Basic Question: Return Calcs with or without Closing Costs?

[Eviano I.]

Hi BP Community,

I'm relatively new and I have a (what I believe should be) basic question: In calculating returns, should one include closing costs as cost basis when estimating cash-on-cash return and why / why not? This is solely for analyzing and comparing different properties, not for tax purposes or anything else.

Illustrative Example

Purchase price - $100k

Closing costs - $5k

Down payment @ 20% down - $20k

Down payment + closing costs - $25k

Annual cash flow - $3k

Cash-on-cash returns (w/o closing costs) - 15.0% [= 3 / 20]

Cash-on-cash returns (w/ closing costs) - 12.0% [= 3 / 25]

I have been including closing costs, because that's the cash out of my pocket on day 1 and also because it's a meaningful amount of the initial cash outlay (e.g. 5/25 = 20% in this example). But if I turn around and try to sell the property 1 day later, the property doesn't automatically appreciate by the $5k amount of the closing costs. That being said, if I think about looking at the cap rate (NOI / purchase price) instead of the cash-on-cash rate ([NOI - debt servicing costs] / cash invested), then I do feel like one should not include the closing costs to the purchase price in denominator of the cap rate calculation; which is the opposite of what I do with my cash-on-cash calculation. My main issue is that the closing costs is such a big amount vs the down payment (for properties I'm looking at), so I don't want to inflate my returns by not including them.

Please let me know if I'm over-complicating this, but I welcome all views. (Btw, I know the best solve for this is to find a rockstar deal, so this will just be a rounding error; but I'm a numbers guy, so please humor me).

Thanks in advance!