# Randomized Estimation of the Net Present Value of a Residential Housing Development
## 2 Materials and Methods  
Estimation of the primary initial data is the first phase of the randomized estimation of the net present value of the residential housing development's efficiency. These data are the basis for further analysis and data randomization for the estimation of efficiency. They directly describe the kinds and values of parameters and characteristics of the project implementation. In the primary analysis, based on an in-depth analysis of the facilities structure and the construction conditions, the residential housing development implementation cycle has to be projected. Such a lifecycle has been defined in a similar way by [PERSON] 2018 [20], [PERSON], [PERSON], [PERSON] 2014 [21], [PERSON],[PERSON] 1998 [22], [PERSON], 1994 [23], et al. In this meaning, the construction project lifecycle consisted of several successive stages \(s=1,2,\ldots,t\). In each stage, the subset \(A^{s}\) of tasks \(a_{i}\) should be executed, \(A^{s}=\left\{a_{i}:i=1,2,\ldots,i^{s}\right\}\). During the project lifecycle implementation, the set \(A\) of all tasks \(a_{i}\) of the project should be carried out, \(A=\left\{A^{s}:s=1,2,\ \ldots,t\right\}=\left\{a_{i}:i=1,2,\ldots,i^{s}\right\}\). Consistently, for each subset \(A^{s}\) of tasks \(a_{i}\), the subset \(C^{s}\) of the initial preliminary execution costs \(c_{i}\) should be estimated, \(C^{s}=\left\{c_{i}:i=1,2,\ldots,i^{s}\right\}\). In this way, the subsets \(C^{s},\ s=1,2,\ldots,t\), contain all costs \(c_{i}\), and each stage \(s\), of the project and form the set \(C=\left\{C^{s}:s=1,2,\ldots,t\right\}=\left\{c_{i}:i=1,2,\ldots,i^{t}\right\}\). According to the stage of construction, the apartments and other facilities can be sold after some objects are finished, or they can be sold after the whole residential housing development\({}^{\prime}\) completion. Each sold part represents one tranche \(b_{i}\) of revenue \(p_{i},i=1,2,\ldots,i^{\frac{p}{p}}\). All paid tranches \(b_{i}\) of revenues \(p_{i}\) constitute the set \(P=\left\{p_{i}:i=1,2,\ldots,i^{\frac{p}{p}}\right\}\). Because of money value changes in time, for both costs and revenues discount rates, \(p_{i}\) paid per year should be set. The primary initial data of costs for the residential housing development implementation cycle can be determined as follows:  
1. Stages \(s\) and subsets \(A^{s}\) of task \(a_{i}\), and subsets \(C^{s}\) of cost \(c_{i}\): feasibility study--s1, the subset \(A^{1}\) of tasks \(a_{i}\), \(A^{1}=\left\{a_{i},i=\overline{1,5}\right\}\) and the subset \(C^{1}=\left\{c_{i}:i=\overline{1,5}\right\}\) of costs \(c_{i}\): \(a_{1}\)--initial analysis and its cost \(c_{1}\). \(a_{2}\)--land acquisition and its cost \(c_{2}\). \(a_{3}\)--determination of the technical conditions and its cost \(c_{3}\). \(a_{4}\)--coverage of overheads and its cost \(c_{4}\). \(a_{5}\)--tracing of economic and financial conditions and its cost \(c_{5}\); design documentation development--s2, the subset \(A^{2}\) of tasks \(a_{i}\), \(A^{2}=\left\{a_{i},i=\overline{1,6}\right\}\) and the subset \(C^{2}=\left\{c_{i}:i=\overline{1,6}\right\}\) of costs \(c_{i}\): \(a_{1}\)--initial concept and nets and their cost \(c_{1}\). \(a_{2}\)--conceptual architectural design and its cost \(c_{2}\). \(a_{3}\)--general conceptual design and its cost \(c_{3}\). \(a_{4}\)--construction project and its cost \(c_{4}\). \(a_{5}\)--detailed design (executive project) and its cost \(c_{5}\). \(a_{6}\)--complementary design documentation and its cost \(c_{6}\); construction--s3, the subset \(A^{3}\) of tasks \(a_{i}\), \(A^{3}=\left\{a_{i},i=\overline{1,8}\right\}\) and the subset \(C^{3}=\left\{c_{i}:i=\overline{1,8}\right\}\) of costs \(c_{i}\): \(a_{1}\)--construction site development and its cost \(c_{1}\). \(a_{2}\)--structure of construction, state zero, and its cost \(c_{2}\). \(a_{3}\)--plumbing and electrical wiring, state zero, and its cost \(c_{3}\). \(a_{4}\)--structure of construction--superstructure and its cost \(c_{4}\).