(a) A license year shall begin on the first day of July of each calendar year and shall expire with the expiration of the next ensuing thirtieth day of June, and licenses shall expire at midnight on the last day of June subsequent to the date of issuance and shall be renewable annually, except such licenses for which the tax or fee is by the day, week, month or other period less than a year, and except as may be provided otherwise by this Code or other ordinance.
(b) The license tax or fee for an initial license upon the commencement of business shall be in proportion to the duration of such license to the annual tax or fee; provided that no license for any purpose for any length of time shall be issued for less than two dollars.