When the improvement is fully completed and accepted by the county engineer, the clerk of the board shall compile and file with the board of county commissioners an itemized statement of the total cost of construction, including engineering and election expenses, the cost of publishing and posting notices, damages, and costs allowed or awarded for property taken or damaged, including compensation of attorneys, including the costs of crossings constructed by the district and the cost of crossings constructed by others and allowed by the board of county commissioners, and including the sum paid or to be paid to the United States, and the discount, if any, on the bonds and warrants sold and including all other costs and expenses, including fees, per diem, and necessary expenses of nonsalaried officers incurred in connection with the improvement, together with interest on such costs and expenses from the time when incurred at the rate of interest borne by the warrants issued for the cost of construction. There shall also be included in said statement, in case the county engineer is a salaried officer, a statement of the services performed by him or her in connection with said improvement at a per diem of five dollars per day and his or her necessary expenses, and a reasonable sum to be fixed by the board of county commissioners on account of the services rendered by the prosecuting attorney. Upon the filing of such statement of costs and expenses the board of county commissioners shall revise and correct the same if necessary and add thereto a reasonable sum which shall be not less than five percent nor more than ten percent of the total thereof in drainage improvement districts, and not less than ten percent nor more than fifteen percent of the total thereof in diking improvement districts, to cover possible errors in the statement or the apportionment hereinafter provided for, and the cost of such apportionment and other subsequent expenses, and interest on the costs of construction from the date of the statement until fifty days after the filing of the assessment roll with the treasurer; and unless the same have been previously appointed, shall appoint a board of appraisers consisting of the county engineer and two other competent persons, to apportion the grand total as contained in said statement as hereinafter provided. Each member of said board of appraisers shall take, subscribe, and file with the board of county commissioners an oath to faithfully and impartially perform his or her duties to the best of his or her ability in making said apportionment, and said board of appraisers shall proceed to carefully examine the system and the public and private property within the district and fairly, justly, and equitably apportion the grand total cost of the improvement against the property and the county or counties, cities, and towns within the district, in proportion to the benefits accruing thereto.