The Use Of Time And Financial Value In Project Decision Trees - A Specific Model And An Algorithm For Rolling Back The Trees

Capital budgeting textbooks usually consider the financial perspective to be the most important, or even the only perspective that should be considered in project evaluation. However, there are often certain factors that cannot be incorporated in the financial value of a project and that are very important in deciding whether or not the project should be undertaken. Time is one important criterion that is often overlooked in the project evaluation literature. In a construction project, for example, there will usually be a deadline. If the company does not meet the deadline, it may have to pay some compensation, and its image may be damaged in a way that is hard to quantify. Other times there may exist some benefits from an early conclusion of the project, like the possibility of undertaking other projects or seizing other opportunities. Competitive interaction will often provide other important reasons to use time as a criterion. In order to deter competitive entries, to gain a competitive advantage or to avoid losses resulting from an early competitive entry, companies may want to undertake a project as soon as possible, while trying to maximise its financial value. In such circumstances, companies may want to use both time and financial value in the definition of their strategies.All these reasons led us to develop a new approach that incorporates both time and financial value in decision trees for the evaluation of investment projects [1]. It focuses on the use of time and financial value, but we think it can be easily extended to other criteria. This new approach allows decision-makers to identify all the non-dominated strategies, letting them use any multicriteria method to choose among them. Decision trees provide an useful way to represent investment projects when different choices or uncertain events are involved. The classical evaluation of such decision trees consisted on the use of the expected value to aggregate the project Net Present Value (NPV) across the decision nodes. However, in recent years it has been acknowledged that this classical evaluation fails to capture the correct value of the project, since the discount rate can no longer be assumed constant in the presence of different options. Instead of the use of the expected value, most authors recommend the use of a valuation model based on Option Pricing Theory: the binomial model. So, we defined an approach that can be used not only with the classical valuation of decision trees but also with the binomial model for option valuation.This communication starts with a brief presentation of decision trees and the binomial model. Then we present our general approach to the use of two criteria - time and financial value - in the evaluation of projects represented by decision trees. Our approach identifies all the non-dominated strategies, allowing the use of any multicriteria method to choose among them. We present a new type of node - the time passage node - that simplifies the definition of these trees, and we particularly discuss the way we handle time and the rules that allow the identification of the non-dominated strategies.Then, we present a more specific model that can be used, for example, in some production planning problems. Although this is a discrete-time model, it may many times be used as a proxy for the continuous-time problem. So, the trees that will be used will usually be very complex, and probably only used within computational systems. Even for computational systems, these trees will be very large and the calculations may take a long time. With that in mind, we present an algorithm that allows a faster identification of the non-dominated strategies, without requiring the complete definition of the corresponding decision trees. We also present the mathematical results in which the algorithm is based.