DRAFT July 1998
Table of Contents
Preface
For managers
For analysts
Acknowledgements
1. Introduction
1.1 Resource-allocation decisions Involve choices
1.2 Who is this guide for?
1.3 Why benefit-cost analysis?
1.4 Where benefit-cost analysis fits into the
decision-making process
2. The benefit-cost analysis model
2.1 Introduction
2.2 The benefit-cost analysis framework
2.3 The steps in benefit-cost analysis
2.4 Why is a point of view important?
2.5 The components of benefit-cost analysis
2.6 Constructing tables of costs and benefits
2.7 Accounting conventions
2.8 The report
3. Defining fair options
3.1 Why are fair options difficult to define?
3.2 An optimised base Case
3.3 How to construct fair options
3.4 Incremental effects analysis
4. Measuring and valuing costs and benefits
4.1 Introduction
4.2 Some Important Concepts
4.3 Valuing costs and benefits by market prices
4.4 Consumer surplus and producer surplus as components
of value
4.5 Valuing costs and benefits without good market
prices
4.6 Some examples of difficult-to-estimate values
4.7 Misuse of benefit multipliers
5. Time values
5.1 Why time matters
5.2 Inflation, nominal dollars and constant dollars
5.3 Changes in relative prices
5.4 Future and present values
5.5 Discount rates
5.6 Strategic effects of high and low discount rates
5.7 The discount rate as a risk variable
6. Decision rules
6.1 Net present value
6.2 Two essential decision rules
6.3 Unreliable decision rules
7. Sensitivity analysis
7.1 What is sensitivity?
7.2 Gross sensitivity
7.3 What determines sensitivity?
7.4 Sensitivity and decision making
7.5 Two-variable sensitivity analysis
7.6 Graphic analysis of sensitivity
7.7 Action on sensitivities
8. General approaches to uncertainty and risk
8.1 Approaches to quantifying uncertainty-related risk
8.2 Expected values of scenarios
8.3 Risk-adjusted discount rates
8.4 Risk analysis through simulation
9. Risk analysis
9.1 Introduction
9.2 The steps of risk analysis
9.3 The mechanics of risk analysis
9.4 Adjusting for the covariance of related risk
variables
9.5 How many times does the model need to run?
9.6 Interpreting the results of the risk analysis
9.7 Decision rules adapted to uncertainty
9.8 Assessing overall risk
9.9 The advantages and limitations of risk analysis
10. Probability data
10.1 Types of risk variables
10.2 Using historical data
10.3 Expert judgement
10.4 Common probability distributions
10.5 Risk preferences
10.6 Common project risks
11. Comparing options of different types against different
criteria
11.1 Issues of fairness
11.2 Multiple objectives
12. Key best practices
Appendix A: Glossary
Appendix B: Questions to ask about a benefit-cost
analysis
A quick guide
Appendix C: Selected readings
General readings
Note: The Guide follows the steps of a benefit-cost
analysis, from defining the problem and fair
comparisons, to measuring costs and benefits, to
dealing with uncertainty and risk. The final chapter
discusses what should be done when the analyst must
step outside the benefit-cost framework to consider
other criteria.
Each chapter ends with a short summary of best
practices and the Guide itself ends with a general
summary. There is a glossary of terms, and terms
flagged in bold type in the text can be found in
that glossary. Terms in bold italic are defined
where they are introduced. At the end of the Guide
there is a bibliography of selected readings,
arranged by topic.
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Preface
This Guide provides a framework for benefit-cost analysis. It
should be used in submissions to the Treasury Board when the
matter has significant social, economic or environmental
implications. A sound benefit-cost analysis should be at the
heart of every business case presented to senior managers and
to ministers. The new Guide is part of the Government of
Canada's focus on evidence-based and analytical decision
making.
However, the Guide is not the last word on benefit-cost
analysis. It is written to be a useful tool for economists
and non-economists alike. It provides the essential framework
and, where possible, indicates best practice; however, it
does not replace the need for training in assessing costs and
benefits.
For managers
Managers can use the Guide to help them design and commission
benefit-cost analyses and improve their understanding of the
findings. Consistent application of the techniques set out in
the Guide is key. Both managers and the Treasury Board need
to be able to compare alternative courses of action in a
standard and rigorous way if scarce resources are to be used
to best advantage.
For analysts
This Guide is meant to be an authoritative statement of how a
benefit-cost analysis should be undertaken for the Government
of Canada. It replaces the previous Treasury Board
Benefit-Cost Analysis Guide which was published in
1976. It provides a consistent framework for comparative
analysis but, of course, it does not cover every aspect of
the measurement of benefits and costs. Nor does it replace
the professional expertise, which the analyst and the manager
bring to each case. There is no cookbook for good decision
making - a good framework is necessary, but insight is
equally necessary.
Acknowledgements
This Guide was developed under the direction of two
inter-departmental committees led by the Treasury Board
Secretariat. One committee comprised experts in the technical
topics; and the other comprised general managers and
potential users of benefit-cost analyses. The principal
author of the Guide was Kenneth Watson, Ph.D., contracted to
Consulting of Audit Canada. Staff of the Treasury Board
Secretariat and of Consulting and Audit Canada made
significant contributions; as did the members of the advisory
committees. This Guide would not have been possible without
the generous intellectual contribution of all involved.
1.
Introduction
1.1
Resource-allocation decisions Involve choices
Managers and analysts throughout the government are often
asked to provide analysis in support of resource-allocation
decisions that affect the government and, perhaps to a
greater degree, also affect resources outside government.
Difficult choices are involved when resources are scarce.
There is also increasing recognition that governments must be
careful how they draw upon and regulate private-sector
resources. Even in the apparently simple 'do it' or
'don't do it' choice, there may be compelling
arguments in favour of the 'don't do it'
option. Any action that consumes resources that could
be put to another, and perhaps better, use must have a
powerful justification. Frequently, there are several
alternatives. In the past, the option of proceeding with a
program was usually set against some theoretical alternative
use of funds. Today, governments are often forced to finance
new programs at the expense of existing ones
Sometimes the decisions go all the way to Cabinet; this
happens, for example, when legislation or regulations change,
or a substantial program initiative is involved. More often,
senior management in the department will settle issues such
as allocation of resources within a program. Sometimes
program heads make the decisions at lower levels. Regardless
of who makes the decision, the principles to be used are the
same; what varies is level of investment in analysis
justified by the resources at stake. As the title of this
guide suggests, the principles are those of
benefit-cost analysis.
1.2 Who is this
guide for?
This guide is intended for two groups:
-
analysts who conduct studies in support of decisions; and
-
managers who use the results of the studies.
Analysts in government are, for the most part, not
economists, although most have some economic training.
To the greatest extent possible, this guide has been designed
for the larger population, rather than specialist.
Economists, however, should find that the standard framework
offered here makes it easier to compare projects from
different sources and easier to communicate results to
managers who are familiar with the framework.
The terminology in this guide tends to be drawn from
economics. There may be same differences in the usage of the
same terms in other fields. For example, in this guide,
risk analysis normally deals with any
uncertainty whether the uncertain factor is negative or
positive, and whether the uncertainty is in the probability
of occurrence, in the magnitude of effect, or in the monetary
value of the effect. In contrast, some fields tend to think
of risk more narrowly as solely an adverse factor with
emphasis on the probability of occurrence. Normally, the
context will make it clear what usage is being followed.
Although attempting to span wide areas within the
policy-analysis community has potential pitfalls, it is
evident that the guide will meet its intended purpose only if
it reaches out to a wide readership. To facilitate this, the
authors have defined terms as they arise and have provided a
glossary (see Appendix A).
In summary, the guide has the following objectives:
-
to provide an understanding of how benefit-cost analysis
can help in decision-making ;
-
to establish a general framework that will lend
consistency to analyses, facilitating their comparison and
ensuring good practices whether the analyses are performed
by departmental specialists or by consultants;
-
to serve as a self-instruction manual with concrete and
detailed guidance on the basic elements of analysis; and
-
to help analysts and managers determine when more
sophisticated analysis might be required than can be
generated internally and to standardize expectations about
what work departmental specialists or consultants will
provide.
1.3 Why
benefit-cost analysis?
Some think of benefit-cost analysis as a narrow financial
tool. However this underestimates its versatility in
addressing intangible values. Recent methodologies can help
to estimate the value to Canadians of intangible benefits. At
least we can often set a clear cost estimate against
alternative ways of achieving an intangible benefit such as
fairness in our immigration program.
Choices that confront policymakers have to be made.
Quantitative analysis of probable outcomes of alternative
courses of action can diminish the uncertainty and improve
the decision-making process.
The current situation, in which programs seem to be
perpetually under review, will probably persist for some
years. Interest payments on the national debt now swallow
such a large proportion of government revenues that funds
available for program expenditures have shrunk considerably.
Many programs that continue to offer useful services and
outputs are being cut. Ministers are faced with
difficult decisions; it is up to analysts to provide the most
solid basis for those decisions.
But what criteria should be used?
Brief reflection on the question suggests that tax money
should go to support programs where it will do the most good
given the choices available. Defining does the most
good and given the choices available captures the
essential focus of benefit-cost analysis.
The basic elements are benefits, costs and choices. It is not
a long step from 'doing the most good' to
'creating the greatest (net) benefit.' The same
resources can not be committed to different ends. With a
limited budget, we must to be certain that each project
chosen has the largest possible value per dollar expended.
1.4 Where
benefit-cost analysis fits into the decision-making
process
New initiatives, especially those requiring legislation, go
to Cabinet or, more commonly, a committee of Cabinet. There
is a guide to drafting memoranda to Cabinet that specifies
the general framework for the analysis necessary. It focuses
on identifying the implications for particular segments of
society and the evaluation of each option. Net benefit is not
the only concern: distributional effects are
often important.
Major redirection of programs often requires a submission to
the Treasury Board, even when legislative change is not
required and sufficient money already exist in the budget.
Expenditure authorisations are usually tied to the
performance of certain activities (not just overall goals),
so major modifications have to come back to the Board for
approval. Major Crown Projects (MCPs) and expenditures in any
department that exceed defined limits also go before the
Board. The Treasury Board Submissions Guide and the
MCP policy both refer to the need for justification in terms
of benefit-cost analysis. The present guide is a reference
that not only sets down the basics of such analysis, but also
establishes reporting conventions to ensure greater
comparability of programs.
The annual process of approving department's expenditure
plans has been undergoing substantial change. Over time, the
Government of Canada has put more emphasis on performance
assessment. In the mid-nineties, the government introduced
new instruments that have performance assessment as a key
component: the departmental business plan (submitted to
Treasury Board and Cabinet); the departmental performance
report (submitted to Parliament); and the Treasury Board
President's report on performance review in the
government (submitted to Parliament).
The business plans set out the departments' strategies,
objectives and performance commitments. For some departments,
these commitments involve serious adjustments, because of the
changes to size, scope and strategy they have had to make.
The business plans also set out the departments'
commitments to review their major projects, programs and
structural or resource changes. The Treasury Board of Canada
Secretariat recommends that departments submit these reviews
in the benefit-cost analysis format described in this guide.
For decisions that do not involve important policy issues, do
not exceed ministers' delegated authority, or can be
made at lower levels (for example by an assistant deputy
minister), the use of this guide is still good practice. Many
departments are adopting the language of the business case to
analyse whether the expected return is worth the effort
(benefits are greater than costs).
2. The benefit-cost analysis model
2.1 Introduction
Benefit-cost analysis is simply rational decision-making.
People use it every day, and it is older than written
history. Our natural grasp of costs and benefits is sometimes
inadequate, however, when the alternatives are complex or the
data uncertain. Then we need formal techniques to keep our
thinking clear, systematic and rational. These techniques
constitute a model for doing benefit-cost analysis.
They include a variety of methods:
-
identifying alternatives;
-
defining alternatives in a way that allows fair
comparison;
-
adjusting for occurrence of costs and benefits at
different times;
-
calculating dollar values for things that are not usually
expressed in dollars;
-
coping with uncertainty in the data; and
-
summing up a complex pattern of costs and benefits to
guide decision-making.
It is important to keep in mind that techniques are only
tools. They are not the essence. The essence is the clarity
of the analyst's understanding of the options.
2.2 The benefit-cost analysis
framework
Even when the measurements of costs and benefits are
complete, they might not speak for themselves until they are
put in a framework. Benefit-cost analysis provides that
framework. It can be used wherever a decision is needed and
is not limited to any particular academic discipline, such as
economics or sociology, or to any particular field of public
or private endeavour. It is a hybrid of several techniques
from the management, financial and social sciences fields.
As far as possible, benefit-cost analysis puts both costs and
benefits into standard units (usually dollars) so that they
can be compared directly. In some cases, it is difficult to
put the benefits into dollars, so we use
cost-effectiveness analysis, which is a
cost-minimization technique. For example, there might be two
highway-crossing upgrade options that will result in the same
saving of lives. In this case, we choose between the options
on the basis of minimum cost.
The feature that distinguishes benefit-cost analysis from
cost-effectiveness analysis is the attempt benefit-cost
analysis makes to go as far as possible in quantifying
benefits and costs in money terms. However, benefit-cost
analysis rarely achieves the ideal of measuring all
benefits and costs in money terms ... so the distinction
is merely a difference in degree and not in kind.
- Treasury Board, Benefit-Cost Analysis Guide, 1976
2.3 The steps in benefit-cost
analysis
There is no 'cookbook' for benefit-cost analysis.
Each analysis is different and demands careful and innovative
thought. It is helpful, however, to have a standard sequence
of steps to follow. This provides consistency from one
analysis to another, which is useful to both the analysts
doing the study and the managers reading the report.
Obviously, the ... steps cannot be performed by the
analyst in isolation and will require consultations with
the decision-maker and others, the gathering of a wide
variety of information, and the use of a number of
analytical techniques. It is important that, as the
analyst proceeds, the decision-maker is kept in touch with
the form of the analysis and the assumptions being made.
- Treasury Board, Benefit-Cost Analysis Guide, 1976
A set of standard steps is listed below. Each step is
explained in the chapter indicated.
-
Examine needs, consider constraints, and formulate
objectives and targets. State the point of view from which
costs and benefits will be assessed. (See this chapter.)
-
Define options in a way that enables the analyst to
compare them fairly. If one option is being assessed
against a base case, ensure that the base case is
optimised. (See Chapter 3.)
-
Analyze incremental effects and gather data about
costs and benefits. Set out the costs and benefits over
time in a spreadsheet. (See Chapter 4.)
-
Express the cost and benefit data in a valid standard unit
of measurement (for example, convert nominal
dollars to constant dollars, and use accurate,
undistorted prices). (See Chapter 5.)
-
Run the deterministic model (using single-value
costs and benefits as though the values were certain). See
what the deterministic estimate of net present value
(NPV) is. (See Chapter 6.)
-
Conduct a sensitivity analysis to determine which
variables appear to have the most influence on the NPV.
Consider whether better information about the values of
these variables could be obtained to limit the
uncertainty, or whether action can limit the uncertainty
(negotiating a labour rate, for example). Would the cost
of this improvement be low enough to make its acquisition
worthwhile? If so, act. (See Chapter 7.)
-
Analyse risk by using what is known about the ranges and
probabilities of the costs and benefits values and
by simulating expected outcomes of the investment. What is
the expected net present value (ENPV)? Apply the
standard decision rules. (See chapters 8 and 9.)
-
Identify the option, which gives the desirable
distribution of income (by income class, gender or region
- whatever categorisation is appropriate). (See
Chapter 10.)
-
Considering all of the quantitative analysis, as well as
the qualitative analysis of factors that cannot be
expressed in dollars, make a reasoned recommendation.
This sequence is the preferred way to structure the
benefit-cost analysis report.
2.4 Why is a
point of view important?
A good way to start a discussion of benefit-cost analysis is
by noting that the benefit-cost analyst must work
consistently from a clear point of view. Whose costs and
benefits are being assessed? The analyst is not restricted to
a single point of view. The government might take the narrow
fiscal point of view, for example, or a broad social point of
view, or both. Whatever the point of view chosen, each
analysis must take a single point of view and it must be
stated clearly at the outset.
It is obvious that a cost from one person's point of
view can be a benefit from another's. What is obvious
when stated, however, is sometimes not obvious in the midst
of an analysis. It is not at all uncommon to see lists of
benefits or costs that are apples and oranges as far as a
consistent point of view is concerned. Should taxes levied be
counted as a benefit or a cost? Should jobs created be
considered a benefit or a cost to the project? The answers
depend on the point of view.
If there is a single decision-maker, then an analysis from
one point of view is often adequate. If the interests of more
than one person or group are affected, then several analyses
might be necessary. Consider the decision to construct a
recreational facility in a national park. The analyst who
wants to provide advice to his or her minister might need to
know how the project would look from the general social point
of view (all costs and benefits to Canadians), from the
fiscal point of view of the park authority, from the
provincial point of view, and from the point of view of local
environmental groups.
The point of view defines the 'in group' and the
'out group.' The in group consists of those people
whose costs and benefits are to be taken into account in the
analysis. For example, suppose that the in group comprises
all the citizens of a town called Bin. In that case, if some
of the resources of the Bin citizens are used up, there is a
cost to be counted. If some of their resources are given to
people outside Bin, there is a cost to be counted as well. If
one citizen of Bin, however, gives resources to another
citizen of Bin without anything being used up, then the total
resources of Bin citizens are not affected and no cost or
benefit is to be counted. A transfer paymenthas been
made (see Section 4.2.1).
As well as identifying costs and benefits correctly, one must
choose parameters that are consistent with the point of
view of the analysis. For example, the appropriate
discount rate depends on what point of view is being
taken in the analysis (see Section 5.5).
2.5 The
components of benefit-cost analysis
All public-investment decisions can be modelled in the same
standard way, using as the general framework for analysis the
same four components:
-
a parameters table;
-
an incremental-effects model;
-
a table of costs and benefits over time; and
-
a table of possible investment results and a statistical
and graphical analysis of NPV and investment risk.
These components are depicted in Figure 2.5.1.
Figure 2.5.1: The general flow of benefit-cost
analysis
Parameters table
|
Parameter 1: Population growth rate
|
2% per annum
|
Parameter 2: Social discount rate
|
10% per annum
|
Parameter 3: Apple price increase
|
5% per annum
|
Incremental effects model
|
|
Period
|
|
t0-t1
|
t1-t2
|
t2-t3
|
Events
|
___
|
___
|
___
|
Consequences
|
___
|
___
|
___
|
Table of costs and benefits over time
(simplified illustration)
|
|
Costs
|
Benefits
|
|
|
|
Period
|
Materials
|
Labour
|
Sales
|
Net
(nominal $)
|
Net
(constant $)
|
Present
values
|
t0-t1
|
($100)
|
($67)
|
$40
|
($127)
|
($124)
|
($113)
|
t1-t2
|
($212)
|
($34)
|
$90
|
($156)
|
($148)
|
($123)
|
t1-t3
|
($455)
|
($84)
|
$600
|
$67
|
$57
|
$43
|
NPV =
|
($193)
|
The first component of this investment model is the
parameter table, which is a list of variables used to
calculate the costs and benefits. For example, both costs and
benefits of a project might be influenced over time by the
population growth rate of the community. Rather than retype
the population growth rate every time it appears in a formula
within the table of costs and benefits, it is better to list
it in the parameter table and refer to it in other parts of
the spreadsheet as it is needed. Although not absolutely
essential, the use of a parameter table also facilitates all
kinds of 'what if' analyses, including sensitivity
analysis and risk analysis (see Chapters 7-9). It
simplifies the analyst's task when changing the value of
the parameter, a key requirement of risk analysis. Instead of
searching through the whole model for all the places where
the population growth rate was used (and perhaps missing
some!), the analyst can change the value in the parameter
table, and all its uses in the benefit-cost model will change
automatically and simultaneously.
The second component is the incremental-effects model.
In business or industrial contexts, this is sometimes called
the production model. It sets out the expected events and
consequences over time. The nature of the events will depend
on the project - from illnesses (an immunization project), to
sales (an export-incentive project), to letters sorted (a
post office capital-investment project). These events
are often subject to uncertainty, so we tie them in with the
parameter table in the same way that we tie in the table of
costs and benefits later.
The third component of the model is the table of costs and
benefits over time. This is a list of all costs
and benefits, with the values for each noted for every period
within the investment horizon. These values are
best-expressed in nominal dollars so that adjustments
normally calculated in nominal dollars can be made
(adjustments for taxes, for example). Nominal dollars cannot
be added or subtracted across periods, however, so they must
at some stage be converted to constant dollars, and then to
present values, before they can be summed up. (For
details on constructing a table of costs and benefits, see
Section 2.6.) There are two ways of doing this. The
first way is to calculate the full table of costs and
benefits in nominal dollars, then another table in constant
dollars, and then in present values. The second way is a
little easier and more concise: the analyst adds all benefits
and subtracts all costs within each period to obtain a single
nominal-dollar net for each period and then converts
thisnominal-dollar net cash flow to constant
dollars and present values (by convention, the analyst is
allowed to add and subtract nominal dollars within a single
period, although this is an approximation of true value
because the worth of a dollar might change if the period is
lengthy). (Nominal and constant dollars are discussed further
in Chapter 5.)
The final component of the model is
the investment results table. Each time the
benefit-cost model is run, it estimates an NPV of the
investment. If it is a deterministic model, in which all the
inputs have fixed values, then the result of each run
will always be the same NPV. If it is a risk-analysis model,
in which the parameters' values vary within a stated
range according to probabilities, the estimated NPV will also
vary. The result of many runs of the model will be a list of
possible NPVs, and this list itself will have to be analyzed
statistically to determine the probable true NPV. This
statistical analysis will show the maximum and minimum values
of the NPV and the probabilities that the NPV is within
various ranges. With this information, the analyst can apply
decision rules to ascertain whether the project is a good one
and whether it is the best alternative.
2.6 Constructing
tables of costs and benefits
By far the greatest amount of time in a benefit-cost analysis
is spent in constructing the tables of costs and benefits
over time. To construct these tables, the analyst identifies
the full set of relevant costs and benefits, estimates their
quantities for each period, and calculates their values by
applying their prices to their quantities in each period.
This needs to be done carefully. A benefit-cost analysis is
no better than its data.
There are no shortcuts. It is seldom, if ever, accurate to
construct one year of costs and benefits and to assume that
this year is repeated 25 times in constant dollars out to
investment horizon t25. The world does not
work like this. Not only do prices change, but also relative
prices change __ land becomes more expensive, computing
power becomes cheaper, commodities follow a price cycle and
so on. One benefit-cost analyst might not have the expertise
to estimate all the quantities and prices needed in the
analysis and may have to draw upon other specialists for data
estimates.
In some cases, the analyst will be working with pro
forma financial operating statements for a proposed program
or project, or with business income and expense statements.
These sorts of data often require some adjusting to fit a
benefit-cost framework. One financial framework is not better
than another is. Each has its own internal consistency, but
data from one framework might not fit in another.
The greatest difference between benefit-cost cash
flows and business cash flows is that the latter may
include accrued values, depreciation and similar
allowances. Benefit-cost analysis does not use accruals,
depreciation allowances or other 'non-cash' items.
In benefit-cost analysis, each cost and benefit is fully
recognised at the time it occurs (not accrued beforehand),
timing is dealt with through discounting, and changes
in the values of assets are dealt with by including
residual values at the investment horizon.
In benefit-cost analysis, accounts receivable and payable are
not recognized until the cash is actually received or paid.
Working capital is not a cost, although the change in working
capital during a particular period is either a cost (if
working capital decreases) or a benefit (if it increases).
Production costs are recognized fully at the time they occur.
Changes in inventory may signal either costs or benefits, but
the actual measurement of these is through production costs
and sales. Benefit-cost cash flows are simple tables with
everything recognized when it occurs. Although this is a
simple concept, it can be uncomfortable at times for a
financial officer who is used to accrual accounting.
2.7 Accounting conventions
Once you are familiar with the general form of the
benefit-cost model, it is useful to think about the
conventions that are used to set it up in a standard way. One
convention is not necessarily better than another is, but
standardization is needed if the model is to be a general
tool for comparison. Conventions are important for many
aspects of the model, such as the investment horizon,
time-of-occurrence assumptions, and the numeraire
__ a common unit of measurement.
2.7.1 The investment horizon
The investment horizon is the end of the period over which
costs and benefits will be compared to ascertain whether an
investment is a good one. If costs and benefits can be
identified for the whole economic life of the project and
uncertainties are low, then the full economic life provides
the best investment horizon. If not, there may be logical
points in the economic life of the project at which to
terminate the investment analysis. For instance, there may be
a point at which relatively certain costs and benefits are
suddenly followed by much less certain values.
Recapitalization of a building, for example, tends to occur
in cycles: 5-7 years for repainting and new carpets; 15-17
years for service systems such as heating; and 25-50 years
for major structural components. These thresholds where major
new uncertainties occur might suggest an appropriate
investment horizon. It is important, however, that the
investment horizon not be chosen to deliberately favour the
project. Even if you are considering a single option, then it
might be advisable to analyse the project within various
investment horizons to see whether a change in investment
horizon affects the outcome. If you are comparing
alternatives, you should use the same investment horizon in
the analysis of each (see Section 3.3.1).
2.7.2 Time-of-occurrence assumptions
Costs and benefits occur at different points within the
standard period being used (within the year, for example).
Therefore, you need a convention for establishing where all
costs and benefits will be assumed to fall within the period.
Normally, the analyst selects one of three possibilities:
either at the beginning of each period, in the middle, or at
the end. Underlying this practice is the need to have a
reasonably simple pattern of costs and benefits over time so
that changing nominal dollars to constant dollars, and to
present values, is not too difficult.
This practice assumes that if all benefits and costs are
shifted to the same point within each period, then, on
balance, the overall outcome will not be affected. This is
generally a reasonable assumption, except in cases where
there is an unusually large cost or benefit being shifted a
long way - say from near the beginning of a period to the
end. A common example of this is a large, initial lump-sum
investment; an analyst using end-of-period accounting will
assume that this investment occurs at the end of the first
year (and therefore is adjusted for inflation once and
discounted once), when in fact it occurs at the beginning.
This artificial adjustment of a large cost can make a major
difference to the outcome of the analysis if there is no
comparable benefit being similarly adjusted in the same
model.
This sort of problem has led to hybrid conventions. For
instance, in a table of costs and benefits, common convention
is to assume that the costs and benefits listed in the first
column of numbers occurred at a single point in time,
t0, rather than in a period. The next
column lists costs and benefits for the period
t0-t 1. Then, if
t0 is selected as the base point in time,
as is commonly done, the initial lump-sum investment is
unchanged by adjustments for inflation or discounting. We
recommend this procedure when there is a large initial
investment.
It is important to know which period conventions your
software uses so that you can avoid inappropriate
calculations. Each benefit-cost report you submit should
state the period convention used.
2.7.3 The numeraire - a common unit of
value
Before they can be summed up, all costs and benefits must be
expressed in a common unit of value. This involves three main
things: expressing them all in a common numeraire (say
Canadian dollars of investment funds); adjusting for
inflation where necessary (converting to constant
dollars); and expressing all in present values (adjusting for
differences in the time of occurrence of costs and benefits).
The costs and benefits must be in a common monetary unit
before they can be compared. Most investment analysis uses a
dollar of investment as the unit of measurement. However,
some public-sector models use a dollar of consumption or a
dollar of foreign exchange as the numeraire. All are
acceptable, but clarity and consistency are essential. If
price distortions are widespread in a particular
economy, the benefit-cost analysis may use border prices or
world prices as the numeraire, that is, as the best measure
of true value of costs and benefits. For most purposes of the
Government of Canada, a dollar of investment expressed in
Canadian prices is an adequate numeraire. It also has the
advantage of being easy to understand.
Both constant dollars and present values (they are not
the same things!) are defined at a particular point in time.
Any point will do, but the most frequent choices for
t0 are the time at which the analysis is
being done, the start of the project, or the start of a new
fiscal year. Costs that are incurred before
t0 would, of course, be inflated, rather
than deflated, to an equivalent t0value.
2.8 The report
In general, reports should contain at least the following:
-
a description of the need, problem or opportunity;
-
a description of the options with an explanation of why
they were chosen and why it is fair to compare them;
-
a statement of the point of view of the analysis;
-
a statement of assumptions and scenarios;
-
a deterministic analysis;
-
a cost-benefit analysis and a risk analysis;
-
a discussion of equity effects and other non-economic
effects; and
-
a ranking of the options.
Best practice - the general benefit-cost
model
-
Benefit-cost analysis can be applied to a
wide range of decisions made by the
Government of Canada.
-
Every benefit-cost analysis must state the
point of view from which benefits and costs
will be assessed.
-
There is no cookbook for benefit-cost
analysis, but a standard set of steps is a
useful starting point.
-
Each benefit-cost analysis should contain a
parameter table; an incremental-effects
model; a table of costs and benefits over
time; a table of possible investment
results; and a statistical and graphical
analysis of expected NPV and investment
risk.
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3. Defining fair options
Unfair comparisons are odorous.
- Shakespeare, Much Ado About Nothing
3.1 Why are fair options difficult to
define?
Two requirements must be met if a comparison of alternatives
in a benefit-cost analysis is to be fair. The first is to
ensure that all the relevant alternatives are
considered. The proposed investment should be compared with
the best alternative uses of the resources. It is not enough
to assume that a proposed project has only to make a return
equal to the discount rate to be acceptable. There may be
alternative projects that would do even better!
The second requirement is that the alternatives to be
compared must each be defined in a consistent and fair way.
In particular, one cannot make a simple comparison between
two investment alternatives if they are at different
scales, occur at different times, or involve different
ownership. This is sometimes not obvious from some texts that
imply that any alternatives, however structured, can be
compared simply by calculating their NPVs. This is not the
case. There is an underlying assumption that may not be
valid.
The dubious assumption is that unused resources earn a normal
rate of return (that is, they earn a rate of return
equivalent to the discount rate). On this assumption their
present value will be zero (for example, if the unused asset
earns 10 per cent per annum and is discounted by
10 per cent per annum, then it is a 'wash' as
far as NPV is concerned). Consequently, adding or subtracting
the unused resources cannot affect the total present value of
any investment under consideration. For example, consider
investment A, which costs $70 and has an
NPV of $30, and investment B, which costs
$200 and has an NPV of $31. According to the NPV decision
rule (see Section 6.1), investment B is better.
However, this assumes that the $130 we have left over if we
invest in A has an NPV of zero and therefore
doesn't affect the investment decision. This assumption
is implicit, in a sense hidden, and might not be valid.
In real situations, the resources left over if one chooses
the smaller investment or an investment further in the future
may not earn a rate of return equivalent to the discount
rate. Indeed, it is not uncommon in government for unused
resources to have a negative return in the short run because
of the holding costs. Consider the case where a department is
deciding whether to renovate an older building it already
owns or to lease a new building. If it decides to lease, what
will happen to the older building? The traditional NPV
decision rule assumes that the resources tied up in the old
building (essentially its existing market value) will earn a
return equal to the discount rate. Of course, this is
unlikely. It is more likely that the building will continue
to sit empty, waiting for some other use, and an NPV
calculation that ignores this reality is likely to give poor
guidance to decision makers.
3.2 An optimised base Case
It is important to identify the set of most promising
options. To do this, the benefit-cost generalist works with
experts in the substantive field. For example, if the
Government of Canada wanted to improve winter transit time
for freighters in the St. Lawrence Seaway, then the options
would be identified mainly by experts in marine
transportation, ice-conditions identification, communications
and related technical fields. The focus is on what will or
will not work, putting aside for the moment the question of
financial attractiveness. No option should not be eliminated
at this stage of the benefit-cost analysis on the grounds of
politics or equity before its net economic values are known.
When you are making a 'go' or 'no go'
decision on a single-project proposal, it is important to
optimise the baseline (without project) case before you
calculate the incremental costs and benefits of the proposed
project. Failure to do this has been a common source of
error. The status quo is not necessarily the appropriate
baseline. It is often possible to improve results without
major capital investment. If so, it is the improved status
quo that provides the baseline against which you should
measure the proposed project. In other words, it is not
'before' or 'after' that we are
interested in but rather the best 'with' and the
best 'without' the project.
When you are identifying the alternatives to be analysed,
keep in mind that public-investment decisions share three
important characteristics. First, to some extent, these
decisions may be irreversible; once committed, the
resources cannot be recovered. Second, the outcome of the
investment may be uncertain because the input data are
uncertain. Third, there may be some leeway with
respect to the timing of the investment.
We will consider the issue of uncertainty in Chapters 7 to 9.
The issues of irreversibility and timing, which were known to
analysts in the past but not given much attention, have
become important considerations in the 1990s. The ability to
wait before making an irreversible investment is important. A
simple case is an initial investment that gives rise to
benefits that increase over time, such as an investment in a
new road where the traffic is expected to increase. Investing
immediately might have a positive NPV, but this might mask
negative NPVs in the early years because the benefits of
later years predominate. In this case, waiting for the
optimum moment to invest is important. Generally, keeping
your alternatives open while waiting for new information that
might affect your decision gives you an option that may be
valuable indeed.
3.3 How to construct fair options
The only way you can be sure that the options whose present
values are being compared are really fair alternatives is to
standardize them for time, for scale and for already-owned
components.
3.3.1 Standardize the options for
timing
If there are two investment alternatives with different time
frames, they must be standardized normally by choosing the
longer time frame for both. If one project starts
earlier and the other finishes later, then the earlier start
and the later finish normally define the standardized time
frame. All resources need to be accounted for, in all
alternative time frame projects, for the full timeframe.
Sometimes, indivisible components determine how the timeframe
can be standardised. For example, if you are choosing between
making a gravel road (surface life of 6 years) or a making a
blacktop road (surface life of 15 years), what investment
horizon would allow a fair comparison? The following are two
possibilities:
Comparison 1: 2 applications of blacktop vs. 5 applications
of gravel (30-year horizon)
Comparison 2: 1 application of blacktop vs. 3 applications of
gravel (18-year horizon)
The first seems to be a fair comparison: (2 ´ 15) = (5 ´ 6). The second does
not: (1 ´ 15)
¹ (3 ´ 6). What happens
to the blacktop road after its surface life expires (years 16
to 18)?
3.3.2 Standardize the options for
scale
Standardizing the options for scale is similar to
standardizing the options for time, as illustrated above. If
you have two investment alternatives involving different
levels of investment, then you must specifically account for
the resources left over after making the smaller investment
rather than just assuming they generate a zero NPV.
3.3.3 Standardize the options for
already-owned components
If one investment option uses a resource that is already
owned by the government, then the analyst must also show what
would happen to this resource for each of the alternative
investment options. For example, if the government owns a
building and one alternative is to renovate it, then the
analysis of each of the other alternatives must also
incorporate what happens to that building. You cannot blindly
assume that the building will earn any particular rate of
return if it is not used for the proposed purpose. In fact,
several mistakes are common. One mistake is to assume without
examination that already-owned resources earn the standard
rate of return (the discount rate). Another is to treat them
as though they were costless. A third mistake is to consider
them only in the one investment scenario where they are most
relevant and assume they do not exist for the alternative
scenarios. The rule is that any already-owned asset that
appears in one alternative should appear in all alternatives,
and the return it generates in each case should be examined
specifically.
The correct way to treat already-owned assets is to recognize
(in all the investment alternatives) their full
opportunity cost at the beginning and at the end of
the standardized investment period. Their opportunity cost is
generally best measured by the net market value of the asset
including, where relevant, sales costs, site clean-up costs,
and the time required to sell the asset.
3.3.4 Fair options diagrams
In practice, it can be difficult to conceptualize the
investment alternatives, standardizing for scale, for timing
and for already-owned components. A diagram can clarify a
complex set of investment alternatives. We call such a
diagram a 'fair options' diagram.
An example is Figure 3.3.4, which depicts three options
for accommodating 350 staff. Note that the options must all
be at the same scale. The best measure of scale is that,
although the four options do not encompass exactly the
same floor space, each could accommodate 350 staff. All
options cover the same period (four years), and all consider
what will happen to already-owned assets.
Figure 3.3.4: An example of a fair options
diagram
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1996
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1997
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1998
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1999
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OPTION 1
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40 Pond St.
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1480 m2
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151 Pond St.
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3340 m2
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243 Scotch St.
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250 m2
temporary
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190 m2
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380 Willis St.
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1055 m2
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OPTION 2
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40 Pond St.
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1480 m2
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151 Pond St.
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3340 m2
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New building
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1670 m2
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OPTION 3
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40 Pond St.
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151 Pond St.
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Lease
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5010 m2
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Empty space held
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Space in use
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The three options shown in Figure 3.3.4 have been
standardized in the following ways:
-
the time frame is the same for each investment
(1996-1999).
-
the project size is the same (350 people accommodated).
-
the already-owned asset (40 Pond St.) appears in all
options.
-
there is a plausible plan for handling already-owned
assets that are not needed in a particular option.
3.3.5
Non-essential components of options
Options must be self-standing, as
well as fair. That is, they must be complete and spare.
Spare means there should not be anything in the
option that is not essential to it. For example, suppose the
federal government owned some land close to an airport and
that land was expected to increase in market value over the
next several years. At the same time, the government is
considering whether to build a training centre. In this situation, the training
facility may be a poor investment, but the overall NPV of the
project may still look good because of the inclusion of the
increasing value of the land. This is not legitimate. You
must be sure that all components of an option are indeed
essential; otherwise, the benefit-cost analysis may be
misleading.
3.4
Incremental effects analysis
Before you can undertake a financial or economic analysis of
a proposed project or program, you need a clear understanding
of the incremental events and consequences to be expected. In
general, you will need input from subject-matter experts. If
the project is to decrease the risk of oil spills, the
analysis team should include engineering and scientific
experts to estimate the expected frequency of spills, assess
the potential consequences of a spill for marine ecosystems,
and to evaluate the extent to which the project will be able
to prevent spills or contain damage once a spill occurs.
Similarly, if the project is to build a road by-pass, the
analysis team should include traffic engineers to estimate
the incremental improvements in safety and travel time that
will result. In benefit-cost analysis, then, two
'subject matter' skills will always be needed:
-
expertise in estimating the expected frequency of events;
and
-
expertise in assessing the potential consequences of
events.
The benefit-cost analyst brings two additional skills to bear
on the information provided by the subject-matter experts:
-
expertise in valuing outcomes in dollars; and
-
expertise in making fair comparisons between benefits and
costs.
One should not exaggerate the difference between the two sets
of skills, however. Both the specialist and the generalist
rely on similar analytical skills. The important point is
that a team effort is often required for a full analysis.
Best practice - defining fair
options
-
For all public investments, a full set of
the most promising options should be
compared.
-
When a single proposal is being considered,
it must be compared with a 'baseline
case' and the baseline case must be
optimized.
-
The option to delay a project to wait for
better information, or for better starting
conditions, can have considerable value.
-
Each option must be standardized for scale,
timing and already-owned components to
permit a fair comparison. A fair options
diagram can clarify a complex set of
investment options.
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4.
Measuring and valuing costs and benefits
4.1 Introduction
This chapter explains how to measure costs and benefits to
obtain information to enter into the benefit-cost framework.
The general benefit-cost framework can be learned in a
week's study, but the measurement of costs and benefits
is a limitless topic and often requires a wide range of
expertise. Because the coverage in this guide is necessarily
brief, analysts will often have to consult more specialized
documents for guidance on measurement (see the suggested
readings in Appendix C).
Measuring costs or benefits and valuing them in dollars
requires many different skills. For example, consider the
case of a project to clean up river pollution from a
manufacturing facility. An industrial chemist is needed to
calculate the incremental change in the amount of pollutants
entering the river; a biologist is needed to determine the
effect of this change on bacteria in the river; a health
scientist is needed, in turn, to evaluate the effects of that
change on the health and recreation opportunities of
residents; and then a benefit-cost analyst is needed to
estimate in dollars the value of these benefits to the
community. Note that the benefit-cost analyst does only one
of the calculations, and not necessarily the most difficult.
4.2 Some Important Concepts
Even when we know how to count in standard units, we still
need to be careful about what we count. In particular,
incrementality, transfers, opportunity cost, sunk cost and
residual value are important concepts in benefit-cost
analysis. Only incremental benefits and costs caused by the
project should be compared, not those are merely associated
with the project in some way. For example, if one did a
benefit-cost analysis of a government grants program to
encourage exporters, one would need to know not just the
export sales made, but specifically what sales were made that
would not have been made in the absence of the program.
To avoid double counting, the analysis must maintain a
consistent point of view. However, it is not the only
requirement. The analysis team also needs an in-depth
understanding of the proposed investment to be able to
identify a coherent set of costs and benefits without double
counting. For example, suppose a new sewage-treatment plant
is installed. The recreation value of the river improves,
land values in the neighbourhood increase, and health
problems decrease. However, if all these effects are counted
as benefits there is probably double counting. The increase
in land values is probably a measure of the other benefits,
not an additional benefit.
4.2.1 Transfers compared with true benefits
and costs
In benefit-cost analysis we count resources that are created
or used up. Resources that are simply transferred from one
pocket to another are not counted as costs or benefits. For
example, income taxes are transfers from the point of view of
the whole country. Taxes move resources around, but, apart
from administrative and disincentive costs, nothing is used
up.
'Point of view' establishes whether a transaction
is a transfer or not. It determines whether resources are
passed from one pocket to another (a transfer) or passed out
of the group or used up (a cost). From the point of view of a
private business, for example, income taxes are definitely a
cost.
In certain circumstances, tariffs, grants, taxes,
social-welfare payments and many other items can be
considered transfers. What is important here is whether
resources are gained by or lost to the stakeholder(s) from
whose point of view the analysis is being done.
4.2.2 Opportunity cost and sunk cost
In calculating the benefits of public projects, the proper
valuation to use is the price consumers are willing to pay
for the output, that is, producer's price plus taxes
minus subsidies. In evaluating costs, the correct approach
is less clear cut. Consider, for example, taxes and
subsidies on intermediate inputs. Taxes increase the cost
of inputs to users above the value of real resources
expended in producing them, while subsidies have the
opposite effect. In evaluating these costs, the proper
measure critically depends on whether the project's
demand for the inputs is met by new supplies, or by
diversions from other uses. If the inputs come from new
supplies, the correct measure is the value of real
resources expended, which is equivalent to the price paid
by other users minus taxes plus subsidies. If the inputs
are obtained by depriving other uses, the correct measure
is the value of the inputs in alternative use, or the
producer's price plus taxes minus subsidies.
- Treasury Board, Benefit-Cost Analysis
Guide, 1976
The opportunity costis the true value of any
resource foregone. It must be counted even if explicit cash
transactions are not involved. For example, if I could sell
my computer for $1000 but instead I use it on a project, the
opportunity cost of the computer (to be counted against the
project) is $1000, although there is no cash transaction
involved.
A cost is 'sunk' if it is irretrievably made or
committed. A sunk cost is not to be counted in a prospective
benefit-cost analysis because it cannot be affected by the
decision in question. For example, if I originally paid $3000
for my computer but its market value at the time of the
analysis is $1000, then $1000 is the opportunity cost if I
decide to use the computer on a proposed project rather than
sell it, and the remaining $2000 is a sunk cost that is no
longer relevant.
4.2.3 Externalities
An attempt should be made to take into account all of the
allocative effects in evaluations of the efficiency of
government expenditures, some of which may be less obvious
than others... Such implicit effects may be internal (to
direct actors in the project) or external (to persons not
directly acting in the project but included in the group
whose point of view is being taken in the analysis). An
example of internal implicit effects is foregone wages
during education... External implicit effects (also
referred to as spillovers, social effects, or third party
effects) are commonly things like pollution or
congestion... Ignoring implicit costs or benefits could
lead to major errors in analysis.
- Treasury Board, Benefit-Cost Analysis Guide, 1976
4.2.4 Residual value
A residual valueis the value of an asset at the
end of the investment horizon. For example, suppose you
invest in a rental property. At the end of the investment
horizon, the land is still a valuable asset. The residual
value is a benefit to be counted when you appraise the
project. In most cases, the residual value is the market
value of the asset. However, governments often maintain
'special-use facilities' (research laboratories,
for example) for which market value might not be a good
measure. The value of a special-use facility may be as little
as the market value of the land minus demolition costs to
remove the buildings. On the other hand, the true value can
be as high as the replacement costs of the buildings and the
land.
In calculations of residual value for a benefit-cost
analysis, the land and the buildings are often treated
separately. The analyst uses an index to estimate the
expected market value of the land. The analyst then estimates
the economic life of the buildings and prorates the
replacement value according to the percentage of economic
life that will have passed by the end of the investment
horizon. For example, suppose at t0 a real
property consists of land worth $1 million and buildings
worth $2 million. By t10 (the investment
horizon in this case), we expect the land value to have
increased to $1.5 million (nominal dollars) and the
replacement value of the buildings to have increased to $3.5
million (nominal dollars). Suppose also that 10 years is
50 per cent of the economic life of the building. The
residual value of the real property at t10
would thus be approximately $1.5 million (land) plus
$1.75 million (half the replacement value of the buildings).
Several problems can arise in treatments of residual values.
One mistake is to count a residual value on an already-owned
asset without counting the balancing opportunity cost at
t0. Whether the asset is already owned or
not, its full value must be counted as a cost at
t0 if its residual value is to be counted
as a benefit at tn.
Another mistake is to make a conservative estimate of cost
and a generous estimate of residual benefit. The way the cost
is computed at t0 must be comparable to the
way the benefit is computed at tn.
A third problem arises if the project itself is not defined
correctly. Sometimes a non-essential component has a good
residual value that masks a bad outcome of the essential
components. When you are counting a residual value as a
benefit, make sure that the asset in question really is an
essential part of the project (see Section 3.3.5).
4.2.5 General administrative and overhead
costs
When a large organization, like a government, analyzes many
possible investments over time, it may have a problem
deciding how to treat general costs that are not specific to
a particular project. Such costs are sometimes called
overhead costs or general and administrative costs. These are
more or less fixed costs. One additional project will
often make little difference. The standard practice in
benefit-cost analysis is to take the marginal or
incremental approach to counting costs and benefits, but this
approach ignores most of the program and overhead costs. The
problem with this as a standard practice, therefore, is that
it is too generous to the investments and overstates the true
returns. In the extreme, overhead costs never get counted
anywhere in the organization's decision-making process.
If the organization only occasionally makes major
investments, it may be reasonable to ignore program and
overhead costs - in essence, letting them be borne by
the run-of-the-mill operations of the organization. In this
case, it is reasonable to take a marginal-cost approach. In
contrast, if the organization makes many investments, it is
preferable to include an 'average' allowance for
overhead in the costs, although any single investment has
little effect on overhead at the margin. If all investment
options bear overhead equally, this factor is unlikely to
influence the choice among them very much. Even so, it is
preferable to have a realistic picture of investment returns,
including overhead costs, than to have an unrealistically
rosy picture.
4.2.6 Insurance and contingencies
Both insurance and contingencies are efforts to adjust for
risk. Do not include the costs for either of these in the
table of costs and benefits if intend to do a risk analysis
through simulation (see Chapter 9). In a simulation,
you take risk into account by using maximum-minimum ranges of
all variables in the model and by assigning probabilities
within these ranges. To include insurance or contingency
costs as well would be to double count and to exaggerate the
risk.
4.3 Valuing costs and benefits by market
prices
In benefit-cost analysis, we normally consider market
prices as being good measures of the costs and benefits
of an investment. (When market prices do not exist in usable
form, then the analyst has to construct them). Frequently,
however, the market price is only an approximate measure of a
cost or benefit. If I buy an apple for $1, for example, the
benefit to me of the apple is at least $1 or I would not have
purchased it. Clearly, though, the benefit could be higher.
The apple might be worth $1.50 to me; that is, I might be
willing to pay $1.50 for it if necessary. If I only have to
pay $1, then I have a total benefit of $1.50, a cost of $1,
and a 'surplus' of $0.50. Therefore, when we use
market prices as measures of benefits, we are ignoring the
consumer surplus, which might be important in some
cases.
4.4 Consumer surplus and producer surplus as
components of value
The concepts of consumer surplus and producer surplus
are basic to modern benefit-cost analysis. Jules Dupuit,
a French engineer, first stated them clearly in 1844. He
pointed out that the market price is the minimum social
benefit produced by the output of a project. In fact, some
consumers would be willing to pay more for the outputs than
they actually have to pay.
Consider Figure 4.4.1, which shows two demand
curves for apples (that is, lines showing the relationship
between the price of apples and the quantity of apples
demanded at each price). In both cases, the total possible
benefit to the community from apple production is given by
the area under the demand curve. This area is easy to
calculate if the demand curves are approximated by straight
lines, as in this example, because the area under the curve
is a triangle formed by the two axes and the demand curve.
Of course, the community actually receives benefits only from
the apples sold and consumed, and this quantity is limited by
the price of apples. The area under the curve represents the
total community benefit to the left of the point where the
price line and the demand curve intersect. To the right of
this price point, there is no effective demand, and so no
benefits can accrue.
The area under demand curve A, to the left of
QA, is very close to the 'price
× quantity' rectangle that we normally assume to
be the total benefit to the community (in this case, $9
× 1 box of apples). Only a small triangle above the
price line is unaccounted for, and this represents the
consumer surplus.
Demand curve B, on the other hand, has a large
consumer-surplus triangle above the price line. In general,
the flatter the demand curve (that is, the more that people
have a standard value for an apple) the closer the price
× quantity rectangle is to capturing the full benefit
to the community. Conversely, the steeper the demand curve
(that is, the more variety in the value that people give to
apples), the less satisfactorily this price × quantity
simplification represents the full benefit to the community,
because a much larger consumer-surplus is ignored.
An analogous component is the producer surplus. If the
producer is prepared to produce a certain quantity of apples
at $6 per box, and the market price is $9, then obviously for
this quantity of apples, at least, the producer will gain a
windfall of $3 per box of apples. The total producer surplus
is the area between the price line and the supply
curve, to the left of their intersection (see Figure 4.4.2).
The benefit-cost analyst must decide whether price ×
quantity is a decent approximation of value; if the
simplification is off the mark, more detailed calculations of
value are needed. More detailed calculations of consumer and
producer surplus are also needed when price × quantity
is not an option because prices do not exist or are highly
distorted.
4.4.1 Consumer surplus when a public
investment changes the price of a good
Public investments in power, water, sanitation and
telecommunications projects (and many others) may lower the
price of the output. If so, valuing the benefits of the
project at the new lower price understates the project's
contribution to society's welfare. With a lower price,
more consumers have access to the product or service;
established consumers pay a lower price and consume more. A
special case of this general rule is when supply is rationed
at a controlled price below that which consumers would be
willing to pay. This situation is rare in Canada (student
places in medical schools would be an example), but it is
common in some other countries. When it does occur, an
increase in supply at the same controlled price involves a
gain in consumer surplus over and above what consumers
actually pay for the increased quantity of the good or
service.
In some cases, part of the increased consumer surplus is
offset by a decrease in revenues to the existing producers.
For example, if a hydroelectric project reduces the average
cost of producing electricity and increases the amount
available, the market price of electricity might fall from
P1 to P2, as shown in
Figure 4.4.3. The established consumers save an amount
equal to shaded area A, but this is offset, from the
point of view of the whole economy, by a corresponding loss
of revenues to the established producers. The net benefit of
the change is therefore only the shaded area B.
(Figure 4.4.3 is accurate but simplified -
consumers' responses are complicated by substitutions
among goods when relative prices are affected.)
In contrast, if electricity was previously imported and the
project is substituting domestic energy for imported energy,
then the gain to consumers should theoretically be the whole
change in consumer surplus (area A + area B).
In reality, however, the outcome is more often different. The
'import-substitution' enthusiasts of the 1960s and
1970s were no doubt disappointed to see that many public
investments produced outputs at prices above the
international (border) prices. This, combined with
protectionism to exclude the cheaper imports, led to marked
reductions in consumer surplus without any offsetting
benefits to domestic producers as a group.
4.4.2 Consumer surplus and loss of financial
viability
If a public investment depends for its viability on estimates
of consumer surplus, and is not viable on a strictly
commercial basis, then the analyst must state clearly the
amount of the financial shortfall and the source of funds to
finance it. In addition, the analysis should explicitly
address the benefits that the government subsidising the
shortfall will derive from the arrangement, because this can
be crucial to the project's sustainability.
If a subsidy is necessary to keep the project operating, then
even if the project has a high economic NPV, there might be a
significant risk of running out of funds for proper
operations. In developing countries, where governments'
fiscal positions are usually more precarious than in Canada,
this has been a serious problem.
4.5 Valuing costs and benefits without good
market prices
When market prices exist but are distorted for some reason,
the analyst must estimate what prices would be in the absence
of the distortions and then use these adjusted market prices
(sometimes called social prices or true prices). When
there is no market for the good or service in question, there
are no market prices - distorted or undistorted. In
this case, the analyst has to start from first principles,
using the concepts of consumer surplus and producer surplus
discussed earlier (see Section 4.4) to estimate the values
for costs and benefits.
4.5.1 Estimating value when market prices are
distorted
How important distortions in prices are depends on the point
of view of the benefit-cost analysis (see Section 2.4).
True value has meaning only when one knows the point
of view. For example, when a private company faces market
prices for its costs, those market prices are a good measure
of true costs to the company. It does not matter to the
company - though it might to an analyst taking the
point of view of Canada as a whole - whether the
market prices are distorted or not. From one point of view,
the prices are good measures of true value; from another
point of view, they are not.
In benefit-cost analyses conducted for the Government of
Canada, the country as a whole is the most important point of
view for the analyst. This requires the analyst to use social
prices (sometimes called shadow prices) rather than
market prices if the market prices are distorted. Such social
prices may be substantially different from market prices in
some situations, including the following:
-
when the currency is misvalued because of foreign-exchange
controls;
-
when wage rates are kept artificially high by union rules
or legislation, despite unemployment;
-
when anti-competitive conditions, monopolies or
monopsonies (only one buyer) exist;
-
when taxes or tariffs are applied directly to the good or
service, as in value-added taxes; and
-
when the government regulates or otherwise controls or
subsidises prices.
4.5.2 Estimating value when no market prices
exist
The true values of resources used or generated by an
investment may be difficult to obtain when there are no
market prices at all or the market mechanisms are indirect
and difficult to observe. The next section explains how
values are estimated where no market exists. Examples are
given for the following:
-
the value of travel-time savings;
-
the value of health and safety;
-
the value of the environment;
-
the value of jobs created;
-
the value of foreign exchange;
-
the residual value of special-use facilities; and
-
heritage values.
4.6 Some examples of difficult-to-estimate
values
4.6.1 The value of travel-time
savings
Many benefit-cost analysis have been undertaken for
transportation projects where the main benefit was timesaving
for commuters, both business and leisure travellers.
Travel-time savings for business travellers are generally
valued at the traveller's gross wage rate before tax
(see Table 4.6.1). In calculating this, researchers have
taken into account differences in the wage profiles of
typical travellers by different modes of transportation; they
have also taken into account time in transit that can be used
for work purposes (some part of the 'cruise' time
in train and air travel, for example). The definition of
gross average wage generally includes an allowance for fringe
benefits and overhead costs. Data are gathered through
surveys such as the Canadian Travel Survey. Transport Canada
undertakes benefit-cost analysis of transportation
investments and has developed standards for business
travel-time values.
Table 4.6.1: Average value of passenger
travel-time savings
Mode
|
Business travel
|
Non-business travel
|
Auto
|
$27.30
|
$7.40
|
Air
|
$38.30
|
$7.40
|
Bus, highway and rail
|
$27.00
|
$7.40
|
Source: Culley and Donkor (1993)
Note: Values are dollars per hour. Base year is 1998
(January).
There is less consensus about how timesaving for leisure
travellers should be valued. Because of the greater
uncertainty, Transport Canada values travel-time savings for
leisure travellers according to some broad principles rather
than precise measurements. These principles include setting
the value of non-work time savings by adult travellers at
50 per cent of the average national wage rate and making
no distinction for differences in demographics (or wages)
between modes of transportation.
The value of timesaving in transit of cargo can also be
estimated. This is taken to be a function of the value of the
cargo and the discount rate. For example, if cargo worth $1
million is in transit for one week less and the cost of
capital is 0.002 per cent per week, then the savings
would be $20. No methodology exists for distinguishing
between business cargo and non-business cargo in this
context.
All travel-time savings are counted, even five-minute ones.
This is controversial, however. Some analysts believe that
consumers do not value small time savings at the same average
rate as they value large time savings - that is, a
saving of 30 minutes on one trip might be worth more to
a traveller than saving one minute on each of 30 trips.
Indeed, some argue that a saving of one minute per trip is
not worth anything no matter how many people are involved. As
well, analysts do not generally take into account
distinctions between the values of travel-time savings of
different groups of people (employed vs. unemployed; retired
vs. working), although it is theoretically possible to do so.
4.6.2 The value of health and safety
For some time, theoreticians thinking about the costs and
benefits of health and safety concerned themselves with the
question of the 'value of a life' in the form of
the question: How much is it worth to avoid death? However,
it gradually became clear that that was not a sensible
formulation of the question. Queen Elizabeth I is
reported to have said on her deathbed, 'All my
possessions for an instant of time.' A better way to
think about health and safety is in terms of small increments
of risk. The result of government investment in health and
safety measures tends to be a small lessening of the risks
encountered by broad segments of the population. It is this
lessening of risk that can be valued in benefit-cost
analysis.
Researchers use three methods to estimate the value of
reductions in risk to health and safety. Method 1 is to
observe people's actual behaviour in paying to avoid
risks or in accepting compensation to assume additional risk.
Method 2 is to ask people to declare how much they value
changes in the risks to which they are exposed. Both of these
methods are based on the willingness-to-pay principle, and
both of them assume that people have the information and
skills needed to assess risk and to report their
risk-and-reward preferences accurately. Unfortunately, this
assumption is almost certainly false. As well, it has not
been demonstrated that people have stable risk preferences,
even when they do have clear information on the costs and
risks and have the skills to assess that information.
Method 3 is to assess statistically the number and type of
injuries expected on the basis of historical data. The
researcher then counts the treatment costs and wage-loss
costs and extrapolates these to the whole affected
population. This is a rational approach because it ignores
people's preferences (which are subjective and may or
may not be well informed and rational) in favour of a
rigorous estimate of the treatment costs and wage-loss costs
that would be avoided by the proposed investment. This method
avoids the methodological difficulties of methods 1 and 2,
but at a cost. It tends to underestimate the true benefit of
an investment that reduces risks. When people avoid injury,
their benefit is almost certainly greater than avoiding
medical treatment costs and wage losses: they also avoid pain
and suffering, as well as perhaps the additional costs of
becoming disabled. So method 3 gives a minimum estimate of
values, but by how much it underestimates the true value we
do not know.
In the research literature, the empirical estimates of the
value of a life, for example, vary from about $200,000 to
about $3 million, with some outliers as high as $50 million.
In recent (1994) benefit-cost studies, Transport Canada used
the following values: for a fatality, $2,500,000; for a
serious injury, $66,000; and for a minor injury, $25,000
(1986 dollars). The values of these parameters are uncertain,
however.
4.6.3 The value of the environment
Environmental benefits and costs are often a composite of
several factors: health, aesthetics, recreation, and respect
for nature. The health and safety aspects are discussed
above. Respect for nature (apart from the health and
aesthetic components) is close to an absolute value and
extremely difficult to quantify, let alone value in dollars.
The aesthetic aspects are also difficult to deal with in
benefit-cost analysis: first, it is difficult to quantify the
aesthetics of a situation at all; and, second, even if
quantified, there is no market for aesthetic environmental
benefits, or at least no direct market.
Although valuation of environmental goods presents problems,
economists have developed some ingenious techniques to
estimate the value that people place on such things as water
quality and environmental protection. Most of these
techniques have specialized applications - they work
well in some situations but poorly or not at all in others. A
general technique, which relies on the willingness-to-pay
principle, does exist (contingent valuation), but its
use in the environmental area is controversial because the
results it produces may not be as reliable as those produced
by other techniques.
In this section we cannot present more than a brief synopsis
of some of the major techniques. Reference to more complete
works will be necessary [see, for example, Hanley and Splash
(1993)].
Sometimes the value of a benefit can be inferred from the
cost (for example, money or time) that a consumer is willing
to spend to enjoy them. Two techniques that use this approach
are the travel-cost (TC) method; and 'hedonic'
pricing and land-valuation (LV) method. These methods are
clearly limited to 'use values' (such as resource
harvesting or direct enjoyment).
As mentioned above, there is a general evaluation technique
that can be used for both use and non-use values (the latter
include such things as the psychic value of preserving the
ecosystem and the value of leaving a viable ecosystem for
future generations). This technique is the contingent
valuation (CV) method.
It is often appropriate to use a combination of techniques to
measure all environmental consequences. This will be
required, for example, if one is trying to measure both
ecological and commercial losses associated with a resource,
such as the loss to the fishery of a toxic spill. In such
cases, care must be taken to avoid counting the same loss
more than once.
4.6.3.1 The
travel-cost (TC) method
The TC method uses the prices for market-traded goods to
establish the value of untraded goods. The untraded goods are
typically recreational in nature. The costs for traded goods
are those that the recreationalist incurs to reach the
destination and carry out the activity (the travel cost
explains the name of this method). Outfitting costs (at home
or on site), equipment rentals, access fees, and so on are
usually included as well.
This defines a minimum value for the good that is
firmly rooted in economic analysis. Whatever the true value
of the experience itself, it cannot be less than what the
recreationalist actually paid to participate. Application of
the TC method is limited to certain use values of the
environment, particularly in relation to site-specific
activities.
The greatest limitation to the method is probably that it
provides no information about non-participants and the value
that they may attach to the site. The treatment of
travel-time value is also controversial, because vacationers
may in fact believe that 'getting there is half the
fun'; thus, high (or relatively high) opportunity-cost
values for time may be misplaced (see section 4.6.1).
4.6.3.2 Hedonic
pricing and the land-valuation (LV) method
Hedonic pricing and the LV method is another technique that
links market values to the enjoyment of untraded
environmental goods. The objective is to find items that are
alike except for one factor (for example, the value of
waterfront cottages compared with similar cottages not on
waterfront and then compare market values. However,
neighbourhoods differ in a myriad of ways: proximity to
shopping and cultural facilities, air quality, taxes, etc.,
not to mention quality of the housing stock (for example,
size, layout, and amenities). Therefore there can be
methodological problems related to omitted-variable bias or
multicollinearity (with two closely related variables, it is
impossible to determine which one 'explains' the
results). As a result, it is often difficult to derive usable
estimates in this fashion.
4.6.3.3
Contingent valuation (CV) method
The CV method essentially asks people what value they give to
a resource (use and non-use values). You can ask people what
they would be willing to pay to avoid some damaging action
or, alternatively, how much compensation they would require
to put up with it. The contingency part is a 'what
if' question, describing some change in present
circumstances, usually some new development. The greatest
advantage to this approach is that it can be applied to any
valuation problem, including those for which other methods
exist.
The CV method is not problem-free, however: numbers put into
the questions may bias the answers; respondents may get much
of their information on the subject from the interviewer
(interview bias); respondents may be influenced by their own
perceived self-interest (strategic bias); and, the (usually)
hypothetical nature of the exercise can induce laziness on
the part of respondents. As a consequence, the results of
these surveys are often contested.
Does this mean that the CV method is not worth the effort?
One of its earliest and best-known uses was in connection
with the proposed construction of a massive, coal-burning
electrical generating station upwind from the Grand Canyon.
The project went ahead despite strong 'expressions of
value' on the part of respondents. Today, a clear day at
the Grand Canyon is a rarity, and the quality of the
experience for millions of visitors is significantly
diminished. This example shows that the CV method can
provide useful information.
4.6.3.4 Other
valuation considerations
Sometimes problems arise when analysts estimate indirect
market values from measurements of their effects. For
example, an aesthetic improvement to the environment might be
measurable through the higher property prices that result
when the locality becomes more desirable, but the analyst
should not double count. Sometimes analysts have listed an
environmental benefit in addition to a benefit such as an
increase in tourism, when in fact they are one benefit, not
two.
4.6.4 The value of jobs created
Whoever argues impact on jobs rather than impact on the
consumer is not an economist but a politician.
- Peter Drucker, The New Realities, 1989
The public and the Auditor General of Canada are justifiably
suspicious of 'job-creation' claims. Therefore, the
analyst should take pains to calculate the figures accurately
and to substantiate them well. In particular, any
job-creation claims should be on the basis of net effects. If
one area of Canada is taxed to make investments in another
area, the net effects on jobs nation-wide might be neutral or
even negative once the taxation itself is taken into account
as a cost. Unfortunately, the benefit of jobs created by
expenditures in the public sector has often been cited as a
benefit without recognition of the parallel cost (jobs lost)
because of the taxation needed to provide the
public-investment capital. A local point of view might take
into account only the jobs created locally and ignore the
jobs lost or displaced elsewhere in Canada, but this is not
an appropriate point of view for the Government of Canada.
This Guide recommends that, as a general practice, the
project analyst should adopt the assumption that resources
used in the project would otherwise be fully employed.
This is especially true of skilled labour which is
relatively mobile ... if the project analyst is of the
opinion that special circumstances warrant the assignment
of shadow prices to the use of otherwise-unemployed
resources, the rationale for making such adjustments must
be carefully outlined and defended.
- Treasury Board, Benefit-Cost Analysis Guide, 1976
In general, job-creation claims are legitimate from the
national point of view only when an investment can be made
equally efficiently in two regions that have markedly
different unemployment rates. In this situation, it may be
legitimate to count a lower-than-market cost of labour in the
area that has severe unemployment. The idea is that part of
the labour force would otherwise be unemployed and therefore
it has a low opportunity cost from the point of view of the
economy as a whole.
To ascertain how labour should be priced, you need to ask
what the workers would be doing in the absence of the
project. If they would otherwise be unemployed but are giving
up only leisure time to participate in the project, then the
shadow wage rate might be low. The previous discussion about
travel-time values (see Section 4.6.1) gives a rough order of
magnitude of the expected price difference between
paid-labour time and leisure time - about 4:1. From a social
point of view, then, labourers who would otherwise be
unemployed might 'cost' only 20 per cent of
their visible wage rate.
Before making such radical adjustments to the shadow wage
rate, though, analysts must be confident that the workers
would truly have been unemployed. In some cases, analysts
have incorrectly taken the overall unemployment rate in a
region as the basis on which to calculate the shadow wage
rate. This is particularly misleading in industrial
regional-development projects, which often require skilled
labour that is not available in the region at all, let alone
among the region's unemployed. If skilled labour has to
be imported for the project, the full wage rate may not be
the only cost; there may be other associated costs, such as
those for travel and new housing and services.
The labour situations in developing countries can be even
more complex than the Canadian situation of dual-labour
markets for skilled and unskilled workers. In some countries,
disguised unemployment in the form of underemployment is
common, especially in rural areas. The withdrawal of surplus
workers from a rural area would be of little consequence for
agricultural output, even if they had been previously
employed. The opportunity cost of unskilled labour, then,
might be zero or, at most, little more than subsistence
costs, provided that travel, re-housing and similar costs are
accounted for elsewhere in the analysis.
Another legitimate use for lower-than-market shadow prices
for labour is in an analysis that takes the narrow fiscal
point of view of the government. From this point of view,
savings from avoiding welfare or unemployment payments are
true savings (not just transfers). The savings can be treated
as separate items or reflected in lower shadow prices for
labour.
4.6.5 The value of foreign exchange
In some cases, a substantial portion of the benefits is
generated because the project earns foreign exchange from
exports. For example, the National Energy Board regulates the
export of natural gas from Canada, and the value of foreign
exchange is an important consideration. The key idea is that
the Canadian dollar might be undervalued or overvalued in
terms of foreign currencies. These distortions can arise if
there is not a free and open market for the country's
currency or if there are major distortions in the domestic
economy because of taxes, subsidies or regulations.
In Canada, the Department of Finance has at times allowed
various levels of premium on net export earnings, depending
on circumstances, to reflect the true value of foreign
exchange to the country. In 1995, Industry Canada calculated
the premium to be between 3.5 and 4.5 per cent. In
countries with more closed economies, the difference between
the market price of foreign exchange and the shadow or true
price can be much greater than this. In some cases, the value
of the domestic currency is so distorted that prices
expressed in it are virtually useless as measures of the true
value of resources to the country as a whole. The calculation
of the shadow price of foreign exchange is, needless to say,
a job for an expert.
4.6.6 The residual value of special-use
facilities
Many of the projects of the Government of Canada involve
special-use facilities, such as laboratories or training
facilities (see Section 4.2.4). At the end of the investment
horizon, these facilities have a residual value that may be
positive or negative. At a minimum, their value might be land
value minus demolition and clean-up costs. At the other
extreme, the residual value might be a substantial positive
number that reflects a stream of benefits from the ongoing
operations of the facility. The Chief Appraiser for Canada
has set out procedures for valuing special-use facilities.
4.6.7 Heritage values
Federal Heritage Buildings Policy guides decisions about
properties with heritage value. Public Works and Government
Services Canada has published a Real Property Best Practice
(dated June 1, 1993) that describes applications of this
policy.
4.7 Misuse of benefit multipliers
When new resources are generated (or consumed) in a
community, the total effect may be larger than the initial
transaction would indicate. For example, suppose
Josh Brown in the town of Bin inherits $1,000 from a
distant aunt. Josh's net income is now $1,000 higher.
Josh saves $600 of this inheritance and buys a new suit for
$400 from Henry Smith. Henry's net income has
increased by the profit on the suit, say $100. Henry saves
$70 and spends $30. Obviously, by the time this chain of
saving and spending peters out, the total increase in income
of the whole community of Bin is larger than the original
$1,000 windfall.
The proportion by which the total effect is larger than the
initial income gains (or smaller than the initial income loss
- the process works symmetrically upwards and downwards) is
called the multiplier or the income
multiplier. The size of the multiplier varies from
one community to another. As the example above shows the
lower the savings rate and the quicker the rate of new
transactions, the higher the multiplier will be. The
plausible range of multipliers in the regions of Canada is
from about 1.1 to about 2.5.
Unfortunately, multipliers have been misused more often than
not. For example, some analysts have applied multipliers to
the benefits of a project without any consideration of the
equivalent multipliers that should be applied to the
(opportunity) costs. This is legitimate only if the analysis
is being undertaken from a local point of view and
some outside agency such as the federal government is paying
all the costs. Except in this special case, multipliers must
be applied even-handedly to both costs and benefits.
If a project is being analyzed from a social (nation-wide)
point of view, the correct application of multipliers is more
likely to work against the project's viability than for
it. If the investment capital is raised by taxing prosperous
areas (where the income multiplier tends to be high) and the
investment is made in remote areas (where the multiplier
tends to be low because many goods and services are purchased
outside the community), then taking the multipliers into
account will make the project look worse than it otherwise
would.
The use of multipliers in federal government analysis is
seldom appropriate. Therefore, multipliers should not
be included unless there is clear justification for their
use.
Best practice - measurement
-
The benefit-cost framework can be learned
in a short time. In contrast, measurement
of costs and benefits is a limitless topic.
Other specialists, in addition to the
benefit-cost analyst, are generally needed
as part of the team.
-
When market prices are distorted or do not
exist, the main methods for estimating the
value of costs and benefits are based on
willingness-to-pay.
-
Income multipliers should generally be
avoided but, when used, must be applied
even-handedly to costs as well as benefits.
-
The literature can sometimes provide
approximate values for such
difficult-to-measure items as the value of
a clean and natural environment, the value
of timesaving for commuters, the value of
jobs created, and the value of foreign
exchange. Government of Canada standard
parameters and benchmarks should be used
whenever possible.
|
5. Time values
5.1 Why time matters
Remember that time is money.
- Benjamin Franklin, "Advice to a Young
Tradesman," 1743
The fact that costs and benefits are spread over time matters
for two reasons. First, people prefer to make payments later
and receive benefits sooner. Our financial system is built on
this basic time preference. There is a loss of
earning power if income is postponed until a future date or
costs are paid early on. Second, the value of the unit of
measurement itself changes over time because of inflation
leading to loss of the purchasing power of the currency.
These two factors, inflation and time preference, are
independent. Even if there were no change in the purchasing
power of a dollar, one would still prefer benefits earlier
and costs later. The benefit-cost analyst should, therefore,
make two separate adjustments to cash flow figures across
time to convert them to standards units of value that can be
added or subtracted. The first adjustment is for changes in
the purchasing power of the dollar, and the second adjustment
involves discounting to reflect time preference.
5.2 Inflation, nominal dollars and constant
dollars
The costs and benefits across all periods should be tabulated
initially in nominal dollars for three reasons. First, this
is the form in which financial data are usually available.
Second, adjustments, such as tax adjustments, are accurately
and easily made in nominal dollars. Finally, working in
nominal dollar enables the analyst to construct a realistic
picture over time, taking into account changes in relative
prices.
Nominal dollars do not have standard purchasing power. They
are sometimes called budget-year dollars or current
dollars. They are simply the face value of the currency that
is paid or received in that period. They cannot be aggregated
if they occur at different times because they are not in
standard units of purchasing power. Theoretically, nominal
dollars can only be added or subtracted if they occur at the
same instant. In practice, it is acceptable to add and
subtract nominal dollars occurring within the same period as
long as the period is short (commonly one year), but it is
not acceptable to add and subtract them across periods.
As soon as you are confident that the tables of
nominal-dollar costs and benefits are complete and accurate,
it is a good idea to convert all figures, or at least the net
cash-flow line, to constant dollars before proceeding with
calculations (constant dollars have constant purchasing
power). To do this, you must select a base point in time at
which to express the constant-dollar values. This can be any
point in time, but it is often convenient to use
t0, which is the start of the investment
period. Selecting the same point in time for constant-dollar
conversions, and for present values, is best but not
essential. By the way, conversion to constant dollars should
not cause you to lose sight of the nominal-dollar tables.
They need to be kept visible in the benefit-cost report at
all times.
If the benefit-cost analysis is retrospective, the conversion
from nominal to constant dollars is simple and accurate
because the actual rate of inflation is known. If the
benefit-cost analysis is prospective, then you will need
projections of inflation. These projections are not easy to
come by, and they tend rapidly to become more uncertain the
further into the future they project. In this case, as in
other cases where data values are uncertain, sensitivity and
risk analysis become important tools.
In deciding which index of inflation to use for the
conversion to 'constant-purchasing-power' dollars
ask yourself this: Constant purchasing power for whom? Every
index of inflation is based on price changes for a specific
basket of goods and services, and the basket is normally
defined by the customary purchases of a particular group of
people. The index you choose should be as broad as possible.
In Canada, the closest thing to a general price index
covering everything is the Implicit Price Index (IPI). But
even the IPI is not the final word on purchasing power
because Canadians purchase many goods and services from
foreign sources. Benefit-cost analysts often use Statistics
Canada's Consumer Price Index to convert nominal dollars
to constant dollars. This is satisfactory if the appropriate
reference group is consumers in general. In some cases, it
will not be. An organization doing a fiscal analysis
of a potential investment will need an index of inflation
that reflects its own typical purchases. National Defence,
for example, constructs its own index for constant-dollar
conversions because the unusual mix of its purchases is not
reflected in any standard index. Once you have chosen a
suitable index of inflation, you are ready to calculate
constant dollars. This part is simple.
In prospective analysis, analysts often assume a constant
rate of inflation (approximated by using an average rate).
This is not a good idea for the early years of the
investment, when inflation can be predicted reasonably well.
For a longer period, however, inflation projections become
largely meaningless (considering the volatility in inflation
rates we have witnessed over the past three decades), so the
assumption of an average future rate of inflation is the best
option. Developing estimates of an average future rate of
inflation, however, is a job for a specialist.
The mechanics of adjusting future values to present values,
and vice versa, is simple. These values are linked by
compound interest. Interest is compounded when the interest
earned on an initial principal becomes part of the principal
at the beginning of the second compounding period. For
example, if Joe Smith invests $100 at 9 per cent
interest compounded annually, then at the end of one year the
investment will be worth $100 ´ (1 + 0.09) = $109. Similarly, at the
end of two years, t2, he will have
$100 ´ (1 + 0.09) ´ (1 + 0.09). Notice that the term
in parentheses is repeated once for each period that elapses.
In general form, at the end of n years,
tn, the investment will be worth $100 ´ (1 + 0.09)n.
The relationship between constant dollars and nominal dollars
is the same. If we start with a constant-dollar amount at
t0 and want to calculate the equivalent
nominal-dollar amount at tn, then we use
the formula:
N = C(1 + i)n [1]
where N is the amount in nominal dollars ($); C
is the same amount in constant dollars ($); i is the
annual rate of inflation (%); and n is the number of
periods between t0 and the actual
occurrence of the cost or benefit at tn. In
benefit-cost analysis, however, we often find ourselves
working in the other direction - that is, we know the
nominal-dollar amount for some cost or benefit that will
occur at some time in the future, so we need to calculate the
equivalent constant-dollar amount for an earlier point in
time, such as t0. In that case, we use this
formula:
C = N/(1+i)n [2]
where C is the amount in constant dollars ($);
N is the same amount in nominal dollars ($); i
is the annual rate of inflation (%); and n is the
number of periods between t0 and the actual
occurrence of the cost or benefit at tn. Of
course, interest rates are not always quoted conveniently in
terms of the period with which you are working. For example,
the interest might compound on a daily, monthly or quarterly
basis. To find the effective annual interest rate, given a
rate quoted for a shorter period, we use the following
formula:
EAR = (1 + r/m)m -
1[3]
where EAR is the effective annual interest rate (%); r
is the quoted interest rate (%); and m is the number
of times per annum the interest is compounded.
EAR is also available from standard tables and as a function
in many spreadsheet software programs.
5.3 Changes in relative prices
Unfortunately, it has been common in benefit-cost analysis to
neglect changes in relative prices over the life of the
project. An extreme example is when the analyst constructs a
'typical year' of cash flows and simply inflates
all input and output values by some standard percentage for
each of the following years. This shortcut ignores not only
changes in relative prices, but also changes in the
composition of inputs and outputs year by year. In general,
it is not an acceptable procedure.
A consistent treatment of inflation and relative price
changes is as follows:
-
Estimate the future relative price changes for each input
and output for each period during the life of the project.
-
Estimate the shadow price of foreign exchange if imports
and exports are involved.
-
Obtain estimates of the expected annual changes in the
general price level (commonly called inflation).
-
Using these two estimates, calculate the nominal
price for each input and output for each year of the
project.
-
Using the prices estimated above, construct the first
complete table of costs and benefits in nominal dollars.
-
Make any adjustments to the cash flows that need to be
calculated in nominal dollars (such as adjustments for
taxes or loan payments and adjustments in the stock of
cash, sometimes called working capital). This gives the
pro forma cash-flow table.
-
Deflate all items in the pro forma cash-flow statement for
each year by the price index. This gives the
constant-dollar table of costs and benefits that is the
basis for all further analysis.
5.4 Future and present values
Even when the table of costs and benefits is in constant
dollars, the figures are not yet in a standard unit. Constant
dollars have standard purchasing power, but it makes a
difference whether this is current purchasing power or future
purchasing power. To make costs and benefits fully
comparable, you must convert their values at various times to
values at a single point in time. Present values are dollar
values that are not only standardized for constant purchasing
power, but are also standardized for the time of occurrence.
To make the conversion to present values, you need a discount
rate that reflects the time preference of the reference
group. How much is it worth to receive a benefit now rather
than at some future time? In federal government benefit-cost
analysis, the choice of discount rate has been contentious.
Advocates of a project have tended to argue against high
discount rates because they make projects look bad (benefits
tend to occur later than costs; therefore, high discount
rates tend to decrease the benefits more than the costs).
Once the discount rate is selected, calculating present
values from future values and vice versa is straightforward.
The formula is similar to equation [2] for the adjustment for
inflation:
PV = FV/(1 + k)n [4]
where PV is the present value at t0 ($); FV
is the future value at tn ($); k is
the discount rate (%); and n is the number of periods
between to and tn.
5.5 Discount rates
It is important to understand that the appropriate discount
rate depends entirely on the point of view taken in the
analysis and that this point of view must be stated
explicitly. If, for example, the point of view is that of a
particular group of people, then the appropriate discount
rate would be one that reflects the time preference of the
members of that group. Research shows that if the members of
the reference group are poor, the discount rate that reflects
their time preference is likely to be high - they will highly
value immediate benefits because they have basic needs that
are unmet. The cost of borrowing might not approximate their
discount rate (unlike the case of a business corporation) if
their access to credit is limited or distorted.
Unlike most individuals and organizations, governments
frequently take two different points of view in assessing
investments - the fiscal point of view (is the project a good
one from the government's narrow fiscal perspective?)
and the social point of view (is the project a good one for
the country?). The discount rates can be quite different from
these two perspectives.
5.5.1 The fiscal discount rate
(Narrow fiscal point of view of government)
The fiscal discount rate is the government's cost of
borrowing. It is appropriate to use the actual cost of
borrowing when the analysis is from the narrow fiscal point
of view of the government and the marginal funds for the
investment come from borrowing rather than from increased
taxes. The fiscal discount rate tends to be low because
governments are generally preferred borrowers (taxation is in
the background as a guarantee of repayment).
The use of the fiscal point of view and thus of the fiscal
discount rate is only appropriate when the proposed
investment has few, if any, social implications. Examples are
decisions to purchase computers or lease minor accommodation.
If the project is large enough to matter to the general
economy or if it has aspects that are of interest to the
public, then the narrow fiscal point of view is probably
inappropriate.
5.5.2 The social discount rate
(Broad social point of view of government)
The social discount rate is roughly equal to the
opportunity cost of capital, weighted according to the
source of investment capital. For the Government of Canada,
this is foreign borrowing, foregone investment in the private
sector, or foregone consumption. If you know what the
government's investment is displacing and what the rates
of return would have been for the displaced uses, then you
can calculate the opportunity cost. Essentially, the argument
is that the government must achieve a return on investment at
least equivalent to what the money would earn if left in the
private section to justify taxing the private economy to
undertake public-sector investments. If the government cannot
achieve this it would be better for Canada if the money is
left untaxed in the private sector.
Since 1976, Treasury Board has required that benefit-cost
analysts use a social discount rate of 10 per cent
'real' per annum - that is, a 10 per cent
discount rate applied to real dollars (constant,
inflation-adjusted dollars). This rate is a stable one
because it reflects an opportunity cost in the private sector
where the average rate of return to investment (over the
whole economy) changes very slowly over the years, if at all.
The government's estimate of the social discount rate
has been robust, despite some challenges over the years.
Social discount rates as low as 7.5 per cent real and as
high as 12 per cent real have been proposed and
supported by various economists. Estimates by the Department
of Finance, however, have consistently supported the
10 per cent real estimate of the social discount rate.
Currently, the only serious challenge to the 10 per cent
social discount rate is from those who argue that high
discount rates unfairly devalue benefits to future
generations, who have as much right to such basics as clean
water and clean air as the current generation does. This
argument for low discount rates in the public sector is not
well based, however. A project with a high rate of return
when all its costs and benefits are counted is better for the
present generation and, through reinvestment, better for
future generations as well. Only when benefits are
non-renewable and consumed rather than reinvested is there
conflict across generations, with one generation paying and
another benefiting. Manipulating the discount rate does not
lessen this conflict. It has to be addressed directly by
intergenerational consumption analysis.
5.5.3 The rate-of-time preference for
consumption
(Point of view of consumers)
Considerable confusion in benefit-cost analysis has been
caused by analysts using different numeraires (the units of
value). To avoid confusion, one should generally use a
'dollar of investment' as the numeraire and
10 per cent per annum real as the social discount rate.
This common approach to investment and rates of return is
familiar to economists and non-economists alike.
On the other hand, it is possible (and perhaps theoretically
more precise) to use a dollar of consumption as the
numeraire. After all, investment is not a final value in the
way consumption is. The social rate-of-time preference for
consumption is normally taken to be about 4 per cent.
This is obviously a much lower discount rate than 10 per
cent and on the surface may seem more attractive to those who
think that benefits in the distant future (say, general
environmental benefits) should not be discounted too heavily.
However if you use a dollar of consumption as the numeraire
and a social rate-of-time preference for consumption as the
discount rate, then (to make the analysis fair and
consistent) you must calculate shadow prices for the
investment funds in terms of a stream of consumption
foregone. Economists who have calculated the shadow price of
a dollar of investment funds in Canada and the United States
have found that it is about $2.50 in 'consumption
dollars'.
The important point is that the rate used in the first
approach (10 per cent discounting of costs and benefits,
expressed in an investment-dollar numeraire) and the rate
used in the second approach (4 per cent discounting of
costs and benefits, expressed in a consumption-dollar
numeraire, with a dollar of investment funds shadow priced at
$2.50) give the same result when properly applied. Because
the outcome of either approach, properly done, is the same,
it makes sense to stay with the more easily understood
concept of an investment-dollar numeraire and a 10 per
cent discount rate (on which everyday thinking about
investment and rate of return is based). What is not
acceptable is to confuse the two approaches. To use a
4 per cent discount rate without shadow pricing the
investment funds is incorrect.
5.6 Strategic effects of high and low
discount rates
The choice of a discount rate is extremely important. It has
a strong (although hidden) influence on the direction of an
organization.
A low discount rate is favourable for the following:
-
an active investment program, because capital seems
inexpensive;
-
outright purchase of assets;
-
many and larger projects and programs; and
-
projects whose benefits may be long-term.
A high discount rate is favourable for the following:
-
a cautious capital investment program, because capital
seems expensive;
-
leasing and other kinds of deferred-payment options;
-
short-term, flexible planning; and
-
labour-intensive rather than capital-intensive solutions.
5.7 The discount rate as a risk
variable
The 1976 Treasury Board Benefit-Cost Analysis Guide
recommended a social discount rate of 10 per cent real, and 5
to 15 per cent real per annum in sensitivity analysis.
Experience has shown, however, that this range was too broad.
Most projects look good at a 5 per cent discount rate
and poor at a 15 per cent discount rate. A credible and
more useful range for the social discount rate is normally
about 8-12 per cent real per annum (for risk analysis),
with a most likely value of 10 per cent real
per annum.
Because there is some uncertainty about the correct value of
the discount rate, you should include it as a risk
variable in the parameter table of a benefit-cost and
risk analysis using simulation. This makes it less important
to fix on a precise value of the discount rate and places
more emphasis on identifying the likely range of values of
the discount rate and on interpreting the results of the
financial simulation (see Chapter 9).
Best practice - inflation adjustments
and discounting
-
To ensure that changes in relative prices
are properly recognized, tables of costs
and benefits should be first constructed in
nominal dollars, and cash flows should be
set out for each period to the investment
horizon. Conversions to constant dollars or
to present value dollars should wait until
all costs and benefits over time are worked
out in nominal dollars.
-
Adjusting for inflation is not the same
thing as discounting to present values, so
each should be done independently.
-
The appropriate discount rate depends on
the point of view of the analysis and also
on the choice of numeraire.
-
The Government of Canada uses a fiscal
discount rate (based on a narrow
'internal' point of view that is
appropriate mostly for small projects) and
a social discount rate (based on a
nation-wide point of view). With the normal
dollar of investment as the numeraire, the
appropriate social discount rate (as
measured by the Department of Finance and
Treasury Board of Canada Secretariat) is
about 10 per cent real per annum. The
plausible range for risk analysis is
8-12 per cent.
|
6. Decision rules
There is nothing so practical as a good theory.
- Kurt Lewin, Field Theory in Social Science: Selected
Theoretical Papers, 1951
A decision rule tells us whether an investment is worthwhile
and whether one investment is better than another is. In this
chapter we consider how decision rules are used with
deterministic data - that is, we ignore uncertainty in the
data for the moment (Section 9.7 shows how the same
decision rules can be adapted for uncertain data).
6.1 Net present value
NPV is the present value of all benefits, discounted at the
appropriate discount rate, minus the present value of all
costs discounted at the same rate. An NPV is always specific
to a particular point in time, generally
ta, the time of the analysis, or
t0 the start of the project.
The formula for the calculation of net present value is as
follows:
NPV = initial investment costs + the sum of the present
values of costs
and benefits for each period within the investment
horizon. [5]
The NPV can be calculated in several different ways.
Obviously, you could calculate the NPV of benefits and the
NPV of costs separately and then subtract them. More often,
the analyst subtracts costs from benefits in each period,
giving a single line of net cash flow, and then discounts the
net cash flow to give the NPV. The arithmetic of this latter
procedure is a little simpler, but, more important, the net
cash flow is itself useful information for managers. Many
projects and enterprises with a positive NPV have failed
because of cash-flow problems.
For example, if the initial investment were $100 and there
were $70 in benefits and $25 in costs for each of 3 years,
and the discount rate were 10 per cent per annum, then
the NPV would be:
NPV
|
=
|
- $100 + ($70 - $25)/(1 + 0.1)1 + ($70 - $25)/(1 + 0.1)2 + ($70 - $25)/(1 + 0.1)3
|
|
=
|
- $100 + $40.91 + $37.19 +
$33.81
|
|
=
|
$11.91
|
This formula follows the accounting convention discussed in
Chapter 2; that is, all costs and benefits are assumed
to occur at the end of their period, except for large initial
expenditures, which occur at t0 and are not
discounted.
6.1.1 Net present
value and break even
An NPV of zero does not mean 'break even' in the
normal sense of costs equalling benefits. NPV is more like
excess profit than it is like profit. If a project has an NPV
of zero, the project earns the normal rate of return (which
is, of course, equal to the discount rate). For example, if a
project earns 10 per cent per annum and its cash flows
are discounted by 10 per cent per annum, the result will
be an NPV of zero.
We value NPV not because it tells us whether the project
breaks even, but because it tells us whether it is worth
doing the project instead of leaving the money in the normal
alternative investment (which earns 10% per annum).
6.2 Two essential decision rules
Many projects have complex patterns of costs and benefits
over time, and you cannot use the 'eyeball' method
to determine which project is preferable. We need decision
rules to guide us. Many decision rules have been proposed.
Some work well only in particular situations; others are
prone to error. Only two rules are consistently accurate and
reliable. These are given below.
Case 1: Single project, unconstrained budget,
'go' or 'no go' decision
Decision rule 1: Do not undertake projects
whose NPV is less than zero, unless you are
willing to 'lose money' to achieve a
non-economic objective.
|
Example 6.2.1
|
|
NPV
|
Decision
|
|
Project A
|
+$3
|
Accept
|
|
Project B
|
+$0
|
Indifferent
|
|
Project C
|
- $1
|
Reject
|
Case 2: Alternative projects, constrained budget, a
'best set' decision
Decision rule 2: Given a choice among
alternative projects, maximize the total NPV.
|
6.2.1 Problem of
independence from the scale of investment
People are generally comfortable with the idea that a project
with an NPV of -$27 is unacceptable, but they are less
comfortable with the idea that project B, whose NPV is
+$3, is always preferable to project A, whose NPV is
+$2, no matter how much investment went into each. The reason
harks back to our previous discussion about NPV being like
excess profit rather than profit.
A simple example for one period should make clear why you
should always prefer the larger NPV. The key is to realize
what happens when we standardize the level of investment -
that is, when we take into consideration what happens to the
capital we have left over if we choose the smaller
investment.
Example 6.2.2
Suppose project A requires an investment of $100 and
project B an investment of $150. If you invest in
project A instead of project B, then you have an unused
residual of $50, which earns the normal rate of return
invested somewhere else. This residual, however, has an NPV
of zero (it earns the same rate of return, say 10 per
cent, as the rate used to discount it to a present value).
Therefore, if you choose project A, you have a total of
$100 earning 10 per cent plus an NPV of $2, and you also
have $50 earning the normal rate of return. If you choose
project B, similarly, you have $150 earning the normal
rate of return plus an NPV of $3.
Project A earns (10% of $100 + 10% of $50) +
$2
Project B earns (10% of $150) + $3
|
The figure in parentheses will be the same for project A
and project B whatever their scale of investment, so it
is only in the NPV that differences will show. The amount of
investment involved in two alternatives is irrelevant to our
decision once we know the NPVs. Simply choosing the better
NPV will always be correct. Another way of looking at the
same calculation follows.
Example 6.2.3
|
Basic return
|
NPV
|
Total return
|
Project A
|
|
|
|
Investment of $100
|
$10
|
$2
|
$12
|
Residual of $50
|
$5
|
$0
|
$5
|
|
$17
|
Project B
|
|
|
|
Investment of $150
|
$15
|
$3
|
$18
|
It is important that the decision-maker grasp this concept if
NPVs are to be a useful guide. An NPV of zero does not mean
'break even.' It means the project earns the normal
rate of return, say 10 per cent. A negative NPV of, for
example, -$300 does not necessarily mean the project makes a
loss in the colloquial sense. It means that it makes the
normal 10 per cent return, less $300.
You can rank projects by their NPVs without worrying about
the scale of the project. In contrast, you cannot rank
projects by their internal rates of return unless you
consider their scale as well (see Section 6.3.1). This is
counter-intuitive for many managers.
6.3 Unreliable decision rules
6.3.1 The
internal rate of return
The Internal Rate of Return (IRR) is the discount rate
that makes the NPV of the project zero. An IRR higher than
the standard discount rate indicates that you should go ahead
with the project, and when you are choosing among alternative
projects, a higher IRR is preferred. If project A earns
an IRR of 15 per cent, for example, whereas the ordinary
project earns 10 per cent, then project A is an
attractive investment.
The IRR has three important limitations (see boxes below)
that make it a poor substitute for NPV as a decision rule.
Nevertheless, many managers find the IRR intuitively
appealing in a way that the NPV is not. They tend to think
that the meaning of an IRR is transparent, but it is not.
When you calculate the IRR, you need to interpret it with
care.
The underlying formula for the IRR is the same as for the
NPV. If you know the discount rate, you can calculate the NPV
and vice versa. The mathematics of the IRR calculation,
however, is not based on a proof and a formula. In practice,
the analyst uses a computer to calculate the IRR by trial and
error iterations. Given a guess at the likely IRR, the
computer enters higher and lower values for i in the
formula until it results in an NPV of zero.
Most spreadsheets in common use have a limit on the number of
iterations the computer will try. If the computer does not
find a discount rate that gives an NPV of zero within this
limited number of iterations, it gives an error message. The
analyst then has to start the process again with a different
guess at the value of the IRR. In addition to this procedural
awkwardness, the IRR has two other limitations that make its
use doubtful. These are given below.
Limitation 1: Simple comparisons between IRRs
may be misleading if the projects are not the
same size. A project with an IRR of 7 per
cent is not necessarily a better choice than one
with an IRR of 6 per cent. The size of each
project and the discount rate can influence which
project is best.
|
Example 6.3.1
|
|
|
|
Project A
|
Project B
|
Total cost
|
$100
|
$10,000
|
IRR
|
7%
|
6%
|
Discount rate
|
5%
|
5%
|
If you choose project A, you will have $100 earning
7 per cent plus the residual $9,900 earning 5 per
cent (total return = $7 + $495 = $502). If you choose
project B, you will have the whole $10,000 earning
6 per cent ($600). Project B is better, even though
it has a lower IRR than project A.
Limitation 2: In many cases, more than one
value of the IRR will solve the equation, and it
may not be apparent to the analyst that other
equally good values exists because the computer
typically stops when it finds any acceptable
value of the IRR.
|
Multiple values of the IRR (some negative, some positive) are
especially likely if the annual net cash flow of the project
alternates between positive and negative figures, a common
event because of the cyclical re-capitalisation requirements
of projects and/or fluctuations in the prices of inputs and
outputs. In some cases, analysts 'bend' the
accounting rules to obtain a cash-flow pattern that gives a
single value for the IRR, but this is not a satisfactory
solution. At best, the possible existence of multiple values
of the IRR throws a shadow over its use; at worst, it may
lead to incorrect choices among projects.
6.3.2 The benefit-cost ratio, payback period,
and present value of costs
Decision rules other than the NPV ones given in Section 6.2
are sometimes used correctly, but none of them are
satisfactory as a general rule. The three most common involve
benefit-cost ratios, payback period and the present
value of costs.
Benefit-cost ratios
A benefit-cost ratio is the ratio of the present value of
benefits to the present value of costs. The decision rule
here is that you should reject any project with a
benefit-cost ratio of less than 1, and you should rank
projects in order of their benefit-cost ratios. The first
part of this rule works. The second part, however, may not.
This is because it is possible to change the benefit-cost
ratio substantially by artificial changes in the accounting
for benefits and costs (although it is not possible to change
a ratio of less than one to a ratio of greater than one or
vice versa __ try it!). Remember that a positive benefit
is equivalent to a negative cost. Almost any cost or benefit
could serve as an example. Consider expenditures on an access
road to a new park. These could be added to the costs of the
park or subtracted from the benefits. Either choice is
correct. However, the benefit-cost ratio would be increased
or decreased artificially, depending on this arbitrary
accounting decision.
Example 6.3.2
|
|
|
|
|
Benefits
|
Costs
|
Benefit-cost ratio
|
Project A
|
$100
|
$60
|
100/60 = 1.66
|
Project A (same project, but netting $30 out of
the benefits rather then listing it as a cost)
|
$70
|
$30
|
70/30 = 2.33
|
Payback period
The payback period is the time it takes for the
cumulative present value of benefits to become equal to the
cumulative present value of costs. In general, shorter
payback periods are better. However, this can be a misleading
decision rule because it ignores everything that happens
after the payback point. It is quite possible for a project
to have a higher NPV and a longer payback period (see Figure
6.4.1). 'A' has a quicker payback, but
'B' reaches a higher NPV.
Present value of costs
When the benefits of two alternatives are exactly the same,
you may choose between them on the basis of the lowest
present value of costs. This is not a reliable decision rule,
however, because you cannot tell from the present value of
costs whether the project should be done at all. As well, the
premise that benefits are constant is generally a
simplification and often may not be valid. For example, a
constructed facility will seldom be exactly the same,
qualitatively and quantitatively, as leased accommodation.
Some of the differences might be quite important.
Furthermore, the present value of costs is subject to
manipulation of the type described above in the discussion of
benefit-cost ratios. That is, the accounting for costs and
benefits (benefits can be counted as negative costs) can
artificially change the apparent present value of costs.
Best practice - decision rules
NPV decision rules are best. Other decision
rules should be used with extreme care.
The two basic decision rules are the
following:
-
Do not undertake projects whose NPV is less
than zero, unless you are willing to
'lose money' to achieve a
non-financial objective.
-
Given a choice among alternative projects,
maximize the total NPV.
|
7. Sensitivity analysis
The whale that wanders round the Pole
Is not a table fish.
You cannot bake or broil him whole.
Nor serve him in a dish.
- Hilaire Belloc, "The Whale," The Bad
Child's Book of Beasts, 1896
7.1 What is sensitivity?
In benefit-cost analysis, the outcome is typically influenced
by several uncertain factors. This is true in fields as
diverse as health, education, employment, and economic
development. It is important to know how
'sensitive' the outcome is to changes in those
uncertain factors. It helps you to determine whether it is
worthwhile spending money to obtain more precise data and
whether you can act to limit uncertainty (for example, you
could redesign the project components or simply keep a
watchful eye when managing the project). As well, sensitivity
analysis helps you to communicate to decision makers the
extent of the uncertainty and risk in the program.
Nevertheless, sensitivity analysis is a limited tool. It
treats variables one at a time, holding all else constant.
Simultaneous actions and interactions among variables in the
real world are ignored. It can be a mistake to take the
results too seriously because a variable that appears to be
key when considered in isolation might or might not be key
when considered along with other variables that strengthen or
weaken its effect on the outcome of the project. Only a risk
analysis (Hertz and Thomas 1983, 1984) can accurately
identify the influence of each variable.
Nevertheless, sensitivity analysis is a helpful (although
limited) step in exploring the deterministic model. It is the
second of three phases in the general analysis:
-
Build a deterministic model using single 'best'
values (base values) for the input variables.
-
Explore the outcome's sensitivity to each input
variable and then take action to reduce the risk of
uncertainty where possible.
-
Make a full risk analysis using probabilities for many
variables simultaneously.
Sensitivity analysis gives you a better understanding of the
model. As this understanding develops, you can take action
when appropriate. In some cases, the only action you can take
is to obtain better data. For example, if you are deciding
whether to purchase a heart-lung machine, the outcome is
sensitive to 'probability of an influenza
epidemic,' a variable that you cannot control. In other
cases, you might be able to fix or constrain the value of the
variable. For example, if the outcome is particularly
sensitive to an operator's wage rate, then you could
negotiate this rate beforehand. Fixing the wage rate would
dramatically lower the sensitivity of the outcome to this
variable. The more you can minimize the sensitivities, the
more precise the estimate of the outcome will be.
7.2 Gross sensitivity
In its simplest form, which we might call gross sensitivity,
sensitivity analysis involves calculating (one variable at a
time) how much the NPV changes if the influencing variable
changes by a standard percentage, say 10 per cent.
Suppose you are deciding whether to purchase a heart-lung
machine whose NPV is affected by four variables: insurance
costs, operating costs, the price of the machine, and the
usage rate. A quick glance at Table 7.2.1 indicates that
the decision is quite sensitive to three of the four
variables.
Table 7.2.1: An example of gross sensitivity of the NPV to
input variables
Variable
|
Change in NPV in response to
a 10% change in the variable
|
Insurance costs
Operating costs
Machine price
Usage rate
|
|
|
7.3 What determines sensitivity?
A superficial interpretation of Table 7.2.1 could be
misleading. The 'effective sensitivity' of the
outcome to a particular variable is determined by four
factors:
-
the responsiveness of the NPV to changes in the
variable;
-
the magnitude of the variable's range of plausible
values;
-
the volatility of the value of the variable (that
is, the probability that the value of the variable will
move within that range of plausible values); and
-
the degree to which the range or volatility of the values
of the variable can be controlled.
The first of these factors, the responsiveness of the NPV to
changes in the variable, has two components. The first
component is the direct influence of the variable on the NPV.
The second component is the indirect influence of the
variable, through its relationships with other variables that
themselves are related to the NPV. Positive correlations with
other influential variables will magnify the ultimate
influence of both, and negative correlations will dampen
their influence. These influences cannot be fully identified
until you have set up a simulation model that is capable of
dealing with the simultaneous interactions of many variables.
7.4 Sensitivity and decision making
We are most interested in the sensitivities that might change
a positive decision on the project to a negative decision and
vice versa. Four calculations help us estimate the likelihood
of such a switch:
-
What is the range of influence? That is, how much
does the NPV change when the variable changes from its
lowest plausible value to its highest plausible value?
-
Does this range of influence contain an NPV of zero? If it
does, then the variable has a switching value -
that is, a value at which our appraisal of the
project switches from positive to negative.
-
What is the switching ratio for the variable? That
is, by what percentage does the variable have to change to
hit a switching value?
-
What is the switching probability? That is, how
likely is the variable to reach the switching value?
If we add this information to the gross-sensitivity
calculation shown in Table 7.2.1, we begin to have a
reasonably complete picture of the likely sensitivity to a
variable, although, of course, within the limits imposed by
considering one variable at a time (see Table 7.4.1).
Table 7.4.1: An example of several indicators of the
sensitivity of NPV to input variables
|
Input variables
|
Indicators
of sensitivity
|
Insurance
costs
|
Operating
costs
|
Machine
price
|
Usage
rate
|
Gross sensitivity
|
15%
|
21%
|
7%
|
19%
|
Range of influence
|
10%
|
17%
|
5%
|
35%
|
Switching value
|
No
|
Yes
|
No
|
Yes
|
Switching ratio
|
-
|
9%
|
-
|
63%
|
Switching probability
|
-
|
40%
|
-
|
42%
|
By scanning all the data in Table 7.4.1, you can easily
see that the NPV is sensitive to neither insurance costs nor
machine price. In particular, neither variable can move the
NPV enough to hit a switching value. In contrast, the NPV is
sensitive to both operating costs and usage rate. Of these
two, usage rate obviously has a more volatile value -
although it has to change by a much larger percentage to hit
a switching value than the value of operating costs does, it
is about equally likely to do so (42 per cent vs.
40 per cent). Although usage rate has to change more
than operating costs to cause a crucial change in the NPV,
its volatility makes it equally likely to do so. On this
evidence, we would tentatively conclude that the two key
variables are equally influential.
7.5 Two-variable sensitivity analysis
So far, we have analyzed sensitivity one variable at a time.
Extending this to two variables is the next step toward true
risk analysis. Scenarios defined by two interacting
variables, although still not complete and realistic
indicators of sensitivity, are at least an improvement on
single-variable analysis. The joint influences of two input
variables on NPV can be shown in a matrix-like
Table 7.5.1.
Table 7.5.1: Influence of combinations of two input
variables on net present value
Discount
Rate
|
Usage rate
|
500
|
475
|
450
|
425
|
400
|
0.10
|
$16,814
|
$12,987
|
$9,161
|
$5,335
|
$1,509
|
0.11
|
$14,923
|
$11,200
|
$7,476
|
$3,753
|
$29
|
0.12
|
$13,082
|
$9,459
|
$5,835
|
$2,212
|
|
0.13
|
$11,288
|
$7,763
|
$4,238
|
$713
|
|
0.14
|
$9,541
|
$6,112
|
$2,683
|
($746)
|
|
0.15
|
$7,840
|
$4,505
|
$1,170
|
($2,165)
|
|
0.16
|
$6,185
|
$2,941
|
($302)
|
($3,545)
|
|
0.17
|
$4,573
|
$1,420
|
($1,734)
|
($4,887)
|
|
0.18
|
$3,004
|
($61)
|
($3,127)
|
($6,192)
|
|
0.19
|
$1,478
|
($1,501)
|
($4,481)
|
($7,460)
|
|
0.20
|
($6)
|
($2,902)
|
($5,798)
|
($8,693)
|
|
For each discount rate, you can see what usage rate has to be
attained if the machine is to be economical. You could draw a
diagonal line (from the lower left toward the upper right)
that represents all the combinations of discount rate and
usage rate that result in a NPV of zero. This diagonal
divides the table into two 'strategy regions'
(defined by combinations of discount rates and usage rates).
In one of these strategy regions, all values of the NPV are
negative (the bold numbers); in the other region, all are
positive.
If most of the sensitivity in the model results from only two
key variables, then this sort of analysis is very
instructive. Even if there are more than two key variables,
two-variable analysis takes us at least one step closer to
understanding the workings of the model in a realistic
setting.
7.6 Graphic analysis of sensitivity
Although we have been interpreting tables to ascertain
sensitivity, in practice, you are more likely to use graphs
because the variable x outcome interaction is visible over a
reasonable range of values. Sensitivity analysis is
exploratory, not definitive, so making the patterns in the
data visible is the first priority.
7.6.1 Sensitivity curves
A graph that shows changes in NPVs against changes in the
risk variable is simple and useful. You can easily read the
switching values to see how sensitive the outcome is to
changes in the variable. If the changes in the variable are
presented on the graph in percentages (and thereby
standardized), it becomes possible to put the curves for two
or more variables (calculated one at a time, of course) on
the same graph. This is useful because the slopes of the
curves indicate the relative sensitivity of each variable.
The more the NPV changes for a given change in a variable,
the more sensitive it is to that variable, volatility being
equal.
If the percentage change in NPV is on the x-axis and
the percentage change in the risk variable is on the
y-axis, then any flat curves indicate a strong
sensitivity. As you can see from Figure 7.6.1 the NPV of
the example project is more sensitive to
variable 'B' than it is to variable
'A'. A 10 per cent change in risk variable
'B' results in a much larger change in NPV than the
same change in variable 'A'.
7.6.2 Spider plots
Sensitivity plots can be consolidated to show many input
variables on one chart. This type of consolidated chart is
called a spider plot (see Figure 7.6.2 for an
example). The centre of the spider plot is the NPV when all
the variables are at their baseline values. The curves on the
spider chart show how the NPV changes as the values of each
variable change, all others being held equal.
The lengths of the spider lines vary because each variable
has its own plausible range within which it can change. The
values of one variable might vary by only 10 per cent up
or down from its baseline value; another variable might be
highly uncertain, varying between +170 per cent and
-60 per cent.
The interpretation box superimposed on the spider plot is an
aid to interpretation. The top and bottom of the box indicate
+5 and -5 per cent change, respectively, in the
variables. Thus, wherever a 'tentacle' of the
spider plot crosses the top or the bottom of the box, it
shows what the NPV would be if there is a 5 per cent
change in the particular input variable.
The NPV at the left side of the interpretation box is zero,
and therefore the tentacles cross this side at the switching
value of the variables. The right side of the box is set at
an NPV of 60 for symmetry (the NPV of the baseline case is
30). These dimensions of the box are reasonable for this
particular analysis, but they will vary in other analyses
(the box is an aid to reading the spider plot, nothing more).
The spider plot shows how much each variable would have to
change, other things held constant, to produce an NPV of zero
(the switching ratio).
7.6.3 Tornado charts
Tornado charts give us another quick, although partial,
picture of relative sensitivity. Each bar in the tornado
chart shows the range of the NPV when each variable is
allowed to change (one at a time) from its highest to its
lowest value. You can see from a quick glance at the shape of
Figure 7.6.3, (which has variables arranged in
descending order of influence from top to bottom), why it is
called a tornado chart. Of course, the magnitude of the
variable's range of plausible values is not the only
factor that determines sensitivity. The volatility - the
probability that the value of the variable will move within
that range - is also important to sensitivity, but you cannot
see volatility on a tornado chart.
The length of each bar is a measure how much
the variable can influence the NPV. The shading within the
bar changes at the NPV, which corresponds, to the
deterministic value of the variable.
7.7
Action on sensitivities
Once you have identified the key sensitivities among the risk
variables, one by one (everything else held constant), you
can start to think about managing risk.
-
Are there input variables in the model that are correlated
and therefore dampen or enhance the influence each might
have in isolation?
-
Can diversification help? Are there other investments that
could be made at the same time where the same variable
works in the opposite direction?
-
Could you identify the value of the key variable with more
certainty by gathering more information, and if so, is the
information worth the cost to gather?
Once you have answered these questions, you can formulate an
action plan to minimize uncertainty and thereby limit risk.
Best practice -
sensitivity analysis
-
Sensitivity analysis is a useful technique
for finding out how important each variable
in the benefit-cost model is.
-
Sensitivity analysis cannot deal with more
than two variables at a time, so it does
not tell us much about the project's
level of risk. Until all variables are
allowed to vary simultaneously, we do not
know whether their individual effects on
risks are magnified or cancelled out by
each other.
-
Four factors contribute to sensitivity: the
responsiveness of the NPV to changes in the
variable; the magnitude of the
variable's range of plausible values;
the volatility of the value of the variable
(that is, the probability that the value of
the variable will move within that range of
plausible values); and degree to which the
range or volatility of the value of the
variable can be controlled.
-
Graphic analysis, including the use of
sensitivity curves, spider plots, and
tornado diagrams, is often useful.
-
The switching value of a risk variable can
be an important consideration in an
investment decision. It can help the
decision maker weigh the risk.
|
8. General approaches to uncertainty and risk
Making risk characterisations more complete, subtler and
more data rich should help decision-makers make more
balanced, subtler and better-informed decisions.
- National Academy of Public Administration, Setting
Priorities, Getting Results, 1995
Dealing with uncertain data is a very large part of practical
benefit-cost analysis. Chapters 3 and 4 discussed uncertainty
in the incremental effects of a program or project. In this
chapter, we look at ways to cope with uncertainty in the
overall financial and economic analysis. Many of the tools
are similar.
8.1 Approaches to quantifying
uncertainty-related risk
There are three approaches to dealing with financial and
economic risk in benefit-cost analysis:
-
expected values (certainty equivalents) of scenarios;
-
risk-adjusted discount rates; and
-
risk analysis through simulation.
Given the present state of the art, the first two approaches
have limited applicability. Only the third method,
simulation, offers a practical technology for analyzing the
overall risk of a project.
8.2 Expected values of scenarios
If an investment has two possible outcomes -$10 and $100- and their probabilities are 30
and 70 per cent, respectively, then the expected
value or certainty equivalent of the investment is
(0.3 x $10) + (0.7 x $100) = $3 + $70 = $73. If you
have a completely rational attitude to risk, then it
shouldn't matter to you whether you make the investment
or accept the $73 instead.
Few benefit-cost analysts take this scenario approach because
in most cases there are so many possible outcomes that it is
too difficult to think clearly about the probability of each
separately. On occasion, however, scenarios can provide
useful information about risk. For example, an oil company is
trying to decide whether to build a new pipeline across an
iceberg-infested strait. The pipeline costs $100 million
(present value at t0). The chief executive
officer (CEO) foresees three possible scenarios; and each of
these has a predictable outcome for the company.
Scenario 1: No iceberg hits the pipe.
Outcome: Company revenue from the pipeline: $135 million,
t0.
Scenario 2: An iceberg hits the pipe, but the
pipe can be repaired.
Outcome: Company revenue from the pipeline: $93 million,
t0.
Scenario 3: An iceberg hits the pipe, and the
pipe cannot be repaired.
Outcome: Company revenue from the pipeline:
$9 million, t0.
Now comes the difficult part. Suppose the CEO commissions a
study by iceberg-risk consultants and is told that there is a
60 per cent chance that no iceberg will hit the pipe, a
30 per cent chance that an iceberg will hit the pipe but
the pipe will be repairable, and a 10 per cent chance
that an iceberg will hit the pipe and the pipe will not be
repairable. Therefore, the expected value of the $100 million
investment is (0.6 x $135 million) +
(0.3 x $93 million) +
(0.1 x $9 million) =
($81 + $27.9 + $0.9 million) =
$109.8 million. The CEO decides to go ahead with the
pipeline since the expected benefit ($109.8 million) is
greater than the cost ($100 million). An iceberg hits the
pipe, but the pipe is reparable. The company loses
$7 million. The CEO, however, had made the right
decision, given the information he or she had to work with.
The main difference between this procedure and the
recommended simulation procedure is in the reliability of the
estimates of probability they make. Did the iceberg-risk
consultants really have the expertise to assign probabilities
to the likelihood of an iceberg collision? There were no
data. Assigning subjective probabilities to
'big-picture' scenarios is essentially a guessing
game. In contrast, it is plausible that an apple-pricing
expert can forecast apple prices within a reasonable range a
year ahead, based on historical price data, demand trends,
and consideration of factors that might intrude. There is a
subjective or judgmental element in forecasting apple prices,
too, but there are data available. Legitimate experts have
developed good judgement in the matter, so they are able to
express expected apple prices as a range and specify a
probability distribution with reasonable confidence.
Risk analysis is part science and part art; and part of the
art is knowing when and where in the benefit-cost model to
use probabilistic data.
8.3 Risk-adjusted discount rates
The practice of changing the discount rate to allow for
uncertainty in project evaluation has limited validity. In
effect, it implies that uncertainty compounds itself at a
fixed rate over time. This is unlikely to be the case.
Where different degrees of uncertainty can be ascribed to
future values of variables, it is preferable to let
estimates of future annual benefits and costs reflect
these different degrees of uncertainty, and to aggregate
present values using an interest rate that has not been
adjusted for risk.
- Treasury Board, Benefit-Cost Analysis
Guide, 1976
Another approach that purports to deal analytically with risk
is risk-adjusted discount rates. The basic idea is that, in a
perfect market, all investments earn the same rate of return.
Otherwise, capital would flow to the high-return areas
pushing average returns down until the rates equalised.
Therefore, visibly different rates of return must incorporate
the same basic rate plus a premium for risk so that, in the
long run, only the basic return is gathered by the investor.
If this is so, then the appropriate discount rate (cost of
capital) is the basic rate plus a premium for risk. This
combination is the risk-adjusted discount rate.
This approach has several flaws. One is that we do not
operate in perfect markets, so the differentials observed in
rates of return might be due to other systematic or random
factors, rather than to project risk. Another objection is
that the argument confuses the lender's risk in lending
capital to the investor with the risk inherent in the
proposed project. They are not the same things.
Furthermore, the use of a risk premium on the discount rate
(which is a compound-interest rate) can lead to odd results.
A risk premium on the discount rate means that the absolute
value of the risk premium in dollars increases as time goes
on, and this does not make sense for many investments that
are uncertain for an initial period but tend to settle down
to a known pattern of costs and revenues and therefore low
risk (real estate development, for example).
These are somewhat abstract objections to an abstract theory,
however. The practical matter is that there is no known way
to calculate the risk premium in a specific case. The closest
one can come to such a calculation is where there are data
for a large number of transactions that can be analyzed
statistically, such as in the stock market. Here, the
variability of a stock price is a reasonable surrogate for
one type of risk, but no one has demonstrated a way to use
this concept of 'volatility risk' to adjust the
discount rate for a single-project investment. Except in a
limited number of special cases, risk is more than volatility
(see Section 9.8).
Making subjective estimates of the risk premium is not a good
idea for two reasons: first, as pointed out earlier, there
are generally no data or clear expertise in the matter; and,
second, putting a risk premium on the discount rate obscures
the outcome of the analysis. The influence of risk estimates
working through a premium on the discount rate is too complex
for intuitive understanding. All in all, discount-rate
adjustment is not a good way to come to grips with
probabilities and risk.
"In my experience, those who finance benefit-cost
analyses have scant patience with (paying for a study of
all for the small-probability risks involved with a
project, even if some of the uncertainties involve
catastrophic losses if they actually occur). The
unfortunate conclusion is that if allowance is to be made
for unfavourable contingencies, it will almost certainly
have to be done quickly, roughly and cheaply. Thinking
about practical ways to bring real-world project profiles
closer to the goal of representing the expected values, I
find myself gravitating more and more to a generalised
advocacy of the use of simulation techniques (Monte Carlo)
... while arguing in favour of maintaining a high
degree of economy and simplicity in their
application"
Arnold Harberger, 1997
The only practical approach to financial and economic risk
analysis is to use simulation. Simulation predicts the
possible outcomes of the benefit-cost model, given the
variables that influence those outcomes. It enables the
analyst to give more comprehensive and realistic advice to
the decision-maker. In the older deterministic method of
benefit-cost analysis, the analyst offered a single figure
for NPV, but it was always unclear what the probability of
this single outcome was. The decision-maker did not know how
much confidence to place in the figure (especially given the
rather esoteric calculations that produced it) and therefore
tended to make a subjective judgement.
Simulation shows the range of NPVs possible, given the
factors that can vary, and provides an overview of the
probabilities within that range. Decision-makers know there
is risk in every decision. There are no guarantees. Sometimes
the right decision doesn't turn out well because the
changeable factors turn unfavourable. The decision-maker
relies on the analyst to give as full and accurate a picture
of the possible risks and rewards as possible. The simulation
tools available for risk analyses are discussed in
Chapter 9.
Best practice _ analysing
uncertainty
-
Risk arises from uncertainty in the data.
The analysis of incremental effects, and
the economic analyses of an investment both
contribute to assessing risk.
-
There are three approaches to analysing
financial and economic risk; expected
values of scenarios, risk-adjusted discount
rates, and risk analysis through
simulation. Of these three, only simulation
offers a reliable methodology for assessing
overall risk.
|
9. Risk analysis
If a man will begin with certainties, he shall end in
doubts; but if he will be content to begin with doubts, he
shall end in certainties.
- Sir Francis Bacon, The Advancement of Learning,
1605
9.1 Introduction
Financial and economic risk analysis is a technique that
enables us to determine how much risk there is in accepting
or rejecting a particular project. We can also use it to
compare the likely outcomes of two or more alternative
projects. It is an important technique because it allows us
to use data that are uncertain to obtain results that are a
good picture of the likely outcomes. The technique takes into
account possible variations in the costs and benefits that we
may be aware of but that we ignore when we use single
best-guess numbers in an everything-goes-according-to-plan
analysis.
Each benefit-cost model generally has several variables that
are subject to uncertainty. To use this model for risk
analysis, you need a computer program for simulations. The
computer runs the model over and over again, each time
selecting a value for each variable. The program is not
difficult to use - you simply instruct the computer to choose
a value within a certain range and to select that value
according to the stated probabilities. For example, suppose
there are three possible values for a given variable in the
range - 3 (50 per cent probability), 4 (30 per cent
probability) and 5 (20 per cent probability) - and the
computer runs the model 1,000 times. For about 50 per
cent of the runs, the computer will choose 3 for the value of
the variable; for 30 per cent of the runs, it will
choose 4; and for 20 per cent, it will choose 5.
A major advantage of a computer simulation is that it can
consider a number of uncertain variables (risks)
simultaneously, choosing values according to the ranges and
probabilities of each. This enables you to model the likely
outcome of the benefit-cost analysis more or less
realistically. In Chapter 7, we pointed out that sensitivity
analysis is a limited technique because it can handle only
one or two variables at a time and has to hold all the others
constant. Risk analysis goes beyond this limitation by
allowing all of the variables to vary at the same time. Their
influence and interactions are then simultaneous, just as
they are in the real world.
9.2 The steps of risk analysis
Benefit-cost analysis is best approached as a risk analysis
because there is always some uncertainty in the data. The
steps in risk analysis are the following:
-
Set up the basic model that will calculate NPV. This model
is sometimes called thedeterministic
modelbecause it uses a single deterministic
value for each variable (see Chapters 2 and 6).
-
Link the uncertain variables in the model to information
about their maximum and minimum values (range) and about
the probabilities of various values within those ranges.
-
Run the model many times to obtain a large number of NPVs
(to see what all the possibilities are) - that is,
construct an investment results table (see Section 2.5).
-
Determine the frequency with which various NPVs occur in
the results, and, on this basis, predict the likely range
of the NPV and the probabilities of various NPVs within
that range.
-
Using the decision rules, interpret this information to
identify the best alternative investment or, if there is
only one, to decide whether it is likely to be a good
investment (see Section 9.7).
9.3 The mechanics of risk analysis
We cannot emphasize enough that setting up a good
deterministic model before you think about risk is extremely
important. Risk analysis is not a substitute for careful and
detailed development of tables of costs, benefits and
parameters.
Risk-analysis software builds on the underlying benefit-cost
model. Once the deterministic model is working adequately,
you use the software for two additional steps:
-
selecting sets of values for the uncertain variables,
according to specified probabilities, for each run of the
benefit-cost model;
-
using these sets of values to calculate the possible
outcomes and analyze the results.
The first step, selecting sets of values for the uncertain
variables, is based on sampling. Most risk-analysis programs
use the Monte Carlo method (simple random sampling
according to a specified probability distribution) or the
Latin Hypercube method (stratified sampling); some use
both. Generally, Latin Hypercube can accurately re-create the
specified probability distributions in fewer iterations than
Monte Carlo can and is therefore the best choice if your
software can use either one. Each run of the program
completely samples for all risk variables and recalculates
the worksheet. This is called an iteration. The
whole procedure of many iterations is a simulation. The
program is simulating the range and probabilities of the
investment's outcomes in the real world.
Different software packages have somewhat different
procedures. However, the basic operations that demand
attention are the same:
-
You must link the uncertain variables in the benefit-cost
model to their range and probability data.
-
You must specify the 'bottom line' of the
benefit-cost model (the spreadsheet cell location of the
NPV) so that the risk-analysis software can link it to the
results table.
All the other operations are automatic. That is, the
risk-analysis software calculates the NPV a large number of
times (to see what all the possibilities are) and analyzes
those results statistically and graphically.
9.4 Adjusting for the covariance of related
risk variables
You must keep in mind that some risk variables might be
correlated. For example, if NPV from a particular run of the
benefit-cost model is based on a high value for 'total
fish catch' and a high value for 'average price of
fish,' then the NPV may be outside the plausible range
in the real world. What normally happens is that a high fish
catch goes with a low fish price and vice versa. If the
outcome of your analysis is to be realistic, you must take
these correlations into account.
You do this by instructing the computer to select values for
the uncertain variables in each run that respect the
specified correlations between them. If the computer selects
a high value for total fish catch, for example, then it must
select a value for fish price in accordance with the stated
correlation. The computer selects an appropriate value for
each variable sequentially. The value it selects for fish
price is guided by not only the probable range of fish prices
and the shape of probabilities within that range, but also
the value for total fish catch already selected during this
run and the correlation between the two variables.
Failure to take covariances into account can lead to large
errors in judging risk. For example, in his pioneering study
of 'Risk Analysis in Project Appraisal,' Pouliquen
(1975) cited a project for which the risk of failure was
15 per cent when labour productivity and port capacity
were treated as independent variables but about 40 per
cent when their positive correlation was taken into account.
Software programs take different approaches to using
information about covariances among the risk variables.
Sometimes measuring the correlation coefficients is a job for
an expert (see Chatterjee 1994). It is often unnecessary,
however, to resort to comprehensive descriptions of
statistical dependence in applied project work. Pragmatic
methods of specifying approximate rank-correlation
coefficients for the key pairs of risk variables are often
adequate.
9.5 How many times does the model need to
run?
Each time the benefit-cost model runs, it generates an NPV;
eventually, there will be enough results to give a full and
accurate picture of the likely outcome of the investment. The
number of runs needed depends on how wide the ranges of the
variables in the model are, and how predictable the values
are within those ranges (how much they cluster around a
central value).
After a certain number of runs, the results table will
stabilise, and more runs will not significantly alter the
distribution of the NPVs. Some risk-analysis programs have a
built-in regulator. Runs continue until new runs alter the
result by less than 1 per cent, for example. If the
program does not have such a regulator then, after a
reasonable number of runs, you have to check that the
probability distribution of results has no obvious gaps and
has settled down to a stable range and shape. This is quite
important because it is certainly possible to get an
incorrect picture of the investment's outcomes from too
few runs.
9.6 Interpreting the results of the risk
analysis
Risk analysis produces a list of NPVs, one for each run of
the benefit-cost model. You can then analyze these NPVs
statistically and graphically to see what the probabilities
of various outcomes are. There are two types of graphs that
show the probability distribution of the NPV. The first type
is a probability-density graph, which shows the
individual probability of each NPV (see Figure 9.6.1). The
second type is a cumulative-distribution graph,
which shows how probable it is that the NPV will be lower
than a particular value (see Figure 9.6.2). Both types of
graphs are useful for communicating with the decision-maker.
As well as constructing the graphs to show the distribution
of results, most simulation software calculates some useful
numbers, including the likely range of the NPV (minimum to
maximum), the key probabilities (such as the probability that
the NPV will be greater than zero), and the expected value of
the investment. Together, these factors guide the investment
decision.
In the example shown in Figure 9.6.1 and 9.6.2, the range of
possible NPVs is from about
minus $2.4 million to plus $4 million. The most likely
outcome (the mode of the distribution) is plus $1.3 million
(most easily read from the probability-density graph,
Figure 9.6.1). The probability of a loss (NPV < 0] is
about 20 per cent (most easily read from the
cumulative-distribution curve, Figure 9.6.2), and the
expected value (the sum of all outcomes multiplied by their
probabilities) is plus $0.997 million. Note that the expected
value is the key figure for the decision maker, not the most
likely value in the sense of the single value that is most
likely to occur. These are quite different figures. For
example consider a distribution of these values
6 (probability 0.4), 7 (probability 0.3) and 8 (probability
0.3). The most likely value is '6'. The expected
value is (6 x 0.4) + (7 x 0.3) + (8 x 0.3) = 6.9.
9.7 Decision rules adapted to
uncertainty
In Chapter 5 we considered decision rules in the context
of deterministic benefit-cost models. Once we recognise
uncertainty in the data, making decisions becomes less clear
cut, although the principles are the same. The general rule
is to choose the project with the highest ENPV. At the same
time it is important to make risk transparent to the
decision-maker. For example, two investments of public funds
may have the same ENPV, but very different risk profiles.
Project A may have possible high gains and possible high
losses. Project B may have less spread in its possible
outcomes. As long as the ENPVs are the same there is no
immediate reason to choose one project over the other. On the
other hand, if one is holding a portfolio of investments,
then either project A or project B might have advantages in
terms of improving the portfolio as a whole. Portfolio theory
is beyond the scope of this guide. However, little is lost
for the Federal government by this omission. It has such a
large portfolio of investments in projects and programs that
its best strategy in choosing between project A and B is
rational risk neutrality. That is, simply, choosing the best
outcome over a large portfolio.
Rules for rational decision making are illustrated by the
following cases. In each case, both the
cumulative-distribution graph and the probability-density
graph are provided for comparison. The
cumulative-distribution graph of the NPV is more useful for
decisions involving alternative projects, whereas the
probability-density graph of the NPV is better for indicating
the mode of the outcomes of a single proposed project and for
understanding concepts related to ENPV.
Decision rule 1: If the lowest possible net
present value is greater than zero (see Figure
9.7.1) accept the project.
|
Figure 9.7.1: Probability-distribution curves for a
single project (positive net present value)
In Figure 9.7.1, the project shows a positive NPV even
in the worst case. There is no probability of a negative
return; therefore, the project is clearly acceptable.
Decision rule 2: If the highest possible
net present value is less than zero (see Figure
9.7.2) reject the project.
|
Figure 9.7.2: Probability-distribution curves for a
single project (positive net present value)
In Figure 9.7.2, the project shows a negative NPV even
in the best case. Clearly, the project should be rejected.
Decision rule 3: If the maximum net present
value is higher than zero and the minimum is
lower (see Figure 9.7.3) accept the project if
the expected net present value (the sum of
all possible outcomes, each multiplied by its
probability) is greater than zero. (Keep an eye
on the risk of loss.)
|
Figure 9.7.3: Probability distribution curves for a
single project
(containing positive and negative net present values)
In Figure 9.7.3, the curves show some probability of a
gain as well as some probability of a loss. The decision,
therefore, depends on the ENPV and the risk tolerance of the
investor. The rational decision-maker (neither risk-averse
nor risk-loving), should accept the project if the ENPV is
positive and reject it if the ENPV is negative.
Decision rule 4: If the
cumulative-probability-distribution curves for
two mutually exclusive projects do not intersect
(Figure 9.7.4, left side), choose the option
whose probability distribution is farther to the
right.
|
Figure 9.7.4: Probability distribution curves for the
NPVs two projects
In Figure 9.7.4, the probability that any specified
positive outcome will be exceeded is always higher for
project B than it is for project A. The decision
maker should, therefore, always prefer project B over
project A.
Decision rule 5: If the
cumulative-probability-distribution curves for
two mutually exclusive projects intersect (see
Figure 9.7.5), be guided by the expected net
present value. If the ENPVs are similar, consider
the risk profile of each project.
|
Figure 9.7.5: Probability distribution curves for the
NPVs of two projects, one of which has a broader range of
possible NPVs
Risk-loving decision-makers might be attracted by the
possibility of a higher return (despite the possibility of
greater loss) and therefore might choose project B in
Figure 9.7.5. Risk-averse decision-makers will be attracted
by the possibility of lower loss and will therefore be
inclined to choose project A.
9.8 Assessing overall risk
Two measures are particularly useful summaries of the overall
level of risk in a public investment: the expected-loss ratio
and the risk-exposure coefficient.
9.8.1 The
expected-loss ratio
The expected-loss ratio is the absolute
value of expected loss (all possible losses weighted by their
probabilities) as a proportion of total expected value of all
possible outcomes. Figure 9.8.1 shows all possible
outcomes, each weighted by its probability. Area A
under the curve of the NPV distribution represents this.
Similarly, area B in Figure 9.8.2 represents the
expected value of all losses. The risk can be thought of as
the relationship between B and A (that is, area
B divided by area A). If the area B is
15 units and A is 100 units, then the
expected loss ratio is 0.15. If B is a large portion
of A, the project is risky.
9.8.2 The
risk-exposure coefficient
In many cases, the expected-loss ratio may be an adequate
indicator of risk, but it does not capture all aspects of
risk. Two projects can have the same expected-loss ratio but
different levels of risk because one's outcomes are more
spread out than the other's is or because more of the
spread is in the negative-NPV area. Figures 9.8.3 and
9.8.4 show projects with the same expected-loss ratios but
very different levels of risk according to other criteria.
We need to look at two additional aspects of risk:
-
How spread out (dispersed) are the possible outcomes
(measured by standard deviation)?
-
What proportion of the possible outcomes is on the loss
side of the outcome distribution (that is, to the left of
the NPV = 0)?
When we consider these two factors along with the
expected-loss ratio, we obtain a risk-exposure coefficient
(REC), a more complete measure of risk:
REC = LE
(SD)(DL/D) [6]
Where LE is the expected loss ratio; SD is
standard deviation of the outcome distribution;
DL is the distance on the NPV axis from the
minimum value to zero; D is the distance on the NPV
axis from the minimum to the maximum value. You may find the
risk-exposure coefficient too mathematically complex to be
intuitively appealing if you are dealing with a relatively
simple 'go' or 'no go' decision on a
single project. In that case, you might find the
expected-loss ratio more useful. If you are comparing two or
more alternatives and if those alternatives involve the
investment of large resources, however, it is worth going the
extra step to calculate the risk-exposure coefficient so that
you can rank the projects according to risk.
9.9 The advantages and limitations of risk
analysis
Some advantages of risk analysis are the following:
-
It can rescue a deterministic benefit-cost analysis that
has run into difficulties because ofunresolved
uncertainties in important variables.
-
It can helpbridge the communications gap
between the analyst and the decision-maker. A range of
possible outcomes, with probabilities attached, is
inherently more plausible to a decision-maker than a
single deterministic NPV. Risk analysis provides more and
better information to guide the decision.
-
It identifies where action to decrease risk might
have the most effect.
-
It aids the reformulation of projects to better suit the
preferences of the investor,
includingpreferences for risk.
-
It induces careful thought about the risk variables and
uses information that is available on ranges and
probabilities toenrich the benefit-cost
data. It facilitates the thorough use of experts.
The limitations of the risk analysis include the following:
-
The problem of correlated variables, if not
properly contained, can result in misleading conclusions.
-
The use of ranges and probabilities in the input variables
makes theuncertainty
visible,thereby making some managers
uncomfortable.
-
If the deterministic benefit-cost model is not sound, a
risk analysis might obscure this by adding a layer of
probabilistic calculations, thereby creating a spurious
impression of accuracy.
Best practice - financial and economic
risk analysis
There are at least three meanings of most
likely outcome: 'the deterministic
value of the NPV' (the outcome when one
assumes best-guess figures for each input);
'the mode of the probability distribution
of NPVs;' and 'the expected
value' (the sum of possible outcomes,
each multiplied by its probability). The last
is the best guide to the choice of investment
option.
-
Simulation techniques provide a realistic
picture of overall risk in the project. The
expected-loss ratio and the risk-exposure
coefficient are useful measures of overall
risk.
-
Commercial software programs make risk
analysis a relatively simple task, once the
basic (deterministic) benefit-cost model
has been constructed and information about
variable ranges and probabilities has been
collected.
-
For situations where there is significant
uncertainty, the following benefit-cost
decision rules apply:
-
If the lowest possible NPV is greater than
zero, accept the project.
-
If the highest possible NPV is less than
zero, reject the project.
-
If the maximum NPV is higher than zero and
the minimum is lower, calculate the ENPV.
If the ENPV is greater than zero, accept
the project. (Keep an eye on the risk of
loss.)
-
If the cumulative-probability-distribution
curves for two mutually exclusive
projects do not intersect, choose the
option whose probability distribution is
farther to the right.
-
If the cumulative-probability-distribution
curves for two mutually exclusive projects
intersect, be guided by the ENPV. If the
ENPVs are similar, consider the risk
profile of each alternative.
|
10. Probability data
High arbiter chance governs all.
- John Milton, Paradise Lost,
Book Two, 1667
In Chapter 4 we discussed some difficult-to-measure
inputs to benefit-cost analysis. In this chapter, we extend
that discussion and consider some general aspects of
collecting data. Keep in mind that this guide provides the
benefit-cost framework, but it can provide only a
glimpse of what are needed in particular cases to measure the
costs and benefits.
10.1 Types of risk variables
Three types of risk variables are used in benefit-cost
analysis:
-
-
full-horizon variables - Some variables are the
same for each period of the analysis: once a value is
selected, it is used throughout the benefit-cost model.
For each run of the model, the risk-analysis computer
program will select a different value within the plausible
range, but only one value is used in each run. The social
discount rate is an example. We know that it is stable
over time.
-
-
single period variables - Some variables
have values that change over time within a known range,
and the true value in each period is independent of the
value in any other period. In this case, it is simplest to
have a separate variable for each period of the analysis.
An example is rainfall. We know that the annual rainfall
in a particular location varies between 73 and 116 cm
and that the probabilities of any particular value in this
range are distributed roughly according to a normal curve.
We also know that precipitation in any year is essentially
independent of the precipitation in the previous year. In
a benefit-cost model that has a 25-year investment
horizon, therefore, we would have 25 values for the
rainfall variable in the parameters table.
-
-
path variables - Some variables change over time in
a regular pattern. The value in one period is related in a
systematic way to the value in the previous period. For
example, the inflation rate in one year is likely to be
within a certain range (up or down) from the rate in the
previous year, and a trend, once established, tends to
continue for some time. We know the starting rate of
inflation - the rate in the current year. We would have 25
inflation rates in our benefit-cost model (as with the
rainfall variable discussed above), but we would also have
to program the model so that each time it runs it selects
a different path of inflation rates for the investment
period. The path selected must be in accordance with the
rules of behaviour for this variable. This is not
difficult programming, but it is beyond the scope of this
guide to describe it in detail.
10.2 Using historical data
To do a risk analysis, you need to know the range of values
each variable can take (minimum to maximum) and the
probability distribution of values in that range. For
example, if the price of a barrel of oil is between $12 and
$32 and the probability of any value in that range is
described by a uniform probability distribution (all values
are equally probable), then the computer has all the
information it needs to sample values of the price of oil to
use in iterations of the benefit-cost model.
If historical data are available, you might use the maximum
and minimum values that occurred in the past as an
appropriate range for the values of the variable. Identifying
the probability distribution within that range is more
difficult. However, software can facilitate the task. Suppose
you have monthly oil-price data for the past 10 years.
The first step in identifying the probability distribution
for oil prices is to group the raw data. How frequently do
various oil prices occur? The raw data are grouped in a
frequency histogram.
In some cases, it might be desirable to filter the raw data
before exploring the frequency patterns. Software can filter
out any data that fall outside a stated absolute or relative
range - outside two standard deviations from the mean of the
data, for example. This is useful when there are data
outliers because of special circumstances that are unlikely
to be repeated. We will not be surprised if the curve that
best fits the data (see Figure 10.2.4) is a symmetrical one
with a strong central mode - the normal, poisson or
triangular distribution, for example.
You can use your software to try all of the standard
distributions in its repertoire and to list them in order of
goodness of fit, using the chi-square test to rank the
various curves by order of fit. You can then select the best
curve to use for oil prices in your benefit-cost analysis.
This selection is aided by a difference graph
(Figure 10.2.2), which shows the differences between the
expected oil price (based on the probability-distribution
curve) and the actual historical price. The smaller these
differences are, the better the curve fits the past data.
10.3 Expert judgement
If we do not have enough historical data to underpin an
estimate of the range and probabilities of a particular
variable, then we have to rely on expert (somewhat
subjective) judgement. For example, the 'take-up'
(participation) rate for a new program might be vital to its
outcome, but there might be no direct experience to draw upon
to forecast the likely rate. At one stage, the Government of
Canada offered to match, dollar for dollar, all research
funds raised by universities from the private sector. A
benefit-cost analysis of this proposed program needed an
estimate of the contributions likely to be gathered by the
universities. There were no specific data available, but
there were experts in the general field - people with a lot
of experience in fundraising in general and in
university/private-sector fundraising in particular.
A committee of these experts was asked to make informed
estimates on the values of the variables to be used in the
benefit-cost analysis. The committee used the Delphi
method. The essence of this technique is that each member
of the committee makes initial estimates based on the
information provided. These initial estimates are then given
to all the members and discussed, after which each member
makes a second estimate. The discussion and re-estimation
continue until the estimates converge.
10.4 Common probability distributions
Various levels of sophistication are possible in specifying
the probability distributions for the input variables to the
benefit-cost model. Most often, a fairly simple,
straightforward approach is adequate. This means selecting
probability-distribution shape in one of two ways:
-
specifying a standard statistical shape, such as a flat,
normal, triangular, or Poisson distribution; or
-
specifying a step distribution, which notes the
probabilities for each segment of the variable's
range.
-
If you have historical data for the variable but are
unsure which probability distribution they fit, you can
use software that will analyze the data and show the best
fit.
10.5 Risk preferences
In our discussion of expected values (see Section 9.7),
we have assumed that the decision-maker is wholly rational
and neither risk-loving nor risk-averse. For example, a 50/50
chance of gaining $10 will be valued at $5. This is a
reasonable assumption for a decision-maker that feels no
wealth constraint - the investment in question is small in
comparison with his or her wealth.
Many decision-makers in the Government of Canada, however, do
feel a wealth constraint. They will view a 50/50 chance of
losing or gaining $1 billion with a lot more trepidation
than a 50/50 chance of losing or gaining $5 million,
although the NPV of each is the same. There are techniques to
ascertain the utility function of the
decision-makers that are risk-averse or risk-loving (rather
than risk-neutral). A utility function simply gives
mathematical form to the strength of the
decision-maker's preferences for various possible
outcomes and can be used to modify the NPV decision rules to
more truly reflect these preferences.
In most cases, governments are risk-neutral. That is, they
are rational decision-makers. A government has a large
portfolio of projects and programs and therefore can act
fully rationally with confidence that, on average, things
will turn out well if the decision rules are strictly
applied. In the case of a single large or politically
sensitive project, however, the question of a wealth
constraint might arise.
10.6 Common project risks
A variety of risks can affect an investment. Some common
sources of risk are the following:
-
-
Investment lumpiness - Can the waters
be tested gradually, or is it all or nothing?
-
-
Timing - What if the project is delayed? What if it
takes longer than expected for the project to reach full
production? Is there a best time to start the project?
-
-
Salvageability - How much of the investment can be
recouped if things go wrong?
-
-
Uncertain incremental effect - What will the
outputs of the project be?
-
-
Uncertain parameter values - What discount rate and
inflation rates are appropriate?
-
-
Volatile preferences - Are the target
beneficiary's needs or preferences unstable?
An investment decision is highly risky if a big investment
has to be made without a chance to test the waters, delay is
highly damaging, little can be salvaged if the project goes
wrong, the likely output is uncertain, some of the key
measurement parameters are uncertain, and the
beneficiary's preferences are unstable.
Best practice - handling probability
data
-
Base the probability estimates on
historical data where possible and on
structured subjective estimates by experts
where necessary.
-
Treat the three types of risk variables
(full-horizon, single period, path)
appropriately in the benefit-cost model.
-
Keep it simple. Don't let the
technique overwhelm the data.
|
11. Comparing options of different
types against different criteria
Some of the arguments in favour of confining benefit-cost
analysis to efficiency considerations seem to rest on a
misconception of the analyst's role in the
policy-making process; such arguments appear to be based
on the assumption that the economist is not competent to
assign prices to distributional effects. One can agree
entirely that the analyst should not attach his own
valuation to such effects. It does not follow however that
equity issues should be ignored in benefit-cost analysis
or that the decision-maker cannot value distribution
effects if given the information on which to base a
judgement. Indeed, the analyst who avoids measuring or
describing non-price effects, which may have an important
influence on a decision, seems to be ducking their
responsibilities. Moreover, the measurement of
distributional effects by the analyst is not an easy task
and may require as much work as measurement of efficiency
effects.
- Treasury Board, Benefit-Cost Analysis Guide, 1976
11.1 Issues of fairness
Money is like muck, not good except it be spread.
- Sir Francis Bacon, The Essayes or Counsels, Civill or
Morall, 1625
Questions of fairness are among the most difficult issues in
benefit-cost analysis. It is essentially a problem of
multiple criteria and not a trivial one. Benefit-cost
analysis generally assumes that everyone in the reference
group takes the same point of view. This is fine when there
is a single investor, but is shaky when the reference group
is a whole economy.
The problem is that the Government of Canada has fairness
objectives as well as efficiency objectives and they often
clash. It wants to maximize Canadians' wealth and
incomes, but it also wants the distribution of the net
benefits of government projects and programs to be equitable.
There is often no way to maximize both objectives at the same
time.
Another factor is the possibility of a dead-weight loss in
redistributing income or wealth. This loss arises partly from
the administrative costs of collecting taxes and running
programs and partly from disincentives caused by taxes that
dampen economic activity. If we add to this taxation-induced
loss the project-specific inefficiency losses that may arise
when projects are justified by their distributional effects,
the transfer of income might be expensive. Taking $100 away
from person A so that we can improve person B's welfare
by $25 is neither sensible nor equitable.
Nevertheless, most Canadians do not believe that a dollar of
benefit to the rich should count the same as a dollar of
benefit to the poor. In some sense, they value a dollar of
benefit to the poor more. Taking this value into account in
benefit-cost analysis, however, raises a host of
difficulties.
For one thing, having a low income is not the same as being
needy. For example, many students, retired people with
substantial capital assets, and rural residents with low
living expenses have relatively low incomes, but they may not
be needy in the sense that justifies special transfers from
the government. A straightforward income-per-household
criterion is thus likely to be an unreliable guide to the
need for social transfers. Governments have recognized this
and have responded in various ways, such as giving everyone
the right to certain basic services (free primary and
secondary education, for example) and establishing a series
of filters through which households must pass to achieve
eligibility (access to public housing, for example). None of
these responses, however, provides a clear and simple way to
adjust benefit-cost calculations to take fairness into
account.
11.1.1 Equity approach 1: Ignore
distributional issues
One school of thought is that income redistribution is best
accomplished through explicit transfers in cash and in kind,
not through skewed capital investments that artificially
favours particular groups of people. The idea is to make
efficient investments to create the largest pie, which can
then be divided as society wishes through instruments that do
not involve high transaction costs or economic
inefficiencies. In Canada, with its tradition of strong and
stable government, there is a lot of force to this argument.
In some other countries, though, capital investments may be
one of the few plausible instruments for income
redistribution.
In Canada, if a project or program is recommended on equity
grounds, then its equity cost should be visible to
decision-makers and to the public. The equity cost is the
difference between the NPV of this project or program and the
NPV of its most efficient alternative. Making this cost
visible is the best safeguard against unreasonable demands by
special-interest groups.
11.1.2 Equity approach 2: Use distributional
weights
In the 1960s and 1970s, the use of distributional
weights was in vogue among many benefit-cost analysts.
The idea was quite simple. Both costs and benefits to
low-income groups would be given extra weight: for example,
$1 in benefits to a low-income group might be counted as $2.
The use of such weights foundered on two shoals: the weights
were arbitrary, and they made the analysis opaque.
Decision-makers could not trust the analyses because they did
not know how its outcome had been affected by the inclusion
of subjective weights to change the values of costs and
benefits.
There were some attempts to infer weights from existing and
past policy decisions, especially from income-tax scales.
Income-tax scales, however, are set with an eye on efficiency
and incentive effects, as well as equity and distributional
concerns. Separating one factor from another proved
impossible.
Nevertheless, some serious attempts were made to implement
distributional weights. For example, the World Bank used them
in its project appraisals for two decades, abandoning the
approach as unworkable only as recently as 1995. The
bank's analysts had often assumed that the marginal
utility of income declines exponentially as income increases.
This implies a very rapid shift in the weight accorded to a
marginal dollar of benefit as one moves up the income or
wealth scale.
One problem with this approach is that it implies that
benefits should be shifted from those at the top of the
income scale to those, say, three quarters of the way to the
top, as well as shifted from those in the bottom half of the
income range to those at the very bottom. This is not
generally what people have in mind when they think about
redistribution.
Most decision makers are more comfortable with a weighting
scheme that gives a premium to benefits to people in a narrow
range at the bottom of the income scale (for example, below a
poverty line). For example, weights might start at 2.0 at
zero income and move fairly rapidly to 1.0 at the 25th
percentile, perhaps adjusted by family size.
11.1.3 Equity approach 3: Focus on basic
needs
Concentrating redistribution on the poorest quintile
(20 per cent) of income earners is an attractive option.
Generally, however, the use of major capital investments that
might help this group is impractical because the poorest of
the poor tend to have few skills or to live in remote areas,
where capital investment is inefficient. Siting projects
where they otherwise would not go, local hiring quotas, and
similar mechanisms are seldom effective.
Providing for the basic needs of such people is probably best
done directly and in kind (free education and health care,
for example), rather than indirectly through the side effects
of capital investments by the Government of Canada. For a
major project or program, however, it is possible to
construct an index of family welfare in a region or community
that would operate something like a system of weights. Such
an index would have component indices of, say, access to
education, access to medical care and sanitary facilities as
defined by the UN Panel on Basic Needs, level of nutrition,
and quality of housing. A level of 100 on the index might
represent the national average. Constructing an index is not
technically difficult, but is nevertheless a job for an
expert, not for the benefit-cost generalist.
Even when an index is available, one still faces the same
question as with other kinds of weights - how much
economic inefficiency is it worth to move the distribution
index one point? Society's willingness to pay is
unknown. The approach is probably best restricted to projects
whose primary purpose is to alleviate poverty or to address
one or more basic needs (education, health, nutrition, etc.).
Innovation in methods to handle distributional issues is a
very high priority for benefit-cost analysis. An interesting
example that is not applicable to Canada in a simple way, but
shows the level of innovation possible, is the map of extreme
poverty developed by Chile in the 1970s. The Chilean approach
is to monitor neighbourhoods, rather than individual
families. The index is used to guide social expenditures
toward the very poor and to try to overcome traditional
biases that result in middle-income earners being the
principal beneficiaries of government programs.
11.1.4 Equity approach 4: Focus on visibility
and transparency
The best way to handle distributional issues in benefit-cost
analysis is to let the decision-makers decide. Distribution
is primarily a political question. If the benefit-cost
analyst compares the best alternatives, using good technique,
then decision-makers will be able to weigh improvements in
income distribution against any loss in economic efficiency.
To a large extent, this is simply a matter of showing what
the costs and benefits are from several points of view. The
analyst should set out a distributional chart or matrix,
showing gains or losses on one axis and the identification of
relevant groups on the other. Such a display should be
included in all benefit-cost analyses, unless the
distributional effects are few (even in this case, the text
of the benefit-cost report should contain a section on
distributional effects).
A potential difficulty, however, is that the matrix can
become complicated if a large number of groups are involved.
Some loss of detail is often acceptable, though, to keep the
display understandable to the decision-maker.
11.2 Multiple objectives
Things should be made as simple as possible, but not any
simpler.
- Albert Einstein, cited in Readers Digest, Oct.
1977
The benefit-cost analyst tries to express the value of all
alternatives in terms of a single criterion with a single
weight - that is, in terms of economic net benefit. This
makes for a simple investment decision. In reducing
everything possible to economic net benefit, however, the
analyst may have ignored other important factors, either
because they cannot be quantified or because they cannot be
valued in dollars. In some cases, these factors are so
different from the economic criterion as to force a choice
between apples and oranges.
The choice between investment options is simple when they are
the same types and their context is also identical. In the
real world of decision making, however, nothing is quite that
simple - a budget most likely has to be allocated among
different types of investments; the context of each
investment varies enough for the criteria weights to vary as
well; scores on various criteria cannot be expressed in
dollars or any single unit of measure (numeraire); and so on.
Making comparisons becomes very difficult when the investment
alternatives are really apples and oranges. In such a case,
three factors can vary:
-
the criteria applied to each project;
-
the weights of the criteria; and
-
the numeraires (units of value used in measuring costs and
benefits)
A government invests in a variety of programs and projects
within a single budget. For example, a department might have
to decide whether to build a new road or a new office
building. These are not just alternative investments, but
alternative investments in different categories. Often, the
decision is made in two stages: first, deciding how much of
the budget to invest in roads and in office buildings; and,
second, deciding on what roads to spend the roads portion of
the budget and on what buildings to spend the buildings
portion of the budget. Often, the first decision (how much to
invest in roads) is made subjectively or politically; and the
second (whether to invest in a particular road) is made on
the basis of benefit-cost analysis.
11.2.1 Attribute scores and trade-off
weights
When a decision involves investment alternatives in different
categories, the relevant criteria and their weights vary from
one alternative to another. Sometimes, though, the variations
are not important enough to completely rule out direct
comparisons. For example, suppose you had to prescribe a set
of criteria and criteria weights for farmers to use when
purchasing animals. Some criteria would be specifically
applicable to one type of animal: a good dog is
friendly; a good pig increases its weight
quickly; a good horse is swift and
sure-footed. Other criteria would be generally
applicable, such as age, health and likely
profit. As well, the importance of a particular criterion
might vary, depending on the context. For instance, if the
farmer has small children, the importance of friendliness in
the dog might be greater.
In spending his or her budget, the farmer does not want to
end up with a friendly pig, a sure-footed dog and a fat
horse. Neither does the farmer want to end up with five dogs
and no horses or pigs. If the farmer applies a fixed set of
criteria to all animals, then this might be the result.
In summary, if you are faced with multiple objectives, you
should approach the decision in two steps: assign resources
for achieving each objective; then select investments to
maximize the achievement of each objective, given its
resources. If this is not possible and all investments must
be considered and ranked together, then the best
(approximately correct) procedure is to fix the criteria and
the trade-off weights; standardize the scores on each
criterion; and then use the scores and weights to rank the
options.
If you are judging alternative investments on the basis of
multiple criteria, some of which cannot be measured in
dollars, then the best way to score the alternatives on each
criterion is to define the range of achievement, using
whatever unit of measurement makes sense, and then to
standardize the scores on that criterion by expressing them
as a percentage of the possible achievement (see Table
11.2.1).
Table 11.2.1: An example of standardized scores of
variable criteria with weights
|
Standard Score*
|
Weight |
|
Weighted standard score
|
Alternative 1
|
|
|
|
Criterion A
|
0.3
|
0.7
|
0.3 × 0.7 = 0.21
|
Criterion B
|
0.5
|
0.3
|
0.5 × 0.3 = 0.15
|
|
|
1.0
|
0.36
|
Alternative 2
|
|
|
|
Criterion A
|
0.4
|
0.7
|
0.4 × 0.7 = 0.28
|
Criterion B
|
0.7
|
0.2
|
0.7 × 0.2 = 0.14
|
Criterion C
|
0.9
|
0.1
|
0.9 × 0.1 = 0.09
|
|
|
1.0
|
0.51
|
* Each standard score must be between 0 and 1.0. |Each
weight must be between 0 and 1.0; the weights for each
alternative must total 1.0.
Suppose alternative projects to provide office accommodation
are to be judged according to four criteria: NPV (dollars);
location (average commuting time for staff); availability
(earliest occupancy date); and healthiness (air exchange rate
for the building).
Let's look a one criterion, location, measured as the
average commuting time for staff. Suppose that the lowest
possible average commuting time is 10 minutes and that
the highest average commuting time that would be acceptable
under any circumstances is 45 minutes. Also suppose that
the staff preferences are a linear function - that is, the
benefit from decreasing their average commuting time by one
minute is the same whether the decrease is from four minutes
to three minutes or from 17 minutes to 16, etc. The
maximum possible location benefit would result from
changing an average commuting time of 45 minutes to an
average commuting time of 10 minutes, a gain of
35 minutes (score of 100). You can standardize an
average commuting time of, say, 20 minutes by expressing
it as a percentage of the maximum possible location benefit:
A commuting time of 20 minutes represents a gain of
25 minutes and would receive a standardized score of
(25/35) × 100 = 0.714.
To complete the example, suppose we decide that the location
is worth a weight of $6,000 (or 6,000 points, if a
dollar weight is inappropriate). When the average commuting
time changes from 45 minutes to 10 minutes, the maximum
possible gain, the benefit is 6,000 units. Therefore the
location benefit of our example project is 0.714 ×
6,000 = 4,284. This is a weighted standard score. Once we
have the weighted standard scores on each criterion, we can
add them to obtain a total standard score for the project,
and we can compare projects on this basis.
11.2.2 Limits to the weight of non-economic
factors
If the primary purpose of a project or program is economic
benefit, then non-economic factors should not receive more
than a small percentage, say 15 per cent, of the total
weight.
Best practice _ equity
analysis
-
Distributional issues are important to the
Government of Canada and should be
considered in-depth in each benefit-cost
analysis. Even a simple analysis showing
who benefits and who pays can often be
helpful to decision-makers.
-
There are no uncontentious ways to combine
efficiency and equity objectives in the
same set of figures, although attempts have
been made to use various types of weights
to this end.
-
Distributional issues should be covered in
every benefit-cost analysis but kept
separate from the economic-efficiency
analysis. If a recommendation to approve a
particular alternative hinges on equity
objectives, then the net cost of choosing
the equity-based recommendation must be
made visible to the decision-makers.
|
Best practice - Ranking by multiple
objectives
-
Sometimes, important factors cannot be
expressed in dollars no matter how
ingenious and skilful the analyst is. In
this case the decision-maker needs other
techniques to compare alternatives against
multiple criteria.
-
If not all the criteria apply to all the
alternatives, or if the criteria have
different importance (weight) in different
cases, then the analyst has a particularly
difficult task. A two-stage approach
(allocating budget to categories and then,
within categories, to cases)
is generally the best way to handle
the multi-criteria problem. In cases where
this is not possible, the weighted-score
approach, using trade-off weights and
standardized scores against the various
criteria, is best. If the primary purpose
of a project or program is economic, then
non-economic factors should not receive
more than a small percentage, say
15 per cent, of the total weight.
|
-
Key best practices
A good benefit-cost analysis meets the following criteria:
-
the objectives and priorities are clear;
-
the best alternative ways of achieving the objectives are
identified for analysis;
-
the alternatives are defined in a way that enables fair
comparison;
-
the 'point of view' of the analysis is stated;
-
assumptions and calculations are visible to the reader at
every stage of analysis;
-
benefits and costs are estimated in detail for every time
period, without short cuts;
-
the technical analysis is well done (in regard to discount
rates, inflation adjustments, choice of decision rule,
etc);
-
uncertainty and risk are carefully considered;
-
distribution effects are clearly set out (who pays, who
benefits?); and
-
the recommendation is well reasoned and gives fair
consideration to all alternatives.
Appendix A: Glossary
Accounting price. Reflects the economic
value of inputs and outputs, rather than a
financial or market value. Synonymous with shadow
price and social price.
Adjustment factor. The percentage by which the
financial price of an input or output
must be raised or lowered to reflect its true economic
value. Synonymous with conversion factor.
Appraisal. A before the fact (ex ante)
evaluation.
Asset. Anything of value, but especially
physical assets, such as machinery or farmland, or monetary
assets (which can be used to finance the purchase of physical
assets).
Base case. The optimised without-project
scenario. Not the same as do nothing or
status quo.
Benefit-cost analysis. A procedure that
evaluates the desirability of a program or project by
weighing the benefits against the costs.
Benefit-cost ratio. The ratio of
benefits to costs. It should be calculated
using the present values of each, discounted at an
appropriate accounting rate of interest. The ratio should be
at least 1.0 for the project to be acceptable. Inconsistent
benefit-cost ratios may arise because they are dependent on
arbitrary accounting conventions.
Budget-Year Dollars. Face value dollars of
varying purchasing power (depending on when a transaction is
undertaken). Synonymous with nominal dollars
and current dollars.
Capital. Resources that will yield benefits
gradually over time. Related to investment (in contrast to
consumption). May be divided into physical and financial;
fixed and working; etc. Sometimes defined more broadly to
include human capital (for example, in regard to an education
that yields benefits over time).
Cash flow. The funds generated or used by the
project. Reflects the costs and benefits over time
from a stated point of view.
Cash-flow statement. A financial statement that
records the cash flow of a project or financial
entity. Synonymous with sources-and-uses-of-funds
statement.
Certainty equivalent. See expected
value.
Constant dollars. Dollars of constant
purchasing power. The units of purchasing power are fixed by
stating the base year, for example, 100 in 1995 constant
dollars. Constant purchasing-power units. A better term is
real dollars.
Constant price. A price that has been deflated
to real terms by an appropriate price index.
Consumer surplus. The value consumers receive
over and above what they actually have to pay. Varies from
one person to another and is measured by willingness to pay.
Contingent valuation. A method of inferring the
value of benefits and costs in the absence of a
market. What people would be willing to pay to gain a benefit
(or willing to accept in recompense for a loss) if a market
existed for the good.
Cost. An expense related to purchase of
inputs, including capital equipment, buildings,
materials, labour and public utilities. Costs such as
environmental damage or injuries to health are sometimes
referred to as negative externalities.
Cost-effectiveness analysis. A type of analysis
commonly used to compare alternative projects or project
designs when the value of outputs (benefits) cannot be
measured adequately in dollars. If it can be assumed that the
benefits are the same for all alternatives being considered,
then the task is to minimize the cost of obtaining them
through cost-effectiveness analysis. Synonymous with
least-cost analysis.
Crossover point. The value that equalizes the
net present values of benefits and costs.
Decision rule. A criterion for accepting or
rejecting a project or for ranking investments in order of
desirability.
Delphi method. A technique for obtaining
subjective judgmental values through iterative estimations by
a group of experts.
Demand. Need or desire for a good or service.
The need varies with person, price and circumstance, so
demand is usually expressed in terms of the quantities
demanded at various prices. The demand curve usually slopes
downward, indicating that people will demand more at lower
prices than at higher prices. Opposite of supply.
Depreciation. Not a term used in
benefit-cost analysis. In other financial
frameworks, depreciation is the allocation of the cost
of an asset over time. This is necessary for a working
estimate of production costs, but because rates of
depreciation are usually determined primarily by legal and
accounting requirements, the amount of depreciation often has
little relationship to the actual rate of use or cost of
replacement.
Deterministic model. A
benefit-cost model that uses single fixed
values for each input (rather than a range of values
and probabilities).
Distributional gain or loss. A change in the
distribution of wealth or income.
Discounted cash flow. The costs and
benefits (cash flows) discounted to present
values to give a common basis for comparison.
Discounting. The process of adjusting future
values to an equivalent present value at a stated point in
time by a discount rate.
Discount rate. The interest rate at which
future values are discounted to the present and vice versa.
Either the opportunity cost of capital (applied to
investment dollars) or the time preference for consumption
(applied to consumption dollars).
Distortion. A difference between market
prices and true values (economic prices).
Distributional effect. A change in the income
or wealth of the people from whose point of view the
benefit-cost analysis is done.
Economic. Having to do with the national
economy, especially as in economic value. The value of
a good or service to the country as a whole, as opposed to
its private or commercial value.
Economic price. Price that reflects the
relative value that should be assigned to inputs and
outputs if the economy is to produce the maximum value
of physical output efficiently. There is no consideration of
income distribution or other non-efficiency goals in such a
price. Synonymous with efficiency price and true
price.
Economic rate of return. An internal rate of
return based on economic prices.
Expected net present value (ENPV). The sum of
all of the possible net present values multiplied by
their probabilities.
Expected value. The sum of all possible
outcomes, each multiplied by its probability.
For example, if there are two possible outcomes, $100 and
$200, and their respective probabilities are 0.3 and 0.7,
then the expected value is ($100 ´ 0.3) + ($200 ´ 0.7) = $170. Synonymous with
certainty equivalent.
Externality. A benefit or cost
falling on third parties who normally cannot pay or be
compensated for it through a market mechanism. An external
benefit is a positive externality; an external cost is a
negative externality. Externalities are not reflected in the
financial accounts. For example, a project may harm
the environment, train workers, or make it easier for other
firms to get started in a related line of business, but these
effects do not show up in the project's financial
statements. For economic analysis, however, it is
necessary to take such externalities into account and place a
value on them.
Financial. Using market prices and
taking a commercial point of view.
Financial rate of return. The financial
profitability of a project. Usually refers to an annual
return on net fixed assets or on investment but may
refer to the internal rate of return, which is
determined through discounted cash-flow analysis.
First-year return. The net cash flow
during one year of a project, including the one-year cost of
capital invested. A measure that may indicate the best
time to begin a project.
Fixed costs. The costs such as
management salaries, interest and loan repayments that must
be met, at least in the short term, regardless of production
volume.
Hurdle rate. The rate of return the
project must achieve to be acceptable.
Incremental. Additional or marginal.
Index number. Any index calculated to compare
an amount in one period with that in another, for example,
growth of production, population. See price index.
Inflation. A general increase in market
price levels (a fall in the general purchasing power of
the currency unit).
Input. That which is consumed by the project
(as opposed to the project's output). Usually
refers to the physical inputs used by the project, including
materials, capital, labour and public utilities.
Inputs like environmental quality, foreign exchange and
workers' health are usually termed externalities.
Internal rate of return (IRR). The yield or
profitability of a project based on discounted
cash-flow analysis. The IRR is the discount rate
that, when applied to the stream of benefits and
costs reflected in the cash flow of a project,
produces a net present value of zero.
Investment horizon. The period over which
benefits and costs will be compared.
Marginal. Last, in the sense of the last
additional unit. For example, the marginal benefit is the
value of one more (or one less) unit of output.
Synonymous with incremental.
Marginal productivity of capital. The
productivity of the last unit of investment that would be
undertaken if all investment alternatives were ranked in
descending order according to their economic
profitability and the available funds were distributed until
exhausted. More loosely, the profitability of the marginal
project (the project that should receive the last dollar of
investment).
Market price. (a) The price of a good in the
domestic market (see financial); as opposed to the
economic price, efficiency price, shadow
price or social price; (b) the cost of a good,
including indirect taxes and subsidies.
Market risk. The risk to which all
enterprises are exposed through cycles in the economy. Unlike
some other risks, market risk cannot be diversified away.
Model. A representation or simulation of
a system or process showing how parameters, benefits and
costs interact to produce a bottom-line result by
which the project can be judged.
Multiplier. The ratio of a change in the total
community income to the initial change in expenditure that
brought it about.
Mutually exclusive. Alternatives that cannot be
undertaken simultaneously: if one alternative is carried out,
the other cannot be. The alternatives may be mutually
exclusive because they represent alternative times of
beginning the same project, because funds are limited, or
because if one is carried out the other will not be required
(for example, a choice between a thermal and a hydro power
station).
National parameter. A shadow price (or
accounting price) that is the same for all projects in
the country. In most cases, the shadow price for foreign
exchange and the premium on savings over consumption are
national parameters.
Net present value (NPV). The net value of an
investment when all costs and benefits expressed in
standard units of value (numeraires) are summed up.
Synonymous with net present worth.
Nominal dollars, nominal prices. Prices
prevailing in a particular year. Synonymous with
budget-year dollars.
Non-tradable. Referring to a good that cannot
be exported (for example, building foundations, haircuts).
Non-traded. Referring to an inherently
non-tradable good or to tradable good that for
economic or policy reasons is neither imported nor
exported.
Numeraire. The standard unit of value that
makes it possible to add and subtract costs and
benefits that are otherwise expressed in unlike units. For
example, apples and oranges, as everyone knows, should not be
added up. But if they are expressed in terms of a common
numeraire, such as pieces of fruit, kilograms or dollars, it
is then possible to say that we have 20 pieces, three
kilograms, or $4 worth of fruit. Common numeraires in
benefit-cost analysis are dollars of
investment, dollars of consumption, and dollars of foreign
exchange.
Operational and maintenance costs. The
recurring costs for operating and maintaining the
value of physical assets.
Opportunity cost. The value of something
foregone. For example, the direct opportunity cost of a
person-day of labour is what the person would otherwise have
produced had the person not been taken away from his or her
best alternative occupation to be employed in the project.
Opportunity cost of capital. The best
alternative return foregone elsewhere by committing
assets to the project.
Option. The opportunity to invest in a
particular program, project or course of action.
Output. That which is produced. Usually refers
to the physical product of the project. Other effects of the
project, such as housing for workers, employment, training of
labour, and foreign-exchange savings, are usually called
externalities.
Payback period. The time required for the
cumulative present value of benefits to become equal to the
cumulative present value of costs.
Present value. A future value discounted to the
present by the appropriate discount rate.
Price index. The market value of a fixed basket
of goods and services at one date divided by the market value
of the same basket at some base date. Subtracting 1.0 from
the index gives the decimal equivalent of the percentage
increase in prices between the two periods. Useful in
measuring rates of inflation.
Probability. The quantified likelihood of
something occurring.
Probability distribution. A graphic
representation of the likelihood of something occurring.
Producer surplus. The value a producer receives
over and above the minimum payment needed to continue to
supply the good.
Rate of return. The profitability of a project.
A shorthand term usually applied in economic analysis
to the internal economic rate of return and in
financial analysis to the annual return on net fixed
assets or to the internal financial rate of
return (it is important to specify which).
Real dollars, real prices. Standard units of
purchasing power, defined by stating a base year.
Residual value. The market value of an
asset at the investment horizon.
Risk. The degree to which outcomes are
uncertain. The extent of possible variation in the outcome.
Risk analysis. A benefit-cost analysis
that recognizes the simultaneous variation of the values of
several inputs, according to specified ranges and
probabilities, and analyzes the resulting variability
in the bottom line.
Risk variable. A variable in risk
analysis, chosen because of its likely importance to the
outcome of the analysis.
Salvage value. The residual value of an
asset at the investment horizon.
Scale. The size of a project.
Scenario. An outline or portrait of a possible
future; usually portrays unfolding events, rather than being
static in time.
Sensitivity analysis. An examination of the
effect that a change in a single variable (parameter,
cost or benefit) has on the outcome of a project.
Shadow price. The true or economic value
of a good (as opposed to the market price,
which might be distorted). Synonymous with accounting
price and social price.
Simulation. A mathematical model that sets out
a system of interacting parameters, costs and benefits
to predict the likely outcome of an investment.
Social net present value. The net present
value of a project, calculated using true or economic
values (social prices or shadow prices).
Social price. A price that reflects the true
value to the country of inputs and outputs of
the project. Synonymous with accounting price and
shadow price.
Standard deviation. A statistical measure of
how spread the values are in a distribution.
Supply. Willingness to provide. Willingness
varies with supplier, price, and circumstance, so supply is
usually expressed in terms of the quantities that would be
supplied at various prices. The supply curve usually slopes
upward, indicating that suppliers will supply more at higher
prices than at lower prices. Where economies of scale exist,
however, the supply price may drop as scale increases over
the range where such economies prevail. Opposite of
demand.
Switching value. The value of an input
that reverses the ranking of two alternative projects. For
example, alternative A will produce shoes with
sophisticated modern equipment and very few workers, whereas
alternative B will consist of a network of small
workshops employing many poor artisans and very little
capital equipment. If income going to the poor is given a
weight of up to 1.5, alternative A has a higher
rate of return. If income going to the poor is given a
weight of greater than 1.5, however, alternative B has the
higher rate of return. Thus, 1.5 is the switching value.
Tradable. Referring to a good that could be
traded internationally in the absence of restrictive trade
policies.
Trade-off. The give and take involved in
compromise or deal making; the negatives that come along with
the positives and vice versa.
Transfer payments. Payments that redistribute
wealth but do not use up resources or create them.
Weight. A factor that, when multiplied by the
value to be weighted, adjusts that value to reflect
certain considerations.
Weighted. Adjusted to reflect relative
importance.
Willingness to pay. What consumers are willing
to pay for a good or service. Consumers willing to pay
substantially more than the actual market price enjoy a
consumer surplus (the amount they would pay minus the amount
they actually have to pay).
Appendix B: Questions to ask about a
benefit-cost analysis
A quick
guide
-
Is the problem or opportunity clearly stated? Is there a
compelling rationale for the federal government acting in
this situation? Are the objectives clear and coherent?
-
Is the analysis set out separately from the point of view
of each important actor?
-
Are the alternatives defined in a fair and comparable way?
Are the important alternatives analyzed?
-
Is this an open and transparent analysis? Is each stage of
the analysis set out so that you can follow the reasoning
and the numbers?
-
Are the likely incremental effects of the project or
program alternatives well analyzed?
-
Are the costs and benefits of these effects measured well
and set out in detail over the full life of the project?
Are likely changes in relative prices taken into account
or does the analyst take short cuts?
-
Are inflation adjustments and discounting done separately?
Are the price index and discount rate the appropriate
ones?
-
Does the analysis take into account uncertainty in the
data and risk in the investment?
-
Does the analysis describe who pays and who benefits?
-
Does the analysis make a reasoned recommendation and give
a fair showing to the alternatives it does not recommend?
Appendix C: Selected readings
General
readings
Australia, Department of Finance. 1991. Handbook of
Cost-Benefit Analysis. Australia, Department of Finance,
Canberra, Australia.
---1992. Introduction to Cost-Benefit Analysis for Program
Managers. Australia, Department of Finance, Canberra,
Australia.
---1993. Value for Your IT Dollar: Guidelines for
Cost-Benefit Analysis of Information Technology
Proposals. Australia, Department of Finance, Canberra,
Australia.
Canada, Treasury Board of Canada Secretariat and Consulting
and Audit Canada. 1995. Benefit-Cost Analysis Guide for
Regulatory Programs, Treasury Board of Canada
Secretariat, Ottawa, ON, Canada.
Gramlich, E.M. 1981. Benefit-Cost Analysis of Government
Programs. Prentice-Hall, Englewood Cliffs, NJ, USA.
Great Britain, Overseas Development Administration. 1988.
Appraisal of Projects in Developing Countries: A Guide for
Economists. HMSO, London, UK.
Harberger, A.C. 1997. Economic Project Evaluation: Some
lessons for the nineties, Canadian Journal of Program
Evaluation, Special Edition.
Jenkins, G., and Harberger, A.C. 1995. Cost-Benefit
Analysis of Investment Decisions. Harvard Institute for
International Development, Harvard University, Cambridge, MA,
USA.
Sassone, P.G. 1978. Cost-Benefit Analysis - A
Handbook. Academic Press, New York, USA.
Stanbury, R., and Vertinski, I. 1989. Guide to Regulatory
Impact Analysis. Office of Privatization and Regulatory
Affairs, Ottawa, Canada.
Sugden, R., and Williams, A. 1985. The Principles of
Practical Cost-Benefit Analysis. Oxford University Press,
Oxford, UK.
Van Pelt, M., and Timmer, R. 1992. Cost-Benefit Analysis
for Non-Economists, Netherlands Economic Institute,
Amsterdam, Netherlands.
Watson, K. 1997. Cost-Benefit Analysis in the
nineties, Canadian Journal of Program Evaluation, Special
issue.
World Bank. 1996. Economic Analysis of Investment
Operations. World Bank, Washington, DC, USA.
World Bank and Economic Development Institute. 1991. The
Economics of Project Analysis: A Practitioner's
Guide. World Bank, Washington, DC, USA.
Defining fair options
Public Works and Government Services Canada. 1995. 2.0
"Real Property Investment Strategies;" and 3.0
"Policies and Practices." Real Property
Investment Guide.Public Works and
Government Services Canada, Ottawa, Canada.
Transport Canada 1994. 4.0 "Option Identification;"
5.0 "A Common Frame for Comparison." Guide to
Benefit-Cost Analysis. Transport Canada, Ottawa,
Canada.
Being clear on the point of view
Boardman, Vining, A., and Waters,W.G., 1993, "Cost and
Benefits through Bureaucratic Lenses: Example of a
Highway Project", Journal of Policy Analysis and
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Inflation adjustments and discounting
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