When one portion of a county is annexed to another county, the county to which it is annexed shall levy a special tax upon all property in such annexed area to cover the cost of survey and transfer or so much thereof as the governing body of the county to which the annexation or addition is made shall deem just and proper, and such governing body may levy upon the property within the original lines of their county such tax as in their judgment shall seem just and fair to augment the amount raised by taxation within the annexed area to reimburse and refund those who made the deposit as provided in § 4-5-120 for the cost of annexation.