I take a totally different approach to this as I have been beaten into the ground on this type thing back when I gave a crap.
If I provide a machine: be it an excavator, loader, skid loader, tamper, on site dump truck, what ever it is. That piece of equipment has a daily rate for the machine with out operator.
My daily rate is less than you could rent it yourself, put fuel in it for the day and pay any associated "damage waiver fees" from the rental company.
I provide an equipment operator that is paid for his time on site, or off site if he is getting material for the job at hand.
This approach has limited the fights I get into about charges for equipment.
You don't want to pay for the machine...go rent one yourself, put some a-hole in it that can pull the levers and get done less than half as much as one of my guys and then, see where you are.
I have used this method and it is the only way I know to get paid for the thousands of dollars of equipment we have, at someone else's immediate disposal and still be fair.
Now don't get me wrong, I'm not inflexible and will work around things such as machine that was only needed for a couple hours, but was needed, could get a break in the daily rate.
But if I'm backfilling a trench, and compacting it with my tamper, I am getting paid for the tamper and the man time to operate it, and the day rate for the loader filling the trench.