When the boundaries of the existing drainage district are extended so as to embrace and include additional territory and land, said district shall have all the rights, powers, and privileges so far as said land is concerned as said district had of the lands originally embraced and included therein, and shall have full power to make and levy assessments thereon and to issue additional bonds, as is now provided by law for the formation and organization of drainage districts under the provisions of this chapter. When the boundaries of any existing drainage district are extended and additional lands and territory added thereto to be drained and improved, the several parcels of land of such drainage districts as were included within the limits of the district as originally organized and formed shall be liable to the district as already organized for assessments of benefits to be thereafter levied, if any benefits are received by them; and in like manner shall receive credit for any work done or improvements made or constructed by the district as already organized, which will benefit the land and territory added thereto in the manner herein provided.