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
At the conclusion of this unit you should be able to:
• Know the various tools of capital budgeting
• Understand the methods under the capital budgeting
• Study the advantages and disadvantages of various methods used in Capital Budgeting
• Review its purpose
Introduction
The attractiveness of any investment proposal depends on the following elements:
1. The amount expended i.e. the net investment
2. The potential benefits i.e. the operating cash Inflows
3. The time period over which these benefits will accrue i.e., economic life of the
project.
A proper investment analysis must relate these three elements to provide an
indication of whether the investment is worthy of being taken up or not. How do
these three basic elements i.e. the net investment, the operating cash flows and the
economic life can be related to determine the proposalÊs worthiness?

Capital Budgeting
Notes
There are different techniques available for evaluation and selection of a proposal.
These techniques can be grouped into two categories as shown below:
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%.
Particulars Project A Project B
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

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