That the $7,500 is not return ON your $100k of equity. The return on your equity is the appreciation plus or minus the net cash flow to the equity position.

I'm not sure I agree. (I think I may not fully understand what you're getting at though.)

The $7,500 is an injection of additional equity and belongs in the denominator, not the numerator.

It's only an injection of additional equity if it's coming out of your pocket. If it's paid out of the rents, then it's part of your return.

I'd calculate one's total return as "however much your net worth increased" divided by the equity you could have extracted.

Things that increase the net worth are appreciation, cash flow, principal paydown, and tax benefits.

I count principal paydown in my total return, but I don't in the real number I'm interested in - cash on cash return. I want cash flow, and principal paydown and appreciation to happen on top. Why just take appreciation and principal paydown when you can have cash flow also?

The problem is your assumption of "the rent covering the expenses" - the rent would have to cover all expenses plus the P&I for it to count as return. Otherwise you're in AR's scenario of where you're injecting capital, and then it's not return on equity.

In this scenario, you're cash flow negative. It's not going to cover the expenses and mortgage payment. Sure, you could say "once you count in appreciation and principal paydown I'm slightly net worth positive" - but what could you do with that 100k of equity instead?

What if you put that as a downpayment on a property that would also get the same principal paydown and appreciation as this property, but also cash flowed a decent return as well?

Either way this doesn't seem like a dilemma, but a clear sell.