To enhance the economic viability of Concentrating solar power (CSP) plant, recent efforts have been directed towards employing high-temperature working fluid in the receiver and incorporating higher-efficiency power cycles. This work presents a techno-economic analysis of a sodium-chloride salt heat exchanger included in a sodium-driven CSP system with a supercritical CO2 power block. A quasi-steady state heat exchanger model was developed based on the TEMA guidelines, with the possibility of being customised in terms of media adopted, constraints, boundary conditions, and heat transfer correlations. The sodium-salt heat exchanger has been designed aiming at minimising the Levelized Cost of Electricity (LCOE) of the plant. The performance and the design of the proposed heat exchanger have been evaluated via multi-objective optimisation and sensitivity analyses. Results show that advanced CSP systems employing sodium and an indirect chloride salt storage can represent an economically viable solution and can drive towards the future goal of 5 USD/MWh. For a base-case 100 MWe plant with 12 h of storage, a LCOE of 72.7 USD/MWh and a capacity factor (CF) higher than 60% were reached. The techno-economic investigations showed the potential LCOE reduction of 6% as well as the flexibility and robustness of the heat exchanger model. The developed tool lays the groundwork to explore potential improvements of this new generation of CSP systems.