This paper presents an analysis of the general cost associated with single- and double-effect vapour absorption and vapour compression air-conditioning systems. The cost analysis covers the initial costs and the operating costs of each of the three systems. The vapour absorption system considered in this paper is based on water as the refrigerant and lithium bromide solution as the absorbent. The analysis is undertaken to help select an air-conditioning system that fulfils a 250 TOR cooling load of a five-floor student hospital in Alexandria, Egypt. The typical meteorological year database for Alexandria was used to estimate the cooling load for the building. The analysis is based on two different methods, the present worth value (PWC) and the equivalent annual cost (EAC), for initial and operating costs of each system. The selection depends on which system requires the minimum life-cycle cost (LCC) and can perform the intended function for its life span. The analysis also considers the interrelationship between economic and thermodynamic aspects, such as the dependence of operating cost on the surrounding climatic conditions. The method used and the results from this study offer useful guidelines for researchers and decision-makers when selecting an air-conditioning system. The results show that the double-effect vapour absorption system is the preferred option for its minimum present worth value as well as the equivalent annual cost.