If a client of yours moves to a new farm (with an indoor) and you teach them in a private hour lesson, how much of a facility fee do you pay to the farm owner and what is your lesson rate? If you start to teach other people at this farm who were previously taught by a staff instructor (so they weren't "your" clients), how much would you expect to be paid for an hour private lesson on a horse owned by the farm?
I think in part it would depend on if you add value to the barn by attacting clients, or if you are taking away from the barn by taking income from the in barn instructor.
Around here, arena fees vary from $10-20. Usually those are for haul ins, but sometimes also for boarders using outside instructors. For an instructor that adds value to the barn, then there is typically no fee for the lessons to boarders.
I suppose it would depend too though, if you are reserving the arena and preventing others from riding/coaching at that time.
Horse use fees for lesson horses vary from $15-$20 depending on the quality of horse/facility and such.