The director shall establish by rule a schedule for the renewal of recorded brands. The fee for renewal of a recorded brand shall be one hundred twenty dollars for each four-year period of brand ownership, except that the director may, in adopting a renewal schedule, provide for the collection of renewal fees on a prorated basis. At least sixty days before the expiration of a recorded brand, the director shall notify by letter the owner of record of the brand that on the payment of the renewal fee the director shall issue proof of payment allowing the brand owner exclusive ownership and use of the brand for the subsequent ownership period. The failure of the owner to pay the renewal fee by the date required by rule shall cause ownership of the brand to expire. For one year following the expiration, the director shall record the brand only to the prior owner upon payment of the renewal fee and a late fee of twenty-five dollars. If the brand is not recorded within one year to the prior owner, the director may issue the brand to any other applicant.