I've read several iterations of 'How to Calculate NOI' here on Bigger Pockets and most all indicate we should not include capital improvements or additions, principal and interest, amortization loan points, income taxes and depreciation into the calculation. 

... and I agree (mostly); however, shouldn't Principal and Interest be accounted for because A.) principal payments are not expense-able and considered income in the eyes of the IRS since principal is not an expense and B.) interest is a true expense in the eyes of the IRS? 

Let's have a look at two examples - one in which we factor in Principal and Interest and one where we follow Dogma.

Setup (Yearly Values):

Income:             $12,500

Principal:           $2,050

Interest:             $3,800

Property Tax:    $1,500

Insurance:         $800

Mgmt Fee:         $1,250

Vac & Cred:       $2,000

Cap Ex:              $500

Scenario 1: 

NOI = (Income + Principal) - (Interest - Property Tax - Insurance - Mgmt Fee - Vac & Cred)

NOI = ($14,550) - ($9,350) = $5,200

Scenario 2:

NOI = (Income) - (Property Tax - Insurance - Mgmt Fee - Vac & Cred)

NOI = ($12,500) - ($5,550) = $6,950

In both cases, Capital Expenditures is NOT included in the formula (and for good reason). However, notice how our Net Operating Income is higher when Mortgage P&I is not factored in to the formula? The only reason I can really think of as to why it is not included in the calculations, traditionally, is because you would then effectively be calculating Cash Flow. So now, another can of worms, isn't Net Operating Income essentially the same thing as Cash Flow?

My head hurts - I'm laying down for a bit.