An optimum design condition for a basic refrigeration cycle is defined as the condition which minimizes the total cost of heat exchanges (condenser and evaporator) and compressor for the refrigeration effect. Thermodynamic properties of ammonia (R717) are approximated by rational functions in order to obtain the optimum condition for a basic refrigeration cycle. Optimum condition depends on the heat capacity rates (mass flow rate times specific heat) of cooling water and brine used in condenser and evaporator. The difference between the cooling water temperature and condensation temperature at the optimum condition increases as the heat capacity rates and the coat of heat exchangers relative to the cost of compressor increase. Numerical examples of optimum conditions are obtained when the condensation temperature is $30^{circ}C$ and the evaporator temperature is $-10^{circ}C$.