are more logical- the longer the property has been sitting the more its costing them and the more likely you are to get a counter or acceptance to a low offer.
Given you have all cash to close, I suggest making a solid offer at a price you feel comfortable with, and a fast closing (7 days as an example) Keep in mind banks are already, as a rule, pricing their homes at a good price to elicit offers. If your agent can submit a CMA with a good case on the price you are offering you have a better shot as well.
I hope this helps. Let me know if I can be of any future assistance to you - Cheers!