A fuzzy real option approach for investment project valuation

Abstract

The main purpose of this paper is to propose a fuzzy approach for investment project valuation in uncertain environments from the aspect of real options. The traditional approaches to project valuation are based on discounted cash flows (DCF) analysis which provides measures like net present value (NPV) and internal rate of return (IRR). However, DCF-based approaches exhibit two major pitfalls. One is that DCF parameters such as cash flows cannot be estimated precisely in the uncertain decision making environments. The other one is that the values of managerial flexibilities in investment projects cannot be exactly revealed through DCF analysis. Both of them would entail improper results on strategic investment projects valuation. Therefore, this paper proposes a fuzzy binomial approach that can be used in project valuation under uncertainty. The proposed approach also reveals the value of flexibilities embedded in the project. Furthermore, this paper provides a method to compute the mean value of a project’s fuzzy expanded NPV that represents the entire value of project. Finally, we use the approach to practically evaluate a project.

Introduction

DCF-based approaches to project valuation implicitly assume that a project will be undertaken immediately and operated continuously until the end of its expected useful life, even though the future is uncertain. By treating projects as independent investment opportunities, decisions are made to accept projects with positive computed NPVs. Traditional NPV techniques only focus on current predictable cash flows and ignore future managerial flexibilities, therefore, may undervalue the projects and mislead the decision makers. Furthermore, for high-risk investment projects, the traditional NPV method may adopt higher discount rates to discount project cash flows for trade-off or compensation. However, higher discount rates may result in the underestimation of project value and the rejection of a potential project. For instance, investments such as new drug development or crude oil exploitation may carry high risk, but may also bring higher returns.

Since DCF-based approaches ignore the upside potentials of added value that could be brought to projects through managerial flexibilities and innovations, they usually underestimate the upside value of projects (Bowman and Moskowitz, 2001, Dixit and Pindyck, 1995, Luehrman, 1998, Trigeorgis, 1993, Yeo and Qiu, 2003). In particular, as market conditions change in the future, investment project may include flexibilities by which project value can be raised. Such flexibilities are called real options or strategic options. The real options approach to projects valuation seeks to correct the deficiencies of the traditional valuation methods through recognizing that managerial flexibilities can bring significant values to projects. According to real options theory, an investment is of higher value in a more uncertain or volatile market because of investment decision flexibilities.

Real options approach, as a strategic decision making tool, borrows ideas from financial options because it explicitly accounts for future flexibility value. Real options analysis is based on the assumption that there is an underlying source of uncertainty, such as the price of a commodity or the outcome of a research project. Over time, the outcome of the underlying uncertainty is revealed, and managers can adjust their strategy accordingly.

The objectives of this paper are to develop a fuzzy binomial approach to evaluate a project embedded with real options, to propose a method suitable for computing the mean value of fuzzy NPV, and to explore the value of multiple options existing in projects. The paper is organized as follows. Section 2 provides a survey of real options analysis. We especially focus on pricing, applications and recent developments of real options analysis. Section 3 presents a fuzzy binomial approach to evaluate a project under vague situations. This section also proposes a method to compute the mean value of fuzzy NPV. Section 4 illustrates a project valuation based on our approach. In the example, the values of the real options are also assessed. Section 5 discusses the results and findings in the example. Finally, conclusions are drawn in Section 6.