This paper applies the Exergy Cost Theory (ECT) to a hybrid system based on a 500 kWe solid oxide fuel cell (SOFC) stack and on a vapor-absorption refrigeration (VAR) system. To achieve this, a model comprised of chemical, electrochemical, thermodynamic, and thermoeconomic equations is developed using the software, Engineering Equation Solver (EES). The model is validated against previous works. This approach enables the unit exergy costs (electricity, cooling, and residues) to be computed by a productive structure defined by components, resources, products, and residues. Most importantly, it allows us to know the contribution of the environment and of the residues to the unit exergy cost of the product of the components. Finally, the simulation of different scenarios makes it possible to analyze the impact of stack current density, fuel use, temperature across the stack, and anode gas recirculation on the unit exergy costs of electrical power, cooling, and residues.