Also, how much does this premium over cost vary by neighborhood in the Phoenix area when estimating market value?

A lot of streets even vary from one end to the other in terms of disturbance, but those streets I listed have just too think a crime density even for me.

In my market,  I haven't had that problem,  but state policy varies.

Please be advised that each market varies so you will want to alter expenses accordingly.  

If you have multiple appraisers give you an appraisal on the same property, they can vary wildly in opinion of value based on the experience level of the appraiser, their knowledge of renovation costs and even their personal bias toward investing.  

@Andy Diaz- I think it varies greatly, I would suggest not to don't bend on your criteria.

Does it vary dependent on the attorney facilitating the foreclosure? 

Real estate prices in Montreal are lower than Vancouver or Toronto for sure, but prices vary widely depending on the area of the city (ex: Downtown vs Point-aux-Trembles), I would suggest getting familiar with 1 area first so that you can tell when you find a good deal.

Lenders will vary greatly.

It may vary from state to state, here's how it works (usually) in Alaska, and probably similar elsewhere:The Earnest Money is deposited when the offer is accepted.