If the initial assessment has been made on the basis of estimated cost, and, upon completion of the work, the cost is found to be greater than the estimated cost, the council may make a deficit assessment for the additional cost, provided, however, the council may not make a deficit assessment for more than ten percent of the initial assessment. Proposed assessments upon the respective lots within the special improvement district for a proportionate share of the deficit shall be made, notices shall be sent, opportunity for objections shall be given, any objections shall be considered, and a determination of the assessment against each particular lot, block, or parcel of land shall be made in the same manner as in the case of the initial assessment, and the deficit assessment shall be spread by resolution.