All property and rights acquired by a city or town outside its boundaries, as provided in N.H. Rev. Stat. § 423:1-4, inclusive, or as provided in any other statute relative to aeronautical facilities hereinbefore or hereinafter enacted, if said property and rights are not leased for profit, shall be exempt from taxation therein; but the city or town shall make payments, on or before December 1 in each year, to each city or town in which such property or rights are located, of such sums as would have been assessed against said property and rights if the same had been included in the tax invoice for such year at the tax valuation of the same on April 1, 1940; provided that in case improvements have been made on said property between April 1, 1940, and the date when acquired for aeronautical facilities, the payments to the city or town in which such property or rights are located shall be based upon the assessed value as of April 1 following such improvements.