Small Public Housing Agency Opportunity Act of 2016 This bill amends the United States Housing Act of 1937 to subject a small public housing agency (PHA) to the same requirements as a PHA. A small PHA is a PHA for which the sum of the number of public housing dwelling units and the number of vouchers under Section 8 (tenant-based assistance) it administers is 550 or fewer. The Department of Housing and Urban Development (HUD) shall: carry out physical inspections of a small PHA public housing project at least once every three years, unless it is a troubled small PHA; determine the financial condition of a small PHA public housing program solely on the basis of the ratio of current assets to current liabilities; and determine management condition of a small PHA public housing program solely on the basis of the ratio of vacant unit months to eligible unit months. A small PHA administering Section 8 tenant-based assistance under the housing voucher program must make physical inspections of assisted units at least once every three years. HUD shall evaluate the management of a small PHA's voucher program solely on the basis of its lease-up rate or the budget utilization rate, which must be at least 90% to be acceptable. HUD shall designate a small PHA as a high-performing agency if it exceeds acceptability criteria. HUD may designate a small PHA as a troubled small PHA with respect to its public housing program or housing voucher program only if it meets certain negative criteria. HUD shall establish an appeals process for a small PHA to dispute a determination of deficiency. HUD and a troubled small PHA shall enter into a one-year corrective action agreement (renewable at HUD option) under which the small PHA must undertake actions to correct deficiencies. The bill prescribes and/or revises requirements to reduce the administrative burden on small PHAs with respect to: certain reports; community service; economic opportunities for low- and very low-income persons; exemption of a small PHA administering not more than 400 public housing dwelling units, upon request, from any asset management requirement; exemption from environmental review for a development or modernization project involving new construction if the new construction portion of the total cost does not exceed $100,000; and streamlined HUD procedures for such reviews. Small PHAs shall also be exempt from Green Physical Needs Assessment requirements for any fiscal year for which a specified circumstance occurs. HUD shall carry out a demonstration project to examine how various methods of determining rent in public housing affect the administrative burden on small PHAs and public housing residents. The bill establishes rent-setting mechanisms for demonstration project participants based on: (1) a tiered system for initial rents for extremely low-income families, very low-income families, and low-income families; (2) a certain range of gross income percentages; or (3) the existing method for establishing rents. A small PHA may elect to be paid for its utility and waste management costs under a HUD assistance formula for a period, at its discretion, of up to 20 years based on its average annual consumption during the three-year period preceding the year in which the election is made. HUD shall develop and deploy all electronic information systems necessary to accommodate full consolidated reporting by PHAs electing to operate in consortia.