9 risk analysis in capital budgeting

Financial Management Unit 9

Sikkim Manipal University 147

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.



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 Year 2 3 lakhs 2 lakhs Year 3 1 lakhs 3 lakhs Year 4 1 lakhs 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 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.

Self Assessment Questions 2

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 in flows

C E Certain cash flows

PV Factor at 10%

PV of certain cash 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

flows

49,119

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.

Self Assessment Questions 3 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.

Self Assessment Questions 4

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

Year Expected cash inflows PV factor at 10% PV of expected 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

Cash inflows

2,36,000

1,54,000 2,00,000 2,36,000

1.10 (110) 2 (1.10) 3

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

Standard Deviation for I year

Cash in flow C

Expected Value E

(C – E) 2 (C – E) 2 x prob

2,00,000 1,54,000 (46,000) 2 (46,000) 2 x 0.3 = 634800 000

1,50,000 1,54,000 ( 4000) 2 ( 4,000) 2 x 0.3 = 9600 000

40,000 1,54,000 ( 1,14,000) 2 ( 1,14,000) 2 x 0.3 = 12996 00 000

Total 1944 000 000

Standard deviation of Cash flows for I year = 44091

For 2 nd year

Cash in flow C

Expected Value E

(C – E) 2 (C – E) 2 x prob

3,00,000 2,00,000 (1,00,000) 2 (1,00,000) 2 x 0.3 = 3000 000 000

2,00,000 2,00,000 (0) 2 (0) 2 x 0.5 = 0

50,000 2,00,000 ( 1,50,000) 2 ( 1,50,000) 2 x 0.2 = 45 00 000 000

Total 7500 00 000

Variance of Cash flows for 2 nd year = 7500 000 000

Standard Deviation of cash flows for 2 nd year = 8660

For the third year

Cash in flow

C

Expected Value

E

(C – E) 2 (C – E) 2 x prob

4,00,000 2,36,000 (1,64,000) 2 (1,64,000) 2 x 0.2 = 53792 00 000

2,50,000 2,36,000 (14,000) 2 (14,000) 2 x 0.6 = 1176 00 000

30,000 2,36,000 ( 2,00,000) 2 ( 2,00,000) 2 x 0.2 = 8000 000 000

Total 13496800 000

Expected NPV = + + 5,00,000



Variance of Cash flows for 3 rd year = 13496800 000

Standard Deviation of cash flows for 3 rd year = 116175

Standard Deviation of NPV

√(44091) 2 (8660) 2 (116175) 2

√(1.10) 2 (1.10) 4 (1.10) 6

= √1606625026 + 51223004 + 7618496131

= √9276344161

= 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

1.10 (1.10) 2 (1.10) 3

= 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.

σNPV = + +

σNPV = + +



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).

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

D

C1

D3

C2

D2

D11 Carry out pilot Production And Market test (20 million)

D12 Do Nothing

C11 Success

C12 failure Probability 0.3

D31 Stop

D22 Stop

D21 Investment Rs.200 million

High Demand Probability 0.6 C21

C22 Low Demand Probability 0.4

Annual Cash inflow Rs.50 million

Annual Cash inflow Rs.20 million

0.7



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

production and market test

Invest

20 million

58.67 – 20 = Rs 38.67 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.

Self Assessment Questions 6 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 Self Assessment Questions 1

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.

Self Assessment Question 3

1. Risk adjustment factor

2. Risk free rate of interest.

3. Conservation.

4. CE

Self Assessment Question 4 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

9 risk analysis in capital budgeting

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