Q: On a short sale, how low a price can you offer and still expect a lender to approve the deal?
A: Lenders usually will accept offers that net at least 82% (after expenses) of the home's current fair market value, regardless of what the borrower owes. Lenders will accept less than what's owed on a mortgage because it will lose less by allowing a short sale than by going through a foreclosure. Taking advantage of a short sale is less risky than buying a foreclosure, because so many repossessed homes need tens of thousands of dollars' worth of repairs. The worst of the bunch have been deliberately vandalized by angry owners just before they were evicted
Q: Is it OK to start low to see if there's room to negotiate with the lender?
A: Short sales aren't the time or place to do a lot of dickering. Lenders don't have the time or staff to evaluate an endless bunch of bids, each a little higher than the last. If you deliberately lowball a bank or mortgage company, it will just write you off as a waste of time. You need to come up with a cheap but reasonable offer, which the bank or mortgage company will accept, in one try.
Start by estimating the fair market value of the home for yourself, using comps (values of comparable properties that have sold near the home in the past few months). Take the condition of the home into account and reduce your estimate if the home needs repairs. It's a buyer's market, and you don't have to treat a fixer-upper like it's in pristine condition. Calculate 82% of the home's value, throw in a few thousand dollars to cover the lender's cost of doing a short, and you have a good starting point.
Now look at the quality of your comps. If they're straightforward deals, and the homes spent at least three or four months on the market, then you're good to go. But if all of the comps are foreclosures that sold within a few weeks of hitting the market, you've got to assume those were damaged homes being dumped at fire sale prices. You'll have to adjust your offer upward, perhaps all the way to the full fair market value calculated with those comps.