The timber cut on lands, where the timber only is purchased, must be cut within the time specified in the contract of sale, but not to exceed fifteen (15) years. The state board of land commissioners shall specify the time within which timber must be cut at the time of sale. If, at the expiration of the contract period named at the time of sale in which the timber must be removed, the purchaser desires further time for the removal of said timber, application may be made to the state board of land commissioners for such extension, giving the legal subdivision or cutting unit upon which such extension is desired, and making satisfactory proof that the timber purchased under the contract has not been cut or removed, and the state board of land commissioners may extend the time from year to year, for a period of not to exceed fifteen (15) years from date of sale, upon payment of such additional interest and extension fees as the board may require. All timber remaining after such period shall be the property of the state.