If the owner of any bridge and the Secretary shall agree that in order to remove an obstruction to navigation, or for any other purpose, a relocation of such bridge or the construction of a new bridge upon a new location would be preferable to an alteration of the existing bridge, such relocation or new construction may be carried out at such new site and upon such terms as may be acceptable to the bridge owner and the Secretary, and the cost of such relocation or new construction, including also any expense of changes in and additions to rights-of-way, stations, tracks, spurs, sidings, switches, signals, and other railroad facilities and property, and relocation of shippers required for railroad connection with the bridge at the new site, shall be apportioned as between the bridge owner and the United States in the manner which is provided for in section 516 of this title in the case of an alteration and the share of the United States paid from the appropriation authorized in section 518 of this title: Provided, That nothing in this section shall be construed as requiring the United States to pay any part of the expense of building any bridge across a navigable stream which the Secretary of the department in which the Coast Guard is operating shall not find to be, in fact, a relocation of an existing bridge.