Said property shall be sold by quit claim deed for cash for a price to be determined as follows: The secretary of administration shall appoint three (3) competent and disinterested appraisers who shall make an appraisal of said land which appraisal shall be in writing and signed by the appraisers under oath and filed with the said secretary, which appraisal shall constitute the price for which said land shall be sold to said Chicago, Rock Island and Pacific railroad company, but in no event shall the sale price be less than five hundred dollars ($500) per acre and the secretary of administration shall have the right to approve or reject any appraisal. In the event an appraisal is rejected, the secretary may in the same manner cause the land to be again appraised and may thereafter sell the same as hereinbefore provided.