From theoretical real options models to pragmatic decision making: Required steps, opportunities and threats

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Highlights

  • Real options are well suited to evaluate port capacity investment decisions.

  • Both the investment timing and size are optimised.

  • Developing a practical real options application is required for practitioner adoption.

  • The advantages and disadvantages of optimising investment decisions through real options are quantified.

Abstract

Port capacity investments are large, irreversible and uncertain projects, involving different decision variables to be optimised. In order to optimise the timing and size of such projects, the literature has indicated that real options (RO) are better suited than the more traditional net present value (NPV) approach. The models are very theoretical and difficult to implement in practice. The objective of this paper is to extend the empirical RO literature in transportation and logistics by bringing continuous-time continuous-state RO models closer to practitioners. This is done by means of developing a blueprint for a practical software application through which port investment managers can easily calculate their optimal decisions. Additionally, the blueprint of this practical implementation allows for a better understanding of the continuous RO logic and way of working. As the discussion of the RO advantages shows, optimising the decision through continuous RO models, rather than applying NPV, can allow ports to realise a much better investment and generate a lot more value from port investment projects. Nevertheless, depending on the specific situation, practitioners might require supplementary assistance of econometricians or consultants to estimate the RO model input parameters. This paper also adds to the literature by quantifying these potential gains and costs.

Introduction

Good logistics performance of ports exhibits two important characteristics, namely low logistics costs and high reliability of the operations (Munim & Schramm, 2018). In order to perform port operations effectively and efficiently and generate added value in a port, investing to build new or expand existing ports is crucial. A port's ability to provide cargo throughput services is quantified in terms of its capacity. Next to building new capacity-increasing elements, capacity can also be increased through the optimisation of existing terminals (ESCAP, 2002; Kauppila, Martinez, Merk, & Benezec, 2016). Each of these investment types will allow generating more throughput at better service levels (Musso et al., 2006). Since port capacity installed by investors increases the service level of the operators, the generalised cost in the logistics chain will fall, and also shippers and consumers will experience benefits from these investments (Talley et al., 2014). Musso et al. (2006) refer to this concept as a port investment chain.

Having insufficient service capacity to handle cargo could cause congestion, leading to increased logistics costs (Novaes et al., 2012). In a port, a service environment, and in transportation in general, it is even more important than in a production environment to have the right amount of capacity, since the transportation service is not storable (de Weille & Ray, 1974). Capacity that is not used at the actual time period cannot be stored and used in the next, as opposed to warehoused goods. Undercapacity cannot be covered either by unused outputs from a previous period. Since the demand for cargo throughput is uncertain and variability may become high, it might occur that moments of empty berths are followed by moments in which ships are waiting to be serviced at a berth that is currently occupied. In this way, congestion and waiting time might start to build up in the port at occupancy rates of about 50% of the theoretical design capacity, the maximum amount of throughput that can be handled by a port in a certain time period. Above an occupancy rate of 75%–80%, waiting times increase more than linearly (Blauwens, De Baere, & Van de Voorde, 2016; Kauppila, Martinez, Merk, & Benezec, 2016; Leachman & Jula, 2011).

A mismatch between demand and capacity can result in periods of capacity scarcity or overcapacity. Without sufficient capacity, i.e., undercapacity, the port risks losing customers, throughput and profit due to the congestion building up. This results in a loss of social welfare in the form of lost consumer surplus. However, installing capacity comes at an investment cost, positively related to the amount of installed capacity. As a result, installing too much capacity, i.e., overcapacity, poses a problem as well, as money is invested in capacity that is not used and that hence does not generate revenues. This gives rise to a trade-off between investing too much money in unused capacity and investing in too little capacity, which leads to higher user waiting costs and which might eventually lead to losing customers and profit (Meersman & Van de Voorde, 2014a). This capacity investment trade-off is even more complicated by the uncertainty in the port (Musso et al., 2006). As a result, installing the right amount of capacity at the right moment is crucial (Vanelslander, 2014).

In practice, the traditional net present value (NPV) approach based on the discounted cash flow (DCF) method is often used to evaluate port investment projects, because practitioners, managers and decision makers find it easier to model and explain (Pimentel, Couto, Tavares, & Oliveira, 2020). However, this traditional approach neglects the value of flexible options in irreversible projects and uncertainty, such as the option to delay investment. Even if uncertainty is low or absent, the NPV decision rule can be (very) wrong, because the irreversible investment decision is considered as a now-or-never decision (Dixit & Pindyck, 1994). Oppositely, real options (RO) models offer a more appropriate method to evaluate flexible investments under uncertainty and make better investment decisions, especially in case of large, very costly, irreversible and uncertain projects with long construction lead times, such as port infrastructure investments. Initially, the RO theory has been elaborated by Dixit and Pindyck (1994), Trigeorgis (1993) and Trigeorgis (1996). RO models monetarily quantify the value of managerial flexibility to react to uncertainty in the best possible way. Only when all relevant options of flexibility are included in the project appraisal, the investment decision can be valued correctly. To this end, RO models use stochastic calculus and dynamic programming to optimise an objective function (such as the value of the firm), including a random term related to an investment decision variable (Dixit & Pindyck, 1994). It is however important to point out that RO models should not necessarily be seen as a replacement for NPV with discounted cash flows. It is complementary to it, because the value of a project can be calculated as the static NPV plus the value of the real options present (Hu & Zhang, 2015; Van Putten & MacMillan, 2004).

The majority of the RO models developed in the academic literature are theoretical models. They allow deriving theoretical insights into the optimal investment decision under uncertainty. Mathews et al. (2007) advocated more than 10 years ago that RO models are often too complex to implement, due to the difficulty to derive realistic parameters that are needed as input for these models. Since this statement, little has changed for continuous-time continuous-state RO models. Some authors however propose useful applications of discrete-time discrete-state RO models to real-life cases in transportation environments. For instance, Pimentel et al. (2018) apply RO to an investment in high-speed rail, whereas Oliveira, Couto, & Pimentel, 2020 consider the expansion of Ponta Delgada airport as an RO application. RO have also been applied to investments in airlines (Hu et al., 2019) and container shipping capacity under uncertainty (Haehl & Spinler, 2018; Rau & Spinler, 2016, 2017). A nice case study containing an application of RO to the expansion of an existing port, is given by Pimentel, Couto, Tavares, & Oliveira, 2020. They confirm that the RO value is the sum of the static NPV and the option value of flexibility under uncertainty. Another interesting example is provided by Martins et al. (2017), who consider port expansion options of a given size (expressed in TEU) and given timing (when the existing capacity has an occupancy rate of 80%), as American-style call options, without taking congestion costs into account. However, since these discrete-time discrete-state models only consider a limited number of (discrete) states and involve Monte Carlo simulations, not all possible investment scenarios are considered by the model in the analysis.

Notwithstanding the large number of applications of discrete-time discrete-state RO models involving binomial trees, Pimentel, Couto, Tavares, & Oliveira, 2020 argue that these models are not sufficiently accurate for complex project evaluation under uncertainty. Moreover, Martins et al. (2017) advocate for a maximal inclusion of flexibility in projects. This is exactly what continuous-time continuous-state RO models do, overcoming some shortcomings of binomial tree models. These continuous-time continuous-state RO models allow to optimise complex port investment decisions under uncertainty with respect to the decision variables that are considered, as an infinite number of possible investment strategies are considered. Balliauw (2020) for example considers the timing and size of a container port expansion as flexible decision variables that need to be optimised, modelling demand uncertainty using a geometric Brownian motion (GBM). His theoretical model shows the management of a port with a single actor that, if demand starts to grow stronger, they are better off by delaying port expansion and investing in more capacity once they invest. In addition, the characteristics of the economic environment, the port type and the investment project type have an influence on the optimal port capacity investment decision as well. The theoretical directions of these influences provide useful information for port managers at the moment when the economic environment changes. However, a practical application of such continuous RO models is still lacking. This would be very useful, since an infinite number of scenarios can be considered, each with a different size and timing of the investment, and the best one can be chosen in the end.

In order to apply continuous RO port models in practice, two conditions need to be fulfilled. On the one hand, the port management needs to have the information at hand to derive and estimate the values of the model parameters. On the other hand, the user needs to be able to apply advanced econometric methods in order to calculate the optimal investment timing and size, possibly supported by external econometricians (Dikos, 2008). This latter condition is less straightforward, as Marmer and Slade (2018) illustrate. They use the model of Bar-Ilan and Strange (1996) with time to build and apply it to the U.S. copper mining industry using advanced econometrics on reduced forms of a set of theoretical equations.

The question however remains: “How can a specific port implement continuous-time continuous-state RO models to derive its own optimal investment decision in reality?” A subsequent question that arises is: “What are the potential gains and costs of implementing RO, compared with currently-used decision making methods.” Therefore, the objective of this paper is twofold: (1) to develop a practical application of continuous-time continuous-state RO models for port investments, to make the gap between theory and practice smaller, and (2) to quantify potential monetary gains from actually using real options models for decision making, compared to NPV, in order to convince port managers to use RO models to improve their decisions. Both objectives are crucial empirical extensions of the existing RO literature in transportation and logistics, in order to allow practitioners to use the theoretically derived insights from continuous-time continuous-state RO models in practice and improve their investment decisions. The intended extension will also allow considering as much flexibility as possible in projects, due to the possibility to select the optimum from many more considered scenarios, compared to NPV and discrete RO models. Moreover, the complex RO model will be moved to run in the back end of the application, whereas the front end will only require relatively easy-to-determine inputs from practitioners. Although the application in this paper considers a seaport, the insights and approach can be used in other transportation settings too.

To respond to both research questions in this paper, the necessary information that serves as the input for the RO models is discussed, as well as a possible, basic programming approach to transform the model into an optimal real-life port investment decision. The required steps that are needed to move from the complex, theoretical RO models available in the literature to a more applicable, user-friendly implementation are discussed. These steps are gathered in a blueprint for a practical tool that can help to come one step closer to the practical implementation of the developed models, since the complex calculations are left for the algorithm. Hence, this tool should be seen as a simplified approach to yield a first approximation of the optimal investment strategy for a port expansion project, based on existing continuous-time continuous-state RO models. This tool could also support transforming the port management's input into the model parameters. Nevertheless, the quality of the input, such as the complex estimates of economic characteristics such as demand growth and uncertainty, will always be important and are left for the human user. Using the entered parameters, the RO model yields an approximation of the optimal investment size and timing in terms of observable, meaningful decision variables. It is however not the objective of this paper to explore the large number of complex estimation techniques for the parameters. These are nonetheless required to accurately implement the RO port models available in the literature. More advanced econometrics and further model extensions (e.g., including phased investment) will be crucial objects of further research to support decision makers and increase the realism and the applicability of RO investment analysis in ports. As for every model, also for this tool the wisdom “Rubbish in, rubbish out” holds.

In order to illustrate the proposed tool, the specific model of Balliauw (2020) has been chosen, because the majority of port capacity investment decisions are expansion decisions (De Langen, Turró, Fontanet, & Caballé, 2018) and involve considerable time to build (Kauppila, Martinez, Merk, & Benezec, 2016; Vanelslander, 2014). Moreover, ports can be owned privately or publicly, which has a specific impact on investments under uncertainty (Li & Cai, 2017). Both types are accounted for in this model. However, the hypothetical case study in this paper, to which the tool is applied, involves a private port expansion. According to Mort et al. (2002), a case study should contain a problem with real or hypothetical set-ups, involving real-life complexities. Since it was not possible to find a complete dataset of an existing port expansion scenario in this study, a hypothetical port expansion project with realistic data, from the Hamburg - Le Havre port range, and assumptions has been considered. Although the model of Balliauw (2020) does not explicitly model port competition, it is still useful to gain insight into the unrestricted optimal investment decision of a single port and to illustrate the model implementation in practice. To take into account the competition of nearby ports, the insights and different strategies of Ishii et al. (2013), who however did not take the endogenous timing decision into account, and Balliauw, Kort, and Zhang (2019) need to be considered afterwards. Subsequently, the aggregate optimal investment decision (valid for a service port model as is used in this paper) might need translation into the decision of multiple actors that are present in a port which is organised as a landlord port. This requires insight into the revenue and cost structures of the port authority (PA) and the terminal operating company (TOC) in order to derive their shares (the α′s of Balliauw et al. (2020)) in the total revenue and costs generated in the port.

This paper is structured as follows. The next section summarises the real options model that is used for the application developed in this paper. Section 3 discusses the blueprint of the practical tool to implement a simplified version of the developed continuous RO models for port managers to get a first idea about their optimal investment decision. Subsequently, Section 4 provides a reflection on the advantages and difficulties of using RO in a port context. These advantages are discussed and quantified for the hypothetical case studied in this paper. The final section provides the conclusion and potential extensions of the tool, based on future research outcomes.

Section snippets

Summary of the real options model

The economic model of Balliauw (2020) is summarised in Table 1, whereas the underlying assumptions are shown in Table 2. With these functions at hand, the steps as described by Dixit and Pindyck (1994), Dangl (1999), Hagspiel et al. (2016) and Balliauw (2020) can be followed to optimise the investment decision as follows. The calculations start from V, the value of a greenfield project without time to build. This equalsV=E0maxq{Π(T+τ)}erτdτ,with r the discount rate, T the timing of the

A real options tool blueprint for port capacity investment decisions

This section explains how a new, practical tool to help port managers make an optimal investment decision should look like and can be developed. This empirical addition to the existing continuous RO literature should present the bridge between these theoretical models and practical decision making for real-life cases. To this end, the next subsection provides an overview of the required inputs and how they can help to derive the required parameters of the RO port model. Section 3.2 illustrates

Quantifying potential advantages and challenges of real options for port investment decisions

Many practitioners consider the RO methodology to be a too complex methodology (Pimentel, Couto, Tavares, & Oliveira, 2020). As shown in the previous section, calculating the value of many investment options involves more steps and more complex algebra than calculating NPV. However, next to additional costs of this approach, there are also considerable potential gains. The critical discussion in this section is hence made up of two parts. First, the potential gains from applying continuous RO

Conclusions and future research

In order to transfer the theoretical insights and potential advantages from the available continuous-time continuous-state RO models to practical calculations for a port's optimal investment decision under uncertainty, the description of a possible algorithm to simplify the calculations of the optimal investment decision in terms of meaningful, observable decision variables is needed. Filling this empirical gap is considered an important step to give complex, continuous RO modelling a place in

CRediT authorship contribution statement

Matteo Balliauw: all CRediT roles (sole author).

Acknowledgements

This research was funded by a PhD grant from Research Foundation Flanders (FWO). I would like to thank Evy Onghena, Anming Zhang, Christophe Smet, Peter Kort, Trevor Heaver, Eddy Van de Voorde, Hilde Meersman, Thierry Vanelslander, Siri Strandenes, Seraphim Kapros and Danny Cassimon for their fruitful insights to improve the paper. I am responsible for the remaining errors.

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