If any such ditch or drain shall be located through or across the right-of-way or other land of a railroad company, the board shall determine the cost of constructing the same and the railroad company shall have the privilege of constructing such improvement through its property in accordance with the specifications made by the board and recover the costs thereof as fixed by the board. Such railroad company before it may exercise such privilege shall file its election to that effect with the auditor within five days after the decision of the board is filed.