ROI & Cash Flow Calculations

[Kim Cooper]

I feel like I am taking crazy pills over here.  I am trying to find a concise answer, but I keep finding answers that contradict each other.  So, I hope this forum will help.  I am super new to all this so thanks in advance. 

QUESTIONS:

1. Does ROI include your mortgage (principle and interest) on a property that you finance? 

2. Does Cash-on-Cash include your mortgage (principle and interest) on a property that you finance?

I realize that Cash-on-Cash is a type of ROI, but I am working off these assumptions:

Simple ROI = (rental income - vacancy - expenses) / (purchase price + closing costs + repairs/renovations)

Cash-on-Cash = (rental income - vacancy - expenses) / total amount of cash actually invested into the property

Basically, do you count mortgage (principle and interest) as an expense for both ROI and Cash-on-Cash?