# Randomized Estimation of the Net Present Value of a Residential Housing Development
## 1 Introduction
The method of assessing the effectiveness of unstable construction projects in the conditions of the impact of significant disturbances on the course and results of implementation uses specific concepts and mathematical formulas in a different scope and at different stages of the investment. The end result of the presented method is a reliable estimation of profitability and a realistic assessment of the cost-benefit balance of unstable construction projects already at the planning stage. Often, a distinction is made between economic and technical efficiency. Economic efficiency means producing and distributing goods at the lowest possible cost. Technical efficiency means the maximum amount of production for a given input, or the maximum amount of an output that can be obtained from a certain input. In many studies, the term \"efficiency\" is often used to evaluate economic activities (Blue Book, [19]). From this point of view, economic and financial efficiency are most often distinguished. The randomized method for estimating the net present value of a construction project's efficiency has been worked out recently. The method has been theoretically finished and verified on simple examples of projects. However, the method is still being tested and verified in the process of estimating the net present value of the housing investment's efficiency. So, the objective of the research was to verify the correct probabilistic method for the analysis and assessment of the net present value of the effectiveness of unstable construction projects for real building investments. In the article, research results for real building investments by the randomized method of the estimation of construction projects' efficiency are presented. Such building investments have been realized by a developer in Warsaw, the capital city of Poland. Here, the randomized method of efficiency estimating of the net present value of one such residential housing development's efficiency is presented. The subject of the study is one of the stages of a five-stage construction of a residential housing development in Warsaw. The settlement was built by a Warsaw real estate developer. The development area takes up approximately 1.3 hectares of land. Inside this area, six multi-family buildings of different size, set on a single garage plate, have been built. Complete with the buildings, some concomitant facilities have been built, for example, new public roads, additional parking spaces, and usable premises. The residential housing development has been built in the system of a general contractor. Implementation cycle of the project consisted of four basic stages, namely: feasibility study (6 months), designing (12 months), construction (18 months), and operation and maintenance (60 months). However, the stage of operation and maintenance concerned only activities resulting from the general guarantee and warranty for defects. The efficiency analysis was carried out as part of the feasibility study. In the first stage of the analysis, the project life cycle was projected, i.e., the stages of implementation and tasks cost of these stages, as well as tranches of revenue payments. Moreover, in this stage, discount rates were established, and the types of random disturbances of the project implementation were determined. In the case of this project, the primary initial data were developed collectively by the team for the real estate purchases and the team for analysis and preparation of investments. The teams identified and estimated this data, taking into account the predicted conditions and projected prices in the country for the entire project lifecycle implementation. The discount rate was determined on the basis of historical data of the investments realized by the developer and accordingly to the current market forecasts. The investment in the initial phase, such as all investments of this company, was financed by an operating loan for the activities of the developer.