Large-scale transformation of agricultural land to forests will reduce atmospheric carbon levels and may help mitigate dryland-salinity emergence. Carbon sequestration is an ancillary benefit of farm forestry, for which payments may provide landholders with an incentive to plant trees. Several approaches have been proposed for accounting for temporary carbon sequestration. In this paper, we investigate the "ideal" accounting system, where the forest owner would be paid for carbon sequestration as the service is provided and redeem payments when the forest is harvested and carbon is released back into the atmosphere. We demonstrate how discounting affects the net present value of the forest when carbon sequestration is taken into account under this ideal system. Not all carbon is released back into the atmosphere at harvest, however, since a large proportion may remain fixed in forest products for many years. Here, we compare the profitability of the forest under full redemption of credits at harvest, with the profitability under partial redemption of credits at harvest followed by annual redemption post-harvest as the carbon in durable forest products decays. The analysis is based on simulation of farm-forestry systems in south-eastern Australia.

Trees and other perennials can help mitigate dryland-salinity emergence. Although there is no doubt that trees can reduce watertable recharge rates, there are mixed messages on how effective they will be as a large-scale solution. In this paper we do not contribute to this debate. We assume that tree planting will be an effective alternative for salinity mitigation in some catchments and concentrate on the question of whether it will also be economically attractive. Particularly in low- to medium-rainfall zones, the long time lag between investment and returns in farm-forestry enterprises often makes this activity unattractive compared with alternative land uses, even at fairly low discount rates. Carbon sequestration is an ancillary benefit of farm forestry and can provide cash flow during early years of a plantation and hence assist in overcoming some of the obstacles to tree planting.

Trees remove carbon dioxide (CO₂) from the atmosphere during photosynthesis, store the carbon (C) in wood, leaves and roots and release the oxygen back into the atmosphere. However, carbon sequestered by trees is not removed from the atmosphere indefinitely, since trees die, are destroyed (e.g. by fire) or are harvested for forest products, and re-emit CO₂. A major concern with the use of forestry and other land-use sinks for greenhouse-gas mitigation is the temporary nature of carbon storage in vegetation and forest products, in contrast to emission reductions in the energy sector which are permanent in the sense that an avoided emission will never reach the atmosphere.

Several approaches have been proposed for accounting for temporary carbon sequestration in land-use change and forestry projects that are implemented to offset permanent emissions of carbon dioxide from the energy sector. Cacho, Hean and Wise (2003) describe some of these approaches and evaluate the incentives they provide for farm-forestry establishment. In this paper, we investigate further the "ideal" system, where carbon-sequestration credits and debits accrue in the year in which they are incurred. This accounting system is equivalent to the "stock-change" method that the Intergovernmental Panel on Climate Change (IPCC) has agreed to use in the implementation of land-use change and forestry projects under the Kyoto Protocol.

In this paper, we use the model to investigate how discounting affects the financial profitability of the forest for timber as well as for carbon. The analysis is conducted from the standpoint of an individual landholder deciding whether to engage in farm forestry for multiple products (i.e. timber plus carbon). It highlights the complex nature of the investment decision and demonstrates how discounting influences the design of viable projects. In the analysis, we compare the profitability of the forest under two different debit payment regimes for a range of discount rates.

The analysis we present is financial in nature. It assumes a single forestry cycle with either partial or total redemption of carbon-credit payments upon harvest. The traditional economic model based on an infinite planning horizon, as applied by Cacho, Hean and Wise (2003), is not considered here. We also abstract away from current climate policy and assume annual payments not constrained to specific Kyoto commitment periods.

The carbon-debit payment regime applied here involves full payment of debits at harvest where the credits received during the life of the forest are paid back to the investor in a lump sum. An alternative is also tested, with staggered payments where some debits are delayed post-harvest based on the decay rate of carbon in forest products. Although a large proportion of sequestered carbon is released back into the atmosphere when trees are harvested and when raw timber is processed and converted into forest products, the fate of the remaining carbon depends on its end use. This is illustrated in Figure 1. For example, carbon in durable forest products such as construction timber may be stored for decades, while carbon in less resilient products such as pulp and paper will be stored for far less time. As carbon decays in forest products, the value of carbon sequestration is offset by the value of post-harvest carbon emissions.

Figure 1. Carbon stocks and flows in forestry systems.

Indicative results from Tomich et al. (1997) for Acacia mangium in South Kalimantan, Indonesia, suggest that discount rates have a significant effect on the financial profitability of that system. In their study, Tomich et al. (1997) found that for discount rates above 15-20 per cent (approximately the real cost of capital in that country), Acacia mangium was unprofitable in the absence of carbon-sequestration payments. Including carbon credits with full debit payments at harvest increased the profitability of the system significantly, and at discount rates above 10-15 per cent, the value of carbon outweighed the value of timber. Acacia mangium is primarily a pulpwood species, however, and Tomich et al. (1997) found that if the half-life of pulp and paper products is 2.5 years, 80 per cent of the carbon value will be offset by post-harvest emissions at a zero discount rate, and that this effect diminishes as the discount rate increases.

In the following sections, we present a general model of a forest in the presence of carbon-sequestration payments and develop a forest-growth model applied to a Eucalypt system in Australia.

Consider the case of a landholder evaluating the prospect of planting trees and an investor who is willing to pay price p_b per tonne of carbon sequestered by those trees. The value of a forest stand at harvest in the presence of annual carbon-sequestration payments is:

where p (T) is the net present value of the forest harvested in year T after planting. The first term on the right-hand side represents the value of the timber harvest, the second term represents the sum of the annual payments for carbon sequestered in the interval (0, ...,T), c_E is the forest establishment cost, p_v is the price of timber which depends on the average stem diameter (d, cm) of the trees at harvest, and r is the discount rate. The state variables v(t) and b(t) are, respectively, the timber (stemwood) volume in cubic meters per hectare (m³/ha), and the carbon stock in forest biomass in tonnes of carbon per hectare (tC/ha). The last term in equation (1), D(T), is the debit applied upon harvest to account for the release of CO₂ into the atmosphere. With full debit this function is:

Equation (2) means that the total amount of carbon credits received during the life of the forest must be paid back (i.e. redeemed) to the investor by the landholder at harvest. This implicitly assumes that the contract ends as the sequestered carbon is no longer under the control of the landholder. This scheme is equivalent to the rental carbon market proposed by Marland, Fruit and Sedjo (2001).

The Chapman-Richards function has been shown to provide a good representation of growth in timber (stemwood) volume, v(t), and basal area, a(t) (Venn, Beard and Harrison, 2000, p. 75). So the growth of the forest stand can be represented as:

where the parameters q , a and b are determined by the species of tree, environmental conditions and forest management. Once parameterised, equation (3a) is used to estimate timber volume at harvest, while equation (3b) is used to estimate the average diameter of the trees:

where tph is the number of trees per hectare. The value of d is used to calculate the price received for the timber harvest:

 (5)

If wood density and the proportion of carbon in stemwood biomass are known, the stock of carbon in stemwood biomass (w(t), tC/ha), can be estimated as:

(6)

where δ is the carbon content per cubic meter of stemwood (tC/m3). The ratio of forest biomass to stemwood biomass depends on the type of tree and its age. Young trees generally have more branches and foliage relative to stem than old trees. This is represented in the following function, derived from the model of Kirschbaum (2000):

(7)

where b(t) is the total carbon stock in the standing forest biomass (tC/ha), and  are parameters determined by tree shape, and the remaining variables have been previously defined. Annual changes in the standing carbon stock can now be estimated by differencing:

(8)

This is the stock-change method defined by the IPCC.

Equations (2) (3a), (5), (7) and (8) are substituted into (1) for t=T to solve the carbon-accounting model. Only above-ground biomass carbon has been considered here; b(t) includes stem, branches, and foliage, but not carbon contained in the soil or roots. Including soil and root carbon will increase the stock of carbon that receives payment but will also increase the cost of measuring that carbon; this is discussed by Cacho, Wise and MacDicken (2002) and is not considered further in this paper.

Land-use scenarios and model calibration

Tree-growth parameters for equations (3a) and (3b) are presented in Table 1 for two sites in south-eastern Australia. These parameters were estimated statistically based on values reported by Wong et al. (2000) for Eucalyptus nitens (commonly known as Shining Gum). Site 1 has high rainfall and Site 2 has moderate rainfall. Further details about the sites are presented in Cacho, Hean and Wise (2003).
Observed and predicted timber volumes for E. nitens for the two sites are presented in Figure 2. It is obvious that the growth function (3a) provides a good fit to the data. However data were only available for trees up to 10 years of age; this means that predictions regarding the steady state which is reached after year 30 are uncertain. However, the predicted maximum volumes (given by  in Table 1) at steady state are plausible (843 m3/ha and 263 m3/ha for sites 1 and 2 respectively).

Table 1. Tree parameter values used in the model, estimated from data reported by Wong et al. (2000)

Base values for other parameters used in the numerical model are presented in Table 2.

The model was implemented for both Site 1 and Site 2 for the base parameter values presented in Tables 1 and 2, for a hypothetical project of 30 years duration (i.e. T=30) and discount rates between zero and 25 per cent.
 

Figure 2. Eucalyptus nitens growth at the two sites. Predicted and observed values for Site 1 (solid line and dots respectively) and Site 2 (dashed line and triangles respectively). Data from Wong et al. (2000).

Results

Figure 3 illustrates the effect of discounting on the net present value of the project for both sites, with full debit at harvest. As expected, the net present value of the timber harvest (given by the first term in equation (1) less the forest establishment cost) decreases as the discount rate increases. Timber returns eventually become negative at a discount rate of 10 per cent for Site 1 and four per cent for Site 2.

In contrast, the net present value of carbon sequestration (the sum of annual credit payments, given by the second term in equation (1), less full redemption at harvest, given by equation (2)) increases until it reaches a maximum (of $2166 for Site 1 and $784 for Site 2, at a discount rate of six per cent) and then decreases as the discount rate increases further. This hump occurs because discounting has less effect on the stream of credit payments than it does on the one-off redemption payment at the end of the project, for discount rates up to six per cent. This is demonstrated in Figure 4, where the value of credit payments initially decreases more slowly than the value of the debit payment. The hump is larger for the higher-quality site (Site 1) at which more carbon is sequestered (Figure 3).

Table 2. Base parameter values
 

* unitless coefficient.
Sources: a: Hassall and Associates (1999); b: estimated as wood density x C content of biomass = 0.7 (t/m3) x 0.54; c: calculated from parameters presented by Kirschbaum (2000); d: linear approximation to assumed data following discussions with Signor (2001, pers. comm.); e: assumed value following discussions with Signor (2001, pers. comm.); f: arbitrary value subject to sensitivity analysis.

Figure 3. Present value of profits for Site 1 (charts A and C) and Site 2 (charts B and D). The top charts are total profits (solid line) and profits from timber harvest (dashed line), and the bottom charts are profits from carbon sequestration (solid line).

Figure 3 shows that temporary carbon sequestration has a positive net value when discount rates are greater than zero, and that this value increases as the discount rate increases (up to a maximum), even when carbon payments are paid back in full at harvest. It also demonstrates that the project is unprofitable in the absence of carbon-sequestration payments for both sites at even conservative discount rates (above 10 per cent for Site 1 and above four per cent for Site 2). However, even with carbon credits, the project is unprofitable at discount rates above 14 per cent for Site 1 and above six per cent for Site 2 (Figure 3).
 

Figure 4. Present value of annual credit payments (solid line) and the one-off debit payment (dashed line) for Site 1 (chart A) and Site 2 (chart B).

The discount rates at which NPVs become zero in Figure 3 represent internal rates of return for the project. These values are 10 per cent and four per cent for timber alone (IRR_W), and 14 per cent and six per cent for timber plus carbon sequestration (IRR_P), for Site 1 and Site 2 respectively. IRR_W and IRR_P form the bounds of a “critical interval” of discount rates. Within this interval carbon payments “swing the deal” and make the project profitable (NPV≥0).

The critical interval is illustrated in Figure 5, by the shaded area, which represents the returns from carbon sequestration. At discount rates below IRR_W, the landholder will establish the forest for timber alone. Between IRR_W and IRR_P, the landholder will establish the forest if carbon payments are also received. Above IRR_P the landholder will not establish the forest because it is unprofitable.

Including carbon payments clearly increases the profitability of the project, and the value of carbon outweighs the value of timber at discount rates above eight per cent for Site 1 and above four per cent for Site 2. This is illustrated in Figure 6, where the two curves intersect. To the left of the intersection point timber is more valuable than carbon and this relationship is reversed to the right of the point.

Figure 5. Present value of total profits (solid line) and profits from timber harvest (dashed line) for Site 1 (chart A) and Site 2 (chart B). The shaded area represents the critical interval where carbon payments “swing the deal”.

Figure 6. Present value of profits from carbon sequestration (solid line) and timber harvest (dashed line) for Site 1 (chart A) and Site 2 (chart B).

Analysis of post-harvest emissions

Carbon decay in forest products can be described by its half-life, which is the time required for one-half of the carbon to decay before being released back into the atmosphere as CO₂.
Below, carbon in forest products is assumed to be released back into the atmosphere after harvest, based on a half-life of H years. Some carbon is lost in the process of harvesting and converting trees into forest products (recovery). The carbon stock remaining in forest products at a given point in time (f(t), tC/ha) is given by:

(9)

and the debit function (2) becomes:

(10)

where N is a suitably long planning horizon to account for the life of forest products (in this analysis assumed to be 30 years). This equation is substituted into (1) to obtain the results presented in Table 3. The recovery (R) is assumed to be 0.5, and a half-life (H) of 50 years is used for illustration. Some debits are therefore paid up-front at harvest, while the remainder are paid annually post-harvest as the carbon decays in the forest product (i.e. the redemption period is extended). In Table 3 this scenario is compared with the results under full debit at harvest from the previous section, which equates to a half-life of zero.

The value of carbon redemption is significantly lower when the half-life is longer (Table 3). This occurs because post-harvest debit payments are delayed and therefore more heavily discounted. The value of carbon redemption offsets the value of sequestered carbon (i.e. the gross carbon payment) by a smaller proportion when the half-life is longer. For Site 1, 42 per cent and 25 per cent of the value of the sequestered carbon is offset by debit payments within the post-harvest time horizon considered here, for the half-lives of zero and 50 years respectively, when r is five per cent. This effect diminishes as the discount rate increases, and is negligible (i.e. one per cent or less) for both half-lives when r is 25 per cent. For Site 2, these trends are similar. Although much of the carbon is returned to the atmosphere within 30 years of harvest, there is still a substantial benefit from carbon sequestration. When r is five per cent, net carbon benefits contribute 23 per cent and 28 per cent for Site 1, and 177 per cent and 153 per cent for Site 2, to the total profitability of the forest, for the half-lives of zero and 50 years respectively. Were the post-harvest time horizon extended for the analysis, a greater proportion of the sequestered carbon value would be offset by post-harvest emissions, and the benefit from carbon sequestration would be reduced.

Table 3 also shows that varying the timing of debit payments has a relatively insignificant effect on the total profitability of the forest, particularly at high discount rates. Although the forest is clearly more profitable at a discount rate of five per cent when H is 50 years, it remains unprofitable at discount rates of 15 and 25 per cent. This result holds for both sites.

Sensitivity analysis

We evaluated the effect of changes in the price of carbon and the duration of the project on the internal rate of return of the project (timber plus carbon sequestration, IRR_P). The model was solved for a range of carbon prices (ranging from $5/tC to $50/tC) and for two project lengths (20 years and 30 years).

Results are presented in Table 4, for both full debit at harvest, and delayed debit payments. As expected, increasing the price of carbon, increases IRR_P, since returns from carbon sequestration, and hence total profits, are higher at all discount rates. Increasing the project length reduces IRR_P. Timber returns are lower at all discount rates, because the growth of the trees is relatively unchanged but the harvest is delayed and hence more heavily discounted. In contrast, carbon returns are higher because discounting has more effect on the value of the one-off redemption payment at the end of the project than on the stream of credit payments. Nevertheless, total project profits are lower at all discount rates. Interestingly, the results are unchanged for delayed debit payments, for any value of N. This result is not investigated further here.

Table 3. Present values of various forest components for both sites ($’000)

Table 4. Internal rates of return (%) for timber plus carbon sequestration (IRR_P), with full debit at harvest, for both sites

We also evaluated the effect of changing the duration of the project on the internal rate of return of timber alone (IRR_W), in order to assess the sensitivity of the critical interval of discount rates over which carbon payments “swing the deal”. (Changing the price of carbon will obviously have no effect on IRR_W and was therefore not considered). Results are presented in Table 5.

Table 5. Internal rates of return for timber (IRR_W), with full debit at harvest, for both sites.

By comparing Tables 4 and 5, it is clear that increasing the project length expands the critical interval of discount rates over which carbon payments provide the incentive for the landholder to establish the forest. This effect is greater at higher carbon prices. For example, when carbon is $50/tC, carbon payments “swing the deal” when discount rates are between 15-23 per cent for a 20-year project, and between 10-21 per cent for a 30-year project, for Site 1.

Discussion

This paper presents a simple financial analysis of a farm-forestry enterprise that shows the conditions under which carbon-credit payments will provide an incentive to plant trees. A complete economic analysis was not presented, as we assumed zero transaction costs and ignored other benefits that may be provided by trees, such as biodiversity, water quality and erosion control. Mitigation of both salinity and climate change is likely to face very high transaction costs, particularly in the initial stages of market development, before the right institutions have evolved. So it is worth briefly reviewing the type of transaction costs that may be expected.

Dudek and Wienar (1996) developed a typology of transaction costs incurred in projects designed to mitigate emissions of atmospheric CO2. The typology comprises six categories. Cacho, Marshall and Milne (2002a,b) modified the typology slightly and added a seventh category. Their categories are: search costs, negotiation costs, verification and certification costs, implementation costs, monitoring costs, enforcement costs, and insurance costs. These papers also discuss the significance of fixed transaction costs for the competitiveness of smallholder-based projects compared to large plantation projects. Although their focus is on smallholders in Southeast Asia, the basic principles also apply to farmers, as compared with industrial plantations, in Australia.

The extent to which specific transaction costs affect farm-forestry operations intending to participate in carbon (and/or salinity) markets, depend to a large extent on the institutional structure available to facilitate information exchange and the design and monitoring of contracts between investors and landholders. This topic is outside the scope of the present paper, but it is an important subject that requires much more research.

Conclusions

In this paper, we developed a simple model of a Eucalypt system in Australia and found the conditions under which carbon-sequestration payments may make the forestry operation profitable. It is shown how discounting affects the profitability of the system for timber as well as for carbon. There may only be a narrow band of discount rates for which carbon-sequestration credits provide landholders with an incentive to plant trees which would not have been attractive under a timber market alone. As expected, the net present value of harvested timber decreases with increasing discount rates (and vice versa for decreasing discount rates). However, in contrast, the net present value of temporary carbon sequestration increases to a maximum and then decreases. We also show the extent to which the value of carbon sequestration is offset by the value of carbon redemption, and how this effect is greater when debits are paid in full at harvest, and diminishes as the discount rate increases. The response of internal rates of return of the project to increases in the carbon price was evaluated. It was also found that decreases in the project length from 30 to 20 years increased internal rates of return and reduced the critical interval of discount rates over which carbon payments “swing the deal”.

References

Cacho, O.J., Hean, R.L. and Wise, R.M. (2003). Carbon-accounting methods and reforestration incentives, Australian Journal of Agricultural and Resource Economics, 47: 153-179.

Cacho, O.J., Marshall, G.R. and Milne, M. (2002a). Smallholder agroforestry projects: potential for carbon sequestration and poverty alleviation. Food and Agricultural Organisation. Working Paper, ESA/FAO WP#08-2002. http://www.fao.org/es/ESA/work-e.htm#wp01_03#wp01_03

Cacho, O.J., Marshall, G.R. and Milne, M. (2002b). Transaction and abatement costs of carbon-sink projects: An analysis based on Indonesian agroforestry systems. Conference of the Australian New Zealand Society for Ecological Economics, University of Technology Sydney, 2-4 December 2002. Working paper CC06 at: http://une.edu.au/febl/Econ/carbon

Cacho, O.J., Wise, R.M. and MacDicken, K.G. (2002). Carbon monitoring costs and their effect on incentives to sequester carbon through forestry. in K. Lin and J. Lin (eds), International Symposium on Forest Carbon Sequestration and Monitoring, Taiwan Forestry Research Institute, Taipei, Taiwan. pp. 77-96. http://une.edu.au/febl/Econ/carbon

Dudek, D.J. and Wienar, J.B. (1996). Joint Implementation, Transaction Costs, and Climate Change, Organisation for Economic Co-operation and Development, Paris. OECD/GD (96)173.
Hassall and Associates. (1999). Greenhouse, Carbon Trading and Land Management. LWRRDC Occasional Paper 23/99, Land and Water Resources Research and Development Corporation, Canberra.

Kirschbaum, M.U.F. (2000). What contribution can tree plantations make towards meeting Australia’s commitments under the Kyoto Protocol? Environmental Science and Policy, 3: 83-90.

Marland, G., Fruit, K. and Sedjo, R. (2001). Accounting for sequestered carbon: the question of permanence, Environmental Science and Policy, 4: 259-268.

Tomich, T.P., Kuusipalo, J., Menz, K.M. and Byron, N. (1997). Imperata economics and policy, Agroforestry Systems 36: 233-261.

Venn, T.J., Beard, R.M. and Harrison, S.R. (2000). Modelling stand yield of non-traditional timber species under sparse data, in S. Harrison and J. Herbohn (eds), Socio-Economic Evaluation of the Potential for Australian Tree Species in the Philippines. Monograph 75, Australian Centre for International Agricultural Research (ACIAR): Canberra, pp. 75-192.

Wong, J., Baker, T., Duncan, M., McGuire, D. and Bulman, P. (2000). Forecasting growth of key agroforestry species in south-eastern Australia. DAV-129A, Joint Venture Agroforestry Program, Rural Industries Research and Development Corporation: Canberra.

***