I am going to be that guy and give you an indirect answer.
But first some Big questions:
Of the 5k monthly expense estimate how much is going toward rent?
What is the national cost of living scale where you will rent?
If 2/3’s of that is for rent you are better off purchasing. I will explain.
Why be the slave when you can be the master?
My first school was/is in a strip mall. Don’t make that bigger than it is. It is a 4-unit complex that I was able to purchase after the school had been there about six months. But the wheels of purchase were set in motion about a year before opening the school.
By starting out with a 30 year variable mortgage , the payment was less than any spot I could rent of equal size in a comparable area. I converted to a fixed 15 year 3 years later and paid it off in less than 10.
Using a rough pen, 2 rented units pay the bills. Especially with the consistent change in the “martial arts as a business” landscape, it allows for maintainability of a commercial size Dojang that I could not see having any other way.
And here is a salient point; I do not believe it would matter what service industry it is. As long as the product is not costing you money it can stay viable.
I don’t ever remember doing the “per student” financial evaluation since it hasn’t been needed but your number will only be relevant to your input/output situation. It is pretty hard for me to picture a commercial school of big enough to support the student numbers you talked about without some way to offset the initial deficits. Yes, that can be working another full time job but that surely changes the dynamic.
Now, for some realities you will need to embrace:
You need to either take a really good business MANAGEMENT class (not sports management), get experience from your work, or have a good, trustworthy mentor. No shame in the latter and it has paid huge dividends to me for years. He has helped me make all my big financial decisions.
Expect to spend more on marketing than rent in the beginning.
Expect to take a loss or make little to no money for 3-years. This is how you have to plan you finances (most people anyway). IF you do it right you will far out pace the 3 year timeframe.
Don’t be afraid to sublet in the beginning.
One of the biggest changes I have seen through the years is what people perceive to be a “nice” gym. Gone are the days of the old sweat boxes. When people pay for a service they want the whole enchilada. And I think that is within reason. This means you must plan and design your Dojang for what works now and that can expand/modify in the future. And teaching classes will be less than 50% of the job.
This is another area visiting as many schools as possible has great value.
If you can show us an actual budget it would give us all great points to talk around. Would also need to see some comps on rentals in the area and then see what is for sale in your area.