Each person, firm, or corporation engaged in the operation of a veneer mill, planing mill, box factory, handle factory or any other factory where lumber or timber is sawed or made into a finished or semifinished product, other than a sawmill licensed under Section 40-12-154, shall pay a privilege tax based on the number of men employed or engaged in the manufacture of the products produced by such mills, as follows: Where there are five or less men employed or so engaged, $5; where there are more than five men and less than 10 so employed or engaged, $10; where there are 10 men and less than 20 so employed or engaged, $30; where there are 20 men and less than 40 so employed or engaged, $80; and where there are 40 men and over, $120. It is the intention hereof that where a person, firm, or corporation shall pay a privilege tax under Section 40-12-154 or under Section 40-12-121, then no privilege license tax shall be charged or collected hereunder.