In order to understand the relationship between capital costs and the cost rate of exergy destruction in the heat exchangers of a combined cycle power plant (CCPP), the economic optimum design of a heat exchanger considered as a single component is explored. Expressions for time rates of profit are written using specific exergy revenues and costs. These expressions are non-dimensionalized, and their derivatives are taken to find the optimum heat exchanger effectiveness. This optimum is shown to be a function of several dimensionless groups. Three of the variables contained within these groups are both of the stream entrance temperatures and the reference temperature. Results of numeric optimization of heat exchangers confirm the validity of the dimensionless groups.