One option to reduce the energy consumption to produce domestic hot water is to replace the electrical heaters by direct expansion solar assisted heat pumps. Although, there are many studies on the performance of this system, there are few studies on economic analysis of the equipment. In this paper, an economic analysis comparing the payback of heat pump over an electrical heater is carried out. The heat pump is modeled using lumped models for heat exchangers and a black box model for the compressor. The results show that the augment of collector size increases the COP, but it decreases the collector efficiency. The economic analysis showed that there is a collector size that minimizes the payback time. Additionally, the influence of the environmental conditions, the refrigerant, the costs and the heating capacity on the payback period and optimum collector size were investigated. The results showed that there is an economically optimum size of collector area for the DX-SAHP, which it is the same for different environmental conditions. A case study was made for three different cities and the payback time found is the range of 1.77-3.24 years.