Yes, you may be charged an additional fee to travel to another country with the car. This fee covers additional coverage, taxes, and so forth. Make sure you get permission beforehand; otherwise, you may be charged a penalty and lose any coverage your car has, thus becoming fully liable for any damage to or loss of the vehicle. 

Gränskorsningsavgiften täcker inte vägtullar eller vägskatter i det land du planerar att köra in i.