§ 421-e. Exemption of cooperative, condominium, homesteading and rental projects from local taxation. The local legislative body of any city, town or village is hereby authorized and empowered to adopt and amend a local law to provide that any cooperative, condominium, homesteading or rental project which receives payments, grants or loans pursuant to article eighteen of the private housing finance law or any new construction project which receives payments, grants or loans pursuant to article nineteen of the private housing finance law shall be exempt from taxation as provided in such local law. Such local law may provide that such eligible property shall be exempt from all or any portion of the taxes imposed by a municipality, including those imposed by a school district, other than assessments for local improvements for a period not to exceed twenty years in the aggregate after the taxable status date immediately following the completion thereof, calculated not to exceed the following exemptions: twelve years of full exemption followed by two years of exemption from eighty percent of such taxation, followed by two years of exemption from sixty percent of such taxation, followed by two years of exemption from forty percent of such taxation, followed by two years of exemption from twenty percent of such taxation; provided that the tax exemption authorized by this section shall be in addition to any other tax exemption or abatement authorized by law, and provided further, however, that in the event a cooperative, condominium, homesteading or rental project ceases to be subject to one or more provisions of article eighteen of the private housing finance law pursuant to the provisions of paragraph (c) of subdivision six-a of section eleven hundred two of such law, any tax exemption authorized pursuant to this section with respect to the eligible property of such project shall terminate.