Every license issued under this chapter, except as herein otherwise expressly provided, shall be for 12 months, shall expire on June 30 next succeeding the date of issue, and shall be for the full amount of the tax prescribed; provided, that if the licensee begins such business or exercises such privilege after the expiration of seven months of the current fiscal year of the city, then such licensee shall be required to pay one-half of the tax prescribed for 12 months.