Armando,
Looked through the numbers of what you gave and see the following:
You purchased at roughly a 83% occupancy or 17% vacancy and are looking to take the property to 100% occupancy (though 100% can be done, at least a 5% vacancy factor should be used). So what I see you doing in your value add is increasing occupancy and rent per door through renovations.
With this said, after renovations are done I see a annual gross rent of $182,400 = $800/unit x 20 units x 12mo x .95 occupancy. $182,400 x 50% expense ratio as you had it = $91,200 NOI / 6% CAP = $1,520,000 valuation ($520k in value added) x 75% LTV refi (could be higher or lower) = $1,140,000 new loan amount. At the refi, to answer your question, you would walk away with $1,140,000 - payoff of current loan ($452k?) - closing costs.
If I'm reading it correctly you have a current loan amount of $452k and put down $548k while looking to put roughly $80k in renovations. If this is right, you would have $628k into the deal. So you would recoup your $628k and have just a small amount left over after closing costs are factored in.
FYI...There is a bit of a flaw in your $42k/yr annual income increase as the 50% expense ratio hasn't been applied to it. Model 2 is a more accurate representation of the value added...though I would add in the 5% vacancy instead of being at 0%.
Annual rate of return, based on amount put into deal/NOI, is a good calculation for returns up to the point of refinance and then it goes out the window...IRR would be your best formula after refi.
Hope this helps!
Stephen