In the event that all persons or property owners to be affected by any proposed improvement agree that such proposed improvement be made and that a special assessment be levied in connection therewith, the city may, in lieu of the foregoing procedure, enter into a written contract with all of the persons or property owners affected thereby, which contract when approved and executed, shall operate as a complete special assessment procedure and the assessment shall be made in accordance with the contract.
(`73 Code, 12.218, § 1.118)