The Department, in its discretion, may expend as provided herein upon such project as is mentioned in § 57-5-770, whether it be the immediate approach, bridge or highway immediately affected thereby or a water-controlling device, two thirds of the amount estimated as necessary to cross such waterway, creek or river without such water-controlling device. And the remainder of the cost of the entire project of the bridge or approach or both the water-controlling device and that part of the highway immediately affected thereby shall be borne by the county or municipality in which the project may be located and any other contributors, including the Federal Government, that may see fit to donate or appropriate money therefor.