Company Vehicle taxation

I work for an auto dealership group as the IT administrator.  They supply me with a company vehicle as I frequently travel from location to location and carry the necessary IT equipment and tools for installation and what not in the back of my Jeep.  They consider that vehicle a "perk" I guess as I am allowed to take it home and use it for personal use as well.   They operate off of some type of dealership related tax guide to determine how much to add to my paycheck as the "value" of the vehicle based of the MSRP every month, I pay tax on that amount.  My paystubs read "demo in" $xxx.xx, the taxes are subtracted, then they "demo out" the same amount as they demo in.  In a nut shell, I am paying tax on "$xxx.xx".  Currently the X amount is $936.  So income tax on that amount comes to thousands of dollars a year.  My question is, should I be paying tax on a vehicle used primarily for my job, supplied by my company.  Prior to this job I worked with a company selling marketing to dealerships and had a company car, all wrapped with advertising and everything, that I used to travel to various dealerships in my area during work hours.  I was allowed to take this vehicle home and use it however I wanted.  I never paid any tax on this as if it were a "perk".  That company was a much larger, nationwide company.  Can I file something to eliminate the tax liability in my current situation?