Whenever the board shall provide that a levy to meet extraordinary maintenance expenditures shall be spread over a term of years and warrants or bonds issued as provided in RCW 85.16.030, said board shall fix a date for and hold a hearing and appoint appraisers as provided in RCW 85.16.060 and 85.16.080. Said appraisers, in addition to discharging the duties imposed upon the appraisers by RCW 85.16.060, 85.16.080 and 85.16.090, shall: (1) Apportion the estimated costs of such extraordinary maintenance work to the properties within the district in proportion to the benefits accruing to said properties from the maintenance of the district's system of improvements as determined by them; and (2) file a complete schedule of said apportionment of costs with the board.