Like Anna, I don't know the specifics of these calculations. But it also seems like the cost of purchase and frequency of use have to be factors too. Specifically there's a difference between renting something I can reasonably buy versus something I can't. I can choose to rent a chainsaw to clean up a tree that fell down on my property, but I can also reasonably buy one. However, I'm much less likely to be able to afford to purchase Bobcat/Skid Steer - so my only choice would be to rent it.
Likewise, I might use a chainsaw every few years and one can be purchased for under $200. On the other hand, most people aren't going to use a Bobcat/Skid Steer very often.
I think the general influence on rental prices would be - if it is relatively cheap and I might use it fairly often, you may need to have a lower rental price (at a certain point they may say, heck if renting it is 75% of the price to buy a new one, then I'll just buy a brand new one), conversely rental prices might be higher than typical for a device/machine that it would be outrageously expensive to buy and that you use rarely.
Of course, you'll also have to factor in marketplace competitors, how much work & time the device saves the renter compared to not having the device (after all, I could try to just saw a tree with a handsaw, etc.). And the likelihood that the renter will destroy the device. Good luck!