When a refund is granted under the provisions of sections 283.09 to 283.11 the county auditor shall reinstate such portion of the tax on the land as the value of the land without any improvements bears to the full value of the erroneous assessment. The reinstated tax shall be placed upon the current tax lists in the office of the county treasurer and, if not paid prior to the first Monday in January of the following year, shall be subject to judgment with the delinquent taxes for the current or other years.