You would never assume 100% vacancy so even at a modest 10% for vacancy, once you throw in $700 in property taxes, $300 in insurance, $1200 in yearly HOA and assuming 10% in variable cost PM you would be lucky to pull a net operating income of $630 however cash flow once debt service is accounted for you'd be more around the $100-$150 range a month.

My experience has been, a refi isn't realistic any sooner than six months from purchase, and a year is more likely.As for the amount you'd be able to pull out, you answered your own question.

Matthew Dion did you ever end up pulling the trigger on a property?

If you give them your SS and DOB it's a credit pull.

I used turnkey with some people I pulled together with help from the folks here on BP.

You could pull some comps off REALTOR.com or Zillow and use them to justify the projected rental income for the duplex and/or your current residence and the 4-plex, if it is not already rented by the time you take this next step.

I would like to refinance one of my investment homes, pull out this amount and re-invest.

I did pull the trigger and purchase my first house which I'm in the process of fixing up right now.  

The homeowner pulled out of the deal last minute for personal reasons.  

Sale date makes sure you're only pulling dates based on when the property was actually sold