The integration of a Concentrating Solar Power (CSP) plant with a Multi-Effect Distillation (MED) plant has shown a significate potential in countries with high solar irradiation and few freshwater resources. Nevertheless, the performance of these schemes is affected by the variations in ambient conditions and operation modes. This study presents an exergy and exergetic cost analysis of a CSP-Rankine Cycle coupled with a MED plant model, considering time-varying conditions. The plant performance is evaluated through the exergetic efficiency while the irreversibilities of each plant component are identified for the nominal and partial load operation. Also, electricity and freshwater exergetic costs are determined. Then, a parametric analysis varying the molten salt flow rate and the ambient temperature is carried out to study their effects on the plant performance, whilst a simulation of a typical day is performed to analyze two different operational modes. A comparison analysis with a stand-alone CSP-Rankine Cycle operation is implemented to identify differences in the exergetic efficiency and product costs. Results showed that MED plant integration increases the exergy destruction and waste exergy in comparison to a stand-alone CSP-Rankine Cycle. Also, it was obtained that the unitary exergetic cost of electricity is highly influenced by the power output, while the unitary exergetic cost of water is more dependent on the ambient temperature. These results allow exploring the distribution of exergy destructions in the CSP-Rankine Cycle coupled with a MED plant under different operating conditions to determine the best operation modes.