Any owner of a vehicle, whether it is currently registered or not currently registered, which is incapable of safe operation for use on the public highway and which has no resale value except as a source of parts or scrap only, or which the owner irreversibly designates as a source of parts or scrap, may junk the vehicle upon presenting to the director of finance a signed statement of fact of the junking together with such other relevant facts as may be required by the director of finance, and the signed certificate of title. All nonrepairable vehicles that are junked under this section shall never again be titled or registered.