Assessing the Economic Impact of Forest Management in the Brazilian Amazon Through Real Options Analysis

Abstract

Reduced-impact logging is a key aspect of sustainable forest management in the Brazilian Amazon. Real Options Analysis (ROA) improves the evaluation of certified projects, increases their value, and supports investor confidence. This study evaluates the economic viability of a forest management investment project in certified areas of the Brazilian Amazon, using ROA to incorporate uncertainty and managerial flexibility into the decision-making process. The analysis focused on an Ombrophilous Dense Forest in its first cutting cycle, with 30 species of diameter at breast height ≥ 50 cm and a projected activity period of 30 years. Timber value was modeled using the mean reversion motion, and a binomial decision model was applied, incorporating options such as deferral, abandonment, and interruption. The deferral option should be exercised with a 100% probability, both in the joint calculation scenario and in separate analyses, highlighting the significant value of this managerial flexibility. In addition, when analyzed using ROA, the value of the project increased by 105% (USD 91,784,176) compared to the traditional net present value approach. The forest management investment project in the Brazilian Amazon is economically viable and the application of ROA reveals significant value added, demonstrating the importance of incorporating flexibility into investment decisions.

1. Introduction

The economic issue of reduced-impact logging is one of the three fundamental principles of sustainable forest management in the Brazilian Amazon. Economic analysis of sustainable forest management projects, guided by the Forest Stewardship Council and the Programme for the Endorsement of Forest Certification, can be more accurate with real options. These certifications guarantee that forest management is environmentally responsible, socially equitable, and economically viable. Real Options Analysis quantifies the added value of these projects, thereby enhancing investor confidence.

The tropics contain the vast majority of the Earth’s biodiversity. The Amazon Rainforest is the largest tropical forest in the world. It plays an important role in regulating the climate and provides a variety of ecosystem services and timber and non-timber forest products [1,2,3].

In the Amazon region, the ongoing conversion of old-growth forests to agricultural and cattle-ranching areas has led to extensive fragmentation of the landscape. The data on deforestation in the Amazon are remarkable in both scale and speed. By 2021, the Amazon had experienced a 17% reduction in its natural vegetation cover [4,5]. In addition, between 2015 and 2021, the period following the signing of the Paris Agreement, the rate of deforestation increased, reaching 12.45% per year [6].

In developed countries, there is an increasing emphasis on socially and environmentally responsible entrepreneurship, but there is still a predominance of businesses in the world where the result of the activity is an increase in financial resources due to environmental degradation [7].

A significant proportion of logging in the Brazilian Amazon is illegal. Illegally harvested timber reaches the market at a lower price than the product from managed areas, so legal timber cannot compete on price with illegally harvested timber. Thus, there is an urgent need to support the development of new models towards a sustainable forest economy, such as sustainable forest management (SFM) [8,9,10,11].

SFM can be defined as a set of techniques for the sustainable extraction of forest resources that generate social, economic, and environmental benefits while minimizing impacts on the remaining vegetation. Forest certification systems have been developed to certify that SFM meets these requirements and to assure consumers of the legal origin of forest products [12,13,14,15,16,17].

The concept of SFM stems from the notion of sustainable development, which has gained worldwide recognition since the late 1980s, popularized by the Brundtland report Our Common Future [18,19]. In Brazil, two important laws have contributed to this transition to SFM. The first, which created the National System of Protected Areas (Law 9985), approved in 2000, distinguishes areas of sustainable use from strictly protected areas. The second, approved in 2006, regulates the management of public forests for sustainable production (Law 11284), which includes forest concessions [20,21].

Over time, the Brazilian government has outlined three main strategies to put SFM into practice: (i) timber management by logging companies in forest concessions; (ii) the use of timber and non-timber forest products by smallholders and communities; and (iii) the sale of environmental services provided by forests, particularly carbon [22].

Studies of SFM to date have tended to focus on biophysical impacts, with inadequate coverage of direct wood recovery and the amount of waste in forest harvesting processes and their impacts on carbon sequestration potential and biodiversity, as well as economic impacts [23].

In order to reap the economic benefits of SFM, it is essential to view reduced-impact logging as an investment project. This requires a thorough economic analysis to verify its viability and economic return. In Brazil, however, little is known about the economic viability of forest management, which is one of the main bottlenecks.

Economic viability is a critical aspect of forest management, and the achievement of good results depends on the consideration of several factors. Characteristics such as species composition, distance between the managed areas, volume of timber harvested, price of standing wood, yield and costs associated with timber processing in sawmills, and the place of consumption are determining for the financial viability of investing in forestry concessions in Brazil [24,25].

Controversial results have been obtained in the economic evaluation of investments in SFM projects in the Amazon using deterministic methods. In the Peruvian Amazon, [26] found that the strip clear-cutting system (or Palcazú Forest Management System), with harvest cycles every 40 years, is not economically sustainable by calculating the net present value at the time of a second harvest in two clear-cut strips.

In the Brazilian Amazon, ref. [27] verified that the financial evaluation of the investment using deterministic methods showed viability, since the net present value method showed a positive value. Although it was considered financially viable, the authors considered the result presented insufficient for decision-making, since it did not take into account the risks and managerial flexibility throughout the investment, which does not represent the reality of the market.

Unlike traditional techniques, such as net present value, often used in economic studies of forest management, which are based on static assumptions about the future, Real Options Analysis (ROA) is an economic approach that represents a novelty in the scientific literature because it incorporates the uncertainty inherent in financial returns, allowing for a more flexible approach to decision making at specific future points in time, i.e., adjusted as new information emerges, such as market conditions, technological changes, or new economic policies [28,29,30,31,32,33,34].

Thus, ROA derived from financial options is a promising technique that allows managers to make necessary adjustments throughout the life of the project, thereby capturing managerial flexibility and improving the value of investment projects placed in dynamic environments such as SFM [35,36,37,38,39].

The concept of a real option was first proposed by [40,41]. It can be defined as a non-mandatory action that allows the investor to take initiative, such as deferring, terminating, restarting, or abandoning an investment project, based on market indicators. Thus, ROA is a valuation technique that takes into account the potential value of future opportunities offered by a stock and allows for accurate valuation of stocks in relation to the investment project [42,43,44].

In the forestry sector, the ROA was first applied to the valuation of natural resource reserves [45]. Subsequently, it was applied in other forestry studies, including the estimation of the conservation value of an urban park [46], the valuation of Pinus planted forests [47,48,49], Eucalyptus [50,51,52], and agroforestry systems [53].

In a typical Brazilian Amazon concession for commercial timber harvesting, ref. [54] found that ROA can increase the market value of the concession by at least 30%, while the traditional technique cannot quantify a profit and therefore discourages forest management. Since forest concessions are public resources, the market value of a forest concession given by ROA becomes an important element for the bidding process and for government policy on forest concessions.

Thus, in the context of SFM, ROA can maximize the economic and ecological value of forests by enabling adaptive decisions that meet sustainable objectives. For example, the use of selective logging and rotational harvesting not only preserves biodiversity, but also captures economic viability by incorporating the flexibility needed in a dynamic, long-term scenario [55,56,57].

The scientific literature suggests additional strategies for maximizing the economic benefits of implementing SFM in natural forests and accelerating the transition to low-deforestation rural development: (i) generating additional income associated with the voluntary carbon credit market; (ii) payment for ecosystem services associated with SFM projects; (iii) differentiated tax management; (iv) legal designation of public lands; (v) expansion of the protected area network; (vi) land tenure certification; and (vii) economic incentives for legal timber trade [58,59,60].

Although the scientific literature shows the consolidation and support of the sustainability paradigm, the integration of multiple dimensions (social, environmental, economic) and disciplines is still needed to achieve a more holistic understanding of SFM in the region. In this sense, scientists can play an important role in establishing a set of guidelines that recognize the role of SFM in mitigating global economic and climate change [61].

The objective of this study was to determine the economic viability of SFM investment projects in certified areas of the Brazilian Amazon, using ROA as a tool to deal with the uncertainties associated with timber valuation and the flexibility inherent in the investment options. In addition, the study aimed to verify whether the flexibility in managing the deferral, interruption, and abandonment options affects the economic value of the investment project when using the mean-reverting methodology to model the project value.

The article is structured as follows. First, the theoretical background shows that ROA could ensure the economic viability of an SFM investment project in the Brazilian Amazon. Then, the survey data and methods used to calculate the real options are presented. Finally, the results, limitations, and possible extensions of ROA are discussed.

2. Materials and Methods

2.1. Study Area

Forest management data were collected in the Saracá-Taquera National Forest, located in the Brazilian Amazon biome, at geographic coordinates 1°48’ S and 56°36’ W, in the state of Pará (Figure 1).

In April 2017, the area was certified by the Forest Stewardship Council and the Institute of Forest and Agricultural Management and Certification. The total certified area of SFM, comprising 26,897.96 hectares, was divided into 30 annual production units. Among these, one annual production unit with 1413 hectares of Ombrophilous Dense Forest in its first management cycle was subjected to analysis.

This SFM involved a series of activities, including forest inventory, planning, road and patch opening (Figure 2A), tree felling (Figure 2B), log planning and cutting (Figure 2C), log cubing and identification (Figure 2D), log transport to the forest yard (Figure 2E), and finally, the evaluation of the cutting cycle in the annual production unit (Figure 2F).

In the selected annual production unit, trees of 30 species with a diameter at breast height greater than or equal to 50 cm were harvested. The trees had straight or slightly twisted, cylindrical, or slightly eccentric trunks, and were free of obvious defects. The minimum utilization rate was 60%, and the total volume of timber harvested was 19,415 m³, with a total gross revenue of 9,468,922.26 USD (Supplementary Materials—Table S1), corresponding to an average of 1.76 m³ per log, as authorized by the exploration permit number 1015.2.2021.40576.

2.2. The Steps of the Investment Decision Model for SFM Projects

The uncertainty of timber value will affect the investment decision in SFM projects, i.e., it is difficult for investors to accurately evaluate SFM investment projects. In order to solve these difficulties, this article proposes a real option model for an SFM project in the Brazilian Amazon. The investment decision model is divided into ten steps as shown in Figure 3.

2.3. Cash Flow

The investment planning horizon was projected to be 30 years, in line with the legal concession period for the management area [62]. The cash flow was identified as unconventional [63] and was structured to include all relevant financial components over the planning horizon.

2.3.1. Main Components

The gross revenue was calculated based on the quantity of round timber transported from the storage yard in the forest to the primary consumer and the value according to the classification of the State Treasury of Pará [64]. The relevant costs and expenses included in the income statement are taxes, certification fees, and operating costs.

Taxes: Tax on the Circulation of Goods and Services, social charges, Brazilian Forest Service contract guarantee costs, production fees, and the Chainsaw Tax from the Brazilian Institute of Environment and Renewable Natural Resources (a two-year Brazilian national tax).

Certification Fees: Forest Stewardship Council and Chain of Custody taxes and fees.

Operational Costs: These included financial reports on labor costs, truck and machine parts, field tools, fuel, transportation of supplies, office supplies, food, telecommunications, and other miscellaneous expenses.

2.3.2. Financial Analysis

The financial analysis included Earnings Before Interest, Taxes, Depreciation and Amortization, Earnings Before Interest and Taxes, income tax provision, Social Contribution on Net Profits provision, and Net Operating Profit After Tax, including depreciation and capital expenditures. Finally, free cash flow to the company and discounted cash flow were considered to provide a comprehensive and clear view of the financial components of the project, whose components are detailed in the Supplementary Material (Table S2).

2.4. Deterministic Input

The traditional net present value was used as an input for ROA. This approach provided an estimate of the present value of the expected cash flows, allowing a static assessment of the project’s economic viability. The traditional net present value was estimated using the methodology outlined in Equation (1) [65]:

$${NPV}_{trad}={\sum }_{i=1}^n{\displaystyle \frac{{CF}_n}{{(1+r)}^n}}-I$$

(1)

where ${NPV}_{trad}$ is the traditional net present value, $CF$ is the cash flow calculated through the difference between revenues and costs in the $n$ period considered, $r$ is the investment project discount rate, and $I$ is the initial investment.

The Weighted Average Cost of Capital was used as the minimum rate of return ($r$) that the project had to generate to recover the cost of investment, weighted by the average cost of equity and third-party capital resources used. The equity was calculated using the Capital Asset Pricing Model, according to market behavior plus country risk (Equation (2)), as adapted from [66]:

$$r=w_{equity}\ast (r_{rf}+{\beta }_i\left(r_m-r_{rf}\right)+r_c)+\left(1-T\right)\ast w_{debt}\ast r_{debt}$$

(2)

where $w_{equity}$ is the equity interest percentage, $r_{rf}$ is the risk-free rate, ${\beta }_i$ is the volatility of the rate of return of the Brazilian forest sector, compared to the rate of return of the market, $r_m$ is the market rate of return, $r_c$ is the country risk, $T$ is the income tax, $w_{debt}$ is the percentage of third-party equity, and $r_{debt}$ is the rate of return on debt capital.

The volatility of the rate of return for the forestry sector was obtained by using the unleveraged average beta coefficient of listed companies in Brazil. The following companies were included in the analysis: Companhia Melhoramentos (São Paulo, Brazil), Dexco S.A. (São Paulo, Brazil), Eucatex S.A. Indústria e Comércio (São Paulo, Brazil), Klabin S.A. (São Paulo, Brazil), and Suzano Papel e Celulose S.A. (São Paulo, Brazil), according to [67]. In order to obtain a more accurate representation of the financial position of the companies, the total debt of the companies was excluded from the calculation of the beta coefficient.

The proportion of assets financed by debt of the respective companies and an income tax factor of 34.00% were taken into account, as these factors allow for the capture of tax benefits resulting from the payment of interest, according to B3 S.A.- Brasil Bolsa Balcão [68].

The releveraged beta applied was 0.45, and deleveraging was weighted by the debt-equity ratio of 56.82%. This ratio was obtained by taking the average of the ratio of onerous liabilities to total assets of listed companies in Brazil. It should be noted that with beta coefficients below one, market risk can be considered low.

The risk-free rate of 5.10% was calculated using the geometric mean of the annual return on 10-year U.S. Treasury bonds [69] for the period between 1 February 1962 and 18 September 2022. The geometric mean was chosen as the most appropriate indicator of long-term returns because it allows for the reduction in trends according to [70].

The country risk was calculated using the geometric mean of the historical series of Brazil risk and the Emerging Markets Bond Index Plus, published by J.P. Morgan [71], resulting in a value of 3.93% for the period between 1 April 1994 and 18 September 2022. The expected return of the market portfolio was determined to be 10.21%, based on the S&P 500 Index, which has tracked the 500 most influential companies over the last 10 years [72].

The market risk premium was estimated at 5.11% using the risk-free interest rate and the expected rate of return on the market portfolio. This resulted in a cost-of-equity rate of 11.25%. The opportunity cost rate was estimated at 7.52% per year, taking into account the equity ratio of 43.18% and the third-party capital ratio.

2.5. Investment Project Volatility

In the Amazon region, timber is classified into three main groups: noble, red, and white timber. Noble timber is highly prized for its durability and aesthetic appeal, with high prices reflecting high demand. Red timber is characterized by its deep color and resistance to fungal attack, making it well-suited for outdoor applications. White timber, on the other hand, is characterized by its lightness and adaptability. Figure 4 shows the historical price development of these timbers, expressed in U.S. dollars, the dominant currency used in international trade.

The only source of uncertainty in the investment project was identified as the selling price of round timber at the consumer unit, calculated using historical series. Historical analysis of round timber prices shows that after deflation using the Internal Availability General Price Index, prices tend to stay within a defined range, suggesting stability and the potential for mean reversion.

As noted by [73], Geometric Brownian Motion is often used to explain the price dynamics of financial assets. However, single-factor mean reversion models are postulated to be more effective in capturing the behavior of most commodity prices. Despite the random fluctuations observed in commodity prices in the short run, they tend to converge to an equilibrium level in the long run.

Accordingly, the Dickey–Fuller unit root test [74] and the Kwiatkowski, Phillips, Schmidt, and Shin test [75] were applied using the Gretl software version 2024c to determine the optimal model for characterizing the behavior of data (Supplementary Materials—Table S3).

The only source of uncertainty in the investment project was the selling price of timber at the consumer unit, which was calculated using the historical series. The uncertainty was modeled according to the mean reversion model, which is characterized by a Markov process with random oscillation over time around a mean value. The logarithm of the log price was measured as a one-factor Ornstein–Uhlenbeck process (Equation (3)), as defined by [76]:

$$d{X}_t=k\left(\overline{X}-X_t\right)dt+\sigma dz$$

(3)

where $X_t$ is the logarithm of the round timber price, $k$ is the mean reversion coefficient, $\overline{X}$ is the logarithm of the long-term average price, $\sigma$ is the volatility, and $dz$ is the Wiener process that describes the oscillation of the timber price.

To estimate the parameters associated with the Ornstein–Uhlenbeck process, the equation presented in reference [77], adapted from reference [78], was used. This is shown in its discrete form in Equation (4):

$$X_t=X_{t-1}{e}^{-\eta ∆t}+\overline{X}\left(1-e^{-\eta ∆t}\right)+\sigma \sqrt{{\displaystyle \frac{1-e^{-2\eta ∆t}}{2\eta }}} N(0, 1)$$

(4)

where $X$ is the stochastic variable, $\overline{X}$ is the long-term average of the stochastic variable, $t$ is the instant of time considered, $e$ is the Euler’s constant (base of natural logarithms), $∆t$ is the time interval, and $\eta$ and $\sigma$ are parameters to be obtained with regression adjustment.

Following the methodology described in [79], the parameters of Equation (5) are estimated:

$$\ln \left(X_t\right)-\ln \left(X_{t-1}\right)=a+\left(b-1\right)\ln \left(X_{t-1}\right)+{\epsilon }_t$$

(5)

where $\mathrm{l}\mathrm{n}$ is the Neperian logarithm, and $a$ and $b$ are the estimated regression coefficients.

The regression fit of Equation (5) was used to estimate the parameters of the Ornstein–Uhlenbeck process (Equations (6) and (7)), as previously described by [80]:

$$\eta ={\displaystyle \frac{-\ln \left(b\right)}{∆t}}$$

(6)

$$\sigma ={\sigma }_{\epsilon }\sqrt{N}\sqrt{{\displaystyle \frac{2\ln b}{(b^2-1)}}}$$

(7)

where $b$ is the estimated coefficient of the regression, $∆t$ is the time interval, ${\sigma }_{\epsilon }$ is the standard error of the regression, and $N$ is the number of observations in the historical series.

The volatility of the investment project was weighted by the standard deviation of the random return sample (Equation (8)), as described by [81]. To generate 100,000 pseudorandom numbers, a Monte Carlo simulation was performed using the @Risk version 8.8.1 software [82], which calculates the options through a stochastic process:

$$Y=\mathit{ln}{\displaystyle \frac{{PV}_1}{{PV}_0}}=\mathit{ln}\left[ {\displaystyle \frac{\sum _{t=1}^n\frac{{CF}_t}{{(1+r)}^{t-1}}}{\sum _{t=0}^n\frac{{CF}_t}{{(1+r)}^t}}}\right]$$

(8)

where ${PV}_0$ is the sum in the base year (year 0) over the present values of all cash flows, ${PV}_1$ is the sum in the first year over the present values of all cash flows, and $r$ is the discount rate of the investment project.

The Monte Carlo simulation was used to generate a range of price scenarios, taking into account the variability and risks associated with historical timber price series. This approach reflected market uncertainty and potential fluctuations over time. The project return (Y) was conditioned on the modeling of the timber price, which was identified as the main source of project uncertainty. Therefore, the price was modeled stochastically using the RiskNormal function in the @RISK software, which meant that the gross revenue, which depended on both timber volumes and prices, also had stochastic variations.

The RiskNormal function generated random numbers from a normal distribution and required two parameters: mean and standard deviation. The mean was calculated based on the natural logarithms of the input values, while the standard deviation was adjusted according to the rate of variation. The EXP function was used to convert the results to real values, effectively modeling uncertainty.

The equation fitting parameters for the application of mean reversion models are detailed in the Supplementary Material (Table S4).

2.6. Calculation of Real Options

Following the methodology outlined in [83], the binomial tree model was used to account for potential fluctuations in the value of the investment project. At time step ∆t, two possible outcomes were identified for the investment project. After the time interval ∆t, the value of the project can either increase by an increase factor u with risk-neutral probability p or decrease by a certain factor d with probability q, where p + q = 1.

The factors $u$ and $d$ were calculated by applying the volatility of the investment project, the time step $∆t$, the risk-free rate $r_{rf}$, and the risk-free probability $p$ (Equations (9)–(11)) according to the methodology outlined in [84]:

$$p={\displaystyle \frac{e^{r_{rf ∆t }}-d}{u-d}}$$

(9)

$$u=e^{\sigma \sqrt{∆t}}$$

(10)

$$d={\displaystyle \frac{1}{u}}$$

(11)

American options are financial instruments that give the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price at any time before or on the expiration date of the option [40]. In order to increase flexibility, the American options of deferral, abandonment, and interruption of the investment project were included in accordance with the methodology proposed by [85]. The calculations were performed using Decision Programming Language version 9.0 software [86].

The costs associated with the options were treated as inputs to the ROA modeling. These parameters influenced strategic decisions over the planning horizon. It should be noted that unlike modeling outputs, such as the flexibility-adjusted present value, the option costs represented the costs associated with the alternatives analyzed.

Thus, the option to postpone the start of the project from the first year to the following year was considered, with an associated cost of USD 2,071,232. The option to abandon the project, also calculated in year zero, was assigned a value of USD 2,071,232. The interruption option was considered in years five and ten of the planning horizon, both with a value of USD 748,071. The abandonment option was considered in year 15 of the planning horizon with a value of USD 569,252 (Figure 5).

It is important to emphasize the importance of the timing of incorporating flexibility in the form of options into the investment project to ensure effective and responsive management. The goal of forest management is to minimize damage to the environment while maximizing revenue. This is achieved by implementing reduced-impact logging techniques that allow for continuous evaluation and adjustment every five years. This approach is adapted to the specific conditions and needs of the ecosystem and the community involved, thereby promoting sustainable forest management.

In the calculation of the combined options, the deferral option allowed the compound exercise of successive real options, abandonment, and interruption, as it is considered a pseudo-American option. The abandonment and interruption real options were included in the investment project as independent real options due to the hierarchical relationship between real options when combined.

According to the methodology proposed by [87], the value of an investment project with flexibility (${NPV}_{exp}$) can be defined as the value of the deterministic project, i.e., without options, calculated by the traditional net present value (${NPV}_{trad}$), plus the Real Option Value (ROV) provided by the incorporated options (Equation (12)):

$${NPV}_{exp}={NPV}_{trad}+ROV$$

(12)

3. Results and Discussion

3.1. Deterministic Input

The initial cost of the forest management investment project in the certified area of the Brazilian Amazon was USD 2,071,232. This was accompanied by a present value of USD 46,877,451 and a traditional net present value of USD 44,806,218. The positive traditional net present value for the forest management investment project in certified areas of the Brazilian Amazon demonstrates the economic viability of the project. As indicated by [88,89,90], the traditional net present value is a metric that quantifies value creation for investment project managers and is therefore a valuable decision-making tool.

3.2. Investment Project Volatility

The volatility of the project, as measured by the mean reversion model, was 6.12%. The maximum and minimum present values were USD 49,216,588 and USD 25,960,335, respectively, with a mean of USD 34,004,590 and a standard deviation of USD 2,214,942.

The study of market price volatility is becoming increasingly important for risk management, asset pricing, and portfolio management [91,92,93]. Consequently, the development of models and techniques for predicting market price volatility is an important area of research. It is well known that the greater the volatility of an investment project, the greater the market fluctuation and, consequently, the greater the economic return.

This Monte Carlo simulation approach provided a more accurate estimate of cash flows over time, capturing uncertainty and helping forest managers make better decisions. Simulations over 30 years with 100,000 iterations helped identify potential outcomes and demonstrate the economic viability of SFM projects. Combining stochastic price modeling with cash flow analysis provided a complete picture of the financial situation, helping to assess the risks and opportunities of the investment.

Regarding the application of the mean reversion model to the analysis of the price behavior of primary commodities, such as wood in logs, ref. [94] points out that there is still no comprehensive consensus on the random process that best fits the observed price fluctuations. The behavior of the value of primary commodities can be attributed to the motion of reversion to the mean [95,96,97]. These authors emphasize that while the prices of these commodities may change randomly in the short run, they will eventually reach equilibrium due to supply and demand.

In practice, a scarce product has a high value. Its production is increased to generate more profit for its investors. With an increased supply of the product, the product is no longer scarce, and its price is reduced. The price reduction causes a decrease in production because it is no longer attractive to investors, making the product scarce again and starting the cycle of supply and demand all over again.

The challenge in identifying the optimal single-factor process, Geometric Brownian Motion or the mean reversion model, can be attributed, for example, to the sample size of the historical data, as shown by [98]. Despite the relatively limited historical series data on the price of round timber, spanning less than 20 years, the tests applied yielded consistent results, indicating that the data were best described by the mean reversion model process.

3.3. Calculation of Real Options

The deferral option at year zero had an expanded net present value of USD 44,906,725 and a Real Option Value of USD 100,507 when based on parameters u = 1.06 and d = 0.94 and a risk-neutral probability p = 0.90 and its complement q = 0.10. The probability of exercise was 100%. The deferral option allows managers to wait for new market information, giving them more certainty at the outset of an investment. In the context of investment projects, as shown in [99,100,101], this option is invariably exercised due to the non-payment of dividends to the managers involved.

Consideration of the abandonment option at the beginning of the project indicated an expanded net present value of USD 44,806,218, a Real Option Value of USD 0.00, and a 100% probability of exercising the option not to abandon the project. At year 15, the Real Option Value for abandonment was USD 1.00, with a 0.00% probability of realization. Given the partially reversible nature of the project, i.e., the possibility of recovering part of the initial investment, the possibility of abandonment was duly considered.

This abandonment option is related to the residual sales value of the assets, as described by [102,103,104], such as machines, truck combinations, and installations. In this way, the amount to be recovered in the case of abandonment of the investment project did not provide the economic return of the permanence of the investment project, indicating its continuity. This result differs from that obtained by [27], where the option to abandon the investment was exercised in 72.47% of the nodes of the option tree.

The interruption option in years five and ten, both with a Real Option Value of USD 0.00, also resulted in an expanded net present value of USD 44,806,218. This outcome was observed with a 100% probability, indicating that these options would not be exercised. The combined ROA resulted in a total Real Option Value of USD 46,977,958 and a total expanded net present value of USD 91,784,176 (Figure 6).

The interruption option was not exercised because revenues exceeded management costs in all simulated scenarios. The interruption option requires critical decisions to be made, including whether to hire or pay salaries during the interruption period, whether to maintain essential expenses such as royalties, and even whether to delay management in the licensed area. Accordingly, its inclusion in strategic decision-making processes can be critical to the economic analysis of forest management.

The combined real options showed a value that was 4.61% higher than that of the deferral option, which was calculated separately. Compared to the conventional net present value, the real options contributed an additional 4.84% to the value of the investment project. As stated by [105,106,107], the calculation of real options in conjunction can elucidate the optimal strategic trajectory and inform managerial decision making.

The optimal strategic course of action, as indicated by the ROA, was to postpone the implementation of the investment project for a period of one year after the originally planned date. Since there were no indications that the options to abandon or suspend the project would be exercised, the project remained unchanged in the following years. In accordance with this strategy, the investment project for forest management in certified areas of the Brazilian Amazon will reach its optimal value for investors.

The ROA is fundamental for evaluating investments in forestry projects because it provides a robust framework for decision making in the face of uncertainty. These results underscore the importance of flexibility in managing investments in dynamic environments such as the Brazilian Amazon. In addition, the inclusion of abandonment and interruption options enriched the valuation of the project, which was 105% higher than the valuation obtained using traditional methods. This approach not only illustrates the importance of incorporating uncertainty into forest resource management, but also suggests that adaptive strategies can lead to more robust and sustainable financial outcomes.

In the works of [108,109], the authors explain the advantages of ROA over the conventional approach to economic analysis. Thorsen [110] found that the value of forest investments can be maximized by allowing managers to adjust harvesting rates to market conditions, which is particularly beneficial in volatile and price-sensitive timber markets. Using a hypothetical southern pine plantation in the US state of Georgia, ref. [111] showed that ROA increased the estimated value of projects by up to 48% as carbon credit prices fluctuated.

According to [112,113], a green financial system, including taxation and financial management mechanisms, needs to be created for a more active introduction of soil conservation and decarbonization processes, as foreseen in SFM in the production of goods and services. However, if these rates are too high, they could harm companies, especially in developing countries. Therefore, approaches such as ROA are needed to account for these flexibilities.

This approach allows an agile response to environmental variability, such as climate change and water stress, which are fundamental aspects of forest resilience. Managers are able to postpone harvesting during market downturns or adjust the intensity of management in response to environmental and market conditions. This flexibility, which is particularly important in long-cycle forests, adds value to the project and is an effective strategy for mitigating risks associated with price fluctuations [114,115].

Therefore, in our work we have observed that the opportunity cost of the investment proves to be highly sensitive to the uncertainties of the modeled value and the flexibilities that make up the investment project scenarios, as confirmed by [116,117,118].

In practice, it is critical that managers adopt strategies that allow them to stay informed about the options available. For example, the decision to postpone a project can be based on an analysis of price trends and timber demand, allowing greater precision in the timing of the investment. In the worst-case scenario, if the project becomes financially unviable, assessing the residual value of assets allows managers to recover part of the investment by selling equipment, thereby minimizing losses.

In addition, variable cost analysis makes it possible to calculate the additional costs of operating under adverse conditions, providing a solid basis for deciding whether to temporarily suspend operations until conditions improve. These practical applications help link financial results to tangible benefits for managers, highlighting the importance of more detailed and strategic use of combined options.

The results of this study have the following policy implications. First, greater political support is needed for the development of SFM projects in the Brazilian Amazon. To achieve sustainability, which includes economic issues, it is necessary to develop new methodologies that can reduce the costs of implementation and certification in these areas.

Second, SFM policies and projects in the Brazilian Amazon that are implemented sequentially should also be subject to evaluations of their economic performance. The present study considered only one annual production unit in the Saracá-Taquera National Forest, located in the Brazilian Amazon biome, so its implications are limited. By evaluating other Brazilian SFM projects and policies, it will be possible to reach more significant conclusions and implications about the economic viability of SFM through ROA. Nevertheless, the economic viability demonstrated here can be used as a benchmark for future comparisons.

4. Conclusions

This investment project of forest management in certified areas of the Brazilian Amazon is economically viable (USD 91,784,176) and shows an increased value of 105% when analyzed through the lens of ROA.

It is recommended to exercise the deferral option with a probability of 100%, calculated jointly and separately. The abandonment and interruption options do not contribute to the economic return of the management’s investment project in the certified areas of the Brazilian Amazon.

Using mean reversion as a modeling technique for the value of the investment project under the ROA configured with the combined options, the Real Option Value is estimated to be USD 46,977,958.

Since ROA is not a widely used methodology in forest management for economic analysis of investment projects, this work can be used to assist forest managers in risk analysis and decision making.

Although ROA is a useful tool for assessing economic viability, some limitations of this study should be considered when interpreting the results. Other sources of uncertainty in addition to the timber price, such as the stochastic project discount rate and variation in the volume of timber harvested, were not tested and could potentially affect the viability of the investment project.

Further studies are recommended to examine the relationship between investment options and market conditions to identify patterns and trends that can better inform timing decisions. In addition, variations in timber demand and forest composition found in other biomes should be considered to better analyze real options in forest investment projects.