A traditional cost-benefit analysis of potential water interventions in a given locality is a laborious and time-intensive process. To help decision makers identify optimal locations for such an in-depth cost-benefit analysis, we describe a new method to combine country-wide survey data and mathematical modeling to conduct a rapid and inexpensive cost-benefit analysis of water interventions for many locations across an entire country at once, identifying which locations and which interventions are likely to have the greatest benefit per cost. Using our method, this analysis can be done cheaply, on a standard desktop computer, in a matter of hours. Also, because our method does not rely on water-point mapping data, it can be used even in countries where water-point mapping is limited or nonexistent. Our new method is made possible by the use of mathematical Monte Carlo methods to address a key problem in the survey data, namely, that geographical and spatial information are obscured in the surveys, due to privacy considerations, which makes the data difficult to use for cost-benefit analysis without methods such as ours. We use a combination of Voronoi diagramming and Monte Carlo sampling to estimate locations while preserving privacy, allowing us to overcome the information loss and to use the data for comparing needs across different locations. Our methods produce an ordered ranking of the areas within a given country which have the highest benefit-to-cost ratio and to identify the optimal intervention. We apply these methods on the countries of Namibia and Angola to demonstrate how they can be used.