Engineering Management Research; Vol. 8, No. 1; 2019 ISSN 1927-7318 E-ISSN 1927-7326 Published by Canadian Center of Science and Education 44 Assessment of the Profitability of an Apartment Building Complex Using a Stochastic Cash-Flow Nazim Noueihed 1 , Fadi Asrawi 2 & Najoie Nasr 2 1 Department of Mathematics, Division of Mathematical Sciences, Faculty of Arts & Sciences, Haigazian University, Beirut, Lebanon 2 Faculty of Business Administration & Economics, Haigazian University, Beirut, Lebanon Correspondence: Nazim Noueihed, Department of Mathematics, Division of Mathematical Sciences, Faculty of Arts & Sciences, Haigazian University, Beirut, Lebanon. E-mail: nazim.noueihed@haigazian.edu.lb Received: March 13, 2019 Accepted: May 15, 2019 Online Published: May 17, 2019 doi:10.5539/emr.v8n1p44 URL: https://doi.org/10.5539/emr.v8n1p44 Abstract The economic feasibility of apartment building complexes is mainly done by using one of the economic analysis methods: present worth, future worth, annual worth, rate of return, or benefit-cost ratio. The cash-flow used is based on the assumption that a certain fraction of the apartments will be sold during the construction period, and the rest equally sold annually over a certain period of time. This model may work sometimes, but its estimated profitability is inaccurate. The actual cash-flow to be used is stochastic. In this paper, we shall use a cash-flow with random separation time between successive sales of apartments after the construction period. We shall find a compact form of the expected present worth, and determine a range for the annual discount rate so that the project is profitable. Keywords: stochastic cash-flow, discount rate, present worth, random variable, probability distribution, moment generating function 1. Background and Introduction A financial investment in a project is random or under risk if at least one of its parameters is a random variable with a known probability distribution. In reality, most of real-life investments are random with stochastic cash-flows. Deterministic cash-flows are used when the variances of the concerned random variables are too small so it can be neglected and the variable is represented by its expected value or mean. The economic worth of apartment building complexes is usually based on a deterministic cash-flow consisting of a construction period with corresponding annual costs plus a heavy initial cost. Some of the apartments are assumed to be sold annually after construction within a certain time period at a given price. In reality, the time between the sale of an apartment and the next one is unpredictable so it is a random variable. This promotes the use of a stochastic cash-flow for the given model. In this paper, we will consider the separation times between successive sales after construction as our random variable, and the construction costs as equally distributed over the construction period. In the analysis that we use, the concept of moment generating functions of random variable will prove to be a powerful tool that leads to a closed form of the expected present worth and the rest of analysis methods except for the rate of return. 2. Literature Review The most important resource for a real estate investment is cash flow. Many real estate investments fail due to a lack of liquidity for supporting their daily activities than because of inadequate management of other resources. Stochastic processes, which imitate the uncertain trend of target variables over time are used to carry out dynamic modelling of the outcome of investments in conditions of uncertainty (Simon, 2002). The main concerns of the modelling of the outcome of investments in conditions of uncertainty have focused on capital costs, the probability of credit default and income flows. Stochastic modelling of rental income have been made by Hughes (1995) and De Wit and van Dijk (2003). Stochastic processes modelling the development of real