@Eric TeranHi Eric,It seem to me that Mathematically (although it's not your strong area),If it were me, I'd initially think about:cash flow from operations %% of the sales profits (or losses)Over all management of the LLC decisions %. 

Mathematical equation(s) can be derived with a fair amount of accuracy simply because its math.

I ran a few other assumptions and options to make it "cash flow positive" but I am not sure I am actually analyzing the situation correctly from a mathematical standpoint.

But it is a fairly advanced concept and difficult to formally mathematically define.  

@Kuron McGraw as for why an owner would keep a vacant property, you're gonna wind up getting into a long discussion about human psychology, how bad we are at making rational and mathematical decisions, and our tendency towards hoarding.

I am currently looking for a reliable and complete way to learn all mathematical knowledge I need to get into real estate investing.

I am a very mathematical formula depending human being...

BP does have some great tools to help you with any mathematical equations that come your way, check the 'Tools' area above.

I think they are only changing the cap rates so that mathematically both properties keep the same sales price.

And in the better market its just a mathematical fact that those that bought props with little to no cash flow after a 10 to 15 year hold have made much more gain or real dollars or real equity than those that thought they needed a few hundred a month in cash flow but the value of the property never really went anywhere and since they are low end assets as it relates there market to exit is HIGHLY limited and totally limited to what the rents are.Compared to those that may buy even in the same market but no cash flow A and B and exit is to homeowner big difference     To me if your going the drip income cash flow model then the goal has to be some scale then paying them off so that at the end of 20 years of dealing with all of it.. you have paid for assets the quicker they are paid for the better off you are in my mind as you have a real asset not an asset leveraged to 75 or 80% which is NO equity really. by the time to do a home inspection and pay sales cost you may make a few bucks or you may have to bring cash to clear your loan..