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Financial Management Unit 9

Sikkim Manipal University Page No. 186

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