Any municipality upon resolution adopted by at least a four fifths vote of its governing body may petition the board for annexation to the district of the area then comprising the municipality, or any part thereof and, if accepted by the board, such area shall be deemed annexed to the district and subject to the jurisdiction of the board under the terms and provisions of sections 458D.01 to 458D.24. The territory so annexed shall be subject to taxation and assessment pursuant to the provisions of sections 458D.01 to 458D.24 and shall be subject to taxation by the board like other property in the district for the payment of principal and interest thereafter becoming due on general obligations of the board, whether authorized or issued before or after such annexation. The board may in its discretion condition approval of the annexation upon the contribution, by or on behalf of the municipality petitioning for annexation, to the board of such amount as may be agreed upon as being a reasonable estimate of the proportionate share, properly allocable to the municipality, of costs of acquisition, betterment and debt service previously allocated to local government units in the district, on such terms as may be agreed upon. For the purpose of paying this contribution, the municipality petitioning annexation may exercise the powers conferred in sections 458D.11 and 458D.12. When such contributions are made by the municipality to the board, they shall be applied in reduction of the total amount of costs thereafter allocated to all other local government units in the district, on such equitable basis as the board deems to be in the best interests of the district, applying so far as practicable and appropriate the criteria set forth in section 458D.09, subdivision 2. Upon annexation of such territory, the secretary of the board shall certify to the auditor and treasurer of the county in which the municipality is located the fact of such annexation and a legal description of the territory annexed.