From your numbers, I would pass. The margin on this deal is not too thin, it doesn’t exist. Nor does it look like you know how much rehab the place will need or any of the other costs either. “…wiggle room for maybe paint or to pay the first few interest only payments”? It either needs paint or it doesn’t and I’m certain the interest payments aren’t going away. Frankly, you are in no position to buy properties with a few hundred dollars in your pocket. Those days are gone - sorry. I’d consider selling the lots to provide the cash you need to do deals like this.
I don’t know Arizona RE, but you must conservatively consider the days on market and assume the property will drop in value each month based on a historically derived percentage that you can calculate, until sold. Your $110k -$115k estimate might be correct right now, but months from now it will be too high. Few homeowners are currently paying list price: everyone wants a deal.
If the bank originally loaned $84k in 2001, then they enjoyed 8 or so years of interest payments and should take substantially less. (Which makes me wonder how a house like this went into foreclosure?) This is not how the bank determines current value, but it might make them more accepting of a low offer.
Ask your agent what comparable REO’s have been selling for and what the sales market for the home rehabbed is like. If your agent shows you comps for this property, as-is, at $84k or so, then walk. It means someone else is willing to overpay. If much less, then you have a chance, but you must consider the expenses you will encounter.
Subtract every possible expense over your anticipated holding duration (closing costs to buy, points, rehab, interest, insurance, utilities, deposits, closing costs to sell, fees, security, etc.) from the predicted future value, and then multiply by something in the 50% ballpark. That would be my firm cash offer to the bank assuming the house is in a desirable area and quickly salable in tip-top shape. If your agent calls you crazy, then find a more aggressive agent.