A Real Options Approach to the Valuation of an Investment in Eucalyptus

A Real Options Approach to the Valuation of an Investment in Eucalyptus M. Ricardo F. Cunha1∗and Dalila B. M. M. Fontes2† 1Lancaster University and Universidade Cat´olica Portuguesa Accounting and Finance Department, The School of Management Lancaster University LA1 4YX Lancaster, U.K. [email protected], phone:+ 44 15245 93660 2Faculdade de Economia da Universidade do Porto and LIACC Rua Dr. Roberto Frias, 4200-464 Porto, Portugal. [email protected] Abstract This paper models optimal tree harvesting decisions using real options theory. In the problem considered, we must find the optimal eucalyptus harvesting timing in order to maximize the expected cash flow. The following specificities of the eucalyptus forest must be incorporated into our model: (i) trees younger than seven years old do not fit the industrial requirements of the pulpwood producers; (ii) trees older than fifteen years have a diameter that is too large for its industrial processing; and (iii) eucalyptus trees allow for two rotations, since the trees planted at the beginning of the project are suitable for two cuts. After the first cut the eucalyptus trees grow again, allowing for a second cut without replantation. Options path dependency is then observed, since the moment of exercise of the first option determines the time interval in which the second may be exercised. In addition, we also consider the option to abandon project and the option to convert land to another use. The option value is estimated by solving a dynamic programming model. The basic idea is to approximate the price by a binomial distribution and then establish a discrete-valued binomial lattice of possible future selling price values. Results are reported for a case study in the Portuguese eucalyptus forestry. Key words. Forestry Investments, Real Options, Binomial Lattice, Dynamic Programming. ∗Corresponding author. The author would like to thank FCT the financial support through a scholarship. †The author would like to thank FCT the financial support through project POCTI/MAT/61842/2004. 1 1 Introduction In the past few years large investments in the paper industry have been made in Portugal, which lead to an increase in the demand for raw materials and inputs to the paper production process. Hence, a growth in the forest area dedicated to the production of eucalyptus globulous, which is unanimously considered to be the tree species whose wood seems to be most suitable for paper production was observed. The number and size of investment projects (and the land used) in the production of eucalyptus globulous, as an input to the paper industry, has increased largely. However, as most investments in natural resources, these projects are not simple to undertake since optimal investment decisions tend to be far from obvious. This happens, due to the flexibility and uncertainty that characterize such decisions. Traditionally, forestry investment decisions have been analyzed by using Discounted Cash Flow (DCF) techniques. Given their inability to account for flexibility, these approaches tend to systematically undervalue investments. DCF techniques are based on the assumption that future cash flows follow a constant pattern and can be accurately predicted. The project uncertainty, which may arise from the uncertainty about costs, selling prices, weather and legal conditions and flexibility, given to managers to react to changing conditions, is dealt with only superficially (Morck, Schwartz & Stangeland 1989). Another disadvantage of DCF is that it is linear and static in nature. It also assumes the project to be either irreversible or if reversible only decisions of now-or-never are allowed (Dixit & Pindyck 1994). Net Present Value (NPV) takes the project risk into consideration by discounting expected cash flows to the present moment. Using this decision process, all projects with positive NPV are undertaken, as they provide an “effective” growth in the wealth of the investor (or market value of the firm). The NPV, by not accounting for managerial flexibility, provides an underestimate of the project value, relative to real options. Therefore, when there is an option element in an investment, traditional DCF methods may result in wrong project valuation and hence inadequate decisions, see e.g. Pindyck (1991) and Dixit & Pindyck (1994). Only in the seventies applications to natural resources management have been known (Henry 1974, Arrow & Fisher 1974). Traditionally, studies addressing real options in a forest context have applied a single option approach (Malchow-Mollera, Strangeb & Thorsen 2004). However, this study goes beyond since we consider two rotations. Therefore, we have to decide when to harvest having in mind that a second harvest is possible. In addition, we also consider other options such as land conversion to another use and project abandonment. In this work, the main objective is to develop a methodology that allows for the valuation of the investment in eucalyptus forest for paper pulp production, considering the managerial flexibility inherent to the process. We apply real options to value a forestry investment. Results are provided 2 for a case study involving the investment in eucalyptus pulp production for the Portuguese paper industry, one of the most developed in the world. In this case study, two scenarios are considered: one where eucalyptus wood is sold to pulp and paper companies (basis problem) and another where vertical integration is considered, i.e. wood is processed into white paper pulpwood, which is then sold (extended problem). 2 Literature Review In eucalyptus forest investments, the starting point is that the owner of the forest holds a call option1, i.e. an option to buy timber at an exercise price given by the cost of cutting the timber. The forest option is similar to what in the finance literature is called an American option2, since it can be exercised at any moment in a given time interval. This interval is given by the period during which the wood is suitable for pulp and paper production. Up to date, not many studies have addressed forestry investments using a real options perspective. Morck et al. (1989) developed a contingent claims analysis of a long-term investment in renewable resource investments. Their model values a forestry lease and determines the optimal timing to harvest the timber. The value of the lease is considered to be the value of an option to cut down the trees at the best possible timing. The timber selling price and the inventory of timber are stochastic processes that follow geometric brownian motions. Zinkhan (1991) proposes a Black-Scholes type of approach for the valuation of the land use conversion option when valuing timberlands. The conversion option represents the ability of the timberland owner to convert the land use from timber to some other alternative use and was modelled as an European option rather than an American one. In the work by Bailey (1991) a model is proposed to value an agricultural producer considering optimal shutting and reopening and volatile output and demand. However, in what concerns forestry, the model is built only for productive trees with periodical (e.g. annual) harvest. This characteristic of the model makes it useless for our purpose of valuation of forestry investment in eucalyptus for paper pulp production, where after two cuts the asset is “worthless” for the paper industry. Abildtrup & Strange (1999) analyze the decision to convert a natural or semi-natural forest into Christmas tree production, when groundwater contamination is irreversible and future returns on non-contaminated groundwater resources and Christmas tree production are uncertain. It is concluded that conventional 1An option is the right, but not the obligation, to take some action in the future under specified terms. A call option gives the holder the right to buy a stock at a specified future date (maturity) by a specified price (exercise or strike price). This option will be exercised (used) if the stock price on that date exceeds the exercise price. 2An American option differs from a European option since the former can be exercised at any time up to the expiration date, while the latter allows for exercise only at expiration date. 3 expected NPV analysis may not lead to an optimal decision rule. It is shown how the option to postpone conversion and acquire new information should be included. Yin (2001) discusses harvest timing, land acquisition, and entry decisions combining forest level analysis and options valuation approach. Most of the studies addressing real options in the forest investment context have applied a single option approach. However, exceptions can be found in literature. Some authors consider additional problem features, while others consider more than a single option. For example, Malchow-Mollera et al. (2004) include temporal and spatial arrangement of harvests. These authors consider that constraints upon harvesting options on adjacent forest stands are imposed and examine the optimal harvest rules under adjacency restrictions and uncertainty. They conclude that the costs of adjacency constraints tend to increase with uncertainty and that the optimal harvesting strategies become rather complex due to the involved stochastic variables. Duku-Kaakyire & Nanang (2004) developed a forestry investment analysis where four management options are considered: delay of reforestation, capacity expansion, investment abandonment, and a compound option obtained considering simultaneously all three previous options. The models developed are evaluated on a standard binomial lattice. The authors solve an example with which they show that DCF techniques value the investment as unprofitable, consequently rejecting it. Real options, however, show the investment to be highly valuable. 3 Problem Description The investment decision under consideration must include four main options: the option to cut down the trees; the option to postpone or defer the trees harvesting until the price or quantity is favorable; the option to convert the land to another use; and the option to abandon the project. These options are all considered simultaneously. In this work, the inventory of wood is considered to be a deterministic process, that follows a known growth pattern depending on the region under consideration, the time since last cut (or plantation), and the rotation. Also, an obviously very important factor for the decision making is the paper pulpwood selling price, since it determines the main positive cash flow. The price is stochastic and it is assumed to follow a geometric brownian motion. This is further discussed in Section 4. The investment decisions When the tree is mature, the landowner possesses the option to cut down the trees and receive the potential cash flow. On the other hand, such a decision may be postponed if price and/or 4 wood inventory conditions are not favorable. This option is similar to a financial option on a stock, where the underlying asset is the amount of wood in the land and the strike price is the cost of cutting the trees and logging the wood. However, the investment process in eucalyptus is normally composed of two rotations (production cycles). The trees planted at the beginning of the process are suitable for two cuts - after the first cut trees regrow, permitting a second cut without replantation. Regarding the timing of cut, the characteristics of the wood that could be extracted from trees which are up to 7 years old do not fit the requirements of the industrial producers of pulpwood. The same happens after 16 years of growth, when the diameter of the trees becomes too large for its industrial processing and the fiber in the wood is not of the required standards. The investor in eucalyptus holds two interdependent options to cut down the trees, as the time of exercise of the first option determines the time window during which the second option may be exercised. Although the frame of the time window is known to be 9 years, the time window temporal location for the second cut option depends on the timing of the first cut. Furthermore, the expected payoff to be received is given by the sum of the first and second harvesting expected cash flows. Given the path dependency observed, the cash flow received from the second harvesting depends upon the timing of the first harvesting. This dependency leads to a multiplicity of possible paths and strategies, as can be seen in the state transition diagram given in Figure 1. In this diagram we have represented the time tand the elapsed time since last cut or plantation xt, with a 2-years step interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xt=17 xt=15 xt=13 xt=11 xt=9 xt=7 xt=5 xt=3 xt=1 t=10 t=8t=6 t=4 t=2 t=0 Figure 1: State transition diagram: 2-years step interval. The cash flow to be received from harvesting the trees depends on the cutting period - since the quantity of wood, although known, evolves through time - and on wood market price and future value expectations. Moreover, the decision of cutting the trees in the first rotation must 5 consider not only the immediate cash flow, but also the expectation of the cash flow from the second rotation. In our analysis, the eucalyptus forest investor is assumed to hold the land. Therefore, at any moment in time holds the option to abandon the project and put it aside, or receive an estimated value from converting to an alternative use. Activities like tourism and hunting have increased the demand for forest land and hence, its value. This alternative value (or capacity to abandonment without a loss greater than the initial investment) must then be considered in the valuation of eucalyptus forest investment. 4 Methodology The solution approach developed consists of a dynamic programming model which is evaluated on a discrete-valued lattice. The uncertainty of the underlying risky asset, wood or paper pulp selling price, is modelled through the use of a standard binomial lattice. In this approach, the stochastic variable (the selling price in our case) is assumed to be governed by a geometric diffusion, which implies that at each period there is only one constant growth/decay rate. If this is assumed, a natural way of obtaining a valued-lattice for the stochastic variable is to discretize it through a standard binomial lattice, see Figure 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 2: A lattice discretizing selling price. A node of price value Pi tcan lead to two nodes with their values being given by Pi+1 t+1 =uP i t and Pi−1 t+1 =dP i twith probability pand q= 1−p, respectively. The probability of reaching each of these nodes is the usual equivalent martingale measure used in the binomial option pricing model of Cox, Ross & Rubinstein (1979): p=(1 + rf)−d u−dand q= 1 −p, (1) where rfis the risk free interest rate over the interval ∆t,u=exp(σ√∆t), and d=exp(−σ√∆t). 6 It should be noticed that, as ∆t→0 the parameters of the multiplicative binomial process converge to the geometric brownian motion. 4.1 Decision and state variables The selling price variable Pi tis modelled as a stochastic variable, which follows a binomial process, as explained. In terms of decisions, as previously described, there are basically three types: to cut the trees, delay trees cutting, and abandon project or convert land to another usage. Hence, we define a decision variable Di tthat may assume three values according to the decision taken at time tand state (price index expectation) i. Di t=        1,if trees are cut, 2,if cut is postponed and investment maintained, 3,if project is abandoned or land converted to another use. The inventory of wood is considered to be a deterministic process, following a known growth pattern according to the considered region, the time since last cut (or plantation), and the rotation. The evolution of the time since the first cut (or plantation) xtis modelled as: xt+1 =   2,if Di t= 1, xt+ 1,if Di t= 2, and initialized as x1= 1. In the second rotation xtis initialized as 2 ,rather than 1 which is the case for rotation 1, since the trees are already there and thus, do not need to be planted. If the decision is to abandon the project or convert land to another use then the project ends. Regarding the inventory of wood, recall that the wood obtained from trees having up to 7 years of growth, as well as from trees with more than 16 years of growth, does not meet paper pulp industrial requirements. Let tcmin = 8 and tcmax = 16 be, respectively, the minimum and maximum time from plantation (or first cut) for the trees to be suitable for paper production. Let SQ(xt, i) be the inventory of wood that can be sold to paper pulp production. SQ(Xt, t) =        0,if xt< tcmin or xt> tcmax, Q1(xt),if xt=t, Q2(xt),if xt< t. where Q1(xt) and Q2(xt) are the inventory of wood extracted from cutting the trees which have been growing for xtyears at rotation 1 and rotation 2, respectively. 7 4.2 Dynamic programming model In each period, the forest investor must decide whether the forestry investment is going to be kept or not. Since both for project abandonment and land use conversion options only a lump sum is received, no subdivision is considered regarding these options. Harvesting the trees yields the owner a revenue from the selling of the wood but also involves costs Kincurred with cutting, peeling, and transporting the wood. Therefore, at period t, given the elapsed time since last cut or plantation xtand the price expectation index i, the net revenue πobtained if the cutting option is exercised is given by π(xt, i, t) = (Pi t−K)×SQ(xt, t)−K. (2) As said before, and in order to allow for earlier exercise, the valuation procedure begins at the last stage and works backwards to the initial moment. At the final lattice nodes, i.e. at the end of the project life t=T, all terminal nodes for each of the possible selling price values and elapsed time since last cut values are computed. For each of these nodes the project value is then given by the largest of (i) the final revenue plus residual value if a harvesting decision is still possible and exercised or (ii) the residual value. Here, by residual value Rwe mean the maximum between land value as it is and land conversion value. V(xT, i, T ) = max    π(xT, i, T ) + R, R. (3) The project value at each intermediate lattice node is computed by performing a backward induction process. The project value at intermediate steps is used to compute the project value at previous steps by using risk neutral probabilities. The decision made at any period (and state variable) has implications not only on the cash flow of the current period but also on the expected cash flow of future periods. Therefore, the optimal project value is obtained by maximizing the sum of the current period’s net revenue with the optimal continuation value considering all possible decisions. The optimal project value at period t, given the elapsed time since last cut or plantation xtand the price expectation index i, is then given by V(xt, i, t) = max Di t          π(xt, i, t) + pV (xt+1,i+1,t+1)+(1−p)V(xt+1,i−1,t+1) 1+rf,if Dt= 1, pV (xt+1,i+1,t+1)+(1−p)V(xt+1,i−1,t+1) 1+rf,if Dt= 2, R. if Dt= 3, (4) where π(xt, i, t) is the net revenue from the selling of the wood, rfis the real risk free interest rate, pis the risk neutral probability of an upward movement in the binomial price, and Ris the abandonment or conversion to another use value, whichever is larger. 8 The estimated project net value is then given by V(1,1,1) minus the initial investment3. Furthermore, the solution to this model also provides an optimal decision strategy for the forest manager. 5 Case study In this section, we start by giving a brief characterization of the Portuguese forest sector. Secondly, we describe the case study to which our model is to be applied, and end by presenting the results obtained. 5.1 Brief characterization of the Portuguese forest sector Portugal, due to its natural characteristics, possesses unique natural and ecological conditions for forestry production, which only recently have started to be methodologically and professionally managed. Regarding productivity, the net annual increment per hectare in forests for wood supply is about 4.6 m3/ha/year for pinus pinaster and 9 m3/ha/year for eucalyptus globulous, which is relatively small. This is mainly due to poor forest management and lack of modern techniques. Professional management and planning could bring a productivity increase of over 20% (Mendes 2004). Nevertheless, the average production of wood per year and hectare is much higher in Portugal than in the Scandinavian countries, which are known for their forestry products. In addition, the average length of the forestry production cycle is much shorter in Portugal (Goes 1991). The eucalyptus globulous, the main sub-species in our country and the one that possesses the best characteristics for paper production, is a fast growing tree. Originally biologically adapted to the poor soils of the Australian continent, in southern Europe, and Portugal in particular, this species grows very rapidly. Normally, the eucalyptus are cut with an age of 12 years and used to produce pulpwood, providing cellulose fibers that have remarkable qualities for the production of high quality paper. Forest and forest related industries are a key sector in the Portuguese economy, generating wealth and employment. The modernization of this sector can be a source of competitive advantage for the country, given the favorable ecological and natural conditions. Due to the development of the paper production industries, and the natural characteristics of the species, eucalyptus globulous has shown to be a key player in the sector, with a huge wave of investment 3The initial investment is considered to be given by the land acquisition costs, the plantation costs, and the cost of a maintenance contract for the full length of the project. 9 seems to be extremely high, and justifies the direct and indirect investment of paper industry companies, out of their core business of paper pulp production, into producing the inputs themselves. However, care should be taken in drawing conclusions since non negletable investments may be required for the vertical integration. C – Applying the optimal strategies In order to be able to find out how many years the trees are left to grow at each rotation we apply the optimal strategy provided by the dynamic programming model that considers all options, to randomly generated price data sets. By doing so, we are able to report not only on the project value but also on the number of years that trees are left to grow (for both rotations). The project value is compared to the one that would be obtained by the common practice of harvesting at years 12 and 24. Five data sets have been randomly generated according to the characteristics given in Table 5. The characteristics reported are relative to the price values used in the case study. Data Price values Set minimum maximum average 1 80% 100% 80% 2100% 100% 90% 3100% 100% 100% 4100% 100% 110% 5100% 120% 120% Table 5: Characteristics of the randomly generated data sets. We report on the project value (value), the years at which harvesting takes place, for both rotations (rot1 and rot2), and when abandonment takes place (aban) if it does take place. These values have been obtained by applying the optimal strategies devised both for the basis and the extended problems. These results are provided for the 5 randomly generated data set types. We also report on the project value obtained by performing the harvest at years 12 and 24. In Table 6 we report on the common practice project value (CPV) obtained by cutting at years 12 and 24 and by using the the all options dynamic programming model (value) for land residual values of 0, 5, 10, 20, and 30 thousand euros. As it can be seen, in most of the above situations the project is better when computed using the real options approach. Region 1, the north central cost, is the most appropriate area in the country for eucalyptus and thus, the most productive. Results for the other two regions are, however, similar. The timing at which rotation 1 and rotation 2 cuts take place are reported in Table 7. In this 16 Region 1 Data R=0 R=5000 R=10000 R=20000 R=30000 Set NPV value NPV value NPV value NPV value NPV value 1 29619 33492 32153 35492 34686 37492 39753 41491 44820 45491 212920 13813 15453 15813 17987 17813 23053 21813 28120 25812 329479 48288 32013 50288 34546 52288 39613 56288 44680 43565 448615 34748 51148 36748 53682 38748 58749 42748 63815 46748 543898 46278 46431 48278 48965 50277 54032 54277 59098 58277 Average 32906 35324 35440 37324 37973 39324 43040 43323 48107 43979 Table 6: Project value for region 1 when decision strategies are applied to specific data sets. table we also report the year at which the project is abandoned whenever abandonment indeed occurs. It should be noticed that the harvesting decisions typically take place after sixteen years Region 1 Data R=0 R=5000 R=10000 R=20000 R=30000 Set rot1 rot2 rot1 rot2 rot1 rot2 rot1 rot2 rot1 rot2 aban 1 16 31 16 31 16 31 16 31 16 31 0 216 31 16 31 16 31 16 31 16 31 0 316 31 16 31 16 31 16 31 16 0 30 416 31 16 31 16 31 16 31 16 31 0 516 31 16 31 16 31 16 31 16 31 0 Table 7: Cutting, postponement, and abandonment strategies for region 1 when decision strategies are applied to specific data sets. of growth for both rotations. This corresponds to the maximum time growth allowed. Thus, it can be concluded that the cutting option is exercised almost always at maturity, which allows for the investor to take advantage of the full tree growth. This fact is inconsistent with the common practice of most forest producers. The urge to cash in the value of their eucalyptus wood, typically made at the 12th year seems to be not optimal. 7 Conclusions In this work, we address the valuation of the investment in eucalyptus for the paper pulp industry by using real options theory. The modelling of the eucalyptus forest investment decisions using 17 real options theory allows valuation results more consistent with the normal positive investment outcomes than the ones obtained using traditional valuation techniques. The interpretation of the two possible tree cuts as two exercise interdependent call options on the wood allows us to introduce managerial flexibility in the forest management process. The inclusion of the abandonment and conversion to another use options increases the closeness to the real decision process. The evidence in this paper, through the application of the developed dynamic programming model to the eucalyptus investments in three Portuguese regions and for randomly generated situations, is consistent with the experts warnings of the under-valuation performed by traditional discounted cash flow techniques. A rationale for the vertical integration of paper pulp and wood production is also provided by the value added difference between the two problems considered. It is also shown that typical cut timing decisions are not consistent with cash flow maximization. According to our model, cutting should be almost in all situations performed at the end of the time interval when wood is suitable for paper pulp production. References Abildtrup, J. & Strange, N. (1999), ‘The option value of non-contaminated forest watersheds’, Journal of Forest Policy and Economics 1, 115–125. Alian¸ca Florestal (2002), Technical Internal Report: www.alflorestal.pt. Arrow, K. & Fisher, A. C. 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