STRATEGIC FLEXIBILITIES: VALUATION OF A COMPANY WITH THE APPLICATION OF THE REAL OPTIONS THEORY

Goal: In this paper, a binomial model is proposed to evaluate the option of deferring an investment and expanding the operational scale of a forest-based company that will perform the de-duplication of Pinus sp. and will market packaging for storage and transportation of vegetables. Design/Methodology/Approach: The proposed model measured the options of deferring an investment and expanding the operational scale of the forest-based company. In this perspective, the model of evaluation used was the binomial model in discrete time using the Real Options. Results: It was observed that the inclusion of management flexibilities in the decision making process has added value to the investment project; therefore, the project of investments in real assets proved to be economically feasible. Limitations of the investigation: The studies that address the corporate finance framework based on real data are a restrictive factor, due to the lack of collaboration of companies, that is, the availability of information that is usually classified. Practical implications: The study was based on the real data of a company; therefore, it can be adopted as a stimulus to the Real Options approach to the decision making of entrepreneurs or researchers. Originality/value: The focus of the study was to contemplate the managerial flexibilities of an industry of the secondary sector of the Brazilian economy, which performs the unfolding of wood, demonstrating the innovation of the technique approach used in this market segment.


INTRODUCTION
Successful economic and market development requires the application of traditional methods in business and the application of new modern methods adapted to the contemporary market needs, requirements and conditions. The application of this methodology consists of evaluating the suitability, efficiency and feasibility of the project, in order to make a final conclusion on whether a proposed investment project is profitable. These methods are mostly based on the comparison of the necessary expenditures and the derived revenues (Dikareva and Voytolovskiy, 2016;Rajnoha et al., 2014;Sujová and Marcineková, 2015).
The most widely used methodology is the discounted cash flow (DCF) analysis, which discounts the balances between costs and revenues within the estimated duration of the investment. The prominent reasons for the usage of DCF techniques by the vast majority of companies are their consideration of time value of money as well as the ability of assessing the wealth of an organization in a period of time. Hence, the cash flow can recognize whether the investment project has successfully sustained over this time interval or not, showing the profits and loss during the project life (Batra and Verma, 2017;Iyer and Kumar, 2016;Sdino et al., 2016;Oliveira and Zotes, 2018).
However, the DCF analysis needs accuracy and it assumes that the scenario and the project life are fixed. According to this approach, the manager will not be able to react to environmental changes and may be in danger of bankruptcy. Therefore this method fails to capture the uncertainties, not proposing the accurate consideration of variations in the environment. It was Myers (1984) who first acknowledged these limitations with standard DCF approaches when it comes to valuing investments with significant options (Kokkaew and Sampim, 2014;Pivorienė, 2015;Ugwuegbu, 2013;Braga et al., 2018).
To overcome the lack of flexibility integration of traditional capital budgeting methods, one can apply the analysis of real options. The technique of applying real options to the evaluation of projects includes factors that the classical methodology -in some cases -has left aside, such as flexibility, uncertainty and volatility. Through the inclusion of these components, one can reach a much more dynamic analysis, because the real options theory views investments as rights but not obligations, conducting the investment's values to be maximized (Čirjevskis and Tatevosjans, 2015;Hammann et al., 2017;Tanaka and Montero, 2016).
Thus, a real option is the right, but not the obligation, to undertake an action, at a predetermined cost, called the exercise price, for a pre-established period: the life of the option. Real options can be divided into investment timing option, operational flexibility option, abandonment option, and growth option. These options can be taken during the execution of the project with the aim of maximizing results or eliminating losses (Copeland and Antikarov, 2002;Lupo and Reiner, 2017;Santos et al., 2015).
From this perspective, a stochastic process becomes appropriate to address a problem that requires good uncertainty modeling as it helps increase confidence in the results. One of the most important basic notions of stochastic processes is Brownian Motion (also called a Weiner process) or Geometric Brownian Motion (GBM). In economic applications the GBM have extensively been used, because it is a common specification to model asset values (Bastian-Pinto, 2015;Carlander et al., 2016;Chávez-Bedoya, 2016;Sampim et al., 2017;Schachter et al., 2016).
For this modeling, it is possible to use the binomial model. The most used binomial valuation model corresponds to the proposal developed by Cox et al. (1979), which is usually adopted for the real options analysis and is based on the creation of recombinant binomial trees that determine the paths that the price of the asset evaluated follows until the time of expiration. The main idea of the binomial model is to replace a continuous distribution of share prices by a simple two-point discrete distribution, keeping the technical framework on a very low level (Bock and Korn, 2016;Cuervo and Botero, 2014;Perufo et al., 2017;Yuen et al., 2013).
The Binomial model proposal is attractive from the academic point of view because it maintains a precise economic view of the traditional models of options pricing and can be easily understood. Thus, the use of more dynamic valuation methodologies, which can add value to investment projects, are necessary. Therefore, the aim was to develop a binomial model to evaluate the economic viability of a forest-based company's investment project in real assets, including managerial flexibilities for postponing the investment and expanding the operational scale.

RESEARCH METHOD
The study was developed from the technical-economic coefficient of a forest-based company to be installed in the Southwest region of the State of São Paulo, whose activity will consist of log breakdown of Pinus sp. with diameters from 14 cm to 30 cm and a maximum length of 2.5 m, with the capacity to saw 950 cubic meters of wood per month. From lumber the packaging for storing and transporting vegetables will be produced.
The economic mission of the company will be the unfolding wood, according to the National Classification of Economic Activities (CNAE), registered under the class number 1610-2. In additi on, the Simplifi ed Nati onal Tax (Simples Nacional) with annual billing of one million US dollars was used to calculate the company's operati ng performance for the processing of the manufacturing industry's tax acti viti es. Hence, a single amount will be 19.00%, which will be distributed in taxes: 13.50% Corporate Income Tax; 10.00% Social Contributi on on Net Income; 28.72% Contributi on to Social Security Financing; 6,13% Social Integrati on Program; 42.10% Employer Social Security Contributi on (Employer Pension Contributi on -EPC).
Monetary values were expressed in US dollars (USD), using the exchange rate of R$ 3.6913 according to informati on provided by the Central Bank of Brazil (Banco Central do Brasil, 2018) on 06/11/2018. The Weighted Average Capital Cost (WACC) was considered, as it was adjusted to the risk-free rate as proposed by Copeland et Anti karov (2001), according to Equati on 1. In this way, the discount rate of the investment project was determined as the minimum rate of return (MRR), i.e. the rate of return required by investors to bring cash fl ows to the present date. (1) where: k e is the cost of equity; k d is the cost of debt; k p is the market value of equity; k t is the market value of debt; Tc is the corporate tax rate.
Thus, a risk-adjusted discount rate, obtained through the Capital Asset Pricing Model (CAPM), was esti mated, according to Equati on 2.
(2) where: K is the risk-adjusted discount rate; R F is the risk free rate (10 years T-Bills rates); β is the systemati c risk; β BR is the country risk premium.
Considering the parameters of Equati on 2, the 2.84% riskfree interest rate issued by the United States Department of the Treasury was used because it was reasonably integrated with the world capital market. Furthermore, the beta value of 1.2 was considered as a measure of the systemic risk of the forest products, and the expected market return in the S & P Global Timber & Forestry Index was 3.42%. The country risk premium of 2.61% was weighted, in accordance with the arithmeti c mean of the last ten years of the Emerging Markets Bonds Index -EMBI + Br.
The discounted cash fl ow (DCF) which determines the value of the company, was considered as conventi onal, that is, it presents a single capital expenditure (CAPEX) followed by several operati ng cash infl ows, taking into considerati on a horizon projecti on of 10 years, which allows us to predict the behavior of revenues and operati onal expenditure (OPEX) in a plausible way. However, for the cash fl ows not contemplated in this horizon, the perpetuity was assumed to have a zero growth rate; therefore, it was considered that the company has an infi nite fi nancial life.
Consequently, it was possible to calculate the net present value without the managerial fl exibiliti es, that is, the traditi onal net present value according to Equati on 3.
( 3) where: T is the durati on of the project; t is the ti me period in which costs and revenues occur; i is the minimum rate of return; CF t is the cash fl ow for t periods; l is the value of the initi al investment.
The standard deviati on of the returns, that is, the project volati lity, was calculated using the methodology proposed by Brandão et al. (2012), which evaluates the volati lity in the fi rst year, conditi oned to the expectati ons of the present values in the other years of the project, assuming that the variati ons in the cash fl ows are independent, and that the volati lity is constant throughout the horizon projected. Knowing that the uncertainti es aff ect the relevant project variables and their impact on returns can be determined by means of the stochasti c processes' simulati on, it was assumed that the fi xed asset price volati lity follows a GBM described in Equati on 4, as predicted by Dixit et Pindick (1994).
(4) P is the price of the asset at ti me ; μ is the rate of growth of (drift ); σ is volati lity; dz is the increment of a Wiener process; Thus, the volati lity, i.e. the percentage standard deviati on of the project return, was calculated (Equati on 5), as Copeland et Anti karov (2001)  To calculate the present value of the project at instants t = 0 and t = 1, we used Equati ons 6 and 7, respecti vely.
Moreover, it was assumed that the main uncertainty which aff ected the project's value was the revenues obtained with the commercializati on of the packages, that followed a lognormal distributi on with mean α and standard deviati on σ, ensuring that only positi ve values were obtained, considering the assumpti on of the GBM. The simulati on was performed using the soft ware @Risk Copyright © 2017 Palisade Corporati on (Palisade, 2017), with the generati on of 100,000 pseudorandom numbers.
The project has managerial fl exibiliti es to postpone the investment, which is equivalent to a call opti on of american stocks and to expand the operati onal scale, also formally equivalent to a call opti on. In this way, investment in fi xed assets could be exercised in the second year, while the opti on to expand by 30% the operati onal scale could be carried out in the tenth year of the project if the company made the investment.
In order to evaluate the real opti ons, the binomial model of Cox et al. (1979) was applied. This model predicts the behavior of the price of the underlying asset, that is, the physical project that is under evaluati on, and can assume two values in the future, according to the up and down multi plicati ve factors.
The values of the multi plicati ve factors, represented by up (u) and down (d) factors are based on the volati lity of the underlying asset and the expirati on ti me and were obtained by means of Equati on 8 and 9, respecti vely. where: ∆t is the ti me variati on that corresponds to the size of the step between the nodes of the binomial tree; e is the constant 2.71828...; with u > d.
To determine the probability of occurrence of these movements, the risk-neutral probability (p) was used. Thus, the investment project has the probability p of increasing its value, or the probability q = 1-p, of decreasing this value, calculated according to Copeland et Anti karov (2001), described in Equati on 10.
(10) Thus, with the multi plicati ve factors and the calculated probabiliti es, it was possible to construct the binomial tree in discrete ti me using the dynamic programming language soft ware DPL 9 (Syncopati on, 2018).
In view of this, once the present value modeling of the project has been defi ned and structured, the inclusion of managerial fl exibiliti es was made by inserti ng the decision instant in which the project value functi on is maximized. The present value of the project in the binomial tree was calculated in each node of the tree, considering whether or not the company manager should perform the opti on to achieve the opti mal result.
The real opti on value () is given by the diff erence between the present value of the project with the included fl exibiliti es and the traditi onal present value, derived from discounted cash fl ow analysis. Consequently, the net present value expanded () was obtained, using the traditi onal net present

Real option analysis
Aft er identi fying all relevant opti ons, it is possible to employ the real opti ons methodology by constructi ng a binomial model (Hartmann and Hassan, 2006). One of the most important factors for this analysis is the volati lity, by explaining the behavior of the asset price object, so the investment project's volati lity under analysis was 56.57%. In additi on, the other parameters intrinsic to the applicati on of the Real Opti ons Theory, such as multi plicati ve factors (up and down), risk-adjusted rate, objecti ve probabiliti es, and monetary values demanded by managerial fl exibiliti es, are presented in Table 1. Moreover, as the project can be postponed in the second year of its useful life and the operati onal scale can be expanded by 30% in the last year, a decision node that models the managerial fl exibility that exists in the project is inserted, as shown in Figure 2.
According to Copeland et al. (2002), when decision intersecti ons are added to an event tree, it becomes a decision tree. Hence, with the inclusion of management fl exibiliti es, the present value of the updated investment project was obtained through the decision tree. It was observed that the decision tree includes bold lines that highlight the opti mal decision, being a more intuiti ve tool for the decision maker.
Decision trees are tools that can be used for making financial decisions, providing an eff ecti ve structure in which alternati ve decisions and the implicati ons of taking those decisions can be laid down and evaluated; besides that, they also help to form an accurate, balanced picture of the risks and rewards that can result from a parti cular choice (Carlsson and Fullér, 2003).
With the valuati on of the opti on, the project's present value is presented in the node referring to Year 1 (Figure 3). In this sense, the present value of the project obtained from the real opti ons was USD 3,823,634.20, with a standard deviati on of USD 88,163.81.1, the minimum amount of USD 378,346.80, and the maximum value of USD 364,414,971.70.
value and the real opti on value, by means of Equati on 11, in agreement with Trigeorgis (1995). (11)

Economic and financial analysis
Capital expenditures (CAPEX) were accounted in the initi al investment year in the amount of USD 862,079.93, and, when weighti ng OPEX, depreciati on and the taxes calculated by the traditi onal investment analysis method, allowed determining that the present investment project value was USD 1,756,218.11. However, when applying the simulati on by the Monte Carlo method, it was found that this resulted in the average value of USD 1,757,801.67 and a standard deviati on of USD 782,512.53, confi rming the presence of volati lity (Figure 1). Thus, the Monte Carlo simulati on proved to be an eff ecti ve tool for advising the decision maker and helping in corporate risk management (Laudares et al., 2019).
The project's volati lity is the uncertainty over expected project returns from period to period (Godinho, 2006). Therefore, parti cularly the price of the asset object will depend on this volati lity, that is, the level of uncertainty of the project to be weighed in the model. It should also be noted that the probabilisti c distributi on resulted in an asymmetry of 0.3019 and kurtosis of 3.1295. These values indicate the lognormality of the data, thereby, it is assumed that the returns of the project are normally distributed, so that the value of the project has lognormal distributi on and can be approximated through a binomial mesh (Brandão and Dyer, 2009).
The NPV with the fl exibiliti es of deferring and expansion was higher when compared to the traditi onal NPV; thus, it was possible to quanti fy the right to exercise the real opti ons, suggesti ng that the investor could exercise them because it allowed maximizing the value of the opportunity of investments. In this way, according to Luehrman (1988), the corporate investment opportunity is a call opti on because the corporati on has the right, but not the obligati on to acquire something.
The decision tree demonstrates the scenarios for decision making, that is, an opti mal decision to be made by the investment project manager. In this sense, it is observed in Figure 4 that all paths demonstrate the feasibility of making an investment, since in 100% of the investment opportuniti es it is possible. Nonetheless, only 40% of the opportuniti es are interesti ng for the decision maker to expand the operati onal scale, indicati ng that it is subject to the risk of witnessing an environment that is not conducive to the intensifi cati on of acti viti es.
Furthermore, it can be seen that the managerial fl exibiliti es increased the value of the project, considering that the value generated by the real opti ons was USD 2,067,416.09, and thus, the USD 2,921,554.27 were obtained. However, it is important to note that the increase in economic parameters may have been infl uenced by the volati lity of the investment project. According to Miller et Waller (2003), the real opti ons and the expected present value of the project are positi vely infl uenced by the volati lity. In view of this, the greater the volati lity of the investment project, the higher the expected value and the lower the likelihood of executi ng the expansion opti on. Therefore, the level of uncertainty has been shown to exert a positi ve eff ect on the price of the underlying asset.

CONCLUSION
The traditi onal cash fl ow methodology is a widely used investment valuati on technique. However, this technique fails to capture the managerial fl exibiliti es present in investment projects inserted in dynamic environments. This paper presents a model for the evaluati on of investments under the real opti ons perspecti ve, considering the opti ons for postponing and expanding the producti ve scale of a forest-based industry in the second and tenth year of the project life, respecti vely.
The binomial model is considered a simple and straightforward way of evaluati ng real opti ons, in additi on to demonstrati ng the opti mal scenario for decision making. Thus, it was observed that the postponement opti on would not be used, because in all the paths generated by the decision tree, the opti on to invest proved viable. Regarding the expansion opti on, it is suggested that in 60% of the opportuniti es the expansion should not be performed.
The volatility present in the investment project corroborated the presence of uncertainty to be weighed in the evaluation of investments, and it is one of the fundamental parameters as input of the binomial model. By means of the sensitivity analysis it was concluded that the volatility has a direct relationship with the expected present value, i.e. the higher the volatility value, the greater the present value. However, for the analyzed condition, there will be a decrease in the probability of expanding the operational scale.
There had been an increase of 231% in investment project when compared to the estimated calculation based on the traditional investment analysis methodology.