At any time after the contract and bond for any work for which a special assessment is required have been executed and approved by the governing body of the municipality and the total cost of such work shall have been estimated as nearly as practicable, the governing body may direct assessments to be levied for the payment of all or any part of such cost, and the city auditor shall ascertain and return, as provided in this chapter, the total assessment against each separate lot, tract, or parcel of land in the improvement district. The total cost of the improvement shall include the estimated construction cost under the terms of the contract; a reasonable allowance as determined by the governing body for cost of extra work which may be authorized under the plans and specifications; engineering, fiscal agent’s, and attorney’s fees for any services in connection with the authorization and financing of the improvement; cost of publication of required notices and printing of improvement warrants; and all expenses incurred in the making of the improvement and levy of assessment therefor. In the event that any error is made in estimating the cost, the governing body may direct a supplemental assessment to be made as provided in section 40-26-02.