Any property that was outside the corporate limits of the municipality at the time of contracting for an improvement, which is benefited by the improvement and is subsequently annexed to the municipality, may be assessed for the improvement subject to the same conditions and by the same procedure as provided in section 40-23-18. The property that is benefited may also be assessed for any improvement, within or outside the corporate limits, which is determined by the governing body and the special assessment commission to benefit property that was outside the corporate limits at the time of contracting for the improvement, whether or not an improvement district was previously created for the improvement. For this purpose, the governing body may create one or more improvement districts comprising all or part of the annexed territory. The governing body may provide for the levy of special assessments upon such property in the manner provided in this title, but may dispense with the requirements of this title as to the adoption of a resolution of necessity and the advertisement and award of a contract for the improvement. Assessment proceedings under this section are valid notwithstanding any failure of the previous proceedings to comply with the provisions of law regarding improvements to be financed by special assessments. The governing body may use a reasonable depreciation schedule for the improvement in determining the amount of any special assessment subsequently levied under this section.