Notwithstanding any change in the boundaries of a state-aided district or the annexation to, or the inclusion in, another district of a state-aided district, the state-aided district as it existed immediately prior to the effective date of the action shall be continued in existence for the determination of the assessed valuation of the property therein and for the purposes of the computations provided by Sections 16070, 16072, 16074, 16075 and 16084; and all the computations required to be made pursuant to those sections shall be made exactly as if there had been no such change of boundaries, annexation, or inclusion, except as otherwise provided in Sections 16163 and 16164. However, that if a state-aided district shall be included entirely in another school district which subsequently becomes state aided, then the unpaid balances of the apportionments made to the original district shall be added to the balances of the apportionments made to the newly aided district. In those cases, no further computations as aforesaid, or repayments, shall be made with respect to the original district, but the computations and repayments shall thenceforth be based solely upon the territory and assessed valuation of the newly aided district, in the manner provided by Sections 16070, 16072, 16074, 16075 and 16084.