(b) Where a municipality acts on behalf of another taxing jurisdiction in assessing real property for the purpose of taxation, or in levying taxes therefor, the consent of the local legislative body of such municipality shall have the effect of exempting the real property in a project from local and municipal taxes, other than assessments for local improvements, levied by or in behalf of both such taxing jurisdictions. As used in this paragraph, the term "taxing jurisdiction" means any municipal corporation or district corporation, including any school district or any special district, having the power to levy or collect taxes and benefit assessments upon real property, or in whose behalf such taxes or benefit assessments may be levied or collected.

(c) Notwithstanding the provisions of paragraphs (a) and (b) of this subdivision, the real property of a state urban development corporation project acquired, owned, constructed, managed or operated by a company incorporated pursuant to the not-for-profit corporation law and this article shall be entitled to all the benefits provided by section four hundred twenty-two of the real property tax law. The real property of a state urban development corporation project, other than a state urban development corporation project acquired, owned, constructed, managed or operated by a company incorporated pursuant to the not-for-profit corporation law and this article, shall be exempt from all local and municipal taxes, other than assessments for local improvements, to the extent of the value of the property included in such project as represents an increase over the assessed valuation of the real property, both land and improvements, acquired for the project on the date of its acquisition by the limited-profit housing company, provided that the amount of such taxes to be paid shall not be less than ten per centum of the annual shelter rent or carrying charges of such project, as defined in paragraph (a) hereof. The tax exemption shall operate and continue so long as the mortgage loans of such limited profit housing company, including any additional mortgage loan the proceeds of which are used primarily for the residential portion of the project, which additional loan is approved by the commissioner or the supervising agency, are outstanding and the project is continued to be operated as a limited-profit housing project. If a state urban development corporation project qualifying for tax exemption pursuant to this paragraph is sold, with the approval of the commissioner, to another limited-profit housing company, such successor company shall be entitled to all the benefits of this paragraph. In the event that such sale is to a company incorporated pursuant to the not-for-profit corporation law and this article, such successor company shall be entitled to all the benefits provided by section four hundred twenty-two of the real property tax law.

(d) Notwithstanding the provisions of paragraphs (a) and (b) of this subdivision, when a project is financed with a mortgage loan pursuant to this article or article three of this chapter and (i) there is a participation, new loan or investment pursuant to section twenty-three-b of this article or (ii) such mortgage loan is assigned, modified or satisfied pursuant to section twenty-three-a or forty-four-b or subdivision twenty-two-a of section six hundred fifty-four of this chapter, the real property of the project shall be exempt from all local and municipal taxes, other than assessments for local improvements, to the extent of the value of the real property included in such project which represents an increase over the assessed valuation of the real property, both land and improvements, acquired for the project on the date of its original acquisition for the project by the original mortgagor under a mortgage loan pursuant to this article or article three of this chapter, provided that the amount of taxes to be paid on the project shall not be less than ten per centum of the annual shelter rent or carrying charges of such project, as defined in paragraph (a) of this subdivision. Such tax exemption shall commence in each instance from the date when the project becomes subject to a mortgage insured by the federal government and shall operate and continue so long as a mortgage on such project is insured or held by the federal government or so long as the project is thereafter owned by the federal government or so long as any residual indebtedness is outstanding, whichever is longer. When there is a participation, new loan or investment pursuant to section twenty-three-b of this article, such participation, new loan or investment shall be deemed to be the equivalent of a federally insured mortgage for purposes of this paragraph. Nothing contained in this paragraph shall be construed to limit or otherwise impair the benefits available to any company eligible for exemption from taxation pursuant to section thirty-one or section thirty-six-a of this article, section four hundred twenty-two or section four hundred sixty-seven-c of the real property tax law, or section fifty-eight of the public housing law. The foregoing shall not be deemed to authorize any company to receive the benefits of any exemption from taxation in contravention of the provisions of section two of article eighteen of the constitution.

(e) Notwithstanding the provisions of paragraph (a) of this subdivision, a municipality, with the approval of the local legislative body, may contract to exclude all or part of any rent subsidies received from the federal government pursuant to section eight of the United States Housing Act of nineteen hundred thirty-seven as amended in the computation of total rents received.

(f) Notwithstanding the provisions of paragraph (a) of this subdivision, if the number of units occupied by persons receiving the benefit of rental assistance payments from the federal government pursuant to section eight of the United States Housing Act of nineteen hundred thirty-seven, as amended, with respect to any project increases by more than one hundred percent within any twelve consecutive months prior to nineteen hundred eighty-five over the number of units for which such subsidies were available during the preceding twelve consecutive months or as July first, nineteen hundred eighty, whichever is later, taxes payable for such additional subsidized units and subsequent units subsidized in the same manner shall be based solely upon that portion of total rents received on account of such additional subsidized units that is not funded by such rental assistance payments, provided, however, that no project shall receive such additional tax exemption (i) unless a minimum of seventeen percent of the units in the project receive the benefit of such subsidies, or (ii) if any mortgage on such project is insured or held by the federal government or if the project is owned by the federal government. The amount of exemption to which a project is entitled pursuant to this paragraph shall be certified annually by the commissioner or the supervising agency, as the case may be. 2. Notwithstanding the provisions of subdivision one hereof, whenever a dwelling in a project is leased to the New York state housing finance agency pursuant to the provisions of section forty-four-a of this chapter, so much of the assessed value of such project attributable to such dwelling (including a pro rata portion of the value of the land and common spaces) as represents an increase over the proportionate assessed value of the real property, both land and improvements, acquired for such project at the time of original acquisition therefor, shall be exempt during the period of such lease from taxation for county, city, town, village and school district purposes and special ad valorem levies; provided that if in any year the aggregate amount of such taxes and levies that would have been attributable to such dwelling but for the exemption provided by this subdivision exceeds the amount payable out of the low rent lease account pursuant to subdivision three of section forty-four-a of this chapter with respect to the agency's rent obligation for such dwelling, the agency shall make proportional payments in lieu of such taxes and levies to the appropriate county, city, town, village, school district or special district, or any combination thereof as the case may be, in an aggregate amount equal to one half of the sum of (a) the amount of such excess and (b) the amount, if any, by which the rent paid to the agency under the sublease for such dwelling exceeds the agency's rent obligation for such dwelling. Nothing contained in this subdivision shall preclude the increase of the taxable assessed value attributable to such dwellings as a result of a net increase in the assessed valuation of the taxable property in the assessing unit as a result of assessing such property at a higher ratio of full value. 3. Notwithstanding the provisions of subdivision one hereof, whenever a dwelling in a project is leased to an authority, pursuant to the provisions of sections seventeen and thirty-one of this chapter, so much of the assessed value of such project attributable to such dwelling (including a pro rata portion of the value of the land and common spaces) as represents an increase over the proportionate assessed value of the real property, both land and improvements, acquired for such project at the time of original acquisition therefor, shall be exempt during the period of such lease from taxation for county, city, town, village and school district purposes and special ad valorem levies. Nothing contained in this subdivision shall preclude the increase of the taxable assessed value attributable to such dwelling as a result of a net increase in the assessed valuation of the taxable property in the assessing unit as a result of assessing such property at a higher ratio of full value. 4. Notwithstanding the provisions of subdivision one hereof, when a mutual company is organized under this article to facilitate the acquisition of a building by residents thereof, the amount of local and municipal taxes, other than assessments for local improvements, to be paid on the real property included in such project, both land and improvements, shall not exceed twenty per centum of the annual shelter rent or carrying charges of such project, as defined in paragraph (a) of subdivision one hereof; provided, however, that where such acquisition of a building by residents thereof involves the financing of rehabilitation or other improvement as well as acquisition, upon the consent of the local legislative body of the municipality in which the project is located the amount of such taxes may be further reduced provided that such amount shall not be less than ten per centum of the annual shelter rent or carrying charges of the project, as defined in paragraph (a) of subdivision one hereof; or the company may in lieu of requesting such consent apply for the benefits of the local law, if any, enacted pursuant to section four hundred eighty-nine of the real property tax law. Such tax exemption, if any, granted pursuant to this article shall operate and continue so long as a loan made under this article or any subsequent loan approved by the commissioner or the supervising agency to enhance the residential portion of the project and the project is continued to be operated for the purposes set forth in this article is outstanding. 5. Bonds, mortgages, notes, income debentures and obligations of a company are declared to be issued for a public purpose and to be public instrumentalities and together with interest thereon shall be exempt from tax including but not limited to the mortgage recording taxes imposed by article eleven of the tax law. 6. Any project that received a tax exemption under paragraphs (a), (c) and (d) of subdivision one, and subdivision four of this section may, upon the expiration of the tax exemption period, be granted an additional tax exemption period of up to fifty years, or until such time as the project is no longer operated under the restrictions and for the purposes set forth in this article, whichever is sooner.