The board of directors to whom a petition to include land within the district is presented may require, as a condition precedent to the granting of the petition, that the petitioners shall severally pay to the district such prospective sums to be determined by the board, as nearly as the same can be estimated, as the petitioners or their grantors would have been required to pay to the district, as assessments, had the lands been included in the district at the time the district was originally formed.
SDCL 46A-4-59