The board may construct any project and acquire all property necessary therefor on such terms and conditions as it may deem advisable. When any part of the work is to be done or performed by any public body or by the United States jointly or in conjunction with the board, the portion of the cost thereof to be borne by the board may be turned over to the government of the United States or to any other public body to be expended by it in the acquisition, construction, or completion of the project.