If the authorities in charge of any street, highway or road, on which there is a bridge or crossing to be removed by the canal and banking company as provided by section 13:12-19 of this title, shall prefer to relocate or otherwise readjust such crossing in a manner and to an extent different from that provided in said section 13:12-19, the canal and banking company, instead and in lieu of constructing any such crossing as required by said section 13:12-19, is authorized to contract with such authorities for the construction, by such authorities, of any such relocated or readjusted crossing, and, in such contract, to agree with such authorities for the payment by the canal company of such portion of the cost of such relocated or readjusted crossing as shall not exceed the estimated cost of the crossing instead of which such relocated or readjusted crossing shall be so contracted for.