§ 414. Public housing, publicly assisted housing and limited-profit nursing homes. Real property owned by a municipal housing authority and "war demobilization emergency housing" shall be entitled to the exemption provided in the public housing law. Real property owned by a limited-profit housing company, a limited dividend housing company or a housing development fund company shall be entitled to the exemption provided in the private housing finance law, except as otherwise provided in section four hundred twenty-two of this chapter. Real property owned by a limited-profit nursing home company shall be entitled to the exemption provided in the public health law.