In the event a disagreement arises between the Department of Finance and any person or persons in charge of any insured property as to its replacement cost or actual cash value or the amount payable under the claim for loss or the proper premium rate or rates, the matter in disagreement shall be determined by a third person to be agreed upon by the Director of Finance on the one hand and the person or persons disagreeing with him on the other. In case of inability to agree on such third person, the Governor shall appoint a third person to determine the question, and his decision thereon shall be binding on all parties concerned.