This paper presents new methods for targeting the minimum capital costs of mass exchange networks. Three cases are considered: a single mass separating agent (MSA), non-overlapping MSAs, and overlapping MSAs. New graphical tools, the y-x composite curve plot and the y-y* composite curve plot, have been introduced for this purpose and these allow the minimum exchanger sizes to be predicted before any design. The new capital cost targets can be traded off against the established operating cost targets by varying the minimum composition difference, in order to optimize the total annual cost (supertargeting). A design technique has been developed which allows the targets to be closely approached. The new targeting and design techniques have been extended to a wide range of Mass Exchange Network Synthesis (MENS) problems which will be considered in Part II of this paper.