Mba 517

Punjab Technical University

World over distance Education is fast growing mode of education because of the unique benefits it provides to the learners. Universities are now able to reach the community which has for so long been deprived or higher education due to various reasons including social, economic and geographical considerations. Distance Education provides them a second chance to upgrade their technical skills and qualifications.

Some of the important considerations in initiating distance education in a country like India, has been the concern of the government in increasing access and reach of higher education to a larger student community. As such, only 6-8% of students in India take up higher education and more than 92% drop out before reaching 10+2 level. Further, avenues for upgrading qualifications, while at work, is limited and also modular programs for gaining latest skills through continuing education programs is extremely poor. In such a system, distance education programs provide the much needed avenue for:

Increasing access and reach of higher education;

Equity and affordability of higher education to weaker and disadvantaged sections of the society;

Increased opportunity for upgrading, retraining and personal enrichment of latest knowledge and know-how;

Capacity building for national interests.

One of use important aspects of any distance education program is the learning resources. Learning material provided to the learner must be innovative, thought provoking, comprehensive and must be tailor-made for self-learning. It has been a continuous process for the University in improving the quality of the learning material through well designed course materials in the SIM format (self-instructional material). While designing the material, the university has researched the methods and process of some of the best institutions in the world imparting distance education.

About the University

Punjab Technical University (PTU) was set up by the Government of Punjab in 1997 through a state Legislative ACT. PTU started with a modest beginning in 1997, when University had only nine Engineering and thirteen Management colleges affiliated to it. PTU now has affiliated

43 Engineering colleges, 56 colleges imparting Management and Computer Application courses, 20 institutions imparting pharmacy education, 6 Architecture institutions, 2 Hotel Management and 12 Regional Centres for imparting M. Tech and Ph. D Programs in different branches of Engineering and Management. During a short span of nine years, the University has undertaken many innovative programs. The major development during this period is that University has restructured its degree program and upgraded syllabi of the course in such a way as to increase the employability of the student and also to make them self-reliant by imparting Higher Technical Education. We at Punjab Technical University are propelled by the vision and wisdom of our leaders and are striving hard to discharge our duties for the overall improvement of quality of education that we provide.

During a short span of nine years, the University has faced various challenges but has always kept the interest of students as the paramount concern. During the past couple of years, the University has undertaken many new initiatives to revitalize the educational programs imparted with the colleges and Regional centers.

Though knowledge and skills are the key factors in increasing the employability and competitive edge of students in the emerging global environment, an environment of economic growth and opportunity is necessary to promote the demand for such trained and professional manpower. The University is participating in the process of technological growth and development in shaping the human resource for economic development of the nation.

Keeping the above facts in mind Punjab Technical University, initiated the distance education program and started offering various job oriented technical courses in disciplines like information technology, management, Hotel Management, paramedical, Media Technologies and Fashion Technology since July 2001. The program was initiated with the aim of fulfilling the mandate of the ACT for providing continuing education to the disadvantaged economically backward sections of society as well as working professionals for skill up-gradation.

The University has over the years initiated various quality improvement initiatives in running its distance education program to deliver quality education with a flexible approach of education delivery. This program also takes care of the overall personality development of the students. Presently, PTU has more than 60 courses under distance education stream in more than 700 learning centers across the country.

About Distance Education Program of PTU

Over the past few years, the distance education program of PTU has gained wide publicity and acceptance due to certain quality features which were introduced to increase the effectiveness of learning methodologies. The last comprehensive syllabus review was carried out in the year 2004-05 and the new revised syllabus was implemented from September 2005. The syllabus once reviewed is frozen for a period of 3 years and changes, if any, shall be taken up in the year 2008. Various innovative initiatives have been taken, which has increased the popularity of the program. Some of these initiatives are enumerated below:

1. Making a pyramid system for almost all courses, in which a student gets flexibility of continuing higher education in his own pace and per his convenience. Suitable credits are imparted for courses taken during re-entry into the pyramid as a lateral entry student.

2. Relaxed entry qualifications ensure that students get enough freedom to choose their course and the basics necessary for completing the course is taught at the first semester level.

3. A comprehensive course on „Communications and Soft Skills‰ is compulsory for all students, which ensures that students learn some basic skills for increasing their employability and competing in the globalized environment.

4. Learning materials and books have been remodeled in the self-Instructional Material format, which ensures easy dissemination of skills and self-learning. These SIMs are given in addition to the class notes, work modules and weekly quizzes.

5. Students are allowed to take a minimum of 240 hours of instruction during the semester, which includes small group interaction with faculty and teaching practical skills in a personalized manner.

6. Minimum standards have been laid out for the learning centers, and a full time counselor and core faculty is available to help the student anytime.

7. There is a wide network of Regional Learning and Facilitation Centers (RLFC) catering to each zone, which is available for student queries, placement support, examination related queries and day-to-day logistic support. Students need not visit the University for any of their problems and they can approach the RLFC for taking care of their needs.

8. Various facilities like Free Waiver for physically challenged students, Scholarship scheme by the government for SC/ST candidates, free bus passes for PRTC buses are available to students of the University.

The university continuously aims for higher objectives to achieve and the success always gears us for achieving the improbable. The PTU distance education fraternity has grown more than 200% during the past two years and the students have now started moving all across the country and abroad after completing their skill training with us.

We wish you a marvelous learning experience in the next few years of association with us!

DR. R. P. SINGH Dean

Distance Education

Dr. S. K. Salwan Vice Chancellor

Dr. S. K. Salwan is an eminent scientist, visionary and an experienced administrator. He is a doctorate in mechanical engineering from the IIT, Mumbai. Dr. Salwan brings with him 14 years of teaching and research experience. He is credited with establishing the Department of Design Engineering at the institute of Armament Technology, Pune. He was the founder-member of the integrated guided missile programme of defence research under His Excellency Honorable Dr. A.P.J. Abdul Kalam. He also established the high technology missile center, RCI at Hyderabad. He has been instrumental in implementing the Rs 1000-crore National Range for Testing Missiles and Weapon Systems at Chandipore, Balance in a record time of three years. He was director of the Armament Research and Development Establishment, Pune. Dr. Salwan has been part of many high level defence delegations to various countries. He was Advisor (Strategic project) and Emeritus Scientist at the DRDO. Dr. Salwan has won various awards, including the Scientist of the Year 1994; the Rajiv Ratan Award, 1995, and a Vashisht Sewa Medal 1996, the Technology Assimilation and Transfer Trophy, 1997 and the Punj Pani Award in Punjab for 2006.

Dr. R.P. Singh Dean, Distance Education

Dr. R.P. Singh is a doctorate in physics from Canada and has been a gold medallist of Banaras Hindu University in M.Sc. Dr. Singh took over the Department of Distance Education in November 2004 and since then the University has embarked on various innovations in Distance Education.

Due to combined efforts of the department, the RLFCÊs and Centers, and with active support of the Distance Education Council headed by Dr. O.P. Bajpai, Director University College of Engineering Kurukshetra University the distance education program of PTU is now a structured system which empowers the learner with requisite skills and knowledge which can enhance their employability in the global market. Dr. R. P. Singh is promoting distance education at the national level also and is a founder member of Education Promotion Society of India and is member of various committees which explores innovative ways of learning for the disadvantages sections of society. The basic aim of the distance education programs has been to assimilate all sections of society including women by increasing the access. Reach, equity and affordability of higher education in the country.

CAPITAL BUDGETING

MBA-517

This SIM has been prepared exclusively under the guidance of Punjab Technical University (PTU) and reviewed by experts and approved by the concerned statutory Board of Studies (BOS). It conforms to the syllabi and contents as approved by the BOS of PTU.

Copyright © Prof. Aruna and Prof. B. Murali Krishna, 2008

No part of this publication which is material protected by this copyright notice may be reproduced or transmitted or utilized or stored in any form or by any means now known or hereinafter invented, electronic, digital or mechanical, including photocopying, scanning, recording or by any information storage or retrieval system, without prior written permission from the publisher. Information contained in this book has been published by Excel Books Pvt. Ltd. and has been obtained by its authors from sources believed to be reliable and are correct to the best of their knowledge. However, the publisher and its author shall in no event be liable for any errors, omissions or damages arising out of use of this information and specifically disclaim any implied warranties or merchantability or fitness for any particular use.

Published by Anurag Jain for Excel Books Pvt. Ltd., A-45, Naraina, Phase-I, New Delhi-110 028 Tel: 25795793, 25795794 email: [email protected]

PTU DEP SYLLABI-BOOK MAPPING TABLE MBA-517 CAPITAL BUDGETING

Syllabi Mapping in Book

Section I

Capital Budgeting: An Introduction, Types of Investment Decisions, Objectives of Capital Budgeting, Estimating Project Characteristics.

Cost of Capital.

Section II

Method of Capital Budgeting: Payback method. Average Return Average Investment, Net Present Value, Internet Rate of Return, Capital Rationing, Reinvestment Rate, Assumptions of NPV and IRR & Conflicting Rankings. Multiple Internal Rate of Return, Inflation & Capital Budgeting. Risk Analysis: Return & Opportunity Cost of Capital, Single Product Analysis Under Risk.

Section III

A Project Is Not A Black Box: Simulation, Sensitivity Analysis & Decision Free Analysis, CAPM Model, Arbitrage Pricing Theory, Comparison Between CAPM & APT. Leasing: Leveraged Leases, Alternative Investment, Measures, Project Abandonment Analysis, Multiple Project Capital Budgeting.

Unit 1: Capital Budgeting (Page 3-12)

Unit 2: Cost of Capital (Page 13-21)

Unit 6: Leasing(Page 101-111)

Unit 3: Methods ofCapital Budgeting

(Page 25-57)

Unit 4: Risk Analysis (Page 59-79)

Unit 5: A Project is Not a Black Box(Page 83-99)

Contents Section-I

UNIT 1 CAPITAL BUDGETING 3

Introduction Definition Process of Capital Budgeting Capital is a Limited Resource Types of Investment Decisions Objectives of Capital Budgeting Estimating Project Characteristics Summary Keywords Review Questions Further Readings

UNIT 2 COST OF CAPITAL 13

Introduction Cost of Different Sources of Finance The Weighted Average Cost of Capital (WACC) Marginal Cost of Capital Summary Keywords Review Questions Further Readings

Section-II

UNIT 3 METHODS OF CAPITAL BUDGETING 25

Introduction Payback Period Method Accounting Rate of Return Discounted Cash Flow Methods Capital Rationing Reinvestment Rate NPV vs. IRR Multiple Internal Rate of Return Inflation and Capital Budgeting Summary Keywords Review Questions Further Readings

UNIT 4 RISK ANALYSIS 59

Introduction What is Risk? Return Opportunity Cost of Capital Yield Single Product Analysis under Risk Summary Keywords Review Questions Further Readings

Section-III

UNIT 5 A PROJECT IS NOT A BLACK BOX 83

Introduction Simulation Sensitivity Analysis Decision Tree Analysis Capital Asset Pricing Model (CAPM) Arbitrage Pricing Theory (APT) Comparison between CAPM and APT Summary Keywords Review Questions Further Readings

UNIT 6 LEASING 101

Introduction Leasing Leveraged Lease Alternative Investment Measures Project Abandonment Analysis Multiple Project Capital Budgeting Summary Keywords Review Questions Further Readings

Unit 1

Capital Budgeting

Unit 2 Cost of Capital

SECTION-I

Capital Budgeting

Notes

Punjab Technical University 3

Unit 1 Capital Budgeting

Unit Structure • Introduction • Definition • Process of Capital Budgeting • Capital is a Limited Resource • Types of Investment Decisions • Objectives of Capital Budgeting • Estimating Project Characteristics • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to understand: • Understand the importance of capital budgeting in marketing decision making • Explain the different types of investment project • Discuss the economic evaluation of investment proposals • Understand the concept and calculation of net present value and internal rate of return in

decision making • Discuss the advantages and disadvantages of the payback method as a technique for

initial screening of two or more competing projects.

Introduction Capital budgeting is a required managerial tool. One duty of a financial manager is to choose investments with satisfactory cash flows and rates of return. Therefore, a financial manager must be able to decide whether an investment is worth undertaking and be able to choose intelligently between two or more alternatives. To do this, a sound procedure to evaluate, compare, and select projects is needed. This procedure is called capital budgeting.

Definition Capital budgeting relates to the investment in assets or an organization that is relatively large. That is, a new asset or project will amount in value to a significant proportion of the total assets of the organization.

The International Federation of Accountants, IFAC, defines capital expenditures as „Investments to acquire fixed or long-lived assets from which a stream of benefits is expected. Such expenditures represent an organization's commitment to produce and sell future products and engage in other activities. Capital expenditure decisions, therefore, form a foundation for the future profitability of a company‰.

Capital Budgeting

Notes

4 Self-Instructional Material

Process of Capital Budgeting In line with our definition of capital budgeting, the term project refers to all investments (resource allocation) of significant size decided and implemented by an enterprise in order to shape its future. All projects are considered to be the result of a capital budgeting decision. Let's look at each step in turn.

1. Have a Good Idea Projects don't just fall out of thin air: someone has to have them. The main point here is that successful, dynamic and growing companies are constantly on the lookout for new projects to consider. In the largest organisations there are entire departments looking for alternatives and opportunities.

2. Look for Suitable Projects Once someone has had the idea to invest, the next step is to look at suitable projects: projects that complement current business, projects that are completely different to current business and so on. Initially, all possibilities will be considered: along the lines of a brainstorming exercise.

As time goes by, and as corporate objectives allow, the initial list of potential projects will be whittled down to a more manageable number.

3. Identify and Consider Alternatives Having found a few projects to consider, the organization will investigate any number of different ways of carrying them out. After all, the first idea probably won't either be the last or the best. Creativity is the order of the day here, as organizations attempt to start off on the best footing.

As the diagram suggests, at each of these first three stages, we need to consider whether what we are proposing fits in with corporate objectives. There is no point in thinking of a project that conflicts with, say, the growth objective or the profitability objective or even an environmental objective.

A lot of data will be generated in this stage and this data will be fed into stage four: Capital Investment Appraisal.

4. Capital Investment Appraisal This is the number crunching stage in which we use some or all of the following methods:

Payback (PB)

Accounting rate of return (ARR)

Net present value (NPV)

Internal rate of return (IRR)

Profitability Index (PI)

There are other techniques of course; but the technique to be used will depend on a range of things, including the knowledge and sophistication of the management of the organisation, the availability of computers and the size and complexity of the project under review.

Capital Budgeting

Notes


5. Analysis of Feasibility Stage four is the number crunching stage. This stage is where the decision is made as to which project is to be assessed as acceptable. That is, which project is feasible?

In order to choose the project, management needs some hurdles:

What must the payback be?

What rate of ARR is acceptable?

What is the NPV cut off?

What IRR is the least that we can accept?

What PI is the least that we can accept?

and so on.

Some projects will be discarded as a result of this stage. For example, if the PB cut off is, say, 2 years, and a project has a PB of 3 years, it will be rejected. The same is true of the ARR, NPV, IRR and PI.

Capital rationing might be a problem here, too, if the organization has general cash flow problems.

Capital Budgeting Policy Manual

Let's pause at this point to make the point that what we have just said about cut off rates and so on, come from formal procedures and documents. One such formal document is the Capital Budgeting Policy Manual, in which formal procedures and rules are established to assure that all proposals are reviewed fairly and consistently. The manual helps to ensure that managers and supervisors who make proposals need to know what the organization expects the proposals to contain, and on what basis their proposed projects will be judged.

The managers who have the authority to approve specific projects need to exercise that responsibility in the context of an overall organizational capital expenditure policy.

In outline, the policy manual should include specifications for:

1. An annually updated forecast of capital expenditures

2. The appropriation steps

3. The appraisal method(s) to be used to evaluate proposals

4. The minimum acceptable rate(s) of return on projects of various risks

5. The limits of authority

6. The control of capital expenditures

7. The procedure to be followed when accepted projects will be subject to an actual performance review after implementation.

6. Choose the Project Once we have determined the feasible/acceptable projects, we then have to make a decision of which to accept.

If we have capital rationing problems, we might be restricted to one project only. If we have no cash problems, we might choose two or more.

Whatever the cash position, we would like to invest in all projects that have a positive NPV, whose IRR is greater than our cut off rate and so on.

Capital Budgeting

Notes


7. Monitor the Project As with any part of the organization, the project must be monitored as it progresses. If the project can be kept as a separate part of the business, it might be classed as its own department or division and it might have its own performance reports prepared for it. If it's to be absorbed within one or more parts of the organization then it could be difficult to monitor it separately: this is something that management has to decide as they implement their new projects.

8. Post Completion Audit The final stage: once the project has been up and running for six months or a year or so, there must be a post completion audit or a post audit. A post audit looks at the project from start to finish: stages 1 - 7 and looks at how it was thought of, analysed, chosen, implemented, monitored and so on.

The purpose of the post audit is to test whether capital budgeting procedures have been fully and fairly applied to the project under review.

Of course, any weaknesses that might be found during the post audit might be specific to one project or they might relate to capital budgeting systems for the organization as a whole. In the latter case, the auditor will report back to his superiors and to management that systems need to be overhauled as a result of what has been found.

Capital is a Limited Resource In the form of either debt or equity, capital is a very limited resource. There is a limit to the volume of credit that the banking system can create in the economy. Commercial banks and other lending institutions have limited deposits from which they can lend money to individuals, corporations, and governments. In addition, the Federal Reserve System requires each bank to maintain part of its deposits as reserves. Having limited resources to lend, lending institutions are selective in extending loans to their customers. But even if a bank were to extend unlimited loans to a company, the management of that company would need to consider the impact that increasing loans would have on the overall cost of financing.

In reality, any firm has limited borrowing resources that should be allocated among the best investment alternatives. One might argue that a company can issue an almost unlimited amount of common stock to raise capital. Increasing the number of shares of company stock, however, will serve only to distribute the same amount of equity among a greater number of shareholders. In other words, as the number of shares of a company increases, the company ownership of the individual stockholder may proportionally decrease.

The argument that capital is a limited resource is true of any form of capital, whether debt or equity (short-term or long-term, common stock) or retained earnings, accounts payable or notes payable, and so on. Even the best-known firm in an industry or a community can increase its borrowing up to a certain limit. Once this point has been reached, the firm will either be denied more credit or be charged a higher interest rate, making borrowing a less desirable way to raise capital.

Faced with limited sources of capital, management should carefully decide whether a particular project is economically acceptable. In the case of more than one project, management must identify the projects that will contribute most to profits and, consequently, to the value (or wealth) of the firm. This, in essence, is the basis of capital budgeting.

Capital Budgeting

Notes


An efficient allocation of Capital is the most important finance function in modern times. It involves decisions to commit the firmÊs funds to the long-term assets. Capital budgeting or investment decisions are of considerable importance to the firm since they tend to determine its value by influencing its growth, profitability and risk.

The investment decisions of a firm are generally known as the capital budgeting or capital expenditure decisions. A capital budgeting decision may be defined as the firmÊs decision to invest its current funds most efficiently in the long-term assets in anticipation of an expected flow of benefits over a service of years. The long-term assets are those that affect the firmÊs operations beyond the one year period. The firmÊs investment decisions would generally include expansion, acquisition, modernization and replacement of the long-term assets. Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firmÊs expenditures and benefits and therefore, they should also be evaluated as investment decisions.

Capital Budgeting versus Current Expenditures

A capital investment project can be distinguished from current expenditures by two features:

a) Such projects are relatively large

b) A significant period of time (more than one year) elapses between the investment outlay and the receipt of the benefits.

As a result, most medium-sized and large organisations have developed special procedures and methods for dealing with these decisions. A systematic approach to capital budgeting implies:

a) The formulation of long-term goals.

b) The creative search for and identification of new investment opportunities.

c) Classification of projects and recognition of economically and/or statistically dependent proposals.

d) The estimation and forecasting of current and future cash flows.

e) A suitable administrative framework capable of transferring the required information to the decision level.

f) The controlling of expenditures and careful monitoring of crucial aspects of project execution.

g) A set of decision rules which can differentiate acceptable from unacceptable alternatives is required.

Types of Investment Decisions Every Investment decision is a specific decision in the given situation, for a given firm and with given parameters and therefore, an almost infinite number of types or forms of capital budgeting decisions may occur. In general, the capital budgeting decisions or investment decisions are categorized as follows.

1. From the Point of View of Firm’s Existence The capital budgeting decisions may be taken by a newly incorporated firm or by an already existing firm.

1. New Firm: Capital Budgeting decision relating to new firms are normally concerned with selection of a particular project, initial capacity utilization etc.

Capital Budgeting

Notes


2. Existing Firm: Capital budgeting decisions relating to existing firms may be concerned with replacement and modernization of assets, expanding the existing capacity, diversifying into new products/markets, investment in Research and Development etc.

(a) Decisions concerned with Replacement and Modernization: In case of an existing plant whose economic life is over, the decision to be made is concerned with replacement of the existing plant. In case the existing firmÊs plant / assets become obsolete (even before its economic life), the decisions to be made is concerned with modernization of its plant. In the former situation, the objective is to restore at least the same (existing) capacity while in the later situation the objective is to increase efficiency or reduce cost. As both of them aim at attaining greater levels of efficiency, these decisions are also called as „Cost reduction decisions‰.

(b) Decisions Concerned with Expansion: Here the decisions are with evaluation of marginal costs and marginal benefit where the management aims at expanding existing production capacity to increase its market share.

(c) Decisions Concerned with Diversification: When the management aims at reducing risk by entering (Diversifying) into new product lines, new markets, the capital budgeting decisions would be concerned with evaluation of marginal costs and margin/benefits associated with new products/markets. Further, the impact of diversification on existing products/markets should be considered. As capital budgeting decisions concerned with expansion and diversification aim at increasing revenue, these capital budgeting decisions are also known as „Revenue increasing Decisions‰.

(d) Decisions concerned with Investments in Research and development: When firms are plagued by technological obsolescence, investments in R&D are important to avoid huge capital expenditures. Hence, a proper evaluation of investments in R&D would be beneficial.

(e) Decisions concerned with Miscellaneous investments: Certain investment decisions like investments in pollution control equipment may not directly concern with either reduction of costs or increase of profits, but are essential due to legal requirements. Evaluation of these proposals/equipment is a specific capital budgeting decision.

2. From the Point of View of Decision Situation The capital budgeting decisions may also be classified from the point of view of the decision situation as follows:

(a) Independent Investments: Independent investments serve different purposes and do not compete with each other. For examples, a heavy engineering company may be considering expansion of its plant capacity to manufacture addition/excavators and addition of new production facilities to manufacture a new product – light commercial vehicles depending on their profitability and availability of funds, the company can undertake both investments.

(b) Contingent or Dependent Investments: Contingent investments are those investments where the choice of one investment necessitates undertaking one or more other investments. For examples, if a company decides to build a factory in a remove, backward area, it may have to invest in houses, roads, hospitals, schools etc for employees to attract the work force. Thus, building

Capital Budgeting

Notes


of factory also requires investment in facilities for employees. The total expenditure will be treated as one single investment.

(c) Mutually Exclusive Investments: Mutually exclusive investments serve the same purpose and compete with each other. If one investment is undertaken, others will have to be excluded. A company may, for example, either use a more labour-intensive, semi-automatic machine, or employ a more capital – intensive, highly automatic machine for production. Choosing the semi-automatic machine preludes the acceptance of the highly automatic machine.

Objectives of Capital Budgeting Capital Budgeting decisions are the most important part of financial management. The decisions concerning the allocations of scarce resources, decide the fate of the company. Any mistake in this stage creeps into other aspect of the firm and impacts the prospects of the firm for a long future period of time. One practical example in this regard is, Ponds Indian Limited have launched Ponds toothpaste, which left bitter memories to the company. This decision not only resulted in financial losses, but also its reputation had taken a beating.

Capital budgeting decisions have the following objectives:

1. Capital budgeting decisions involve commitment of huge amount funds. These funds if not allocated to projects with sufficient rate of return, it would result in the erosion of capital.

2. Capital budgeting decisions have long-term effects on the risk-return composition of the firm. Any discrepancy in this aspect would result in accepting unprofitable projects whose impact would be felt for a long future period of time.

3. Capital budgeting decisions are irreversible. Once funds are committed to projects it is not possible to revert back, unless the management is ready to absorb heavy losses. Hence, it is of almost importance to carry out a meticulous evaluation of the project.

4. Capital budgeting decisions affect a companyÊs ability to compete. Right decision to expand or modernize can work wonders for the company. All the same time, wrong decisions can till the company.

5. Capital budgeting decisions are complex in nature. This complexity arises due to the difficulty in estimating the cash inflows that arise in distant uncertain future.

Estimating Project Characteristics Business firms have scarce resources that must be allocated among competitive uses. The available capital must be used in a manner which is consistent with the over all socio-economic objectives. This becomes more difficult when there are several competing projects, each giving a rate of return higher than the minimum cut-off rate.

For a detailed evaluation of the project, the following project characteristics have to be estimated.

1. Technical feasibility

2. Economic feasibility

3. Financial feasibility

4. Managerial competence

5. Market feasibility

Capital Budgeting

Notes


1. Technical Feasibility A project must be technically feasible. This can be judged by a detailed assessment of the following factors:

i) Location of the project: The project must be located at a place where saw materials, transport facilities, manpower, market for the products will be readily available.

ii) Technology used: The technology used has been tested and suits the local conditions. The technical know how is available and technical collaborators are persons of good reputation.

iii) Plant and equipment: The supplier of plant and equipment needed for the projects are of experience and reputation. Plant layout is in accordance with the production flow diagram.

iv) Construction and installation: These schedules have been drawn out and they will be adhered to as scheduled. Technical feasibility seeks to determine whether prerequisites for the successful commissioning of the project have been considered and reasonably good choices have been made with respect to location size process etc.

2. Economic Feasibility Economic feasibility analysis is also referred to as a social cost benefit analysis which is considered with judging a project from the larger social point of view but mot in monetary terms. In such an evaluation, the focus is the social costs and benefits of a project which may often be different from the monetary costs and benefits of the firm.

The economic necessity aspect may be taken care of by taking into account the following factors. The extent to which

a) The market will absorb the additional production of the new project.

b) The project is expected to contribute to the natural government department.

c) The project can bring about development in the area.

d) The project will create more employment etc.

3. Financial Feasibility Financial appraisal is done to ascertain whether the proposed project will be financially viable in the sense of being able to meet the burden of servicing debt and whether the proposed project will satisfy the return expectations of those who provide capital. While appraising a project financially, the following aspects should be kept in mind.

1. Cost of the Project: The estimates of the cost of the project should cover all items of expenditure and should be realistic.

2. Sources of Finance: Sources of finance contemplated by the promoters should be adequate and necessary finance should be available during installation. Financial institutions give special emphasis to the following aspects which have to be kept in mind while evaluating a project on financial criteria.

1. Investment outlay and Cost of Project

2. Means of Financing

3. Cost of Capital

4. Projected Profitability

Capital Budgeting

Notes


5. Break Even Point

6. Cash flows of the Project

7. Investment worthiness judged in terms of various criteria of merit

8. Projected financial position and flows

9. Level of risk

4. Managerial Competence The technical competence, administrative ability, integrity and resourcefulness of borrowing concernÊs to p managerial personnel determines to a great extent the willingness of a financial institution to accept a term loan proposal.

The loan application from firms having competent and honest management finds favorable considerations. It can therefore be stated that the appraisal of the managerial competence is of primary importance in the overall appraisal of the project.

5. Market Feasibility Market feasibility is concerned with two questions:

i) What would be the aggregate demand of the proposed product / service in future?

ii) What would be the market share of the project under appraisal?

In order to answer these two questions, a market analyst requires a wide variety of information and suitable forecasting methods.

The information required includes:

a) Consumption trends in the past and present level.

b) Past and present supply position.

c) Production possibilities and constraints.

d) Imports and exports.

e) Structure of competition.

f) Cost structure.

g) Elasticity of demand.

h) Consumer behavior, intentions, motivations, preferences etc.

i) Distribution channels and marketing policies in use.

j) Administrative, technical and legal constraint.

Student Activity Fill up the blanks:

1. Capital budgeting is also known as __________

2. Estimating the return period on investment is known as ___________

3. Capital budgeting techniques is classified into ________ methods.

Capital Budgeting

Notes


Summary In brief, this unit has demonstrated that capital budgeting involves a lot more than just carrying out a few calculations for payback, ARR and so on.

The capital budgeting process involves expenditures and investments that are relatively large and that must then be undertaken and controlled in a serious, professional way.

Keywords Capital Budgeting: The firmÊs decision to invest its current funds most efficiently in the long-term assets in anticipation of an expected flow of benefits over a service of years.

Independent Investments: Independent investments serve different purposes and do not compete with each other.

Contingent Investments: Contingent investments are those investments where the choice of one investment necessitates undertaking one or more other investments.

Review Questions 1. Define the concept of capital budgeting and explain its objectives.

2. Briefly explain the process of capital budgeting.

3. What are the different types of capital budgeting?

4. Explain the differences between the capital budgeting and current expenditure.

Further Readings I M Pandey, Financial Management

Dr. S.N. Maheswari, Financial Management (Principles & Practices)

Khan and Jain, Financial Management (Text, Problems and Cases)

Prasanna Chandra, Financial Management (Text, Problems and Cases)

Cost of Capital

Notes


Unit 2 Cost of Capital Unit Structure • Introduction • Cost of Different Sources of Finance • The Weighted Average Cost of Capital (WACC) • Marginal Cost of Capital • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to: • Know the concept of cost of capital • Understand the various types of cost of capital • Know the concept of marginal cost of capital

Introduction The term „cost of capital‰ refers to the minimum rate of return a firm must earn on its investment so that the market value of the companyÊs equity shares does not fall. This is possible only when the firm earns a return of the projects financed by equity share holderÊs funds at a rate which is at least equal to the rate of return expected by them.

More specifically, "cost of capital" is defined as "the opportunity cost of all capital invested in an enterprise."

Let's dissect this definition:

1. "Opportunity cost" is what you give up as a consequence of your decision to use a scarce resource in a particular way.

2. "All capital invested" is the total amount of cash invested into a business.

3. "In an enterprise" refers to the fact that we are measuring the opportunity cost of all sources of capital which include debt and equity.

The cost of capital has two aspects to it:

1. The cost of funds that a company raises and uses, and the return that investors expect to be paid for putting funds into the company.

2. It is therefore the minimum return that a company should make on its own investments, to earn the cash flow out of which investors can be paid their return.

The cost of capital is an opportunity cost of finance, because it is the minimum return which an investor requires. For shareholders it is the dividend they expect to receive plus a capital gain on the value of their shares, while for loan holders it is the rate of interest which is quoted on the loan. Failure to pay such required return will result in

Capital Budgeting

Notes


the providers of finance transferring their holdings to other opportunities with a better rate of return. The cost of capital has three elements:

1. Risk free rate of return: Return required from a completely risk free investment. E.g. yield on government securities.

2. Business risk premium: Increase in required rate of return due to uncertainty about future and business prospects.

3. Financial risk premium: Dangers of high debt levels, variability in equity earnings after payments to debt capital holders.

The above three components of cost of capital may be put in the form of following equation.

K = ro + b + f

Where k = cost of capital

ro = return at zero risk level

b = premium for business risk

f = premium for financial risk

In capital budget decisions, the cost of capital is often used as a discount rate (or) hurdle rate on the basis of which the firmÊs future cash flows are discounted to find out their present values. Thus, the cost of capital is the very basis for financial appraisal of new capital expenditure proposals. The decision of the finance manager will be irrational and wrong in case of capital is not correctly determined. This is because the business must earn at least at a rate which equals to cost of capital in order to make at least a break-even.

Cost of Different Sources of Finance Where a company uses a mix of equity and debt capital its overall cost of capital might be taken to be the weighted average cost of each type of capital. Thus

Cost of Ordinary Shares

Cost of Equity

In finance, the cost of equity is the minimum rate of return a firm must offer shareholders to compensate for waiting for their returns, and for bearing some risk.

The cost of equity capital for a particular company is the rate of return on investment that is required by the company's ordinary shareholders. The return consists both of dividend and capital gains, e.g. increases in the share price. The returns are expected future returns, not historical returns, and so the returns on equity can be expressed as the anticipated dividends on the shares every year in perpetuity. The cost of equity is then the cost of capital which will equate the current market price of the share with the discounted value of all future dividends in perpetuity.

The cost of equity reflects the opportunity cost of investment for individual shareholders. It will vary from company to company because of the differences in the business risk and financial or gearing risk of different companies.

The cost of equity is calculated by the following formula:

Ke = Earning per share/Market Price per share

Ke = Cost of Equity

EPS = Earning Per Share

MPS = Market Price Per Share

Cost of Capital

Notes


The formula above calculates the cost of equity based on a firm's current rate of return. If one assumes a perfect market, industry-specific costs of equity reflect the riskiness of particular industries. A high cost of equity would then indicate a higher-risk industry that should command a higher return to compensate for the higher risk.

However, there are also a variety of other ways to estimate the cost of equity. For example, using the CAPM model, the cost of equity is the product of the Market Risk Premium and the equity's Beta_(finance) plus the Risk-free_interest_rate.

New fund for equity shareholders are obtaining from:

New issuance of shares.

Cash derived from retained earnings.

Shareholders can not subscribe for new shares unless they are promised a better return on those shares. Retained earnings also have a cost, the dividend forgone by shareholders. The dividend payable to ordinary shareholders represents the cost of shares.

Dividend Valuation Model Ignoring share issue costs, the cost of equity for both new issue and retained earnings, could be estimated by means of a dividend valuation model. The assumption that the market of shares is directly related to expected future dividends on the shares.

1. Constant dividend: Where is it assumed that dividend will remain constant through out the years the cost of equity is calculated as follows:

Ke = D

MP

Ke is the shareholdersÊ cost of capital.

D1 is the annual dividend per share, starting at year 1 and then continuing annually in perpetuity.

MP = Market price per share

From the formula above the market value of shares can be calculated as:

2. The dividend growth model:

(a) Capital Asset Pricing Model: The required return on ordinary shares can also be calculated by an alternative approach called the capital asset pricing model. This topic is covered much in next chapter. It is a model based on the proposition that the return on any shares equals to the risk – free rate of return plus a risk premium on risk which cannot be diversified.

Systematic risk - the risk that can be minimized through diversification.

Unsystematic risk - the risk, which remains even after diversification (or market risk)

Under the capital asset pricing model (CAPM), the required rate of return for ordinary shares can be described by the formula:

Ke = 10% + 0.6 (15% - 10%)

= 10% +0.6(5%)

= 10% + 3%

= 13%

Capital Budgeting

Notes


(b) If the risk of the shares was a little bit high say 1.6 then the cost of shares will also be high to compensate for the increased risk levels.

Ke = 10% + 1.6 (15% - 10%)

= 10% +1.6(5%)

= 10% + 8%

= 18%

Cost of Preference Shares The preference shareholder is entitled to a fixed rate of dividend which is quoted together with the shares. i.e. 12% K4 Preference shares means the shares have a nominal value of 12% and are entitled to an annual dividend of 12% per the nominal value.

So the cost of preferred shares is the rate which is given.

Cost of Debt The cost of debt capital, which has already been issued, is the rate of interest (the internal rate of return), which equates the current market price with the discounted future cash flow from the security.

Irredeemable debt: For redeemable debt the cost is calculated as the interest payable over the market value of debt.

The tax is included because interest on loan is allowable for tax purposes so if a company use borrowed capital there is always a saving due to tax relief on interest paid.

Cost of redeemable debt: These are debts with a defined period or date of repayment. The cost of these debts will be found by using the internal rate of return.

Example:

Peet Ltd. has 7% debentures in issue. The market price is K95.75 ex interest. Ignoring taxation, calculate the cost of this capital if the debenture is:

(a) Irredeemable.

(b) Redeemable at par after 5 years.

Solution

(a) The cost of debt capital is 7.3% if irredeemable. The capital profit that will be made from now to the date of redemption is K4.25 (K100 – K95.75). This profit will be made over five years which gives an annualised profit of K0.85.(4.25/5) which is about 0.9% of current market value. The best trial and error figure to try first is, therefore, 7.3% + 0.9% = 8.2% say 8% to the nearest.

Year Cash flow Discount PV Discount PV

8% K 10% K

0 Mkt value (95.75) 1.000 (95.75) 1.000 (95.75)

1 – 5 Interest 7 3.993 27.95 3.791 26.54

5 Repayment 100.00 0.681 68.10 0.621 62.10

0.30 (7.11)

Cost of Capital

Notes


The approximate cost of debt capital is therefore:

The cost of debt capital estimated above represents the cost of continuing to use the finance rather than redeeming the debt securities at their current market price. It would also represent the cost of raising additional finance if we assume that the cost of additional capital would be equal to the cost of that already issued. A company with no debt capital can make the calculations using the information of another company which is judged to be similar as regards to risk.

The Weighted Average Cost of Capital (WACC) As stated above the structure of a company consists of equity capital and various forms of debt capital, and each capital item has its own cost. The weighted average cost of capital is the average cost of a companyÊs different sources of finance.

The WACC is calculated on the assumption that the company will maintain the same level of debt equity ratio. The WACC calculated is used as the discount rate for capital project appraisals. This is will be ideal where:

In projects of a standard level of business risk, and

By raising funds in the same equity/ debt proportions as its existing capital structure.

The general formula for WACC is:

if you need to calculate the WACC where debt is redeemable, you should calculate the after-tax cost of debt using the techniques set out earlier and substitute this into the formula in place of Kd ( 1 – t).

We calculate a company's weighted average cost of capital using a 3 step process:

1. Cost of capital components. First, we calculate or infer the cost of each kind of capital that the enterprise uses, namely debt and equity.

A. Debt capital. The cost of debt capital is equivalent to actual or imputed interest rate on the company's debt, adjusted for the tax-deductibility of interest expenses. Specifically:

The after-tax cost of debt-capital = The Yield-to-Maturity on long-term debt x (1 minus the marginal tax rate in %)

B. Equity capital. Equity shareholders, unlike debt holders, do not demand an explicit return on their capital. However, equity shareholders do face an implicit opportunity cost for investing in a specific company, because they could invest in an alternative company with a similar risk profile. Thus, we infer the opportunity cost of equity capital.

We can do this by using the "Capital Asset Pricing Model" (CAPM). This model says that equity shareholders demand a minimum rate of return equal to the return from a risk-free investment plus a return for bearing extra risk. This extra risk is often called the "equity risk premium", and is equivalent to the risk premium of the market as a whole time a multiplier·called "beta"·that measures how risky a specific security is relative to the total market.

Thus, the cost of equity capital = Risk-Free Rate + (Beta times Market Risk Premium).

2. Capital structure. Next, we calculate the proportion that debt and equity capital contribute to the entire enterprise, using the market values of total debt and equity to reflect the investments on which those investors expect to earn a minimum return.

Capital Budgeting

Notes


3. Weighting the components. Finally, we weight the cost of each kind of capital by the proportion that each contributes to the entire capital structure. This gives us the Weighted Average Cost of Capital (WACC), the average cost of each Rs. of cash employed in the business.

Illustration 1:

Kwacha transport LTD is financed partly by bonds. The equity proportion is always kept at two-thirds of the total. The cost of equity 14% and that of debt is 8%. A new project is under consideration that will cost K200,000 and yield a return before interest of K75,000 a year for four years. Should the project be accepted? Ignore taxation.

Solution:

The WACC is the best rate to be used in appraising the project.

Proportional Cost Cost x Proportion

Equity 2/3 14% 9.33%

Debt 1/3 8% 2.67%

WACC 12.00%

Year Cash flow Discount factor P.V.

12%

0 (200,000) 1.000 (200,000)

1 75,000 0.893 66,975

2 75,000 0.797 59,775

3 75,000 0.712 53,400

4 75,000 0.636 47,700

Net present value 27,850

The NPV of the investment is K27,850 and the project appears financial viable.

Illustration 2:

A firm has the following capital structure and after tax costs for the different sources of funds used:

Source of funds Amount Proportion After tax cost (Rs.) (%) (%) Debt 1500000 25 5 Preference shares 1200000 20 10 Equity Shares 1800000 30 12 Retained Earning 1500000 25 11

Total 6000000 100

You are required to compute the weighted average cost of capital

Solution:

Source of Funds Amount Proportion After tax cost (Rs.) % % Debt 25 5 1.25 Preference shares 20 10 2.00 Equity Shares 30 12 3.6 Retained Earning 25 11 2.75

Weighted Average Cost of capital 9.60%

Cost of Capital

Notes


Illustration 3:

Continuing the above illustration 2, if the firm has 18000 equity shares of Rs. 100 each outstanding and the current price is Rs. 300 per share, calculate the market value weighted average cost of capital assuming that the market values and book values of the debt and preference capital are same.

Solution:

Source of funds Amount Proportion Cost Weighted Cost Rs. % (W) % (X) W.X %

Debt 1500000 18.52 5 0.93 Preference shares 1200000 14.81 10 1.48 Equity Shares 5400000 66.67 12 8.00 (18000@300)

Weighted Average Cost of capital 10.41%

1. Weighting: In the example the weighting for debt and equity was simplified, but in real environment the can be determined by using

(a) Weights could be based on the market values of debt and equity.

(b) Weights could be based on balance sheet values( book value)

2. Arguments for using the WACC as a discounting rate are relevant if the following assumptions hold:

(a) The project is small relative to the overall size of the company.

(b) The weighted average cost of capital reflects the companyÊs long-term future capital structure and capital costs.

(c) The project has the same degree of business risk as the company has now. When the new project has a different business risk the WACC cannot be used.

(d) New investments must be financed by new sources of funds, retained earnings, share issue, new loans and so on.

(e) The cost of capital to be applied to project evaluation reflects the marginal cost of new capital.

Marginal Cost of Capital

Definition The cost associated with raising one additional Rs. of capital. The marginal cost will vary according to the type of capital used. For example, raising funds through the use of unsecured or subordinated debt, or through debt that requires higher interest rates to offset risk, will be more expensive than debt that is backed by collateral, such as a secured bond.

Some times, we may be required to calculate the cost of additional funds to be raised, called the marginal cost of capital. The marginal cost of capital is the weighted average cost of new capital calculated by suing the marginal weights. The marginal weights represent the proportions of various sources of funds to be employed in raising additional funds. In case, a firm employs the existing proportion of capita; structure and the component cost remain the same the marginal cost of capital; shall be equal to the weighted average cost of capital. but in pract6ice, the proportion and/ or the component costs may change for additional funds to be raised. Under the

Capital Budgeting

Notes


situation the marginal cost of capital shall not be equal to the weighted average cost of capital. However the marginal cost of capital ignores the long term implications of the new financing plans, and thus weighted average cost of capital should be preferred for maximization of shareholders wealth in the long run

Illustration 4:

A firm has the following capital structure and after tax costs for the different sources of funds used:

Source of Funds Amount Proportion After tax cost Rs. % % Debt 450000 30.0 07 Preference shares 375000 25.0 10 Equity Shares 675000 45.0 15

1500000 100

(a) Calculate the weighted cost of capital using book-value weights.

(b) The firms wish to raise further Rs. 600000 for the expansion of the project as below:

Rs.

Debt 300000

Preference capital 150000

Equity Capital 150000

Assuming these specific costs do not change, compute the weighted marginal cost of capital

Solution:

Computation of Weighted Average Cost of Capital (WACC)

Source of funds Proportion after Tax Cost Weighted Cost % (W) % %

Debt 30.0 07 2.10 Preference shares 25.0 10 2.50 Equity Shares 45.0 15 6.75

Weighted Average Cost of Capital 11.35%

Computation of Weighted Marginal Cost of Capital (WMCC)

Marginal Weight

Source of funds Proportion after Tax Cost Weighted Cost

% (W) % %

Debt 50.0 07 3.50

Preference shares 25.0 10 2.50

Equity Shares 25.0 15 3.75

Weighted Marginal Cost of Capital 9.75%

Cost of Capital

Notes



1. The most appropriate rate is the firmÊs ________________.

2. A project can be accepted only when its rate of return is excess of the firms _________________.

3. The term „cost of capital‰ refers to the ___________ a firm must earn on its investment so that the market value of the companyÊs equity shares does not fall.

4. A firm has the following capital structure and after tax costs for the different sources of funds used:

Source of funds Amount Proportion After tax cost

Rs % %

Debt 1500000 25 5

Preference shares 1500000 25 10

Equity Shares 1500000 25 12

Retained Earning 1500000 25 11

Total 6000000 100

You are required to compute the weighted average cost of capital

Summary The cost of capital is the very basis for financial appraisal of new capital expenditure proposals. The decision of the finance manager will be irrational and wrong in case of capital is not correctly determined. This is because the business must earn at least at a rate which equals to cost of capital in order to make at least a break-even.

Keywords Mutually Exclusive Investments: Mutually exclusive investments serve the same purpose and compete with each other. If one investment is undertaken, others will have to be excluded.

Cost of Capital: IT refers to the minimum rate of return a firm must earn on its investment so that the market value of the companyÊs equity shares does not fall.

Review Questions 1. Define the concept of cost of capital and explain its components.

2. What are the different types of cost of capital?

Further Readings IM Pandey, Financial Management

Dr. S.N. Maheswari, Financial Management (Principles & Practices)

Khan & Jain, Financial Management (Text, Problems and cases)

Unit 3

Methods of Capital Budgeting

Unit 4 Risk Analysis

SECTION-II


Notes


Unit 3 Methods of Capital Budgeting

Unit Structure • Introduction • Payback Period Method • Accounting Rate of Return • Discounted Cash Flow Methods • Capital Rationing • Reinvestment Rate • NPV vs. IRR • Multiple Internal Rate of Return • Inflation and Capital Budgeting • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to: • Know the various tools of capital budgeting • Understand the methods under the capital budgeting • Study the advantages and disadvantages of various methods used in Capital Budgeting • Review its purpose

Introduction The attractiveness of any investment proposal depends on the following elements:

1. The amount expended i.e. the net investment

2. The potential benefits i.e. the operating cash Inflows

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

A proper investment analysis must relate these three elements to provide an indication of whether the investment is worthy of being taken up or not. How do these three basic elements i.e. the net investment, the operating cash flows and the economic life can be related to determine the proposalÊs worthiness?

Capital Budgeting

Notes


There are different techniques available for evaluation and selection of a proposal. These techniques can be grouped into two categories as shown below:

Payback Period Method The payback period method is the simplest method of evaluating investment proposals. Payback period represents the number of years required to recover the original investment. The payback period is also called payout or payoff period.

The CIMA defines payback as 'the time it takes the cash inflows from a capital investment project to equal the cash outflows, usually expressed in years'. When deciding between two or more competing projects, the usual decision is to accept the one with the shortest payback.

Payback is often used as a "first screening method". By this, we mean that when a capital investment project is being considered, the first question to ask is: 'How long will it take to pay back its cost?' The company might have a target payback, and so it would reject a capital project unless its payback period were less than a certain number of years.

a. When annual cash inflow is constant

Payback period = Original Cost of the Project

Annual Cash inflow

Note: Annual cash inflow is the annual earnings (profit before depreciation but after taxes)

b. When annual cash inflow is not constant

PBP = E + B/C

Where

PBP = pay back period

E = immediate preceding year before the year of final recovery

B = Balance amount yet to be recovered

C = cash flow during the year of final recovery.

Capital Budgeting Techniques

Traditional (or) Non-discounting Methods

Payback period Accounting rate of return

Net present value Internal rate of returns Profitability Index

Time adjusted (or) Discounted cash flow method


Notes


Example 1:

A project costs Rs.50, 000 and yields annual cash inflow of Rs 10,000 for 7 years. Calculate its payback period?

Solution:

Payback period = Original Cost of the Project

Annual Cash inflow

= 50, 000

10, 000= 5 years

Example 2:

Determine the payback period for a project which requires a cash outlay of Rs. 12,000 Rs. 4,000, Rs. 4,000 and Rs. 50,000 in the first, second, third and fourth years respectively.

Solution:

Year Annual Cash inflow Accumulated Cash inflow 1 2000 20,000 2 4000 6,000 3 4000 10,000 4 5000 15,000

(Hint: The total investment i.e. 12,000 can be recovered in 4th year only. But the preceding year of 4th year is 3rd year. Therefore, E=3. In the 3rd year, the accumulated cash inflow is only Rs.10, 000, which implies a balance of Rs.2000 has to be recovered. Therefore B= 2000. The annual cash inflow in the recovery year is Rs. 5000 therefore C = 5000)

PBP = E + B

C

= 3 + 2, 000

5, 000

= 3 + 0.4 = 3.4 years.

Example 3:

Years 0 1 2 3 4 5

Project A 1,000,000 250,000 250,000 250,000 250,000 250,000

For a project with equal annual receipts:

PP = IoCt

= $1, 000, 000

$250, 000

= 4 Years

Example 4:

Years 0 1 2 3 4

Project B - 10,000 5,000 2,500 4,000 1,000

Capital Budgeting

Notes


Payback period lies between year 2 and year 3. Sum of money recovered by the end of the second year

= Rs. 7,500, i.e. (Rs 5,000 + Rs 2,500)

Sum of money to be recovered by end of 3rd year

= Rs 10,000 - Rs 7,500

= Rs 2,500

Payback period = $2, 500

2 +$4, 000

years

= 2.625 years

Advantages of Payback Period Method 1. Simple to understand and easy to calculated.

2. It reduces the chance of loss through obsolescence. As the project with a short payback period is preferred, the chance of obsolescence is reduced.

3. A firm which has shortage of funds finds this method very useful. Project that makes a quick return is preferred.

Disadvantages 1. This method does not take into consideration the cash inflows beyond the

payback period.

2. It does not take into consideration the time value of money. It considers the same amount received in the second year and third year as equal.

Acceptance Criteria 1. The shorter the payback period, the less risky the investment is i.e. The

shorter the payback period, the better is the project.

2. In case of mutually exclusive projects, the project with less pack back period is preferred.

Accounting Rate of Return The ARR method (also called the return on capital employed (ROCE) or the return on investment (ROI) method) of appraising a capital project is to estimate the accounting rate of return that the project should yield. If it exceeds a target rate of return, the project will be undertaken.

Average rate of return is found out by dividing the average income after depreciation and taxes i.e. the accounting profit by the average investment.

Thus, ARR= Annual Earning

Average Investment×100

Where average annual earnings is the total of anticipated annual earnings after depreciation and tax (accounting profit) divided by the number of years.

Average investment is calculated in three ways:

1. When there is no salvage value (scrap value) ,then

Average investment = Total Investment

2


Notes


2. If there is scrap value, then average investment is calculated as

Average investment = Total Investment + Scrap Value

2

3. If there is additional working capital, then average investment is calculated as

Average investment = Total Investment + Scrap Value

2

+ Additional Working Capital

Acceptance Criteria 1. The higher the ARR, the better is the project.

2. In the case of mutually exclusive projects, the project with high ARR is Preferred.

Example 5:

Calculate the average rate of return for projects A and B from the following:

Particulars Project A Project B

Investment Rs. 20,000 Rs. 30,000

Expected life 4 years 5 years

Projected Net Income (After depreciation and taxed)

Years Project A Project B

1 2000 3000

2 1500 3000

3 1500 2000

4 1000 1000

5 ----- 1000

Total 6000 10,000

Solution:

ARR = Average Earnings

Average Investment× 100

Project A

Average Earnings = 6, 000

4 = 1,500

Average investment = 20, 000

2= 10,000

ARR = 1, 500

10,000× 100 = 15%

Project B

Average Earnings = 10, 000

5= 2,000

Average Investment = 30,000

2= 15,000

Capital Budgeting

Notes


ARR = 2, 000

15,000× 100 = 13.33%

Project A is accepted as the ARR for project A is higher than Project B.

Example 6:

Project x required an investment of Rs. 50,000 and has a scrap value of Rs 2000 after five years. It is expected to yield profits after depreciation and taxed during the five years amounting to Rs. 4,000, Rs. 6,000, Rs. 7,000, Rs.5, 000 and Rs 2,000. Calculated the average rate of return.

Solution:

ARR = Average Earning

Average Investment× 100

Average Earnings = Total Earnings

No. of years

= 4,000 +6,000 + 7,000 + 5,000 + 2,000

5

= 24,000

5= 4,800

Average Investment = Total Investment + Scrap Value

2

= 50, 000 2,000

2= 26,000

ARR = 4, 800

26, 000× 100 = 18.46%

Example 7:

A project has an initial outlay of $1 million and generates net receipts of $250,000 for 10 years.

Assuming straight-line depreciation of $100,000 per year:

The RR on total investment = $250,000 $100,000

1, 000,000= 15%

ARR on Total Investment = Net Annual Profit

Investment Outlay/2or a

o

C – DR

I /2

= $250,000 $100,000

$1, 000,000 2

= $150, 000$500, 000

= 30%

Advantages 1. It is easy to understand and calculate.

2. It can be compared with the cut off point of return and hence the decision to accept or reject is made easier.

3. It considers all the cash inflows during the life of the project, not like payback method.


Notes


4. It is a reliable measure because it considers net earnings that is, earnings after depreciation, interest and taxes.

Disadvantages 1. The concept of time value of money is ignored.

2. Unless we have a cut off point of return, accounting rate of return cannot be meaningful and effective.

3. The average concept is not reliable, particularly in time of high or wild fluctuations in the returns.

Discounted Cash Flow Methods Discounted cash flow methods are the improved methods over the traditional methods. They consider the time value of money. They consider the whole earnings of the proposal and the cost of the cost of the project. Because of these reasons, these methods are also called modern methods of investment appraisal. Discounted cash flow methods are:

1. Net present value

2. Internal rate of return

3. Profitability Index

1. Net Present Value Method This is generally considered to be the best method for evaluating the capital investment proposals. The Net present valued (NPV) is the difference between the total present value of future cashing flows and total p[resent value of the future cash outflows.

Each potential project's value should be estimated using a discounted cash flow (DCF) valuation, to find its net present value (NPV) - (see Fisher separation theorem). This valuation requires estimating the size and timing of all of the incremental cash flows from the project. These future cash flows are then discounted to determine their present value. These present values are then summed, to get the NPV. See also Time value of money. The NPV decision rule is to accept all positive NPV projects in an unconstrained environment, or if projects are mutually exclusive, accept the one with the highest NPV.

The NPV is greatly affected by the discount rate, so selecting the proper rate - sometimes called the hurdle rate - is critical to making the right decision. The hurdle rate is the minimum acceptable return on an investment. It should reflect the riskiness of the investment, typically measured by the volatility of cash flows, and must take into account the financing mix. Managers may use models such as the CAPM or the APT to estimate a discount rate appropriate for each particular project, and use the weighted average cost of capital (WACC) to reflect the financing mix selected. A common practice in choosing a discount rate for a project is to apply a WACC that applies to the entire firm, but a higher discount rate may be more appropriate when a project's risk is higher than the risk of the firm as a whole.

NPV = CFAT CPV – PV

Where CFATPV refers to the present value of future cash inflows after taxes.

CPV Refers to the present value of original investment or capital.

Capital Budgeting

Notes


The equation for calculating NPV in case of conventional cash flows can be put as follows:

NPV = 31 2 n1 2 3 n

RR R R(1 K) (1 K) (1 K) (1 K)

– I

In case of non-conventional cash inflows (i.e. when there are a series of cash inflows as well as cash out flows) the equation for calculating NPV is as follows:

NPV = 31 2 n1 2 3 n

RR R R(1 K) (1 K) (1 K) (1 K)

–

31 2 no 1 2 3 n

II I II

(1 K) (1 K) (1 K) (1 K)

Where NPV = Net Present Value, R = cash inflows at different time periods, K = cost of capital or cut off rate, I = cash out flows at different time periods.

Acceptance Criteria 1. If NPV is positive or zero, the project is accepted and if NPV is negative, the

project is rejected.

2. In case of mutually exclusive projects, the project with more NPV is selected or preferred.

Example 8:

Calculate the net present value of the two projects and suggest which of the two projects should be accepted assuming a discount rate of 10%.


Initial Investment Rs 40,000 Rs 60,000

Estimated Life 5 years 5 years

Scrap Value Rs 2,000 Rs 4,000

The project before depreciation but after taxes is as follows:

Year Project A Project B

1 12,000 35,000

2 18,000 25,000

3 7,000 12,000

4 5,000 4,000

5 4,000 4,000

Solution: Project A

Year Cash inflows *Present value of Re 1 at 10% Present value of cash inflows

1 2 3 4 = 2 * 3

1 12,000 0.909 10,908

2 18,000 0.826 14,868

3 7,000 0.751 5,257

4 5,000 0.683 3,415

5 4,000 0.621 2,484

5(scrap) 2,000 0.621 1,242

Total 38,174


Notes


*Observe present value of Re 1 table

Present value of cash inflows = 38,174

Less: Present value of investment = 40,000

Net present value = -1,826

Project B

Year Cash Inflows *Present value of Re 1 at 10% Present value of cash inflows

1 2 3 4 = 2 * 3

1 35,000 0.909 31,815

2 25,000 0.826 20,650

3 12,000 0.751 9,012

4 4,000 0.683 2,732

5 4,000 0.621 2,484

5(scrap) 4,000 0.621 2,484

Total 69,177

Present value of cash inflows = 69,177

Less: Present value of investment = 60,000

Net present value = 9,177

Since project B gives positive NPV, it is to be selected.

Note: The scrap value is considered as a cash inflow at the end of the 5th year

Example 9:

The cash inflow and cash out flow of a certain project are given below:

Year Cash out flow (Rs.) Cash in flow (Rs.)

0 2, 00,000 —

1 50,000 30,000

2 50,000

3 70,000

4 1, 20,000

5 80,000

The net salvage value at the end of 5th year is 30,000. The cost of capital is 12%. Calculate the net present value.

Solution:

NPV = CFAT CPV – PV

Year Cash Inflow Discount Factor at 12% Present Value of Cash Inflows

1 30,000 0.893 26,790

2 50,000 0.797 39,850

3 70,000 0.712 49,840

4 1, 20,000 0.635 76,200

5 80,000 0.567 45,360

5(scrap) 30,000 0.567 17,010

Total 2, 55,050

Capital Budgeting

Notes


Present Value of Initial Investment = Rs 2, 00,000

Present Value of Additional Investment made at the end of the 1st year = Rs. 44,650

Present Value of the Total Investment = Rs 2, 44,650 (2, 00,000 + 44,650)

NPV= CFAT CPV – PV

= 2, 55,050 – 2, 44,650

= Rs 10,400

Example 10:

Rank of following investment project is order of the profitability according to NPV assuming cost of capital to be 10%.

Project Initial Cash Outflow Annual Cash Outflow Life (in years)

X 20,000 4,000 8

Y 10,000 4,000 5

Solution:

Project X

Present value of Rs 4,000 is received annually for 8 years

4,000 × 5.335 = Rs 21,340

NPV = 21,340 – 20,000 = 1,340

Project Y

Present value of Rs 4,000 is received annually for 5 years

4,000 × 3.791 = Rs 15,164

NPV = 15,164 – 10,000 = 5,164

According to NPV method, Project Y is ranked first and Project X is ranked second.

Note: When the cash flows are uniform or equal then annuity discount factor is to be considered.

In the above example, 5.335 is the annuity discount faction for 8 years at 10%

Where as 3.791 is the annuity discount factor for 5 years at 10%.

Advantages

1. It considers the time value of money

2. It considers the earnings over the entire life of the project

3. It is helpful in comparing two projects requiring same amount of cash outflows.

Disadvantages

1. Not helpful in comparing two projects with different cash outflows.

2. This method may be misleading in comparing the projects of unequal lives.

2. Internal Rate of Return (IRR) The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. It is a commonly used measure of investment efficiency.

The IRR method will result in the same decision as the NPV method for independent (non-mutually exclusive) projects in an unconstrained environment, in the usual cases


Notes


where a negative cash flow occurs at the start of the project, followed by all positive cash flows. In most realistic cases, all independent projects that have an IRR higher than the hurdle rate should be accepted. Nevertheless, for mutually exclusive projects, the decision rule of taking the project with the highest IRR - which is often used - may select a project with a lower NPV.

In some cases, several zero NPV discount rates may exist, so there is no unique IRR. The IRR exists and is unique if one or more years of net investment (negative cash flow) are followed by years of net revenues. But if the signs of the cash flows change more than once, there may be several IRRs. The IRR equation generally cannot be solved analytically but only via iterations.

One shortcoming of the IRR method is that it is commonly misunderstood to convey the actual annual profitability of an investment. However, this is not the case because intermediate cash flows are almost never reinvested at the project's IRR; and, therefore, the actual rate of return is almost certainly going to be lower. Accordingly, a measure called Modified Internal Rate of Return (MIRR) is often used.

Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV, although they should be used in concert. In a budget-constrained environment, efficiency measures should be used to maximize the overall NPV of the firm. Some managers find it intuitively more appealing to evaluate investments in terms of percentage rates of return than dollars of NPV.

Internal Rate of Return is that rate at which the sum of discounted cash outflows. In other words, it is the rate which discounts the cash flows to zero.

Cash in flows/Cash outflows = 1

In this method, the discount rate is not known but the cash outflows and cash inflows are known. For example, if a sum of 800 invested in a project becomes Rs. 1,000 at the end of a year, the rate of return comes to 25 %, calculated as follows:

I = R

1 R

Where I = Cash outflow i.e. initial investment

R = Cash inflow

r = Rate of return yielded by the investment (or IRR)

Thus,

800 = 1,0001 r

800 + 800r = 1000

800r = 200

r = 200/800

= .25 or 25%.

Acceptance Criteria 1. If internal rate of return (r) is more than required rate of return (k) then the

project is selected.

2. In case of mutually exclusive projects, the project with more IRR is preferred.

The required rate of return (k) is also known as cut off rate or hurdle rate of cost of capital. The internal rate of return is not a predetermined rate; rather it is to be found out by trial and error method. It implies that one has to start with a discounting rate

Capital Budgeting

Notes


to calculate the present value of cash inflows. If the obtained present value is higher than the initial cost of the investment one has to try with a higher rate. Likewise if the present value of the expected cash inflows obtained is lower than the present value of cash outflow, a lower rate is to be taken up.

Example 11:

A firm has an investment opportunity involving Rs. 50,000. The cost of capital is 10% from the details given below find out the internal rate of return and see whether the project is acceptable.

Cash flow of 1st year Rs 5,000

Cash flow of 2nd year Rs 10,000

Cash flow 3rd year Rs 15,000

Cash flow 4th year Rs 25,000

Cash flow 5th year Rs 30,000

Solution:

As it is a trial and error method we can start with any rate. Let us try 15% and 20%

Year Cash inflows PV at 15% Discounted cash inflows

PV at 20% DiscountedCash inflows

1 2 3 4=2*3 5 6=2*5

1 5,000 0.870 4,350 0.833 4,165

2 10,000 0.756 7,560 0.694 6,940

3 15,000 0.658 9,870 0.571 8,685

4 25,000 0.572 14,300 0.482 12,050

5 30,000 0.497 14,910 0.402 12,060

Total 50,990 43,900

The present value of cash inflows at 15% is Rs 50,990 which is more than initial investment of Rs. 50,000 and at 20% Rs. 43,900 which is less than the required one. Hence, the actual IRR lies in between 15% and 20% and can be computed by way of interpolation as follows:

IRR = CFAT C1

C

PV – PVr r

PV

Where r1= lower discount rate 15%

CFATPV = Present value of earnings at lower rate Rs 50,990

CPV = Actual investment Rs 50,000

PV = difference in present value of earnings at lower rate and higher rate

= (50,990- 43,990) = 7,090

r = difference in rate of return = 5% (20 – 15)

IRR = CFAT C1

C

PV – PVr r

PV

= 50, 990 – 50,000

15 550, 990 – 43, 990


Notes


= 990

15 57090

= 15 + 0.7 = 15.7%

As the internal rate of return (15.7%) is above the cost of capital (10%) the project is acceptable.

Example 12:

Find out the IRR of the following, investment proposal:

Initial investment Rs. 70,000

Expected annual cash inflow Rs 24,000

Economic life of the project 4 years

Solution:

As the annual cash inflows are uniform the present value can be calculated with the help of annuity table.

Present value of total cash inflows.

At 12% discount factor = 24,000 x 3.037 =Rs.72,888

At 14% discount factor = 24,000 x 2.917 =Rs. 69,936

Note: You can use or take any discount factor. It is not mandatory that you should take only 12% and 14% but it is to be noted that one should be positive NPV and one should be negative NPV.

IRR can be computed as follows:

IRR = CFAT C1

C

PV – PVr r

PV

r1 = 12%

CFATPV = 72,888

CPV = 70,000

PV = 72,888 – 69,936 = 2952

r = 14 – 12 = 2%

IRR = CFAT C1

C

PV – PVr r

PV

= 72,888 – 70, 000

12 272, 888 – 69, 936

= 2, 888

12 22, 952

= 12 + 1.96 = 13.96%

Advantages

1. It considers the time value of money.

2. The earnings over the entire life of the project are considered.

3. Effective for comparing projects of different life periods with different timings of cash inflows.

Capital Budgeting

Notes


Disadvantages

1. This method is tedious and difficult to calculate.

2. This method is on the assumption that the earnings are reinvested at the IRR which is not always true.

Modified IRR (MIRR) The MIRR is similar to the IRR, but is theoretically superior in that it overcomes two weaknesses of the IRR. The MIRR correctly assumes reinvestment at the projectÊs cost of capital and avoids the problem of multiple IRRs. However, please note that the MIRR is not used as widely as the IRR in practice.

There are three basic steps of the MIRR:

(1) Estimate all cash flows as in IRR.

(2) Calculate the future value of all cash inflows at the last year of the projectÊs life.

(3) Determine the discount rate that causes the future value of all cash inflows determined in step 2, to be equal to the firmÊs investment at time zero. This discount rate is know as the MIRR.

Project L

PV Costs = TV

n1 + MIRR

MIRR is better than IRR because

1. MIRR correctly assumes reinvestment at projectÊs cost of capital.

2. MIRR avoids the problem of multiple IRRs.

0 1 2 3

-100.00 10 60 80.00 66.00 12.10 $158.10 = TV of

inflows 100.00 $ 0.00 = NPV PV outflows = $100 TV inflows = $158.10. MIRR = 16.5% MIRRS = 16.9%.

10%


Notes


3. Profitability Index Method This method is also called benefit cost ratio. Profitability index is the ratio of present value of cash inflow to present value of cash outflow.

Profitability Index = Present Value of Cash inflow

Present Value of Cash outflow

While NPV is an absolute measure, the PI is a relative measure.

The Profitability Index, or PI, method compares the present value of future cash inflows with the initial investment on a relative basis. Therefore, the PI is the ratio of the present value of cash flows (PVCF) to the initial investment of the project.

In this method, a project with a PI greater than 1 is accepted, but a project is rejected when its PI is less than 1. Note that the PI method is closely related to the NPV approach. In fact, if the net present value of a project is positive, the PI will be greater than 1. On the other hand, if the net present value is negative, the project will have a PI of less than 1. The same conclusion is reached, therefore, whether the net present value or the PI is used. In other words, if the present value of cash flows exceeds the initial investment, there is a positive net present value and a PI greater than 1, indicating that the project is acceptable.

PI is also know as a benefit/cash ratio.

Project L

PI = PV of cash flows

initial cost

= 118.79

100= 1.10

Accept project if PI > 1.

Reject if PI < 1.0

Acceptance Criteria

1. If the profitability index is greater than or equal to 1, the proposal is accepted else rejected.

2. In case of mutually exclusive projects, the project with more PI should be selected.

0 1 2 3

-100.00 10 60 80

PV1 9.09 PV2 49.59 PV3 60.11 118.79

10%

Capital Budgeting

Notes


Example 13:

The initial cash outlay of project is Rs. 50,000 and it generates cash inflows of Rs. 16,000, Rs. 19,000,Rs.22,000 and Rs.13,000 in four years. Ascertain the profitability index of the proposed investment assuming 10% rate of discount.

Solution:

Year Cash Inflow Discount Factor at 10% Present Value of Cash Inflows

1 16,000 0.909 14,544

2 19,000 0.826 15,694

3 22,000 0.751 16,522

4 13,000 0.683 8,879

Total 55,639

Profitability Index = Present Value of Cash inflow

Present Value of Cash outflow

= 55,63950,000

= 1.11

Since the profitability index is greater than one, the proposal may be accepted.

Advantages

1. It is easy to calculate, given the present value of cash inflows.

2. Projects of different magnitude in terms of duration and cash flows can be short-listed on their basis of their profitability.

3. It is recommended for use particularly when there is shortage of funds, because it correctly ranks the proposals.

Capital Rationing Capital rationing is a situation where a firm has more investment proposals than it can finance. It may be defined as Â a situation where a constraint is placed on the total size of capital investment during a particular period. In such an event the firm has to select combination of investment proposals that provided the highest net present valued subject to the budget constraint for the period.

Exists whenever enterprises cannot, or choose not to, accept all value-creating investment projects. Possible causes:

Banks and investors say „NO‰

Managerial conservatism

Analysis is required. One must consider sets of projects, or „bundles‰, rather than individual projects. The goal should be to identify the value-maximizing bundle of projects.

The danger is that the capital-rationing constraint heightens the influence of nonfinancial considerations, such as the following:

Competition among alternative strategies

Corporate politics

Bargaining games and psychology

The outcome could be a sub-optimal capital budget, or, worse, one that destroys value!


Notes


Some remedies are the following:

Relax and eliminate the budget constraint.

Manage the process rather than the outcomes.

Develop a corporate culture committed to value creation.

Example 14:

ABC Company is considering the following six proposals:

Project Cost (Rs.) NPV (Rs.)

1 1,000 210

2 6,000 1,560

3 5,000 850

4 2,000 260

5 2,500 500

6 500 95

You are required to calculate the profitability index for each project and rank them. Which projects would you choose if the total funds are Rs 8,000?

Solution:

Project Cost NPV NPV PI

1 2 3 4=2+3 5=4/2

1 1000 210 1210 1.21

2 6000 1,560 7,560 1.26

3 5000 850 5,850 1.17

4 2000 260 2260 1.13

5 2500 500 3000 1.20

6 500 95 595 1.19

Ranking of the projects as per PI method is project 2, 1, 5,6,3,4.

If the total funds are restricted to Rs 8,000 the best combination of projects may be found with the help of feasibility set approach as follows:

Combination Outlay NPV

1, 2, 6 7500 1865

2, 4 8000 1820

1, 3, 4 8000 1320

3, 4, 6 7500 1205

3, 5, 6 8000 1445

1, 4, 5, 6 6000 1065

The best combination of projects is 1, 2 and 6 and it gives the highest NPV of Rs. 1,865.

Capital Budgeting

Notes


Reinvestment Rate Example 15:

XYZ Ltd. is having required rate of return of 8% is evaluating two mutually exclusive proposals A and B for which the relevant data is as follows:

Year Cash flows (A) Cash flows (B)

0 -2500 -3000

1 2000 500

2 1000 1000

3 500 3000

Evaluate and rank these proposals.

Solution:

NPV and IRR of both the proposals are as follows:

Projects NPV at 8% (Rs.) IRR

Proposal A 606 24.8%

Proposal B 702 17.5%

In the above case, the NPV and IRR techniques are giving contradictory results. According to NPV, proposal B is preferred and according to IRR, proposal A is preferred. The difference in ranking is due to the fact that the timing of cash inflows of the two proposals is different. Proposal A is producing higher inflows in early years while proposal B is producing higher cash inflows in later years. But why then the different rankings? The answer to this question is found in the implied assumption of the NPV and the IRR techniques, known as the Reinvestment rate Assumption.

It is assumed that when the cash inflows are received, they are immediately reinvested in another project or asset. This implied reinvestment rate assumption allows us to consider any proposal independently of

1. Where the cash inflows are going after they are received?

2. How they are being used?

3. At what rate they are being reinvested by firm.

The NPV technique assumes that all the intermediate cash inflows are reinvested at a rate equal to the discount rate. So, in case of mutually exclusive proposals, all the intermediate cash inflows are assumed to be reinvested at the same rate i.e. the discount rate regardless of which proposal is accepted.

The IRR technique on the other band, assumes that the intermediate cash inflows are reinvested at a rate equal to the proposals IRR itself thus, different alternative proposals will have different reinvestment rates.

Thus, in the above problem, NPV technique assumes that the cash inflows of both the proposals A and B are being reinvested at 8% for the rest of the economic life of the proposal. On the other hand, the IRR technique assumes that the cash inflows of proposal A will be reinvested at 24.8% while the cash inflows of proposal B will be reinvested at 17.5%.

In practice, however it may not be realistic to assume that the reinvestment rate of firm will depend upon the proposal being accepted. The reinvestment rate is fixed and being an external variable it has nothing to do with the proposal being accepted or rejected.


Notes


NPV vs IRR Though NPV and IRR are discounted cash flow methods, they are different from each other in several respects. The chief points of difference between the two are as follows:

1. The net present values method takes the interest rate as a known factor while internal rate of return method takes it as unknown factors.

2. The net present values method seeks to find out the amount that can be invested in a given project so that its anticipated earnings will exactly suffice to repay this amount with interest at market rate. On the other hand, internal rate of return method seeks to find the maximum rate of interest at which the funds invested in the project could be repaid out the cash inflows arising out of that project.

3. Both the net present value method and internal rate of return method proceed on this presumption that each inflow can be reinvested at the discounting rate in the new projects. However, reinvestment of funds at the cut off rate is more possible than at the internal rate of return. Hence, NPV method is more reliable than the IRR method for ranking two or more capital investment projects.

Similarities in Results under NPV and IRR Both NPV and IRR will give the same result (i.e. acceptance or rejection) regarding the investment proposal in following cases:

1. Projects involving conventional cash flows i.e. when and initial outflow is followed by a series of inflows.

2. Independent investment proposals i.e. proposals where the acceptance of one does not preclude the acceptance of others.

Conflict in Results under NPV and IRR NPV and IRR methods may give conflicting results in case of mutually exclusive projects i.e. projects where acceptance of one would result in non acceptance of the other. Such conflict of result may be due to any one or more of the following reasons:

1. The project require different cash outlays.

2. The projects have unequal lives.

3. The projects have different patterns of cash flows.

In such a situation, the result given by the NPV method should be relied upon. This is because the objective of company is to maximize its share holderÊs wealth.IRR method is concerned with the rate of return on investment rather than total yield on investment. Hence it is not compatible with the goal of wealth maximization.NPV method considers the total yield on investment.Hence,incase of mutually exclusive projects, each having a positive NPV,the one with the largest NPV will have the most beneficial effect of shareholders wealth.

Independent vs Dependent Projects NPV and IRR methods are closely related because:

i) Both are time-adjusted measures of profitability, and

ii) Their mathematical formulas are almost identical.

So, which method leads to an optimal decision: IRR or NPV?

Capital Budgeting

Notes


a) NPV vs IRR: Independent Projects

Independent Project: Selecting one project does not preclude the choosing of the other.

With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to the same accept/reject decisions.

Figure 3.1: NPV vs IRR Independent Projects

If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project.

If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project.

Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e. n n

t to o ot t

t–1 t–1

C C – I > 0 or – I > I

(I+k) (I+k)

Similarly for the same project to be acceptable: n

tot

t–1

C = I

(I+R)

where R is the IRR.

Since the numerators tC are identical and positive in both instances:

Implicitly/intuitively R must be greater than k (R > k);

If NPV = 0 then R = k: the company is indifferent to such a project;

Hence, IRR and NPV lead to the same decision in this case.

b) NPV vs IRR: Dependent Projects

NPV clashes with IRR where mutually exclusive projects exist.


Notes


Example 16:

Agritex is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a prime site. The following information is available:

Initial Investment Outlay Net Inflow at the Year End

Project A -9,500 11,500

Project B -15,000 18,000

Assume k = 10%, which project should Agritex undertake?

A

$11, 500NPV – $9, 500

1.1

= $954.55

B

$18, 000NPV – $15,000

1.1

= $1,363.64

Both projects are of one-year duration:

IRRA: A

$11,500$9, 500

1+R

$11,500 = $9,500 (1 +RA)

$11,500$9,500

= 1+ RA

RA= $11,500$9,500

– 1

= 1.21 – 1

therefore IRRA = 21%

IRRB: B

$18,000$15, 000

1+R

$18,000 = $15,000(1 + RB)

= 1.2-1

therefore IRRB = 20%

Decision:

Assuming that k = 10%, both projects are acceptable because:

NPVA and NPVB are both positive

IRRA > k And IRRB > k

Which project is a "better option" for Agritex?

If we use the NPV method:

NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B.

If we use the IRR method:

IRRA (21%) > IRRB (20%): Agritex should choose Project A.

Capital Budgeting

Notes


Figure 3.2: NPV vs IRR: Dependent Projects

Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A.

Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B.

The two methods do not rank the projects the same.

Differences in the Scale of Investment NPV and IRR may give conflicting decisions where projects differ in their scale of investment.

Example 17:

Years 0 1 2 3

Project A -2,500 1,500 1,500 1,500

Project B -14,000 7,000 7,000 7,000

Assume k= 10%.

NPVA = $1,500 x PVFA at 10% for 3 years

= $1,500 × 2.487

= $3,730.50 – $2,500.00

= $1,230.50.

NPVB = $7,000 x PVFA at 10% for 3 years

= $7,000 x 2.487

= $17,409 - $14,000

= $3,409.00.

IRRA = o

t

IC

= $2,500$1,500

= 1.67.


Notes


Therefore IRRA = 36% (from the tables)

IRRB = o

t

IC

= $14,000$7,000

= 2.0

Therefore IRRB = 21%

Decision:

Conflicting, as:

NPV prefers B to A

IRR prefers A to B

NPV IRR

Project A $ 3,730.50 36%

Project B $17,400.00 21%

See figure 3.3.

Figure 3.3: Scale of Investments

To show why:

i) The NPV prefers B, the larger project, for a discount rate below 20%

ii) The NPV is superior to the IRR

a) Use the incremental cash flow approach, "B minus A" approach.

b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".

0 1 2 3

Project B - 14,000 7,000 7,000 7,000

Project A - 2,500 1,500 1,500 1,500

"B minus A" - 11,500 5,500 5,500 5,500

Capital Budgeting

Notes


IRR"B Minus A"= $11,500$5,500

= 2.09 = 20%

c) Choosing B is equivalent to: A + (B - A) = B

d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of $11,500 of which $5,500 will be realised each year for the next 3 years.

e) The IRR"B minus A" on the incremental cash flow is 20%.

f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.

g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.

h) At the point of intersection, NPVA = NPVB or NPVA - NPVB = 0, i.e. indifferent to projects A and B.

i) If k = 20% (IRR of "B - A") the company should accept project A.

This justifies the use of NPV criterion.

Advantage of NPV

It ensures that the firm reaches an optimal scale of investment.

Disadvantage of IRR

It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in absolute terms and not in % terms, e.g. target sales figure of $2.5 million.

The Timing of the Cash Flow

The IRR may give conflicting decisions where the timing of cash flows varies between the two projects.

Note that initial outlay 0I is the same.

0 1 2

Project A - 100 20 125.00

Project B - 100 100 31.25

"A minus B" 0 - 80 88.15

Assume k = 10%

NPV IRR

Project A 17.3 20.0%

Project B 16.7 25.0%

"A minus B" 0.6 10.9%

IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A, that is B + (A - B) = A. See Figure 3.4.


Notes


Figure 3.4: Timing of the Cash Flow

The Horizon Problem NPV and IRR rankings are contradictory. Project A earns $120 at the end of the first year while project B earns $174 at the end of the fourth year.

0 1 2 3 4

Project A -100 120 - - -

Project B -100 - - - 174

Assume k = 10% NPV IRR

Project A 9 20%

Project B 19 15%

Decision:

NPV prefers B to A

IRR prefers A to B.

The profitability index - PI

This is a variant of the NPV method.

o

PVPI

I

Decision rule:

PI > 1; accept the project

PI < 1; reject the project

If NPV = 0, we have:

NPV = PV - Io = 0

Capital Budgeting

Notes


PV = Io

Dividing both sides by 0I we get:

V

o

PI

> 1

PI of 1.2 means that the project's profitability is 20%. Example:

PV of CF Io PI

Project A 100 50 2.0

Project B 1,500 1,000 1.5

Decision:

Choose option B because it maximises the firm's profitability by $1,500.

Disadvantage of PI:

Like IRR it is a percentage and therefore ignores the scale of investment

Example 18:

A firm has to make a choice between two projects A and B which is mutually exclusive. The cash flows are as follows:

Year Project A Project B

0 Rs 5,000 Rs 7,500

1 Rs 6,000 Rs 8,800

The cost of capital is 10%.Suggest which project should be taken up using:

1. NPV method

2. IRR Method.

Solution:

The NPV and IRR for the two projects A and B are as follows:

Projects NPV IRR

A 454 20%

B 499 17.33%

According to NPV method, project B is superior where as according to IRR method, project A is superior. Since acceptance of project B would result in maximization of wealth of share holders as indicated by NPV, it will be appropriate to reject project A.

The same conclusion can be drawn but adopting the incremental approach, modified form of IRR method as follows:

Project A (Rs.) B (Rs.) B – A

Cash outlays 5000 7,500 2500

Cash inflows 6000 8,800 2800

IRR for incremental cash flows = 12%

The IRR of differential cash outlays of project B comes to 12% while the required return is 10%.Project B is therefore better than Project A in spite of its having a lower IRR. This is because it offers the benefits offered by project A and also a return in excess of the required rate of return on incremental investment of Rs 2500.


Notes


Multiple Internal Rate of Return There is a mathematical possibility that a complex proposal with varied cash inflows and outflows may result in two different IRR because of the pattern and timing of the inflows and outflows. For example, a firm is evaluating a project requiring a cash outlay of RS800 in the beginning and RS 1300 at the end of the second year. The project is expected to generate only 1 cash inflow of RS 2100 at the end of first year. The IRR of the proposal calculated as follows:

Rs. 800 = 1

2,100(1+r)

– 2

1,300(1+r)

Taking (1 + r) = x and dividing both sides of the above equation by 100

8 = 21x

– 2

13x

8x2 =21x – 13

0 = 8x2 – 21x + 13

The value of x in the quadratic equation can be calculated as

X = 2-b b 4ac

2a

By applying the values a,b,c as equal to 8,-21 and 13,the value of x can be identified as 1 and 1.62.since x=(1+r),therefore ,value of r becomes Zero and 62%.Thus the above proposal has two IRRÊs i.e. 0% and 62%.

The above problem is overcome by modifying the cash flows in such a way that the multiple changes in signs of cash flow can be modified by discounting the future cash flows at cutoff rate to year 0 and then the proposal will have cash out flows in the beginning only and thereafter only the cash flows will occur. In the above example, the cash out flow of Rs 1300 at the end of second year is discounted say at 15% to time zero as the Rs 1300 X PVF (15% 2y) = 1300 X 0.756 = Rs 983.

Now the cash flow data can be presented as

Time Cash Flow (Rs) 0 -800 0 -983 1 +2100

The IRR of this stream of cash flow can be ascertained in normal way and is found to be 18%. This IRR of 18% can be composed with the cut off rate of 15% and hence the proposal is acceptable. The above proposal of modifying the cash flows to avoid the occurrence of multiple IRR is know as Extended Internal Rate of Return.

Inflation and Capital Budgeting In capital budgeting, the cash flows are generally in money terms of that period in which they occur. If the inflation effect is ignored, then the firm might loose in terms of purchasing power of money. In order to incorporate the inflation effect, there are two options.

Real discount rate = minimum required rate of return

Nominal Discount rate = Inflation adjusted rate of discount (1+ Inflation rate) X (1+real discount rate) – 1

Money Cash flows= Actual cash flows to be expected in monetary terms

Real cash inflows = cash flows expressed in real values.

Capital Budgeting

Notes


Allowing for Inflation So far, the effect of inflation has not been considered on the appraisal of capital investment proposals. Inflation is particularly important in developing countries as the rate of inflation tends to be rather high. As inflation rate increases, so will the minimum return required by an investor. For example, one might be happy with a return of 10% with zero inflation, but if inflation was 20%, one would expect a much greater return.

Example 19:

Keymer Farm is considering investing in a project with the following cash flows:

Time Actual Cash Flows (Z$)

0 (100,000)

1 90,000

2 80,000

3 70,000

Keymer Farm requires a minimum return of 40% under the present conditions. Inflation is currently running at 30% a year, and this is expected to continue indefinitely. Should Keymer Farm go ahead with the project?

Let us take a look at Keymer Farm's required rate of return. If it invested $10,000 for one year on 1 January, then on 31 December it would require a minimum return of $4,000. With the initial investment of $10,000, the total value of the investment by 31 December must increase to $14,000. During the year, the purchasing value of the dollar would fall due to inflation. We can restate the amount received on 31 December in terms of the purchasing power of the dollar at 1 January as follows:

Amount received on 31 December in terms of the value of the dollar at 1 January:

= 1

$14, 000(1.30)

= $10,769

In terms of the value of the dollar at 1 January, Keymer Farm would make a profit of $769 which represents a rate of return of 7.69% in "today's money" terms. This is known as the real rate of return. The required rate of 40% is a money rate of return (sometimes known as a nominal rate of return). The money rate measures the return in terms of the dollar, which is falling in value. The real rate measures the return in constant price level terms.

The two rates of return and the inflation rate are linked by the equation:

(1 + money rate) = (1 + real rate) x (1 + inflation rate)

where all the rates are expressed as proportions.

In the example,

(1 + 0.40) = (1 + 0.0769) x (1 + 0.3)

= 1.40

So, which rate is used in discounting? As a rule of thumb:

a) If the cash flows are expressed in terms of actual dollars that will be received or paid in the future, the money rate for discounting should be used.

b) If the cash flows are expressed in terms of the value of the dollar at time 0 (i.e. in constant price level terms), the real rate of discounting should be used.


Notes


In Keymer Farm's case, the cash flows are expressed in terms of the actual dollars that will be received or paid at the relevant dates. Therefore, we should discount them using the money rate of return.

Time Cash Flow ($) Discount Factor (40%) Pv ($)

0 (150,000) 1.000 (100,000)

1 90,000 0.714 64,260

2 80,000 0.510 40,800

3 70,000 0.364 25,480

30,540

The project has a positive net present value of $30,540, so Keymer Farm should go ahead with the project.

The future cash flows can be re-expressed in terms of the value of the dollar at time 0 as follows, given inflation at 30% a year:

Time Actual Cash Flow ($) Cash Flow At Time 0 Price Level ($) 0 (100,000) (100,000) 1 90,000 1

90,000× 1(1.30)= 69,231

2 80,000 180,000× 2(1.30)

= 47,337

3 70,000 170,000× 3(1.30)

= 31,862

The cash flows expressed in terms of the value of the dollar at time 0 can now be discounted using the real value of 7.69%.

Time Cash Flow ($) Discount Factor (7.69%) Pv ($) 0 (100,000) 1.000 (100,000) 1 69,231 1

1(1.0769)

64,246

2 47,337 12(1.0769)

40,804

3 31,862 13(1.0769)

25,490

30,540

The NPV is the same as before.

Expectations of Inflation and the Effects of Inflation

When a manager evaluates a project, or when a shareholder evaluates his/her investments, he/she can only guess what the rate of inflation will be. These guesses will probably be wrong, at least to some extent, as it is extremely difficult to forecast the rate of inflation accurately. The only way in which uncertainty about inflation can be allowed for in project evaluation is by risk and uncertainty analysis.

Inflation may be general, that is, affecting prices of all kinds, or specific to particular prices. Generalised inflation has the following effects:

a) Inflation will mean higher costs and higher selling prices. It is difficult to predict the effect of higher selling prices on demand. A company that raises its prices by 30%, because the general rate of inflation is 30%, might suffer a serious fall in demand.

Capital Budgeting

Notes


b) Inflation, as it affects financing needs, is also going to affect gearing, and so the cost of capital.

c) Since fixed assets and stocks will increase in money value, the same quantities of assets must be financed by increasing amounts of capital. If the future rate of inflation can be predicted with some degree of accuracy, management can work out how much extra finance the company will need and take steps to obtain it, e.g. by increasing retention of earnings, or borrowing.

However, if the future rate of inflation cannot be predicted with a certain amount of accuracy, then management should estimate what it will be and make plans to obtain the extra finance accordingly. Provisions should also be made to have access to 'contingency funds' should the rate of inflation exceed expectations, e.g. a higher bank overdraft facility might be arranged should the need arise.

Many different proposals have been made for accounting for inflation. Two systems known as "Current purchasing power" (CPP) and "Current cost accounting" (CCA) have been suggested.

CPP is a system of accounting which makes adjustments to income and capital values to allow for the general rate of price inflation.

CCA is a system which takes account of specific price inflation (i.e. changes in the prices of specific assets or groups of assets), but not of general price inflation. It involves adjusting accounts to reflect the current values of assets owned and used.

At present, there is very little measure of agreement as to the best approach to the problem of 'accounting for inflation'. Both these approaches are still being debated by the accountancy bodies.

Example 20: Inflation

TA Holdings is considering whether to invest in a new product with a product life of four years. The cost of the fixed asset investment would be $3,000,000 in total, with $1,500,000 payable at once and the rest after one year. A further investment of $600,000 in working capital would be required.

The management of TA Holdings expect all their investments to justify themselves financially within four years, after which the fixed asset is expected to be sold for $600,000.

The new venture will incur fixed costs of $1,040,000 in the first year, including depreciation of $400,000. These costs, excluding depreciation, are expected to rise by 10% each year because of inflation. The unit selling price and unit variable cost are $24 and $12 respectively in the first year and expected yearly increases because of inflation are 8% and 14% respectively. Annual sales are estimated to be 175,000 units.

TA Holdings money cost of capital is 28%.

Is the product worth investing in?

Example 21:

ABC Ltd. is evaluating a proposal involving cash outflow of Rs 40,000 at year 0 and cash out flows of Rs 18,000, Rs 19,020, Rs 20,224 and Rs 21,438 at the end of each of next 4 years after which the project is expected to have a scrap value of Rs 40,000. The cash flows are expected to be Rs 28,000, Rs 42,000 Rs 42,000 and Rs 34,000 at the end of year 1 to year 4 respectively. All the above estimates of cash inflows have been made in terms of money of today i.e. year 0. Evaluate the proposal in real terms by applying the NPV technique given that the inflation rate is 6% p.a and the discount rate is 18%.


Notes


Solution: Year Cash outflow Cash inflow Net cash flow

0 40,000 — - 40,000

1 18,000 28,000 10,000

2 19,020 42,000 22,980

3 20.224 42,000 21,776

4 21,438 34,000 12,562

Scrap Value 4,000

Since the rate of inflation is 6% p.a, therefore the money net cash flows occurring at the end of different years would be affected by the inflation.

Year Net cash flow Actual Cash flow

1 10,000 10,000 (1.06)1=10,600

2 22,980 22,980 (1.06)2=28,820

3 21,776 21,776 (1.06)3=25,935

4 16,562 16,662 (1.06)4=20,909

Discount rate is 18% and inflation rate is 6%.

Therefore Nominal Discount rate =(1+Inflation rate) X (1+ real rate of discount) –1

= (1.18 X 1.06) -1 = 0.2508 or 25.08%

The last step is evaluation of NPV.

Year Cash Flow PVF Present Value

0 -40,000 -- -40,000

1 10,600 1/ (1.208)1 8,474

2 25,820 1/ (1.208)2 16,503

3 25,935 1/ (1.208)3 13,253

4 20,909 1/ (1.208)4 8,542

Total 6,772

Therefore, the NPV of the project in real terms is Rs 6,772.

Student Activity A company is considering an investment proposal of Rs 50,000 to install new milling controls. The facility has a life expectancy of 5 years and his salvage value. The companyÊs tax rate is 55% and no investment tax credit is allowed. The firm uses straight line depreciation. The estimated cash flow before tax (CFBT) from the proposed investment proposal is as follows

Year: 1 2 3 4 5

CBFT: 10,000 11,000 14,000 15,000 25,000

Compute the following:

a) Payback period

b) Average rate of return

c) Internal rate of returns

d) Net present value at 10% discount rate

e) Profitability index at 10% discount rate.

Capital Budgeting

Notes


Summary The attractiveness of any investment proposal depends on net investment , the operating cash inflow and, economic life of the project.

Capital budgeting techniques are classified into two types viz Traditional methods or non discounting methods. The traditional methods are payback methods and accounting rate of returns. The discounting, methods are net present value method, Internal rate of return method and profitability index method. In case of accounting rate of return, the higher the ARR, the better is the project. The project is accepted only if the NPV is positive or zero. The acceptance criteria for IRR method is the project is selected if and only if the internal rate of returns(R) is greater than or equal to cost of capital (K). If the profitability index is greater than or equal to 1, then the project is accepted otherwise, it is rejected. Capital rationing is a situation where a firm has more investment proposal than it can finance. The NPV method takes the interest rate as a known factor while IRR method takes it as an unknown factor. NPV and IRR will give the same result when the projects involve conventional cash flows and projects are independent proposals. NPV and IRR give conflicting results when

1) The projects require different cash out flows

2) The projects have unequal lives

3) The projects have different patterns of cash flows.

Keywords Payback Period: It is that Period required to recover the original cash outflow invested in a project.

Accounting Rate of Return: It is the ratio of average annual earnings to average investment.

Net Present Value: The difference between the total present value of future cash outflows and total present value of future cash outflows.

Internal Rate of Return: The rate at which the sum of discounted cash inflows equals the sum of discounted cash outflows.

Profitability Index: It is the ratio of present value of cash inflow to present value of cash outflow.

Capital Rationing: It is a situation where a firm has more investment proposals than it can finance.

Reinvestment Rate: The rate at which the cash inflows that are received are immediately reinvested in another project or asset.

Multiple Internal Rate of Return: It is a situation where a complex proposal with varied cash inflows and outflows may result in two different IRRÊs because of the pattern and timing of the inflows and outflows.

Review Questions 1. What are traditional methods of capital budgeting?

2. What do you mean by NPV?

3. What do you mean by discounting of cash flows?

4. Bring out the differences between the NPV and IRR method.

5. How do you calculate accounting rate of return? What are the limitations?

6. What is capital rationing?


Notes


7. Discuss the discounted cash flow technique of capital budgeting.

8. Discuss about reinvestment rate.

9. What is the importance of inflation in capital budgeting?

Further Readings Khan and Jain, Financial Management,Text,Problems and Cases

I. M. Pandey, Financial Management

S. N. Maheswari, Financial Management, Principles and Practices

Sudhindra Bhatt, Financial Management, Principles and Practices

Risk Analysis

Notes


Unit 4 Risk Analysis Unit Structure • Introduction • What is Risk? • Return • Opportunity Cost of Capital • Yield • Single Product Analysis under Risk • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to: • Study the risk and return analysis • Know the various models of risk • Understand concept of risk and return in a precise manner • apply the concept in real study

Introduction Risk is inherent in almost every business decision. More so in capital budgeting decisions as they involve costs and benefits extending over a long period of time during which many things can change in unanticipated way.

Risk analysis is one of the most complex and slippery aspects of capital budgeting. Many different techniques have been suggested and no single technique can be deemed as best in all situations.

What is Risk? Risk Risk consists of two components the systematic risk and unsystematic risk. The systematic risk is caused by factors external to the particular company and uncontrollable by the company the systematic risk affects the market as a whole. In case of unsystematic risk the factors are specific, unique ad related to the particular industry or company.

Systematic Risk The systematic risk affects the entire market. Often we hear that stock market is bear hug or in bull grip. This indicates that the entire market is moving in particular direction either downward or upward. The economic conditions, political situations and the sociological changes affect the security market. There are factors which are beyond the control of corporate and investor. They cannot be entirely avoided by the investor. It drives home the point that the systematic risk is unavoidable. The systematic risk is further sub divided into:

1. Market risk

Capital Budgeting

Notes


2. Interest rate risk

3. Purchasing power risk

1. Market Risk: It is defined as that portion of total variability of return caused by the alternating forces of bull and bear market. When the security index moves upward haltingly for a significant period of time it is known as bull market. In bull market the index moves from a low level to the peak. Bear market is just a reverse to the bull market.

The forces that affect the stock market are tangible and intangible events. The tangible events are real events such as earthquake, war, political uncertainty and fall in the value of currency.

Intangible events are related to market psychology. The market psychology is affected by the real events. But reactions to the tangible events become over reactions and they push the market in a particular direction.

Any untoward political or economic event would lead to a fall in the price of the security which would be further accentuated by the over reactions and the herd like behavior of the investors. If some institutions start disposing stocks the fear grips in and spreads to other investors. This results in a rush to sell the stocks. This type of over reaction affects the market adversely and the prices of the scrip fall below their intrinsic values. This is beyond the control of the corporate.

2. Interest Rate Risk: It is the variation in the single period rates of return caused by the fluctuations in the market interest rate. Most commonly interest rate risk affects the price of bonds, debentures and stocks. The fluctuations in the interest rates are caused by the changes in the government monetary policy and the changes that occur in the interest rates of treasury bills and the government bonds, the bonds issued by the government and quasi government are considered to be risk free. If higher interest rates are offered, investor would like to switch his investments from private sector bonds to public sector bonds. If the government to tide over the deficit in the budget floats a new loan of a higher rate of interest, there would be a definite shift in the funds from low yielding bonds to the high yielding bonds and from stocks to bonds.

If stock market is in a depressed condition investors would like to shift their money to the bond market to have an assured rate of return.

The rise or fall in the interest rate affects the cost of borrowing. When the call money market rate changes, it affects the badla rate too. Most of the stock traders trade in the stock market with the borrowed funds. The increase in the cost of margin affects the profitability of the traders. This would dampen the spirit of the speculative traders who use the borrowed funds. The fall in the demand for securities would lead to a fall in the value of stock index.

Interest rates not only affect the security traders but also the corporate bodies who carry their business with borrowed funds. The cost of borrowing would increase and a heavy outflow of profit would take place in the form of interest of the capital borrowed. This would lead to a reduction in earnings per share and a consequent fall in the price of share.

3. Purchasing Power Risk: Variations in the returns are caused also by the loss of purchasing power of currency. Inflation is reason behind the loss of purchasing power. The level of inflation proceeds faster than the increase in capital value. Purchasing power risk is the probable loss in purchasing power

Risk Analysis

Notes


of the returns to be received. The rise in rice penalizes the returns to the investor, and every potential rise in price is a risk to the investor.

Inflation may be demand pull or cost push inflation. In demand pull inflation the demand for goods and services are in excess of their supply. At full employment level of factors of production, the economy would not be able to supply more goods in the short run and the demad for products pushes the price upward.

The cost push inflation as the name itself indicates that the inflation or the rise in rice is caused by the increase in the cost. The increase in the cost of raw material, labor and equipment makes the cost of production high and ends in high price level. The cost push inflation has a spiraling effect on price level.

Unsystematic Risk It is unique and peculiar to a firm or an industry. Unsystematic risk stems from managerial inefficiency, technological change in the production process, availability of aw material, changes in the consumer preference, and labor problems. The nature and magnitude of the above mentioned factors fifer from industry to industry, and company to company. They have to be analyzed separately for each industry and firm. The changes in the consumer preference affect the consumer products like TV, washing machines, refrigerators more than that of consumer product industry. The nature and mode of raising finance and paying back the loans, involve a risk element. Unsystematic risk can be classified into

1. Business risk

2. Financial risk

1. Business risk: It is that portion of unsystematic risk caused by the operating environment of the business risk arises from the inability of a firm to maintain its competitive edge and the growth or stability of earnings. Variation that occurs in the operating environment is reflected on the operating income and expected dividends. The variation in expected operating income indicates the business risk. Business risk is further divided into external business risk and internal business risk.

(a) Internal business risk: It is associated with the operational efficiency of the firm. The operational efficiency of operation is reflected on the companyÊs achievement of its pre set goals and the fulfillment of the promises to its investors.

(i) Fluctuations in the sales: The sales level has to be maintained. It is common in business to lose customers abruptly because of competition. Loss of customers will lead to a loss in operational income. Hence the company has to build a wide customer base through various distribution channels. Diversified sales force any help to tide over this problem.

(ii) Research and Development: Sometimes the product may go out of style or become obsolescent. It is the management, who has to overcome the problem of obsolescence by concentrating on the in house research ad development program.

(iii) Personnel Management: The personnel management of the company also contributes to the operational efficiency of the firm. Frequent strikes and lock outs result in loss of

Capital Budgeting

Notes


production and high fixed capital cost. The labor productivity also would suffer. The risk of labor management is present in all the firms. It is up to the company to solve the problems at the table level and provide adequate incentives to encourage the increase in labor productivity. Encouragement given to the laborers at the floor level would boost morale of the labor force and leads to higher productivity and less wastage of raw materials and time.

(iv) Fixed Cost: The cost components also generate internal risk if the fixed cost is higher in the cost component. During the period of recession or low demand for product the company cannot reduce the fixed cost. At the same time in the boom period also the fixed factor cannot vary immediately. The high fixed cost component in a firm would become a burden to the firm. The fixed cost component has to be kept always in a reasonable size so that it may not affect the profitability of the company.

(v) Single Product: The internal business risk is higher in case of firm producing a single product. The fall in demand for a single product would be fatal for the firm. Hence the company has to diversify the products if it has to face the competition and the business cycle successfully.

(b) External risk: It is the result of operating conditions imposed on the firm by circumstances beyond its control. The external environments in which it operates exert some pressure on the firm. The external factors are:

(i) Social and regulatory factors

(ii) Monetary and fiscal policies of the government

(iii) Business cycle and general economic environment within which a firm operates.

(i) Social and regulatory factors: Harsh regulatory climate and legislation against the environmental degradation may impair the profitability of the industry. Price control, volume control, import export control and environment control reduce the profitability of the firm. This risk is more in industries related to public utility sectors such as telecom, banking and transportation.

(ii) Political risk: It arises out of the change in government policy. With a change in the ruling party, the policy also changes. Political risk arises mainly in the case of foreign investment. The host government may change its rules and regulations regarding the foreign investment.

(iii) Business cycle: The fluctuations of the business cycle lead to fluctuations in the earnings of the company. Recession in the economy leads to a drop in the output of many industries. Steel and white consumer goods industries tend to move in tandem with the business cycle. During the boom period there would be hectic demand for steel products ad white consumer goods. But at the same time, they would be hit much during recession period. This risk

Risk Analysis

Notes


factor is external to the corporate bodies and they may not be able to control it.

2. Financial risk: It refers to the variability of the income to the equity capital due to the debt capital. Financial risk in a company is associated with the capital structure of the company. Capital structure of the company consists of equity funds and borrowed funds. Th presence of debt and preference capital results in a commitment of paying interest or prefixed rate of dividend. The residual income alone would be available to the equity holders. The interest payment affects the payments that are due to the equity investors. The debt financing increases the variability of the returns to the common stock holders and affects their expectations regarding the return. The use of debt with the owned funds to increase the return to the shareholders is known as financial leverage.

How Can We Best Deal with Risk? If the stakes are high enough, we can and should deal with risk explicitly, with the aid of a quantitative model. As humans, we have heuristics or "rules of thumb" for dealing with risk, but these don't serve us very well in many business and public policy situations. In fact, much research shows that we have cognitive biases, such as over-weighting the most recent adverse event and projecting current good or bad outcomes too far into the future, that work against our desire to make the best decisions. Quantitative risk analysis can help us escape these biases, and make better decisions.

It helps to recognize up front that, when uncertainty is a large factor, the best decision does not always lead to the best outcome. The "luck of the draw" may still go against us. Risk analysis can help us analyze, document, and communicate to senior decision makers and stakeholders the extent of uncertainty, the limits of our knowledge, and the reasons for taking a course of action.

The process of risk analysis: The process of risk analysis includes identifying and quantifying uncertainties, estimating their impact on outcomes that we care about, building a risk analysis model that expresses these elements in quantitative form, exploring the model through simulation and sensitivity analysis, and making risk management decisions that can help us avoid, mitigate, or otherwise deal with risk.

Identify and Quantify Uncertainty

In risk analysis, our goal is to identify each important source of uncertainty, and quantify its magnitude as well as we can. For example, we may not know our competitor's exact price, but we can place bounds on it, based on known production and marketing costs. While we can't predict the exact number of people shopping at a store each day, we can examine past data for the frequency of days when (say) 10, 20, 30, ..., 100 people shopped, and use this to estimate a distribution of shoppers on future days. This process of identifying and quantifying uncertainties is a key step in risk analysis.

Compute the Impact of Uncertainty

Our next step is to accurately estimate the impact of the uncertainties on the outcomes we care about. For example, we may not be able to predict demand for our product exactly; but given a number for demand, since we know our costs and margins, we can often calculate the impact on our Net Profit. We may not know the exact number of shoppers on any future day; but given a number of shoppers, we can calculate how many store salespeople we need to service them, and estimate the sales we're likely to generate. In doing this, we build a model that allows us to compute "outputs" · outcomes such as Net Profit · for any given "inputs".

Capital Budgeting

Notes


Complete a Risk Analysis Model If we can complete these steps, we'll have a risk analysis model (or simply risk model). The model has inputs which are uncertain -- these may be called uncertain variables, random variables, assumptions, or simply inputs. For any given set of input values, the model calculates outputs · outcomes such as Net Profit.

Unlike other kinds of models, a risk analysis model requires us to think in ranges: Because the inputs are uncertain and may take on many different values, the outputs are also uncertain and may take on a range of values. If management asks, "Give me a number for next year's sales", a risk analyst must respond that a single number is not going to be meaningful · it will defeat the purpose of risk analysis.

Explore the Model with Simulation

We can use our risk model in several ways -- but one effective way is to explore the possible outcomes using simulation. For a model in Excel, we can use software, such as Frontline's Risk Solver, to perform a Monte Carlo simulation on our model. Simulation performs many (thousands of) experiments or trials · each one samples possible values for the uncertain inputs, and calculates the corresponding output values for that trial.

The first run of a simulation model can often yield results that are surprising to the modelers or to management · especially when there are several different sources of uncertainty that interact to produce an outcome. Even before an in-depth analysis of the results, simply seeing the range of outcomes · for example, how low and how high Net Profit can be, given our model and sources of uncertainty · can encourage a re-thinking of the risks we face, and the actions we can take.

Analyze the Model Results

Because a simulation yields many possible values for the outcomes we care about · from Net Profit to environmental impact · some work is needed to analyze the results. It is very useful to create charts to help us visualize the results -- such as frequency histogram charts and cumulative frequency charts. We can summarize the range of outcomes using various kinds of statistics, such as the mean or median, the standard deviation and variance, or the 5th and 95th percentile or Value at Risk.

Another powerful tool for assessing model results is sensitivity analysis, which can help us identify the uncertain inputs with the biggest impact on our key outcomes. For example, a tornado chart can give us a quick visual summary of the uncertainties with the greatest positive and negative impact on Net Profit. Using software, we can also run multiple simulations, with an input we choose taking a different value on each simulation, and assess the results. Analyzing the model can give us more information, but also insight about our real-world problem.

Make Decisions to Better Manage Risk

The payoff comes when we use our risk analysis model and simulation results to make choices or decisions, that may help us avoid or mitigate risk · or perhaps earn greater returns that help compensate us for taking these risks. We can also compare the risk and return of different projects or investments, and we can seek to diversify our position so that no single risk can do too much harm. By doing this, we can practice risk management.

While we can't avoid uncertainty and risk altogether, there are often many steps we can take to better cope with risk. Risk analysis helps us determine the right steps to take.

Risk Analysis

Notes


Return The return on an asset generally consists of two components, current yield and capital gain or loss yield.

The rate of return on an asset for a given period (usually at period of one year) is defined as follows.

Risk adjusted return on capital (RAROC) is a risk based profitability measurement framework for analyzing risk-adjusted financial performance and providing a consistent view of profitability across businesses. The concept was developed by Bankers Trust in the late 1970s. Note, however, that more and more Risk Adjusted Return on Risk Adjusted Capital (RARORAC) is used as a measure, whereby the risk adjustment of Capital is based on the capital adequacy guidelines as outlined by the Basel Committee, currently.

Basic formula

1. RAROC = (Expected Return)/(Economic Capital) or

2. RAROC = (Expected Return)/(Value at risk)

Broadly speaking, in business enterprises, risk is traded off against benefit. RAROC is defined as the ratio of risk adjusted return to economic capital. The economic capital is the amount of money which is needed to secure the survival in a worst case scenario that is it is a buffer against heavy shocks. Economic capital is a function of market risk, credit risk, and operational risk and is often calculated by VaR. This use of capital based on risk improves the capital allocation across different functional areas of banks, insurance companies, or any business in which capital is placed at risk for an expected return above the risk-free rate.

RAROC system allocates capital for 2 basic reasons:

1. Risk management

2. Performance evaluation

For risk management purposes, the main goal of allocating capital to individual business units is to determine the bank's optimal capital structure·that is economic capital allocation is closely correlated with individual business risk. As a performance evaluation tool, it allows banks to assign capital to business units based on the economic value added of each unit.

Rate of return= EBIT / CAPITAL EMPLOYED

The rate of return can be split into two components viz current yield and capital gain/loss yield as follows.

Rate of return = (Current yield) + (Capital gain/loss yield)

Opportunity Cost of Capital

Opportunity Cost Relevant costs may also be expressed as opportunity costs. An opportunity cost is the benefit foregone by choosing one opportunity instead of the next best alternative.

Example

A company is considering publishing a limited edition book bound in a special leather. It has in stock the leather bought some years ago for Rs 1,000. To buy an equivalent quantity now would cost Rs2,000. The company has no plans to use the leather for other purposes, although it has considered the possibilities:

Capital Budgeting

Notes


a) Of using it to cover desk furnishings, in replacement for other material which could cost Rs900

b) of selling it if a buyer could be found (the proceeds are unlikely to exceed Rs800).

In calculating the likely profit from the proposed book before deciding to go ahead with the project, the leather would not be costed at Rs1,000. The cost was incurred in the past for some reason which is no longer relevant. The leather exists and could be used on the book without incurring any specific cost in doing so. In using the leather on the book, however, the company will lose the opportunities of either disposing of it for Rs800 or of using it to save an outlay of Rs900 on desk furnishings.

The better of these alternatives, from the point of view of benefiting from the leather, is the latter. "Lost opportunity" cost of Rs900 will therefore be included in the cost of the book for decision making purposes.

The relevant costs for decision purposes will be the sum of:

i) 'avoidable outlay costs', i.e. those costs which will be incurred only if the book project is approved, and will be avoided if it is not

ii) The opportunity cost of the leather (not represented by any outlay cost in connection to the project).

This total is a true representation of 'economic cost'.

Now attempt exercise 4.1.

Exercise 4.1 Relevant costs and opportunity costs

Zimglass Industries Ltd. has been approached by a customer who would like a special job to be done for him, and is willing to pay Rs60,000 for it. The job would require the following materials.

Material Total units required

Units already in stock

Book value of units in stock Rs/unit

Realisable value Rs/unit

Replacement cost Rs/unit

A 1000 0 - - 16.00

B 1000 600 12.00 12.50 15.00

C 1000 700 13.00 12.50 14.00

D 200 200 14.00 16.00 19.00

a) Material B is used regularly by Zimglass Industries Ltd, and if units of B are required for this job, they would need to be replaced to meet other production demands.

b) Materials C and D are in stock due to previous over-buying, and they have restricted use. No other use could be found for material C, but the units of material D could be used in another job as a substitute for 300 units of material E, which currently costs Rs15 per unit (of which the company has no units in stock at the moment).

Calculate the relevant costs of material for deciding whether or not to accept the contract. You must carefully and clearly explain the reasons for your treatment of each material.

The assumptions in relevant costing

Some of the assumptions made in relevant costing are as follows:

a) Cost behaviour patterns are known, e.g. if a department closes down, the attributable fixed cost savings would be known.

Risk Analysis

Notes


b) The amount of fixed costs, unit variable costs, sales price and sales demand are known with certainty.

c) The objective of decision making in the short run is to maximise 'satisfaction', which is often known as 'short-term profit'.

d) The information on which a decision is based is complete and reliable.

In finance, rate of return (ROR) or return on investment (ROI), or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. ROI is usually given as a percent rather than decimal value.

ROI is also known as rate of profit.

ROI does not indicate how long an investment is held. However, ROI is most often stated as an annual or annualized rate of return, and it is most often stated for a calendar or fiscal year. In this article, „ROI‰ indicates an annual or annualized rate of return, unless otherwise noted.

ROI is used to compare returns on investments where the money gained or lost · or the money invested · are not easily compared using monetary values. For instance, a Rs1,000 investment that earns Rs50 in interest generates more cash than a Rs100 investment that earns Rs20 in interest, but the Rs100 investment earns a higher return on investment.

1. Rs50/Rs1,000 = 5% ROI

2. Rs20/Rs100 = 20% ROI

When considering a continuous process of gaining or losing money with a constant rate of return, the annual rate of return is any value greater than -100%; a positive percentage corresponds to exponential growth of the capital, a value between -100% and 0% exponential decay.

Measuring Rate of Return

The initial value of an investment does not always have a clearly defined monetary value, but for purposes of measuring ROI, the initial value must be clearly stated along with the rationale for this initial value. The final value of an investment also does not always have a clearly defined monetary value, but for purposes of measuring ROI, the final value must be clearly stated along with the rationale for this final value.

Return on investment is a rate of profit or income (realized or unrealized). The return is sometimes adjusted for taxes in geographical areas or historical times in which taxes consumed or consume a significant portion of profits or income. Taxes are an expense which may or may not be considered when calculating ROI. Similarly, a return may be adjusted for inflation to better indicate its true value in purchasing power.

Cash Flow (Income Stream)

Cash Flow Example on Rs1,000 Investment

Year 1 Year 2 Year 3 Year 4

Return Rs100 Rs55 Rs60 Rs50

ROI 10% 5.5% 6% 5%

Capital Budgeting

Notes


ROI is a measure of cash (or potential cash) generated by an investment, or the cash lost due to the investment. It measures the cash flow or income stream from the investment to the investor. Cash flow to the investor can be in the form of profit, interest, dividends, or capital gain/loss. Capital gain/loss occurs when the market value or resale value of the investment increases or decreases. Cash flow here does not include the return of invested capital.

Annual Returns An Annual Rate of Return is the return on an investment over a one-year period, such as January 1 through December 31st, or June 3rd 2006 through June 2nd 2007. Each ROI in the cash flow example above is an annual rate of return. An Annualized Rate of Return is the return on an investment over a period other than one year (such as a month, or two years) multiplied or divided to give a comparable one-year return. For instance, a one-month ROI of 1% could be stated as an annualized rate of return of 12%. Or a two-year ROI of 10% could be stated as an annualized rate of return of 5%.

In the cash flow example above, the Rs. returns for the four years add up to Rs265. The annualized rate of return for the four years is Rs265 Á (Rs1,000 x 4 years) = 6.625%.

Arithmetic Return In mathematical terms, the arithmetic return is defined as the following:

where

1. Vi is the initial investment value 2. Vf is the final investment value

This return has the following characteristics:

1. ROIArith = + 1.00 = + 100% when the final value is twice the initial value 2. ROIArith > 0 when the investment is profitable 3. ROIArith < 0 when the investment is at a loss 4. ROIArith = − 1.00 = − 100% when investment can no longer be recovered

Yield In financial economics, the term yield indicates a rate of return that is based on compounding, reinvestment, and/or the changing market value of a security. Yield indicates that the value of the investment increases or decreases during the investment period.

Effective annual rate (EAR) or Annual percentage yield (APY) indicates an annual yield from compound interest. The yield depends on the frequency of compounding.

Effective Annual Rate Based on Frequency of Compounding

Rate Semi-Annual Quarterly Monthly Daily Continuous

1% 1.002% 1.004% 1.005% 1.005% 1.005%

5% 5.062% 5.095% 5.116% 5.127% 5.127%

10% 10.250% 10.381% 10.471% 10.516% 10.517%

15% 15.563% 15.865% 16.075% 16.180% 16.183%

20% 21.000% 21.551% 21.939% 22.134% 22.140%

30% 32.250% 33.547% 34.489% 34.969% 34.986%

40% 44.000% 46.410% 48.213% 49.150% 49.182%

50% 56.250% 60.181% 63.209% 64.816% 64.872%

Risk Analysis

Notes


Logarithmic or Continuously Compounded Return Academics often use in their research natural log return called logarithmic return or continuously compounded return. The main advantage is that the continuously compounded return is symmetric, while the arithmetic return is not: positive and negative percent returns are not equal. A 50% (arithmetic) return results in 40.55% continuously compounded return while a -50% return results in -69.31% continuously compounded return. This means that a Rs. in an investment that increases a 50% arithmetic return and then falls a 50% arithmetic return will result in 0.75 Rs.s, while if it increases +50% and falls -50% continuously compounded returns it will remain one Rs.. The difference between continuously compounded return and arithmetic return is large only when percent changes are high, as both are approximately equal for small returns.

1. Vi is the initial investment value

2. Vf is the final investment value

3. ROILog > 0 is profit

4. ROILog < 0 is a loss

5. Doubling occurs when

6. Total loss occurs when .

7. ROIArith = exp(ROILog) –− 1.

ROI Calculations for Various Uses ROI values typically used for personal financial decisions include Annual Rate of Return and Annualized Rate of Return. For nominal risk investments such as savings accounts or Certificates of Deposit, the personal investor considers the effects of reinvesting/compounding on increasing savings balances over time. For investments in which capital is at risk, such as stock shares, mutual fund shares and home purchases, the personal investor considers the effects of price volatility and capital gain/loss on returns.

Profitability ratios typically used by financial analysts to compare a companyÊs profitability over time or compare profitability between companies include Gross Profit Margin, Operating Profit Margin, ROI ratio, Dividend yield, Net profit margin, Return on equity, and Return on assets.

During capital budgeting, ROI values typically used within a company to select which projects to pursue in order to generate maximum return or wealth for the company's stockholders include Average rate of return, Payback period, Net present value, Profitability index, and Internal rate of return.

In many countries, it is also important to consider the after-tax rate of return.

After-tax Returns The after-tax rate of return is calculated by multiplying the rate of return by the tax rate, then subtracting that percentage from the rate of return.

1. A return of 5% taxed at 15% gives an after-tax return of 4.25%

0.05 × 0.15 = 0.0075

0.05 – 0.0075 = 0.0425 = 4.25%

2. A return of 10% taxed at 25% gives an after-tax return of 7.5%

0.10 × 0.25 = 0.025

0.10 - 0.025 = 0.075 = 7.5%

Capital Budgeting

Notes


Cash or Potential Cash Returns

Time Value of Money

Investments generate cash flow to the investor to compensate the investor for the time value of money.

Except for rare periods of deflation where the opposite is true, a Rs. in cash is worth less today than it was yesterday, and worth more today than it will be worth tomorrow. The main factors that are used by investors to determine the rate of return at which they are willing to invest money include:

1. estimates of future inflation rates

2. estimates regarding the risk of the investment (e.g. how likely it is that investors will receive regular interest/dividend payments and the return of their full capital)

3. whether or not the investors want the money available („liquid‰) for other uses.

The time value of money is reflected in the interest rates that banks offer for deposits, and also in the interest rates that banks charge for loans such as home mortgages. The „risk-free‰ rate is the rate on U.S. Treasury Bills, because this is the highest rate available without risking capital.

The rate of return which an investor expects from an investment is called the Discount Rate. Each investment has a different discount rate, based on the cash flow expected in future from the investment. The higher the risk, the higher the discount rate (rate of return) the investor will demand from the investment.

Any investment with a return less than the annual inflation rate represents a loss of value, even though the return might well be greater than 0%. When ROI is adjusted for inflation, the resulting return is considered an increase or decrease in purchasing power. If an ROI value is adjusted for inflation, itÊs stated explicitly, such as „The return, adjusted for inflation, was 2%.‰ Investors usually seek a higher rate of return on taxable investment returns than on non-taxable investment returns.

Compounding or Reinvesting Compound interest or other reinvestment of cash returns (such as interest and dividends) does not affect the discount rate of an investment, but it does affect the Annual Percentage Yield, because compounding/reinvestment increases the capital invested.

For example, if an investor put Rs1,000 in a 1-year Certificate of Deposit (CD) that paid an annual interest rate of 4%, compounded quarterly, the CD would earn 1% interest per quarter on the account balance. The account balance includes interest previously credited to the account.

Compound Interest Example

1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Capital at the beginning of the period Rs1,000 Rs1,010 Rs1,020.10 Rs1,030.30

Rs. return for the period Rs10 Rs10.10 Rs10.20 Rs10.30

Account Balance at end of the period Rs1,010.00 Rs1,020.10 Rs1,030.30 Rs1,040.60

Quarterly ROI 1% 1% 1% 1%

Risk Analysis

Notes


The concept of 'income stream' may express this more clearly. At the beginning of the year, the investor took Rs1,000 out of his pocket (or checking account) to invest in a CD at the bank. The money was still his, but it was no longer available for buying groceries. The investment provided a cash flow of Rs10.00, Rs10.10, Rs10.20 and Rs10.30. At the end of the year, the investor got Rs1,040.60 back from the bank. Rs1,000 was return of capital.

Once interest is earned by an investor it becomes capital. Compound interest involves reinvestment of capital; the interest earned during each quarter is reinvested. At the end of the first quarter the investor had capital of Rs1,010.00, which then earned Rs10.10 during the second quarter. The extra dime was interest on his additional Rs10 investment. The Annual Percentage Yield or Future value for compound interest is higher than for simple interest because the interest is reinvested as capital and earns interest. The yield on the above investment was 4.06%.

Bank accounts offer contractually guaranteed returns, so investors cannot lose their capital. Investors/Depositors lend money to the bank, and the bank is obligated to give investors back their capital plus all earned interest. Since investors are not risking losing their capital on a bad investment, they earn a quite low rate of return. But their capital steadily increases.

Example #1 Level Rates of Return


Rate of Return 5% 5% 5% 5%

Geometric Average 5% 5% 5% 5%

Capital at End of Year Rs105.00 Rs110.25 Rs115.76 Rs121.55

Rs. Profit/(Loss) Rs21.55

Compound Yield 5.4%

Returns when Capital is at Risk

Average Returns

There are three common ways investment returns are calculated over multiple periods of time

1. Arithmetic Average Rate of Return Arithmetic mean

2. Geometric Average Rate of Return (Time-Weighted Average Return)

3. Rs.-Weighted Average Return Internal rate of return

These calculations use averages of periodic percentage returns. None will accurately translate to Rs. gains or losses if percent losses are averaged with percent gains. A 10% loss on a Rs100 investment is a Rs10 loss, and a 10% gain on a Rs100 investment is a Rs10 gain. When percentage returns on investments are calculated, they are calculated for a period of time – not based on original investment Rs.s, but based on the Rs.s in the investment at the beginning and end of the period. So if an investment of Rs100 loses 10% in the first period, the investment amount is then Rs90. If the investment then gains 10% in the next period, the investment amount is Rs99.

A 10% gain followed by a 10% loss is a 1% Rs. loss. The order in which the loss and gain occurs does not affect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a 50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment returns are published as "Average Returns", itÊs important to note that average returns do not always translate into Rs. returns.

Capital Budgeting

Notes


To the right and below are some examples of what can happen to a 4-year Rs100 investment with an Arithmetic Average Rate of Return of 5%.

Example #2 Volatile Rates of Return, including losses


Rate of Return 50% -20% 30% -40%

Geometric Average 50% 9.5% 16% -1.6%


Rs. Profit/(Loss) (Rs6.40)

Compound Yield -1.6%

Example #3 Highly Volatile Rates of Return, including losses


Rate of Return -95% 0% 0% 115%

Geometric Average -95% -77.6% -63.2% -42.7%


Profit/(Loss) (Rs89.25)

Compound Yield -22.3%

Capital Gains and Losses Many investments carry significant risk that the investor will lose some or all of the invested capital. For example, investments in company stock shares put capital at risk.

A stock share is partial ownership of a company, and the value of the stock depends on many factors, including the likelihood that the company will pay a dividend (a distribution of profit to shareholders). When stock shares are first offered for sale, the company receives the capital from the stock purchaser and uses the capital to operate its business. Once stock shares are sold to investors, the investors can sell the shares to other investors. Publicly-traded companiesÊ stock shares are bought and sold (traded) on the stock markets.

The value of a stock share depends on what someone is willing to pay for it at a certain point in time. Unlike capital invested in a savings account, the capital value (price) of a stock share constantly changes. If the price is relatively stable, the stock is said to have „low volatility.‰ If the price often changes a great deal, the stock has „high volatility.‰ All stock shares have some volatility, and the change in price directly affects ROI for stock investments.

Stock returns are usually calculated for holding periods such as a month, a quarter or a year.

Holding Period Return The holding period return an arithmetic return, is calculated:

Example: Stock with low volatility and a regular quarterly dividend

End of: 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Dividend Rs1 Rs1 Rs1 Rs1

Stock Price Rs98 Rs101 Rs102 Rs99

Quarterly ROI -1% 4.08% 1.98% -1.96%

Annual ROI 3%

Risk Analysis

Notes


Holding-Period Return = (Ending Price – Beginning Price + Cash Dividend) / Beginning Price.

To the right is an example of a stock investment of one share purchased at the beginning of the year for Rs100. At the end of the first quarter the stock price is Rs98. This is a capital loss. The stock share bought for Rs100 can only be sold for Rs98, which is the value of the investment at the end of the first quarter. The first quarter return is:

(Rs98 - Rs100 + Rs1) / Rs100 = -1%

Since the final stock price is Rs99, the annual ROI is:

(Rs99 ending price - Rs100 beginning price + Rs4 dividends) / Rs100 beginning price = 3% ROI.

If the final stock price had been Rs95, the annual ROI would be:

Example: Stock with low volatility and a regular quarterly dividend, reinvested

Example: Stock with low volatility and a regular quarterly dividend, reinvested

End of: 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Dividend Rs1 Rs1.01 Rs1.02 Rs1.03

Stock Price Rs98 Rs101 Rs102 Rs99

Shares Purchased 0.010204 0.01 0.01 0.010404

Total Shares Held 1.010204 1.020204 1.030204 1.040608

Investment Value Rs99 Rs103.04 Rs105.08 Rs103.02

Quarterly ROI -1% 4.08% 1.98% -1.96%

(Rs95 ending price - Rs100 beginning price + Rs4 dividends) / Rs100 beginning price = -1% ROI.

Reinvestment when Capital is at Risk: Rate of Return and Yield Yield is the compound rate of return that includes the effect of reinvesting interest or dividends.

To the right is an example of a stock investment of one share purchased at the beginning of the year for Rs100.

1. The quarterly dividend is reinvested at the quarter-end stock price.

2. The number of shares purchased each quarter = (Rs Dividend)/(Rs Stock Price).

3. The final investment value of Rs103.02 is a 3.02% Yield on the initial investment of Rs100. This is the compound yield, and this return can be considered to be the return on the investment of Rs100.

To calculate the rate of return, the investor includes the reinvested dividends in the total investment. The investor received a total of Rs4.06 in dividends over the year, all of which were reinvested, so the investment amount increased by Rs. 4.06.

1. Total Investment = Cost Basis = Rs100 + Rs4.06 = Rs104.06.

2. Capital gain/loss = Rs103.02 - Rs104.06 = -Rs1.04 (a capital loss)

3. (Rs4.06 dividends - Rs1.04 capital loss ) / Rs104.06 total investment = 2.9% ROI

Capital Budgeting

Notes


The disadvantage of this ROI calculation is that it does not take into account the fact that not all the money was invested during the entire year (the dividend reinvestments occurred throughout the year). The advantages are: (1) it uses the cost basis of the investment, (2) it clearly shows which gains are due to dividends and which gains/losses are due to capital gains/losses, and (3) the actual Rs. return of Rs3.02 is compared to the actual Rs. investment of Rs104.06.

For American income tax purposes, if the shares were sold at the end of the year, dividends would be Rs4.06, cost basis of the investment would be Rs104.06, sale price would be Rs103.02, and the capital loss would be Rs1.04.

Since all returns were reinvested, the ROI might also be calculated as a continuously compounded return or logarithmic return. The effective continuously compounded rate of return is the natural log of the final investment value divided by the initial investment value:

1. Vi is the initial investment (Rs100)

2. Vf is the final value (Rs103.02)

Mutual Fund Returns Mutual Funds and exchange-traded funds (ETFs) hold portfolios of various companies' stock shares. When the companies pay a dividend, and when the fund trades shares, dividends and capital gains are distributed to the mutual fund shareholders. Mutual funds trade at the net asset value of the stock shares.

Total Returns Mutual funds report total returns based on reinvestment factors. Reinvestment factors are based on total distributions (dividends plus capital gains) during each period.

Total Return = ((Final Price x Last Reinvestment Factor) - Beginning Price) / Beginning Price

Average annual return (geometric)

Example: Mutual Fund with low volatility and a regular annual dividend, reinvested at year-end share price, initial share value Rs100

End of: Year 1 Year 2 Year 3 Year 4 Year 5

Dividend Rs5 Rs5 Rs5 Rs5 Rs5

Capital Gain Distribution Rs2

Total Distribution Rs5 Rs5 Rs7 Rs5 Rs5

Share Price Rs98 Rs101 Rs102 Rs99 Rs101

Shares Purchased 0.05102 0.04950 0.06863 0.05051 0.04950

Shares Owned 1.05102 1.10053 1.16915 1.21966 1.26916

Reinvestment Factor 1.05102 1.05203 1.07220 1.05415 1.05219

Using a Holding Period Return calculation, after 5 years, an investor who reinvested owned 1.26916 share valued at Rs101 per share (Rs128.19 in value). (Rs128.19-Rs100)/Rs100/5 = 5.638% yield. An investor who did not reinvest received a total of Rs27 in dividends and Rs1 in capital gain. (Rs27+Rs1)/Rs100/5 = 5.600% return.

Mutual funds include capital gains as well as dividends in their return calculations. Since the market price of a mutual fund share is based on net asset value, a capital gain distribution is offset by an equal decrease in mutual fund share value/price.

Risk Analysis

Notes


From the shareholder's perspective, a capital gain distribution is not a net gain in assets, but it is a realized capital gain.

Summary: Overall Rate of Return Rate of Return and Return on Investment indicate cash flow from an investment to the investor over a specified period of time, usually a year.

ROI is a measure of investment profitability, not a measure of investment size. While compound interest and dividend reinvestment can increase the size of the investment (thus potentially yielding a higher Rs. return to the investor), Return on Investment is a percentage return based on capital invested.

In general, the higher the investment risk, the greater the potential investment return, and the greater the potential investment loss.

Single Product Analysis under Risk This section considers some mathematical ways of measuring volatility -- and thus risk.

Probability Distribution Assessing the risk of a single asset requires that we have some sense for the range of possible outcomes. For example, a judge sentencing a youthful offender might consider different scenarios: (1) worst case (pessimistic), the offender will commit only another minor crime; (2) expected case (normal), she will commit no more crimes; (3) best case (optimistic), she will dissuade other youth from committing crimes. Given this distribution, what should the judge do?

Assessing the risk of an asset requires that we have some sense for the range of possible outcomes. For example, a judge sentencing a youthful offender might consider the likelihood of different scenarios:

1. worst case (pessimistic), the offender will commit only another minor crime;

2. expected case (normal), she will commit no more crimes

3. best case (optimistic), she will prevent others from committing crimes

Given this distribution, the judge might suspend the youthful offender's sentence.

Predicting a range of outcomes and assigning to them different probabilities can give further insight into risk. Using a probability distribution, we can model different outcomes. For example, the probability distribution of the results of throwing two dice is shown in the table to the right --

Example

The most likely throw is a 7 - but it happens only one-sixth of the time. Possible outcomes range from 2 to 12, although the likelihood of throwing a 2 or 12 is significantly lower than throwing a 7. What if you wanted to throw at least a 7? You would have to consider variability in assessing risk. Even though 7 would be the most frequent throw, you might throw less. In fact, there is a 41.6% chance that you will throw less than a 7.

Result Probability

2 1/36 = 2.8%

3 2/36 = 5.6%

Contd…

Capital Budgeting

Notes


4 3/36 = 8.3%

5 4/36 = 11.1%

6 5/36 = 13.9%

7 6/36 = 16.7%

8 5/36 = 13.9%

9 4/36 = 11.1%

10 3/36 = 8.3%

11 2/36 = 5.6%

12 1/36 = 2.8%

Total 36/36 = 100%

Expected Return What is the espected return when you roll two dice? Suppose the number you throw represents the return, and suppose you throw the dice thousands of times. What would you expect your return to be on average? We can compute the expected return for each possible result and then sum these results.

What is the expected return when we throw two dice? Suppose the number you throw represents the return, and suppose you throw the dice thousands of times. What would you expect your return to be on average? We can compute the expected return for each possible result and then sum these results.

Return Probability Weighted expected return

Rs.2 1/36 = 2.8% Rs.0.056

Rs.3 2/36 = 5.6% Rs.0.168

Rs.4 3/36 = 8.3% Rs.0.252

Rs.5 4/36 = 11.1% Rs.0.555

Rs.6 5/36 = 13.9% Rs.0.833

Rs.7 6/36 = 16.7% Rs.1.167

Rs.8 5/36 = 13.9% Rs.1.111

Rs.9 4/36 = 11.1% Rs.1.000

Rs.10 3/36 = 8.3% Rs.0.833

Rs.11 2/36 = 5.6% Rs.0.611

Rs.12 1/36 = 2.8% Rs.0.333

Total 36/36 = 100% Rs.7.00

The expected return Rs.7.00.

Consider a probability distribution example with less variability · that is, a distribution with less risk that your returns deviate from the average. This time suppose you are throwing two six-sided dice, but each dice has only three 3's and three 4's · with corresponding returns. The probability distribution for returns throwing a pair of these strange dice is

Return Probability Weighted expected return

Rs.6 9/36 = 25% 1.500

Rs.7 18/36 = 50% 3.500

Rs.8 9/36 = 25% 2.000

Total 36/36 = 100% Rs.7.00

Risk Analysis

Notes


Again, the most likely return is Rs.7 and the expected return is Rs.7, but now the range is narrower -- from Rs.6 to Rs.8. This smaller variability affects risk. It is less likely you will have a miserable return. (Less variability also diminishes the possibility of a fabulous return.) For a person who is risk averse, it would be more desirable to throw the strange 3-4-only dice. There is less variability, and thus less risk, than with regular dice.

Standard Deviation(s) Variability can be measured. That is, risk can be quantified! The most common measure of risk is the standard deviation – a numerical measure of the dispersion around the expected value. Here is how the standard deviation is calculated for our two dice probability distributions:

This variability can be measured. That is, risk can be quantified! The most common measure of risk is the standard deviation – a numerical measure of the dispersion around the expected value. Here is how the standard deviation (designated by s ) is calculated for our two dice probability distributions:

1. compute the expected return;

2. square the variance of each return from the expected return;

3. multiply this by the probability;

4. sum these weighted values;

5. calculate the square root of this sum (the standard deviation).

This gives a numerical indication of how far the returns are dispersed from the average.

There are various measures of risk: beta, standard deviation, R-squared. (See a comparison of these three measures of risk.) For an excellent primer on risk in securities markets, see Vanguard's Investing Primer.

Return Square of variance Probability Weighted square

Rs.2 (7 - 2)2 = 25 1/36 = .028 0.694

Rs.3 (7 - 3)2 = 16 2/36 = .056 0.889

Rs.4 (7 - 4)2 = 9 3/36 = .083 0.750

Rs.5 (7 - 5)2 = 4 4/36 = .111 0.444

Rs.6 (7 - 6)2 = 1 5/36 = .139 0.139

Rs.7 (7 - 7)2 = 0 6/36 = .167 0.000

Rs.8 (7 - 8)2 = 1 5/36 = .139 0.139

Rs.9 (7 - 9)2 = 4 4/36 = .111 0.444

Rs.10 (7 - 10)2 = 9 3/36 = .083 0.750

Rs.11 (7 - 11)2 = 16 2/36 = .056 0.889

Rs.12 (7 - 12)2 = 25 1/36 = .028 0.694

Statistics:

Sum of weighted squares 5.833

Standard deviation (square root of sum) 2.415

Capital Budgeting

Notes


Normal Distribution If a dice-throwing distribution were normally distributed (a classic "bell curve"), a standard deviation indicates the percentage of likely results around the mean. Specifically, 38.3% of all returns are within one-half standard deviation of the expected return; 68.3% of all returns are within one standard deviation of the average return, and 95.4% of the returns are within two standard deviations of the average return. The larger the standard deviation, the greater the dispersion and the greater the risk.

If the dice-throwing distribution were normally distributed (a classic "bell curve"), a standard deviation of 2.415 would indicate the following

1. 38.3% of all returns are within one-half standard deviation of the expected return – in our example, from Rs.5.793 to Rs.8.207 (within Rs.1.207 of Rs.7.00)

2. 68.3% of all returns are within one standard deviation of the average return – in our example, from Rs.4.585 to Rs.9.415 (within Rs.2.415 of Rs.7.00)

3. 95.4% of the returns are within two standard deviations of the average return – in our example, from range from Rs.2.170 to Rs.11.830 (within Rs.4.830 of Rs.7.00)

The larger the standard deviation, the greater the dispersion and the greater the risk. In our example of the weird dice with only 3s and 4s, the standard deviation is 0.707.

Coefficient of Variation What happens when there are two distributions with different expected returns? How do you decide which distribution involves greater dispersion and thus greater risk? For example, suppose you are presented with two investment strategies.

What happens when there are two distributions with different expected returns? How do you decide which distribution involves greater dispersion and thus greater risk? For example, suppose you are presented with two investment strategies.

Standard Deviation Plan A 5%

Plan B 6%

Coefficient of variation Plan A .333

Plan B .300

Plan A offers a lower expected return, but with less variability, than Plan B. Which is less risky? Actually, Plan B has less relative risk. The coefficient of variation -- that is, the ratio of variability to return -- is higher for Plan A (5/15 = .33) compared to Plan B (6/20 = .30). There is greater relative risk that returns will deviate from the expected return under Plan A.


1. The larger the standard deviation, the greater the ________________ and the greater the risk.

2. The most common measure of risk is the __________________

3. An _______________is the return on an investment over a one-year period.

Risk Analysis

Notes


Summary Risk is the inherent in almost every business decision. More so in capital budgeting decisions as they involve costs and benefits extending over a long period of time during which many things can change in unanticipated ways.

Any firm can reduce the risk factor but it cannot be eliminated.

The term risk with reference to capital budgeting decisions may be defined as the variability that is likely to occur in future between the estimated and actual returns. The greater is the variability between the two, the more risky is the project and vice versa.

Keywords Risk: The variability that is likely to occur in future between the estimated and the actual returns.

Opportunity cost of capital: Also called hurdle rate or cost of capital. It refers to the minimum rate of return a firm must earn on its investment so that the market value of the companies equity shares does not fall.

Review Questions 1. What do you mean by risk?

2. What is the opportunity cost of capital?

3. What is the rate of return?

4. What are the components of cost capital?

Further Readings A Khan & Jain, Financial Management (Text, Problems & Cases)

M.Pandey, Financial Management

Dr.S.N.Maheswari, Financial Management (Principles and Practice)

Sudhindra Bhatt, Financial Management (Principles and Practice)

Unit 5

A Project is Not a Black Box

Unit 6 Leasing

SECTION-III


Notes


Unit 5 A Project is Not a Black Box

Unit Structure • Introduction • Simulation • Sensitivity Analysis • Decision Tree Analysis • Capital Asset Pricing Model (CAPM) • Arbitrage Pricing Theory (APT) • Comparison between CAPM and APT • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to: • Know the various statistical analysis • Study the CAPM models • Know the APT theory • Study the difference between the CAPM and APT

Introduction A black box is something that we accept and use but do not understand for most of us a computer is a black box. We may know that it is supposed to do, but we do not understand it works and if something breaks, we cannot fix it.

We have been treating capital projects as black Boxes. In other words, we have talked as if managers are handed unbiased cash-how forecasts and their only task is to assess risk, choose the right discount rate m and rank out net present value. Actual financial managers will not rest until they understand what makes the projects tick and what could to wrong with it.

Discount cash-how analysis commonly assumes that compromise holds assets passively, and it ignores the opportunities to expand the projects it is successful or to bail out it is not. However, wise manger value-these opportunities they look for ways to capitalize on success and to reduce the acts of failure and they are prepared to pay for projects that give them this flexibility.

Simulation Simulation is a statistical technique to deal with uncertainty and is based on the concept of probabilities, Simulation, refers to representation of a system which reacts to a change in any of input variable in a similar way as to that variable which us being simulation.

Capital Budgeting

Notes


When simulation analysis applied to capital budgeting, the simulation requires the generation if values of cash flows using predetermined probability distribution and the random numbers. The different components of cash flows are places in relation to one another in a mathematical model. The process of generating the values of cash flows is repeated numerous times to results in a probability distribution of cash flows. The process 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.

Example 1:

PQR and Co. is evaluating the installation of a new automatic machine in order to reduce the labor costs. The new machine can also meet the demand for greater capacity needed to meet increase in demand for the product and hence resulting in increase in profits for at least three years. However, due to uncertainty in the expected demand for the product, the cash flows cannot be accurately estimated. The following probabilities have been assigned in this reference.

Year 1 Year 2 Year 3

CF (Rs.) Probability CF (Rs.) Probability CF (Rs.) Probability

10000 0.3 10000 0.1 10000 0.3

15000 0.4 20000 0.2 20000 0.5

20000 0.3 30000 0.4 30000 0.2

- - 40000 0.3 - -

The new machine is having a cost of Rs. 70,000 and the scrap value of the old machine is estimated to be Rs. 28,000. Evaluate the proposal given that the discount factor is 15%. Also analyze the risk inherent in this situation by simulating the NPV values. Random numbers for 5 sets of cash flows are given hereunder. On the basis of simulation exercise, find out the expected NPV and the probability that the NPV of the proposal will be less than 0.

Random Numbers

Year Set 1 Set 2 Set 3 Set 4 Set 5

1 4 7 6 5 0

2 2 4 8 0 1

3 7 9 4 0 3

Solution:

Year Cash flows Probability Exp. Value PVF (15%n) Exp Values

1 10000 0.3 3000

15000 0.4 6000

20000 0.3 6000

Total 15000 0.870 13050

2 10000 0.1 1000

20000 0.2 4000

30000 0.4 12000

40000 0.3 12000

Total 29000 0.756 21924


Notes


3 10000 0.3 3000

20000 0.5 10000

30000 0.2 6000

Total 19000 0.658 12502

Less: Expected present value of Cash inflows 47476

Net cash outflows (70000-28000) 42000

Net Present values 5476

The project is having NPV of Rs. 5476 and therefore, viable to be accepted.

In order to apply the simulation analysis, the random numbers are to be allocated to the cash flows.

Allocation of random numbers to Cash Flows.

Year Cash flow Probability Appearance No.

1 10000 0.3 0,1,2

15000 0.4 3,4,5,6

20000 0.3 7,8,9

2 10000 0.1 0

20000 0.2 1,2

30000 0.4 3,4,5,6

40000 0.3 7,8,9

3 10000 0.3 1,2,3

20000 0.5 3,4,5,6,7

30000 0.2 8,9

Note: The last column in the above table i.e. appearance numbers refers to specific number of occurrences when a particular cash flow may appear. For example, in year 1 cash flow of Rs. 10000 has a probability of 0.3 i.e. this cash flow may appear 3 times out of 10; for year 2 cash inflow of 30000 has a probability of 0.4i.e. this cash flow may appear 4 times out of total 10. On this basis, the appearances number for the cash flows of year 1 has been assigned i.e. 0-9, first 3 i.e. 0, 1, 2 have been assigned to cash inflow of Rs. 10000 next 4 i.e. 3,4,5,6 have been assigned to cash flow of Rs. 15000 and the last 3 i.e. 7, 8, 9 have been assigned to the cash flow of Rs. 20000. The same procedure is adopted for year 2 and year 3 also.

Set Year 1 Year 2 Year 3

App. No CF (Rs.) PV (Rs.) App. No.

CF (Rs.) PV (Rs.) App. No.

CF (Rs.) PV (Rs.)

1 4 15000 13050 2 20000 15120 7 20000 13160

2 7 20000 17400 4 30000 22680 9 30000 19740

3 6 15000 13050 8 40000 30240 4 20000 13160

4 5 15000 13050 0 10000 7560 0 10000 6580

5 0 1000 8700 1 2000 15120 3 20000 13160

Capital Budgeting

Notes


Set No. Total PV (Inflows) Outflows NPV

1 41300 42000 670

2 59820 42000 17820

3 56450 42000 14450

4 27190 42000 14810

5 36980 42000 5020

Total 11770

Average NPV is 11770 / 5 = Rs. 2354

In the above table, it is observed that out of 5 situations, 3 situations i.e. set 1, 4, 5 have negative NPV and only 2 situations i.e. set 2 and 3 have positive NPV. Therefore, there is a 60% probability (i.e. 3 out of 5) that the NPV of the project may turnout to be negative.

Sensitivity Analysis "Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the output of a mathematical model can be apportioned, qualitatively or quantitatively, to different sources of variation in the input of a model.‰

In more general terms uncertainty and sensitivity analyses investigate the robustness of a study when the study includes some form of mathematical modelling. While uncertainty analysis studies the overall uncertainty in the conclusions of the study, sensitivity analysis tries to identify what source of uncertainty weights more on the study's conclusions. For example, several guidelines for modelling (see e.g. one from the US EPA) or for impact assessment (see one from the European Commission) prescribe sensitivity analysis as a tool to ensure the quality of the modeling/ assessment.

The problem setting in sensitivity analysis has strong similarities with Design of experiments. In design of experiments one studies the effect of some process or intervention (the 'treatment') on some objects (the 'experimental units'). In sensitivity analysis one looks at the effect of varying the inputs of a mathematical model on the output of the model itself. In both disciplines one strives to obtain information from the system with a minimum of physical or numerical experiments.

Overview Most mathematical problems met in social, economic or natural sciences entail the use of mathematical models, which are generally too complex for an easy appreciation of the relationship between input factors (what goes into the model) and output (the modelÊs dependent variables). Such an appreciation, i.e. the understanding of how the model behaves in response to changes in its inputs, is of fundamental importance to ensure a correct use of the models.

A mathematical model is defined by a series of equations, input factors, parameters, and variables aimed to characterize the process being investigated.

Input is subject to many sources of uncertainty including errors of measurement, absence of information and poor or partial understanding of the driving forces and mechanisms. This uncertainty imposes a limit on our confidence in the response or output of the model. Further, models may have to cope with the natural intrinsic variability of the system, such as the occurrence of stochastic events.

Good modeling practice requires that the modeler provides an evaluation of the confidence in the model, possibly assessing the uncertainties associated with the modeling process and with the outcome of the model itself. Uncertainty and


Notes


Sensitivity Analysis offer valid tools for characterizing the uncertainty associated with a model. Uncertainty analysis (UA) quantifies the uncertainty in the outcome of a model. Sensitivity Analysis has the complementary role of ordering by importance the strength and relevance of the inputs in determining the variation in the output.

In models involving many input variables sensitivity analysis is an essential ingredient of model building and quality assurance. National and international agencies involved in impact assessment studies have included section devoted to sensitivity analysis in their guidelines. Examples are the European Commission, the White House Office for Budget and Management, the Intergovernmental Panel on Climate Change and the US Environmental Protection Agency.

Methodology There are several possible procedures to perform uncertainty analysis (UA) and sensitivity analysis (SA). The most common sensitivity analysis is sampling-based. A sampling-based sensitivity is one in which the model is executed repeatedly for combinations of values sampled from the distribution (assumed known) of the input factors. Sampling based methods can also be used to decompose the variance of the model output.

In general, UA and SA are performed jointly by executing the model repeatedly for combination of factor values sampled with some probability distribution. The following steps can be listed:

1. Specify the target function and select the input of interest

2. Assign a probability density function to the selected factors

3. Generate a matrix of inputs with that distribution(s) through an appropriate design

4. Evaluate the model and compute the distribution of the target function

5. Select a method for assessing the influence or relative importance of each input factor on the target function.

Applications Sensitivity Analysis can be used to determine:

1. The model resemblance with the process under study

2. The quality of model definition

3. Factors that mostly contribute to the output variability

4. The region in the space of input factors for which the model variation is maximum

5. Optimal - or instability - regions within the space of factors for use in a subsequent calibration study

6. Interactions between factors Sensitivity Analysis is popular in financial applications, risk analysis, signal processing, neural networks and any area where models are developed.

Environmental Computer environmental models are increasingly used in a wide variety of studies and applications. For example global climate model are used for both short-term weather forecasts and long-term climate change.

Capital Budgeting

Notes


Moreover, computer models are increasingly used for environmental decision making at a local scale, for example for assessing the impact of a waste water treatment plant on a river flow, or for assessing the behavior and life length of bio-filters for contaminated waste water.

In both cases sensitivity analysis may help understanding the contribution of the various sources of uncertainty to the model output uncertainty and system performance in general. In these cases, depending on model complexity, different sampling strategies may be advisable and traditional sensitivity indexes have to be generalized to cover multivariate sensitivity analysis, heteroskedastic effects and correlated inputs.

Business In a decision problem, the analyst may want to identify cost drivers as well as other quantities for which we need to acquire better knowledge in order to make an informed decision. On the other hand, some quantities have no influence on the predictions, so that we can save resources at no loss in accuracy by relaxing some of the conditions. See Corporate finance: Quantifying uncertainty Sensitivity analysis can help in a variety of other circumstances which can be handled by the settings illustrated below:

To identify critical assumptions or compare alternative model structures

Guide future data collections

Detect important criteria

Optimize the tolerance of manufactured parts in terms of the uncertainty in the parameters

Optimize resources allocation

Model simplification or model lumping, etc. However there are also some problems associated with sensitivity analysis in the business context:

Variables are often interdependent, which makes examining them each individually unrealistic, e.g.: changing one factor such as sales volume, will most likely affect other factors such as the selling price.

Often the assumptions upon which the analysis is based are made by using past experience/data which may not hold in the future.

Assigning a maximum and minimum (or optimistic and pessimistic) value is open to subjective interpretation. For instance one persons 'optimistic' forecast may be more conservative than that of another person performing a different part of the analysis. This sort of subjectivity can adversely affect the accuracy and overall objectivity of the analysis.

Sensitivity analysis provides information about cash flows under three assumptions:

(i) Pessimistic

(ii) Most likely

(iii) Optimistic out-comes associated with the project.

It explains how sensitive the cash flows are under these different situations. The larger is the difference between the pessimistic and optimistic cash flows, the more risky is the project and vice-versa.


Notes


Example 2:

ABC Company Limited is attempting to evaluate two mutually exclusive projects A and B. Each project requires a net investment of Rs. 10000 and the annual cash flows from each of the projects is estimated at Rs. 2000 pa in the next 15 years. The companyÊs cost of capital may be taken as 10%. The management has made the following optimistic, most likely and pessimistic estimates of the annual cash inflows associated with each of these projects.


Initial Investment Rs. 10000 Rs. 10000

Estimated cash inflow (per annum)

Pessimistic Rs. 1500 -

Most likely Rs. 2000 Rs. 2000

Optimistic Rs. 2500 Rs. 4000

You are required to give your considered opinion for helping the management in arriving at a decision.

Solution:

Project A (Initial Investment Rs. 10000)

Particulars Cash inflows for each of the 15years.

Discount factor at 10%

Present Value Net Present Value

Pessimistic Rs. 1500 7.606 Rs. 11409 1409

Most likely Rs. 2000 7.606 Rs. 15212 5212

Optimistic Rs. 2500 7.606 Rs. 19015 9015

Project B (Initial Investment 1st Rs. 10000)

Particulars Cash inflows for each of the 15years.

Discount factor at 10%

Present Value Net Present Value

Pessimistic - 7606 - (-) 10000

Most likely 2000 7606 15212 5212

Optimistic 4000 7606 30424 20424

The above data indicates that Project B is more risky than Project A. It will depend upon the management whether they would like to take project A or B depending upon the management whether they would like to take project A or B depending upon the risk they want to undertake Project B has a higher risk together with a higher profitability. In case, the management is venture some, it can go for project B and in case, it is orthodox, it may go for Project A.

Decision Tree Analysis Decision tree analysis is another technique which is helpful in tackling risky capital investment proposals. Decision tree is a graphic display of relationship between a present decision and possible future events, further decisions and their consequences. The sequence of events is mapped out over time in a format resembling branches of a tree. In other works, it is pictorial representation in tree form which indicates the magnitude, probability and interrelationship of all possible outcomes.

An outstanding feature of decision tree analysis is that it links events chronologically with forecasted probabilities and thus gives systematic appearance of decisions and their forecasted results.

Capital Budgeting

Notes


Example 3:

X Ltd is considering the purchase of a new plant requiring a cash outlay of Rs. 20000. The plant is expected to have a useful life of 2 years without any Salvage Value. The cash inflows and their associated probabilities for the two years are as follows:

1st Year Cash flows Probability

i 8000 0.3

ii 11000 0.4

iii 15000 0.3

2nd year. If the cash flows in the 1st year are:

Rs.8000 Rs. 11000 Rs.15000

Cash flows Probability Cash flows Probability Cash flows Probability

i 4000 0.2 13000 0.3 16000 0.1

ii 10000 0.6 15000 0.4 20000 0.8

iii 15000 0.2 16000 0.3 24000 0.1

Presuming that 10% is the cost of capital, you plot the above data in the form of a decision tree and suggest whether the project should be taken up or not.

Solution:

Computation of Net Present Values

Cash flow Present value at 10% NPV Alternatives

1st year 2nd year 1st year 2nd year Total

a. i 8000 4000 7272 3304 10,576 -9424

ii 8000 10000 7272 8260 15532 -4468

iii 8000 15000 7272 12390 19662 -388

b. i 11000 13000 9999 10738 20737 737

ii 11000 13000 9999 12390 22389 2389

iii 11000 13000 9999 13216 23215 3215

c. i. 15000 16000 13635 13216 26851 6851

ii 15000 20000 13635 16520 30155 10155

iii 15000 24000 13635 19824 33459 13459


Notes


Year Year 1 Year 2 Net Present Value

Joint Probability

Expected NPV

Probability Cash flows

Probability Cash flows

0.3 8000 0.2 4000 -9424 0.06 -565.4

0.6 10000 -4468 0.18 -804.2

0.2 15000 -388 0.06 -20.3

0.4 11000 0.3 13000 737 0.12 88.4

0.4 15000 2389 0.16 382.2

0.3 16000 3215 0.12 385.8

0.3 15000 0.1 16000 6851 0.03 205.5

0.8 20000 10155 0.24 2437.2

0.1 24000 13459 0.03 403.8

Cash outlay

Rs. 20000

1.00 2513

This project gives a positive net present value of Rs. 2513 at 15% discount factor, hence it may be accepted.

Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) is used in finance to determine a theoretically appropriate required rate of return of an asset if that asset is to be added to an already well-diversified portfolio given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta ( �) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor, William Sharpe John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in Economics (jointly with Markowitz and Merton Miller) for this contribution to the field of financial economics.

The Formula The CAPM is a model for pricing an individual security (asset) or a portfolio. For individual security perspective, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

Individual security’s / beta = Market’s securities (portfolio) Reward-to-risk ratio

Reward-to-risk Ratio The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E (Ri), we obtain the Capital Asset Pricing Model (CAPM).

Capital Budgeting

Notes


Where:

is the expected return on the capital asset,

is the risk-free rate of interest,

(the beta co-efficient) is the sensitivity of the asset returns to market returns, or also,

is the expected return of the market,

is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return). Note 1: the expected market rate of return is usually measured by looking at the arithmetic average of the historical returns on a market portfolio (i.e. S&P 500). Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

Asset Pricing Once the expected return, E(Ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate (E(Ri)), to establish the correct price for the asset.

In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation).

Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

Asset-specific Required Return The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. The CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and Diversification The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as UK or US will render the portfolio sufficiently


Notes


diversified to limit exposure to systemic risk only. In developing markets a larger number is required, due to the higher asset volatilities.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor.

The Efficient Frontier

Figure 5.1: The (Markowitz) Efficient Frontier

The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta.

The Market Portfolio An investor might choose to invest a proportion of his or her wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund his or her purchase of risky assets in which case there is a negative cash weighting). Here, the ratio of risky assets to risk free asset does not determine overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways:

1. By investing all of one's wealth in a risky portfolio, or

2. By investing a proportion in a risky portfolio and the remainder in cash (either borrowed or invested).

Efficient Frontier

Best possible CAL

Individual Assets

Tangency Portfolio

Risk free rate

Standard Deviation

Expe

cted

Ret

urn

Capital Budgeting

Notes


For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2 will generally have the lower variance and hence be the more efficient of the two.

This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio.

Assumptions of CAPM All Investors:

1) Aim to maximise utilities.

2) Are rational risk-averse.

3) Are price takers i.e. they cannot influence prices.

4) Can lend and borrow unlimited under the risk free rate of interest.

5) Securities are all highly divisible into small parcels.

6) No transaction or taxation costs incurred.

Shortcomings of CAPM

The model assumes that asset returns are (jointly) normally distributed variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.

The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).

The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.

The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).

The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.


Notes


The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.

The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the in observability of the true market portfolio, the CAPM might not be empirically testable.

The CML is given by the equation.

r r (r – r ) *p m m pf f

Where pr = return on portfolio

fr = risk less return or risk free return

mr = market risk

m = Standard deviation of risky asset.

p = Standard deviation of portfolio.

Example 4:

If the risk free rate is 10% expected return on NSE Index is 18% and standard deviation of market is 5%, find out the portfolio risk.

r r (r – r ) *p m m pf f

16 10 (18 – 10)/5 * p

3.75p

The security market line (SML) relates the expected return and risk of individual securities.

SML is represented symbolically by an equation as:

i f i m fR R B (R – R )

Where iR = Return on the security i.

fR = Risk free return

mR = Market return

iB = Beta of Scrip i

Example 5:

Tisco Company has a Beta equal to 1.5 and the risk free rate is 6%. The required rate of return on the market is 15%. Find the return on TISCO stock

iR = f i m fR B (R – R )

= 6 + 1.5 (15-6)

= 19.5%

Capital Budgeting

Notes


Arbitrage Pricing Theory (APT) The arbitrage pricing theory advocates that two identical securities will have the same risk return pattern. Given the similar risk pattern of securities, the returns ought to be similar; otherwise there will be an arbitrage opportunity in the market. The arbitrage opportunity will increase the demand for the security with a risk X that is giving higher returns on the one hand, and on the other hand it increase the supply of the security with a risk x that is giving lesser returns. The higher demand without matching supply will automatically reduce the return from the security and the large supply not matched by the demand will automatically increase the return for the other security. This arbitrage will ensure that all securities having similar risk will provide similar returns.

The assumptions of the APT model are:

1. Investors prefer more returns to fewer returns.

2. Investors are risk averse.

3. Investors have homogenous risk expectations.

4. Capital markets do not have any transaction costs and there are no taxes. The arbitrage pricing for a single factor model is given by the following:

i i i iR E b S

Where iR = expected return for a asset i

iE = is the return for a zero beta portfolio

ib = is the factors risk premium

iS = the sensitivity of the security to the specific risk factor.

Example 6:

Determine the equilibrium arbitrage pricing line using the APT from the following two portfolios.

Portfolio P1 P2

Return 10% 15%

Risk (beta) 0.8 1.6

Solution:

The APT equation is derived as follows:

10% = i iE + b x 0.8 ⁄.. 1

15% = i iE + b x 1.6 ⁄.. 2

Equation (2) – Equation (1) gives

5% = ib x 0.8

Therefore ib = 6.25

Substituting ib = 6.25 in equation (1), we get iE = 5%

The equilibrium APT line is iR = 5% + iS x 6.25

Comparison between CAPM and APT 1. Risk is equal to zero in the APT equation; the return must equal the risk less

rate of return of return for an asset with zero sensitivity to all the risk factors.


Notes


Unlike the CAPM, the derivation of the APT does not depend on the existence of a risk less asset.

2. The CAPM is equivalent to the one-factor APT model, because both contain only one factor. The mathematical equivalence of the APT one-factor model and the CAPM shows that the two models do not conflict. Infact, they complement each other – they use different economic logic to arrive at similar asset pricing implications.

3. APT employs fewer assumptions. All economic theories are based on one or more simplifying assumptions. Economic theories that are based on fewer and more realistic assumptions are easier to appreciate than more highly contrived theories because they are easier to learn, apply and explain. APT and capital market theory both employ simplifying assumption. One of the arguments favoring APT over the CAPM is that the APTÊs greater generality is accomplished in spite of the fact that APT is based on fewer simplifying assumptions.

4. Like the capital market theory, APT assumes that investors prefer more wealth over less wealth. Both theories also assume that investors dislike risk. Stated in terms of utility theory, both theories assume that all investors have positive but diminishing marginal utility and make investment decisions that will maximize their expected utility. These are realistic assumptions.

5. Other CAPM simplifying assumptions that are shared by the APT and CAPM are (1) Capital markets are perfect and (2) investors have homogenous expectation. Perfect market is an assumptions widely used by economists. By assuming that capital markets are perfect, economists exclude the possibility that prices are manipulated or distorted away from their equilibrium values.

6. Homogenous expectations imply that all investors share the same risk and return perceptions for any given asset. Both the CAPM and APT theories allow divergent statistical assessments for different assets. Assuming homogenous expectations for any individual asset, however simplifies the economic model by obviating the need for the model to explain the differences of opinion between investors assessments of any one particular investment opportunity.

7. The CAPM is based on four assumptions:

(1) Rates of return conform to a normal probability distribution.

(2) Investors utility of wealth functions exhibit positive but diminishing marginal utility.

(3) A uniquely desirable investment called the market portfolio exists and,

(4) Risk less borrowing and lending is possible. Some supporters of the APT borrowing and lending is possible. Some supporters of the APT argue that it is superior to the CAPM because only the second assumption is needed to generate the APT.

Capital Budgeting

Notes


Student Activity A firm has an investment proposal, requiring an outlay of Rs. 80000. The investment proposal is expected to have two year economic life with no salvage value. In year 1 there is a 0.4 probability that cash inflow after tax will be Rs. 50000 and 0.6 probability that cash inflow after tax will be Rs. 60000. The probability assigned to Cash Inflow after tax for the year 2 is as follows:

The Cash Inflow Year 1 Rs. 50000 Rs. 60000

The Cash Inflow Year 2

Cash inflows Probability Cash inflows Probability Rs. 24000 0.2 Rs. 40000 0.4

Rs. 32000 0.3 Rs. 50000 0.5

Rs. 44000 0.5 Rs. 60000 0.1

The firm uses 10% discount rate:

Required:

1. Construct a decision tree for the proposed investment project and calculate the expected NPV.

2. What net present value will be project yield, if worst outcome is realized? What is the probability of occurrences of this NPV?

3. What will be the best outcome and the probability of that occurrence?

4. Will the project be accepted?

Summary Simulation is a statistical technique to deal with uncertainty and is based on the concept of probabilities. Sensitivity analysis provides information about cash flows under three assumptions, they are pessimistic, most likely and optimistic. Decision tree analysis is another technique which is helpful in tackling risky capital investment proposals. It is a graphic display of relationship between a present decision and possible future events, future decisions and their consequences. CAPM asserts that the selection of a portfolio will depend upon the risk free rate and market return. APT advocates that two identical securities will have the same risk return pattern.

Keywords Simulation: It refers to representation of a system which reacts to a change in any of input variable in a similar way as to that variable which is being simulated.

Sensitivity Analysis: It is an analysis where it explains how sensitive the cash flows are under different situations i.e. Pessimistic, most likely and optimistic.

Decision Tree: It is a graphic display of relationship between a present decision and possible future events, future decisions and their consequences.

Capital Market Line: It relates expected return and risk for a portfolio of securities.

Security Market Line: It relates the expected return and risk of individual securities.


Notes


Review Questions 1. What do you mean by simulations?

2. What is the sensitivity analysis in capital budgeting?

3. What is decision tree analysis? Explain with the help of an example.

4. What are the major difference between APT and CAPM?

5. What are the basic assumptions underlying the CAPM?

6. Explain about Arbitrage Pricing Theory.

Further Readings Khan and Jain, Financial Management-Text, Problems and Cases

I. M. Pandey, Financial Management

S. N. Maheswari, Financial Management-Principles and Practice

Leasing

Notes


Unit 6 Leasing Unit Structure • Introduction • Leasing • Leveraged Lease • Alternative Investment Measures • Project Abandonment Analysis • Multiple Project Capital Budgeting • Summary • Keywords • Review Questions • Further Readings

Learning Objectives At the conclusion of this unit you should be able to: • Know the concept of leasing • Study the process of leasing • Know about the leveraged leases • Understand the multiple project capital budgeting

Introduction The traditional financing is related to the liability side of the balance sheet. The firm issues long-term debt or equity to meet its financing needs, and in the process, expands its capitalization. The dangers of traditional financing are that equity becomes an expensive method of financing because of decreasing corporate earnings and low price-earning ratios. The high rate of inflation causes long-term debt to be an expensive source of financing as interest rates rise. The corporate finance managers therefore are developing financing alternatives related to the asset side of the balance sheet. These alternatives may lower the cost and redistribute the risk. Asset-based financing methods are lease, hire purchase and project financing.

Leasing A lease is a legal document, but can be a verbal arrangement, which confers a right on one person (called a tenant or lessee) to possess property belonging to another person (called a landlord or less or of the owner landlord. The relationship between the tenant and the landlord is called a tenancy, and can be for a fixed or an indefinite period of time (called the term of the lease). The consideration for the lease is called rent.

Under normal circumstances, an owner of property is at liberty to do what they want with their property, including destroy it or hand over possession of the property to a tenant. However, if the owner has surrendered possession to another (i.e. the tenant) then any interference with the quiet enjoyment of the property by the tenant in lawful possession is unlawful.

Similar principles apply to real property as well as to personal property, though the terminology would be different. Similar principles apply to sub-leasing, that is the

Capital Budgeting

Notes


leasing by a tenant in possession to a sub-tenant. The right to sub-lease can be expressly prohibited by the main lease.

Formality of a Lease The formal requirements for a lease are determined by the law and custom of the jurisdiction in which real property is located. In the case of personal property, it is determined by the law and custom of the jurisdiction in which the rental agreement is made.

A tenancy for years greater than 1 year must be in writing in order to satisfy the Statute of Frauds.

Term of a Lease The term of the lease may be fixed, periodic or of indefinite duration.

If it is for a specified period of time, the term ends automatically when the period expires, and no notice needs to be given, in the absence of legal requirements.

The term's duration may be conditional, in which case it last until some specified event occurs, such as the death of a specified individual.

A periodic tenancy is one which is renewed automatically, usually on a monthly or weekly basis.

A tenancy at will last only as long as the parties wish it to, and be terminated without penalty by either party.

It is common for a lease to be extended on a "holding over" basis, which normally converts the tenancy to a periodic tenancy on a month by month basis.

Rent Rent is a requirement of leases in common law jurisdiction, but not in civil law jurisdiction. There is no requirement for the rent to be a commercial amount. "Pepper corn" rent or rent of some nominal amount is adequate for this requirement.

Leasing of Real Property There are different types of ownership for land but, in common law states, the most common form is the fee simple absolute, where the legal term fee has the old meaning of real property, i.e. real estate. An owner of the fee simple holds all the rights and privileges to that property and, subject to the laws, codes, rules and regulations of the local law, can sell or by contract or grant, permit another to have possession and control of the property through a lease or tenancy agreement. For this purpose, the owner is called the lessor or landlord, and the other person is called the lessee or tenant, and the rights to possess and control the land are exchanged for some payment (called consideration in legal English), usually a monthly rent The acceptance of rent by the landowner from a tenant creates (or extends) most of the rights of tenancy even without a written lease (or beyond the time limit of an expiring lease). Although leases can be oral agreements that are periodic, i.e. extended indefinitely and automatically, written leases should always define the period of time covered by the lease. In the 1930s, the British government introduced infinite leases, only to remove the power to create these in the early 1990s. A lease may be:

A fixed-term agreement, in other words one of these two:

for a specified period of time (the "term"), and end when the term expires;

Leasing

Notes


conditional, i.e. last until some specified event occurs, such as the death of a specified individual; or

A periodic agreement, in other words renewed automatically

usually on a monthly or weekly basis

at will, i.e. last only as long as the parties wish it to, and be terminated without penalty by either party.

Because ownership is retained by the lessor, he or she always has the better right to enforce all the contractual terms and conditions affecting the use of the land. Normally, the contract will be express (i.e. set out in full and, hopefully, plain language), but where a contract is silent or ambiguous, terms can be implied by a court where this would make commercial sense of the transaction between the parties. One important right that may or may not be allowed the lessee, is the ability to create a sublease or to assign the lease, i.e. to transfer control to a third party. Hence, the builder of an office block may create a lease of the whole in favour of a management company that then finds tenants for the individual units and gives them control.

Under common law, a lease should have three essential characteristics:

1. A definite term (whether fixed or periodic)

2. At a rent

3. Confer exclusive possession

Leasing of Tangible Personal Property An owner can allow another the use of a vehicle (such as vehicle leasing of a car, a truck or an airliner) or a computer either for a fixed period of time or at will. This can be a simple leasing transaction, or it can be a transaction intended to allow the user the right to buy the item at some future time.

In a simple lease (rental) of a car, P pays O a rental for the use of the car during the agreed period which may be a few days (e.g. for a holiday trip) or longer where it is more economic to pay for use rather than pay for the ownership of an asset of depreciating value. Normally, only P will be allowed to use the vehicle and, in such a case, P has possession and control. But, P could be an employer who allows C the use of the car to visit clients, and thereby gives C control.

In a lease with the possibility of purchase, O could allow P to lease the car for a specified period of time. If all the rental payments are made in full, P will then be allowed to buy the car at the contractual purchase option price. In a consumer lease subject to the federal Consumer Leasing Act and the Truth in Lending Act, the purchase option price can not be a "bargain" purchase, that is, it cannot be less than the originally estimated fair market value. A "bargain" purchase creates an installment sale, to which the Truth in Lending Act (TILA) applies including the standardized disclosures, most importantly the Annual Percentage Rate (APR). Typically, the vehicle dealer or other personal property seller offers the leasing terms and contract of a third party finance company. Hence, O leases the vehicle to P, and upon execution of the contract simultaneously sells ownership of the car to F and assigns the lease contract to F. It is standard for the contractual terms to prohibit P from parting with possession or control of the car to another (if P does part with possession, this can be a theft of the car from F).

There are two principal types of leasing, depending upon the party taking the risk of the value of the vehicle (or other leased property) at lease end. In the U.S. this is called Closed-end leasing. In other jurisdictions, it is called hire purchase, lease purchase or

Capital Budgeting

Notes


finance leasing. These transactions are complicated. The most common problem arises when O makes specific representations as to the quality and reliability of the car to P during the initial negotiations. If what is said induces P to buy the car from O, those representations would usually be enforceable against O. But, in this transaction, O first sells the car to F who makes no representations to P. The laws vary from state to state on the extent to which P might be allowed a remedy if the car proves to be of poor quality.

To clarify the concept, the owner of tangible movables has the power to keep possession and only to transfer control. This may be for:

Short or long-term storage (e.g. leaving a passport with hotel staff or depositing valuable property in a bank vault · a hotel or bank holding property is a bailee); or

For delivery purposes (e.g. using a carrier to transport goods to a specific destination); or

It may be a form of mortgage · a pawnshop holds a pledge over the goods deposited until the money lent is repaid.

Leasing is a common method by which airlines acquire their aircraft, usually from companies specialised in the field of Commercial Aircraft Sales and Leasing. Aircraft leasing transactions are typically divided into finance leasing and operating leasing.

Businesses often choose to lease rather than buy office equipment, including computers. Since office equipment depreciates rapidly, leasing can be more cost-efficient than ownership.

In addition, more and more unconventional items are becoming available for lease, such as handbags and luxury watches.

Real Leases Whether it is better to lease or buy land will be determined by each state's legal and economic systems. In those countries where acquiring title is complicated, the state imposes high taxes on owners, transaction costs are high, and finance is difficult to obtain, leasing will be the norm. But, freely available credit at low interest rates with minimal tax disadvantages and low transaction costs will encourage land ownership. Whatever the system, most adult consumers have, at some point in their lives, been party to a real estate lease which can be as short as a week, as long as 999 years, or perpetual (only a few states permit ownership to be alienated indefinitely). For commercial property, whether there is a depreciation allowance depends on the local state taxation system. If a lease is created for a term of, say, ten years, the monthly or quarterly rent is a fixed cost during the term. The term of years may have an asset value for balance sheet purposes and, as the term expires, that value depreciates. However, the apportionment of relief as between business expense and depreciating asset is for each state to make (all that is certain is that the lessee cannot have a double allowance).

Private Property Rental Rental, tenancy, and lease agreements are formal and informal contracts between an identified landlord and tenant giving rights to both parties, e.g. the tenant's right to occupy the accommodation for an agreed term and the landlordÊs right to receive an agreed rent. If one of these elements is missing, only a tenancy at will or bare licence comes into being. In some legal systems, this has unfortunate consequences. When a formal tenancy is created, the law usually implies obligations for the lessor, e.g. that the property meets certain minimum standards of habitability. With a bare licence, some states do not imply any significant lessee protections.

Leasing

Notes


A tenancy agreement can be made up of:

Express Terms: These include what is in the written agreement (if there is one), in the rent book, and/or what was agreed orally (if there is clear evidence of what was said).

Implied Terms: These are the standard terms established by custom and practice or the minimum rights and duties formally implied by law.

Commercial Leasehold

Advantages of Commercial Leasing For businesses, leasing property may have significant financial benefits:

Leasing is less capital-intensive than purchasing, so if a business has constraints on its capital, it can grow more rapidly by leasing property than it could by purchasing the property outright.

Capital assets may fluctuate in value. Leasing shifts risks to the lessor, but if the property market has shown steady growth over time, a business that depends on leased property is sacrificing capital gains.

Because of investments which are done with leasing, new businesses are formed. Furthermore, unemployment in that country is decreased.

Leasing may provide more flexibility to a business which expects to grow or move in the relatively short term, because a lessee is not usually obliged to renew a lease at the end of its term.

In some cases a lease may be the only practical option; such as for a small business that wishes to locate in a large office building within tight locational parameters.

Depreciation of capital assets has different tax and financial reporting treatment from ordinary business expenses. Lease payments are considered expenses, which can be set off against revenue when calculating taxable profit at the end of the relevant tax accounting period.

Disadvantages of Commercial Leasing For businesses, leasing property may have significant drawbacks:

A net lease may shift some or all of the maintenance costs onto the tenant.

If circumstances dictate that a business must change its operations significantly, it may be expensive or otherwise difficult to terminate a lease before the end of the term. In some cases, a business may be able to sublet property no longer required, but this may not recoup the costs of the original lease, and, in any event, usually requires the consent of the original lessor. Tactical legal considerations usually make it expedient for lessees to default on their leases. The loss of book value is small and any litigation can usually be settled on advantageous terms. This is an improvement on the position for those companies owning their own property. Although it can be easier for a business to sell property if it has the time, forced sales frequently realise lower prices and can seriously affect book value.

If the business is successful, lessors may demand higher rental payments when leases come up for renewal. If the value of the business is tied to the use of that particular property, the lessor has a significant advantage over the lessee in negotiations.

Capital Budgeting

Notes


Lease is a contract between a lessor, the owner of the asset and a lessee, the user of the asset. Under the contract, the owner gives the right to use the asset to the user over an agreed period of time for a consideration called the lease rental. The lessee pays the rental to the lessor as regular fixed payments over a period of time at the beginning or at the end of a month, quarter, half-year or year. Although generally fixed, the amount and timing of payment of lease profit or cash flows. In up-fronted leases, more rentals are charged in the initial years and less in the later years of the contract. The opposite happens in back-ended leases. At the end of the lease contract, the asset reverts to the lessor, who is the legal owner of the asset. As the legal, it is the lessor not lessee, who is entitled to claim depreciation on the leased asset. Although the lessor is the legal owner of a leases asset, the lessee bears the risk and enjoys the returns. The lessee benefits if the leased assets operates profitably and suffers if the asset fails to perform.

Lease may be classified as a financial lease and operating lease. There are different types of finance lease like Direct Lease, Leveraged Lease, Sales and Lease Back lease.

Leveraged Lease Under a leveraged lease, four parties are involved : the manufacturer of the asset, the lessor, the lender from whom the lessor borrows a substantial portion of the assetÊs purchase price and the lessee. In a direct lease, the lesser buys the asset and becomes the owner by making the full payment of the asset. In a leveraged lease, the lessor makes substantial borrowing, even up to 80% of the assetÊs purchase price. He provides the remaining amount up to 20% or so as equity to become the owner. The lessor claims all tax benefits related to the ownership of the asset. Lenders, generally the large financial institutions, provide loans on a non-recourse basis to the lessor. Their debt is serviced exclusively out of the lease proceeds. To secure the loan provided by lenders, the lessor also agrees to give them a mortgage on the asset. Thus, lenders have the first claim on the lease payments together with the collateral on the asset. Lenders will take charge of the asset if the lessee is unable to make lease payments.

Leveraged lease are called so because the high non-recourse debt creates a high degree of leverage. The effect is to amplify the return of the equity-holder (that is, the lessor). But the risk is also quite high if the lease payments are not received. Leveraged lease is quite useful for large capital equipment with long economic life say 20years or more. It is one of the popular means of financing large infrastructure projects.

Alternative Investment Measures Leasing is a source of financing provided by the lessor to the lessee. The lessee receives the services of the asset for a specific period to time in exchange for the payment of fixed lease rental. The only other way, the lessee could obtain the services of the given asset would be to purchase it outright, and the outright purchase of the asset would require sufficient founds. The lessee might have these sufficient founds to purchase the assets outright without borrowing, but the founds would not be free as there is always an opportunity cost of the founds. Every time, therefore, a firm has to acquire an asset, it may have to decide between two mutually exclusive situations. First, should the assets be purchased and become the owner of the asset and second, should the asset be acquired on a lease basis.

Example 1:

A firm can purchase for Rs. 2,500 an asset having life of 5 years after which it salvage value is Rs 500. The firm provides depreciation on straight line method. Purchasing and using the asset will increase the firmÊs expected revenues by Rs. 1,500 per year

Leasing

Notes


and will raise its expected operating expenses (not including depreciation) and interest by Rs 700 per year. The corporate tax is 50% and the cost of capital of the firm is 10%.

The firm can also lease the asset for a yearly rental of Rs 650. The incremental revenue will be the same at Rs 1500 per year and the increase in the firmÊs expected non-depreciated expense is Rs 600 per year only. Evaluate the proposals.

Solution:

In this case, the firm has two options as follows:

i) To lease

ii) To buy the asset. The incremental revenue are same at Rs. 1500 per year in both the options. However, in case of lease option, a lease rent of Rs. 650 and expense of Rs. 600 is payable per year and both are tax deductible. In case of buying option, the operating expense are Rs. 700 per year and the depreciation will be Rs. 400 per year i.e. (Rs. 2500-500)/5.

The depreciation is tax deductible. The two proposals can be evaluated as follows:

Computation of Net Present Value of “Buying” option

Year Profit (Rs.)

Expenses Depreciation PAT Cash flows

PVF (10%)

PV

1 1500 700 400 200 600 0.909 545

2 1500 700 400 200 600 0.826 496

3 1500 700 400 200 600 0.751 451

4 1500 700 400 200 600 0.683 410

5 1500 700 400 200 600 0.621 373

(Scrap) 500 0.621 310

PV of cash inflows 2585

Less: cost of asset 2500

Net present value 85

Computation of Net Present Value of “Leasing” Option

Year Project (Rs.)

Expenses (Rs.)

Rental (Rs.)

PAT or Cash Flows (Rs.)

PVF (10%)

PV

1 1500 600 650 125 0.909 114

2 1500 600 650 125 0.826 103

3 1500 600 650 125 0.751 94

4 1500 600 650 125 0.683 85

5 1500 600 650 125 0.621 77

Net present Value 473

As NPV of leasing option is higher at Rs. 473 than the NPV of the buying option, the firm should lease the asset.

Project Abandonment Analysis It is quite possible in practice that though a proposal has been evaluated and implemented offer a careful analysis of all types of risks associated with it, yet at a later stage, it may be found that the project is no longer economically viable even if its

Capital Budgeting

Notes


economic life is not yet over. The firm may be faced with a situation when it is to take a decision whether to abandon project which has failed before the end of its estimated economic life.

Once the project having positive NPV, has been implemented, there is always available an option to the firm that it can be terminated or abandoned or scraped away. Obviously, at the end of each of the subsequent years after implementation, each project will have (i) a scrap value at that stage and (ii) the NPV of a project for remaining yearÊs o the life of the project. The firm can compare these two values at the end of each of subsequent years and in case the scrap value is found to be higher, the project may be abandoned, otherwise the firm may continue with the proposal.

Example 2:

The projectÊs cost is Rs. 20,000 and economic life of 5 years is being evaluated on the basis of the following information.

Year Inflows (Rs) Scrap value (Rs)

1 10,000 14,000

2 8,000 10,000

3 6000 6000

4 4,000 2000

5 2000 –

Solution:

Calculation of NPV

Year Inflows (Rs) PVF (10%, n) PV

1 10,000 0.909 9090

2 8,000 0.826 6608

3 6,000 0.751 4506

4 4,000 0.683 2732

5 2,000 0.621 1242

Total 24,178

NPV of the project is Rs. 24,178 – 20,000 = Rs. 4, 178

As the project is having a positive NPV it may be accepted, however it may be reviewed at the end of different years as follows:

At the end of year I, the firm will have an option either to scrap away the project for Rs. 14,000 or to get cash inflows of Rs. 8000, Rs. 6000, Rs. 4000 and Rs. 2000 at the end of next 4 years respectively. Therefore, the scrap value of Rs. 14,000 may be taken as the cash outflow to earn the cash inflows over next 4 years and therefore, the NPV at the end of year 1 may be ascertained as follows:

NPV = -14,000 + 8000 (0.909) + 6000 (0.826) + 4000 (0.751) + 2000 (0.683)

= Rs 2,598.

On the same lines, the NPV at the end of year 2 (scrap value Rs. 10,000) at the end of year 3 (scrap value Rs. 6000) and at the end of year 4 (scrap value Rs. 2,000) can also be ascertained.

NPV (year 2) = -10,000 + 6000 (0.909) + 4000 (0.826) + 2000 (0.751)

= Rs. 260

NPV (year 3) = -6,000 + 4000 (0.909) + 2000 (0.826)

= Rs. - 712

Leasing

Notes


NPV (year 4) = -2000 + 2000 (0.909)

= Rs. – 182

At the end of year 3, the NPV of the project is less than 0 and the firm should abandon the project and realize than the present values of the remaining cash inflows. Obviously, a firm should consider abandoning a project it at any stage the scrap value is more than the then present value of remaining cash flows. This type of reviewing exercise by the firm makes it possible to weed out those projects which have failed to perform as expected or whose subsequent cash flows expectations have reduced. This type of analysis can stop a firm from continuing with a losing project for unnecessarily extended period of time.

Multiple Project Capital Budgeting In case of capital budgeting, standard deviation measure is used to compare the variability of possible cash flows of different projects from their respective mean or expected values. Standard deviation is a measure of dispersion it may be defined as the square root of squared deviations calculated from the mean.

Example 3:

From the data given below, find out which project is more risky by adopting standard deviation approach.

Possible Event Project X Project Y

Cash inflows Provability Cash inflows Probability

A 4000 0.10 12,000 0.10

B 5000 0.20 10,000 0.15

C 6000 0.40 8,000 0.50

D 7000 0.20 6000 0.15

E 8000 0.10 4000 0.10

Solution:

Project X

Possible Events

Cash Inflows

(CF)

Deviation From Mean

(6000) (D)

Deviations Squared

(D2)

Probability

(P)

PD2

i ii iii iv v vi = iv * v

A 4000 -2000 40,00,000 0.10 400000

B 5000 -1000 10,00,000 0.20 200000

C 6000 0 0 0.40 0

D 7000 1000 10,00,000 0.20 200000

E 8000 2000 40,00,000 0.10 400000

2PD∑ 1200000

2PD

= 12,00,000

= 1095

Capital Budgeting

Notes


Project Y Possible Events

Cash Inflows(CF)

Deviation From Mean (6000) (D)

Deviations Squared

(D2)

Probability (P)

PD2

i ii iii iv v vi=iv*v A 12000 4000 160,00,000 0.10 1600000 B 10000 2000 40,00,000 0.15 600000 C 8000 0 0 0.50 0 D 6000 -2000 40,00,000 0.15 600000 E 4000 -4000 160,00,000 0.10 1600000 2PD∑ 4400000

2PD

= 44, 00, 000

= 2098

The standard deviation for project x is 1095 and for project y is 2098. Thus the variability of cash flow is more in case of Project Y as compared to Project X. Hence, project Y is more risky. However the decision maker will be in a dilemma because project Y has a higher monetary value of expected cash flows as compared to Project X. This problem can be solved by calculating coefficient of variations.

Coefficient of Variations = Standard Deviation

Expected mean Cash Flow

Project X = 1095/6000 = 0.1825 or 18.25%

Project Y = 2098/8000 = 0.2623 or 26.23%

The coefficient of variations of projects Y is more as compared to project x. Hence, project Y is more risky. The choice would depend upon the capacity of the investor to bear the risk. Project Y has a higher expected monetary value as compare to project x. Thus, with higher risk the profitability is also higher. In case the investor is not averse to risk, he may accept project Y. However, if he is averse to risk, he will accept project x.

Student Activity ABC & Co is evaluating a proposal costing Rs. 300000 and an economic life of 2 years over which the expected cash flows together with probabilities have been estimated as follows:

Year 1 (Rs ’000) Year 2 (Rs ‘000) Inflows Probability Inflows Probability

200 0.3 100 0.3 200 0.5 300 0.2

300 0.4 200 0.3 300 0.5 400 0.2

400 0.3 300 0.3 400 0.4 500 0.3

Evaluate the project given that the abandonment value of the proposal at the end of year 1 is Rs. 250000 and the rate of discount is 12%.

Leasing

Notes


Summary Lease is a contract between a lessor, the owner of the asset and a lessee, the user of the asset. The lessee pays the rental to the lessor as regular fixed payments over a period of time at eh beginning or at the end of a month, quarter, half-year or year. In up-fronted leases, more rentals are charged in the initial years and less in the later years of the contract. The different types of finance lease are direct lease, leveraged lease, sales and lease back lease. Under a leveraged lease, four parties are involved: the manufacturer of the asset, the lessor, the lender from whom the lessor borrows a substantial portion of the assetÊs purchase price and the lessee. Every time, when a firm has to acquire an asset, it may have to decide between two mutually exclusive situations. First, should the assets be purchased and become the owner of the asset and second, should the asset be acquired on a lease basis. Though the project having positive NPV is implemented, there is always an option available to the firm that it can be terminated or abandoned or scraped away.

Keywords Lease: It is a contract between a lessor, the owner of the asset and a lessee, the user of the asset.

Lease Rental: Under the contract, the owner gives the right to use the asset to the user over the right to use the asset to the user over an agreed period of time for a consideration called the lease rental.

Leveraged Lease: The lessor makes substantial borrowing even up to 80% of the assets purchase price. He provides the remaining amount up to 20% or so as equity to become the owner.

Standard Deviation: It is a measure of dispersion. It may be defied as the square root of squared deviations calculated from the mean.

Review Questions 1. What do you mean by leasing?

2. What is a leveraged Lease? What are its merits and demerits?

3. Write short notes on Abandonment Evaluation of a Project.

4. Discuss about multiple project capital budgeting.

Further Readings I M Pandey, Financial Management

Dr. S. N. Maheswari , Financial Management (Principles and Practices)

Khan and Jain , Financial Management (Text, Problems and Cases)

PUNJAB TECHNICAL UNIVERSITY LADOWALI ROAD, JALANDHAR

INTERNAL ASSIGNMENT

TOTAL MARKS: 25

NOTE: Attempt any 5 questions All questions carry 5 Marks. Q 1. Define the concept of capital budgeting and explain its objectives. Q 2. Briefly explain the process of capital budgeting. Q 3. What do you mean by NPV? Q 4. What do you mean by discounting of cash flows? Q 5. Bring out the differences between the NPV and IRR method. Q 6. What is the Rate of Return? Q 7. What are the basic assumptions underlying the CAPM? Q 8. What is the sensitivity analysis in capital budgeting? Q 9. Write short note on Abandonment Evaluation of a Project. Q10. Discuss about multiple project capital budgeting.

PUNJAB TECHNICAL UNIVERSITY LADOWALI ROAD, JALANDHAR

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Mba 517

Economy & Finance

Transcript of Mba 517