THE REAL OPTIONS METHOD APPLIED TO DECISION MAKING – AN INVESTMENT ANALYSIS

Goal: This study aims to assess the impact of using the method of real options in investment analysis through a case study on a retail firm. Design / Methodology / Approach: It was targeted the applications of the real options method in a different type of environment and it was compared to another method more commonly used, the discounted cash flow method (DCF). The implementation and assessment of the real options method was investigated by means of a case study conducted in an investment analysis in a retail units firm. Results: The use of the real options method showed a more concise applicability over the DCF method. The results show that the project’s value, after the inclusion of managerial flexibility, increased significantly, which indicates that the analysis of the discounted cash flow undervalued the investment in question, since it disregarded the flexibility to expand or abandon the project. Limitations of the investigation: The presented method is proper to long-term processes where it is possible to make changes during the project. Investments in this sector usually are more related to short and medium-term decisions, making the application difficult due to the short decision-making period available to the managers. Practical Implications: The study provided the incorporation of flexibility through different pathways during the building project in a retail units firm. It was showed different scenarios where practitioners could decide among expanding, proceeding, reducing or abandoning the retail units based on the characteristics of their investments. Originality/value: The results obtained are an indication of this methodology to industrial businesses that are relatively volatile and that need a certain degree of flexibility in order to burgeon, such as the case of the retailing sector.


INTRODUCTION
Factors such as competitiveness, competition and increasing market demands typically require the business environment a more specific planning in which the decision-making process is done through assessment methods. These assessment methods serve to support decision making and are significantly important for companies in order to consider all possible investment alternatives (Liu et al., 2012;Keller et al., 2017). Traditional investment analysis tools ignore a relevant principle of many investment projects that is to allow project delay, the possibility of expansion or even discontinuation, when the project has already been started (Bodie and Merton, 1999;Scotelano et al., 2017). Without estimating these options, there is a great chance that the project's Net Present Value (NPV) will be underestimated by the analyst.
Questions, such as what path to follow, which project to choose, how costs and revenues will be generated, as well as the capital needed, should all be considered in deciding on the best plan to follow (Casarotto Filho and Kopittke, 2008). Hence, an alternative approach that can be adopted is known as the assessment of real options (Borges et al., 2018;Lambrecht, 2017;Andalib et al., 2018).
In a nutshell, the theory of real options, when applied to projects with associated intangibles, tries to overcome the limitations of the conventional criteria and the lack of analytical discipline, which characterizes the qualitative assessment (Samanez, 1994;Fernandes et al., 2011;Lambrecht, 2017). This theory encompasses the investment opportunity as finance and business strategies. Hence, it creates an assessment tool supported by a quantitative approach that transforms the investment into financial options. The main objectives of this paper are to analyze the impact of real options by means of a case study conducted in a distribution center opening for retail units and to evaluate whether the investments should be expanded, abandoned, contracted or continued. Although the usefulness of this work serves to enhance the academic comprehension of the subject matter, it is believed that it is the practical community who will greatly benefit from this study, since they will have a handson and detailed vision of how the Real Options method was conducted.
The remainder of this paper is structured as follows. First, the authors' theoretical background section "Theoretical Background" will be introduced to the concepts and the main literature on Real Options. After this, the study's methodological procedures will be explained on the section "Methodology". In the section "Results" the results of this case study will be presented. Finally, the authors' discussions and conclusions will be presented on the section "Discussions and conclusions".

THEORETICAL BACKGROUND
As most part of the literature advocates, the main objective of companies should be the creation of a system in which managers make investments that maximize the long-term value of their companies (Porter, 1991;Cooper et al., 2001;Grillo et al., 2018). In order to analyze project options, it is necessary to verify whether the economic analysis of investments is centered on the elaboration of a cash flow that reflects all the inflows and outflows of the firm's resources, that is, the elaboration of an estimative of both revenue and benefits when considering the costs of a new project (Lambrecht, 2017;Andalib et al., 2018). Most decisions made about investments involve three important factors: (i) if the investment is partially or completely irreversible; (ii) if there is uncertainty about future return, and (iii) if the investment is flexible, which comprehends the possibility of the investment to be postponed so that more information on the main points that affect the return of the investment itself can be obtained.
The option assessment theory makes it possible to capture the different paths that a company's management could take during the investment phase (Lambrecht, 2017). Moreover, it takes into account the uncertainties of the investment outcomes. In this way, an "option" can be defined as a contract that gives the buyer a future right over an asset, although there is no obligation to buy or sell it at a previously established price, the so-called "exercise price" (Andalaft-Chacur et al., 2011;Trigeorgis and Tsekrerkos, 2018). There are two types of options: the purchase, in which it is offered the right, but not the obligation to buy a given asset, and the sale, which offers the same conditions of buying, for the selling of a given asset. The option market allows the use of various strategies, some for protection, and others for speculation. Among the main reasons for using the option strategy are: (i) the obtaining of greater returns through the leverage aspect and (ii) the pricing of a future acquisition, allowing the acquisition of an asset with an attractive price on the current date at the same value in later periods, and to protect against falling prices. Regarding the performing possibilities, the classification can be made according to Figure 1.

Purchase option Selling option
Inside money The asset's price is greater than the exercise price.
The asset's price is lower than the exercise price.

In money
The asset's price is equal to the exercise price.
The asset's price is equal to the exercise price.

Outside money
The asset's price is lower than the exercise price.
The asset's price is greater than the exercise price. The greatest problem in the decision to invest or to abandon a project is the duration devoted for the decision-making process (Martinsuo and Lehtonen, 2007;Liu et al., 2012;Scotelano et al., 2017). Typically, this duration, may delay the project, consequently, hampering the effectiveness of the decision itself. Thus, the real options theory brings flexibility as an advantage over the NPV method, because it presents explicit criteria for the decision as to when operations should be started, finished or discontinued. According to Copeland and Antikarov (2002), the NPV offers a decision of the present expectation about the future data. In contrast, the evaluation by real options provides the necessary flexibility for the decision making according to data availability.
The economic analysis through real options is an investment analysis methodology that incorporates managerial flexibility, uncertainty and learning. One of the major benefits of such a methodology is the appreciation of decisions that would otherwise not be considered in a project, such as postponement, discontinuation and expansion, to mention but a few. This methodology, nevertheless, does not reject the discounted cash flow model, but rather it complements it by adding the value of the built-in opportunities with the resulting NPV (Miranda Filho, 2005). Literature provides some relevant applications regarding this topic. Figure  2 brings some applications and the main authors that have studied the real options theory.
Among the listed authors on Figure 2, Brennan and Schwartz (1985), Dixit and Pindyck (1994) and Dias (1996), are the ones who mostly contributed to the field of Real Options. They not only extended the theoretical understanding on the topic, but also conducted studies related to the application of the real options method for investment analysis. In addition, some other authors who also largely contributed to the development of this method in different scenarios are Fuss et al. (2008), Reniers et al. (2011) and Szolgayová et al. (2011). Lastly, it could be verified that besides contributing to the analysis of investments, the theory of real options also serves to solve socio-economic problems (Kogut and Kulatilaka, 1994).

METHODOLOGY
The present analysis consists in a case study made on a retail company. The identity of the company will be kept confidential, as requested by the company's management. Hence, for discussions about this work, the data used in this study were transformed, without changing the final outcomes. The case encompasses an investment assessment in the opening of a retail unit in a new location. For this purpose, it will be necessary to open a local merchandise distribution center with small capacity. The other part of the operation will be served by distribution centers from other

Authors
Year Application Roberts and Weitzman 1981 Examination of projects with sequential investments using information collection models. Brennan and Schwartz 1985 Assessment of natural resources, options for temporary standstill or discontinuation of a mine.  Kogut and Kulatilaka 1994 Input, capacity and adequacy options for multinational companies undergoing operations in a volatile exchange rate environment. Dixit and Pindyck 1994 Social-economic problems. Dias 1996 Investments under uncertainty in oil exploration and production projects. Kallberg and Laurin 1997 Capital budgeting in a pharmaceutical company. Alvarez 1999 Discussion about optimal market exit and the evaluation of uncertain demand projects.

Pennings and Lint 2000
Input, capacity and adequacy options for multinational companies undergoing operations in a volatile exchange rate environment.

Castro 2000
Assessment of capital invested in thermoelectric generation projects in the Brazilian electric sector. Fuss et al. 2008 Portfolio analysis using real options for investments in markets and change uncertainties. Reniers et al. 2011 Real options for evacuation decisions in areas within the chemical industry. Szolgayová et al. 2011 Portfolio analysis using real options for energy investments. Figure 2. List of authors per year and their real options theory applications. locati ons. For a possible expansion, it would be necessary to set up a permanent distributi on center with a considerably high investment value. If the company decides to reduce the operati on in the new locati on, this local distributi on center would become, consequently, inacti vated, and the operati on in the region would be carried out by a distributi on center in another distant locati on. This would negati vely impact the operati ng margin.
Hence, the primary objecti ve of the analysis is to evaluate the impact of real opti ons method used in the investment under analysis. For this purpose, an assessment will be performed fi rstly using the discounted cash fl ow method. Then, the same investment will be analyzed using the real opti ons method. As seen in Figure 3, the real opti ons assessment method employed follows previous works of  and consists of four steps:  The fi rst step consists in discounti ng the projected future cash and fl ow projecti ons using a rate that refl ects the risks ti ed to the project. The cash fl ow is used to identi fy the actual generati on of project value, once Damodaran (2002) points out that book values do not demonstrate the actual outf lows and infl ows to shareholders.
The second step encompasses the elaborati on of the event tree considering the degree of project's uncertainty. For this, it is necessary to esti mate the project's variance, which can be done in three ways: (i) using the variance of the projects already carried out that resemble the project under analysis; (ii) using project esti mates of other companies operati ng in the same sector and assigning diff erent probabiliti es to diff erent market situati ons; (iii) esti mati ng the cash fl ow of the project in each case and esti mati ng the variance in relati on to the present value (Damodaran, 2002). For this study, the fi rst opti on will be adopted, since the company already has a portf olio of other similar projects.
For the constructi on of the event tree, the initi al value is multi plied by the upward [u] and downward [d] movement factors given by the following formulas: (1) ( 2) where, σ is the esti mated project volati lity.
Aft er the constructi on of the event tree, there is the third stage of the analysis, which corresponds to the incorporati on of fl exibility aspects. Firstly, the values were all converted to dollar. The dollar-real quotati on was $1.00 to R$ 3.12 by the ti me the study was conducted. This study considers three fl exibiliti es: (i) to expand the operati on in 100%, with additi onal investment of $ 641,025.64; (ii) to reduce the operati on by 40%, with a gain of $ 128,205.00; (iii) and to disconti nue the project, with a gain of $ 240,385.00. The next step corresponds to the calculati on of the risk-adjusted probability, given by: ( 3) where r is the risk-free interest rate.
Using the risk-adjusted probabiliti es, the decision tree must be constructed with the inclusion of the opti mal management fl exibiliti es at each node. The analysis of opti mal choices should be made starti ng at the fi nal nodes. Then, the fi nal value of the project is calculated, composed of the value without managerial fl exibility plus the value of the opti on: This fi nal value obtained is then compared to the present value of the project obtained through the discounted cash fl ow method.

RESULTS
The cash fl ow esti mati on of the project was based on the company's business model, using a standard model developed by the project department for the analysis of this type of investment. Figure 3 shows the cash fl ow esti mati on for 5 years. The model is monthly updated, with assumpti ons found in data from previous and similar projects. Furthermore, the risk-free rate considered is 14.4%, and the values found for "u" and "d" are 1.492 and 0.670 respectively. Using this data, we have the following resulting event tree in Figure 5: After the construction of the event tree (Figure 5), the decision tree was obtained with the inclusion of the three managerial flexibilities. The three managerial flexibilities included are: to expand by 80%, with the additional investment of $641,025.64; contracting, with a reduction of 60% and a gain of $128,205.00; and discontinue, with a gain of $240,385.00. The optimal decisions were obtained in each node, from the end nodes, as seen in Figures 6 to 10: aligned with the monthly forecast model of the company. The model contemplates more than 200 variables and has a very high level of assertiveness.
After the cash flow calculations, the project assessment was carried out through the discounted cash flow. The perpetuity used in the calculation experienced a 5% growth. The weighted average cost of the capital adopted follows other similar projects conducted inside the company (18.40%). The NPV obtained was $1,361,655.61 and the IRR was about 40%.
For the real options analysis, it is necessary to define the project's volatility. As described in the methodology, a 40% degree of volatility was adopted in this study, which can also be       The opti mum choices and the results at each moment are illustrated by the decision trees in Figures 11 and 12: Finally, the calculati on of the project's fi nal value was made encompassing the opti ons value which was priced using the binomial method. The result obtained was $1,579,845.90. The diff erence between the new present value calculated through the real opti ons theory and the present value obtained by the discounted cash fl ow shown in Figure 13 is $218,185.00, which corresponds to an increase of 16.02%. The results show that the opti on to expand investments is presented several ti mes in the decision tree. The decision to contract is the less advantageous one. The NPV increase of the project was signifi cant (16%), which, in the company's case, could be decisive for its inclusion in the investment portf olio. In this way, it is important to adopt methods that take into account managerial fl exibiliti es, especially in the case presented, given the great volati lity and dynamism of the retail segment.

DISCUSSIONS AND CONCLUSIONS
The use of the real opti ons theory allowed a bett er assessment of the possible returns achieved along the years in which the project takes place. The traditi onal method of project fi nancial viability analysis through discounted cash fl ow underesti mates the value of the project analyzed and does not consider possible alternati ves for the investor, such as expanding or disconti nuing the project. The value of the project's fl exibility is $218,185.00, which corresponds to a 16% increase over the amount calculated by the discounted cash fl ow. In this study, however, it was investi gated a new approach for the same situati on and, according to the results presented, it has been found that the implementati on of the real opti ons method for investment analysis and assessment is the best opti on for the case. The results obtained are an indicati on of this methodology to industrial businesses that are relati vely volati le and that require a certain degree of fl exibility in order to burgeon, such as the case of the retailing sector. Although investments in this sector may be more related to short and medium-term decisions, the opening of new units in new locati ons has a characteristi c of being a long-term process and usually demands a great level of attenti on. Furthermore, the process characterizes a long-term decision, since it requires massive investments and usually takes more ti me to get fully established. Therefore, given the nature of the project management, it is bett er for the business as a whole to incorporate fl exibility and adaptability. In additi on, the dynamism of the sector makes it appropriate to incorporate fl exibility into the analyzes.
Finally, the outcome of this study is in accordance to previous studies (Kallberg and Laurin, 1997;Alvarez, 1999;Reniers et al., 2011;Szolgayová et al., 2011). These works indicate a clear advantage of the Real Opti ons Method use over others (in the case, the discounted cash fl ow method was compared), because it allows more extreme decisions to be taken. Differently from these previous studies on Real Options (e.g. Klingebiel and Adner, 2015;Trigeorgis and Reuer, 2017), the main objective of this work was to contribute to the literature with a more practical view of the subject. Furthermore, future studies are recommended to analyze the applicability of the Real Options method in other types of industrial businesses, with different levels of accuracy and demand for flexibility. It is believe that the incorporation of this method in other environments can bring substantial contributions in terms of the type of business that are more suitable and, consequently, more likely to benefit from the implementation of the Real Options Method.