In this paper, we present an analysis of the convenience of setting up a 1 MW solar thermodynamic power plant made with Fresnel linear mirrors in a medium-high direct sunlight intensity area. After a brief review on the state of the concentrated solar power technology and an analysis of the projections for the future development of this technology, we introduce a case study based on realistic assumptions for plant characteristics, capital costs and financial conditions. After introducing a simple and comprehensive economic model, we report the results in terms of discounted payback period, net present value, and internal rate of return. Finally, to generalize the results, we introduce a sensitivity analysis with respect to the different variables involved that could positively or negatively affect the economic results.