Oops, I had not finished my first cup of coffee. Still not awake. You don't subtract interest from net OPERATING income.. Interest is a cost of financing the property, not a cost of operating it. -

So you don't subtract interest to get NOI. Subtract only your operating expenses to get NOI.

You subtract interest from your NOI to get your NI. ( Net income,- see all I did here was subtract the word operating to get the abbreviation "NI")

Now, I am going to pour a second cup. Ah, Monday.

Positive Cash Flow is the term that I would use instead of NOI for the formula you posted as NOI.
The letter "P" stands for Principal. If you are paying an interest only loan then your NOI and cash flow are pretty similar. However if you are making principal payments on an amortized loan, the principal is removed from cash flow, but it is not an "expense" for the purpose of reducing the calculation of net income.

Using your P/E ratio comparison, think of your cash flow as dividends and your principal payments as retained earnings. Both combine to make the "E" in the P/E calculation.

A cap rate is the inverse of a P/E thus if the P/E is 20 to 1 the cap rate is 5. If the P/E is 12.5 the cap rate is 8.
10 is 10. and so on. Divide a hundred by the P/E and you get the cap rate.

A cap rate that I may find acceptable for one property may unacceptable to me on a different property. I am likely to be happy with a lower cap rate on a property that is fully rented out and in good condition than I would be on a vacant property that I will have to rehabilitate. Numerous factors will affect my decision.

For a ball park answer, If I was looking for a duplex in Oroville. I would probably seek an 8 cap rate, for myself, as an investor. That may or may not work for you,