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Unit 9 Risk Analysis in Capital Budgeting
Structure:
9.1 Introduction
Learning objectives
9.2 Types and Sources of Risk in Capital Budgeting
Sources of risk
Conventional techniques
9.3 Risk Adjusted Discount Rate
Evaluation of risk adjusted discount rate
9.4 Certainty Equivalent
Evaluation of certainty equivalent
9.5 Sensitivity Analysis
9.6 Probability Distribution Approach
Variance
9.7 Decision Tree Approach
Evaluation of decision tree approach
9.8 Summary
9.9 Terminal Questions
9.10 Answers to SAQs and TQs
9.1 Introduction
Capital budgeting decisions typically involve forecasting the future operating
cash flows. Forecasting involves making certain assumptions about the
future behaviour of costs and revenues.
Such forecasting, however, suffers from uncertainty because the future is
highly uncertain. Assumptions made about the future behaviour of costs and
revenues may change and can significantly alter the fortunes of a company.
The process is thereby inherently risky.
Analysing the risks to reduce the element of uncertainty has therefore
become an essential aspect of today’s corporate project management.
This unit will help you understand the various types of risks involved in
capital budgeting decisions. In this unit, you will study how sensitivity
analysis is used to determine the most critical uncertainties in the
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estimation. You will also study the pitfalls of using uncertain single-point
estimates for the cash flows associated with the project.
This unit will help the capital budget decision-makers to avoid costly
mistakes.
9.1.1 Learning Objectives
After studying this unit, you should be able to:
Define risk in capital budgeting
Examine the importance of risk analysis in capital budgeting
Determine the methods of incorporating the risk factor in capital
budgeting decision
Understand the types and sources of risk in capital budgeting decision
9.1.2 Definition of Risk
Before we start to discuss about risk analysis in capital budgeting, let us first
understand what risk in capital budgeting means.
Risk in capital budgeting may be defined as the variation of actual cash
flows from the expected cash flows.
Every business decision involves risk. Risk exists on account of the inability
of a firm to make perfect forecasts of cash flows. The inability can be
attributed to factors that affect forecasts of investment, cost and revenue.
Some of these are as follows:
The business is affected by changes in political situations, monetary
policies, taxation, interest rates and policies of the central bank of the
country on lending by banks
Industry specific factors influence the demand for the products of the
industry to which the firm belongs
Company specific factors like change in management, wage negotiations
with the workers, strikes or lockouts affect company’s cost and revenue
positions
Let us see a case explaining why making a perfect forecast of cash flows is
difficult.
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9.2 Types and Sources of Risk in Capital Budgeting
Having understood what risk in capital budgeting means, let us now
understand the types of risk and their sources.
Capital budgeting involves four types of risks in a project – stand-alone risk,
portfolio risk, market risk and corporate risk (see figure 9.1)
Figure 9.1: Types of risks
Stand-alone risk
Stand alone risk of a project is considered when the project is in isolation.
Stand-alone risk is measured by the variability of expected returns of the
project.
Caselet
A company wants to produce and market a new product to their
prospective customers and 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 and sub-prime crises may trigger
economic slow-down. This may create a pessimistic demand drastically
bringing down the estimate of cash flows.
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Portfolio risk
A firm can be viewed as portfolio of projects having a certain degree of risk.
When new project is added to the existing portfolio of project, the risk profile
of the firm will alter. The degree of the change in the risk depends on:
The co-variance of return from the new project
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.
Market risk
Market risk is defined as the measure of the unpredictability of a given stock
value. However, market risk is also referred to as systematic risk. The
market risk has a direct influence on stock prices. Market risk is measured
by the effect of the project on the beta of the firm. The market risk for a
project is difficult to estimate.
Corporate risk
Corporate risk focuses on the analysis of the risk that might influence the
project in terms of entire cash flow of the firms. Corporate risk is the projects
risks of the firm.
9.2.1 Sources of risk
The five different sources of risk are:
Project – specific risk
Competitive or Competition risk
Industry – specific risk
International risk
Market risk
Project-specific risk
Project-specific 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 the projected.
Competitive or Competition risk
Unanticipated actions of a firm’s competitors will materially affect the cash
flows expected from a project. As a result of this, the actual cash flows from
a project will be less than that of the forecast.
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Industry-specific risk
Industry-specific risks are those that affect all the industrial firms. Industry-
specific risk 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.
Technological risk
The changes in technology affect all the firms not capable of adapting
themselves in emerging into a new technology.
Commodity risk
Commodity risk is the risk arising from the effect of price-changes on
goods produced and marketed.
Legal risk
Legal risk arises from changes in laws and regulations applicable to the
industry to which the firm belongs.
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.
Example
The best example is the case of firms manufacturing motor cycles
with two stroke 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.
Example
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.
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Let us now look at the firms facing such kind of risk:
The rupee-dollar crisis affected the software and BPOs because it
drastically reduced their profitability.
Another example is that of the textile units in Tirupur in Tamil Nadu,
which exports the 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 affected the operations
of certain firms.
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.
There are many techniques of incorporation of risk perceived in the
evaluation of capital budgeting proposals. They differ in their approach and
methodology as far as incorporation of risk in the evaluation process is
concerned.
9.2.2 Techniques for incorporation of risk factor in capital budgeting
The techniques for incorporation of risk factor in capital budgeting decisions
could be grouped into conventional and statistical techniques.
In this chapter, we are going to discuss mainly the conventional techniques
– pay-back period.
Pay-back period
The oldest and the most commonly used method of recognising risk
associated with a capital budgeting proposal is pay-back period. Pay-back
period is defined as the length of time required to recover the initial cash
out-lay. Pay-back period ignores time value of money (cash flows).
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Pay-back 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, makes the fashion business risky and
therefore, pay-back period has been endorsed as a tradition in India to take
decisions on acceptance or rejection of such projects.
The usual risk in business is more concerned with the forecast 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.
This method considers only time related risks and ignores all other risks of
the project under consideration.
Caselet -1
Table 9.1 gives the details related to two projects:
Table 9.1: Details of two projects
Particulars Project A (Rs.) Project B (Rs.)
Initial cash outlay 10lakhs 10 lakhs
Cash flows
Year 1 5 lakhs 2 akhs
Year 2 3 lakhs 2 lakhs
Year 3 1 lakh 3 lakhs
Year 4 1 lakh 3 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 whereas 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.
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9.3 Adjusted Discount Rate
The basic principle of risk adjusted discount rate is that there should be
adequate reward in the form of return to the firms which decide to execute
risky business projects. Man by nature is risk-averse 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 during the
evaluation of risky project proposals.
Risk adjusted discount rate is more briefly described as:
Risk free rate is computed based on the returns on government
securities.
Risk premium is the additional returns that the investors require for
assuming the additional risk associated with the project to be taken up
for execution.
The more the uncertainty in the returns of the project, higher is the risk.
Higher the risk, greater is the premium
Self Assessment Questions
Fill in the blanks:
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
the example of _______________________
Risk Adjusted Discount rate = Risk free rate + Risk premium
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Solved Problem -1
An investment will have an initial outlay of Rs 100,000. It is expected to
generate cash inflows as shown in table 9.2.
Table 9.2: Cash inflows
Year Cash in flows
1 40000
2 50000
3 15000
4 30000
If the risk free rate and the risk premium is 10%,
a) Compute the NPV using the risk free rate
b) Compute NPV using risk-adjusted discount rate
Solution
a) NPV can be computed using risk free rate from the table 9.3.
Table 9.3 NPV using Risk free rate
Year Cash flows (inflows) Rs.
PV factor at 10%
PV of cash flows (inflows)
1 40000 0.909 36,360
2 50000 0.826 41,300
3 15000 0.751 11,265
4 30000 0.683 20,490
PV of cash inflows
1,09,415
PV of cash outflows
(1,00,000)
NPV 9,415
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9.3.1 Evaluation of risk-adjusted discount rate
The advantages and limitations occurring during the evaluation of risk-
adjusted discount rate are listed as follows:
Risk adjusted discount rate is simple and easy to understand
Risk premium takes care of the risk element in future cash flows
Risk adjusted discount rate satisfies the businessmen who are risk –
averse
b) NPV can be computed using risk-adjusted discount from the
table 9.4.
Table 9.4: NPV using Risk-adjusted discount rate
Year Cash inflows Rs. PV factor at 20% PV of cash inflows
1
40000 0.833 33,320
2 50000 0.694 34,700
3 15000 0.579 8,685
4 30000 0.482 14,460
PV of Cash in flows 91,165
PV of cash outflows (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.
By doing so, it moves from positive NPV to negative NPV. If the firm
were to use the internal rate of return (IRR), then the project would be
accepted, when IRR is greater than the risk-adjusted discount rate.
Merits of risk adjusted discount rate
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There are no objective bases of arriving at the risk premium. In this
process the premium rates computed become arbitrary.
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
Cash flows are not adapted to incorporate the risk adjustment for net
cash inflows
9.4 Certainty Equivalent
Under the method of certainty equivalent, risking is found to be uncertain
and unexpected 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 α (Alpha). Risk
adjustment factor is the ratio of certain net cash flow to risky net cash flow.
Certainty equivalent = f lowCashRisky
flowCashCertain
Self Assessment Questions
Fill in the blanks:
5. Risk premium is the __________________ that the investors require as
compensation for assumption of additional risks of project.
6. RADR is the sum of ______________ and ______________.
7. Higher the risk __________________ the premium.
Demerits of risk adjusted discount rate
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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.
Solved Problem - 2
A project costs Rs. 50,000. It is expected to generate cash inflows as
shown in table 9.5.
Table 9.5: Generation of cash inflows
Year Cash inflows Certainty equivalent
1 32000 0.9
2 27000 0.6
3 20000 0.5
4 10000 0.3
If the risk free rate is 10%, compute NPV.
Solution
Table 9.6: Computation of NPV
Year Uncertain cash
inflows
CE Certain cash flows
PV factor at
10%
PV of certain cash
inflows
1 32000 0.9 28800 0.909 26179
2 27000 0.6 16200 0.826 13381
3 20000 0.5 10000 0.751 7510
4 10000 0.3 3000 0.683 2049
PV of certain cash inflows
49119
Initial cash out-lay
(50000)
NPV (881)
The project has negative NPV, therefore it is rejected.
If internal rate of return (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
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IRR is greater than specified minimum risk free rate, the project is accepted,
otherwise rejected.
9.4.1 Evaluation of certainty equivalent
Evaluation of certainty equivalent 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 inconsistency in the procedure
employed from one project to another.
When forecasts pass through many layers of management, original
forecasts may become highly conservative. Due to high conservation in this
process, 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.
9.5 Sensitivity Analysis
There are many variables like sales, cost of sales, investments and tax rates
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.
Sensitivity analysis 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 forecasts go
wrong on account of changes in assumed economic environments, reliability of NPV
& IRR is lost. Therefore, forecasts are made under different economic conditions
like pessimistic, expected and optimistic. NPV is arrived at for all the three
assumptions.
Following steps are involved in sensitivity analysis:
Self Assessment Questions
Fill in the blanks:
8. CE coefficient is the _______ .
9. Discount factor to be used under CE approach is _________.
10. Because of high ______________ CE clears only good projects.
11. ___________ is considered to be superior to RADR.
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Identification of variables that influence the NPV & IRR of the project.
Examining and defining the mathematical relationship between the
variables.
Analysis of the effect of the change in each of the variables on the NPV
of the project.
Solved Problem -3
A company has two mutually exclusive projects under consideration-
project A and project B.
Each project requires an initial cash outlay of Rs.300000 and has an
effective life of 10 years. The company’s cost of capital is 12%. The
forecast of cash flows made by the management is as shown in the table
9.7. What is the NPV of the project?
Table 9.7: Details of project A and B
Economic Project A Project B
Environment Annual cash inflows Annual cash inflows
Pessimistic 65, 000 25, 000
Expected 75, 000 75, 000
Optimistic 90, 000 1, 00, 000
Which project should the management consider?
Given PVIFA = 5.650.
Solution
Table 9.8: NPV of project A is as shown in table 9.6
Economic Project PVIFA PV of cash inflows
NPV
Environment Cash inflows
At 12% for 10 years
Pessimistic 65000 5.650 367250 67250
Expected 75000 5.650 423750 123750
Optimistic 90000 5.650 508500 208500
Table 9.9: NPV of project B
Pessimistic 25000 5.650 141250 (158750)
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Expected 75000 5.650 423750 123750
Optimistic 100000 5.650 565000 265000
Self Assessment Questions
Fill in the blanks:
12. ________ analyse the changes in the project NPV on account of a given change in one
of the input variables of the project
13. Examining and defining the mathematical relation between the variable
of the NPV is _________________________
14. Forecasts under sensitivity analysis are made under __________
Solution
PROJECT A PROJECT B
NPV ACCEPT /
REJECT
NPV ACCEPT /
REJECT
Pessimistic (+ )
Rs.67,250
ACCEPT
(-)
Rs.158750
REJECT
Expected (+)
Rs.1,23,750
ACCEPT
(A) OR (B)
(+)
Rs.1,23,750
ACCEPT
(A) OR (B)
Optimistic (+)
Rs.2,08,500
REJECT
(+)
Rs.2,65,000
ACCEPT
(HIGHER
NPV)
Which project is more riskier?
Project B is risky compared to Project A because the NPV range
is large.
Difference between Optimistic and Pessimistic NPV
Project A = 1,41,250
Project B = 4,23,750
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9.6 Probability distribution approach
Net present value becomes more reliable when we incorporate the chances
of occurrences of various economic environments. 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.
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Solved Problem - 4
A company has identified a project with an initial cash outlay of Rs. 50,
000. The following distribution of cash flow as shown in table 9.10 gives
the life of the project for three years.
Table 9.10: Life of the project for three years
Year 1 Year 2 Year 3
Cash inflow
Probability Cash inflow
Probability Cash inflow
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
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9.6.1 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.
Table 9.11 gives the complete illustration of the entire procedure
Table 9.11: Illustration of entire procedure
Year Expected cash inflows
PV factor at 10% PV of expected cash inflows
1 28,400 0.909 25,816
2 24,00 0.826 19,824
3 28,500 0.751 21,403
PV of expected cash inflows
67,043
PV of initial cash out-lay
(50,000)
Expected NPV 17,043
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Solved Problem -5
The details shown in the table 9.12 are related to a project which requires an
initial cost of Rs. 500 thousand.
Table 9.12: Details of a project (in‟000)
Year Economic conditions
Cash flows Probability
1 High growth 200 0.3
Average growth 150 0.6
No growth 40 0.1
2 High growth 300 0.3
Average growth 200 0.5
No growth 500 0.2
3 High growth 400 0.2
Average growth 250 0.6
No growth 30 0.2
Discount rate is 10%
Determine the NPV and the standard deviation for the respective
years.
Solution
Table 9.13: NPV for the first year (in‟000)
Economic condition
Cash inflow Probability Expected value of cash inflow
High growth 200 0.3 60
Average growth 150 0.6 90
No growth 40 0.1 4
Expected value
154
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Table 9.14: NPV for the second year (in‟000)
Economic condition
Cash inflow Probability Expected value of cash inflow
High growth 300 0.3 90
Average growth 2000 0.5 100
No growth 500 0.2 10
Expected value 200
Table 9.15: NPV for the third year (in „000)
Economic condition
Cash inflow Profitability Expected value of cash inflow
High growth 400 0.2 80
Average growth 250 0.6 150
No growth 30 0.2 6
Expected value 236
Expected NPV
= 154 + 200 + 236 - 500
1.10 (1.10)2 (1.10)3
= 140 + 165.3 + 177.3 – 500 = (17.4) negative NPV
Table 9.16: Standard deviation for the first year (in „000)
Cash inflow
C
Expected value
E
(C-E)2
(C-E)2× probability
200 154 (46)2
(46)2 × 0.3 = 634.8
150 154 (- 4)2
(- 4)2 × 0.6 = 9.6
40 154 (-114)2 (-114)2 × 0.1 = 1299.6
Variance 1944.0
Variance = 4538.4
Standard deviation of cash flows for one year= √1944 = 44.1
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Self Assessment Questions
Fill in the blanks:
15. Probability distribution approach incorporates the probability of occurrences of
various economic environment, to make the NPV ________.
16. _______ is likelihood of occurrence of a particular economic
environment.
Table 9.17: Standard deviation for the second year (in‟000)
Cash inflow
C
Expected value
E
(C-E)2
(C-E)2 × probability
300 200 (100)2
(100)2 × 0.3 = 3,000
200 200 (0)2
(0)2 × 0.5 = 0
50 200 (-150)2
(-150)2 × 0.2 = 4,500
Total = 7,500
Variance of cash flows for 2nd year = 7,500
Standard deviation of cash flow for 2nd year = √7500 = 86.6
Table 9.18: Standard deviation for third year (in‟000)
Cash inflow
C
Expected value
E
(C-E)2
(C-E)2× probability
400 236 (164)2
(164)2×0.2 = 5,379.2
250 236 (14)2
(14)2×0.6 = 117.6
30 236 (-206)2
(-206)2×0.2 = 8487.2
Total 13984.0
Variance of cash flows for the 3rd year=13984
Standard deviation of cash flows for the third year=118.25
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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
Present decision and future events
Future decisions and the consequences of such decisions
Solution
Working Notes: Start from right hand side (C2) of the decision tree
Step 1: Computation of Expected Monetary Value at point C2. Here EMV
represents expected NPV.
Solved Problem -6
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 takes six months. Management believes that there is a
70% chance that the pilot production and test marketing will be
successful.
In case of success, the company can build a plant costing Rs 150
million. The plant will generate annual cash inflow of Rs 30 million for
20 years if the demand is high or an annual cash inflow of 20 million if
the demand is low. High demand has a probability of 0.6 and low
demand has a probability of 0.4 with a cost of capital of 12%.
What is the optimal course of action using decision tree analysis?
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Table 9.19: Computation of Expected Monetary Value at point C2
Cash in flow
(1)
Probability
(2)
Expected value of cash inflows
(1) X (2) = (3)
30 [PVIFA( 12%, 20yrs)
30 x 7.469 = 224.07
0.6 134.4
20 [ PVIFA(12%,20 yrs)
20 x 7.469 = 149.38
0.4 59.8
EMV 194.2
Step 2 is the Decision point.
Table 9.20: Computation of EMV at decision point D2
Decision taken Consequences The resulting EMV at this level
D 21 Invest Rs150 million 194.2 – 150 = 44.2 million
D 22 Stop 0
Step 3: Here the decision criterion is “select the EMV with the highest value”.
So select D21 and truncate D22
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9.7.1 Evaluation of Decision tree approach
The evaluation of decision tree approach leads to the following assumptions
Decision tree approach portrays inter – related, sequential and critical
multi dimensional elements of major project decisions
Adequate attention is given to the critical aspects in an investment
decision which spread over a time sequence
Complex projects involve huge out lay and hence are risky. There is the
need to define and evaluate scientifically the complex managerial
problems arising out of the sequence of interrelated decisions with
Step 4 Calculate the EMV at chance point C1
Table 9.21: Computation of EMV at point C1
EMV Probability Expected value
44.2 0.7 30.9 million
0 0.3 0
Step 5 Evaluate the EMV of the decision alternatives at D1
Table 9.22: Computation of EMV at point D
Decision taken Consequences The resulting EMV at this level
D 11 carry out pilot production and market test
Invest 20 million 30.9 - 20= Rs.10.9 million
D 12 Do nothing 0 0
(Apply the EMV criterion) i.e. select the EMV with the highest value
Based on the above evaluation, we find that the optimal decision
strategy is as follows:
1. Choose D11 ( carry out pilot production and market test) at the
decision point D1 and wait for the outcome at the chance point C1
2. If the outcome at C1 is C11 (success) invest Rs150 million, if the
outcome at C1 is C12 (failure) stop.
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consequential outcomes of high risk. It is effectively answered by
decision tree approach
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
Ability to eliminate unprofitable outcomes helps in arriving at optimum
decision stages in time sequence
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 types of risk in any
project-stand-alone risk, corporate risk and market risk. The sources of risks
are:
Project
Competition
Industry
International factors and
Market
The techniques for incorporation of risk factor in capital budgeting decision could be
grouped into conventional techniques and statistical techniques.
Self Assessment Questions
Fill in the blanks:
17. Decision tree can handle the _____________ of complex investment
proposals
18. _____ portrays inter-related, sequential and critical multi dimensional
elements of major project decisions
19. Adequate attention is given to the ______ in an investment decision
under decision-tree approach
20. ____________ are effectively handled by decision-tree approach
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9.9 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 Decision-tree approaches.
9.10 Answers to SAQs and TQs
Answers to Self Assessment Questions
1. Stand-alone risk.
2. Beta
3. Diversify
4. International risk
5. Additional return
6. Risk free rate, risk premium
7. Greater
8. Risk - adjustment factor
9. Risk free rate of interest
10. Conservation
11. CE
12. Sensitivity analysis
13. One of the steps of sensitivity analysis
14. Different economic conditions
15. More reliable
16. Probability
17. Sequential decisions
18. Decision tree
19. Critical aspects
20. Complex projects
Answers to Terminal Questions
1. Refer to 9.1
2. Refer to 9. 2
3. Refer to 9.3
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4. Refer to 9.5
5. Refer to 9.7