Each acute hospital shall pay to the commonwealth an amount for the estimated expenses of the division and of the health safety net office, established by section 35. This amount shall be equal to the amount appropriated by the general court for the expenses of the division of health care finance and policy and of the health safety net office minus amounts collected from (1) filing fees, (2) fees and charges generated by the division's publication or dissemination of reports and information, (3) federal matching revenues received for these expenses or received retroactively for expenses of predecessor agencies. Each acute hospital shall pay such net amount multiplied by the ratio of the hospital's gross patient service revenues to the total of all such hospital's gross patient services revenues. Each acute hospital shall make a preliminary payment to the division on October first of each year in an amount equal to one-half of the previous year's total assessment. Thereafter, each hospital shall pay, within thirty days notice from the division, the balance of the total assessment for the current year based upon its most current projected gross patient service revenue. The division shall subsequently adjust the assessment for any variation in actual and estimated expenses of the division of health care finance and policy and for changes in hospital gross patient service revenue. Such estimated and actual expenses shall include an amount equal to the cost of fringe benefits, as established by the division of administration pursuant to section six B of chapter twenty-nine. In the event of late payment by any such hospital, the treasurer shall advance the amount of due and unpaid funds to the division prior to the receipt of such monies in anticipation of such revenues up to the amount authorized in the then current budget attributable to such assessments, and the division shall reimburse the treasurer for such advances upon receipt of such revenues. The provisions of this paragraph shall not apply to any state institution or to any acute hospital which is operated by a city or town.