A drainage district may contract with any city, town or village to furnish an outlet for the drainage of such city, town or village, through any ditch, drain or watercourse constructed, or to be constructed by the drainage district, for such compensation to be paid by such city, town or village as may be agreed upon, which compensation shall inure to the benefit of such drainage district, either in improving its ditches, or in diminishing the original cost thereof, or in retiring bonds of the district, or in such way as the county commission shall determine to be just and fair; and thereafter said city, town or village, and the inhabitants thereof, shall have and enjoy all the rights of said drainage that other property owners may have and enjoy.