PROJECT EVALUATION & SELECTION
The process that determines whether a project or investment is desirable (based on financial
or not criteria). It addresses two sorts of questions:
• Is any individual project worthwhile? Does it meet the company's goals or minimum
• Given a list of projects, which is best? How does each project rank or compare to others
on the list?
It is highly unlikely that companies will approve a project where the costs exceed the
benefits. Benefits can be measured in either financial or non-financial terms. The process of
identifying the financial benefits is called capital budgeting, which may be defined as the
decision making process by which organisations evaluate projects that include the purchase
of major fixed assets such as buildings, machinery and equipment.
Project selection models: numeric and non-numeric.
Numeric models are usually financially based and quantify the project in terms of either
percentage return on investment or time to repay the investment.
Non-numeric models look at a much wider picture of the project, considering items from
market share to environmental issues.
The purpose of models: They aid decision making; they cannot make decisions on their own;
their limitations should be appreciated as they are only a prediction of what could happen and
as accurate as the data they are based on.
Important criteria in selecting a model
Realism: The model should accurately reflect the company’s and manager’s objectives. It
should take into account the company’s limitations on facilities, capital, personnel, etc.; risks
in various areas (technical risks, market risk).
Capability: The model should deal with multiple time periods, changes in operating
characteristics both within and outside company (i.e. strikes, interest rate changes, etc.) and
optimise the decision. It should make important comparisons, consider major risks and
constraints and then select the best overall project / sets of projects.
Flexibility: The model should cover all conditions likely to be encountered and be easily
modified or self-adjusting in response to changes in the firm's environment (changes in law,
changed risk levels with advancing technology, changes to company’s goals).
Ease of Use: The model should be convenient and easy to use, not take a long time to
execute, not require special interpretation, not use data which is difficult to acquire, excessive
personnel or unavailable equipment. Variables should relate to real parameters that are
significant to the project. It should easily simulate expected outcomes associated with
investments in different projects.
Cost: Modelling costs should be low relative to the cost of project and less than potential
Easy computerization: It should be easy and convenient to manipulate data through widely
used computer packages.
A number of factors should be considered when selecting a project such as production (eg
time until ready to install, length and degree of disruption, safety etc), marketing (eg. size of
potential market for output, probable market share of output, etc), financial (profitability, net
present value of investment, impact on cash flows, payout period, etc), personnel (training
and labour skill requirements, availability of required labour skills, etc), administrative and
other issues (meet government safety & environmental standards, impact on information
systems & computer usage.
NON-NUMERIC SELECTION METHODS
The Sacred Cow
The project is suggested by a senior and influential person in company: "If you have a
chance why don't you look into....." and follows an undeveloped idea for a new
production, a new market etc. The project is 'sacred', it will be continued until
successful or until the boss personally recognises the idea as a failure and terminates
it. The advantage is that it is supported by ‘the powers that be’ (full support by top
This selects any project that is necessary for continued operation of a group or facility
or for maintaining a competitive position.
Comparative Benefit Model
When there are many projects to consider. A selection committee is appointed with
the task to arrange projects into a rank ordered set. (e.g. the peer review used by
research funding organizations).
NUMERIC SELECTION METHODS
FINANCIAL ASSESMENT METHODS - ECONOMIC PROJECT EVALUATION
The techniques described below are widely known in management accounting as capital
investment decisions or capital investment appraisal techniques. In order to simplify the
introduction to these techniques the following assumptions are made:
All future cash flows (inflows and outflows) can be predicted with certainty.
There are no taxes or inflation to cause the prices to increase over the life of the project.
1. Payback Period
Payback period is the length of time (number of years) required for a project to repay its
initial fixed investment. For uniform annual cash flows is given by:
payback period =
uniforms annual cash flows
The most desirable project under the payback method is the one that pays back the cash
outlay in the shortest time.
Example 1 (uniform annual cash flows). Assume a project costs £100,000 to implement and
has annual cash inflow of £25,000. Therefore, the payback period = £100,000 / £25,000 = 4
Example 2 (Non-uniform annual cash flows). A company wishes to buy a new machine for a
four year project. The manager has to choose between machine A and B. Both machines have
the same initial cost (£35,000) but their cash flows behave differently over the 4-year period.
Cash flows (£)
Year Machine A Machine B
0 (35,000) (35,000)
1 20,000 10,000
2 15,000 << 10,000
3 10,000 15,000 <<
4 10,000 20,000
Payback period 2 years 3 years
Cash flows (£)
Year Project A Project B Project C
0 (120,000) (120,000) (120,000)
1 60,000 45,000 40,000
2 60,000 45,000 70,000
3 60,000 45,000 80,000
Payback period 2 years 2.67 years 2.125
Workings 120/60 120/45 40+70+10/80
1 2 3 years
cash flow profile
1 2 3 year
Figure 2.1. Illustration of payback period for project C above.
Simple and easy to use; uses readily available accounting data to determine cash flows.
Reduces the project's exposure to risk and uncertainty by selecting the project that has the
shortest payback period; the uncertainty of future cash flows is reduced.
Quantifies the criteria the decision makers are more familiar with.
It is an appropriate technique/cautious approach to evaluate high technology projects
where technology is changing quickly and the project could run the risk of being left
holding out of date stock and for products built to last only for a short period of time.
It may be important to organisations which face cash flow constraints or need a measure
of speed of cash recovery.
It fails to measure profitability.
It does not consider the time value for money. Payback period is indifferent to the timing
of cash flows. The project with high early repayments would be ranked equally with a
project which had late repayments if their payback periods were the same (Figure 2.2).
Figure 2.2. Payback period (projects A and B have the same payback period even though
cash flows are different).
It assumes inflows will persist for long enough to pay back investment. It does not look at
the total project. It ignores the importance of cash inflows beyond the payback period. A
project that build up slowly to give excellent returns would be rejected in favour of a
project with lower early returns if the payback period was shorter (Figure 2.3).
Figure 2.3. Payback period (does not consider cash-flow after the payback period. In this case
project B may be a better option even though project A has shorter life cycle).
It is not a suitable technique to evaluate long term projects where the effects of
differential inflation and interest rates could significantly change the results.
The figures are based on project cash flows only, other financial data are ignored.
Although payback period would reduce the duration of risk, it does not quantify risk.
Payback period the most widely used technique, initial filter for project selection. Can be
modified to consider the time value of money (discounted payback period).
2. Accounting Rate of Return (ARR) or Return on Investment (ROI)
This differs from payback period in using accounting profits rather than cash flows expected
from a project as a percentage of capital invested.
The accounting rate of return (ARR) is the ratio of average annual profit (either before or
after taxes) to initial or average investment in project. The average annual profit is simply the
project outlay deducted from the total gains, divided by the number of years the investment
average annual profit =
total gains - outlay
ARR (or ROI) =
average annual profit
initial or average investment
Example 1. Assume, in example 1 above, that average annual profits are £15,000. Therefore,
the average rate of return = £15,000 / £100,000 = 0.15 =15%.
Example 2. Using example 2 above calculate the average rate of return or return on
Year Machine A Machine B
Cash flow (£) Cash flow (£)
0 (35,000) (35,000)
1 20,000 10,000
2 15,000 10,000
3 10,000 15,000
4 10,000 20,000
Total gains £55,000 £55,000
Profit = ( £55,000 - £35,000) / 4 years = £20,000 / 4 = £5,000 per year (same for both
Average rate of return = £5,000 / £35,000 x 100 = 14%.
Please note that in all the above examples the initial investment is used in the denominator.
However, in some textbooks the average investment is used instead. This involves making
some assumptions about the way that capital is used in the project e.g. if a project requires
£1,000 invested at the start and there is nothing left (i.e. no salvage, scrap or residual value1
at the end and the amount is used equally every year then the average investment will be
£1000 divided by number of years or life of project.
Hint: if there is no depreciation use initial investment; if straight line depreciation2
assumed then average investment should be used defined as 1/2 (initial investment + salvage
Advantages: A simple technique like payback period, based on the familiar accounting
measure of profit, considers all the profits expected over the project life.
Salvage value (or scrap value or residual value) is an asset’s estimated value at the end of its life; it is the
amount eventually recovered through sale, trade-in or salvage.
Depreciation can be defined as the gradual decrease in utility of fixed assets with use and time.
Straight-line method of depreciation: charges as an expense an equal fraction of the net cost of the asset each
year, i.e. Depreciation charge during year n = (investment – salvage value at end of useful life)/ (number of
years or useful life), e.g. if piece of machinery cost £10,000 and has a useful life of 5 years and an estimated
salvage value of £2,000 then the annual depreciation will be £(10,000-2,000)/5 = £1,600. The average
investment will be 1/2(10,000+2,000)=6,000.
Disadvantages: It averages out the profit over successive years. An investment with high
initial profits would be ranked equally with a project with high late profits if average profit is
the same. Clearly the project with high initial profits should take preference. For example,
machine A and B projects above have the same average rate of return although they have
different cash flows. It also depends on profit, which includes a subjective accounting
estimate of depreciation; this is not a problem when the same depreciation policy is used.
Both Accounting Rate of Return and Payback Period are simple but neither takes into
account time value of money which is important unless interest rates are extremely low and
rate of inflation is zero. Profits and cash inflows are not reduced to actual present-day values.
3. Discounted Cash Flow (DCF) techniques
DCF techniques seek to remedy some of the defects of the payback period and accounting
rate of return by taking into consideration the time value of money. Many projects evolve
over long periods, costs that are incurred in one period may generate benefits for many years
to come; when evaluating these projects one must compare costs and benefits that occur at
different times; to make a valid comparison we need to translate all cash flows into
Time value of money. Everyone knows that £100 today will not have the same worth or
buying power as £100 next year or in some years time. If £100 is invested at 10% per annum
it will grow to £110 by the end of the year, i.e. the future value (FV) of an amount of money
invested today (PV) in n years is given by:
FV = PV(1 + k)n
where k is the interest rate.
This process is known as compounding. If the £100 is spent on an item of business machinery
then the interest is lost, so the act of investing leads to a lost opportunity of earning
investment. The idea of applying calculations of the time value of money is a way of
recognising the reward needed from a project to compensate for the lost opportunity.
Now let us look at the formula from a different perspective. If an investment yields £100 a
year from now, how much it will worth today if the cost of money or interest rate is 10%? To
solve the problem we must discount the future value to the present value. The present value
of an amount of money FV receivable at the end of n years when the interest rate is k per cent
per annum is given by:
(1 + k)n (Eq. 5)
where k represents the annual rate of interest expressed in decimal form and n represents the
time period when the cash flow will be received. The process of calculating the present value
is called discounting and the interest rate used is the discount rate, minimum required rate of
return or minimum attractive rate of return or cost of capital. The discount rate represents the
way money now is worth more than money later; it determines by how much any future
amount is reduced to make it correspond to an equivalent amount today. It is a key factor in
the evaluation of projects over time; it is the parameter that allows us to compare costs and
benefits incurred at different instances in time. The discount rate is similar to the prevailing
interest rate but quite a different concept: it represents the real change in value to a person as
determined by their possibilities for productive use of the money and the effects of inflation,
whereas the interest rate defines a contractual agreement between a borrower and a lender.
This implies that discount rate > interest rate; however, it is common to use terms
3.1. Net Present Value (NPV)
The net present value of a project is equal to the present value of the cash inflows minus the
present value of the cash outflows all discounted at the cost of capital
∑ − Io
where FVt = the expected cash inflows period t (minus all expenses incurred in that
k= the discount rate or cost of capital
Io= initial cash investment and
n the numbers of years or life of project.
Inflation can be treated in two ways: either by deflating the cash flows before using Eq. 6 or
by adding the inflation rate to the discount rate k.
The NPV decision rule is:
When NPV is positive the project is accepted.
When NPV is negative the project is rejected.
When NPV is zero the project is acceptable in meeting the cost of capital but gives no
surplus to its owners.
Between two mutually exclusive projects the one with higher NPV is selected.
Example 1. Assume an initial investment of £100,000 with a net cash inflow of £25,000 per
year for a period of 8 years, a required rate of return of 15% and an inflation rate of 3% per
(1+ 0.15 + 0.03)t
∑ − £100,000
NPV is positive, therefore project is acceptable.
Example 2. Consider example 2 above again using NPV. Assume a discount rate of 15% and
(1) (2) (3) (2)x(3)
Year Cash flow (£) Discount factor Present value (£)
0 (35,000) 1 (35,000)
1 20,000 0.8333 16,666
2 15,000 0.6944 10,416
3 10,000 0.5787 5,878
4 10,000 0.4823 4,823
Net Present Value 2,783
(1) (2) (3) (2)x(3)
Year Cash flow (£) Discount factor Present value (£)
0 (35,000) 1 (35,000)
1 10,000 0.8333 8,333
2 10,000 0.6944 6,944
3 15,000 0.5787 8,681
4 20,000 0.4823 9,646
Net Present Value (1,396)
NPV analysis would select machine A in preference to machine B because it has higher NPV.
NPV can be easily calculated using spreadsheet packages. Present value tables are also
available in most accounting textbooks, containing both single and cumulative present value
Advantages of NPV:
• It introduces the time value of money.
• It expresses all future cash flows in today's values enabling direct comparisons
• It allows for inflation.
• It looks at the whole project from start to finish.
• It can simulate project what-if analysis using different values.
• It can give a more accurate profit and loss forecast than non DCF calculations.
• The accuracy is limited by the accuracy of predicted future cash flows and discount factors.
• It is biased towards short run projects.
• It does not include non financial data like marketability of the product.
3.2. Internal Rate of Return (IRR)
The internal rate of return (IRR) is the discount rate at which the net present value of the cash
flows generated by the projects is equal to the present value of the capital invested so that the
net present value of the project is zero i.e.
(1 + IRR)
∑ = Io
IRR is calculated by trial and error or by plotting NPV against discount rate k. It expresses
the real return on any investment.
The IRR decision rule:
Where IRR is greater than the cost of capital accept the project.
Where IRR is less than cost of capital reject the project.
Where IRR equals cost of capital the project is acceptable in meeting the required rate of
return of those investing in the business but gives no surplus to its owners.
Between two mutually exclusive projects, the project with higher IRR is selected since
IRR is a measure of the return of investment.
Advantages: It eliminates the need to determine or argue about appropriate discount rate; its
rankings cannot be manipulated by choice of discount rate.
Limitation: It uses the same discount rate throughout the project.
Note: For most projects NPV and IRR will generate the same accept-reject decision.
3.3. Profitability Index
Profitability index is the sum of the present values of all future cash flows (discounted at the
cost of capital) divided by initial cash investment. If greater than 1.0 the project may be
accepted, less than 1.0 rejected. Between two mutually exclusive projects the project with the
highest profitability index is selected.
PV (£) Initial investment (£) Profitability index
Project A 1,000 500 2.0
Project B 1,800 1,000 1.8
According to profitability index project A is to be preferred.
Advantages of financial assessment methods
Undiscounted models simple to use and understand.
All use readily available accounting data to determine cash flows.
Model output is in terms familiar to business decision makers.
Model outputs mainly on ‘absolute’ profit - profitability scale and allow ‘absolute go/no-
Some profit models account for project risk.
Disadvantages of financial assessment methods
Models ignore all non-monetary factors except risk.
Some models (which do not include discounting) ignore timing of cash flows and time
value of money.
Models that reduce cash flows to their present value are strongly biased towards the short
Payback type models ignore cash flows beyond the payback period.
All models are sensitive to errors in input data for the early years of the project.
All discounting models are nonlinear, and the effects of changes or errors in the variables
or parameters are generally not obvious to most decision makers.
Which methods are used in practice?
Survey research has shown that payback period is the most frequently used techniques in UK
but discounted cash flow methods are found more commonly in the US. It is also found that
organisations will use more than one method of capital budgeting. The popularity of
discounted cash flow techniques is growing. Where discounting methods are used internal
rate of return appears more popular than the superior net present value; managers find IRR
easier to understand.
Use multiple criteria to evaluate a project.
1. Unweighted 0-1 factor model
A set of relevant factors is selected by management and projects are scored on each factor by
‘raters’ selected by senior management and ratings are then compared between projects, eg:
Factor Qualifies Does not
No increase in input energy requirements x
Potential market size (£) x
Potential market share (%) x
No requirement for new facilities x
No requirement for new technical expertise x
No decrease in the quality of the final product x
No new personnel required to manage the project x
No need for overall reorganisation x
Impact on workforce safety x
Impact on environmental standards x
Time to break even x
Need to employ external consultants x
The outcome will be consistent with current production x
Impact on company image with customers x
Impact on company image with the industry x
Totals 11 5
Advantage: Several criteria used in decision process.
Disadvantage: Assumes that all criteria are of equal importance
2. Unweighted factor scoring model
Marks are replaced by numbers on a scale (1-5 is usually adopted). E.g. 5 could be ‘very
good’, 4 ‘good’, 3 ‘fair’, 2 ‘poor’, 1 ‘very poor’. Scores are summed and either projects with
scores above a certain value can be selected or a certain number having the highest scores can
be chosen (depending on budget), eg:
Profitability Time to Development Commercial
Market risks success
Score 3 2 1 3 2 1 3 2 1 3 2 1 score
Project A X X X X 10
Project B X X X X 6
Project C X X X X 8
An alternative means of displaying the information above is the multidimensional diagram
known as polar graph in Figure 2.4 below.
Disadvantage: Assumes that all criteria of equal importance.
3. Weighted factor scoring model
This adds numeric weights which reflect the relative importance of each individual factor.
iji wsS ∑=
where: Si = total score of project i
sij= score of project i on criterionjth
wj = weight of jth criterion
Additional criteria might enter model as constraints (Constrained weighted factor scoring
Figure 2.4. Polar graph illustrating scoring model.
Relative Excellent Good Fair Poor
Criteria weight 30 20 10 0 score
Marketability 0.20 X 6
Risk 0.20 X 4
Competition 0.15 X 3
Value added 0.15 X 0
Technical opportunities 0.10 X 3
Material availability 0.10 X 1
Patent protection 0.05 X 0
Current products 0.05 X 1
Advantages of scoring models
Allow multiple criteria to be used for evaluation and decision, including financial models
and both tangible and intangible criteria.
Relatively simple and easy to understand and use.
A direct reflection of managerial policy.
Easily altered to accommodate changes in environment or managerial policy.
Weighted scoring models take into account that some factors more important than others.
Allow easy sensitivity analysis. Trade-offs readily observable.
Output is a strictly relative measure. Scores do not represent value or 'utility' associated
with the project and do not clearly indicate whether or not the project should be supported.
Scoring models are linear and the elements of such models assumed independent - not
always strictly true.
Un-weighted scoring models assume that all criteria of equal importance which is almost
certainly never the case.
Due to simplicity, it is easy to introduce a large number of criteria, most of which might
have very little impact on the total project score.
Advantages of scoring models over financial models
Allow multiple objectives of all organisations to be reflected in decision of acceptance or
More easily adapted to changes in managerial philosophy or changes in environment.
Do not suffer from bias towards short run that is inherent in profit models that discount
future cash flows.
RISK & UNCERTAINTY-PROJECT RISK MANAGEMENT
An organisation may wish to evaluate a project about which there is little information
available (e.g. research and development). Often no uncertainty about whether a product, a
process, or service can be developed but considerable uncertainty about when it will be
developed and at what cost.
In all projects, time and cost are often uncertain. There are three distinct areas of uncertainty
when an organisation undertakes a project in which it has little or no experience:
• Uncertainty about the timing of project and the cash flows expected to be generated.
• Uncertainty about the direct outcomes; what the project will actually accomplish.
• Uncertainty about the side effects of the project; its unforeseen consequences.
A distinction is often drawn by decision theorists between risk and uncertainty.
Risk is applied to a situation where there are several possible outcomes and there is relevant
past experience to enable statistical evidence to be produced for predicting the possible
Uncertainty exists where there are several possible outcomes but there is little previous
statistical evidence to enable the possible outcomes to be predicted.
Distinction often of little importance and terms used interchangeably.
Project risk management includes the processes concerned with identifying, analysing and
responding to risk. Risk identification and risk quantification are treated as a single process
and called risk analysis or risk assessment whereas risk response development and control
are often called risk management.
This focuses the decision maker’s attention on understanding the nature and extent of
uncertainty associated with some variables used in the decision-making process. It
incorporates uncertainty in decision input data. Traditional methods to quantify risk include
standard deviations and probability distributions, simulation and sensitivity analysis.
Probability distributions are usually determined for each of uncertain variables (i.e. on rate of
return and future cash flows) plus variability of estimates as measured by the standard
deviation are obtained. Probabilistic information is usually obtained by simulation
Suppose you have a choice of 2 projects both of which require the same initial investment,
have identical NPVs and require the same yearly cash flows to break even. If the cash inflow
of the first alternative has a probability of occurrence of 95% and that of the second 70% then
risk analysis would indicate that the first investment is better. In capital budgeting risk
analysis is almost entirely based on how well we can predict cash inflows since the initial
investment is usually known with some degree of certainty. Sensitivity analysis is a simple
way of assessing risk; it enables managers to assess how responsive the NPV is to changes in
the variables used to calculate it. The common approach is to estimate NPV based on
optimistic, most likely and pessimistic approach. The project with smallest range of NPV is
less risky. A risk avoider will choose this whereas a risk lover will go for the highest
Avoidance-eliminate risk event
Mitigation-reduce the expected value of a risk event by reducing the probability of
occurrence (e.g. using proven technology), reducing the risk event value (e.g. buying
Acceptance-accepting the consequences actively (e.g. by developing contingency plan) or
passively (e.g. by accepting lower profit if activities overrun).
Decision making under uncertainty
Probabilities cannot be assigned so decision making criteria is used that reflect how the
decision maker arrives at the decision, including maximax, maximin, minimax regret,
Hurwicz and equal likelihood.
The criteria reflect different degrees of conservatism or liberalism of decision maker, or the
risk he wishes to incur.
Payoff tables are used to facilitate decision analysis; they are a means of organising and
illustrating the payoffs from different decisions given various states of nature. Payoff is the
outcome of the decision typically expressed in terms of profit, revenues or cost.
Table 1. Payoff Table.
STATES OF NATURE
Decision a b
1 Payoff 1a Payoff 1b
2 Payoff 2a Payoff 2b
The decision - making criteria are illustrated with the following example:
A company is contemplating the future of one of its major plants. Three alternative decisions
are being considered: 1. to expand the plant, 2. to maintain the status quo in the plant 3. to
sell the plant now. The amount of profit that could be earned depends on foreign market
conditions. The following payoff table describes the decision situation:
STATES OF NATURE
Decision Good foreign competitive
Poor foreign competitive
1. expand £800,000 £500,000
2. maintain the status quo £1,300,000 £-150,000
3. sell now £320,000 £320,000
1. Maximax criterion (go-for-broke strategy): The decision maker selects the decision that
results in the maximum of the maximum payoffs (maximum of the maxima). It is very
optimistic and the decision maker assumes that the most favourable state of nature for
each decision alternative will occur. In this example the company will assume that good
competitive conditions will prevail which will result in the following maximum payoffs:
status quo: 1,300,000 <- maximum
Decision: maintain status quo
2. Maximin: (pessimistic),: Concerned with how much we can afford to lose. The decision
maker selects the decision that reflects the maximum of the minimum payoffs. For each
decision alternative the decision maker assumes that the minimum payoff will occur and
the maximum is selected as follows:
expand: 500,000<- maximum
status quo: -150,000
3. Minimax regret: Assumes that project manager is a sore loser; he attempts to avoid regret
by selecting the alternative that minimises the maximum regret. The regret for each
decision is calculated by selecting the maximum payoff under each state of nature and
subtracting all other payoffs from these:
STATES OF NATURE
Good competitive conditions Poor competitive conditions
£1,300,000 - 800,000 = 500,000 500,000 - 500,000 = 0
£1,300,000 -1,300,000 = 0 500,000 – (-150,000) = 650,000
£1,300,000- 320,000 = 980,000 500,000 - 320,000 = 180,000
The above values represent the regret experienced if a decision was made that resulted in
less than the maximum payoff. Under this criterion, firstly the maximum regret for each
decision is determined and the decision corresponding to the minimum of these regret
values is selected:
expand: 500,000<- minimum
status quo: 650,000
4. Hurwicz criterion: This is a compromise between maximax and maximin; decision payoffs
are weighted by a coefficient of optimism (a) which is a measure of the decision maker’s
optimism ranging from 0 (pessimistic) to 1 (optimistic). For each decision alternative the
maximum payoff is multiplied by (a) and the minimum payoff by (1-a).
For example, if (a) = 0.3 (then (1-a) = 0.7):
expand: 800,000 x 0.3 + 500,000 x 0.7 = 590,000 <- maximum
status quo: 1,300,000 x 0.3 –150,000 x 0.7 = 285,000
sell: 320,000 x 0.3 + 320,000 x 0.7 = 320,000
5. Equal likelihood criterion (or Laplace): This attempts to transform the decision making
under uncertainty to decision making under risk. Each state of nature is weighted equally,
assuming that the states of nature are equally likely to occur. Since there are two states of
nature a probability or weight of 0.5 is assigned to each one. Payoffs are multiplied by
these weights and the maximum of the weight values is selected:
expand: 800,000 x 0.5 + 500,000 x 0.5 = 650,000 <- maximum
status quo: 1,300,000 x 0.5–150,000 x 0.5 = 575,000
sell: 320,000 x 0.5 + 320,000 x 0.5 = 320,000
The decision to expand is designated more often in this example; however the use of several
criteria often results in a mix of decisions. The criterion selected depends on philosophy of
Decision making under conditions of risk
This is when the decision maker knows enough about the future states of nature and he can
assign probabilities to their occurrence.
In that case the expected value for each decision is calculated by multiplying each outcome
by the probability of its occurrence and then summing these products:
i xxpxEV )()( ∑=
where xi is the outcome i and p(xi) the probability of outcome i. In the example above if the
probability that good market conditions will exist is 0.7 and of poor conditions 0.3 then the
best decision using expected value will be:
EV (expand): 800,000 x 0.7 + 500,000 x 0.3 = 710,000
EV (status quo): 1,300,000 x 0.7 – 150,000 x 0.3 = 865,000 <- maximum
EV (sell): 320,000 x 0.7 + 3320,000 x 0.3 = 320,000
Decision : maintain because it has the highest expected value
The same methodology is followed in decision trees discussed below.
Expected value of perfect information (EVPI): Is the maximum value of perfect information
to the decision maker. It represents the maximum amount of money the decision maker is
willing to pay to acquire additional information about future events e.g. by hiring an
economic forecaster/consultant to determine more accurately the economic conditions that
will occur in the future.
EVPI= EV given perfect information – EV without perfect information.
If perfect information could be obtained, ie to tell us which state of nature was going to occur
then the best decision for that state of nature would be selected. For example, if the company
executives knew that good competitive conditions will prevail then they would maintain the
status quo, if poor they would expand. The probabilities indicate that good competitive
conditions will prevail 70% of the time and poor 30% and thus the expected value with
perfect information would be:
1,300,000 x 0.7 + 500,000 x 0.3 = 1,060,000.
The expected value without perfect information calculated earlier is 865,000 and therefore:
Decision trees: These are also known as decision flow diagrams and decision diagrams; They
are a powerful means of depicting and facilitating the analysis of problems that require
sequential decisions and variable outcomes over time- the payoff table cannot be used in such
A decision tree is a graphical method of expressing in chronological order alternative actions
that are available to the decision maker and the outcomes (payoffs) determined by chance
(states of nature). They are composed of the following elements:
Decision nodes: designated by a square; the decision maker must select one alternative
course of action from a finite set of possibilities drawn as branches emanating from the right
side of the square (see figure below).
Event or chance nodes: designated as a circle, indicates a random event, one of a finite
number of states of nature; a situation over which the decision maker has no control. States
of nature are shown as branches to the right of the event node.
Figure 2.5. Segments of a tree
Constructing and solving a tree: A tree is constructed starting from left of page with decision
nodes and all possible alternatives branching out to the right. Event nodes or a second
decision node is added. Each time an event node is added the appropriate states of nature
together with probabilities emanate rightward from it. The process continues from left to
right until the final payoffs are reached. The solution process starts from the right side of the
tree, with the segments ending in the final payoffs and continues to the left segment by
segment in reverse order from which it was drawn (‘rollback’ procedure). In event nodes, the
EV of all emerging states of nature are calculated by multiplying payoffs by probabilities and
summing the results, the EV is written above the node and considered as payoff for the
branch to the left. In decision nodes the payoffs for each alternative are compared and the
best one is selected.
Example: A company is considering whether to develop and market a new product.
Development costs are estimated to be £180,000 and there is 0.75 probability that the
development effort will be successful and a 0.25 probability that the development effort will
be unsuccessful. If the development is successful, the product will be marketed and it is
1. If the product is very successful profits will be £540,000.
2. If the product is moderately successful profits will be £100,000.
3. If the product is a failure there will be a loss of 400,000.
Each of the above profit and loss calculations is after taking into account the development
costs of £180,000. The estimated probabilities of each of the above events are as follows:
very successful 0.4, moderately successful 0.3 and failure 0.3.
Figure 2.6. Decision tree for example above.
This is the documentation required to evaluate a project being considered. A set of
documents submitted for evaluation called the ‘project proposal’. Important issues
considered when preparing the proposal are:
• Which projects should be put forward for a bid.
• How much should be spent on preparing the proposal.
• How should the bid prices be set? (What is bidding strategy?)
These decisions are usually made on basis of their overall expected values (as reflected in a
Proposals made to outside organisation are usually far more extensive than for inside the
All proposals should begin with a short summary (Executive Summary) covering the nature
of the project in a non-technical language and the benefits expected from its implementation.
Four distinct issues should be covered by any proposal:
a) Technical approach
The proposal begins with general description of problem. If the problem is complex, major
subsystems are noted together with company’s approach to each. The general method of
resolving specific problems should be outlined. With several subsystems proposed, the
method of interfacing them should be stated. The client’s requirements are listed with
proposed ways of meeting these. All test and inspection procedures (to assure performance,
quality, reliability, and compliance with specification) are noted.
Do not develop
v. successful (0.4)
m. successful (0.3)
b) Implementation Plan
The implementation plan contains estimates of time required, cost and materials to be used.
Each major subsystem of project should be listed plus estimates of its cost. The costs are
aggregated for the whole project. Hours of work and quantities of materials to be used are
noted plus wage rates and unit material costs. All equipment costs plus overhead and
administrative costs should be added.
Time charts, Gantt charts or critical path charts (as necessary) should be given for all
subsystems and the whole project. Major milestones should be indicated on the time charts.
Load charts should be prepared for any facility which might be critical. Personnel, equipment
and resource usage should be estimated on a period by period basis to ensure resource
constraints not violated.
c) Planning for logistical and administrative support
The proposal should include description of the ability to supply routine facilities, equipment
and skills. It should indicate how the project is to be administered. Timing of progress
reports, budgetary reports, audits and evaluations should stated. The form of the final report
should be stated. The procedure for terminating the project should be described with an
iIndication of how personnel, equipment and materials are to be deployed.
d) Past Experience
It is advisable to list past experiences of members of group plus titles and qualifications.
Shtub et al, Project Management, Prentice Hall
Kerzner Project Management, 6th
edition, John Wiley.
Meredith and Mantel, Project Management, 3rd
edition, John Wiley.
PMI, The implementation of Project Management: The professional’s handbook, Addison
Drury, Management Accounting.