Correct Definition of "Return" in Return on Equity (ROE) & Return on Investment (ROI)

[Kim Hopkins]

Hello! 

I've put together a portfolio KPI calculator for our properties and am now realizing that I'm unclear on the best definition of "return" to use in calculations for things like Return on Equity (ROE) and Return on Investment (ROI) .

I've always defined "Return" here as Cash Flow, where Cash Flow is defined as: 

Cash Flow := NOI - Debt Service - Other Expenses.

Here, Other Expenses (or perhaps better named "One Time Expenses") include non-operating expenses such as Leasing Commissions, Capital Expenditures, and Tenant Improvements. 

My definition of ROE has always been: 

ROE := Cash Flow / Equity. 

But if I want to use ROE as a measurement of the property's general performance and to help inform potential buy/sell decisions, using Cash Flow in the numerator doesn't make a lot of sense. It's including the Other / One Time Expenses. So if I replaced a roof or had a large new lease, it could drastically lower the ROE in a given year, making it look like an underperforming property whereas that typically might not be the case. 

Instead, I think we should define ROE as either: 

ROE := NOI/Equity

OR

ROE := (NOI - Debt Service) / Equity.

Investopedia disagrees with all three definitions above and says to use Net Income in the numerator which deducts things like depreciation which makes zero sense for our purposes of analyzing property performance since one good cost seg study would wipe out your income all together. 

Why can't I find this discussion anywhere? What do you think is the correct answer?