At the time of the initiation of the proceedings for any improvement as contemplated by this chapter, or at any time afterward, the city council shall cause plans and specifications for said improvement to be prepared and shall cause an estimate to be made of the cost and expense of making said improvement, including the cost of supervision and engineering, abstractor's fees, interest and discounts and all other expenses incidental to said improvement, including an estimate of the amount of damages for property taken or damaged, which plans, specifications and estimates shall be approved by the city council.