Whenever the Department is furnished with satisfactory evidence of the destruction of a motor vehicle, either complete or to such an extent as to render it impossible to operate such vehicle as a motor vehicle during the period for which it has been registered, and if the owner thereof desires to register another motor vehicle during the period for which such destroyed motor vehicle was registered, such owner shall be entitled to a credit on the new registration fee of the unexpired portion of the registration fee of the destroyed motor vehicle from the date of the new registration.