Notwithstanding the provisions of § 56-3-900, when the owner or lessee of a motor vehicle or vehicle including, but not limited to, trailers and semitrailers, licensed and registered for a biennium pursuant to § 56-3-253 surrenders the license plate and registration to the Department of Motor Vehicles in the first twelve months of the licensing period, the department shall refund to the owner or lessee an amount equal to one-half the registration fee paid on the vehicle. If the owner or lessee is simultaneously registering another vehicle, the refund amount, at the owner’s or lessee’s option, may be applied against the registration fee due.