DCF & Weak Sustainability Analysis
Discounting the Children’s Future?
Does the Non-symmetrical Depreciation of Natural and
Human-made Capital Invalidate the Assumption of Substitutability in
"Weak" Sustainability Analysis?
Alastair McIntosh* and Gareth Edwards-Jones**
for Human Ecology, 12 Roseneath Place, Edinburgh
of Agricultural and Forest Sciences, University of Wales, Bangor,
Road, Bangor, Gwynedd, LL55 2UW, UK.
(http://www.bangor.ac.uk/safs/; email firstname.lastname@example.org)
Published in Geophilos, 00(1), Autumn 2000, Land Research Trust, London, ISSN 1472-6300, pp. 122-133.
Alastair McIntosh is a fellow of the Open University-accredited Centre for Human Ecology in Edinburgh.
Gareth Edwards-Jones is professor of Agriculture and Land Use Studies at the University of Wales, Bangor.
provides diminishing utility as it depreciates over time. Natural capital, which
includes the planet itself, all minerals, all species, water, soil and air, does
not depreciate over time, and theoretically may provide positive utility over
time periods that tend towards infinity. From a utilitarian standpoint,
therefore, it is unlikely that, when analysed over the long run, the
substitution of non-renewable natural capital for human-made capital will ever
this reason, argue the authors, discussion of substitutability between human
capital and the resources of nature should be omitted from sustainability
analysis. The key concept that renders sustainable development different from
any other development or social model is that of intergenerational equity.
Sustainable development has at its heart the idea that every generation should
leave behind sufficient resources so as not to prevent future peoples from
achieving their needs. This principle is undermined by the values that underpin
the techniques of discounting the flow of future income, which reinforce the
idea that it is legitimate to destroy natural capital.
In fact, argue McIntosh and Edwards-Jones, the “weak” form of sustainable development legitimises destruction which, in the long run, would short-change future generations.
Cover: Portrait of Francis Bacon, Viscount St. Albans, "the greatest of the moderns."
Geophilos is available from the Land Research Trust, 7 Kings Road, Teddington, TW11 0QB, England, ISSN: 1472-6300, £28 per annum individuals, £50 institutions
Views on Sustainability and Substitutability
The term, “sustainable development” first came to
prominence in the World Conservation
Strategy of the International Union for the Conservation of Nature in 1980.
The 1987 Brundtland Report, Our Common
Future, defined it as development that meets the needs of the present
generation, “without compromising the ability of future generations to meet
their own needs.” In 1992 the
principle was endorsed by those national governments, including the British
government, which became signatories to the Rio
Declaration on Environment and Development (Reid 1995).
The key concept which renders sustainable development different from any
other development or social model is that of intergenerational equity.
Sustainable development has at its centre the idea that every generation
should leave behind sufficient resources so as not to prevent future peoples
from achieving their needs.
One of the problems with this concept, is determining
how many of the existing resources we should use now, and how many we should
leave for future generations. In an
attempt to aid this decision Pearce et al. (1989) classified all existing resources into one of three
classes of capital: natural capital, human-made capital and human capital.
Here, natural capital includes the planet itself, all minerals, all
species, water, soil and air. Human-made
capital covers all material items which are non-natural such as roads, cars and
buildings, while human capital is concerned with the knowledge, experience and
culture which exist largely in the human mind.
Possible variations in the stock of capital in these classes over time
then leads to the recognition of two forms of sustainability: so called
‘weak’ and ‘strong’ sustainability.
to the idea of ‘weak’ sustainability the relative proportions of each of the
classes of capital that we leave for the next generation do not matter.
Rather we need to ensure that we leave a total stock of capital to the
next generation that is at least as big as the one we inherited from our
ancestors (i.e. a non-declining stock of capital).
Thus ‘weak’ sustainability entertains substitutability between the
different classes of capitals, and within this definition it is considered
acceptable to deplete natural capital so long as other forms of capital are
correspondingly increased. Turner
and Pearce (1993) are quite explicit about the consequences of accepting the
substitution of capital. They state, "It would for example, be justified on
this rule to run down the environment provided the proceeds of environmental
degradation were reinvested in other forms of capital."
Thus, if adopted, the assumption of "substitutability" would
justify the conversion of non-renewable resources into objects of consumption,
while remaining within a rubric of "sustainable development." In
contrast, ‘strong’ sustainability requires the total stock of capital to be
constant (or increasing) between generations, and further it recognises that
certain items of ‘critical natural capital’ must be preserved intact.
This would be analogous to humankind living off “natural revenue”
without causing material reduction of the natural capital base.
have developed techniques which enable financial values to be placed on
non-market goods e.g. contingent valuation methodologies (see Edwards-Jones et
al. 2000, Mitchell & Carson 1989,
Shogren & Nowell 1992),
and in this way natural capital can be valued. However, these valuation
techniques have the effect of eliminating the distinction between monetary and
non-monetary considerations. In philosophical terms, they commit the
“naturalistic fallacy,” which is to say, they confound quantity with quality
(Frankena 1939). The acceptability of so doing is a matter for intense
philosophical debate that goes beyond the scope of this article. Suffice to say
that whether we like it or not, “weak” sustainability’s common assumption
of the financial quantifiability of the natural world is often forced upon us.
As El Serafy (1996) of the World Bank asserts:
genuine income is of fundamental importance to economists, and it is the proper
measurement of that income that will satisfy the ‘weak sustainability’
criterion. This is a technical or value-free requirement that has little to do
with the environment. As such, ‘weak sustainability’ is indispensable for
accurately assessing economic performance. ‘Strong sustainability,’ by
contrast, is a normative concept, and relates to the immensely complex stock of
environmental assets and properties. Many of these are not easy (in the famous
Pigouvian phrase) ‘to bring into a relationship with the measuring rod of
Differences in Depreciation Rates over Time between natural and
application of the ‘weak’ sustainability concept appears simple when
considered within a static framework and it may be perfectly rational to trade
natural capital of a given value for human-made capital of equal or greater
value. However, the analysis
becomes more complex when considered within a dynamic framework – that is to
say, one that models economic systems through
time. One of the reasons for this increased complexity is that many
items of human-made capital depreciate over time, and as they depreciate, so the
utility derived from them declines. It remains unclear, however, if the utility
derived from natural capital declines over time, and even if it does, it may not
do so at the same rate as human-made capital. Accordingly, it may be the case
that direct comparison between natural and human-made capital is invalid, or
must be qualified, because the respective rates at which each depreciates are
is apparent from a consideration of almost any development project (e.g.
roads, houses, industrial complexes, dams and irrigation schemes) or consumer
goods (e.g. domestic appliances,
clothes, leisure equipment) that human-made capital does depreciate over time.
All such items suffer from wear and tear and in the absence of repair, this
causes a decline in their functionality and a concomitant decline in the utility
derived from them. It is not so
apparent, though, whether or not natural capital depreciates over time, nor
whether any future changes in the form of natural capital will lead to a
decrease in utility. A mountain,
for instance, does not depreciate. In
accounting terminology it might be likened to “a going concern,” and be
treated as such in terms of “going concern” accounting conventions of
valuation which do not necessarily imply depreciation. Inasmuch as the mountain
erodes over geological time, such "depreciation" is arguably
compensated for by related geomorphological processes such as soil formation,
sedimentary rock formation and fresh tectonic uplift. These changes can be
viewed, from the perspective of our current geological era, as little more than
the self-compensating ups and downs of planetary middle age.
Consequently, when considering any utility derived from mountains the
analytical time span ought to be nothing short of geological.
contrast to geological systems, changes in ecological systems may occur quite
naturally over relatively short time spans.
For example, during secondary succession, communities of annual plants
are typically replaced by woody perennials in less than a century (Southwood,
Brown and Reader 1979). In addition
to ecological change, other examples of natural capital dynamics abound.
For example in the 1960's fresh terrestrial natural capital was created
when the volcanic island of Surtsey emerged from the sea near Iceland.
The rise in biodiversity and processes of soil formation were carefully
monitored. Assuming these changes
provide satisfaction to humans or had intrinsic biodiversity value in their own
right, then this item of natural capital would seem to have
"appreciated" in "worth" in a matter of decades.
at the gross level, there is no evidence to suggest that natural capital
depreciates with time. The
"value" to humankind of any one unit of "natural capital"
may vary with time according to changes in the magnitude of time specific use
and non-use values, (e.g. as a provider of genetic material for biotechnology, as a
refuge for wildlife, or as an element in the landscape), but as long as humans
derive some satisfaction from the existence of natural capital, then whether it
be biotic or geological, the utility derived from such natural capital will
never reach zero. Accordingly, the
natural depreciation rate of natural capital tends towards zero, and in some
situations, such as where an evolutionary dynamic is taking place, it may
arguably be negative (i.e. utility
will increase over time).
points are illustrated in Figure 1. The long-term utility function for natural
capital is represented by C-D. That for human-made capital represented by the
line A-B, which makes the simplifying but often realistic assumption of
straight-line (and therefore, finite) depreciation. Total utility for natural
and human-made capital is therefore, respectively, the area within the rectangle
OCDE and within the triangle, OAB. In
order for the substitution of natural capital for human capital to be rationally
consistent with the principles of “weak” sustainability analysis, the total
utility derived from the human-made capital must be equal to or greater than
that foregone from using up the natural capital.
That is, only substitute if OAB > OCDE.
Given that it is unlikely that either geological or ecological capital naturally depreciate over the short to medium term (i.e. in time spans of less than millions of years, which effectively tends towards infinity) then as long as natural capital maintains a positive utility value it would seem likely that the total utility derived would outweigh that derived from human-made capital, which will depreciate to negligible value over short time periods (i.e. often less than 100 years). That is, OCDE is probably usually greater than OAB.
Figure 1: Trends in the utility derived from hypothetical items of human-made and natural capital over time. For simplicity, a linear rate of decline in utility is assumed for human-made capital, while for natural capital a zero rate of decline is assumed. In reality many functional forms are possible for both of these rates, but regardless of form, that for human-made capital will usually be of negative gradient, while in the long run, that for natural capital will tend towards zero.
Analytic Variations due to the Form of the Natural Capital
though, the exact outcome of any such analysis will depend upon the
characteristics of the items of natural capital under consideration.
Compare for example the characteristics of mineral oil and the entire
species of Blue Whale. Oil and
other minerals probably provide little utility in their natural state, i.e.,
they have extremely low non-use values, whereas the Blue Whale does provide
significant amounts of positive utility through its existence as an extant
species (Semples, Gowen and Dixon 1986). Conversely,
oil may provide a large amount of utility through it use-values, whereas the
use-values provided by Blue Whales, in terms of food stuffs, ecotourism or other
products, may be lower. Thus it would be more acceptable to substitute oil for
human-made capital than Blue Whales.
this example is clearly a little simplistic and contrived, a more complex and
realistic problem is provided by considering a project such as the proposed and
opposed development of the Lafarge Redland Aggregates superquarry on the Isle of
Harris in the Outer Hebrides of Scotland (McIntosh 1994-95). Here it is proposed
to quarry some ten million tonnes of aggregate per annum over sixty years from a
mountain in order to build new roads throughout Europe. While these roads will
provide utility to many people, they will inevitably degrade over time. The rock
used in them will reach a point, through the effects of pounding by traffic,
where it provides very little or no utility and has to be replaced in the course
of routine roads maintenance. In other words, the aggregate will depreciate –
typically over a period of ten to thirty years. In the case of Britain, most
used aggregate is not recycled. It is landfilled into quarry sites from which
fresh product has been extracted, therefore it could be said to have a residual
value that is nil or even negative.
proposed superquarry will require the substantial destruction of the mountain in
order to permit the removal of geological natural capital from the site. It
would be 50 times larger than a conventional (200,000 tonne per annum) large
British quarry. It would leave an opencast scar six times the height of the
White Cliffs of Dover and require 36 tonnes of explosive per week once geared up
to full production (1998 draft Scottish Office Public Inquiry Report). Over the
life of the project this would represent the equivalent of dropping six
Hiroshima-sized (13 kilotonne) atomic bombs on Harris.
a development will inevitably destroy some of the ecological communities which
currently inhabit the mountain. Golden Eagles have an eyrie just 400 metres from
the quarry boundary, Golden Plover nest there and otters have their holts down
by the shore. The reporter in the draft Public Inquiry report stated (ibid. 1999
amended version, 14:295-303):
find that the proposed quarry will completely change the landscape
characteristics of Lingerbay by changing the scale and character of the
coastline and its hinterland. Furthermore … the inevitable scale and
characteristics in terms of industrialisation of the superquarry will be so
significant that the underlying objectives of the NSA (National Scenic Area) in
terms of scenic beauty and the landscape characteristics will be materially
affected by virtue of the change from a small scale landscape of detailed
variety to a large scale industrial area… I find that the impact cannot be
described as minimal – on the contrary, it would be locally severe… The
present remote, peaceful, and traditional ensemble of a semi-natural and
crofting agriculture environment would be disrupted by the intrusion of a man
made excavation and associated quarry and harbour installations on an enormous
scale… Altogether, I find that this would have a very disruptive effect on the
character of the area affecting local residents… It would … introduce a form
of industrial activity incompatible with an area of scenic beauty.
utility currently derived by humans from the site to be quarried may only be
small, but it is positive. Summing up in the 1994-95 public inquiry – the
longest ever to run in Scotland – Mr John MacAulay, representing the local
community, said (West Highland Free Press, 9-6-95, 5):
provides peat for fuel from the lower slopes; clean fresh water from the upper
streams for public water supplies; grazing for sheep; salmon and trout from the
surrounding lochs; the very best of shellfish from round its coastline. It is of
excellent educational and recreational value, both from the geological and
historical significance of the area. It quietly dominates the crofting townships
of Strond, Borosdale, Rodel, Lingerabay and Finsbay, as well as the main
southerly village of Leverburgh. It is not a ‘holy mountain,’ but is
certainly worthy of reverence for its place in Creation.
that both Homo sapiens and the mountain with its biodiversity could both be
viewed, in accordance with standard accounting conventions, as “going
concerns,” it is possible that such utility could continue to be positive over
geological time periods. The mountain is already 1.8 billion years old (Piper
1992). The sun is not expected to go into supernova for another 4 billion years.
Yes, there will be ice-ages and other upheavals, but the rocks by and large
endure, and who are we to presume that this mountain will not therefore have
some sort of value “for as long as the Earth endures”?
against this ongoing low-level trickle of utility, if the mountain (or a
disfiguring chunk of it) is taken away, then the public inquiry report considers
that it will provide Harris people with 33 direct jobs and 10 indirect jobs,
with a further 70 or so direct jobs filled by people from surrounding islands
and the mainland. Total annual income from these jobs, at full production which
would be for only 50 years of the 60-year project life, would be £1.3 million.
In addition, there would be other benefits to stakeholders, like shareholder
dividends, which are not quantified in the report. The bottom line
consideration, however, is that a mountain that would otherwise yield utility
over a very long period of time (OCDE in Figure 1) would be turned into
roadstone, which would depreciate over a relatively short period of time (OAB in
July 2000 Sarah Boyack, Environment Minister in the Scottish Parliament
announced that a decision as to whether or not the superquarry would go ahead
was to be further delayed, pending scientific advice being taken as to whether
the mountain merited European status as a Special Area of Conservation. If this
goes ahead, the area will be safeguarded, hopefully in perpetuity, on grounds of
intrinsic value. However, let us suppose that the decision was being made on
purely economic criteria. How, then, might the considerations outlined above be
Discounting and Utility over the Long Run
standard economic approach to such a question would be to apply discounted cash
flow (DCF) methodology (see, for example, Bromwich 1976). This would quantify
and then discount the future stream of benefits from both options respectively,
and reduce them to a “net present value” (NPV) by which a comparison of the
options can be made. DCF accordingly degrades or “discounts” the value of
future returns by treating a given return in, say, ten years time as being less
valuable than the same sum received tomorrow. For example, if a discount rate of
5% is assumed, a £1 million return in 14 years’ time would be counted as
being worth only about £500,000 in today’s terms, and after 100 years the
same return would discount down to a mere £7,600 or thereabouts (put another
way, £7,600 invested today at a 5% real rate of compound interest would yield
£1 million after 100 years).
discounting presumption, “the time-value of money,” is an inevitable
consequence of money having acquired time-value in its own right, instead of
being merely a medium of exchange. It is intrinsic to any economy that allows
money to be loaned at interest. Interestingly, Islamic economics and certain
other theocratic systems explicitly try to prevent this, perhaps partly because
of its intrinsic discounting implications (Visser & McIntosh 1998).
any positive discount rate to any future return assumes that at some time in the
future an item will cease to provide material positive utility (Dixon et
al. 1988). This is a well-known economic phenomenon, and while not
necessarily problematical when used within a project analysis framework, this
property of discounting causes problems when applied to environmental goods
(Hanley and Spash 1993). In the case of natural capital, it remains undeniable
that environmental goods which exist over spans of time greater than a few
decades will supply positive utility which will not be adequately captured
within typical calculations of net present value. As Norgaard and Howarth (1995
p. 150) surmise, “A fundamental contradiction exists: all [such DCF-based]
techniques to measure benefits are developed in the context of current
generations, whereas sustainability is concerned with the future… Questions of
intertemporal resource use have been addressed only … as if the present
generation had all the rights to resources.” Harris (in Harris, J.M. & Goowin, N.R. 1992, p.
102) says of this position:
point is of extraordinary importance, for it means that hidden in the apparently
‘neutral’ principle of inter-period efficiency is a normative judgement that
gives absolute primacy to short-term, present-generation interests over future
interests in the resource and environmental area. The only justification for
this would be the assumption that future citizens are fully compensated for
resource loss and environmental degradation by the accumulation of human-made
capital. But since most of this capital itself has a lifetime of only 20 to 50
years, and since the substitutability of human-made and natural capital is a
serious question, this clearly shortchanges the future.
other words, discounting future flows of natural revenue arguably steals the
children’s future and predicates decisions made for the short-term. It is to
this mindset that we might look to discern some of the economic roots of the
the above analysis, it is suggested that the total utility derived from
non-renewable natural capital (over the long term) will almost always be greater
than that derived from any form of human-made capital for which it could be
substituted. The permanent destruction of significant parts of the natural world
can only be rationally justified if a values basis is assumed, which contrary to
El Serafy’s assumption is not a “value-free” one that presumes
discounting. From a utilitarian standpoint then, it is probably impossible to
maintain a constant stock of capital, as any loss of natural capital may result
in utility foregone. This holds true for all items of natural capital that would
provide any positive utility over a span of time which, in human terms, tends
toward infinity. However, the same does not hold true for items which might be
considered as "natural revenue," such as an individual plant or
animal. Thus, while it may be
rational to substitute between an individual tree and some timber products, it
may not be rational to substitute an entire forest for some produce. This is
because the forest, as an ecosystem, has capital attributes prerequisite to
producing a continuous flow of natural revenue, i.e., utility. The idea that the
individual members of a set may be substitutable, but that a species, community,
habitat or ecosystem is not, supports the idea of minimum impact selective
harvesting, which is a concept central to achieving the sustainable utilisation
of the environment. It implies that it is acceptable to take part of what nature
provides, but not to exhaust the whole.
this discussion is purely qualitative, several conclusions may be drawn.
Firstly, if items of natural capital provide positive utility and have the
ability to exist over long time spans, then despite fluctuations in the actual
level of utility they provide, it is unlikely that it would ever be rational to
substitute these for items of human-made capital that depreciate. That does not
mean that in practice we should not do it: it simply means that living for the
short-term cannot be classed as rational behaviour for a species that might like
to think of itself as a “going concern.”
as most of the utility provided by the items of natural capital will be related
to their non-use values, it may be possible to establish a ranking of items of
natural capital in terms of the utility foregone if they are destroyed. It is
suggested that little utility is foregone from losing pockets of minerals as
elements of natural capital, but greater amounts of utility may be foregone if
items such as whole mountains, species or forest ecosystems are lost.
the concept of "weak" sustainability is presented in many texts as the
easiest form of sustainable development that may be achieved (Pearce 1993,
Pearce and Turner 1990). However
our analysis suggests that when a dynamic element is introduced into the
analysis, it becomes apparent that even meeting the criterion of "weak”
sustainability places severe constraints on any future development requiring the
destruction of natural capital. In
fact when taken to its limit, it may be argued that so few substitutions between
"human-made" and "natural" capital will ever be rational, in
terms of utility foregone, that the whole concept of the substitution of capital
should be omitted from future discussions of "sustainable
does such an assiduous, if not to say, ascetic conclusion leave us in practical
terms? It suggests that a far more honest approach for planning future
developments than that of applying DCF to nature is to recognize that, in
addition to any other ethical considerations, any irreversible loss of natural
capital will result in a loss of utility to humankind. Therefore all such losses
should be minimised. Adherence to the idea of the substitutability of capital
simply provides a mechanism for justifying developments that are environmentally
damaging. If such developments are to continue, then their proponents
should be aware of the full consequences of their actions, rather than hiding
behind the idea of maintaining a constant stock of capital.
There are no easy answers to the conundrums of sustainable development. Probably as much as can be said was summed up by Aldo Leopold in a famous dictum in his Land Ethic: “A thing is right when it tends to preserve the integrity, stability, and beauty of the biotic community. It is wrong when it tends otherwise.”
M. (1976). The Economics of Capital Budgeting, Penguin, London.
M. and Perrings, C. (1992). Towards an Ecological Economics of Sustainability, Ecological
Economics, 6, 7-34.
J. A., Carpenter, R. A., Fallon, L. A., Sherman, P. B. and Manipomoke, S.
analysis of the environmental impacts of development projects, Earthscan Publications Ltd, London.
G, Davies B B & Hussein S (2000). Ecological
Economics: an introduction, Blackwell Scientific, Oxford.
Serafy, S. (1996). In Defence of Weak Sustainability,
Environmental Values, 5:1, 75-81.
W. K. (1939). The Naturalistic Fallacy, Mind,
N. and Spash, C. L. (1993). Cost-benefit
analysis and the environment, Edward Elgar Publishing Ltd, Aldershot.
J.M. & Goodwin, N.R. (eds.) (1992). A Survey of Ecological Economics,
Island Press, Washington.
R C and Carson
R T (1989). Using Surveys to Value
Public Goods: The Contingent Value Method. Resources for the Future,
A. (with MacLeod, D. and Stone Eagle Herney, S.) (1994-95).
Public Inquiry on the Proposed Harris Superquarry: Witness on Theological
Considerations Concerning Superquarrying and the Integrity of Creation,
Journal of Law and Religion, Hamline University School of Law, XI:2,
R. B. and Howarth, R. B. (1992). Economics, Ethics and the Environment,
summarised in Harris, J.M. & Goodwin, N.R. (eds.) (1992).
D. W. (1993). Blueprint 3: Measuring
sustainable development, Earthscan Publications Ltd, London.
D. W. and Atkinson, G. D. (1993). Capital theory and the measurement of
sustainable development: an indicator of "weak" sustainability, Ecological
Economics, 8, 103-108.
D W, Markandya A and Barbier E B (1989). Blueprint
for a green economy. Earthscan Publications Ltd, London.
D. W. and Turner, R. K. (1990). Economics
of natural resource and the environment,
Harvester Wheatsheaf, Hemel Hempstead and London.
J.D.A. (1992). Post-Laxfordian magnetic imprint in the Lewisian metamorphic
complex and strike-slip motion in the Minches, NW Scotland, Journal of the
Geological Society, 149, 127-137.
D. (1995). Sustainable Development: an Introductory Guide, Earthscan
Publications Ltd, London.
K., Gowen, M. and Dixon, J. (1986). The validity of contingent valuation method
for estimating non-use components of preservation values for unique natural
resources, paper presented to the American Agricultural Economics Association,
Reno, July 1986 (cited in Pearce, D. W., (Editor) Blueprint
2: Greening the World Economy,
Earthscan Publications Ltd, London.
J. F. and Nowell, C. (1992). Economics and Ecology: A Comparison of Experimental
Methodologies and Philosophies, Ecological
Economics, 5, 101-126.
T. R. E, Brown, V. K. and Reader, P. M. (1979).
The relationships of plant and insect diversities in succession, Biological
Journal of the Linnean Society. 12, 327-348.
R. K. and Pearce, D. W. (1993). Sustainable
economic development: economic and ethical principles.
In E. D. Barbier (Ed.) Economics
and ecology: new frontiers and sustainable development, Chapman & hall,
London, pp. 175-194.
Visser, W. & McIntosh, A. (1998). A Short Review of the Historical Critique of Usury, Accounting, Business and Financial History, 8:2, Routledge, London, 175-190.
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