The board is authorized to place any child committed to or received at a state institution in a private children‘s home. The board may enter into contractual agreements with any private children’s home to provide adequate care, custody, education, training and treatment for any child so placed and to pay the costs of said care, custody, education, training and treatment if the costs are not paid by the child’s parents or guardian or if the child is not eligible to receive assistance under Kan. Stat. Ann. § 39-709, or any amendments thereto. Any such contract shall be for a period of not to exceed five (5) years but the same may be renewed upon its expiration.