The board of directors may require as a condition precedent to the granting of the petition that the petitioners shall severally pay to the district such respective sums, as nearly as the same can be estimated by the board, as the petitioner or petitioners, or his or their grantor or grantors, would have been required to pay to such district as assessment for the payment of his or their pro rata of all bonds and the interest thereon which prior thereto may have been issued by said district, or his or their pro rata share of the cost of construction under any contract between the district and the United States, accompanying which bonds of the district have not been deposited with the United States, as in this act N.M. Stat. Ann. § 73-8-1 to 73-8-60 provided, had such lands been included in such district at the time the same was originally formed, or when such bonds were so issued or when such contract with the United States was made.