Prior to the acquisition of an improvement or commencement of the construction of an improvement described in the ordinance organizing the central business improvement district or upon completion of the improvements, at the discretion of the board of assessment commissioners, the board of assessment commissioners shall apportion the totality of all costs of such improvement district upon the various properties located within the district in accordance with the benefits to each property upon the completion of the work by such improvements conferred. If the board of assessment commissioners determines that certain improvements benefit only certain properties within a district, the board may apportion the costs of the improvements upon the various properties that benefit from the improvements.