After the contract for the work of construction of the improvement has been let, the board of viewers shall ascertain the total cost of the improvement, including damages awarded to be paid to owners of land, all costs of incidental expenses, and including a reasonable attorney’s fee to counsel for petitions for conducting the proceedings on behalf of the petitioners, the amount of such fee to be fixed by the board of viewers and also including an amount sufficient to pay the necessary expenses of maintaining the improvement for a period of three years after the completion of the work of construction, after deducting therefrom any special assessments made against any railroad or highway. Thereupon the board of viewers under the hand of the chairman and secretary of the board, shall certify to the clerk of the circuit court the total cost, ascertained as aforesaid; and the certificate shall forthwith be recorded in the drainage record and open to inspection of any landowner in the district.