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UNIT 10 APPLICATIONS OF DISCOUNTED MEASURES
OF PROJECT WORTH
Structure
10.0 Objectives
10.1 Introduction
10.2 Sensitivity Analysis
10.3 Switching Value
10.4 Choosing among Mutually Exclusive Alternatives
10.5 Entirely Different Projects
10.5.1 Different Timings of a Project
10.5.2 Choice between Technologies
10.5.3 Additional Purposes in Multipurpose Projects
10.5.4 Applying Contingency Allowances
10.6 Replacement Cost
10.7 Residual Value
10.8 Domestic Resource Cost
10.9 Let Us Sum Up
10.10 Key Words
10.11 Some Useful Books / References
10.12 Answers / Hints to Check Your Progress
10.0 OBJECTIVES
After going through this unit, you will be able to:
 apply discounted measures of project worth in project analysis;
 define and use the sensitivity analysis in project evaluation; and
 choose among mutually exclusive alternative projects.
10.1 INTRODUCTION

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The various methods of project evaluation we have studied so far are based on the
assumption that both costs and benefits are known with certainly. But this may not be
true in real world. They may not provided a sufficient framework upon which the various
benefits and costs involved could be set out in their true perspective. The agricultural
projects are usually sensitive to changes in the factors such as prices, delay in
implementation, and cost over-run and yield. There are techniques/approaches, which are
useful in applying discounted measures of project worth to evaluate the projects under
such situation. In this unit we will be studying some of the approaches useful in details
for evaluating the agriculture project under varied conditions. .
10.2 SENSITIVITY ANALYSIS
Sensitivity analysis is an analytical technique to test systematically what happens to the
earning capacity of a project if events differ from the estimates made about them in
planning. Sensitivity analysis is a means of dealing with uncertainty about future events
and values. A sensitivity analysis is done by varying one element or a combination of
elements and determining the effect of that change on the outcome, most often on the
measure of project worth. In agricultural project analysis, most projects should be tested
at least for the effects on earning capacity of changes in prices, cost overrun, delay in
implementation, and changes in yield. Sensitivity tests need not be directed at the effect
of a change on a measure of project worth. A Sensitivity test may be made, for example,
to determine the effect of a delay in benefits on the cash position of a farmer who has
borrowed for an irrigation pump. A variation of sensitivity analysis is to determine the
switching value, Compare with risk analysis
In circumstances where firm probabilities cannot be attached to the future value of
parameters which are likely to affect the outcome of a benefit-cost study, sensitivity
analysis may represent the only method of describing quantitatively uncertain outcomes
to decision makers. In this simple technique, different values for uncertain variables are
used to construct alternative scenarios of outcomes for presentation to the decision-
maker. It has already been suggested that the analyst should carry out such sensitivity
analysis where questions arise as to the magnitude of the social discount rate, future price
ratios and shadow prices for unemployed resources, but the technique is generally
valuable in dealing with any type of environmental or technological uncertainty.
Sensitivity analysis may be a useful step in tackling problems created by uncertainty in
benefit cost analysis even where probabilities can be attached to outcomes. Moreover,
even, where sensitivity analysis reveals that foreseeable uncertainty may affect the
viability of a single project or the ranking of alternative projects, the technique may still
be useful in revealing those parameters in the analysis with respect to which a decision is
most sensitive. Other techniques may then be used to examine more closely the problem
of uncertainty in these sensitive parameters.
The more explicit techniques for incorporating information on uncertainty directly into
benefit cost calculations will be examined next. We will first consider short-cut
techniques such as using higher social discount rates or artificially limiting the economic

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lives of projects. Problems with the use of point estimates of probability will then be
examined. Finally, some more extensive technique, such as Monte-Carlo simulation
methods and decision-trees, will be discussed briefly.
(a) Short-cut methods of allowing for uncertainty:
(Premiums in the social discount rate and artificial limits to the life of project)
Short-cut methods of incorporating uncertainty into benefit-cost analyses are occasionally
encountered. For instance, some analysts use discount rates for this purpose, as well as to
express the social opportunity cost of capital or social time preference. The rationale
underlying this procedure is that forecasts of the benefits and costs of a project become
more speculative the longer the time horizon or project life considered. Adding a
premium to the discount rate reduces the importance in the analysis of data forecasted for
the remote future. This procedure may also be justified on the ground that, in the private
sector of the economy, higher rates of return are needed to attract capital into risky
investments.
This practice of using 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 a risk less discount rate.
A second rough-and ready method of allowing for uncertainty in benefit cost calculations
is to impose an artificial limit on the life of a project. Thus, if the benefits from a project
are expected to continue to 20 years or so, it may be stipulated that the project must meet
some specified investment criterion within five or 10 years, depending upon the degree of
uncertainty which it is assumed will prevail in the future. The arbitrariness in selection of
the length of such cut-off periods should be evident. It should also be noted that the
procedure is superfluous where long cut-off periods are used in conjunction with any
sizeable discount rate.
(b) Collapsing the distribution of possible outcomes into several numbers
We have already seen that a single valued estimate of an uncertain outcome, such as the
expected value of a project, constitutes insufficient information for a decision-maker,
because data on possible variance in project outcomes is concealed.
Often one finds such single valued “best estimates” augmented by most optimistic and
most pessimistic projections of likely outcomes. Such calculations give the decision
maker an idea of the range of possible project outcomes, but again do not reveal the
probabilities attached to the most likely, most optimistic or most pessimistic forecasts.
The problems with these various forms of point estimates can be illustrated with the aid
of the example outlined in Table 10.1 below. The table contains a series of annual

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estimates of the net benefits from a project (net present value of benefits minus the net
present value of costs), and the probabilities attached to these various annual net benefit
streams. It is assumed that each of the probabilities associated with these annual net
benefit streams is independent of the annual net benefits achieved in earlier periods. In
Table 10.1, this implies that there is a 50 percent probability of achieving a net benefit
of 9 in the second period, regardless of whether the Period I net benefits were five or
10. The problems of dealing with uncertainty when probabilities are dependent are much
more difficult, requiring more complicated techniques. It will be briefly discussed after
the independent case.
Table 10.1: Probabilities of net benefits from a project
Period 1 Period 2 Period 3 Period 4
NB* Prob** NB Prob NB Prob NB Prob
5 .2 3 .3 5 .4 3 .1
10 .6 9 .5 9 .5 8 .6
20 .2 12 .2 13 .1 11 .3
*NB - Net benefits
** Prob - Probability of occurring
As can be seen from the table, the most likely estimate of total net benefits accruing in
the four-year period considered, or the sum of the most likely net benefits in each year, is
36. Similarly the most optimistic and least optimistic projections of total net benefits
from the project are 56 and 16 respectively. To find the total probability of each of these
projections occurring, we have to find the product of the probabilities for each component
of the outcome in each period. Thus, the most likely estimate has only a .09 chance of
occurring (.6 x.5 x .5 x .6 = 091). Similarly, the most optimistic and least optimistic
outcomes have total probabilities, the decision maker might well like to know more
about the chances of other outcomes occurring and, indeed, to have a picture of the total
probability distribution of outcomes.
(c) Direct and simulated calculations of probability distributions of outcomes
when events are independent
Direct calculation of probability distribution of outcomes requires specification of the
probability distributions of variables affecting the outcomes, and the interrelationships
between these distributions, as in Table 10.1. The probability distribution for the
example illustrated in Table 3 might be most economically worked out by hand. Since
there are only three net benefit figures for each year in the four year period, there are a
total of 34
or 81 possible outcomes when the various combinations of probabilities are
considered. However, it can be seen that it becomes rather impractical to work out
probability distribution of outcomes by had when larger total combinations of
probabilities are involved. For instance, if the project life for the example in Table 10.1
we quintupled to 20 years, and three estimates of net benefits were made for each year of
project life, there would be a total of 320
or nearly 3 ½ million possible benefit streams

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for the project. In such circumstances, what is required is a sample of what possible
outcomes might be.
Computer simulation methods can be used to generate a manageable synthetic sample of
such outcomes. The probability distribution of values for each variable affecting the
outcomes (for example, each year’s benefits in table 10.1) is first specified. A value for
each of the underlying variables affecting the total outcome is then selected at random.
The sum of the randomly selected values for variables affecting the outcome is then
obtained. This process of assigning random values to variables affecting the outcome and
calculation of the outcome is then simply repeated many times to build up a probability
distribution of outcomes. The computation process, often termed the Monte Carlo
technique, is concluded when further calculations no longer affect the relative frequency
of outcomes.
Having calculated the total distribution of outcomes by hand or having simulated this
distribution by the computers, the analyst can then summarize the implications of the
distribution for the decision maker by computing the usual estimates of central tendency
and dispersion such as the mean and the standard deviation or variance.
(d) Dependent decision-making involving uncertainty
Decision involving uncertainty in a project may be sequential in time and executed in
stages, the decision-maker having options open at some stage of a project which are
closed off by taking a particular course of action. One method which has been developed
to deal with this problem is that of using ‘decision trees”. Briefly stated, decision-trees
aid the decision maker by revealing the time sequence of points in a project at which
decisions have to be taken, the options or strategies available at the decision points, the
uncertainties associated with particular courses of action, and the costs of alternative
courses of action foreclosed by the choice of a particular option. Due to their complexity,
decision-trees are used infrequently in benefit-cost analysis. They are unwarranted in
cases where the range of outcomes is independent of previous decisions or previous
outcomes. In cases where the relationship between each year’s outcomes is unclear, the
burden of proof must rest on showing that the independence assumption is inappropriate.
10.3 SWITCHING VALUE
A variation of sensitivity analysis is the “switching value”. In straight forward sensitivity
analysis we choose an amount by which to change an important element in the project
analysis and then determine the impact of that change on the attractiveness of the project.
In contrast, when we calculate a switching value we ask how much such an element
would have to change in an unfavourable direction before the project would not longer
meet the minimum level of acceptability as indicated by one of the measures of project
worth. Then those responsible for determining whether to proceed with the project can
ask themselves how likely they feel it is that there will be a change of that magnitude.
10.4 CHOOSING AMONG MUTUALLY EXCLUSIVE ALTERNATIVES

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Quite often in project design, and not infrequently in evaluating complete
projects, analysts are faced with having to choose among mutually exclusive
alternatives – project design options or whole projects of a nature that if one
is chosen the other cannot be undertaken. This can apply to such cases as development of
surface irrigation and not tube well irrigation, river development upstream rather than
downstream, and plants in alternative locations but serving the same limited market. It
can also apply to such design issues as the choice among different scales for projects in
which one size precludes implementing a similar project of another size, the time
phasing of what is essentially the same project the different designs for project
components, or the purposes of a multipurpose project. The need to compare mutually
exclusive design options is one of the principal reasons to apply economic analysis early
in the project cycle.
The preferred discounted measure of project worth for choosing among mutually
exclusive projects or project options is the net present worth. Direct comparison of the
internal rates of return, the benefit-cost ratios, or the net benefit-investment ratios can
lead to an incorrect investment decision. This is so because undertaking a small, high-
paying project may preclude generating more wealth through a moderately remunerative
but larger alternative.
Sometimes what may at first be posed as a pair of mutually exclusive projects can,
instead, be seen as successive phases of development. If a small project can be expanded
by phases to become a larger alternative, no analytical problem is posed. To implement a
small, first-phase project does not pre-empt a larger, phase-two project; both phases can
be under taken, with each phase judged by any of the measures of project worth.
Although net present worth is the preferred criterion for choosing among mutually
exclusive alternatives, it is possible to manipulate the internal rate of return to use it to
choose among mutually exclusive alternatives. The net benefit-investment ratio can be
used to rank mutually exclusive projects only when the ratios of all projects in the
investment programme are known; therefore it is not a practical measure to use for this
purpose.
To use the internal rate of return to choose between two mutually exclusive alternatives,
the cash flow of the smaller alternative is subtracted year by year from the cash flow of
the larger alternative. This stream of differences is then discounted to determine the
internal rate of return of the stream. This is the financial or economic rate of return to the
additional resources necessary to implement the larger alternative as opposed to the
smaller one. How this method is applied will be illustrated in the course of our
discussion of the kinds of mutually exclusive projects, below.
When there are several mutually exclusive alternatives, determining the net present
worth of each enables us to choose directly the best among them. In contrast, discounting
the differences between cash flows of alternatives can only be applied to select between a
single pair of alternatives. To use the internal rate of return criterion when there are more
than two alternatives, one can proceed by determining the rate of return to the stream of

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the differences between any pair of alternatives. If the return is above the cut-off rate, the
larger alternative is selected; if the return is below, the smaller is selected. The procedure
is then repeated by testing the alternative chosen against another alternative, the better of
this second pair is selected, and so forth in a kind of elimination tournament until all
alternatives have been tested and the best identified.
We will take up five instances of mutually exclusive alternatives:
1. The most general case is where we have entirely different alternative projects that
are mutually exclusive – say, a choice between a small irrigation project that pre-
empts a site and a larger one using the same site.
2. We will discuss the scale of a project as a variation of mutually exclusive
alternatives, viewing a large project as a mutually exclusive alternative to a small
version of the same project.
3. Another instance is the special case of timing – whether it would be better to
begin a project now or later. In effect, postponing a project is a mutually
exclusive alternative to undertaking it immediately.
4. Yet another special case involves the choice of alternative technologies in which
selection of one technology rules out its alternative.
5. The final case is that of additional purposes in multipurpose projects – the river
basin projects to control floods and generate hydropower that also includes an
irrigation purpose is a mutually exclusive alternative to the same project
without the irrigation purpose.
10.5 ENTIRELY DIFFERENT PROJECTS
Occasionally in agriculture we may be faced with the choice between two mutually
exclusive alternative projects of an entirely different nature, one small and high-yielding
and the other large but low-yielding. At a given location we may have a choice either of
constructing a small irrigation project that is limited to the best land and uses rather
simple equipment or of building a considerably larger project that involves a more
extensive area and more costly, complicated engineering works. If the small scheme is
built, it pre-empts the site so that the larger project cannot be built. When mutually
exclusive alternatives of this nature are met, we can choose between them by selecting
the project that has the larger net present worth when discounted at a suitable opportunity
cost of capital.
10.5.1 Different Timings of a Project
A special case of the choice among mutually exclusive project is the question of whether
to begin a project immediately or to postpone it. The same project begun today or at

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some future time may be considered, from an analytical standpoint, to be two different
mutually exclusive projects.
10.5.2 Choice between Technologies
When there are technological alternatives by which we can realize the same result when
designing a project, we have an instance of mutually exclusive alternative because the
choice of one technology precludes the use of another for the same purpose. The
alternative we choose will be the one with the lower present worth – but, if the total
undiscounted cost of using the different alternatives is different and they have differing
time profiles, the alternative we choose may depend on the opportunity cost of capital.
10.5.3 Additional Purposes in Multipurpose Projects
A variation of the problem of mutually exclusive alternatives arises in multipurpose
projects. In these, a project design that includes one group of purposes is a mutually
exclusive alternative to another project design that includes a different group of purposes.
The problem is frequently met in rural development projects, and another common
example is found in river basin development projects.
10.5.4 Applying Contingency Allowances
For many estimates of project costs, especially costs of those projects in which there is a
considerable element of construction in the earlier years, the engineers will often include
a contingency allowance. Physical contingency allowances and contingency allowance
intended to reflect relative price changes are real costs in both financial and economic
analysis and should be incorporated directly into the project accounts even when the
analyst is working in constant prices.
The contingency allowance intended to allow for general inflation, however, does not
enter into the project accounts, either financial or economic, when the analyst is working
in constant prices. This means that when inflation is expected to be significant, a separate
financing plan will be needed to give those responsible for making budget allocations a
better idea of the amounts in current terms that they will be asked to make available.
10.6 REPLACEMENT COSTS
Many agricultural projects require investments that have different lifetimes. A good
example is found in the case of a pump irrigation scheme in which the earthworks and
pump platforms may be expected to last twenty-five to fifty years but the pumps
themselves may have a life of only seven to fifteen years. In preparing the analysis,
allowance may be made for the replacement cost of the pumps during the life of the
project.
10.7 RESIDUAL VALUE

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Often at the end of a project there may reasonably be expected to be some residual (or
terminal) value. That is, the capital asset will not have been all used up in the course of
the project period, and there will be a residual asset. The way to handle this is to treat the
residual value of any capital item (say a dam or a stand of trees) as a project “benefit”
during the last year of the analysis period.
10.8 DOMESTIC RESOURCE COST
In countries where there are balance of payments problems and where import substitution
or export promotion is an important objective, it is useful to estimate the cost in the
domestic currency required to earn a unit of foreign exchange through a proposed project.
The usefulness of doing so might arise, for instance, in preparing an oil palm project in
which export or avoidance of vegetable oil imports is the objective or in evaluating a
fertilizer plant intended to reduce or avoid future increases in imports. It is not enough
just to earn or save foreign exchange. Some idea must be formed of the cost of saving
foreign exchange, and a judgment must be made about whether that cost is too high. By
expressing the cost of earning or saving a unit of foreign exchange as domestic resource
cost, a direct comparison may be made with the official exchange rate and various
shadow prices for foreign exchange. Such a comparison is one basis for evaluating a
project.
Check Your Progress 1
Note: Use the space below for writing your answer.
1) What are the different investment criteria for selecting the project?
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2) In which circumstances sensitivity analysis is used?
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10.9 LET US SUM UP
Sensitivity analysis is an important technique to test systematically what happens to the
earning capacity of a project it events different from the estimates made about them in

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planning. A valuable means of dealing with uncertainty about future events and values. It
is performed by varying the effect of a combination of elements and determining the
effect of that change on the outcome. A sensitivity test may not be directed at the effect
of a change on a measure of project worth. A variation of sensitivity analysis is to
determine the switching value compare with risk analysis.
10.10 KEY WORDS
Benefits : Benefits are defined as advantageous effects. They represent real
values resulting from any action which brings about increases in the
output of useful goods and services.
Costs : Primary or direct costs consist of the goods and services which must
be surrendered in order to construct and operate a given project or
program. Not only do they include all of the monetary expenditures,
but provision must also be made for economic losses whether
compensated or not. Interest during construction should be taken
into account, as should promotional expenses, engineering and
supervision, acquisition of land and the relocation of existing
facilities. The cost of financing is also a factor the problem of tax
allowances is a difficult one.
Sunk Cost : A cost that occurred in the past and cannot be recovered even if is
operation in totally shut down and all investments are sold. The
cost of digging a tube well cannot be recovered if the pump set is
later sold.
Shadow
Price
: The value used in economic analysis for a cost or a benefit in a
project when the market price is felt to be a poor estimate of
economic value.
10.11 SOME USEFUL BOOKS/ REFERENCES
Benefit-Cost Analysis Guide (1976). Planning Branch, Treasury Board Secretariat,
Ottawa, Canada
Bierman, Harold, Jr., and Seymour Smidt (1980). The Capital Budgeting Decision.5th
ed. New York, Macmillan.
Dasgupta, P. (1982). The Control of Resources. Oxford University Press, New Delhi.

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Dasgupta, P. Amartya Sen and Stephen Marglin (1972). Guidelines for Project
Evaluation, United Nations Publications, New York.
Gittinger J. Price (1976). Economic Analysis of Agricultural Projects. The John Hopkins
University Press, Baltimore, Maryland 212118, U.S.A.
Reddy, S.S. and P.Raghu Ram (2000). Agricultural Finance and Management, Oxford
and IBH Publishing Company, Private Limited, New Delhi.
Sewell, W.R.D., J. Davis, A.D. Scott and D.W. Ross (1969). Guidelines to Benefit Cost
Analysis, Queen’ Printer for Cananda, Ottawa.
10.12 ANSWERS/ HINTS TO CHECK YOUR PROGRESS
Check Your Progress 1
1) Where projects being considered for selection are neither interdependent nor
mutually exclusive, and where decision-makers are not restricted in their choice
of projects by limitations on funds or other constraints, all projects should be
undertaken which have a positive net present value, that is which have
discounted benefits that exceed their discounted costs. Alternative investment
criteria which are also valid in these circumstances are that all projects should be
undertaken which have benefit-cost ratios exceeding unity, or have internal rates
of return which are greater than the social discount rate.
2) In circumstances where firm probabilities cannot be attached to the future value of
parameters which are likely to affect the outcomes of a benefit-cost study,
sensitivity analysis may represent the only method of describing quantitatively
uncertain outcomes to decision-makers. In this simple technique, different values
for uncertain variables are use to construct alternative scenarios of outcomes for
presentation to the decision-maker.