Decision SupportApplying the maximum NPV rule with discounted/growth factors to a flexible production scale model
Introduction
Most decision-making in capital budgeting follows the net present value (NPV) method. Typically, the NPV method can be applied in making a decision and relevant conditions are assumed to be static and certain. Giri and Dohi (2004) regarded the NPV method as an approach of determining the economic manufacturing quantities for an unreliable production system over an infinite planning horizon. The NPV of the expected total cost was obtained under general failure and repair time distributions, and its asymptotic characteristics were examined via the perturbation of the instantaneous discounted rate in the EOQ (economic order quantity) model. Kylaheiko et al. (2002) focused on the difficult issue of managing and valuing dynamic capabilities for designing the firm’s strategic boundaries in decision-making regarding network relations, and took a broad look at the real options approach (ROA) as a special method of the NPV rule to illuminate the issue of coping with technological and market uncertainty.
Meanwhile, the ROA is devised based on the options pricing model of Black and Scholes (1973). Dixit and Pindyck (1994) revealed a lot of similarities in findings and the mathematical methods for investment strategic behavior with the ROA. The ROA provides the appropriate heuristic framework for competency and exploratory searching. Miller and Park (2002) comprehensively reviewed the research on the ROA, focusing on the decision-making of engineering economy under uncertainty. Furthermore, the decision-making process based on the ROA is more realistic than that based on the NPV rule since it considers the uncertainty regarding future costs and output prices, investment irreversibility, and managerial flexibility, meaning the decision is not “now or never” but rather “now or later”. Thus, the ROA is a novel approach for assessing projects, investments, businesses, and technologies by applying the financial options theory.
Bengtsson and Olhager (2002) introduced the ROA to demonstrate that the flexibility value of strategic adoption decreases with increasing demand volatility, flexible resources are substantially more valuable than dedicated resources, and the flexibility value of marginal capacity decreases with an increasing capacity level. Boute et al. (2004) studied that project management can wait for additional information to serve as the basis for rescheduling the project. This management flexibility enhances the value of the project by improving its upside potential while limiting its downside losses relative to the initial expectations.
McDonald and Siegel (1986) studied the investment timing problem and evaluated the value of waiting so as to derive an optimal decision rule and the value of the investment opportunity. The authors introduced the correct discounted rate success for assessing the actual rate of return on the investment opportunities. However, this study examines the maximum NPV of the market entry and exit thresholds derived by the simple discounted and growth factors, facilitating the complicated calculations required to identify the discounted and growth rates and thus determine the expected present value of uncertain cash flow streams. Consequently, this investigation successfully combines applying the maximum NPV rule and the ROA to decision-making with the simple consideration of the discounted and growth factors in the flexible production scale model.
The remainder of this paper is organized as follows: Section 2 introduces the discounted and growth factors into the stochastic market entry and exit models involving cash flow uncertainty. Section 3 then discusses the flexible production scale system under the constraint that margin profit equals margin cost, and evaluates the optimal entry threshold using the ROA and the maximum NPV rule. Section 4 presents some numerical analyses while conclusions are finally drawn in Section 5.
Section snippets
Single stochastic market entry model
The first part of this subsection considers a fixed production scale model only when income streams follow stochastic cash flows, presents the general formulation in the market entry model, and analyses the optimal production threshold under the consideration of irreversible entry cost. Specifically, when the risk-adjusted neutral probability measure
Flexible production scale in the entry model
The stochastic market entry and exit models discussed in Section 2 ignore the possibility that most manufacturers will implement the project in the market and thus the production scale will be expanded. If these factors are considered in the entry model, the most appropriate investment timing will be generally assessed based on the NPV of the project investment and the NPV will be accommodated to be zero for decision-making. To cope with the above issues, Section 3 explores the imperfectly and
Numerical example in the stochastic entry and exit models
This subsection simulates the stochastic market entry and exit cases by using the proposed model mentioned previously in Section 2. The numerical analysis employs the following base case parameters: μ = 0.02, σ = 0.3, and r = 0.15 per period. Thus, α = −1.56897 and β = 2.12453 can be derived from Eq. (4). This study assumes the setup cost K = 300 million dollar, the initial cash flow C = 50 million dollar, and the exit lump sum cost I = 200 million dollar. Based on these base parameters, the entry and exit
Conclusions
The proposed approach is different from the value-matching and smooth-pasting conditions which can be found in the examples mentioned by Dixit and Pindyck (1994). The author tries to introduce the other way to link the optimal solution with the maximum NPV rule and the ROA. Following the discounted and growth factors, the author can find out the entry and exit thresholds for pricing the firm value involving the potential value of adopting the entry and exit strategies in the future.
This study
Acknowledgements
The author would like to thank the National Science Council of the Republic of China, Taiwan and the Office of Research and Development, National Dong Hwa University for financially supporting this research under Contract No. NSC96- 2416-H-259-009-MY2.
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