people's intelligence on this forum. You are not the only one working in the financial industry with a CFA. And clearly you are not the only landlord. You don't think people understand that the higher the IRR, the better an investment?
The problem is that you keep saying positive cash flow means the formula you cited can be positive for an investment. That's just not right. Your formula solves for IRR. No question about it.
1. But depending on the property, the solution(IRR) to your formula can be very small or very large. Even for a lousy property investment, very likely you can still find a very small r to make your formula positive. Does it mean it is a good investment? No. So having a positive sign in your formula doesn't mean much. It's the magnitude of r that determines whether an investment is good or bad. I am sure you know that. I am not questioning you on that.
2. In order to solve for IRR, you have to estimate terminal sales value. That's very hard to estimate.
3. Even if a property can meet your definition of positive cash flow(having a positive sign to your formula), but if it keeps losing money in the first few years, the owner may not be able to remain liquid to keep the property. That's where the real definition of positive cash flow comes in. As long as you bring in more than you spend, at least you don't have liqudity issue and won't be forced to sell. Whether you eventually make money is another matter, which is a solvency issue.
So positive cash flow is a liqudity issue while IRR and income/return is a solvency issue.
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