The jointly contracting municipalities may at any time after the execution of the joint contract, contract with any municipality through whose territory such improvements or works are to pass or be constructed, or with any other municipality, for the privilege of connecting its or their sewers and drains with such joint improvements or works, and for the participation in the use and cost of construction of such joint improvements or works, upon such terms, and for such consideration and length of time as may be mutually agreed upon by all the parties. Such contract shall state all the terms thereof including the share of the cost to be borne by, and the quantity of sewage per diem entitled to be discharged by such other municipality.