The board shall prepare an annual budget designating the proposed expenditures for operation of the area hospital and payment of bonded indebtedness, and the amount to be raised by taxation, following the requirements of chapter 24. The board shall prorate the amount to be raised for operations by local taxation among the respective political subdivisions forming a part of the merged area in the proportion that the product of the value of taxable property and the maximum tax levy rate in each political subdivision bears to the total product of the value of taxable property and the maximum tax levy rate in the entire merged area, as set out in the published order of merger. The board of hospital trustees shall certify the amount so determined to the respective levying officials of the affected counties, and the officials shall levy a tax sufficient to raise the annual budget. Taxes collected pursuant to the levy shall be paid by the respective county treasurers to the treasurer of the area hospital in the same manner that school taxes are paid to local school districts.