Thermoeconomics is defined as attaching monetary values to heat exchanger conductances of a given plant. In this study, optimum allocation of heat transfer inventory for heat exchangers in a refrigeration system with specified power input or cooling capacity, and for a heat pump with specified heating capacity is investigated. The ratio of hot- to cold-end conductance unit cost ratio, G, was considered in the analysis as an additional parameter of considerable importance to the designer. A closed-form expression is given in terms of unit cost of conductances of both the heat exchangers. The results show a strong dependence of the total cost on the absolute temperature ratios as well as the hot- to the cold-end conductance cost ratio. It is demonstrated in the illustrative example that for G=0.1, the conductance of the hot-end heat exchanger is about three times the cold-end heat exchanger.