I subtract those off the net cash coming back.Are you saying you ha zero down payment when you bought and no closing costs?

Based upon an appraisal of $50,000 and subtracting the principal I owe the bank of $27,500, this leaves $22,500 in equity.

So if your purchasing a place all cash then you would do something like this, Gross rental income - Operating expenses = Net Operating income (normally you would subtract debt service too but you wouldn't have it in this situation)You would then divide that left over number by the cash you invested. 

In the JV scenario you would look at the ARV subtract out the repairs and the first mortgage as well as the cost to sell.

Not to mention the buyer subtracts the commission from his offer.  

I take the ARV and subtract the total cost. 

Since the co-op investor doesn’t own the property or land beneath, can he depreciate the entire purchase price without subtracting a land value?

If you'll notice, if the subject property has a single garage and a comp property has a double garage, the appraiser will "adjust" the comp to match the subject property by subtracting say $5,000 for the larger garage.

I have not yet experienced that, my guess is that they subtract it from their next payment to you. 

Okay, only because your next question is kinda hard to understand....it's not 75% LTV (loan to value) it's ARV (after repair value less rehab costs) I think is what some goby.I don't use rules of thumb, I sharpent a pencil and use my calculator, see what the MV will be repaired, subtract costs of the sale, subtract cost of the rehab and my profit, costs to acquire it and then arrive at my offer.