Risk analysis in capital bugeting

Financial Management Unit 9

Unit 9 Risk Analysis in Capital Budgeting

Structure

9.1 Introduction
9.2 Types and sources of Risk in capital Budgeting
9.3 Risk Adjusted Discount Rate
9.4 Certainty Equivalent
9.5 Sensitivity Analysis
9.6 Probability Distribution Approach:
9.7 Decision – tree approach
9.8 Summary:
Terminal Questions
Answer to SAQs and TQs

9.1 Introduction
In the previous chapter on capital budgeting the project appraisal techniques were applied on the
assumption that the project will generate a given set of cash flows.
It is quite obvious that one of the limitations of DCF techniques is the difficulty in estimating cash
flows with certain degree of certainty.  Certain projects when taken up by the firm will change the
business risk complexion of the firm.
This business risk complexion of the firm influences the required rate of return of the investors.
Suppliers of capital to the firm tend to be risk averse and the acceptance of a project that changes
the risk profile of the firm may change their perception of required rates of return for investing in
firm’s project.
Generally the projects that generate high returns are risky.  This will naturally alter the business
risk of the firm. Because of this high risk perception associated with the new project a firm is
forced to asses the impact of the risk on the firm’s cash flows and the discount factor to be
employed in the process of evaluation.
Definition of Risk:  Risk may be defined as the variation of actual cash flows from the expected
cash flows.  The term risk in capital budgeting decisions may be defined as the variability that is
likely to occur in future between the estimated and the actual returns.  Risk exists on account of
the inability of the firm to make perfect forecasts of cash flows.

Sikkim Manipal University 147


Risk arises in project evaluation because the firm cannot predict the occurrence of possible future
events with certainty and hence, cannot make any correct forecast about the cash flows. The
uncertain economic conditions are the sources of uncertainty in the cash flows.
For example, a company wants to produce and market a new product to their prospective
customers.  The demand is affected by the general economic conditions.  Demand may be very
high if the country experiences higher economic growth.  On the other hand economic events like
weakening of US dollar, sub prime crises may trigger economic slow down.  This may create a
pessimistic demand drastically bringing down the estimate of cash flows.
Risk is associated with the variability of future returns of a project.  The greater the variability of
the expected returns, the riskier the project.
Every business decision involves risk.  Risk arises out of the uncertain conditions under which a
firm has to operate its activities. Because of the inability of firms to forecast accurately cash flows
of future operations the firms face the risks of operations. The capital budgeting proposals are
not based on perfect forecast of costs and revenues because the assumptions about the future
behaviour of costs and revenue may change.  Decisions have to be made in advance assuming
certain future economic conditions.
There are Many factors that affect forecasts of investment, cost and revenue.
1) The business is affected by changes in political situations, monetary policies, taxation, interest
rates, policies of the central bank of the country on lending by banks etc.
2) Industry specific factors influence the demand for the products of the industry to which the
firm belongs.
3) Company specific factors like change in management, wage negotiations with the workers,
strikes or lockouts affect company’s cost and revenue positions.
Therefore, risk analysis in capital budgeting is part and parcel of enterprise risk management.
The best business decisions may not yield the desired results because the uncertain conditions
likely to emerge in future can materially alter the fortunes of the company.
Every change gives birth to new challenges. New challenges are the source of new
opportunities.  A proactive firm will convert every problem into successful enterprise opportunities.
A firm which avoids new opportunities for the inherent risk associated with it, will stagnate and
degenerate.  Successful firms have empirical history of successful management of risks.
Therefore, analysing the risks of the project to reduce the element of uncertainty in execution has
become an essential aspect of today’s corporate project management.



Learning Objectives:

After studying this unit, you should be able to understand the following.
1. Define risk in capital budgeting.
2. Examine the importance of risk analysis in capital budgeting.
3. Methods of incorporating the risk factor in capital budgeting decision.
4. Understand the types and sources of risk in capital budgeting descision

9.2 Types and sources of Risk in capital Budgeting
Risks in a project are many.  It is possible to identify three separate and distinct types of risk in
any project.
1) Stand – alone risk:  it is measured by the variability of expected returns of the project.
2) Portfolio risk: A firm can be viewed as portfolio of projects having as certain degree of risk.
When new project added to the existing portfolio of project the risk profile the firm will alter.
The degree of the change in the risk depend on the covariance of return from the new project
and the return from the existing portfolio of the projects. If the return from the new project is
negatively correlated with the return from portfolio, the risk of the firm will be further diversified
away.
3) Market or beta risk:  It is measured by the effect of the project on the beta of the firm.  The
market risk for a project is difficult to estimate.
Stand alone risk is the risk of a project when the project is considered in isolation.  Corporate
risk is the projects risks to the risk of the firm.  Market risk is systematic risk.  The market risk
is the most important risk because of the direct influence it has on stock prices.
Sources of risk:  The sources of risks are
1. Project – specific risk
2. Competitive or Competition risk
3. Industry – specific risk
4. International risk
5. Market risk
1. Project – specific risk:  The sources of this risk could be traced to something quite specific
to the project. Managerial deficiencies or error in estimation of cash flows or discount rate
may lead to a situation of actual cash flows realised being less than that projected.
2. Competitive risk or Competition risk: unanticipated actions of a firm’s competitors will
materially affect the cash flows expected from a project. Because of this the actual cash
flows from a project will be less than that of the forecast.



3. Industry – specific:  industry – specific risks are those that affect all the firms in the industry.
It could be again grouped into technological risk, commodity risk and legal risk.  All these risks
will affect the earnings and cash flows of the project.  The changes in technology affect all the
firms not capable of adapting themselves to emerging new technology.
The best example is the case of firms manufacturing motor cycles with two strokes engines.
When technological innovations replaced the two stroke engines by the four stroke engines those
firms which could not adapt to new technology had to shut down their operations.
Commodity risk is the risk arising from the effect of price – changes on goods produced and
marketed.
Legal risk arises from changes in laws and regulations applicable to the industry to which the firm
belongs.  The best example is the imposition of service tax on apartments by the Government of
India when the total number of apartments built by a firm engaged in that industry exceeds a
prescribed limit.  Similarly changes in Import – Export policy of the Government of India have led
to the closure of some firms or sickness of some firms.
4. International Risk: these types of risks are faced by firms whose business consists mainly
of exports or those who procure their main raw material from international markets. For
example, rupee – dollar crisis affected the software and BPOs because it drastically reduced
their profitability. Another best example is that of the textile units in Tirupur in Tamilnadu,
exporting their major part of the garments produced. Rupee gaining and dollar Weakening
reduced their competitiveness in the global markets. The surging Crude oil prices coupled
with the governments delay in taking decision on pricing of petro products eroded the
profitability of oil marketing Companies in public sector like Hindustan Petroleum Corporation
Limited.  Another example is the impact of US sub prime crisis on certain segments of Indian
economy.
The changes in international political scenario also affect the operations of certain firms.
5. Market Risk: Factors like inflation, changes in interest rates, and changing general economic
conditions affect all firms and all industries.
Firms cannot diversify this risk in the normal course of business.
Techniques used for incorporation of risk factor in capital budgeting decisions
There are many techniques of incorporation of risk perceived in the evaluation of capital
budgeting proposals. They differ in their approach and methodology so far as incorporation of
risk in the evaluation process is concerned.
Conventional techniques
Pay Back Period



The oldest and commonly used method of recognising risk associated with a capital budgeting
proposal is pay back period.  Under this method, shorter pay back period is given preference to
longer ones. Firms establish guidelines for acceptance or rejections of projects based on
standards of pay back periods.
Payback period prefers projects of short – term pay backs to that of long – term pay backs.  The
emphasis is on the liquidity of the firm through recovery of capital.  Traditionally Indian business
community employs this technique in evaluating projects with very high level of uncertainty. The
changing trends in fashion make the fashion business, one of high risk and therefore, pay back
period has been endorsed by tradition in India to take decisions on acceptance or rejection of
such projects.  The usual risk in business is more concerned with the fore cast of cash flows.  It is
the down side risk of lower cash flows arising from lower sales and higher costs of operation that
matters in formulating standards of pay back.
Pay back period ignores time value of many (cash flows).  For example, the following details are
available in respect of two projects.

Particulars Project A (Rs) Project B (Rs)
Initial cash outlay 10 lakhs 10 lakhs
Cash flows
Year 1 5 lakhs 2 lakhs

Both the projects have a pay back period of 4 years.  The project B is riskier than the Project A
because Project A recovers 80% of initial cash outlay in the first two years of its operation where
as Project B generates higher Cash inflows only in the latter half of the payback period. This
undermines the utility of payback period as a technique of incorporating risk in project evaluation.
This method considers only time related risks and ignores all other risks of the project under
consideration.

Self Assessment Questions 2
1. _____________ is measured by the variability of expected returns of the project.
2. Market risk is measured by the effect of the project on the ____ of the firm.
3. Firms cannot ____ market risk in the normal course of business.
4. Impact of U.S sub prime crisis on certain segments of Indian economy is and example of
_______________________.



9.3 Risk Adjusted Discount Rate
The basis of this approach is that there should be adequate reward in the form of return to firms
which decide to execute risky business projects. Man by nature is riskaverse and tries to avoid
risk. To motivate firms to take up risky projects returns expected from the project shall have to be
adequate, keeping in view the expectations of the investors. Therefore risk premium need to be
incorporated in discount rate in the evaluation of risky project proposals.
Therefore the discount rate for appraisal of projects has two components.
Those components are
1. Risk – free rate and risk premium
Risk Adjusted Discount rate = Risk free rate + Risk premium
Risk free rate is computed based on the return on government securities.
Risk premium is the additional return that investors require as compensation for assuming the
additional risk associated with the project to be taken up for execution.
The more uncertain the returns of the project the higher the risk. Higher the risk greater the
premium. Therefore, risk adjusted Discount rate is a composite rate of risk free rate and risk
premium of the project.
Example: An investment will have an initial outlay of Rs 100,000. It is expected to generate cash
inflows as under:
Year Cash in flows
1 40,000
2 50,000
3 15,000
4 30,000

Risk free rate of interest is 10%. Risk premium is 10% (the risk characterising the project)
(a) compute the NPV using risk free rate
(b) Compute NPV using risk – adjusted discount rate
Solutions = (a) using risk – free rate

Year Cash flows (inflows) Rs PV Factor at 10% PV of Cash flows (in flows)
1 40,000 0.909 36,360
2 50,000 0.826 41,300
3 15,000 0.751 11,265
4 30,000 0.683 20,490
PV of cash in flows 1,09,415



PV of Cash outflows 1,00,000
NPV 9,415

(b) Using risk – adjusted discount rate
Year Cash in flows Rs PV factor at 20% PV of cash inflows
1 40,000 0.833 33,320
2 50,000 0.694 34,700
3 15,000 0.579 8,685
4 30,000 0.482 14,460
PV of Cash in flows 91,165
PV of Cash out flows 100,000
NPV (8,835)

The project would be acceptable when no allowance is made for risk.
But it will not be acceptable if risk premium is added to the risk free rate. It moves from positive
NPV to negative NPV.
If the firm were to use the internal rate of return, then the project would be accepted when IRR is
greater than the risk – adjusted discount rate.
Evaluation of Risk – adjusted discount rate:
Advantages:
1. It is simple and easy to understand.
2. Risk premium takes care of the risk element in future cash flows.
3. It satisfies the businessmen who are risk – averse.

Limitations:
1. There are no objective bases of arriving at the risk premium. In this process the premium
rates computed become arbitrary.
2. The assumption that investors are risk – averse may not be true in respect of certain investors
who are willing to take risks. To such investors, as the level of risk increases, the discount
rate would be reduced.
3. Cash flows are not adapted to incorporate the risk adjustment for net cash in flows.


1. Risk premium is the __________________ that the investors require as compensation for



assumption of additional risks of project.
2. RADR is the sum of ______________ and ______________.
3. Higher the risk __________________ the premium.
4. Man by nature is riskaverse and tries to avoid risk.

9.4 Certainty Equivalent:
Under this method the risking uncertain, expected future cash flows are converted into cash flows
with certainty. Here we multiply uncertain future cash flows by the certainty – equivalent
coefficient to convert uncertain cash flows into certain cash flows. The certainty equivalent
coefficient is also known as the risk – adjustment factor. Risk adjustment factor is normally
denoted by αt (Alpha).  It is the ratio of certain net cash flow to risky net cash flow
= Certainty Equivalent = Certain Cash flow
Risky Cash flow

The discount factor to be used is the risk free rate of interest.  Certainty equivalent coefficient is
between 0 and 1.  This risk – adjustment factor varies inversely with risk.  If risk is high a lower
value is used for risk adjustment.  If risk is low a higher coefficient of certainty equivalent is used

Illustration (Example)
A project costs Rs 50,000.  It is expected to generate cash inflows as under
Year Cash in flows Certainty Equivalent
1 32,000 0.9
2 27,000 0.6
3 20,000 0.5
4 10,000 0.3

Risk – free discount rate is 10% compute NPV
Answer:
Year Uncertain cash C E Certain cash PV Factor at PV of certain cash
in flows flows 10% inflows
1 32,000 0.9 28,800 0.909 26,179
2 27,000 0.6 16,200 0.826 13,381
3 20,000 0.5 10,000 0.751 7,510
4 10,000 0.3 3,000 0.683 2,049



PV of certain cash in 49,119
flows
Initial cash out lay 50,000
NPV (881) negative

The project has a negative NPV.
Therefore, it is rejected.

If IRR is used the rate of discount at which NPV is equal to zero is computed and then compared
with the minimum (required) risk free rate.  If IRR is greater than specified minimum risk free rate,
the project is accepted, other wise rejected.

Evaluation:
It recognises risk.  Recognition of risk by risk – adjustment factor facilitates the conversion of risky
cash flows into certain cash flows.  But there are chances of being inconsistent in the procedure
employed from one project to another.
When forecasts pass through many layers of management, original forecasts may become highly
conservative.
Because of high conservation in this process only good projects are likely to be cleared when this
method is employed.
Certainty – equivalent approach is considered to be theoretically superior to the risk – adjusted
discount rate.
1. CE coefficient is the _______ .
2. Discount factors to be used under CE approach is _____________.
3. Because of high ______________ CE clears only good projects.
4. ___________ is considered to be superior to RADR
9.5 Sensitivity Analysis:
There are many variables like sales, cost of sales, investments, tax rates etc which affect the
NPV and IRR of a project. Analysing the change in the project’s NPV or IRR on account of a
given change in one of the variables is called Sensitivity Analysis.  It is a technique that shows the
change in NPV given a change in one of the variables that determine cash flows of a project.  It
measures the sensitivity of NPV of a project in respect to a change in one of the input variables of
NPV.



The reliability of the NPV depends on the reliability of cash flows. If fore casts go wrong on
account of changes in assumed economic environments, reliability of NPV & IRR is lost.
Therefore, forecasts are made under different economic conditions viz pessimistic, expected and
optimistic. NPV is arrived at for all the three assumptions.
Following steps are involved in Sensitivity analysis:
1. Identification of variables that influence the NPV & IRR of the project.
2. Examining and defining the mathematical relationship between the variables.
3. Analysis of the effect of the change in each of the variables on the NPV of the project.

Example: A company has two mutually exclusive projects under consideration viz project A &
project B.
Each project requires an initial cash outlay of Rs 3,00,000 and has an effective life of 10 years.
The company’s cost of capital is 12%. The following fore cast of cash flows are made by the
management.

Economic Project A Project B
Environment Annual cash inflows Annual cash in flows
Pessimistic 65,000 25,000
Expected 75,000 75,000
Optimistic 90,000 1,00,000

What is the NPV of the project?
Which project should the management consider?
Given PVIFA = 5.650
Answer / Solutions
NPV of project A

Economic Project PVIFA PV of cash in flows NPV
Environment cash inflows at 12% 10
years
Pessimistic 65,000 5.650 3,67,250 67,250
Expected 75,000 5.650 4,23,750 1,23,750
Optimistic 90,000 5.650 5,08,500 2,08,500



NPV of Project B
Pessimistic 25,000 5.650 1,41,250 (1,58,750)
Expected 75,000 5.650 4,23,750 1,23,750
Optimistic 1,00,000 5.650 5,65,000 2,65,000

Decision
1. Under pessimistic conditions project A gives a positive NPV of Rs 67,250 and Project B has a
negative NPV of Rs 1,58,750 Project A is accepted.
2. Under expected conditions, both gave some positive NPV of Rs 1,23,000. Any one of two
may be accepted.
3. Under optimistic conditions Project B has a higher NPV of Rs 2,65,000 compared to that of
A’s NPV of Rs 2,08,500.
4. Difference between optimistic and pessimistic NPV for Project A is Rs 1,41,250 and for
Project B the difference is Rs 4,23,750.
5. Project B is risky compared to Project A because the NPV range is of large differences.
Statistical Techniques:
Statistical techniques use analytical tools for assessing risks of investments.


1. _____________ analysis the changes in the project NPV on account of a given change in one
of the input variables of the project.
2. Examining and defining the mathematical relation between the variable of the NPV is
_________________________.
3. Forecasts under sensitivity analysis are made under __________.

9.6 Probability Distribution Approach:
When we incorporate the chances of occurrences of various economic environments computed
NPV becomes more reliable. The chances of occurrences are expressed in the form of
probability. Probability is the likelihood of occurrence of a particular economic environment. After
assigning probabilities to future cash flows expected net present value is computed.

Illustration: A company has identified a project with an initial cash outlay of Rs 50,000. The
following distribution of cash flow is given below for the life of the project of 3 years.



Year 1 Year 2 Year 3
Cash in flow Probability Cash in flow Probability Cash in flow Probability
15,000 0.2 20,000 0.3 25,000 0.4
18,000 0.1 15,000 0.2 20,000 0.3
35,000 0.4 15,000 0.2 20,000 0.3
32,000 0.3 30,000 0.2 45,000 0.1

Discount rate is 10%
Year 1
= 15,000 x 0.2 + 18,000 x 0.1 + 35,000 x 0.4 + 32,000 x 0.300
3,000 + 1,800 + 14,000 + 9,600 = 28,400
Year 2
20,000 x 0.3 + 15,000 x 0.2 + 30,000 x 0.3 + 30,000 x 0.2
= 6,000 + 3,000 + 9,000 + 6,000 = 24,000
Year 3
25,000 x 0.4 + 20,000 x 0.3 + 40,000 x 0.2 + 5,000 x 0.1 =
10,000 + 6,000 + 8,000 + 4,500 == 28,500

PV of expected
Year Expected cash inflows PV factor at 10%
cash in flows
1 28,400 0.909 25,816
2 24,000 0.826 19,824
3 28,500 0.751 21,403
PV of expected cash in flows 67,043
PV of initial cash out lay 50,000
Expected NPV 17,043
Variance:
A study of dispersion of cash flows of projects will help the management in assessing the risk
associated with the investment proposal. Dispersion is computed by variance or standard
deviation. Variance measures the deviation of each possible cash flow from the expected.
Square root of variance is standard deviation.

Example: Following details are available in respect of a project which requires an initial cost of
Rs 5,00,000.



Year Economic Conditions Cash flows Probability
1 High growth 2,00,000 0.3
Average growth 1,50,000 0.6
No growth 40,000 0.1
2 High growth 3,00,00 0.3
No growth 5,00,000 0.2
3 High growth 4,00,000 0.2
No growth 30,000 0.2

Discount rate is 10%
Solution:
Year 1
Economic Condition Cash in flow Probability Expected value of Cash in flow
1 2 3
High growth 2,00,000 0.3 60,000
Average growth 1,50,000 0.6 90,000
No growth 40,000 0.1 4,000
Expected Value 1,54,000

Year 2
High growth 3,00,000 0.3 90,000
Average growth 2,00,000 0.5 1,00,000
No growth 50,000 0.2 10,000
Expected Value 2,00,000

Year 3
High growth 4,00,000 0.2 80,000
Average growth 2,50,000 0.6 1,50,000
No growth 30,000 0.2 6,000



Expected Value of 2,36,000
Cash inflows
1,54,000         2,00,000 2,36,000
Expected NPV = 1.10               (110)
+ 2 + (1.10)
3 5,00,000

= 1,40,000 + 1, 65, 289 + 1, 77, 310 – 5,00,000 = (17,401) negative NPV

Standard Deviation for I year

2 2
Cash in flow Expected Value (C – E) (C – E) x prob
C E
2 2
2,00,000 1,54,000 (46,000) (46,000) x 0.3 = 634800  000
2 2
1,50,000 1,54,000 ( 4000) ( 4,000) x 0.3 = 9600  000
2 2
40,000 1,54,000 ( 1,14,000) ( 1,14,000) x 0.3 = 12996 00 000
Total 1944  000 000

Standard deviation of Cash flows for I year = 44091
nd
For 2 year
2 2
C E
2 2
3,00,000 2,00,000 (1,00,000) (1,00,000) x 0.3 = 3000 000  000
2 2
2,00,000 2,00,000 (0) (0) x 0.5 = 0
2 2
50,000 2,00,000 ( 1,50,000) ( 1,50,000) x 0.2 = 45 00 000 000
Total 7500 00 000

nd
Variance of Cash flows for 2 year = 7500 000 000
nd
Standard Deviation of cash flows for 2 year = 8660
For the third year
2 2
C E
2 2
4,00,000 2,36,000 (1,64,000) (1,64,000) x 0.2 = 53792 00 000
2 2
2,50,000 2,36,000 (14,000) (14,000) x 0.6 = 1176 00 000
2 2
30,000 2,36,000 ( 2,00,000) ( 2,00,000) x 0.2 = 8000 000 000
Total 13496800 000



rd
Variance of Cash flows for 3 year = 13496800 000
rd
Standard Deviation of cash flows for 3 year = 116175
Standard Deviation of NPV

2 2 2
Ö(44091) (8660) (116175)
sNPV = 2 + 4 + 6
Ö(1.10) (1.10) (1.10)
= Ö1606625026 + 51223004 + 7618496131
= Ö9276344161
= 96314

Here the assumption is that there is no relationship between cash flows from one period to
another. Under this assumption the standard deviation of NPV is Rs 96,314.
On the other hand, if cash flows are perfectly correlated, cash flows of all years have
linear correlation to one another, then

44091                8660                116175
sNPV = + (1.10)
2 + (1.10)
3
1.10
= 40083 + 7157 + 87284 = 134524

The standard deviation of NPV when cash flows are perfectly correlated will be higher
than that under the situation of independent cash flows.
Self Assessment Questions. 5
1. Probability distribution approach incorporates the probability of occurrences of various
economic environment, to make the NPV ________.
2. _______ is likelihood of occurrence of a particular economic environment.

9.7 Decision – tree approach:
Many project decisions are complex investment decisions.  Such complex investment decisions
involve a sequence of decisions over time.  Decisions tree can handle the sequential decisions of
complex investment proposals. The decision of taking up an investment project is broken into
different stages.  At each stage the proposal is examined to decide whether to go ahead or not.
The multi – stages approach can be handled effectively with the help of decision trees. A
decision tree presents graphically the relationship between a present decision and future events,
future decisions and the consequences of such decisions.



Example
R & D section of a company has developed an electric moped.  The firm is ready for pilot
production and test marketing. This will cost Rs 20 million and take six months. Management
believes that there is a 70% chance that the pilot production and test marketing will be successful.
If successful the company can build a plant costing Rs 200 million.
The plant will generate annual cash in flow of Rs 50 million for 20 years if the demand is high or
an annual cash inflow or 20 million if the demand is low.

High demand has a probability of 0.6 and low demand has a probability of 0.4.  Cost of capital is
12%.
Suggest the optimal course of action using decision tree analysis (Bangalore University MBA,
adapted). High Demand
Probability 0.6
C21
D21 Investment Annual Cash inflow
Rs.200 million Rs.50 million
C2
D11 Carry out pilot
Production C11 Success Annual Cash inflow
And Market D2 Rs.20 million
test (20 million)
0.7 D22 Stop C22 Low Demand
C1 Probability 0.4

D D3
C12 failure D31 Stop
Probability 0.3

D12 Do Nothing

Working Notes:  From right hand side of the decision tree
I step: Computation of Expected Monetary Value at point C2. Here EMV represents expected
NPV.

Cash in flow Probability Expected value of cash inflows
50 0.6 30
20 0.4 8
EMV 38

Present Value of EMV = Expected value of cash inflow x PVIFA (12% 20)
38 x 7.469 = Rs 283.82 million



Step 2:
Computation of EMV at decision point D2.
Decision taken Consequences The resulting EMV at this level
D2 Invest Rs 200 million 283.82 – 200 83.82 million
D22 Stop 0
Here the decision criterion is “select the EMV with the highest value”.

Stage 3:
Therefore EMV with Rs 83.82 million will be considered therefore; we select the decision taken at
D2,
Stage 4:
Computation of EMV at the point C,
EMV Probability Expected Value
83.82 0.7 58.67
0 0.3 0
EMV at this stage 58.67

Step 5:
Compute EMV at decisions point D,
Decision taken Consequences The resulting Em at this
level
D11 carry out pilot Invest 58.67 – 20 = Rs 38.67 Million
production and market test 20 million
D12 Do nothing 0 0
EMV at this stage 38.67 Million
(Apply the EMV criterion) i.e
select the EMV with the
highest value

Therefore optimal strategy is
1. Carry out pilot production and market test.
2. If the result of pilot production and market test is successful, go ahead with the investment
decision of Rs 200 million in establishing a plant.
3. If the result of pilot production and market test is future, stop.



Evaluation of Decision tree approach:
1. It portrays inter – related, sequential and critical multi dimensional elements of major project
decisions.
2. Adequate attention is given to the critical aspects in an investment decision which spread over
a time sequence.
3. Complex projects involve huge out lay and hence risky. There is the need to define and
evaluate scientifically the complex managerial problems arising out of the sequence of
interrelated decisions with consequential outcomes of high risk.  It is effectively answered by
decision tree approach.
4. Structuring a complex project decision with many sequential investment decisions demands
effective project risk management.  This is possible only with the help of an analytical tool like
decision tree approach.
5. Able to eliminate unprofitable outcomes and helps in arriving at optimum decision stages in
time sequence.

1. Decision tree can handle the _____________ of complex investment proposals.
2. _____ portrays interrelated, sequential and critical multi dimensional elements of major project
decisions.
3. Adequate attention is given to the ______ in an investment decision under decision tree
approach’s.
4. ____________ are effectively handled by decision tree approach’s .

9.8 Summary
Risk in project evaluation arises on account of the inability of the firm to predict  the performance
of the firm with certainty. Risk in capital budgeting decision may be defined as the variability of
actual returns from the expected. There are many factors that affect forecasts of investment,
costs and revenues of a project. It is possible to identify three type of risk in any project, viz stand
alone risk, corporate risk and market risk. The sources of risks are:
a. Project
b. Competition
c. Industry
d. International factors and
e. Market



The techniques for incorporation of risk factor in capital budgeting decision could be grouped into
conventional techniques and statistical techniques.

Terminal Questions
1. Define risk. Examine the need for assessing the risks in a project.
2. Examine the type and sources of risk in capital budgeting .
3. Examine risk adjusted discount rate as a technique of incorporating risk factor in capital
budgeting.
4. Examine the steps involved in sensitivity analysis.
5. Examine the features of Decisiontree approaches.

Answer for Self Assessment Questions
1. Standalone risk.
2. Beta
3. Diversify
4. International risk

Self Assessment Question 2
1. Additional return
2. Risk free rate, risk premium.
3. Greater.

1. Risk adjustment factor
2. Risk free rate of interest.
3. Conservation.
4. CE

1. Sensitivity analysis
2. One of the steps of sensitivity analysis
3. Different economic conditions



1. More reliable
2. Probability

1. Sequential decisions
2. Decision tree.
3. Critical aspects
4. Complex projects.

Answer for Terminal Questions
1. Refer to units 9.1
2. Refer to units 9. 2
3. Refer to units 9.3
4. Refer to unit 9.5
5. Refer to unit 9.7


Risk analysis in capital bugeting

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