50% to the coach seems very fair to me.
We charge $110 per hour for privates, the majority goes to the gym, the coach who coaches the private will get their usual hourly rate, the same as they would for coaching group lessons.
The gym is generally doing a lot more than just providing the space. But as it is the space itself is VERY expensive. Gyms need to be in very large buildings, with very high ceilings, great location, lots of parking the cost of rent is very high. If the gym was to hire the venue out to an outside
person it would cost a lot more than the cost of the lesson.
The equipment is also incredibly expensive and needs constant upkeep. There are so many other facility costs too such as cleaning, electricity, rates etc. All of which would be included in a usual hire fee.
The gym is also providing the insurance, and taking the risks if something was to happen.
The cost of running privates will be high for a gym too, there is a great deal more profit in running group classes. Having a private means space in the gym and staff who could be on group classes are otherwise engaged and the gym can not run lessons at the same time.
The gym is also usually the one to arrange and schedule and privates, advertise for the students, build the programs that keep them in the gym year in, year out etc.