If the Fed pushed overnight rates to zero and nominal 10 year rates went negative it would mean the deflationary environment is accelerating - which mathematically would mean "real" rates are rising and the risk premium on loans would spike.

The mathematical equilibrium.

Your number comes to 3 months' vacancy at a mathematical average of all rents.  

Elizabeth Colegrove I got lost with your mathematics here: With $50,000, you can buy 3 (3.3, .3 goes towards closing/extra costs) of these houses.

It's not mathematically possible for IRR to be lower than CoC. 

Mathematically speaking all of the limited partner's outside basis (80% interest) would have to be multiplied by .63 to compress to 50%.

Nina,I'll give you the philosophical answer, and then provide an excellent link for the mathematical response.Ultimately, paying cash or leveraging to buy more properties is a win-win choice.  

This would be purely a mathematical decision upon evaluating the proportions of the loans in respects to their potential interest rates.

I find a lot of comfort in knowing that there is a concrete way of valuing a property by use of mathematical equations.

although they are all right, mathematically speaking, there are couple of elements to be consider as well.