In this article, by using exergoeconomic approach, an economic evaluation of reverse Brayton cycle-based refrigerator has been performed for 10 kW range cooling capacity at 65 K. One of the typical application domains of this refrigerator at the considered heat load is cooling of high-temperature superconductor for future power transmission lines that are in the developmental phase in different parts of the world. Multi-objective optimization and sensitivity analysis have been performed to investigate the sources of cost attached to the exergy destruction. Based on exergoeconomic evaluation parameters, recommendations have been provided for deciding the cost-effective design parameters for refrigerators. The significant finding of this analysis is that, for the basic reverse Brayton cryocooler, component performance, the turbine being the major one, needs to be improved to meet the economic criteria of 25 $/W as enumerated in the cryogenic road map for high-temperature superconductor cooling. The exergoeconomic design applied on the reverse Brayton refrigerator for high-temperature superconductor cables cooling can be adapted for other applications such as recondensation and liquefied natural gas cold energy utilization.