1. In California, while assessed values typically don't relate to appraised values because assessed values get calculated using the proposition 13 formula, in some situations, proposition 8 creates an exception. Proposition 8 says that if the current market value is lower than the prop 13 value, then the current market value on 1/1 is the assessed value. I believe that means that when you a house that sold four years ago for $400,000 and now "assesses" at $200,000, that the county appraiser thinks he 1/1 market value is $200,000. Obviously, that's a good at a particular point in time... but the Riverside County assessors office is staffed full of appraisers, so I understand... so I think equating appraised values with prop 8 assessed values is more reasonable than you might think.
2. In California, the standard purchase contract (at least the ones I've seen) have an appraisal contingency... so California buyers (like me) probably always have that available...
Thanks to everybody for your great answers.
At this point you will have to write an addendum asking them to lower the price based on the appraised value, make sure you include a copy for the appraisal and then ask for a credit for the pool, inlcude pictures and at least 2 estimates and include that all hoa fees shall be paid as of closing.
Please see my blog with tips on buying a short sale
I guess the real question is what would you be willing to pay for the property now knowing what you know. Then I would have your agent present that new offer. Either BofA agrees or they don't.