In any year the General Assembly may appropriate to the Department of Revenue funds to provide homeowner tax relief grants to counties and local school districts. When funds are so appropriated, the General Appropriations Act shall specify the amount appropriated and the eligible assessed value of each qualified homestead in the state for the specified tax year. If for any reason the amount appropriated in the General Appropriations Act is insufficient to fund the eligible assessed value stated in the General Appropriations Act, the amount appropriated may be adjusted in amendments to the General Appropriations Act.