Harvard Institute forInternational Development

HARVARD UNIVERSITY

Development Discussion Papers

Discounting Costs and Benefitsin Carbon Sequestration Projects

Marco Boscolo, Jeffrey R. Vincent,and Theodore Panayotou

Development Discussion Paper No. 638June 1998

© Copyright 1998 Marco Boscolo, Jeffrey R. Vincent, Theodore Panayotou,and President and Fellows of Harvard College

HIID Development Discussion Paper no. 638

Discounting Costs and Benefits in Carbon Sequestration Project

Marco Boscolo, Jeffrey R. Vincent, and Theodore Panayotou

Abstract

The desirability of carbon offset projects is often expressed in terms of “dollars spent per tons of carbonsequestered.” The inconsistent way in which this summary statistic has been derived prevents a direct comparisonof alternative carbon offset projects. This inconsistency centers on the way in which inter-temporal carbon flowsare being accounted for. This paper addresses the issues of selecting the social discount rate and of accounting forintertemporal carbon flows in the case of carbon sequestration projects. Our concern is to ensure that analyses ofdifferent projects are comparable, particularly with regard to the costs of carbon sequestration, and thereby identifyaccurately the socially most desirable projects. We review four main methods that are available to derive anestimate of the social discount rate and recommend using either the shadow-price or weighted-average method. Inpractice, the latter is likely to be more straightforward to apply. On the issue of carbon accounting we concludethat discounting should be applied to not only monetary flows, but also carbon flows. We present an example toclarify the assumptions involved in, and the implications of, selecting the social discount rate.

Keywords: discounting, carbon sequestration, forestry

Support for the research reported in this paper was provided by the U.S. Environmental Protection Agency,through a cooperative agreement on “Economic Analysis of International Forestry Issues”; the SmithsonianTropical Research Institute’s Center for Tropical Forest Science, through a grant from the Southern Company; andthe Harvard Institute for International Development. We gratefully acknowledge the assistance of Jens Rosebrockin the preparation of earlier manuscripts.

Marco Boscolo is Research Associate at the Harvard Institute for International Development and the SmithsonianTropical Research Institute's Center for Tropical Forest Science. His research interests include economics oftropical forest management and conservation, modeling environmental and economic interactions, developmentand evaluation of environmental projects.

Jeffrey R. Vincent is a Fellow of the Institute at the Harvard Institute for International Development (HIID) andthe director of HIID's Environmental Economics and Policy Project in the Newly Independent States. His researchinterests include forest economics, national accounts and the environment, and environmental policy issues intransition economies.

Theodore Panayotou is a Fellow of the Institute at the Harvard Institute for International Development (HIID),Director of HIID's International Environment Program; Project Director for Central and Eastern Europe,Environmental Economics and Policy Project; and Lecturer on Economics, Harvard University. His researchinterests include natural resource economics (forestry, land and water, fisheries, energy, minerals andenvironment), agricultural economics, development economics, capital theory and growth, optimal control andduality theory, social welfare economics and policy analysis.

HIID Development Discussion Paper no. 638

1. INTRODUCTION

The desirability of carbon offset projects is often expressed in terms of “dollars spent per

tons of carbon sequestered.” In other words, carbon offset projects are often compared on the

basis of their cost-effectiveness. Cost-effectiveness analysis in the context of carbon offset

projects raises two important issues: How should these projects be compared with alternative

projects? And how should we account for monetary and carbon flows that span over several

years, often decades? Both issues center on the selection of an appropriate social discount rate

for monetary and physical (carbon) impacts generated by the projects. With respect to monetary

flows, some economists have proposed using very low discount rates in analyzing carbon-

abatement investments (Cline, 1992, 1993; Rothenberg, 1993). Others, however, have argued

that “meeting the needs of future generations will only be possible if investible resources are

channeled to projects and programs with the highest environmental, social, and economic rates of

return [which is not likely] to happen if the discount rate is set significantly lower than the

opportunity cost of capital” (Birdsall and Steer, 1993). In short, the choice of the discount rate

remains a controversial issue in the climate change literature (cf. Nilsson, 1995; Hoen and

Solberg, 1995). With respect to carbon, inconsistent methods have been used to summarize

different carbon sequestration trajectories and compare them to costs.

This paper addresses the issue of discounting in the particular case of carbon sequestration

projects, i.e. projects intended to either absorb carbon dioxide from the atmosphere (e.g.,

reforestation) or to reduce carbon releases from existing activities (e.g., reduced impact logging).

Our concern is to ensure that analyses of different projects are comparable, particularly with

regard to the costs of carbon sequestration, and thereby identify accurately the socially most

desirable projects. Our perspective is a partial-equilibrium one (the projects under consideration

2

are assumed to be small relative to the overall economy), but our conclusions are consistent with

general-equilibrium treatments, such as those by Arrow et al. (1996) and Barrett et al. (1996).

Our focus is therefore narrower than the economic analysis of global climate change per se. Our

intention is not to advocate or dismiss action to mitigate climate change. Instead, it is to provide

guidelines for selecting an appropriate discount rate, given a desire to sequester carbon from the

atmosphere.

The paper is organized as follows. First, the basic rationale for using a social discount

rate in evaluating investment projects is summarized. Second, alternative methods for

calculating the social discount rate are presented and evaluated. Although agreement does not yet

exist regarding which method is best, the economic determinants of the social discount rate are

well understood, and have been for some time. This section of the paper amounts to a review of

pertinent literature, with the intention being to make the technical economic arguments accessible

to a broader range of researchers and policymakers concerned with the design and evaluation of

carbon offset projects. The method that we suggest for its theoretical validity and practicality is

best illustrated through the effect of the social discount rate on saving and investment. Therefore,

our discussion of the various methods is made with reference to saving and investment. Third,

the issue of discounting is discussed with reference to the various methods employed to deal with

intertemporal carbon accounting. Arguments for and against the application of discounting to

physical units of carbon are summarized. Our conclusion is that physical units should be

discounted in calculating unit costs of carbon sequestration. Finally, we present an example to

clarify the assumptions involved in, and the implications of, selecting the social discount rate.

3

2. THE RATIONALE FOR DISCOUNTING

Discounting is used to compare benefits and costs that occur at different points in time.

The basic argument for using a positive social discount rate is articulated along two lines: (i)

consumption today is preferred to consumption tomorrow because the social rate of time

preference (SRTP) is positive, and (ii) capital investments enhance future production and

consumption because the social return on investment (SRI) is positive. Because the financing of

a new project displaces other potential investments and/or requires additional savings, we

illustrate the determination of the social discount rate through its effects on savings and

investments. On this basis, we review the above consumption and production arguments in turn.

2.1 The Social Rate of Time Preference

The Social Rate of Time Preference (SRTP) describes the trade-offs between present and

future consumption as the sum of two components: a “pure” or “myopic” preference for present

over future welfare (r), and a term (µg). The latter indicates that if g (expected growth in per

capita consumption) is positive, a unit of consumption in the future will yield less utility than in

the present. The term µ is the absolute value of the elasticity of marginal utility with respect to

consumption (a measure of the relative effect of a change in consumption on welfare). Thus, the

SRTP, or consumption rate of interest i, is defined as (Koopmans, 1960; Arrow and Kurz, 1970):

i = r + µg , (1)

The first component in (1) reflects the fact that one may care less about the future than the

present (selfishness, if r > 0). The second component in (1) reflects the fact that, if consumption

is expected to grow (g > 0), the SRTP can be positive even when r equals zero. This is because,

as consumers become more and more better off, the utility derived from a given change in

4

consumption becomes smaller and smaller. In this case, society needs to save less in the current

period to finance a given amount of future consumption. In practice, this means that when

individuals expect consumption to rise in the future, e.g. due to rising income, higher interest

rates are required to draw forth a given amount of savings. Markandya and Pearce (1988)

illustrate the derivation of (1) by describing the welfare (W) associated with a level of

consumption at time t (Ct) as

W(Ct) = Ct1-µ * e-rt * (1-µ)-1. (2)

Consumption levels are inter-temporally efficient (the present value of welfare is maximized

over time) if, between any two sequential time periods:

W’(Ct) = W’(Ct+1) / (1 + i) . (3)

Given consumption in two periods, equation (3) illustrates the needed change in Ct+1 to keep total

(intertemporal) utility constant for a given (infinitesimal) change in Ct. It is equivalent to

i = [W’(Ct+1) – W’(Ct)] / W’(Ct), (4)

or, using a more compact notation,

)('

)('

t

t

CWdt

CdW

i = (5)

Substituting for the derivatives of (2) in (5), we obtain

idC

dtC r= +−µ 1 . (6)

By noting that dC/dt * C-1 is the rate of growth in per capita consumption, we obtain equation

(1). The social rate of time preference can be thought of as the supply curve for savings in the

economy, with r being the intercept and µg yielding an upward-sloping relationship between

savings (foregone consumption) and the interest rate earned on those savings. This savings

5

function is depicted in Figure 1 by the line S(i). Individuals are willing to postpone consumption

(i.e., save) only if they are compensated for their “sacrifice” with a positive return. The higher

the return, the more they save.

2.2. The social return on investment

The other rationale for discounting stems from the fact that capital is productive, i.e., $1

invested in productive activities instead of consumed will generate additional income, hence

additional consumption, in the future. The SRI therefore measures the opportunity cost of

investing in, say, carbon sequestration instead of other activities.

If Y=F(K,z) is a well-behaved production function, where K is capital and z is a vector of

other variables (e.g. labor, technology, etc.), the marginal product of capital, FK, yields the

economy’s investment demand curve. Assuming that capital exhibits diminishing marginal

returns, an additional unit of capital yields a lower return than the previous unit. Hence, the

demand curve slopes downward. We therefore expect that an additional unit of investment will

be made only if the additional funds required can be borrowed at a cost lower than for the

previous unit. The investment function is depicted in Figure 1 by the line I(π), where π is the

cost of borrowing funds.

2.3. Market equilibrium

The market interest rate results from the interplay of the supply of savings (positively

correlated with the rate of interest) and the demand for investment (negatively correlated with the

interest rate). In the absence of distortions (taxes, market imperfections, risk, etc.), supply and

demand cross at the market clearing rate i* (see Figure 1). Note that i* = i = π : the market

6

interest rate equals both the SRTP and the SRI (Ramsey, 1928). In this situation, there is no

ambiguity about the social discount rate. It is simply the market interest rate, which reflects

equally consumer and producer rates of time preference.

Of course, a distortion-free market is an idealized situation. Taxes and other distortions

can shift the market supply and demand curves. For example, taxes on interest income cause

savers to require compensation of more than i for their postponed consumption. They demand a

higher interest rate to save a given amount, because they must share part of their income with the

government. The upward shift of the savings supply function to S′(i) reflects this reality.

Taxation of corporate profits introduces similar distortions. Firms that earn π on their productive

investments will not be willing to borrow funds at π, as they must use some of the earnings to

cover their tax obligations. As a result, the investment demand curve shifts downward to I′(π).

The interest rate determined by market interactions is now im, with the associated amount

of savings and investment represented by Qm. Note that im does not equal either the SRTP or the

SRI. At Qm, im could be much higher than the SRTP and much lower than the SRI. For example,

if im is 8% and consumers face a 25% income tax and firms face a 50% profit tax, the values of i

and π would be 6% and 16%, respectively. Firms return 8% to their investors after paying the

profit tax, while investors retain 6% after paying the income tax. What, then, is the social

discount rate? Is it π, i, or a combination of the two?

7

3. METHODS FOR CALCULATING THE SOCIAL DISCOUNT RATE

The foregoing discussion indicates that funds made available to finance carbon

sequestration projects generally come at the expense of both consumption and investment, but

the market interest rate is unlikely to reflect the marginal social opportunity cost of either

displaced activity. Four major methods have been proposed to calculate the social discount rate

in this situation: the after-tax return on savings, the pre-tax return on investment, the shadow

price of capital, and the weighted-average (social opportunity cost of capital) method. We

review the particular features of each method in the following sections.

3.1. After-tax return on savings

Expression (1) in section 2.1 indicates that the SRTP can be calculated directly by adding

the pure rate of time preference to the product of the elasticity of the marginal utility of

consumption times the expected growth rate of consumption. The few available estimates

suggest that the rate of pure time preference ranges from 0 to 2% and the elasticity of marginal

utility from 1 to 2, while consumption growth of course varies from country to country

(Markandya and Pearce, 1988). Direct calculation of the SRTP can be expected to yield discount

rates that are higher in developing countries than industrialized ones. The marginal utility of

consumption, and its elasticity, are high when people live at a subsistence level and are focused

on sheer survival from one period to the next. Moreover, the theory of economic convergence

predicts that poor countries will have, on average, higher income growth rates (hence, higher

consumption growth rates) than rich countries (Barro and Sala-i-Martin, 1995). If the SRTP is

used as the discount rate in carbon sequestration projects, these points suggest that the same

8

project may look very different to developing and developed countries for reasons other than the

distribution of benefits and costs.

Direct calculation of the SRTP is subject to several criticisms. On the value of r, some

have argued that impatience discounting is “irrational” (cf. Pearce and Turner, 1990, for a

review). Regarding µ, some economists dispute whether there is a meaningful way to measure

the social marginal utility of consumption. The debate centers around the measurability of

utility, both across individuals and over time. Finally, projections of future consumption growth

are not perfect, and such imprecision makes them relatively easy to criticize.

Due to these measurement difficulties, economists often compute the SRTP indirectly by

calculating the real, after-tax rate of return on savings. This is typically done by taking the

interest rate on long-term, low-risk investments (such as treasury bills) and correcting for

inflation and taxes. When the SRTP is computed in this way, time-series data covering a long

period should be used to avoid short-term fluctuations. Moreover, the SRTP should reflect the

marginal, not the average, return on savings. The former is higher than the latter, as can be seen

by referring to Figure 1. Boardman et al. (1996) also warn that even if the individual rate of time

preference equals the real after-tax savings rate, the social rate may not. Risk in particular is

perceived quite differently by individuals and by society at large. The individual risk of death,

which is one of the reasons sometimes offered to justify a positive rate of time preference, is

higher than the risk of society’s disappearance. Based on risk considerations, we might therefore

expect the SRTP to be lower than the real, after-tax savings rate that individuals collect.

Others have argued that a time-invariant SRTP is inappropriate (Kula, 1992; Rothenberg,

1993). Some of these arguments are based on ethical grounds, while others hinge on the premise

(consistent with growth theory) that future consumption growth will not proceed at rates

9

experienced in the past (Nordhaus, 1994). Because consumption growth is positively correlated

with the SRTP due to the µg term in (1), a reduction over time in the consumption growth rate

necessarily leads to a declining SRTP.

Cropper et al. (1992) have provided empirical evidence of a diminishing social rate of

time preference stemming from (presumably) ethical considerations. In their survey, participants

were asked to express their willingness to tradeoff lives saved today with lives saved in the

future. The authors found that people were indifferent between a life saved today and two lives

saved in five years’ time, or 11 lives saved in 50 years’ time, or 44 lives saved in 100 years. The

implicit rates of time preference were 16.8% for the five-year horizon, 4.8% for the 50-year

horizon, and 3.8% for the 100-year horizon.

The most fundamental criticism of equating the social discount rate to the SRTP,

however, is that the SRTP is purely a measure of the opportunity cost of consumption. It ignores

the opportunity cost of production given by the return on investments. We turn next to a method

that computes the social discount rate using the opportunity cost of capital, and then to a method

that attempts to rectify this shortcoming of the SRTP.

3.2. Pre-tax return on investment

Some economists have suggested that all investment projects, both private and public,

should employ a discount rate equivalent to the marginal productivity of capital in the private

sector. They argue that, even for public investments, it is in the public interest to sponsor

projects that yield the highest return. If the private sector is able to achieve higher returns than

prospective public-sector projects, then the government should invest in private rather than

10

public projects. To approximate the marginal productivity of capital, i.e. the SRI, economists

often compute the pre-tax rate of return on private investments.

This method contains three potential biases (Boardman et al., 1996). First, as in the case

of the post-tax savings rate, the relevant rate is the marginal, not the average, productivity of

capital. The rate of return is lower on the margin than on average because the “best” deals will

be struck first. Hence, additional investments are unlikely to yield as much as the existing ones.

Using the average rate of return thus biases the estimated discount rate upward. Second, private

rates of return may be distorted by externalities or monopoly pricing. Many economic activities

cause some degree of environmental degradation. Thus, additional expenditures on

environmental cleanup might be necessary to rectify this degradation and achieve the socially (if

not privately) optimal level of environmental quality. These expenditures cause some of the

project’s output to “evaporate,” with the net effect of lowering the marginal social productivity of

capital (Weitzman, 1994). Ignoring such negative externalities of investments biases the

estimated SRI upward (Barrett et al. 1996), although the bias might be small (Weitzman, 1994).

Similarly, if monopoly power allows firms to increase prices above their socially optimal levels,

the private return on investment overestimates the SRI. Finally, the private return on investment

reflects premia for risk. Since society has wider opportunities to diversify its portfolio than

individual investors, social risk premia are probably lower than private risk premia. Again, the

SRI is likely to be lower than the pre-tax private return.

As with the SRTP, one might expect the SRI to decrease over time (Pearce and Turner,

1990; Weitzman, 1994). There are two main reasons for this. First, capital is usually assumed to

exhibit diminishing marginal returns. This argument can be connected to the theory of economic

convergence referred to earlier (cf. Barro and Sala-i-Martin, 1995). Second, in a world that is

11

apparently evolving toward an ever-increasing degree of environmental concern, the proportion

of expenditures directed toward environmental improvement might also increase. The

implication is that the difference between the private rate of return and the social return should

decline over time (Weitzman, 1994).

The fundamental criticism of the pre-tax investment return method is the mirror image of

the one for the post-tax return on savings: it ignores the opportunity cost of savings (Jenkins and

Harberger, 1996). From Figure 1, we can see that π can be much higher than i and thereby

greatly overstate consumers’ rate of time preference.

3.3. The shadow price of capital

This method applies the SRTP to both consumption and investment flows, after the latter

are converted to “consumption equivalents” through the application of a shadow price of capital.

This method is associated with contributions by Eckstein (1958), Arrow (1966), Arrow and Kurz

(1970), Feldstein (1972), Bradford (1975), and Lind (1982).

The estimation of the shadow price of capital is straightforward if we assume that each

dollar invested today yields a perpetual return π that is entirely consumed. In that case, the

present value of the annual flow of consumption is given by π/i, where i is the SRTP. This

means that π/i can be taken as the shadow price of investments in terms of consumption.

Alternative formulas are necessary when less restrictive assumptions are made regarding the

proportion of π that is consumed. For example, Cline’s (1992) revised formulation of Lind’s

method (Lind, 1982) defines the shadow price of capital as

Shadow price ∑=

+=N

t

tN iA

1, )1(/π , (7)

12

where

Aπ, N = π/[1-(1+π)-N]. (8)

Aπ,N is the annual payment from an annuity lasting N years and having a present value of $1 when

discounted using π. It can be easily verified that, in case of a perpetual annuity (N = ∞), Aπ,N

becomes π. Equations (7) and (8) were used by Cline (1992) in his benefit-cost analysis of

mitigation options for global warming. He computed a shadow price of capital of approximately

2 (one unit of capital is worth two units of consumption), consistent with i = 0.015, π = 0.1, and a

15-year capital life (N). After converting investment flows to consumption equivalents using this

shadow price, he then discounted them along with all other benefits and costs using the SRTP.

The shadow-price method is conceptually correct. It allows one to use the SRTP as the

social discount rate without ignoring the opportunity cost of displaced investment. Hence, it is

preferable to either of the first two methods. The main issue with this method has been its

practical feasibility. We discuss this issue in the next section.

3.4. The weighted-average method

With this method, the social discount rate is defined as the weighted average of the SRTP

(usually computed as the post-tax savings rate) and the SRI (usually computed as the pre-tax

investment return). It is associated with contributions by Krutilla and Eckstein (1958), Haveman

(1969), Sandmo and Dréze (1971), and Harberger (1976). It is the principal conceptually sound

alternative to the shadow-price method. According to it, the social discount rate iw is defined as

iw = wc i + (1-wc) π , (9)

where wc is the proportion of investment funds obtained at the expense of current consumption

and 1-wc is the proportion obtained at the expense of investment in alternative opportunities.

13

The determination of wc is based on the following reasoning. A new project increases the

demand for funds, which causes market interest rates to rise. In turn, this prompts consumers to

save more and investors to borrow less for other projects. This displacement of consumption and

investment adds up to what Jenkins and Harberger call the social opportunity cost of funds.

Given a private savings function S(x, im) and a private investment function I(y, im), where x and y

are vectors of socio-economic characteristics (including tax rates) and im is the market interest

rate, the proportion of incremental funds obtained at the expense of current consumption is

mm

mc

i

I

i

Si

S

w

∂∂

∂∂

∂∂

−= . (10)

Substituting (10) into (9), we obtain

)/()/(

)/()/(

mm

mmw iIiS

iIiSii

∂∂∂∂∂∂π∂∂

−−

= . (11)

Multiplying numerator and denumerator by im ·IT/ST ·IT, (11) can be expressed in elasticity form,

)/()/(

TTIs

TTIsw SI

SIii

ηεπηε

−−

= , (12)

where εs is the elasticity of supply of savings and ηI is the elasticity of demand for funds for

private investments with respect to the market interest rate. IT/ST is the ratio of total private

sector investments to total savings. As an illustrative example, for i = 0.015 and π = 0.1 (the

same values used by Cline) and values of εs = 0.3, ηI = -1.0 and IT/ST = 0.9 (as suggested by

Jenkins and Harberger), we obtain a value of iw of approximately 8%.

In practice, the shadow-price and the weighted-average methods yield generally

equivalent results in terms of the ranking of alternative projects (Sjaastad and Wisecarver, 1977:

14

p.528; Jenkins and Harberger, 1996), although they obviously yield different discount rates (with

discount rates from the latter method being higher). The shadow price method, however, has at

least one disadvantage compared to the weighted-average method, namely that it requires

calculating shadow prices in addition to the discount rate. In fact it requires the computation of a

different shadow price for investment goods with different lifetimes. This can be seen from

equation (7), which indicates that a different annuity, and thus a different shadow price, is

obtained when different time horizons are considered. In contrast, the discount rate from the

weighted-average method can be used for all projects in a given country. While maintaining

consistency with economic theory, the weighted-average method provides a convenient way to

define a discount rate that is independent of shadow-pricing issues for investment goods. This

does not mean however that the social discount rate based on the weighted-average method is

necessarily constant over time. As discussed earlier, there are reasons to expect both of its

components, the SRTP and SRI, to decline over time.

The choice of which method to use will not necessarily resolve disagreement over the

choice of the discount rate, as both methods leave ample room for disagreement about

assumptions. In the March 1993 issue of Finance and Development, William Cline’s advocacy

of a low discount rate contrasted sharply with the views of Nancy Birdsall and Andrew Steer of

the World Bank. At the heart of the debate was not the method, as both accepted the shadow-

price method, but rather differing assumptions about parameters such as the pure rate of time

preference (r), the expected growth rate in per capita consumption (g), and the fraction of funds

that would come from displaced consumption (wc). Table I summarizes the assumptions made in

the debate and the resulting effects on the effective (i.e., weighted-average) discount rate.

Differences in assumptions about displaced consumption (wc) lead to a threefold difference in the

15

estimates SRTP. However, even with identical wc, divergent assumptions about r and g would

have lead to a nearly threefold difference in the SRTP.

4. DISCOUNTING AND ACCOUNTING OF CARBON FLOWS

Having reviewed the rationale for discounting and methods to compute the social

discount rate, we now come to a potentially tricky question facing analysts of carbon

sequestration projects: how should carbon flows be summarized and compared to sequestration

costs? Benefit-cost analysis requires monetization of all effects caused by a project. Monetary

valuation of the economic benefits of carbon sequestration remains a controversial and difficult

matter, and it has been attempted by only a few scholars (Cline, 1992; Nordhaus, 1994;

Fankhauser and Pearce, 1994). Furthermore, Mendelsohn et al. (1994) have criticized existing

valuation work on the economic damages from climate change, at least with respect to effects on

the US agricultural sector.

As an alternative to the evaluation of allocative efficiency, which requires expressing

benefits as well as costs in monetary terms, most studies have focused instead on evaluating the

cost-effectiveness (C-E) of carbon sequestration options. Nordhaus (1991), Richards and Stokes

(1995), and Stavins (1996) review these studies. C-E analysis produces a summary statistic such

as “dollars spent per ton of sequestered carbon.” Although this statistic is silent on the overall

economic desirability of carbon sequestration, it permits identification of the options that

sequester carbon at the lowest cost. That is, it facilitates estimation of the supply schedule for

carbon sequestration: the marginal cost of sequestration for progressively greater amounts of

sequestered carbon (cf. Nordhaus, 1991; Richards and Stokes, 1995; Stavins, 1996).

16

The obvious attraction of the C-E approach is that tons of sequestered carbon are easier to

quantify than the economic benefits of sequestration. Indeed, documentation on most carbon

sequestration projects includes information on physical flows of carbon (e.g., Faeth et al., 1994;

Fundecor, 1994; Barres et al., 1995). Application of the C-E approach demands, however, an

answer to the question as to how these flows should be summarized over time and compared to

project costs.

At least three different methods are used in the literature to account for carbon flows at

different points in time. Richards and Stokes (1995) classify them as flow summation, mean

carbon storage, and levelization/ discounting. Flow summation measures the total tons of carbon

sequestered (in net terms) over the lifetime of a project, regardless of when sequestration occurs.

If we have a carbon sequestration project lasting T years with net annual (and not necessarily

constant) carbon flows Xt (Xt > 0 indicates sequestration, Xt < 0 indicates release), flow

summation involves calculating

∑=

T

t 1

Xt. (13)

This is then divided into the discounted sum of net project costs (Ct, which can vary from year to

year) to estimate the cost per ton of sequestered carbon:

∑

∑

=

=

−+

T

tt

T

t

twt

X

iC

1

1

)1(. (14)

Mean carbon storage is the average cumulative amount of carbon stored per year. Defining

cumulative storage, the stock of sequestered carbon at a given point in time, as

St = ∑=

t

s 1

Xs , (15)

17

Mean carbon storage equals

∑=

T

t 1

St / T. (16)

This tends to be smaller than the value given by (13). For example, if Xt is constant (Xt = X � t),

then (13) yields TX, while (16) yields (T+1)X/2. Cost per ton of sequestered carbon now equals

T/

)1(

1

1

∑

∑

=

=

−+

T

tt

T

t

twt

S

iC . (17)

Like flow summation, this method assumes indifference between carbon sequestration in the near

or distant future.

Levelization involves converting the net cost stream to an annual equivalent:

C =

∑

∑

=

−

=

−

+

+

T

t

tw

T

t

twt

i

iC

1

1

)1(

)1((18)

Then, unit costs of carbon sequestration are set equal to

C / Xt (19)

Which varies from period to period due to variations in Xt.

None of the three methods yields correct estimates of unit sequestration costs. To

illustrate, suppose we know p, the unit value of a ton of sequestered carbon (i.e., the avoided

damage cost of climate change). Then the net present value of the project is

NPV = ∑=

T

t 1

pXt (1+iw)−t − ∑=

T

t 1

Ct (1+iw)−t . (20)

As noted earlier, reliable estimates of p are not available. As an alternative, we can ask, what

value of p would cause the discounted benefits of the project to just equal the discounted costs?

18

This is the definition of the break-even price of carbon (pBE), the value that yields a net present

value of zero. Setting (20) equal to zero and solving for p (= pBE), we obtain

pBE = ∑=

T

t 1

Ct (1+iw)−t / ∑=

T

t 1

Xt (1+iw)−t . (21)

The right-hand side of this expression gives the unit cost of carbon sequestration, consistent with

the benefit-cost analysis principles from which (21) is derived. This is the correct expression for

comparing the cost-effectiveness of alternative projects.

The key point from this simple exercise is that tons of carbon in the denominator of (21)

are discounted. The unit cost expression for the flow summation method (14) is incorrect

because it discounts net costs, as in the numerator of (21), but not net carbon flows. The mean

carbon storage method (16) fails for the same reason. The levelization method yields accurate

estimates only if Xt is constant over time, as then (18) and (19) imply

C / Xt = C / X =

∑

∑

=

−

=

−

+

+

T

t

tw

T

t

twt

i

iC

X

1

1

)1(

)1(1

=

∑

∑

=

−

=

−

+

+

T

t

tw

T

t

twt

iX

iC

1

1

)1(

)1( =

∑

∑

=

−

=

−

+

+

T

t

twt

T

t

twt

iX

iC

1

1

)1(

)1( .

Table II provides a partial review of the methods used in empirical studies to estimate

unit carbon sequestration costs. Some, including several studies of carbon sequestration projects

in the United States, have used the correct discounting method given by (21). Most studies in

developing countries, however, have used the flow summation or mean carbon storage methods.

This difference makes it impossible to compare directly the estimated costs of carbon

sequestration across the studies. Since an undiscounted sum is usually larger than a discounted

sum (assuming a positive discount rate, and flows that are mainly positive), the implication is

that studies in developing countries have tended to understate the costs of carbon sequestration.

19

A simple example illustrates how the treatment of carbon flows and the choice of the

discount rate affects estimates of the costs of carbon sequestration. Consider two hypothetical

projects, reforestation and natural forest management (NFM). The former occurs on private

farmland currently used for cattle grazing, while the latter occurs in an area where the annual

deforestation rate is 12%. Other basic assumptions are summarized in Table III. Using a

discount rate of 6% and flow summation as the summary statistic, reforestation attains carbon

sequestration at a unit cost of $4/ton (see Table IV). This is far superior to natural forest

management, which achieves sequestration at $7/ton. However, when physical units of carbon

are discounted, the two projects sequester carbon at the same unit cost, $10/ton. Reforestation is

actually no more cost-effective than NFM. Increasing the discount rate by one percentage point,

to 7%, has a significant impact on these findings. Under flow summation, the two activities now

achieve carbon sequestration at about the same unit cost, $7-8/ton. When we discount carbon

flows, however, the cost of carbon sequestration through reforestation is $20/ton, twice as high as

the cost of NFM.

This example illustrates three points. First, summary statistics such as “dollars spent per

ton of carbon sequestered” must be carefully defined (see also Richards 1995 and IPCC 1996).

They offer meaningful information on cost-effectiveness across projects only if they incorporate

the discounting of net carbon flows as well as net project costs. Second, discounting, while

necessary, has a major impact on analyses of carbon sequestration projects. Results are sensitive

to even small changes in the discount rate, particularly if costs or carbon flows tend to occur at

the beginning or end of the project. It is therefore especially important that careful thought be

given to the choice of the discount rate, with sensitivity analysis employed whenever substantial

uncertainty about its magnitude exists. Third, advocating a lower discount rate for conservation

20

reasons, which is inappropriate in any event, can be counter-productive when a carbon-

sequestration project more consistent with conservation of natural habitat (the NFM option)

yields sequestration benefits earlier than a project less consistent with conservation (the

plantation option).

5. CONCLUSIONS

The viability of alternative mitigation options to combat climate change strongly depends

on their credibility, effectiveness, and efficiency. These issues require the development of clear

guidelines that will inform project proposals preparation and evaluation. It is unfortunate that

dozens of valuable studies (in this paper we cite mostly forestry-based ones) provide estimates of

costs of carbon sequestration that are not comparable. This is due, in part, to the different

approaches used to deal with inter-temporal carbon accounting and their interaction with the

discount rate.

Discounting is fundamental in accounting for the passage of time and the use of scarce

resources in carbon sequestration projects. With the hope to make its rationale and selection

more amenable to practitioners, we reviewed four main methods that are available to derive an

estimate of the discount rate and recommended using either the shadow-price or weighted-

average method. In practice, the latter is likely to be more straightforward to apply. Through an

example, we illustrated how discounting physical units of carbon may have less than an

immediate appeal, but it is important to ensure comparability across project with different carbon

sequestration trajectories. Thus, our conclusion is that, in carbon offset projects, discounting

should be applied to not only monetary flows but also carbon flows.

21

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26

TABLE I: Weighted average social discount rate implied by assumptions in Cline (1992) andBirdsall and Steer (1993)

Study r µ g i=µg+r π wc iw

Cline (1992) 0% 1.5 1% 1.5% 10% 0.8 3.2 %Birdsall and Steer (1993) 1% 1.5 2% 4% 10% 0.0 10 %Note: iw is calculated using (12). Estimates of r, µ, g, π, and wc based on Cline (1992) andBirdsall and Steer (1993).

TABLE II: Methods and rates used to discount carbon flows in selected empirical studiesSource Method Discount ratea Country

Moulton and Richards (1990) Levelization 10% (4%-8%) USANordhaus (1991) Levelization 6% global (forestation option)Dixon, Schroeder and Winjum (1991) MCS - boreal, temperate and

tropicalVan Kooten et al. (1992) Flow summation - CanadaAdams et al. (1993) Levelization 10% USARichards et al. (1993) Levelization/

DiscountingUSA

Dixon et al. (1994) MCS - S.America, Africa, S.AsiaFaeth, Cort and Livernash (1994) Flow summation - Developing countriesHoen and Solberg (1994) Discounting 2%-7% NorwayStavins (1995) Discounting 5% (2.5%- 10%) USAParks and Hardie (1995) Levelization 4% USAEnglin and Callaway (1995) Discounting 2%-10% USAFernside (1995) Discounting 0%, 1%, 5% BrazilIsmail (1995) Discounting 0%, 1%, 3% MalaysiaMakundi and Okiting’ati (1995) MCS - TanzaniaMasera et al. (1995) MCS - MexicoRavindranath and Somashekhar (1995) Flow summation - IndiaWangwacharakul and Bowonwiwat (1995) Flow summationb - ThailandXu (1995) MCS - ChinaBoscolo, Buongiorno and Panayotou (1997) Discounting 6% (10%) Malaysia

Notes: a Includes in parenthesis rates used for sensitivity analyses; b The authors assumed thatthe value of carbon increases at the rate of interest. This makes their flow summation approachequivalent to discounting.

27

TABLE III: Assumptions for hypothetical analysis of two carbon sequestration projects(reforestation and natural forest management)

REFORESTATIONGross stand growth (commercial assumed 2/3of gross growth)

0 m3/ha/yr (years 1-2);6.9 m3/ha/yr (years 3-12);15.5 m3/ha/yr (years 13-16);24.2 m3/ha/yr (years 17-20)

Biomass/volume ratio 0.45 tons/m3

Carbon/biomass ratio 0.5Commercial harvest 10 m3 (at year 12)

142 m3 (at year 20)Price of wood $45/m3

Compensation to farmers(1) $50/haPlantation and other costs see Faris et al. (1997)

NATURAL FOREST MANAGEMENTStanding volume 116 m3/haDeforestation rate(1) 12%Volume harvested 20 m3/ha (in year 1)

10 m3/ha (in year 11)10 m3/ha (in year 20)

Stand growth rate 1 m3/haStumpage price $33.84/m3

Compensation to farmers(1) $25/haOther costs see Faris et al. (1997)Source: Unit management and implementation data have been taken from Faris et al. (1997) whopresent a case study of the CARFIX project (FUNDECOR, 1994). Stand growth follows thetrajectory of a sigmoid curve: growth rates are higher when the stand is young. The growth ratesreported by FUNDECOR correspond to plausible estimates for a fast growing species inplantation (see, e.g., Arias 1997). (1) Our assumptions made for illustrative purposes and whichdo not correspond to either Faris et al. (1997) or FUNDECOR (1994).

TABLE IV: Costs of carbon sequestration ($/ton) for two alternative projectsCarbon Project

Accounting Reforestation Natural Forest Managementmethod r = 6% r = 7% r = 6% r = 7%

Flow summation $4/ton $8/ton $7/ton $7/tonDiscounting $10/ton $20/ton $10/ton $10/ton

28

Figure 1. Determination of the market interest rate

Interest rate andrate of return (%)

Quantity of Investment and Savings

S(i) savings net oftaxes on interestincome

S’(i) rate of returnreceived by saversbefore paying taxes

I(π) return oninvestment gross oftaxes

I’(π) return oninvestment net of taxes

Qm

i

im

π

i*

Source: Adapted from Jenkins and Harberger (1996)