Here is my logic - At a prior bank 1 director was a surveyor & he got paid for surveys on RE loans & 1 director did pest inspections, ditto.
If what the director is doing relates to his area of expertise and you are paying what you would pay anyone else who provided the service, including paying mileage (keep it arms length) then you should be o.k.
My question is what is the director doing that you are paying mileage?
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My opinions are just that, and might be worth what you paid for them.