Upon such request being so made, it shall be the duty of said department to make an estimate of the expense of opening or tearing up the roadway of the street wherein such construction, reconstruction or repair is to be made and of the restoration of the same to as good a condition as it was in before said opening or tearing up, together with the estimated expense of labor to be performed and materials to be used in such construction, reconstruction or repair, including a fee of $5 to be applied as for services for official supervision.