The board may construct any project, and may acquire all property necessary therefor, on any 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 the United States jointly or in conjunction with the board, the portion of the cost of the project 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.