When specific provision is made anywhere by ordinance for the division of a license for less than the full annual license fee or for the issuance of a license for a part or portion of a license year upon the payment of a proportionate amount of the annual license fee, the amount to be so paid for such license shall be computed from the first day of the period during which such license is issued, if the license year be divided into periods, or if provisions be made for monthly periods, it shall be computed as running from the first day of the month in which such license is issued; provided, that no person shall be entitled to the benefit of the provisions of this section who has engaged without a license so to do in the business for which he applies for license at the time of such application. (R.O. 1959, Ch. 24, Art. 1, Sec. 15)