Section 63A. Whenever in any fiscal year a town, which term, as used in this section, shall include a city, shall sell any real estate, the board or officer executing the deed therefor in the name and behalf of the town shall, as a condition precedent to the power to deliver such deed, receive from the grantee as a payment in lieu of taxes allocable to the days ensuing in said fiscal year after the date of such deed, a sum which shall be equal to such portion of a pro forma tax computed as hereinafter provided as would be allocable to the days aforesaid if such pro forma tax were apportioned pro rata according to the number of days in such fiscal year; provided, however, that whenever the said real estate shall be sold between January second and June thirtieth of the fiscal year, the town shall also receive an additional amount equal to the entire pro forma tax computed as hereinafter provided and allocable as a payment in lieu of taxes for the next succeeding fiscal year. Such pro forma tax shall be computed by applying the town’s tax rate for the fiscal year of the sale, or, if such rate is not known, the town’s tax rate for the fiscal year next preceding that of the sale, to the sale price after crediting any exemption to which, if the deed had been executed and delivered on January first of such next preceding fiscal year, the grantee would have been entitled under section five of chapter fifty-nine. A recitation in the deed that there has been full compliance with the provisions of this section shall be conclusive evidence of such fact. Sums received under this section shall not be subject to section sixty-three of this chapter or to section forty-three of chapter sixty, but shall be credited as general funds of the town.