Whenever the commission makes any special assessment, the commission shall determine the particular lots and parcels of land which, in the opinion of the commission, will be especially benefited by the construction of the work for which the assessment is to be made. The commission shall determine the amount in which each of the lots and parcels of land will be especially benefited by the construction of the work for which such special assessment is to be made, and shall assess against each of such lots and parcels of land such sum, not exceeding the benefits, as is necessary to pay its just proportion of the total cost of such work, or of the part thereof which is to be paid by special assessment, including all expenses incurred in making such assessment and publishing necessary notices with reference thereto and the per diem of the commission. However, as an alternative to the procedure provided in this section, the special assessment commission may, in its discretion, determine and allocate the cost of special assessments in accordance with the method provided for in chapter 40-23.1. Property owned by a nonprofit entity and used exclusively as a cemetery is exempt from collection of special assessments for benefits conferred under this title and the city in which such property is located shall provide for the payment of special assessments, installments, and interest against such property by the levy of taxes according to law or by payment from other funds available to the city which are derived from sources other than special assessments. Benefited property belonging to counties, cities, school districts, park districts, and townships is not exempt from such assessment, and such public corporations whose property is so assessed shall provide for the payment of such assessments, installments thereof and interest thereon, by the levy of taxes according to law. Nothing in this section may be deemed to amend other provisions of law with reference to the levy of assessments on property sold for delinquent taxes.