At the final hearing on a proposed improvement, the board of county commissioners shall hear any application that is filed for a change of the route or course of the proposed improvement, or of either terminus thereof, from that shown in the report of the county engineer. The board may hear any application to make any change in the nature, kind, or extent of the work proposed to be done, as shown in the report of the engineer. If the board finds that such changes will better accomplish the purpose and object of the proposed improvement, it may make such change. If a change is made in the plan, or if the damages and compensation allowed by the board exceeds the estimate of damages filed by the engineer, thereby increasing the cost of the improvement, the final hearing shall be continued until the engineer makes proper schedules, which will include such changes. Before proceeding to make such change, all owners who will be affected thereby shall be notified of such proposed change, in the manner provided in sections 6131.01 to 6131.64, inclusive, of the Revised Code.