Poject Analysis and Appraisal Notes

8/8/2019 Poject Analysis and Appraisal Notes

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Projects Analysis and Implementations

Introduction

Project management is the discipline of planning, organizing and managing resources to

bring about the successful completion of specific project goals and objectives.

A project is a finite endeavor (having specific start and completion dates) undertaken to

create a unique product or service which brings about beneficial change or added value. This

finite characteristic of projects stands in sharp contrast to processes, or operations, which are

permanent or semi-permanent functional work to repetitively produce the same product or

service.

Project is an organised programme of activity carried out to reach a defined goal, often of a

non-recurring nature. It is a package of time-bound, scheduled and assembled activities

dedicated to the attainment of a specific activities of successful completion of a work on time

and within the allotted budget.

The primary challenge of project management is to achieve all of the project goals and

objectives while honoring the project constraints. Typical constraints are scope, time and

budget.

As a discipline, Project Management developed from different fields of application including

construction, engineering and defense. In the United States, the two forefathers of project

management are Henry Gantt, called the father of planning and control techniques, who isfamously known for his use of the Gantt chart as a project management tool, and Henry Fayol

for his creation of the 6 management functions, which form the basis for the body of

knowledge associated with project and program management.

Characteristics of a project

A project has a mission or a set of objectives.

A project has to terminate at some time or other.

All project has a life cycle represented by growth maturity and decline.

A project is a unique and no two projects are similar

A project is a customer specific.

A project is exposed to risk and uncertainty and the extent of these two depend uponhow the project moves through the various stages in its life span.

A substantial portion of work in a project is done by sub-contracting.
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Project classifications

1 Quantifiable and Non Quantifiable projects.

Quantifiable: Industrial development, power generation, mining etc.

Non Quantifiable: Health education and defence etc.

2 Sectoral projects.

Agriculture and allied sector

Irrigation and power sector

Industry and mining sector

Transport and communication sector

Social services sector

Miscellaneous.

Financial Institutions classifications.

(Based on National and state financial Institutions)

New projects

Expansion Projects

Modernization Projects Diversification Projects.

Project Life Cycle/ Project development stages

Traditionally, project development includes a number of elements: four to five stages, and a

control system. Regardless of the methodology used, the project development process will

have the same major stages:

Initiation,

Planning or development,

Production or execution,

Monitoring and controlling, and

Closing.


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Initiation

The initiation stage determines the nature and scope of the development. If this stage is not

performed well, it is unlikely that the project will be successful in meeting the businesss

needs. The key project controls needed here are an understanding of the business

environment and making sure that all necessary controls are incorporated into the project.

Any deficiencies should be reported and a recommendation should be made to fix them.

The initiation stage should include a cohesive plan that encompasses the following

areas:

Study analyzing the business needs in measurable goals.

Review of the current operations.

Conceptual design of the operation of the final product. Equipment and contracting requirements.

Financial analysis of the costs and benefits including a budget.

Stakeholder analysis, including users, and support personnel for the project.

Project charterincluding costs, tasks, deliverables, and schedule.

Planning and design

After the initiation stage, the system is designed. Occasionally, a small prototype of the final

product is built and tested. Testing is generally performed by a combination of testers and end

users, and can occur after the prototype is built or concurrently. Controls should be in place

that ensure that the final product will meet the specifications of the project charter.

The results of the design stage should include a product design that:

Satisfies the project sponsor, end user, and business requirements.

Functions as it was intended.

Can be produced within quality standards.

Can be produced within time and budget constraints.

Executing
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Executing consists of the processes used to complete the work defined in the project

management plan to accomplish the project's requirements. Execution process involves

coordinating people and resources, as well as integrating and performing the activities of the

project in accordance with the project management plan. The deliverables are produced as

outputs from the processes performed as defined in the project management plan.

Monitoring and Controlling

Monitoring and Controlling consists of those processes performed to observe project

execution so that potential problems can be identified in a timely manner and corrective action

can be taken, when necessary, to control the execution of the project. The key benefit is that

project performance is observed and measured regularly to identify variances from the project

management plan.

Monitoring and Controlling includes:

Measuring the ongoing project activities (where we are);

Monitoring the project variables (cost, effort, ...) against the project management plan

and the project performance baseline (where we should be);

Identify corrective actions to properly address issues and risks (How can we get on

track again);

Influencing the factors that could circumvent integrated change control so only

approved changes are implemented

Closing/ Project clean up

Closing includes the formal acceptance of the project and the ending thereof. Administrative

activities include the archiving of the files and documenting lessons learned.

Closing phase consist of two parts:

Close project: to finalize all activities across all of the process groups to formally closethe project or a project phase

Contract closure: necessary for completing and settling each contract, including the

resolution of any open items, and closing each contract applicable to the project or a projectphase.

Phases of a Project /Capital Budgeting

Planning

Analysis

Selecting


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Financing

Implementation

Review1.Planning

It is a Preliminary screening of the project proposal. It is done to Assess whether the project is

worthwhile

2.Analysis

Market Analysis Demand, Market share

Technical Analysis technical viability production process, m/c, plant size

Financial Analysis Risk and Return, meet the debt and return expectations?

Economic Social cost benefit analysis, impact on income, savings and investment in

the society

Ecological Damage and corrective actions

3. Selection

It Involves risk analysis with the tools and techniques for risk analysis. Appraisal tools used

includes.

Non Discounting Pay Back Period and ARR

Discounting NPV, IRR and BCR

4. Financing

Capital structure decision Debt and Equity

Flexibility, risk, income, control and taxes influence the capital structure decision

5. Implementation

Designing, Construction, Training and Plant Commissioning

PERT and CPM are used for effective implementation

6.Review

Feedback

Provides information for future decision making

Suggest corrective actions

Judgmental biases can be discovered

Generation & screening of Project ideas


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Search for promising project ideas is the first step towards establishing a successful venture.

Barring few new ideas based on technological breakthroughs, most of the project ideas

involve combining existing fields of technology or offering variants of present products or

services.

Generations of Ideas

To stimulate the flow of ideas, the followings are helpful.

SWOT analysis identifying opportunities that can be profitably exploited.

Clear articulation of objectives- Helps the employees to think more imaginatively.

Fostering a conducive climate- helps to tap the creativity of the employees.

Monitoring the environment

A promising investment idea enables a firm to exploit the opportunities in the

environment by drawing on its competitive strengths. Hence the firm must systematically

monitor the environment and assess its competitive abilities.

Business environment may be divided into 6 categories.

Economic sector

Governmental sector

Technological sector

Socio-demographic sector

Competition sector

Supplier sector.

Scouting for project ideas.

Wide variety of sources to be tapped to identify project ideas.

Analyse the performance of existing industries.

Examining the input and out put of various industries.

Review of imports and exports.

Study plan outlays and governmental guidelines.

Suggestions from financial institutions and developmental agencies.

Investigating local material and resources.

Analysis of economical and social trends. Study of new technological developments.

Clues from consumption abroad.

Possibility of revive of sick units.

Trade fairs.

Stimulating creativity for generating new product ideas.

Preliminary screening


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From the list of ideas generated, some kind of preliminary screening is required to eliminate

which prima facie not promising. Preliminary screening is based on the following.

Compatibility with the promoter.

Consistency with government priorities.

Availability of inputs.

Adequacy of markets.

Reasonableness of cost.

Acceptability of risk level.

Facets of Project Analysis

Market/ Demand analysis.

Technical Analysis.

Financial analysis.

Economic analysis.

Ecological analysis.

1.Market and Demand analysis

Market analysis is concerned with

Find out the aggregate demand

Aggregate market share

Kinds of information required

Past and present consumption level

Past and present supply condition

Production possibilities and constraints

Imports and exports

Structure of competition

Cost structure


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Elasticity of demand

Consumer behavior, intentions, preferences

Distribution and marketing policies in use

Administrative, technical and legal constraints.

1. Situational Analysis

Informal talk with customers, competitors, middlemen and others in the industry.

Situational Analysis is done when

- there is cost and time constraints

- the analysis generates enough data to measure the market

2.Collection of Secondary information

Sources Census of India, National Sample survey reports, annual survey of

industries etc..

Evaluate the secondary information

Examine the reliability, accuracy and relevance

3 Conduct Market Survey

Information sought in a market survey

Total Demand and rate of growth

Income and price elasticities of demand

Motives for buying

Satisfaction with existing products

Unsatisfied needs

Socio-economic characteristics of buyers

Attitude towards various products

Types of surveys includes

(1) Census Survey

For goods which are used by a small no. of firms. Costly and infeasible in other cases


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(2) Steps in Sample survey

Define the target population

Select the sampling scheme and size

Develop questionnaire

Recruit and train the field investigators

Obtain information as per the questionnaire

Scrutinise the information

Analyse and interpret the information

4. Charaterisation of Market

Based on information gathered from secondary sources and through the market survey, the

market for the product/service may be described in terms of the following

Effective demand in the past and present

Breakdown of Demand

Price

Methods of Distribution and sales promotion

Consumers

Supply and competition

Govt. policy

5. Demand Forecasting

(a) Qualitative methods

(1) Jury of executive method

(2) Delphi method

(b) Quantitative methods

(1) Trend projection method

(2) Exponential smoothing method(3) Moving Average method

(4) Chain ratio method

(5) Consumption level method

(6) End use method

(7) Leading indicator method

Techniques of Demand Forecasting


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(a) Qualitative methods

(1) Jury of executive method-

opinions of a group of managers

(2) Delphi method Taking the opinions of a group of experts with the help of a mail

survey.

6.Market Planning

Market analysis includes analyzing current Market situation which includes competitive,

distribution and macro environment. Market analysis calls for SWOT analysis of the

organization.

Objectives

Marketing strategy target segment, product positioning, product line, distribution,sales force, sales promotion and advertising

Action Programme

Technical Analysis

Analysis of technical and engineering aspects of a project need to be done continually when a

project is formulated. TA seeks to determine whether the prerequisite for the successful

commissioning of the project have been considered and reasonably good choice have beenmade with respect to location, size, process, etc.

Objective of Technical Analysis is to make sure that the project is technically feasible, Project

is optimal in terms of technology, size, location etc..

Essentials of Technical Analysis

Manufacturing Process / Technology

-choice of suitable technology among the alternatives

- Technology appropriate to local economic, social and cultural conditions.

Flexibility with respect to product mix.

Plant capacity- considering technological reqmt, input constraints, investment cost,

market conditions

Location and site - proximity to RM, infrastructure, labour, govt. policy etc.


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Machineries and Equipment depending on the production technolgy, plant capacity,

investment capacity, workers able to operate etc..

Structures and Civil works site preparation and development, building and structures,

outdoor works etc..

Environmental Aspects types of emissions, action for effluent treatment.

Project charts and layouts to define scope of the project and provide basis for project

engineering and estimation of the investment and production cost.

Schedule of project implementation

- PERT & CPM Analysis

- Prepare work schedule

Financial Analysis

Financial analysis seeks to ascertain whether the proposed project will be financially viable inthe sense of being able to meet the burden of servicing the debt and whether the proposed

project will satisfy the return expectations of those who provide the capital.

Factors looked into while conducting the financial analysis are

Investment outlay and cost of project

Means of financing

Cost of capital

Projected profitability Break even point

Cash flows of the project

Projected financial position

Level of risk.

Financial Analysis

Make financial estimates and projections by analyzing

Cost of the project supported by long term funds Plan the means of financing considering cost, risk, control & flexibility

Estimate of sales & production ( qty & value)

Calculate the cost of productions matl, utilities, labour, factory o/h etc.

Financial Analysis

Working Capital requirement and the means of financing

Make profitability projections

Prepare a projected cash flow statement

Prepare a projected Balance Sheet


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Economic analysis

EA also referred to as social cost benefit analysis, is concerned with judging a project from

the larger social point of view. In this evaluation focus is on the social cost and benefit of a

project which may often be different from its monetary costs and benefit.

The questions sought to be naswered in this analysis are.

What would be the impact of project on the distribution of the income in the society.

What would be the contribution of the project on employment, social order, savings and

investments etc.

Ecological analysis

Environmental concerns have assumed greater significance.

Mainly for those projects which have significant ecological implications.

Analysis of likely damage caused by the project to the environment.


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Mod 2

PROJECT ESTIMATION AND SELECTION

NATURE OF INVESTMENT DECISIONS

From the above discussion, you must be clear about the distinctive features of capital

investment:

They have long-term consequences

They often involve substantial outlays

They may be difficult or expensive to reverse

Now that you know the nature of investment decisions, lets discuss the various forms ofinvestment decisions:

1. Replacement projects: Firms routinely invest in equipments meant to replace obsolete

and inefficient equipments, even though they may in serviceable condition. The

objective of such investments is to reduce costs (of labour, raw material, and power),

increase yield, and improve quality. Replacement projects can be evaluated in a fairly

straightforward manner; though at times the analysis may be quite detailed.

2. Expansion projects: These investments are meant to increase capacity and/ or widen

the distribution network. Such investments call for an explicit forecast of growth. Since,this can be risky and complex, expansion projects normally warrant more careful

analysis than replacement projects. Decisions relating to such projects are taken by

the top management.

3. Diversification projects: These investments are aimed at producing new products or

services or entering into entirely new geographical areas. Often diversification projects

entail substantial risks, involve large outlays, and require considerable managerial

efforts and attention. Given their strategic importance, such projects call for a very

thorough evaluation, both quantitative and qualitative. Further, they require a

significant involvement of the board of directors.

4. Research and development projects: Traditionally, R%D projects absorbed a very

small proportion of capital budget in most Indian companies. Things however are

changing. Companies are now allocating more funds to R&D projects, more so in

knowledge intensive industries. R&D projects are characterised by numerous

uncertainties and typically involve sequential decision-making. Hence the standard

DCF analysis is not applicable to them. Such projects are decided on the basis of


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managerial judgment. Firms, which rely more on quantitative methods, use decision

tree analysis and option analysis to evaluate R&D projects.

5. Mandatory investments: These are expenditure required to comply with statutory

requirements. e.g., pollution control equipment, medical dispensary, fire fitting

equipment etc. These are often non-revenue producing investments. In analysing such

investments the focus is mainly on finding the most cost-effective way of fulfilling a

given statutory need.

ACCEPT-REJECT VERSUS RANKING APPROACHES

Two basic approaches to capital budgeting decisions are available. The accept- reject

approach involves evaluating capital expenditure proposals to determine whether they meet

the firms minimum acceptance criterion. This approach can be used then the firm has

unlimited funds, as a preliminary step when evaluating mutually exclusive projects, or in a

situation in which capital must be rationed. In these cases only the acceptable projects shouldbe considered.

The second method, the ranking approach, involves ranking projects on the basis of some

predetermined measure, such as the rate of return. The project with the highest return is

ranked first, and the project with the lowest return is ranked last. Only acceptable projects

should be ranked. Ranking is useful in selecting the best of a group of mutually exclusive

projects and in evaluating projects with a view to capital rationing.

EXPANSION VERSUS REPLACEMENT CASH FLOWS

Developing relevant cash flow estimates is most straightforward in the case of expansiondecisions. In this case, the initial investment, operating cash inflows, and terminal cash flow

are merely the after-tax cash outflow and inflows associated with the proposed outlay.

Identifying relevant cash flows for replacement decisions is more complicated; the firm must

find the incremental cash outflow and inflows that would result from the proposed

replacement. The initial investment in this case is the difference between the initial investment

needed to acquire the new asset and any after-tax cash inflows expected from liquidation

today of the asset being replaced. The operating cash inflows are the difference between the

operating cash inflows from the new asset and those from the replaced asset. The terminal

cash flow is the difference between the after-tax cash flows expected upon termination of the

new and the old assets.

INDEPENDENT PROJECTS

Independent projects are those where cash flows are unrelated or independent from one

another. The acceptance of one project does not necessarily eliminate other projects.


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MUTUALLY EXCLUSIVE PROJECTS

Mutually exclusive projects are projects that are competing with one another. The acceptance

of mutually exclusive projects automatically eliminates other mutually exclusive projects that

are competing with one another.

CAPITAL BUDGETING:

EVALUATION TECHNIQUES

In essence, capital funds are invested for one basic reason: To obtain sufficient future

economic returns to warrant the original outlay i.e., sufficient cash receipts over the life of the

project to justify the investment made. Analytical methods of evaluation of capital projects

should take into account in one way or another, this basic trade-off of current cash outflows

against the future cash inflows.

To judge the attractiveness of any investment proposal, the financial manager must consider

the following elements

(i) The amount expended i.e., The net investment,

(ii) The potential benefits i.e., the operating cash inflows, and

(iii) The time period over which these benefits will accrue i.e., economic life of the project.

TRADITIONAL OR NON-DISCOUNTING TECHNIQUES

As the name itself suggests, these techniques do not discount the cash flows to find out theirpresent worth.

There are two such techniques available i.e.,

(i) The Payback period method, and

(ii) The Accounting rate of return.

1 . PAYBACK PERIOD

The payback period as name suggest is defined as the number of years required for the

proposal's cumulative cash inflows to be equal to it cash outflows. In other words, the

payback period is the length of time required to recover the initial cost of the project. The

payback period therefore, can be looked upon, as the-length of time required for a proposal to

'break even' on its net investment.

The Decision Rule:

The payback period does not give any clear indication of the decision rule. The payback

period calculated for a proposal is to be compared with some predetermined target period. If


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the payback period is more than the target period, then the proposal should be rejected,

otherwise-it-may be accepted if the payback-period is less than the target period. There is no

systematic or accepted way of determination of target period and choosing a target period is

subject to some arbitrariness on the part of the decision maker. Further, if the different

proposals are to be ranked in order of priority, then the proposal with the shortest payback

period will be first in the priority list.

Critical Evaluation:

Out of all the available Capital budgeting technique (some of which are discussed later), the

payback period is the easiest to understand and apply. The payback period measures the

direct relationship between annual cash inflows from a proposal and the net investment

required. . This technique has been a popular method of evaluation of capital budgeting

proposals merely because of its simplicity. Yet, it is having its own problems and

disadvantages. The payback period as a technique of evaluation of capital budgeting

proposals can be critically examined in terms of its advantages and disadvantages as follows:

Advantages of payback method:

1. The payback period is simple and easy, in concept as well as in its applications. In

particular, a small firm having limited manpower, which does not have any special skill to

apply other sophisticated techniques, can adopt it.

2. It gives an indication of liquidity. In case a firm is having liquidity problems, then the

payback period is a good method to adopt as it emphasizes the earlier case inflows.

3. In a broader sense, the payback period deals with the risk also. The project with a shorter

payback period will be less risky as compared to project with a longer payback period, as the

cash inflows which arise further in the future will be less certain and hence more risky. So, thepayback period helps in weeding out the risky proposals by assigning lower priority.

Disadvantages of payback method:

1. The payback period entirely ignores many of the cash inflows, which occur after the

payback period. This could be misleading and could lead to discrimination against the

proposal, which generates substantial cash inflows in later years. By restricting itself to

answering the question when will this project make it initial investment? it ignores what

happens after the initial investment is recouped.

2 ACCOUNTING RATE OF RETURN OR AVERAGE RATE OF

RETURN (ARR)

The ARR is based on the accounting-concept of return on investment or rate of return. The

ARR may be defined as the annualized net income earned on the average funds invested in a

project. In other words, the annual returns of a project are expressed as a percentage of the

net investment in the project.


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This clearly shows that the ARR is a measure based on the accounting profit rather than the

cash flows and is very similar to the measure of rate of return on capital employed, which is

generally used to measure the over all profitability of the firm.

The decision rule:

The ARR calculated as above is compared with the pre-specified rate of return. Obviously, if

the ARR is more than the pre-specified rate of return, then the project is likely to be accepted,

otherwise not. For example, in the above case the ARR of the proposal has been found to be

20%. In case, the firm requires a rate of return of at least 18%, then this proposal is

acceptable. However, if the minimum rate of return of the firm is 22% then this proposal is

likely to be rejected. The ARR can also be used to rank various mutually exclusive proposals.

The project with the highest ARR will have the top priority while the project with the lowest

ARR will be assigned lowest priority.

The Critical Evaluation:

No doubt, the ARR is relatively simple to calculate and easy to apply. The relevant data andinformation required for its calculation is readily available in the accounting records. The ARR

state the economic desirability of an investment in terms of a percentage return on the original

outlay. Unlike the payback period, the ARR considers all the benefits arising out of the

proposal through out its economic life.

However, the ARR has certain limitations and drawbacks when used as a technique of

project evaluation as follows.

1. It ignores the time value of money and considers the profit earned in the 1st year as

equal to the profits earned in later years. It does not discount the future profits.

2. The ARR is based on the accounting profits rather than the cash flows. It has already

been noted in the previous chapter that accounting profits are affected by different

accounting policies. It has also been noted earlier that a sound evaluation technique

should be based on the cash flows rather than the accounting profits.

3. The ARR also ignores the life of the proposal. A proposal with a longer life may have

the same ARR as another proposal with a shorter life has. On the basis of ARR, both

the proposals may be placed at par, but the proposal with a longer life should be

preferred over the proposal with a shorter life (as the former proposal will generate the

returns for a longer period). However, the ARR method fails to distinguish between the

two.

4. The ARR technique also ignores the salvage value of the proposal. In real sense,

the salvage value is also a return from the proposal and should be considered.


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5. The ARR also fails to recognize the size of the investment required for the project.

Particularly, in case of mutually exclusive proposals, the two projects having

significantly different initial costs may have same ARR.

3 NET PRESENT VALUE (NPV) METHOD

The NPV is the first and the foremost of the discounted cash flow techniques. NPV is used

simply to weigh the elements of trade-off between investment outlays and the future benefits

in equivalent terms, and to determine whether the net balance of the present values is

favorable or not. The NPV of an investment proposal may be defined as the sum of the

present values of all the cash inflows less the sum of present values of all the cash outflows

associated with a proposal. In other words, the NPV of any proposal, that involves cash

inflows and outflow over a period of time, is equal to the net present value of all the cash

flows. Thus, the NPV is the sum of the discounted values of the cash flows of a proposal. In

case, the cash outflows i.e. the investment in the proposal occur only in the beginning at time

0, then NPV may be defined as the sum, of the present values of cash inflows less the initialinvestment.

A rate of discount must be specified and applied to both inflows and outflows in order to find

out their present values. When the present values of all inflows and. outflows are added, the

resultant figure is denoted as net present value. The figure can be positive or negative,

depending on whether there is a net inflow or outflow from the project. A word should be said

about the rate of discount. From an economic point of view, this rate of discount should be the

rate of return, the investor normally enjoys from investments of similar nature and risk. In

effect, it is opportunity rate of return. In case of a firm, the choice of a discount rate is

complicated by the variety of investments available and by the type of financing provided by

both the shareholders and the debt investors. The rate so employed is the overall cost ofcapital, which takes into account shareholders expectations, business risk and the leverage.

The merits of the NPV technique can be enumerated as follows.

1. It recognizes the time value of money. It helps evaluation of proposals involving cash

flows over a period of several years. The cash flows occurring at different point of time

are not directly comparable, but they can be made comparable by the application of

the discounting procedure.

2. The NPV technique considers the entire cash flow stream and all the cash inflows and

outflows, irrespective of the timing of their occurrence, are incorporated in the

calculation of the NPV.

3. The NPV technique is based on the cash flows rather than the accounting profit and

thus helps in analysing the effect of the proposal on the wealth of the shareholders in a

better way.


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4. The discount rate, k, applied for discounting the future cash flows is in fact, the

minimum required rate of return, which incorporates both the pure return as well as the

premium required to set off the risk.

5. The NPV technique represents the net contribution of a proposal towards the wealth of

the firm and is therefore, in full conformity with the objective of maximization of the

wealth of the shareholders. The NPV concept has a built in earnings requirements in

addition to the recovery of the investment. Thus, the cushion implicit in the positive

NPV is truly an economic gain that goes beyond satisfying the required rate of return.

The NPV technique has the following shortcomings:

i. It involves difficult calculations. Moreover, it may not be able to overcome the uncertainty

involve with cash flows occurring after a sizeable time gap. It fails to answer questions

such as: How to quantify the potential error inherent in the cash flow estimates, and

how does the measure help making investment choices if such errors are significant?ii. The NPV technique requires the predetermination of the required rate of return, k, which

itself is a difficult job. If the value of the 'k' is not correctly taken, then the whole

exercise of the NPV may give wrong results.

iii. The NPV technique does not provide a measure of project's own rate of return; rather it

evaluates a proposal against an external variable i.e. the minimum required rate of

return.

iv. The decision under the NPV technique is based on a value, which is an absolute

measure. It ignores the difference in initial outflows, size of different proposals etc.while evaluating mutually exclusive proposals.

4 PROFITABILITY INDEX (PI)

Quite often one may be faced with a choice involving several alternative investment of

different size. In such a case, he cannot be indifferent to the fact that even though the NPV of

different alternatives may be close or even equal, these involve commitments of widely

ranging amounts. In other words, it does make a difference whether an investment proposal

promises a NPV of Rs. 1,000 for an outlay of Rs. 10,000; or whether an outlay of Rs. 25,000

is required to get the same NPV of Rs. 1,000, even if the lives of the, projects are assumed to

be same. In the first case, the NPV is much larger fraction (Rs. 1,000/10,000) then what it is

in the second case i.e., (Rs. 1,000/ 25,000), which makes the first proposal clearly more

attractive. The PI technique is a formal way of expressing this cost/benefit relationship.

This technique which is a variant of the NPV technique, is also known as Benefit- cost

ratio, or preset Value index. The PI is also based upon the basic concept of

discounting the future cash flows and is ascertained by comparing the present value of


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the future cash inflows with the present value of the future cash outflows. The PI is

calculated by dividing the former by the latter.

Calculation:

The PI is calculated as follows:

PI = Total present value of cash inflows

Total Present Value of cash outflows

5 TERMINAL VALUE (TV)

The other variant of the NPV technique is known as the TV technique. In this case, a new

dimension is added to the NPV technique. As already discussed in the NPV technique, the

future cash flows are discounted to make them comparable. In the TV technique, the future

cash flows are first compounded at the expected rate of interest for the period from their

occurrence till the end of the economic life of the project. The compounded values are then

discounted at an appropriate discount rate to find out the present value. This present value iscompared with the initial outflow to find, out the suitability of the proposal.

6 DISCOUNTED PAYBACK PERIOD

This method is a combination of the original payback method and the discounted cash flow

technique. In this method, the cash flows of the project are discounted to find their present

values. The present value of the cash inflows is then compared with the present value of the

outflow, in order to identify the period taken to recover the initial cost or the present value of

outflow. This method thus, takes care of the main drawback of the pay back period method

and allows the consideration of the time value of money of cash flows. However, it still doesnot take into account those cash inflows, which occur subsequent to the payback period, and

sometimes these cash inflows may be substantial. Since, it is a variant of the original payback

period method, the discounted payback period method is also calculated in the same way as

the payback period, except that the future cash inflows are first discounted and then the

payback is calculated. However the discounted payback method is superior as, in addition to

the recovery of original investment, the time value of money is also considered.

6 INTERNAL RATE OF RETURN (IRR)

The other important discounted cash flow technique of evaluation of capital budgeting

proposals is known as IRR technique. The IRR of a proposal is defined as the discount rate,

which produces a zero NPV i. e., the IRR is the discount rate which will quite the present

value of cash inflows with the present value of cash outflow. The IRR is also known as

Marginal Rate of Return or Time Adjusted Rate of Return. Like the NPV, the IRR is also

based on the discounting technique. In the IRR technique, the future cash inflows are

discounted in such a way that their total present value is just equal to the present value of

total cash outflows. The time-schedule of occurrence of the future cash flows is known but the


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rate of discount is not. Rather this discount rate is ascertained, by the trial and error

procedure. This rate of discount so calculated, which equates the

present value of future cash inflows with the present value of outflows, is known as the

The Decision Rule:

In order to make a decision on the basis of IRR technique; the firm has to determine, in the

first instance, its own required rate of return. This rate, k, is also known as the cut-off rate or

the hurdle rate. A particular proposal may be accepted if its IRR, r, is more than the minimum

rate i. e., k, otherwise rejected. However, if the IRR is just equal to the minimum rate, k, then

the firm may be indifferent. In case of ranking of mutually exclusive proposals, the proposal

with the highest IRR is given the top priority while the project with the lowest IRR is given the

lowest priority. Proposals whose IRR is less than the minimum required rate, k, may

altogether be rejected. This decision rule is based on the fact that the NPV of the project is

zero if its cash flows are discounted at the minimum' required rate i. e., k. If the proposal cangive a return higher than this minimum required rate, then it is expected to contribute to the

wealth of the shareholders. It may be noted however, that the IRR, r, of the proposal is

internal to the project while the minimum required rate, k, is external to the project.

The Critical Evaluation:

Besides the NPV technique, the IRR technique is the other important discounted cash flow

technique of evaluation of capital budgeting proposals. The IRR technique has been

compared with the NPV technique at a later stage.

However, the merits of the IRR technique can be summarized as follows:

i. The IRR technique takes into account the time value of money and the cash flows occurring

at different point of time are adjusted for time value of money to make them comparable.

ii. It is a profit-oriented concept and helps selecting those proposals which are expected to

earn more than the minimum required rate of return. So, the IRR technique helps achieving

the objective of maximization of shareholders wealth.

iii. The IRR of a proposal is expressed as a percentage and is compared with the cutoff rate,

which is also expressed as a percentage. Thus, the IRR has an appeal for those who want to

analyze proposal in terms of its percentage return.

iv. Like NPV technique, the IRR technique is also based on the consideration of all the cash

flows occurring at any time. The salvage value, the working capital used and released etc. are

also considered.

v. The IRR technique is based on the cash flows rather than the accounting profit.

Thus, it can be stated that the IRR technique possesses all the ingredients of a sound

evaluation technique. Still it has, on the other hand, some draw backs, as follows:

a) As far as the calculation of IRR is concerned, it involves a tedious and

complicated trial and error procedure.


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b) An important drawback of the IRR technique is that it makes an implied assumption that

the future cash inflows of a proposal are reinvested at a rate equal to the IRR. Say, in case of

mutually exclusive proposals, say A and B having IRR of 18% and 16%, the IRR technique

makes an implied assumption that the future cash inflows of project A will be reinvested at

18% while the cash inflows of project B will be reinvested at 16%. It is imaginary to think that

the same firm will have different reinvestment opportunities depending upon the proposal

accepted.

c) Since, the IRR is a scaled measure, it tends to be biased towards the smaller projects

which are much more likely to yield high percentage returns over the larger projects.

CAPITAL BUDGETING UNDER CAPITAL RATIONING

It is a situation where the firm has limited funds available but cannot be undertaken in view of

the limited funds. This situation may occur when a firm is either unable or unwilling to obtain

additional funds in order to undertake financially viable capital budgeting proposals. Thus afirm by choice or under compulsions sets absolute ceiling on its capital spending in a period at

a level that will cause it to reject or avoid some of the profitable projects. For example, if a firm

has different proposals with positive NPV but the initial funds required for the implementation

of all these proposals are not available or cannot be procured from the capital market for one

reason or the other, the firm is said to be operating under condition of capital rationing. In

other words, a firm faces capital rationing when it finds itself unable to take on projects that

earn returns more than the cut-off rate because it does not have (i) the funds on hand, or (ii)

the capacity to raise the funds needed to finance these projects. In the context of the NPV

rule, this implies that the firm does not have and cannot raise the funds to take all the posi-

tive NPV proposals. The fact that a firm has many projects and limited resources does notneces-sarily imply that it faces capital rationing, as the firm might still have the capacity to

raise funds from the capital market. The capital rationing may be described as:

1.Internal Capital Rationing:

It is a situation where the firm has imposed limit on the funds allocated for fresh investment

though (i) the funds might otherwise be available within the firm, or (ii) additional funds can be

procured by the firm from the capital market. Some firms may follow a policy of using only

internally generated funds (by ploughing back of profits) for new investments. Some firms

avoid debt capital because of the associated financial risk and avoid external equity because

of a desire not to loose control. This type of capital rationing implies that the firm is not willing

to grow further. Obviously, the internal capital rationing is not in the best interest of the

shareholders in the long run, as it results in foregoing the profitable proposals.

2. External Capital Rationing:

It is a situation when the firm is willing to undertake the financially viable proposals but is

unable to do so because either it is not having sufficient funds available at its disposal or the


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capital market conditions are not conductive enough to let firm raise the required funds from

the market.

A firm having no capital rationing will like to take all the capital budgeting proposals which

have positive, NPV and reject those which are having negative NPV. In case-of mutually

exclusive proposals, the firm will like to take that proposal which has the highest positive NPV

irrespective of the funds requirements. But the problem is that if the firm is facing capital

rationing, then how to distribute the available scarce and limited capital funds among

competitive proposals.

At this stage, it is also necessary to classify different projects into 2 classes i.e.,

divisible projects and indivisible projects.

a) Divisible Projects:

There are certain projects, which can either be taken in full or can be taken in parts. For

example, it building (having 5 floors) can be constructed at a cost of 5 crores. However, if the

funds are not sufficiently available then only a part of the building, say only 2 floors, can beconstructed for the time being. But all the proposals may not be divisible.

b) Indivisible Projects:

There are certain proposals, which are indivisible. These proposals have a feature that

either the proposal as a whole be taken in its totality or not taken at all. For example, a

proposal to buy a helicopter cannot be taken in parts. Similarly, a multi stage plant can

only be installed fully but not in parts. There can be many instances of indivisible

projects.

Modified Internal Rate Of Return - MIRR

While the internal rate of return (IRR) assumes the cash flows from a project are reinvested at

the IRR, the modified IRR assumes that all cash flows are reinvested at the firm's cost of

capital. Therefore, MIRR more accurately reflects the profitability of a project.

For example, say a two-year project with an initial outlay of $195 and a cost of capital of 12%,

will return $121 in the first year and $131 in the second year. To find the IRR of the project so

that the net present value (NPV) = 0: NPV = 0 = -195 + 121/(1+ IRR) + 131/(1 + IRR)2 NPV

= 0 when IRR = 18.66% Solving for NPV using MIRR, we will replace the IRR with our MIRR

= cost of capital of 12% : NPV = -195 + 121/(1+ .12) + 131/(1 + .12)2 NPV

= 17.47 when MIRR = 12% Thus, using the IRR could result in a positive NPV (good project),

but it could turn out to be a bad project (NPV is negative) if the MIRR were used. As a result,

using MIRR versus IRR better reflects the value of a project.


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In capital budgeting decision it helps accepting those proposals whose rate of return is more

than the cost of capital of the firm and hence results in increasing the value of the firm.

Similarly, the firm's value is reduced when the rate of return on the proposal falls below the

cost of capital. Thus, the concept of cost of capital is consistent with the goal of maximization

of shareholders wealth and it works as a tool to achieve this goal. Further, the cost of capital

has a useful role to play in deciding the financial plan or capital structure of the firm. It may be

noted that in order to maximize the value of the firm, the cost of all the different sources of

funds must be minimized. The cost of capital of different sources usually varied and the firm

will like to have a combination of these sources in such a way so as to minimize the overall

cost of capital of the firm.


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Module 3

RISK ANALYSIS IN CAPITAL BUDGETING

The cash flows from an investment are estimated when the proposal is evaluated, however,

the returns are not known until the cash flows actually occur. The uncertainty of returns from

the moment, the funds are invested until management and investor know how much the

projects has earned, is a primary determinant of a proposal's risk. The owner of a firm are

ordinarily concerned with the riskiness of their capital, and management must therefore, take

risk into account in evaluation of capital budgeting proposals.

In case, the cash flows associated with a proposal are known with certainty then the

techniques such as NPV, IRR or any other may be used to evaluate the desirability of the

proposal. However, when the cash flows are not known with certainty, a measure of risk of

the proposal should also be brought into the evaluation system. Such resultant capital

budgeting decision criterion will then evaluate the proposals by considering both the risk and

return associated with the proposal. As already discussed above a proposal is said to containrisk when the set of possible cash flows is known but it is not possible at time 0 (when the

decision is being taken) to predict the specific cash flows that will actually occur in future.

TYPES AND SOURCES OF RISK IN CAPITAL BUDGETING:

The risk in a project can be classified into different groups such as the project itself,

competition, shifts in the industry, international considerations etc., as follows:

1. Project Specific Risk:

This type of risk is project specific i.e., an individual project may have higher or lower cash

flows than expected, either because of the wrong estimation or because of factors specific to

that project. When firms takes a large number of similar projects, it may be argued that muchof this project specific risk would be diversified away The project specific risk affects only the

project under consideration and may arise from factors specific to project or estimation error.

2. Competition Risk:

The second type of risk is competition risk where the cash flows of a project are affected by

the actions of the competitors. Although, a good project analysis might consider the reactions

of the competitors, the actual actions taken by the competitors may be different from those

expected. In most of the cases, this risk will affect more than one project and is therefore

difficult to be diversified away in the normal course of business.

3. Industry Specific Risk:

The third type of risk is the industry specific risk i.e., the risk that primarily affects the earnings

and cash flows of a specific industry only. This risk may arise because of three factors. The

first is technology risk, which reflects the effects of technologies that change or evolve in

ways different from those expected when the project was originally analyzed. The second is

legal risk, which reflects the effect of changing laws and regulation affecting a particular

industry only. The third may be the commodity risk, which reflects the effects of price

changes in goods and services that are used or produced.


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4. International Risk:

A firm faces this type of risk when it takes on projects outside its domestic market. In such

cases, the earnings and cash flows might be different than expected owing to exchange rate

movements or political changes. Some of this risk may be diversified away by a firm in the

normal course of business by taking on projects in different countries whose currencies may

not all move in the same direction. Multinational firms who hold projects in number of

countries are able to diversify away this risk.

5. Market Risk:

The last type of risk arises by the factors that affect essentially all companies and all projects,

of course in varying degrees. For example, changes in interest rate structure will affect the

projects already taken as well as those yet to be taken, both directly through the discount rate

and indirectly through cash flows. Other factors that affect all the projects may be inflation,

economic conditions etc. Although the expected values of these entire variables may be

considered in the capital budgeting analysis, changes in these variables will affect their

values. Firms cannot diversify away this risk in the normal course of business, although may

be considered to some extent only.

.Assumptions of capital Budgeting under risk:

The discussion on capital budgeting under risky situations is based upon the following

assumptions:

1. That the firm is not having any capital rationing, and no profitable project will be rejected

for want of funds.

2. That the proposals net investment is known with certainty.

3. Each set of cash flows is known with certainty, and is mutually exclusive and

exhaustive.

4. The required rate of return of the firm is given and is indicative of the risk-return

characteristics of the proposal.

5. The firm is basically risk-averse. This assumption is important as it implies that the finance

manager will not accept a risky proposal unless its expected profits are sufficient to

compensate for the risk. The risk aversion also means that the additional risk will be

accepted only if it results in disproportionately larger increase in expected returns.

This assumption of risk aversions can be expressed in terms of the

followingprepositions:

If the two proposals have the same expected return, then theproposal with lesser

risk will be preferred, and

If two proposals have same degree of risk then proposal with thehigher expected

return would be preferred.


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Incorporating Risk in the Capital Budgeting Analysis:

In all the capital budgeting decisions, there is always an element of risk involved which must

be considered while evaluating different investment proposals. There are several techniques

available to handle the risk perception of capital budgeting proposals. These techniques differ

in their approach and methodology to incorporate risk in the evaluation process. Broadly

speaking, these techniques can be grouped into conventional techniques and statistical

techniques as follows:

Conventional Techniques Statistical Techniques

1. Payback period

2. Risk adjusted Discount Rate

3. Certainty equivalents

4. Sensitivity Analysis

5. Financial Break-even

1. Probability Distribution Approach

2. Simulation Analysis

3. Decision Tree Approach

CONVENTIONAL TECHNIQUES OF RISK ANALYSIS

These techniques are also known as traditional or non-mathematical techniques to evaluate

risk. These approaches are simple and based on theoretical assumptions. Some of the

conventional techniques are as follows:

1 PAYBACK PERIOD:

As already discussed, the Payback Period method considers the time period over which the

original investment in the project will be recovered by the firm out of the cash inflows of the

project. The payback period is then compared with the target payback period. If the proposal's

payback period is less than or equal to the target payback period, it may be accepted,

otherwise rejected. In order to incorporate risk of the proposal, the target payback period may

be shortened. As a result some project, which would have been on the verge of being

selected, otherwise, will now be rejected. The shortening of the target payback period is

based on the assumption that larger the recovery period, more risky the proposal would

be.

The Payback Period as an approach to handle risk is simple and straight forward. But it fails

to measure the risk, which may be of different degree in different alternative proposals.

Moreover, it reduces only that risk which arises due to time period and thus allows for other


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risks to prevail. The payback period also ignores the time value of money as well as the cash

flows arising after the payback period.

2 RISK ADJUSTED DISCOUNT RATE (RADR):

Another way of adjusting for risk is to modify the rate of return to include a risk, premium

wherever needed. In a sense, the reasoning behind this is quite simple i.e., the greater the

risk, the higher should be the desired return from a proposals. The RADR approach to handle

risk in a capital budgeting decision process is a more direct method. The RADR is based on

the premise that riskiness of a proposal may be taken care of, by adjusting the discount rate.

The cash flows from a more risky proposal should be discounted at a relatively higher

discount rate as compared to other proposals whose cash flows are less risky.

An investor is basically risk averse and try to avoid risk. However, he may be ready to take

risk provided he is rewarded for undertaking risk by higher returns. So, more risky the

investment is, the greater would be the expected return. The expected return is expressed in

terms of discount rate, which is also termed as the minimum required rate of return generatedby a proposal if it is to be accepted. Therefore, there is a positive, correlation between risk of

a proposal and the discount rate.

A firm at any point of time has a risk level emanating from the existing investment. The firm

also has a discount rate to reflect that level of risk. In case, there is no risk of the existing

investment, then the present discount rate may be known as the risk free discount rate. If the

risk level of the new proposal is higher than the risk level of the existing investment, then the

discount rate to be applied to find out, the present values of the cash flows of the proposal

should also be higher than the present discount rate. Similarly two different proposals having

varying degree of risk should be evaluated at different discount rates. The difference betweenthe discount rate applied to a risk less proposal and a risky proposal is known as the risk

premium. The RADR may be expressed in terms of Equation as follows:

Ka = k +

Where Ka = Risk Adjusted Discount Rate

k = Risk free Discount Rate, and

= Risk Adjustment Premium

It may be noted that the risk free discount rate is described as the rate of return on the

government securities. Since all the business proposals have higher degree of risk as

compared to zero degree of risk of government securities, the RADR is always greater than

the risk free rate. As the risk of a proposal increases, the risk adjustment premium i.e., a, also

increases. The relationship between the risk free rate, the risk premium the RADR and the

risk return line has been explained in the following figure.


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3 CERTAINTY EQUIVALENTS (CE):

An alternative approach to incorporate the risk is to adjust the cash flows of a proposal to

reflect the riskiness. The CE approach attempts at adjusting the future cash flows instead of

adjusting the discount rates. The expected future cash flows, which are taken as risky and

uncertain, are converted into certainty cash flows. Intuitively, more risky cash flows will be

adjusted down lower than will the less risky cash flows. The extent of adjustment will vary and

it can be either subjective or based on a risk return model. These adjusted cash flows are

then discounted at risk free discount rate to find out the NPV of the proposal.

The procedure for the CE approach can be explained as follows:

Step1.

Estimation of the future cash flows from the proposal. These cash flows do have some degree

of risk involved.

Step 2.

The calculation of the CE factors for different years. These CE factors reflect the proportion of

the future cash flow a finance manager would be ready to accept now in exchange for the

future cash flow. The CE factors represent the level of present money at which the firm wouldbe indifferent between accepting the present money or the future cash flow. For example,

cash inflow of Rs. 10,000 is receivable after 2 years. However, if the inflow is available right

now, the firm may be ready to accept even 70% of Rs. 10,000 i.e., Rs. 7,000 only. This 70%

or .7 is the CE factor. For different years the CE factors, will be different to account for the

timing as well as the varying degree of risk involved. It may be noted that higher the riskiness

of a cash flow, the lower will be the CE factor.

Step 3.

The expected cash flows for different years as calculated in step 1 above are multiplied by the

respective CE factors and the resultant figures are described as certainty equivalent cash

flows.Step 4.

Once all the cash flows are reduced to CE cash flows then these CE cash flows are dis-

counted at risk free rate to find out the NPV of the proposal.

Decision rule in CE approach

Accept a proposal with positive CE NPV. In case of mutually exclusive proposals the rule is

that the proposal having the highest positive CE NPV is accepted.

4 SENSITIVITY ANALYSIS:

As discussed that the NPV of a project is based upon the series of cash flows and the

discount factor. Both these determinants depend upon so many variables such as sales

revenue, input cost, competition etc. Given the level of all these variables, there will be a set

series of cash flows and hence there will be a NPV of the proposal. However, if any of these

variables changes then the value of the NPV will also change. It means that the value of NPV


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is sensitive to all these variables. However, in most of the cases, the value of NPV will not

change in the same proportion for a given change in anyone of these variables. For some

variables the NPV may be less sensitive while for others the NPV may be more sensitive. The

Sensitivity Analysis (SA) deals with the consideration of sensitivity of the NPV in relation to

different variables contributing to the NPV. .

In general, the SA is a theoretical procedure whereby values of the variable parameters

(inputs) are changed to denote different situations/assumptions, and the effect of these

changes is measured on the expected value of the outcome (result). When applied to the

capital budgeting situations, the SA is a technique to evaluate the effect of changes in factors

contributing to cash flows on the value of the NPV of the proposal .

The single point estimates of cash flows or the expected results are based on the judgment

of the analyst and the information available. In fact, these are the averages of the possible

outcome, implicitly weighed by their respective probabilities. By introducing a range of high,

low and expected levels of cash inflows and outflows, the analyst can use a form of sensitivity

analysis to indicate the consequences of expected fluctuations, and thus the degree of risk. At

times, the past experience can provide clues to the range of future outcomes, but essentiallythe projection of future cash flows has to be judgmental and based on specific estimates.

The following steps are required to apply the SA to, capital budgeting proposals:

A) Based on the expectations for the future, the cash flows are estimated in respect of the

proposal.

B) To identify the variables which have a bearing on the cash flows of a proposal. For

example, some of these variables may be the selling price, cost of inputs, market share,

market growth rate etc.,

C) To establish the relationship, between these variables and the output value i.e., the effectof these variables on the value of NPV of the proposal.

D) To find out the range of variations and the most likely value of each of these variables, and

E) To find out the effect of change in any of these variables on the value of NPV. This

exercise should be performed for all the factors individually. For example, in case of a project

involving .the product sale, the effect of change in different variables such as number of units

sold, selling price, discount rate etc., can be taken up on the NPV or IRR

of the project. This information can be used in conjunction with the basic capital budgeting

analysis to decide whether or not to take up the project.

5 BREAK-EVEN ANALYSIS:

Traditional break-even analysis attempts to estimate the revenues that will be needed in order

for a project to break even in accounting terms- that is, to make a net income zero. However,

a capital budgeting proposal may be analyzed as to how much revenue will be needed for a

project to break even in financial terms-that is, to make the net present value zero.


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The financial break-even is computed by first estimating the annual cash flows needed to

make the net present value zero, then ascertaining the revenues needed to generate this

annual cash flow, and finally estimating the number of units that have to be sold to create this

revenue.

In fact, the financial Break-even is a higher hurdle because it requires the firm to make

sufficient returns to cover the discount rate on the funds invested in the project.

Consequently, the financial break-even will be higher (in units and amount) then the

accounting break-even.

STATISTICAL TECHNIQUES OF RISK ANALYSIS

The different techniques discussed in the previous lesson were conventional techniques to

study, analyze and incorporate the risk associated with a proposal, fail to measure and

quantify the risk in precise terms. On the other hand, there are certain statistical techniquesavailable to measure and incorporate risk in a capital budgeting decision process. These

techniques, as discussed below, can be used to evaluate the risk-return characteristics of a

capital budgeting proposal. The most important concept used in these statistical techniques is

that of probability. Therefore, before analyzing the statistical techniques of incorporating risk,

the concept of probability must also be understood.

The Concept of Probability:

The probability may be defined as the likelihood of happening or non-happening of an event.

It may be described as a measure of chance of happening or non-happening of an event. Forexample, one may say that there are 20% chances that the sales will increase by 80% during

the year, or that there are 75% chances that the firm will be able to achieve 50% market

share over a period of next 5 years. These descriptions of 20% and 75% chances are the

description of probability of the respective events. So, the probability may be taken as a

measure of an opinion about the likelihood of happening of an event. If the event is certain to

happen, then the probability is defined as one and if the event has no chance of occurrence,

then the probability is described as 0. So, the probability always has a value between 0 and 1.

While estimating the cash inflows resulting from a proposal say, at the end of year 1, a

finance manager may find that he is not having one estimation of cash inflow rather he has a

series of estimation of cash inflows for the that year and for each estimation there is a

probability that the actual cash flows may be same as estimated. For example, the following is

the series of estimated cash inflows together with their probabilities at the end of year 1.

Cash flows Probabilities

Rs. l,00,000 .2

1,50,000 .4

1,75,000 .3


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2,00,000 .1

Similarly, series of estimated cash inflows may be available for different other years also.

Two points are worth noting here.

First, that the total of probabilities for anyone year would always be equal to one, and

Second, that the actual cash inflow may be any figure, even other than the cash inflows

given in the series. It may be noted that the series of expected cash inflows together withthe associated probabilities for a particular year is also know as probability distribution.

1 Probability Distribution:

The probability distribution may be defined as a set of possible cash flows that may occur at a

point of time and their probabilities of occurrence, In the probability distribution given above

for year 1, there are 4 possible cash inflows.

The probabilities given for these cash inflows can be interpreted as follows: There is a 20%

chance that the cash inflows will be Rs. 1,00,000; there is 40% chance that the cash inflow

will be Rs. 1,50;000 and so on.

In some cases, the probabilities can be assigned on the basis of past experience or historical

data. But it may not always be possible in a capital budgeting decision. The reason for this is

obvious. The capital budgeting decisions are, generally, not of repetitive nature. Moreover,

data available from the experience of other firms may not be available or not at all relevant,

because each capital budgeting situation is a specific situation. Therefore, in most of the

capital budgeting situations, the decision maker on the basis of some relevant facts and

figures and his subjective considerations usually assigns the probabilities.

If the decision maker foresees a risk in the proposal then he has to prepare a separate

probability distribution to summarize the possible cash flow for each year through the

economic life of the proposal. Thereafter, the next step is to find out the expected value ofprobability, distribution for each year.

Expected value of a Probability Distribution:

The initial step required in evaluating a risky proposal is to find out the expected value of

probability distribution for each year. For this, each cash flow of the probability distribution is

multiplied by the respective probability of the cash flow and then adding the resulting

products. This final figure is then considered as the expected value of the cash inflow for that

year for which the probability distribution has been considered. This procedure is to be

adopted for the probability distributions for all the years and then the expected value of cash

inflows are discounted at an appropriate discount rate to find out the NPV of the proposal.

Standard Deviation: An Absolute Measure of Risk and Variability.

The statistical tool of standard deviation provides a measure of spread of the distribution of

expected cash flows. The standard deviation as a technique of measuring dispersion can be

used to measure the deviations of each possible cash flow about the expected value of cash

flow. It is also named as root-mean-square deviation and is calculated by taking the square

root of the mean of squared deviations. These deviations refer to the difference between,


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possible cash flow and the expected value of the cash flow. The following steps are needed to

ascertain the standard deviation of the probability distribution of cash flows:

Step1.

Find out the probability distribution of the cash flows over different years and find out

expected value of cash flow for each year.

Step 2.

Subtract each cash flow (CF) from the expected value of the cash flow i.e., EVCF and get thesquare of the differences i.e., (CF-EVCF)2.

Step 3.

Multiply the squared deviations i.e., (CF-EVCF)2 by the probabilities of the occurrence of its

corresponding cash flow, i.e., find out PI (CF1-EVCF)2, or P2 (CF2-EVCF)f or P3 (CF3-EVCF)2

etc. where Pi is the probability of a particular cash flow.

Step 4.

Add these products i.e., find out the sum of Pi (CFi-EVCF)2 and get the square root of this

figure i. e., find out the value of,

21)(EVCFCFPiini==This value is called the standard deviation, . It may be noted that the standard deviation is

calculated by taking all deviations positive or negative. This implies that the risk aversion

extends to, all the deviations from the expected value even if the deviations are positive i.e.,

when the possible cash flow are more than the expected value of the cash flow. The larger

dispersion will produce a larger standard deviation and therefore, larger standard deviation

indicates riskier capital budgeting proposals.

Coefficient of Variation: A Relative Measure of Risk.Coefficient of Variation (CV) is a relative measure of dispersion and can be applied in capital

budgeting decision process to measure the risk of a project particularly in case when the

alternative projects are of different sizes. The CV is defined as the standard deviation of the

probability distribution divided by its expected value i.e.,

CV = /EVCF.

It may be noted that the CV is a pure number and is not affected by the measuring unit. The

advantage of CV over standard deviation is that the former can be used to compare the

riskiness of mutually exclusive proposals even if their expected values are not equal. The CVis also useful in evaluation of those proposals whose initial outlays differ substantially.

PROBABILITY DISTRIBUTION APPROACH:

In the preceding section the concept of probability has been introduced to take care of the risk

and variability of cash flows. The expected values of cash flows were calculated for difference

year and then the NPV and the standard deviation were calculated, in order to reach at a


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capital budgeting decision. Now this analysis can be extended and the probability theory can

be applied to know something more about the variability cash flows.

The concept of probability has been used to find out the NPV of the proposal. It results in

acceptance of those proposals, which have a positive NPV. However, in actual practice

the value of NPV may be less than 0 or just 0 or a positive value. The probability

distribution approach attempts to determine the probability that the actual NPV occurrence

is going to be less than 0 and that the project has therefore, been accepted wrongly. Thus,

the probability distribution approach helps in determining the error of judgment of the firm

in selecting a proposal, which at a later stage turns out to be a negative NPV project. In

order to develop the probability distribution approach, an important assumption regarding

the behavior of cash flows needs to be made. The re-quired assumption is whether the

cash flows associated with a project are independent cash flows or dependent cash flows.

A proposal is set to be having independent cash flows when the cash flow of any period is not

affected by the cash flow or flows of any of the preceding period. For example, the expectedcash flow of year 2 is not affected by the cash inflow of year 1 and similarly the cash flow of

year 5 is not affected by the cash inflow of year preceding period i.e., year 1 through year 4.

On the other hand, a proposal is said to have dependent cash flows when the favorable or

unfavorable cash flow in a particular period affects the cash flow of any period thereafter. In

practice, most of the proposals have dependent cash flows. The effect of the nature of cash

flow on the calculation of the value of NPV may be analyzed as follows:

2 SIMULATION ANALYSIS:

Simulation is yet another statistical technique to deal with uncertainty and is also based on

the concept of probabilities. Theoretically speaking, simulation refers to 'Creation of an

Appearance without the Reality'. Thus, in simulation, the appearance seems to be true but it

is not real. Simulation therefore, refers to representation of a system that reacts to a change

to any of input variable in a similar way as to that variable which is being simulated. There are

several techniques of simulation, however, the Monto Carlo Method is the most common. The

Monto Carlo Method is based on the concept of random numbers and is useful in the analysis

of uncertainty.

The simulation analysis can be applied to capital budgeting decision situations also. When

applied to capital budgeting, the simulation requires the generation of values of cash flows

using predetermined-probability distribution and the random numbers. The different

components of cash flows are placed in relation to one another in a mathematical model. The

process of generating the values of cash flows is repeated numerous times to result in a

probability distribution of cash flows. The process of generating the random number and using

the probability distribution of cash flows help generating values of different variables. These

values are then put in a mathematical model to develop a NPV. By repeating the same

process for number of times say a thousand or ten thousands times, a probability distribution


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of NPV is created. The simulation allows considering the projects under alternative scenarios.

The decision maker can consider the effect of a limited number of plausible combinations of

variables affecting the outcome of a proposal. The application of simulation analysis has been

analyzed in the following example.

3 DECISION TREE APPROACH:

Quite often a firm may have to take a sequential decision i.e., the present decision is affected

by the decisions taken in the past or it affects the future decisions of the same firm. In capital

budgeting, the evaluation of a project frequently requires a sequential decision making

process where the accept-reject decision is made in several stages. Instead of taking a

decision once for all, it is broken up into several parts and stages. At each stage there may be

more than one option available and the firm may have to decide every time that which option

is to be taken for. This can be explained with the help of a simple situation.

A firm is considering to launch a new product and to install a plant with capacity of 10,000units a month. It is hopeful of selling the entire production. However, if due to one or the

other factor, the demand is not generated to lift even the break-even level of production,

then the firm will face a heavy loss. In this case, it will be better for the firm to first install a

pilot project and go for test marketing. If the market accepts the product, full-fledged plant

may be installed in the next stage. This is a two-stage decision. The first occurs before the

test market. At that point, the cash flows related to both the test and to the production

must be considered. After the test, another decision must be made. At this point, the cash

flows related to the market test are sunk costs and are irrelevant to the decision to be

made. At this second point, the decision to be made cannot affect the cash flows already

made in connection with the market test. Hence according to the incremental cash flowsrule, they are not relevant. The only relevant flows are those related to the production

phase. However, in practice there may be multi stages decisions also.

An analytical technique used in sequential decisions is decision tree. The decision tree

approach can take care of these types of multi stages decisions. The decision tree approach

gets its name because of the resemblance with a tree having number of branches. A decision

tree is a branching diagram representing a decision problem as a series of decisions to be

taken under conditions of uncertainty. A present decision depends upon the past decision and

their outcomes. The decision trees are the diagrams that permit the various decisions

alternatives, their outcomes and probabilities of their occurrences to be mapped in a clearfashion. In a typical decision tree, therefore, the project is broken down in to clearly defined

stages, and the possible outcomes at each stage are listed along with the probabilities and

cash flows effect of each outcome.


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Steps in Decision Tree Approach:

While constructing a decision tree for a given problem the following steps may be required.

1. Break the Project into clearly defined stages. In some cases, this is fairly easy to do

so. For example, a computer software company may take up the project of new

package in different stages, i.e., research and development, market testing, limited

production and then full production. Similarly, other capital budgeting decisions may

also be broken up in different stages.

2. List all the possible outcomes at each stage. Specify the probability of each outcome

at each stage based on information available. This task will become progressively

more difficult as more and more stages introduced.

3. Specify the effect of each outcome on the expected cash flows form the project.

4. Evaluate the optimal action to be taken at each stage in the decision tree, based on

the outcome at the previous stage and its effect on cash flows.

5. Estimate the optimal action to be taken at the vary first stage , based on the

expected cash flows over the entire projects and all the likely outcomes of the cash

flows. Following example illustrates the decision tree approach.

CAPM ( CAPITAL ASSET PRICING MODEL )

CAPM was developed by financial economist william sharpe. Its based on idea that

investment includes systematic and un systematic risk. CAPM is evolved as a way tomeasure systematic risk. General idea behind CAPM is that investors need to be

compensated in two ways.

1) time value of money, thats given by risk free rate of interest

2) compensation for taking additional risk.

This compensation is calculated by taking a risk measure (beta) that compares the return of

the asset to the market over a period of time.

CAPM FORMULA

Rs = Rf + Bs (Rm Rf )

Where,

Rs = return required on the investment

Rf = return on risk free investment

Bs = beta of the security (systematic risk)


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Rm = average return on all the securities

CAPM reflects the mathematical relationship bet risk and return. Higher the risk (beta) the

higher is the required return.

ASSUMPTIONS UNDER CAPM

A) all investors have rational expectations

B) there are no arbitrage opportunities

C) returns are distributed normally

D) fixed quantity of assets

E) perfect capital market

F) risk free rates exists with time less borrowing capacity an

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