For the property it is entitled to tax, a city or town situated in a single county shall accept and adopt the appraisals and assessments fixed by the authorities of that county as modified by the Department of Revenue under the provisions of this Subchapter. However, the requirement of this section shall not be construed to modify the appraisal and assessment authority given cities and towns with respect to discovered property by N.C. Gen. Stat. § 105-312 (1939, c. 310, s. 1201; 1971, c. 806, s. 1; 1973, c. 476, s. 193.)