@Allan Smith
To a large degree, I have to agree with Bill's math. But I would add that there are a few other nuances to each person's formula. It all depends on your personal goals. Are you trying to create a stable portfolio with minimal risks or are you trying to scale up by leveraging your equity?
I personally do not follow any specific math but I do take I to account some general rules of thumb. The biggest one I use is the realistic sales number and what the net proceeds would be. On top of that, I also account for the current costs of available inventory in the market I'm investing in.
If the net proceeds are over 5X the annual income, I think it's safe more me to say that it would be wiser to cash out and reinvest. If not, then I better have an upleg ready to go that would allow higher leverage with upside.
Recent example, I had a really good performing 6 unit (all 1/1), plus 1 unpermitted studio. I purchased June 2021 for $700K. It cost about $240K to cost that deal. It produced about $50K cash flow. It had enough room to grow to about $70K cash flow in next few years. That $240K came from a 1031X SFR that I purchased summer of 2015 with about $30K down payment. It was a live in for 2 years.
I sold it for $900K last month. It was grossing $7903/month in rent at the time of sale and I helped increase it by another $400 to get the new owners even more income. After the dust settled, I net about $400k in the 1031. I found an upleg that is 14 units for about $2M. I will use $400K as down payment and finance the rest. The 14 units had a better mix... several 3/2s in the mix, spanning 7 parcels. Additionally, I also included a large vacant lot. The gross on this new purchase is about $18500/month. There is some upside left, may be bring up to $20K/month.
But here is the fine print, it in the same area. The price per door for multi-bedroom multifamily units in the area are about $180K/door. For regular units, its $220+/door.
These are the things that go into the decisions of whether to refi some equity or sell and exchange. Your personal goal will dictate the strategy and the speed in which to employ these tactics.
There is nothing wrong with refi to use tax free equity to purchase more either. It's just slower and less efficient. I did it a few times. I fact, I did it with the SFR that is used for the exchange I mentioned above. I had extracted some equity before to purchase a 2plex in 2018.