There shall be an exemption in every case of twelve dollars ($12.00) in the amount of tax computed under the provisions of this article. A person exercising a privilege taxable hereunder for a fractional part of a tax year shall be entitled to an exemption of the sum bearing the proportion to twelve dollars ($12.00) that the period of time the privilege is exercised bears to a whole year. Only one exemption shall be allowed to any one person, whether he exercises one or more privileges taxable hereunder. There shall be no exemption if the taxpayer fails to make timely payment of taxes within sixty days of the close of the tax period.