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Journal of Forest Economics

Journal of Forest Economics 16 (2010) 1–10

1104-68

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.de/jfe

Optimizing joint production of timber and carbonsequestration of afforestation projects

Roland Olschewski a,�, Pablo C. Benıtez b

a Swiss Federal Research Institute WSL, Zurcherstr. 111, CH-8903 Birmensdorf, Switzerlandb Department of Economics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6

a r t i c l e i n f o

Article history:

Received 7 May 2008

Accepted 23 March 2009

JEL classification:

Q23

Q51

Q57

Keywords:

Carbon sinks

Certified Emission Reductions

CDM

Faustmann

Hartman

99/$ - see front matter & 2009 Elsevier GmbH

016/j.jfe.2009.03.002

esponding author. Tel.: +4144 739 25 62; fax:

ail address: roland.olschewski@wsl.ch (R. Olsc

a b s t r a c t

Optimizing harvesting decisions has been a matter of concern

in the forestry literature for centuries. However, in some

tropical countries, growth models for fast-growing tree species

have been developed only recently. Additionally, environmental

services of forests gain importance and should be integrated in

forest management decisions. We determine the impact of a

joint production of timber and carbon sequestration on the

optimal rotation of a fast-growing species in north-western

Ecuador, comparing different optimization approaches and

taking the latest developments of the Kyoto Protocol into

account. We find that payments for carbon sequestration have

substantial impact on the rotation length: in contrast to an

optimum of 15 years when focusing on timber production only,

joint production leads to a doubling of the rotation length,

which means that timber harvest should be postponed until the

end of the carbon project.

& 2009 Elsevier GmbH. All rights reserved.

Introduction

Optimizing the harvesting decision has been a matter of concern in the forestry literature forcenturies. However, in some tropical countries growth models, which allow for determination ofoptimal rotation periods for certain fast-growing tree species, have been developed only recently.Additionally, environmental services provided by forests – besides timber production – are gainingimportance and need integration into the forest management decision. Payments for such services

. All rights reserved.

+4144 739 2215.

hewski).

ARTICLE IN PRESSR. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–102

might have an impact on optimal rotations as well as the attractiveness and financial outcome ofafforestation projects.

We aim at determining the influence of payments for environmental services on the optimizationof the harvesting decision, assuming joint production of timber and carbon sequestration.Early contributions to this topic have been provided, e.g., by Price and Willis (1993) focusing ondiscount-rate aspects, and Hoen and Solberg (1994) reporting a case study of forest managementplanning in northern Europe. In contrast, we focus on afforestation projects in the tropics, comparingthree different optimization approaches, while taking the latest developments of the CleanDevelopment Mechanism (CDM) and in the markets for Certified Emission Reductions (CER)into account.

Methodology

Three approaches concerning the determination of the optimal rotation period are to becompared: first, we focus on the maximum sustained physical timber yield, followed by a financialanalysis of the optimal timber management decision and, finally, we deal with the optimal conditionfor a joint production of timber and carbon sequestration.

Maximum sustained timber yield

The maximum sustained timber yield (MSY) is determined by choosing the rotation age, whichmaximizes average annual physical timber production. Eq. (1) gives the condition to be satisfied,with V standing for timber volume and T indicating rotation age:

MaxTfVðTÞ=Tg; V 0ðTÞ¼

! VðTÞ

T(1)

The optimal rotation reflects a situation where the marginal timber increment equals the averageannual harvest volume (Bowes and Krutilla, 1989). For illustration purposes, Eq. (1) can be rearrangedresulting

V 0ðTÞ

VðTÞ¼

1

T(2)

Fig. 1 shows optimal rotation TY based on maximum sustained timber yield. However, as thiscalculation is based on yield data only, financial aspects such as opportunity costs of delaying theharvest are neglected.

TTY

V'(T)V(T)

1 T

V'(T)V(T)

V'(T)V(T)

1 T

Fig. 1. Optimal rotation for maximum sustained timber yield.

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Optimal financial timber management decision

As is well known, Faustmann (1849) based the optimal rotation calculation on the maximizationof the net present value (NPV) of an infinite chain of rotations (Eq. (3)) with P representing timberstumpage price, C planting costs, k number of rotation, i real interest rate:

NPV ¼ lðTÞ ¼X1k¼1

ðPVðTÞ � CÞe�kiT � C ¼PVðTÞe�iT � C

1� e�iT(3)

MaxTflðTÞg; l0ðTÞ¼! 0

PV 0ðTÞ ¼ i½PVðTÞ þ ln�(4)

Eq. (4) provides the condition for the optimal Faustmann rotation, where marginal benefits ofdelaying the harvest (on the left-hand side) equal opportunity costs caused by this delay (on theright-hand side). The term [PV(T)+l*] reflects the combined value of land l* and timber stock PV(T) attime of harvest. Replacing l* by the right term of Eq. (3) and rearranging Eq. (4) gives Eq. (5) andallows for a graphical illustration in Fig. 2 (compare Bowes and Krutilla, 1989):

PV 0ðTÞ

PVðTÞ � C¼

i

1� e�iT(5)

Compared with the maximum sustained yield calculation, the Faustmann solution leads to ashorter optimal rotation TF due to the fact that the rotation events are monetized and discounted.This conventional Faustmann model refers to timber production only. Further environmental servicesprovided by forests, such as carbon uptake, watershed protection or the provision of recreationalsites, are not taken into account. Note, however, that for specific levels of rotation costs as well as aprice – size gradient effects a longer rotation than MSY could result.

Joint production of timber and carbon sequestration

Joint production is given when the same production activity leads to several outputs. Here, weconsider forests providing commercial timber as well as non-timber forest amenities and assumethat forest management strives for maximizing the net present value of this joint production over aninfinite planning horizon. The rotation age that maximizes the net present value is called theHartman rotation (Hartman, 1976). In our case an afforestation project generates a growing stock oftimber and simultaneously provides an environmental service, namely the sequestration of carbonfrom the atmosphere leading to a growing carbon stock in biomass. Eq. (6) shows the combined NPVr of the joint production of timber l and carbon sequestration c, where the monetary flow generated

TTY

Rates

V'V 1

T

PV' PV-C

i 1-e -iT

TF

Fig. 2. Optimal rotation TF for economic timber management.

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T

V'

V 1 T

PV' PV-C

i

1-e-iT

TFTHTY

Rates

Fig. 3. Optimal rotation TH for joint production.

R. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–104

by the environmental service is denoted by g (compare Bowes and Krutilla, 1989):

NPV ¼ rðTÞ ¼ lðTÞ þcðTÞ ¼PVðTÞe�iT � C þ

R T0 gðtÞe�it dt

1� e�iT(6)

MaxTflðTÞ þcðTÞg; r0ðTÞ¼! 0

PV 0ðTÞ þ gðTÞ ¼ i½PVðTÞ þ rn� (7)

The condition for the optimal rotation is given in Eq. (7). Similar to Eq. (4), the opportunity costs ofpostponing the harvest equal the benefits of this delay, which now comprise additional revenuesfrom sequestering carbon. Inserting the right term of Eq. (6) as r* into Eq. (7) gives

PV 0ðTÞ

PVðTÞ � C¼ i

1

1� e�iTþ

R T0 gðtÞe�itdt

½PVðTÞ � C�ð1� e�iT Þ

" #�

gðTÞPVðTÞ � C

(8)

Eq. (8) differs from (5) on the right-hand side by taking carbon revenues into account, whichmakes a delay of the harvesting decision more attractive (Hartman, 1976). Consequently, a longeroptimal rotation period is to be expected as shown in Fig. 3, where the intersection point of thedotted line (representing the right side of Eq. (8)) and the graph for [PV0/(PV�C)] gives the Hartmanrotation TH for joint production of timber and carbon sequestration.

While timber revenues can be derived based on market prices, carbon revenues deserve a closerlook, as withdrawing carbon dioxide from the atmosphere is a public good characterized by non-rivalry in and non-excludability from enjoying the positive effect of mitigating climate change.

Carbon accounting

The Conference of the Parties (COP9) of the Kyoto Protocol decided on the accounting rules fornon-permanent Certified Emission Reductions (CER, tonnes of CO2) of reforestation and afforestationprojects, and, thereby, provided a framework for establishing markets for carbon credits. CER arecertificates of greenhouse gas emission reductions obtained from project activities in developingcountries and include permanent reductions through emission avoidance as well as non-permanentreductions by forestry projects (Olschewski and Benıtez, 2005). These certificates, which have to beverified by an independent entity, are expected to be traded like any other commodity.

ARTICLE IN PRESSR. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–10 5

During the first commitment period from 2008 to 2012 there are two possible ways to account fornon-permanent carbon sequestration in forests: temporary and long-term credits (UNFCCC, 2003).While both are measured in tonnes of carbon dioxide, a temporary credit (tCER) is defined as aCER issued for an afforestation or reforestation project activity under the CDM, which expires at theend of the commitment period following the one during which it was issued. Once expired, atCER can be reissued several times during the project as long as the forest exists. In contrast, along-term credit (lCER) expires at the end of the crediting period of the overall afforestationor reforestation project (Olschewski and Benıtez, 2005), and cannot be reissued (Neef andHenders, 2007). These different types of accounting procedures have impact not only on theamount of CER ascribed to reforestation projects but also on the risk and the value of thecertificates.

CO2-emitting enterprises in Annex-1 countries, which have to fulfil reduction commitments, mustdecide whether to reduce their own emissions or to buy credits at market prices. Potential buyers aresupposed to be indifferent between (i) buying a permanent credit today and (ii) buying a non-permanent credit (lCER or tCER) today and replacing it by a permanent one when the initial creditexpires. This indifference is reflected by Eq. (9), where t is the lifetime of CER units, p is the price ofCER units, the sub-index of p indicates the lifetime of the CER units (pt is the price per tCO2 for acredit valid for t-years and pN is the price for a permanent credit), and d is the discount rate ofpotential buyers in Annex-1 countries (Olschewski et al., 2005):

p1 ¼ pt þp1ð1þ dÞt

(9)

Buying a non-permanent CER becomes attractive if its price is lower than the price per tonne CO2

of a permanent CER minus the discounted price of a permanent CER in year t, when the expiring non-permanent CER has to be replaced. Therefore, the maximum price that an enterprise would bewilling to pay for temporary carbon credits, pt, results from Eq. (7):

pt ¼ p1 1�1

ð1þ dÞt

� �(10)

Note that Eq. (10) is valid for both lCER and tCER since these credits only differ with respect to theirexpiring time. In the following we focus on temporary credits with an expiring time of 5 years andassume a project with maximum duration of 30 years, which is given by official carbon accountingrules (compare Olschewski and Benıtez, 2005; UNFCCC, 2003).

Results

We selected a region in the north-western part of Ecuador, which is considered one of the world’shot-spots for biodiversity (Myers et al., 2000). Land use is very dynamic with the highestdeforestation rates within the country due to timber extraction and conversion to agricultural land(Sierra and Stallings, 1998; de Koning et al., 1999). Pasture area has doubled in the region between1974 and 1995, mainly caused by clear-cutting forests (INEC, 1995). However, most of the pasturesare degraded and only a few forest plantations exist (de Koning et al., 2005).

Maximum sustained timber yield

The calculation of the maximum sustained timber yield is based on a Cordia alliodora growthmodel of Alder and Montenegro (1999) for medium-quality sites. Marginal timber incrementequals the average annual harvest volume according to Eq. (2) at the age of 18 (see Fig. 4). Notethat, due to unreliable estimates close to zero age, we assumed a linear increment during the first5 years. This procedure runs the risk of overestimating true increment and carbon storage at an earlyphase of a forestry project (Price, 1994). However, it did not affect any of the optimal rotationscalculated.

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Growth Rates Cordia alliodora-Plantation(based on Alder & Montenegro, 1999)

0%

5%

10%

15%

20%

25%

0Rotation length (years)

V'(T)

V(T)

1 T

TY5 10 15 20 25 30 35 40

Fig. 4. Optimal rotation for maximum sustained yield of Cordia alliodora.

Growth Rates Cordia alliodora-Plantation(based on Alder & Montenegro, 1999)

0%

5%

10%

15%

20%

25%

0Rotation Length (years)

PV' PV-C

i 1-e-iT

TF TY5 10 15 20 25 30 35 40

Fig. 5. Optimal Faustmann rotation for Cordia alliodora.

R. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–106

Optimal economic timber management decision

Based on a field survey we considered economic aspects in determining the optimal rotationcomprising the following: planting costs in the first year sum to $408/ha and the present value offurther maintenance between years 1 and 10 amounts to $376/ha. Commercial timber volume iscalculated according to growth estimates determined by Alder and Montenegro (1999). We ignoreprice–size effects on rotation length, assuming that the timber price per m3 is unaffected byincreasing trunk diameter above 20 cm. Applying these data and a timber price of $20/m3, results inan optimal economic rotation of 15 years according to the Faustmann rotation model and therespective condition of Eq. (5) (Fig. 5).

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0

100

200

300

400

500

600

700

0 5 10 40

267267 267

120 120 120

77 7756

267 267

120

775636

(tCO

2/ha

)

267267 267

120 120 120

77 7746

267 267

120

774636

Accumulated CO2-Storage

Years15 20 25 30 35

Fig. 6. Accumulated CO2 storage in Cordia alliodora plantation.

R. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–10 7

Joint production of timber and carbon sequestration

Before the optimal rotation for the joint production can be calculated, carbon revenues of theplantation have to be determined. Fig. 6 illustrates the carbon sequestration potential and shows howtemporary CER are assigned to the afforestation project. We determined the carbon sequestrationpotential based on stem biomass estimations for trees with a minimum diameter of 10 cm at breastheight. Owing to lack of specific data we followed Brown (1997) and applied general expansionfactors for tropical broadleaf species to take biomass of roots, stump, branches and leaves intoaccount. In the next step we calculated the accumulation of carbon by multiplying the overall drybiomass per hectare by 0.5, which represents the proportion by mass of carbon. Finally, we obtainedmass of carbon dioxide as the basis for credit calculation by the molecular mass of carbon dioxide inrelation to the atomic mass of carbon.

During the first 5 years of growth, the cumulative carbon storage is equivalent to 267 tCO2/ha, thus,267 temporary CER are to be issued and rewarded by a one-off payment in year 5. They expire after 5years, but could be reissued and sold together with additional 120 tCER corresponding to the carbonaccumulation between years 5 and 10. Consequently, 387 tCER are available for the next 5 years. In year15 an additional 77 certificates are generated; together with the reissued 387 tCER they add up to 464credits available until year 20. During the following 5-year periods a further 56 and 36 credits areproduced so that 510 and 546 tCER, respectively, can be provided and generate a corresponding incomeat the beginning of the last two 5-year periods before the project ends in year 30. For successor rotationswe assume constant prices and the same timber volume as well as carbon accumulation.

Obviously, there is a huge difference between the project duration of 30 years, which maximizescarbon revenues, and the optimal Faustmann rotation of 15 years concerning timber production only.The optimization condition in Eq. (8) allows us (i) to calculate the optimal rotation for the jointproduction of timber and carbon sequestration and (ii) to determine the impact of changes in pricesfor the environmental service on the harvesting decision.

Various estimates of prices for permanent credits have been developed in the past. The BioCarbonFund proposes a lower limit for a price margin of $3/tCO2 (The World Bank, 2003). Den Elzen and deMoor (2002) estimated an equilibrium price of about $4.5–$5.5 per tCO2. The International EmissionTrading Association forecasts CER prices that range from $9.9 to $13.7 (IETA, 2003), whereas theOECD Global Forum on Sustainable Development expects prices from $9 to $22 referring to emissionallowance trading within the European Union ETS (Grubb, 2003). During the course of the year 2007,the market price of ETS credits for the Phase II (2008–2012) floated between $20 and $30 and iscurrently about $35 per tonne of CO2 (PointCarbon, 2008).

Given this range of prices for permanent credits, we apply Eq. (10) with a discount rate of threepercent, which reflects the current low interest level in Annex-I countries, and a permanent credit

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Growth Rates Cordia alliodora-Plantation(based on Alder & Montenegro, 1999)

0%

3%

6%

9%

12%

15%

0Rotation Length (years)

i 1-e-iT

PV' PV-C

5 10 15 20 25 30 35 40

Fig. 7. Optimal Hartman rotation for Cordia alliodora.

Table 1Optimum rotation for joint production depending on carbon prices.

Permanent certificate price ($/tCO2) Equivalent tCER price ($/tCO2) Optimum rotation length (years)

0 0 15

7 1 17

20 3 21

30 4 24

35 5 29

45 6 -

R. Olschewski, P.C. Benıtez / Journal of Forest Economics 16 (2010) 1–108

price of approximately $7, which results in a conservative estimate of the equivalent price fortemporary CER of $1 per tCO2. The payments corresponding to the accumulated carbon storage areassumed to occur every 5 years and are transformed into constant annuities for the respective timeperiods.

The optimal rotation for the joint production for timber and carbon sequestration according to Eq.(8) is 17 years (Fig. 7), and thus, longer than the Faustmann rotation TF but still shorter than TY (notethat the dotted line represents the right-hand side of Eq. (8)). However, harvesting is delayed onlyslightly for 2 years and the question arises of what impact higher CER prices would have on theresult. Thus, we conducted a sensitivity analysis based on the same data but assuming variouspermanent certificate prices. Table 1 shows the results.

If the carbon credit price is zero, Eq. (8) reduces to the Faustmann condition given by Eq. (5) andthe optimal rotation is 15 years. With rising prices for permanent certificates, tCER prices increase aswell, and timber harvest is to be delayed substantially. Interestingly, with permanent certificateprices above $45 (corresponding to a tCER price of $6 per tonnes of CO2) the Hartman condition hasno solution within the given project duration. This indicates that, due to the economic attractivenessof sequestering carbon, timber would not be harvested. However, the project length is determined bythe CDM rules, which in our case limits the carbon payments until year 30 only.

Discussion and conclusions

We analysed three different approaches to determine the optimal rotation of an afforestationproject in north-western Ecuador. As a result, the maximum sustained yield approach leads to an

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optimal rotation of 18 years, whereas the Faustmann rotation turned out to be shorter: focusing ontimber revenues and taking opportunity costs of a delayed harvest into account, 15 years wasdetermined as the optimal financial rotation.

Concerning the joint production of timber and carbon sequestration, the Hartman rotation modelhas been applied as the traditional approach for accounting externalities in forests (van Kooten andFolmer, 2004). An early application of the Hartman rotation model to carbon sequestration in forestshas been described in van Kooten et al. (1995). They assume that a forest owner receives a subsidy forcarbon uptake, whereas a tax has to be paid in the case that carbon is released. While no country hasimplemented such a tax – subsidy scheme in practice, this analytical approach – though coherentand important for the economic optimization – remains theoretical in nature. In contrast, weconsider the carbon accounting rules recently established in the international carbon market withthe aim to develop an optimization model that could be applied in practice. However, other aspectssuch as liability in case that carbon is released before the certificates expire (e.g. by natural hazards)play an important role and have to be considered for a comprehensive analysis of practicability.

Interestingly, at low carbon price levels, as forecasted a few years ago, we detected just a slightchange in the harvesting decision, with a harvesting age even remaining below the result of themaximum sustained yield approach. Including current higher carbon prices in the analysis, leads tosubstantially different results: the plantation should not be harvested until the end of the carbonproject, which means a doubling compared with the Faustmann rotation. Note that this result isbased on the assumption that future carbon prices will remain constant (compare Eq. (9)). However,public projections of carbon prices often suggest increasing prices as mitigation efforts increase overtime (Clarke et al., 2007). Such a development would considerably reduce the attractiveness of tCERand lCER, as higher carbon prices have to be taken into account when replacing non-permanentcredits by permanent ones (compare Eq. 9).

These results might have strong implications for management decisions concerning carbon sinkprojects in the tropics. Land owners willing to participate in CDM afforestation projects have to takeinto account that their land-use decision will be irreversible for 30 years instead of 15, with timberrevenues occurring at the end of the carbon project, only. However, the high volatility in the marketfor permanent carbon credits leads to a substantial uncertainty concerning future carbon revenues.In consequence, many afforestation projects in the tropics might not be realized in spite of aconsiderable carbon sequestration potential. This could be one reason why until today only oneafforestation project has been officially registered under the CDM.

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