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:
z Increasing access and reach of higher education;
z Equity and affordability of higher education to weaker and disadvantaged sections of the
society;
z Increased opportunity for upgrading, retraining and personal enrichment of latest
knowledge and know-how;
z 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
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knowledge. However, the publisher and its author shall in no event be liable for any errors,
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Published by Anurag Jain for Excel Books Pvt. Ltd., A-45, Naraina, Phase-I, New Delhi-110 028
Tel: 25795793, 25795794 email: eb@excelbooks.com

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 3: Methods of
Capital Budgeting
(Page 25-57)
Unit 4: Risk Analysis
(Page 59-79)
Unit 5: A Project is Not
a Black Box
(Page 83-99)
Unit 6: Leasing
(Page 101-111)

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

SECTION-I
Unit 1
Capital Budgeting
Unit 2
Cost of Capital

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:
z Payback (PB)
z Accounting rate of return (ARR)
z Net present value (NPV)
z Internal rate of return (IRR)
z 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:
z What must the payback be?
z What rate of ARR is acceptable?
z What is the NPV cut off?
z What IRR is the least that we can accept?
z 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
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:
z New issuance of shares.
z 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.
z 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.
z 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:
z In projects of a standard level of business risk, and
z 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
Student Activity
Fill up the blanks:
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)

SECTION-II
Unit 3
Methods of Capital Budgeting
Unit 4
Risk Analysis

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
Learning Objectives
• 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:
Capital Budgeting Techniques
Traditional (or)
Non-discounting Methods
Time adjusted (or) Discounted
cash flow method
Payback period Accounting rate of return
Net present value Internal rate of returns Profitability Index
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.

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 =
Io
Ct
=
$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
Total Investment + Scrap Value
2
3. If there is additional working capital, then average investment is calculated as
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
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 =
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:
$250,000 $100,000
The RR on total investment =
1, 000,000
= 15%
ARR on Total Investment =
Net Annual Profit
Investment Outlay/2
or a
C–D
o
R
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 C PV – PV
Where CFAT PV refers to the present value of future cash inflows after taxes.
C PV 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:
R R R R
(1 K) (1 K) (1 K) (1 K)
NPV = 1 2 3 n
1 2 3 n
– 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:
R R R R
(1 K) (1 K) (1 K) (1 K)
NPV = 1 2 3 n
1 2 3 n
–
I I I I
1 2 3 n
o 1 2 3 n
I
(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 C PV – 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 C PV – 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, 000
1 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 Æ Rs 5,000
Cash flow of 2nd year Æ Rs 10,000
Cash flow 3rd year Æ Rs 15,000
Cash flow 4th year Æ Rs 25,000
Cash flow 5th year Æ 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:
PV – PV
IRR = CFAT C
r r
1
PV
C
Where r1= lower discount rate 15%
CFAT PV = Present value of earnings at lower rate Rs 50,990
C PV = 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)
PV – PV
IRR = CFAT C
r r
1
PV
C
=
50, 990 – 50,000
15 5
50, 990 – 43, 990

Notes
=
990
15 5
7090
= 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:
PV – PV
IRR = CFAT C
r r
1
PV
C
r1 = 12%
CFAT PV = 72,888
C PV = 70,000
PV = 72,888 – 69,936 = 2952
r = 14 – 12 = 2%
PV – PV
IRR = CFAT C
r r
1
PV
C
=
72,888 – 70, 000
12 2
72, 888 – 69, 936
=
2, 888
12 2
2, 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
0 1 2 3
-100.00 10 60 80.00
PV Costs =
TV
n
1+MIRR
66.00
12.10
$158.10 = TV of
MIRR is better than IRR because
1. MIRR correctly assumes reinvestment at projectÊs cost of capital.
2. MIRR avoids the problem of multiple IRRs.
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
10%
-100.00 10 60 80
PV1 9.09
PV2 49.59
PV3 60.11
118.79
PI =
0 1 2 3
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.

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
=
55,639
50,000
= 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.
z Exists whenever enterprises cannot, or choose not to, accept all value-creating
investment projects. Possible causes:
™ Banks and investors say „NO‰
™ Managerial conservatism
z 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.
z 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
z 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
C C
t t
– I > 0 or – I > I
t o t o o
(I+k) (I+k)
t–1 t–1
Similarly for the same project to be acceptable:
n
t
t o
t–1
C
= I
(I+R)
where R is the IRR.
Since the numerators t C are identical and positive in both instances:
z Implicitly/intuitively R must be greater than k (R > k);
z If NPV = 0 then R = k: the company is indifferent to such a project;
z 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, 500
NPV – $9, 500
1.1
= $954.55
B
$18, 000
NPV – $15,000
1.1
= $1,363.64
Both projects are of one-year duration:
IRRA:
$11,500
A
$9, 500
1+R
$11,500 = $9,500 (1 +RA)
$11,500
= 1+ RA
$9,500
RA=
$11,500
$9,500
– 1
= 1.21 – 1
therefore IRRA = 21%
IRRB:
$18,000
B
$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
I
C
=
$2,500
$1,500
= 1.67.

Notes
Therefore IRRA = 36% (from the tables)
IRRB = o
t
I
C
=
$14,000
$7,000
= 2.0
Therefore IRRB = 21%
Decision:
Conflicting, as:
z NPV prefers B to A
z 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 0 I 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.
PV
o
PI
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 0 I we get:
P
I
V
o
> 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)
1,300
(1+r)
– 2
Taking (1 + r) = x and dividing both sides of the above equation by 100
8 =
21
x
13
x
– 2
8x2 =21x – 13
0 = 8x2 – 21x + 13
The value of x in the quadratic equation can be calculated as
X =
-b b2 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 ($)
0 (100,000) (100,000)
1 90,000 1
90,000×(1.30)1
= 69,231
2 80,000 1
80,000× 2 (1.30)
= 47,337
3 70,000 1
70,000× 3 (1.30)
= 31,862
The cash flows expressed in terms of the value of the dollar at time 0 can now be
discounted using the real value of 7.69%.
Time Cash Flow ($) Discount Factor (7.69%) Pv ($)
0 (100,000) 1.000 (100,000)
1 69,231 1
(1.0769)1
64,246
2 47,337 1
(1.0769)2
40,804
3 31,862 1
(1.0769)3
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
Learning Objectives
• 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.
Student Activity
Fill up the blanks:
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)

SECTION-III
Unit 5
A Project is Not a Black Box
Unit 6
Leasing

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
Learning Objectives
• 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:
z To identify critical assumptions or compare alternative model structures
z Guide future data collections
z Detect important criteria
z Optimize the tolerance of manufactured parts in terms of the uncertainty in
the parameters
z Optimize resources allocation
z Model simplification or model lumping, etc.
However there are also some problems associated with sensitivity analysis in the
business context:
z 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.
z Often the assumptions upon which the analysis is based are made by using
past experience/data which may not hold in the future.
z 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
Alternatives Cash flow Present value at 10% NPV
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:
z is the expected return on the capital asset,
z is the risk-free rate of interest,
z (the beta co-efficient) is the sensitivity of the asset returns to market returns,
or also,
z is the expected return of the market,
z 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. SP
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
Expected Return

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
z 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.
z 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.
z 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).
z 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.
z 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).
z 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
z 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.
z 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.
rp rf (rm – rf ) m * p
Where p r = return on portfolio
f r = risk less return or risk free return
m r = 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.
rp rf (rm – rf ) m * p
16 10 (18 – 10)/5 * p
p 3.75
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 f R R B(R –R)
Where i R = Return on the security i.
f R = Risk free return
m R = Market return
i B = 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
i R = f i m f R 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 i R E bS
Where i R = expected return for a asset i
i E = is the return for a zero beta portfolio
i b = is the factors risk premium
i S = 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 i E + b x 0.8 ⁄.. 1
15% = i i E + b x 1.6 ⁄.. 2
Equation (2) – Equation (1) gives
5% = i b x 0.8
Therefore i b = 6.25
Substituting i b = 6.25 in equation (1), we get i E = 5%
The equilibrium APT line is i R = 5% + i S 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
Learning Objectives
• 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:
z 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
z 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.
z 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.
z 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:
z 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
z For delivery purposes (e.g. using a carrier to transport goods to a specific
destination); or
z 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:
z 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).
z 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:
z 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.
z 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.
z Because of investments which are done with leasing, new businesses are
formed. Furthermore, unemployment in that country is decreased.
z 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.
z 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.
z 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:
z A net lease may shift some or all of the maintenance costs onto the tenant.
z 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.
z 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
ΣPD2 1200000
PD2
= 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
ΣPD2 4400000
PD2
= 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
ASSIGNMENT SHEET
(To be attached with each Assignment)
________________________________________________________________________
Full Name of Student:_____________________________________________________________
(First Name) (Last Name)
Registration Number:
Course:__________ Sem.:________ Subject of Assignment:________________________________
Date of Submission of Assignment:
(Question Response Record-To be completed by student)
On Page Number of
Assignment
Total Marks:_____________/25
S.No. Question Number
Responded
Remarks by Evaluator:__________________________________________________________________
__________________________________________________________________________________
Note: Please ensure that your Correct Registration Number is mentioned on the Assignment Sheet.
Signature of the Evaluator
Signature of the student Name of the Evaluator
Date:_______________ Date:_______________
Marks
1
2
3
4
5
6
7
8
9
10

Mba 517

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