Improvement districts also may be formed of land proposed to be annexed to the district, contingent upon the annexation being completed. The petition for annexation may request that the land to be annexed shall be included in and form a part of any improvement district existing within the district or shall constitute a new improvement district within the district when annexed or the board of directors of the district may determine, as one of the terms and conditions for the annexation, that the land shall be included in and form a part of any improvement district then existing within the district or shall constitute a new improvement district when annexed.