Upon a determination by the county mayor that a reappraisal program may not be completed timely whereby notices of reappraised values will be mailed to taxpayers prior to July 1 of the tax year scheduled for completion, the county mayor shall notify in writing the executive secretary to the state board of equalization of the possibility that the program may not be completed timely and the reasons therefor, no later than the preceding December 1. The state board of equalization shall then evaluate the program to determine whether an extension of time to complete the reappraisal program is justified, and shall notify the county mayor accordingly. Unless the board has given notice to the county mayor no later than February 1 of the tax year scheduled for completion that the program is to be completed and the reappraised values used for that tax year, the county governing body may act to extend the reappraisal until the next tax year; provided, that all values will be updated to January 1 next following, with all costs of such updating being borne directly and exclusively by the county and cities, if the reappraisal program is conducted by the county, the state of Tennessee, if the reappraisal program is conducted by the state, or in accordance with a binding agreement between the county and the private contractor, if the reappraisal program has been contracted to a nongovernment entity.