Was This Correct Analysis

[Lawrence L.]

I made an offer today on a 5 family house in the Bronx. Please let me know what you think about my analysis,calculations, and offering price. 
Asking price..850,000 GR.....75,600...No vacancy added 10% for vacancy....75600-7560=68,040 Expenses...26,879.15...not showing management....Insurance......Gas 
Took 50% of adjusted gross income 
Which equaled..34,020 The cap rate with the price of 850,000 and NOI of 48,721 = 5.7%. When I used the same 5.7 cap rate on the adjusted expenses and income the NOI was 34,020 the valuation calculated was 596,140. I made an offer of 536,000. 
 This is the response I received: the residential market in the Bronx has gotten very hot. The cap rates are are out the window. 2-families are selling for $650,000 so I think we’re just playing in different sand boxes. 
Should I make another offer?