1. A computation apparatus for computing an exchange rate used in exchanging one or more shop points into one or more common points, the shop points being issued for each shop and usable for payment to the shop, and the common points being usable for payment common to each shop, the computation apparatus comprising: a shop point storage unit that stores, in association with each shop, a used house point (UHP) and an active general point (AGP), the used house point (UHP) representing a portion of shop points issued by the shop and has been already used for payment to the shop, and the active general point (AGP) representing a portion of common points that is exchanged from shop points issued by the shop and has not been yet used for payment to any shop; a function storage unit that stores, for each shop, a function for an exchange rate that a) when the used house point (UHP) of the shop is larger, computes an exchange rate with which shop points of the shop are exchanged into a larger number of common points, and b) when the active general point (AGP) of the shop is larger, computes an exchange rate with which shop points of the shop are exchanged into a smaller number of common points; and an exchange rate computation unit that, for each shop, computes an exchange rate, based on the used house point (UHP) and the active general point (AGP) of the shop stored in the shop point storage unit and by using the function of the shop stored in the function storage unit.