Chapter 11 Cost benefit analysis

1
Chapter 11 Cost benefit analysis
11.1 Intertemporal welfare economics 11.2 Project
appraisal 11.3 Cost-benefit analysis and the
environment Learning objectives          learn
about the conditions necessary for intertemporal
efficiency          revisit the analysis of
optimal growth introduced in Chapter
3          find out how to do project
appraisal          learn about costbenefit
analysis and its application to the
environment          be introduced to some
alternatives to costbenefit analysis
2
Cost-benefit analysis
Cost-benefit analysis, CBA, is the social
appraisal of marginal investment projects, and
policies, which have consequences over time It
uses criteria derived from welfare economics,
rather than commercial criteria. CBA seeks to
correct project appraisal for market
failure Environmental impacts of
projects/policies are frequently externalities,
both negative and positive CBA seeks to attach
monetary values to external effects so that they
can be taken account of along with the effects on
ordinary inputs and outputs to the project/policy
CBA is the same as BCA Benefit-cost analysis.
3
Intertemporal efficiency
Given that CBA is concerned with consequences
over time, and based in welfare economics, a key
idea is that of intertemporal efficiency.
(11.1)
An allocation is efficient if it is impossible to
make one individual better off without thereby
making the other worse off. Intertemporal
efficiency requires the satisfaction of 3
conditions Equality of individuals consumption
discount rates Equality of rates of return to
investment across firms Equality of the common
consumption discount rate with the common rate
of return
4
Discount rate equality

otherwise one could be made better off without
making the other worse off
MRUS
MRUS

defines As consumption discount rate
Then the first intertemporal efficiency condition
is stated as rArB r (11.2) Note
consumption discount rates are not constants.
5
Shifting consumption over time
Foregoing Cb0Ca0 makes Ca1Cb1 available next
period. The rate of return to, on,investment is
defined as
where ?C1 is the second period increase in
consumption, Ca1Cb1, resulting from the first
period increase in investment ?I0, Cb0Ca0. For
?I0 ?C0, this is
which is the negative of the slope of the
transformation frontier minus 1, which can be
written
where s is the slope of the frontier.
6
Rate of return equality
If each firm were investing as indicated by C01b
and C02b, then period 1 consumption could be
increased, without loss of period 0 consumption,
by having firm 1, where the rate of return is
higher, increase investment by the amount firm 2,
where the rate of return is lower, reduced its
investment. Only where rates of return are equal
is this kind of period 1 gain impossible. For N
firms, the second intertemporal efficiency
condition is
(11.3)
7
Equality of discount rate and rate of return
If the first two conditions are satisfied, we can
consider representative individual and
firm. Point a corresponds to intertemporal
efficiency, b and c do not as from either could
reallocate consumption as between periods so as
to move on to a higher consumption indifference
curve. At a the slopes of the consumption
indifference curve and the consumption
ttansformation frontier are equal. The third
condition is
(11.4)
8
Intertemporal optimality
As in the single period situation, the
intertemporal efficiency conditions do not fix a
unique intertemporal allocation. That requires a
social welfare function with utilities as
arguments Will consider this under Optimal
growth models
9
Markets and intertemporal efficiency futures
markets
Futures Markets X at t is treated as a different
commodity from X and t1 For N commodities and M
periods there are MN dated commodities. Contracts
are written at the start of the first period for
trades an all commodities at all future
dates. Then, it is effectively the static
case. Given that all ideal circumstances apply in
all MN markets, the conditions for intertemporal
efficiency will be satisfied. Futures markets
are, in fact, rare standardised raw materials,
financial instruments.
10
Markets and intertemporal efficiency loanable
funds market
Loanable Funds Market
x is the bond coupon paid on the first day of
period 1 Pb is the price the bond trades for on
the first day of period 0 i is the interest
rate A seller is a borrower A buyer is a lender
11
Individuals - utility maximisation
UU is a consumption indifference curve, slope
(1r) Line C1max C0max is the budget constraint,
slope (1i) Optimum is at C0 in period 0 and
C1 in period 1, where r i which will hold for
all individuals, satisfying the first
intertemporal efficency condition
12
Firms present value maximisation
Owners of firms can shift consumption
by investing in firm dealing in the bond
market AB shows C0 C1 combinations on account of
varying investment, slope (1 d), d is the rate
of return to investment RS with slope -(1i)
shows how consumption can be shifted via bond
market dealing.
The optimum level of investment is at a, where
the present value of the firm is maximised, and
where i d In the second stage the owner
maximises utility, by bond market dealing, at b
where i r All owners so act, and the three
conditions for intertemporal efficiency are
satisfied.
13
Optimal growth modelling discrete time
A representative individual model for two
periods Maximise
(11.5a)
subject to Q0(K0) (K1 K0)
C0 (11.5b) Q1(K1) (K2 K1) C1 (11.5c)
Here the efficiency problem is trivial
consumption in one period can only be increased
by reducing it in the other period. A necessary
condition is
(11.6)
So with diminishing marginal utility, C1 greater
than C0 implies that ? (the utility discount
rate) is less then d (the rate of return on
investment). For ? d, consumption is constant.
14
Optimal growth modelling continuous time
Maximise
(11.7a)
Subject to
Q(Kt) - Ct
(11.7b)
has necessary condition
(11.8)
where ? is a parameter, the utility discount
rate, and d is a variable, the rate of return to
capital accumulation. For d gt ?, given
diminishing marginal utility, C is growing.
Consumption growth ceases when d ?.
15
Optimal growth in the basic model
16
A model with resource input to production
Maxximise
(11.9a)
Subject to
(11.9b)
(11.9c)
In this model intertemporal efficiency is not
trivial. There are two forms of investment, in
capital and in the resource stock. Efficiency
requires that the rates of return on the two are
equal. See chapter 14 especially
17
Utility and consumption discount rates 1
Figure 11.8 Indifference curves in utility and
consumption space
intertemporal welfare function for panel a
slope of WCWC in panel b
(11.10)
18
Utility and consumption discount rates 2
In continuous time
(11.11)
where r is the consumption discount rate ? is
the utility discount rate ? is is the elasticity
of marginal utility for the instantaneous
utility function g is the growth rate For ggt0
rgt ? and r would be positive for ? 0 For g 0
r ?
19
Private project appraisal the Net Present Value
test 1
The present value of expenditures E is
(11.14)
The present value of receipts R is
(11.15)
The present value of the project is
(11.16)
Which for N R - E is
(11.17)
The project should go ahead iff NPV0
20
Private project appraisal the Net Present Value
test 2
Table 11.2 Example net cash flow 1
at i 0.05, NPV 4.6151 at i 0.075, NPV
0 at i 0.10, NPV -4.27874 The NPV of a
project is the amount by which it increases the
firms net worth. It is the present value of the
surplus, after financing the project, at the end
of the project lifetime.
21
Private project appraisal - risk
Table 11.4 One project, two possible cash flows
Table 11.5 Calculation of expected NPV
Where the firm is prepared to assign
probabilities, the criterion for going ahead with
the project is the expected NPV the probability
weighted sum of the mutually exclusive cash flow
outcomes. This assumes that the decision maker is
risk-neutral Chapter 13 on decision making in
the face of imperfect knowledge of the future.
22
Social project appraisal
CBA is the social appraisal of projects CBA uses
the NPV test CBA can be approached in two
ways As an extension of private appraisal where
externalities are taken into account In terms
of social welfare enhancement The first stages of
CBA are proper project/policy identification for
ecasting all of the consequences of the
project/policy for all of the affected
individuals in each year of the project/policy
lifetime Then expressing consequences in terms
of monetary gains/losses for aggregation to an
NPV number
23
Social appraisal an illustrative project
Table 11.6 Net benefit (NB) impacts consequent
upon an illustrative project
Generally, go ahead if
(11.19)
24
CBA as a potential pareto improvement test
A positive NPV indicates that, with due allowance
for the dating of costs and benefits, the project
delivers a surplus of benefit over cost. The
consumption gains involved are greater than the
consumption losses, taking account of the timing
of gains and losses. The existence of a surplus
means that those who gain from the project could
compensate those who lose and still be better
off. Finance by taxation two periods The
initial investment is ?I0, equal to -?C0, and the
consumption increment on account of going ahead
with the project is ?C1. First period consumers
lose an amount ?C0, equal to ?I0, and second
period consumers gain ?C1, and the question is
whether the gain exceeds the loss. From the
viewpoint of the first period, the second period
gain is worth ?C1/(1r), so the question is
whether ?C1/(1r) gt ?I0 (11.20)   is
true, which is the NPV test discounting at
r. Finance by borrowing two periods The
government funds the project by borrowing and the
project displaces the marginal private sector
project with rate of return d. In this case the
cost of the public sector project is ?I0 in the
first period plus d?I0 in the second, this being
the extra consumption that the private sector
project would have generated in the second
period. In this case, from the viewpoint of the
first period, the gain exceeds the loss if
(11.21)   This is the NPV test with the
consumption gain discounted at the consumption
rate of interest, and compared with the cost of
the project scaled up to take account of the
consumption that is lost on account of the
displaced private sector project.  
25
CBA as welfare increase test 1
Table 11.7 Changes in utility (?U) consequent on
an illustrative project
?W W(?UA,0,..., ?UC,3) positive the project
should go ahead Or with an intratemporal social
welfare function mapping individual utilities
into a social aggregate ?Ut ?W W(?U0, ?U1,
?U2, ?U3) positive the project should go ahead
where a widely entertained particular form
is
is exponential discounting
26
CBA as welfare increase test 2
Utility variations consequent on going ahead with
the project cannot be estimated. But, using the
methods of chapter 12, monetary equivalent gains
and losses can be estimated.
implies
(11.22)
where
or r ? ?g (11.23)
or
27
CBA as welfare increase test 3
The NPV test is interpreted as a test that
identifies projects that yield welfare
improvements - positive and negative consumption
changes, net benefits that is, are added over
time after discounting, so that
(11.24)
and for ?W gt 0 the project is welfare enhancing
and should go ahead
Finance by taxation two periods
(11.25)
where the rhs is NPV, positive for ?C1/(1r) gt
?I0 Finance by borrowing, two periods If the
project crowds out the marginal private sector
project
(11.26)
where the rhs is NPV, positive if
28
Choice of discount rate 1
There is disagreement about the discount rate
that should be used in CBA This matters because
the result of the NPV test can be very sensitive
to the number used for the discount rate. This is
especially true where the project lifetime is
long, as it often is with projects with
environmental consequences the lifetime is when
the longest lasting consequence ceases, not when
the project stops yielding the benefits which
were its purpose nuclear electricity generation
and waste products.
Table 11.8 Present values at various discount
rates For 100 at futurity shown
29
Choice of discount rate 2
With no market failure r i d Given market
failure which to use? Generally agreed that
whichever way looking at CBA potential pareto
improvement or welfare enhancing should use r,
the consumption discount rate. Shadow pricing
While it is agreed that r should be used to
discount, d appears in the NPV criterion as
(11.21) and
(11.26)
which apply with finance by borrowing when there
is crowding out d is there to adjust the
initial cost, shadow price it, for the
displacement of the marginal private sector
project. At one time it was thought that, on
account of crowding out, proper shadow pricing of
all inputs and outputs was important in CBA. And
difficult. Now the dominant view is that given
international capital mobility, crowding out is
not a problem that the supply of capita for
private sector projects could be treated as
perfectly elastic. Shadow pricing is not now seen
as necessary in CBA
30
Choice of discount rate 3 descriptive versus
prescriptive
Regarding CBA as about potential pareto
improvement aligns with the descriptive approach
to determining a number for r it should be the
post tax return on risk free lending reflecting
the rate at which people are willing to exchange
current for future consumption. Those who regard
CBA as a test for welfare enhancement tend to
adopt the prescriptive approach to a number for
r, according to
r ? ?g (11.23)
where ? is the utility discount rate ? is the
elasticity of the marginal utility of
consumption g is the growth rate Some economists
want to get values for ? and ? from observed
behaviour, some from ethical considerations. Much
of the controversy among economists over the
Stern Review of the climate change problem
focussed on the numbers used in (11.23) Stern
took an ethical prescriptive position
31
Box 11.2 Discount rate choices in practice
US Office of Management and Budget 7 as an
estimate of pre-tax return on capital US
Environmental Protection Agency For
intragenerational descriptive, r as 2-3 For
intergenerational - r ? ?g with ? 0 on
ethical grounds, gives r 0.5 to 3 HM Treasury
UK Green Book instructions based on r ? ?g
evidence suggests ? 1.5, ? 1 and g 2
giving r 3.5.
For lifetimes greater than 30 years
because of uncertainty about the future The
Stern Review Implicit r of 2.1 from r ? ?g
with ? 0.1, ? 1, and g 2.
32
Environmental cost-benefit analysis
Look at wilderness area development. With Bd for
development benefits and Cd for development
costs, and ignoring environmental impact
Denote this as NPV. Then the proper NPV taking
account of environmental impacts is NPV Bd Cd
EC NPV EC (11.27) where EC is the
present value of the stream of the net value of
the projects environmental impacts over the
lifetime of the project. EC stands for
Environmental Cost From (11.27) the project
should go ahead if NPV Bd Cd gt EC
(11.28)
33
Inverse ECBA
A wilderness development project should not go
ahead if EC NPV Bd Cd so that EC NPV
Bd Cd (11.29) defines a threshold
value for EC. For EC EC the project should not
go ahead. The exercises ( Chapter 12 ) that seek
to ascertain EC are typically expensive, and
sometimes controversial. Consideration of EC can
put their results in perspective. As can
consideration of EC/N, where N is the size of
the relevant affected population, which is not
necessarily restricted to visitors, and may
include people from a wider area than the host
country, as with an internationally recognised
wilderness/ conservation area inscribed as world
heritage.
34
Box 11.3 Mining at Coronation Hill?
In 1990 there emerged a proposal to develop a
mine at Coronation Hill in the Kakadu national
park, which is listed as a World Heritage Area.
The Australian federal government referred the
matter to the Resource Assessment Commission,
which undertook a very thorough exercise in
environmental valuation using the Contingent
valuation Method, implemented via a survey of a
sample of the whole Australian population. This
exercise produced a range of estimates for the
median willingness to pay, WTP, to preserve
Coronation Hill from the proposed development,
the smallest of which was 53 per year. If it is
assumed, conservatively, that the 53 figure is
WTP per household, and this annual environmental
damage cost is converted to a present value
capital sum in the same way as the commercial NPV
for the mine was calculated, the EC to be
compared with the mine NPV' is, in round numbers,
1500 million. This 'back of the envelope'
calculation assumes 4 million Australian
households, and a discount rate of 7.5.   It was
pointed out that given the small size of the
actual area directly affected, the implied per
hectare value of Coronation Hill greatly exceeded
real estate prices in Manhattan, whereas it was
'clapped out buffalo country' of little
recreational or biological value. In fact,
leaving aside environmental considerations and
proceeding on a purely commercial basis gave the
NPV' for the mine as 80 million, so that the
threshold per Australian household WTP required
to reject the mining project was, in round
numbers, 3 per year, less than one-tenth of the
low end of the range of estimated household WTP
on the part of Australians. Given that Kakadu is
internationally famous for its geological
formations, biodiversity and indigenous culture,
a case could be made for extending the existence
value relevant population, at least, to North
America and Europe. In the event, the
Australian federal government did not allow the
mining project to go ahead. It is not clear that
the CVM application actually played any part in
that decision.
35
The Krutilla-Fisher model 1
NPV is the result of discounting and summing over
the projects lifetime an annual net benefit
stream which is   NBt Bd,t Cd,t
ECt (11.30)   where Bd,t, Cd,t and ECt are the
annual, undiscounted, amounts for t 1, 2,...,
T, and where T is the project lifetime,
corresponding to the present values Bd, Cd and
EC. The environmental costs of going ahead with
the project, the ECt, are at the same time the
environmental benefits of not proceeding with it.
Instead of ECt we could write B(P)t for the
stream of environmental benefits of
preservation.4 If we also use B(D)t and C(D)t for
the benefit and cost streams associated with
development when environmental impacts are
ignored, so that B(D)t C(D)t is what gets
discounted to give NPV?, then equation 11.30 can
also be written as   NBt B(D)t C(D)t
B(P)t (11.31)

Switching to continuous time, instead of
we use
which can be written as
(11.32)
36
The Krutilla-Fisher model 2
Krutilla-Fisher (1975) argued that value of
wilderness services relative to those of
development outputs will increase over time due
to substitution possibilities wrt development
output technical progress in development
activities income elasticity of demand for
wilderness services, fixed in supply Assume
preservation benefits grow at rate a -
(11.33)
which with B and C for constant flows of
development benefits and costs, and Peat as the
growing flow of preservation benefits, can be
written
(11.34)
For given NPV, agt0 reduces NPV a development
is less likely to pass the NPV test if the
Krutilla-Fisher arguments hold For a r means
preservation benefits effectively not
discounted agtr means effective negative
discounting on preservation benefits
37
The Krutilla-Fisher model 3
Let T? ? for two reasons For a constant flow
of x, the present value is x/r For wilderness
impacting projects, T will generally be very
large For T? ?, (11.34) becomes NPV NPV
P/(r-a) (11.35)
Table 11.9 P/(r-a) for P 1
38
Discount rate adjustment?
Working with a lower discount rate does not
always favour preservation.
With D for net development benefits
For large T this is approximated by
(11.36)
With X for start-up costs
(11.37)
X 1000, D 75, P 12.5. For a 0. r 0.055
gives NPV 136.37, r 0.045 gives NPV 388.89
lowering the discount rate increases NPV For a
0.025. r 0.055 gives NPV -53.03, r 0.045
gives NPV 41.66 lowering the discount rate
makes the project viable.
39
Objections to environmental cost-benefit analysis
ECBA is based in welfare economics which is
consequentialist and subjectivist. Essentially it
accepts that the natural environment should be
subject to consumer sovereignty Two main classes
of objection at the level of principle. 1. Accept
that only human interests count, but reject
consumer sovereignty as proper guide to those
interests on the grounds of inadequate
information about consequences insufficiently
deliberative lacking self-knowledge preference
shaping 2. The interests of other living entities
should be taken into account Some question the
ECBA agenda at the level of practice can
Chapter 12 methods actually deliver the necessary
information?
40
Limits to applicability of ECBA -sustainability
and environmental valuation
There is no guarantee that the subjective
assessment of their utility losses by individuals
will be large enough to stop a project that
threatens resilience, and thus sustainability.
Implicit in ECBA is the assumption of weak
sustainability, which ignores critical natural
capital and non-substitutabilities as between
reproducible and natural capital. ECBA should be
restricted in its application
41
Alternatives to environmental cost-benefit
analysis
Two stage processes Assessment of consequences
Environmental Impact Assessment, Impact
Assessment, Social Impact Assessment. (
Assessment estimation ) This can be left to
experts Evaluation of consequences Not to be
left to experts Multi-criteria
analysis Deliberative polling Citizens juries
42
An illustrative transport problem
The results of the impact assessment are
Table 11.10 Options for reducing traffic
delays
Cost effectiveness analysis gives priority to one
aspect of performance - select the option that
achieves specified objective at least cost. For
minimum acceptable time saving 8000 million hours
per year, A over achieves and costs less than B.
43
MCA - weighted sums 1
There are several forms of MCA according to how
evaluations on different criteria are combined to
choose an option weighted sums is the simplest.
44
MCA weighted sums 2
Convert the data to dimensionless form, so as to
permit aggregation. This is done by expressing
the criterion outcome for each option as a ratio
to the best outcome for the criterion which is
set equal to 1. Gives the dimensionless
evaluation table
For weights
multiplying dimensionless evaluation table and
summing gives
This ranks options 1. Highway 2. Railway 3.
Highway and buses
45
MCA weighted sums 3
For weights
get
and the ranking is 1. Railway 2. Highway 3.
Highway and buses
46
Deliberative polling
1. Run an opinion poll 2. Get respondents to a
meeting to collectively consider the issues by
hearing and questioning expert witnesses, and
debating ( deliberation ) 3. Get respondents to
respond again to original survey Given that the
idea is to poll a random sample of sufficient
size to produce results of standard expected in
opinion polling, 100s, the deliberative part of
the exercise is expensive. Deliberative polling
is rare.
47
Citizens juries
Citizens juries involve the public in their
capacity as ordinary citizens with no special axe
to grind. They are usually commissioned by an
organisation which has power to act on their
recommendations. Between 12 and 16 jurors are
recruited, using a combination of random and
stratified sampling, to be broadly representative
of their community. Their task is to address an
important question about policy or planning. They
are brought together for four days, with a team
of two moderators. They are fully briefed about
the background to the question, through written
information and evidence from witnesses. Jurors
scrutinise the information, cross-examine the
witnesses and discuss different aspects of the
question in small groups and plenary sessions.
Their conclusions are compiled in a report that
is returned to the jurors for their approval
before being submitted to the commissioning
authority. The jurys verdict need not be
unanimous, nor is it binding. However, the
commissioning authority is required to publicise
the jury and its findings, to respond within a
set time and either to follow its recommendations
or to explain publicly why not. As compared with
deliberative polling, a major advantage of the
citizens jury is cost.  
48
Box 11.4 Deliberative polling and nuclear power
in the UK
In the early years of the twenty-first century
the UK government came to the view that, on
account of the age of the existing nuclear plant,
security of supply issues, and the climate change
problem, it was necessary to re-visit the
question of whether new nuclear plant was
desirable. The UK government initiated a
consultation process and subsequently, in July
2006, it issued a report giving its view that
nuclear power had a continuing role in the
electricity supply system, and that it would look
favourably on projects to build new nuclear power
stations. Consequent upon a legal challenge by
Greenpeace, the High Court ruled that the
government's decision making process had been
unlawful in as much as it had failed to engage in
adequate consultation. Following this
decision, in May 2007 the UK government initiated
a new consultation process, one element of which
was a deliberative polling exercise. This took
place in September 2007. The report on this
exercise written by the market research firm,
Opinion Leader. On most questions, the change in
the response percentages as between the initial
and the final polls was small. Greenpeace
looked at the information provided to the
participants and took the view that it was biased
in favour of nuclear power. In October 2007,
Greenpeace complained about the work of Opinion
Leader to the Market Research Standards Board
The MRSB considered the Greenpeace complaint
against B14 of the MRS code of conduct, which
states that MRS members 'must take reasonable
steps to ensure that Respondents are not led to a
particular answer.' The MRSB found that Opinion
Leader had not complied with B14, noting that
'deliberative research is a relatively new
technique and that there are no current MRS
guidelines on preparation or review of research
materials specific to deliberative research'.
The UK government published Meeting the Energy
Challenge A White Paper on Nuclear Power in
January in 2008, in which it drew on the results
of the consultation exercise, and in which it
stated its conclusion that 'it would be in the
public interest to allow energy companies the
option of investing in new nuclear power
stations' and that ' the government should take
active steps to facilitate this'.