After the governing body of any city with a population of three hundred fifty thousand or more inhabitants which is located in more than one county, or the governing body of the county of the first classification without a charter form of government that has a population of at least one hundred sixty thousand inhabitants, or the governing body of any county of the first classification without a charter form of government containing a portion of a city with a population of at least three hundred fifty thousand inhabitants, or the governing body of any county of the first classification without a charter form of government as of August 28, 1995, that has a population of more than one hundred five thousand but less than one hundred twenty thousand inhabitants, has made the findings specified in sections 249.929 to 249.933 and plans and specifications for the proposed sewage or storm water facility improvements have been prepared, the governing body shall, by resolution, order assessments to be made against each property deemed to be benefitted by an improvement based on the revised estimated cost of the improvement or, if available, the final cost thereof, and shall order a proposed assessment roll to be prepared.