assessment for drainage costs.] If any district shall contract with the United States for the construction of drainage works, it shall be within the powers and the duties of the board of directors on or before September 1 next preceding the initial payment for such works under contract with the United States to fix and determine the rate or percentage of the benefits from the proposed works for all real property within the district to be affected by said works, subject to judicial confirmation as provided by Section 53 [73-11-6 N.M. Stat. Ann.] of this act. The board shall also assess the damages inflicted upon any real property by the works of the district and such amount shall be deducted from the assessments payable by each owner of lands damaged until compensation for the damages shall have been fully made. If the damage shall be found to exceed the benefits as regards any parcel of real property or any easement, a cash award of the difference shall be made. The said rate of benefits shall be subsequently used as the basis for the annual assessment, but such rate may be changed from time to time by the board of directors as new or changing conditions may, in their judgment, require, subject to judicial confirmation as aforesaid. Irrigation districts, as regards drainage costs, may assess realty within the district boundaries owned by all such classes of persons and corporations, to the same extent as now permitted by the laws of this state to drainage districts.