Should the city or town so altering or rearranging its boundary lines absorb or annex any part of another city or town, the city or town so altering or rearranging its boundary lines shall assume and pay the proportionate share of the bonded indebtedness of the city or town from which said territory is taken that the cost of the municipal improvements in such territory taken from such city or town bears to the whole cost of municipal improvements made in the whole of the city or town from which such territory is taken immediately before such annexation; provided, that this section shall apply only to that part of bonded indebtedness actually expended for municipal improvements.