Thermoeconomics is defined as the integration of thermodynamics with economics of thermal systems. In this paper, we discuss the thermoeconomics of heat exchanger units in a power plant for cost based optimal design conditions. In this regard, unit cost parameters of hot and cold end heat exchangers in distributing the heat transfer surface area of the power plant are considered for minimum total cost of the heat exchangers. A closed form expression is given in terms of unit costs of the conductances of both heat exchangers, and the results are presented in terms of a unit cost ratio, G, and the hot and cold end heat exchangers costs. The results demonstrate a strong dependence of the total cost function on the absolute temperature ratios as well as the hot to cold end conductance cost ratio. It is also shown that for the case of equal unit costs of the hot and cold end heat exchangers, the total conductance is equally divided between the two heat exchangers.