capital budgeting group 6
TRANSCRIPT
- 1 -
UNIVERSITY OF NAIROBI
SCHOOL OF BUSINESS (MBA)
DFI605: FINANCIAL SEMINAR
1.7 GROUP ASSIGNMENT: CAPITAL BUDGETING
COURSE LECTURER: DR. ADUDA/ MR. MIRIE
PRESENTED BY:
OGOLO AKOTH DORINE D61/62963/2011
RAEL JELAGAT ROTICH D61/62980/2011
PETER KAMAU WAGEREKA D61/60380/2010
ANTHONY MAINA MWAI D61/67629/2011
JOSEPH BORO NJOROGE D61/68186/2011
WARUTERE JOSEPHINE NYAKIO D61/63326/2011
September 2012
- 2 -
CHAPTER ONE
1.0 INTRODUCTION
Capital budgeting is obviously a vital activity in any business. Vast sums of money can be easily wasted if
the investment turns out to be wrong or uneconomic. In modern times, the efficient allocation of capital
resources is a most crucial function of financial management. This function involves organization‟s decision
to invest its resources in long term assets like land, buildings, equipment, and vehicles. All these assets are
extremely important to the firm because in general, all the organizational profits are derived from the use of
its capital investment in assets which represent a very large commitment of financial resources, and these
funds usually remain invested over a long period of time.
The future development of a firm hinges on the capital investment projects, the replacement of existing
capital assets, and/or the decision to abandon previously accepted undertakings which turn out to be less
attractive to the organization. The business environment calls for the efficient allocation of resources by the
management of any organization. Lately, a lot of emphasis has been placed on the view that a business firm
facing a complex and changing environment will benefit immensely in terms of improved quality of decision
making if investment decisions are taken in the context of its overall corporate strategy. This approach
provides the decision maker with a central theme or a great picture of investment to keep in mind at all times
as a guideline for effectively allocating corporate resources in any investment opportunities.
1.1 Definition of capital budgeting
Capital budgeting, sometimes referred to as investment appraisal, is a management process which involves
evaluation of the investments of the company to determine whether they are viable or not and thus determine
whether to accept a project or reject it all together. Some of the investment decisions that have to be made by
the companies include replacement decisions for the company's fixed assets such as machinery, introduction
of new products to the already existing products produced by the company, engaging in long term
investments such as purchasing shares of other companies among other investment (Ross, Westerfield&
Bradford, 1998). As such, capital budgeting decisions have a major effect on the value of the firm and its
shareholders wealth.
Investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decision.
It is defined as the firm decision to invest its current funds most efficiently in the long-term assets in
anticipation of an expected flow of benefits over a series of years (the long term assets are those that affects
- 3 -
the firms operations beyond the one-year period) it includes expansion, acquisition, modernization and
replacement of the long-term assets, sale of a division or business(divestment), change in the methods of
sales distribution, an advertisement campaign, research and development programme and employee training,
shares (tangible and intangible assets that create value) (Pandey 2010).
Horne, (2000) define investment decisions as the allocation of capital to investment proposal whose benefits
are to be realized in the future and includes, new product or expansion of existing products, replacement of
equipment or buildings, research and development, exploration and others.
Capital expenditure includes all those expenditures which are expected to produce benefits to the firm for a
period of over one year, and this includes both tangible and intangible assets. Lynch (2001) looked at the
tactics for improving the capital budgeting process to produce results, as a way of maximizing firm‟s
contribution to shareholders‟ value. He argued that shareholders‟ value can be increased by improving the
capital expenditures process for fixed assets with the caveat that an understanding of the process and a
functioning continuous capital budgeting system were prerequisite to improvement activities.
Capital budgeting/investment appraisal is the “process of evaluating and selecting long-term investments
that are consistent with the business‟s goal of maximizing owner‟s wealth” (Gitman, 2002). Financially
successful companies have a continuing need for capital investment. Typically every organization that
embarks on this process must take all necessary steps to ensure that their decision making processes and/or
criteria supports the business‟s strategy and enhances its competitive advantage. However, growth of a
business can be limited by unavailability of capital. When capital is limited, allocating resources
appropriately is a critical skill which involves taking into consideration current and future market conditions,
such as inflation and demand for a certain product.
Essentially it is the requirement of the management to pursue all the investments options that are available to
the company in order to create wealth of the owners of the company or the shareholders but the resources
available to the company are not sufficient and thus the management are required to conduct project
appraisal in order to determine the projects that would bring the maximum return to the investors (Shim &
Siegel, 2008).
According to Pandey, (2010) investment decisions are decisions that influence a firm‟s growth in the long-
term, affect the risk of the firm, involve commitment of large amount of funds, are irreversible or reversible
at substantial loss, and among the most difficult decisions to make.
Investments should be evaluated on the basis of criteria that are compatible with the objectives of the
shareholders wealth maximization. Therefore, all the stakeholders to some extent have an interest in seeing
- 4 -
sensible financial decisions being taken. Many business decisions do not involve a conflict between
objectives of each of the stakeholders. Nevertheless, there are occasions when someone has to decide which
claimants are to have their objectives maximized and which are merely to be satisfied-that is, given just
enough of a return to make their contributions (Arnold 2005).
It is important for organizations to engage in capital budgeting before they invest in a certain projects
because of the enormous resources required to start the project. Incase the project fails there would be huge
losses that would be incurred by the firms. Another reason is that the investments decisions that managers
make are not easily reversible, the projects that the company invest in have a long term implications on the
operations of the organization and lastly due to the fact that the investments involves risks and uncertainty to
the firm and thus the organization evaluate the suitability of the investment to the firm through carrying out
capital budgeting. There are various methods that are used in capital budgeting which are classified into two;
traditional methods and the discounting methods. Traditional methods of capital budgeting include payback
period and the Average rate of return which the discounted methods of capital budgeting include Net Present
Value (NPV) and Internal Rate of Return (IRR). Every method of capital budgeting has its weaknesses and
strengths and thus no method is superior or inferior to the other (Brigham & Houston, 2008).
A good capital budgeting system does more than just make accept-reject decisions on individual projects. It
must tie into the firm‟s long range planning process-the process that decides what lines of business the firm
concentrates in and sets out plans for financing, production and marketing etc. It must also tie into a
procedure for measurement of performance (Brealey& Myers, 2007)
The term 'Capital Budgeting' is used interchangeably with capital expenditure management, capital
expenditure decision, long term investment decision, management of fixed assets, etc. It may be defined as
"planning, evaluation and selection of capital expenditure proposals." Capital budgeting involves a current
outlay or serves as outlays of cash resources in return for an anticipated flow of future benefits.
In other words, the system of capital budgeting is employed to evaluate expenditure decisions which involve
current outlays, but likely to produce benefits over a period of time longer than one year. These benefits may
be either in the form of increased revenue or reduction in costs. Capital expenditure management therefore
includes addition, disposition, modification and replacement of fixed assets.
The basic features of capital budgeting are:
a) Potentially large anticipated benefits;
b) A relatively high degree of risk;
c) A relatively long time period between initial outlay and anticipated returns
- 5 -
1.2 Historical Background of Capital Budgeting
The Period up to 1950
Earlier approaches to capital budgeting models were concerned mostly with theeconomic evaluation of
individual projects. For many years, most firms used Payback period to evaluate investment project. In 1899,
Irving Fisher first articulated the concept of NPV as the market value of securities minus cost of resources.
Fisher (1930) advanced the Theory of Interest in which he suggested that NPV is the key part in theory of
optimal resource allocation. Fisher labeled his theory of interest the “impatience and opportunity” theory. He
put forward that Interest rates, were as a result of the interaction of two
forces:the “time preference” people have for capital now and the investmentopportunityprinciple (that
income invested now will yield greater income in the future). The interest rate, or what is called cost of
Capital, forms the basis of the Internal Rate of Return (IRR) defined as the discount rate that will equate the
present value of future cash flows to the resources employed now. Fisher defined capital as any asset that
produces a flow of income over time. A flow of income is distinct from the stock of capital that generated it,
although the two are linked by the interest rate. Specifically, wrote Fisher, the value of capital is the present
value of the flow of (net) income that the asset generates. In the period between 1930s and 1950s non owner
managed firms put in place capital budgeting control systems that identified planned capital investments
going forward. The size of non financial investments and the number of non owner managed firms increased
during the industrial revolution. These simultaneous changes created fertile ground for use of more
sophisticated evaluation techniques and for the capital budgeting processes in use today (Chapman &
Hopwood, 2007)
1951 to date
During the 1950s, practicing financial controllers began to network with each other, with consultants and
with academicians to develop models for capital budgeting (Chapman &Hopwood, 2007). Dean (1951), in
his book Capital Budgeting, advanced the implementation of Discounted Cash flows (DCF) methodology in
its current form. Managers are required to maximize return on investment at a given level of risk. However
capital budgeting models only consider the return on investment. As a result, managers don‟t usually have
all the information to make the right decisions as far as risk is concerned. To address this law, Hertz (1964)
provided a discussion on how computer simulation can be used to provide managers with of Risk on a
Capital Investment Project. Agency theory that developed in the late 1970s and early 1980s gave rise to
analytical models of capital investment process. These models suggest that current capital
budgeting procedures are a means of reducing agency costs that emanate from the conflict of interest
- 6 -
between owners of firms and management. The internal rate of return (IRR) and the net present value (NPV)
have long been the accepted capital budgeting measures preferred by corporate management and financial
theorists, respectively. While corporate management prefers the relevancy of a yield-based capital budgeting
method, such as the IRR, financial theorists, based on Orthodox economic theory, endorse the NPV method.
The debate between NPV and IRR methods dates from the inception of modern interest theory. The
introduction of the NPV as Amore superior model created the impetus for conflict
between the two methods. However, both methods suffer from inconsistencies when ranking potential
investment projects based on the assumption of wealth maximization. Therefore, a consistent capital
budgeting method must be robust when correctly ranking and selecting superior investments in varying
Investment conflict between the two methods. However, both methods suffer from inconsistencies when
ranking potential investment projects based on the assumption of wealth maximization. Therefore, a
consistent capital budgeting method must be robust when correctly ranking and selecting superior
investments in varying Investment environments, remain theoretically sound by maintaining the assumption
of wealth maximization, and be expressed as a yield based measure as preferred by corporate management
(Chapman & Hopwood, 2007)
1.3 Importance of Capital Budgeting
Capital budgeting is of paramount importance in financial decision making. Special care should be taken in
making these decisions on account of the following reasons (Pandey, 2010):
(a) Growth
The effects of investment decisions extend into the future and have to be endured for a longer period than the
consequences of current operating expenditures. A firm‟s decision to invest in long term assets has a
decisive influence on the rate and direction of its growth. A wrong decision can prove disastrous for the
continued survival of the firm; unwanted or unprofitable expansion of assets will result in heavy operating
costs for the firm. On the other hand, inadequate investment in assets would make it difficult for a firm to
gain competitive advantage over its competitors.
(b) Risk
A long term commitment of funds may also change the risk complexity of the firm. If an investment in
assets makes the earnings of an organization to fluctuate significantly over time, the firm will become more
risky, hence investment decisions shape the basic character of a firm.
- 7 -
(c) Funding
Since investment decisions generally involve an outlay of large amounts of funds, an organization would
need to plan well ahead and very carefully for such investments. It is imperative for the firm to make
advance arrangement for procuring of finances internally or externally.
(d) Irreversibility
Most investment decisions are irreversible because it may be difficult to find market for such capital items
once they have been acquired. The firm will incur heavy losses if such assets are scrapped. The Nation
Media Group has for example invested in a printing press and refurbished it in the recent past. It would be
very difficult for the media house to make an overnight decision to scrap the press since it may not be easy
to find ready market owing to the small number of local media houses that are involved in printing and its
affordability.
(e) Complexity
Investment decisions are among the firm‟s most difficult decisions. They are an assessment of future events
and the future is very difficult to predict. Political, economic, social, technological forces make the business
environment very volatile.
1.4 Objectives
a) To explain the motives for capital expenditures and the steps followed in capital budgeting
b) To describe and compute cash flow components
c) To explain the basic terminologies used to describe projects, funds, availability, decisions approaches
and cash flow patterns therein
d) To determine the payback periods, the net present values, profitability index and the rates of return of
proposed investments
e) Evaluate projects and rank them based on budgeting techniques
f) Determine difficulties and conflicts in using discounted cash flow methods
- 8 -
1.8 1.5 Capital Expenditure Motives
A capital expenditure is an outlay of funds by the firm that is expected to provide benefits over a period of
time greater than one year. The basic motives for capital expenditures are expansion, replacement or renewal
of non-current assets, or to obtain some other less tangible benefits over a long period of time. These key
motives may be outlined as follows;
a) Expansion: The most common motive is to expand the cause of operations through acquisition of
non-current assets. Growing firms therefore need to acquire new assets more rapidly. A company
may add capacity to its existing product lines to expand existing operations. Nation Media Group, for
example, refurbished its printing press in the year 2010 to expand its printing capacity and colour
quality.
b) Replacement and Modernization: As a firm‟s growth slows down and reaches its maturity, most
capital expenditures will be made in replacing obsolete and worn out assets. Outlays of repairing old
machines should be compared with the net benefit of replacement. The main objective of
modernization and replacement is to improve operating efficiency and reduce costs. Most of the
times, modernization reduces costs only but sometimes also increases revenues resulting in increased
profits. Monitor Publications, a subsidiary of Nation Media Group, for example, replaced its printing
press in 2011 and disposed off the old press.
c) Renewal: An alternative to replacement may involve rebuilding, overhauling or refitting an existing
fixed asset an example being addition of air conditioning as a means of renewing a physical facility.
d) Other purposes: Some expenditure may involve long-term commitments of funds in expectations of
future returns such as advertising, Research and Development, management, consulting and
development of view products. Others include installation of pollution control and safety devises
mandated by the government.
1.9 1.6 Classification of Investment Projects and Terminologies
Investment projects may be classified into three categories on the basis on how they influence investment
decision process: independent projects, mutually exclusive projects and contingent projects.
a) Independent Project: Is one the acceptance or rejection of which does not directly eliminate other
projects from consideration or affect the likelihood of their selection. For example, management may
want to introduce a new product line and at the same time may want to replace a machine which
currently producing a different product. The projects will thenbe considered independently of each
other if sufficient resources are available for both considerations, provided they meet the firm‟s
- 9 -
investment criteria. The projects therefore, can be evaluated independently and a decision to accept
or reject be made depending on whether the project (s) add value to the firm.
b) Mutually Exclusive Investments: These are proposals, which compete with each other in a way that
the acceptance of one precludes the acceptance of other or others. For example, if a company is
considering use of ether a more labor intensive, semi-autonomous machine or a highly automated
machine for production, it can only choose either of the two and not both. Choosing the semi-
autonomous machine precludes the acceptance of the highly automated machine (Pandey 2010,
p160).
Mutually exclusive projects can be evaluated separately to select one which yields the highest net
present value of the firm. The earlier identification of mutually exclusive alternatives is crucial for a
logical screening of investments.
c) Contingent Project: Is one acceptance or rejection of which is dependent on the decision to accept
or reject one or more other projects. Contingent projects may be complementary or substitutes. For
example, a decision to construct a pharmacy may be contingent upon a decision to establish a
doctors‟ surgery in an adjacent building. In this case the projects are complementary to each other.
The cash flows of the pharmacy will be enhanced by the existence of a nearby surgery and
conversely, the cash flows of the surgery will be enhanced by the existence of a nearby pharmacy.
d) In contrast, substitute projects are those that the degree of success of one project is increased by the
decision to reject the other project. For example, market research indicates demand sufficiency to
justify two restaurants in a shopping complex and the firm is considering one Chinese and one Thai
restaurant. Customers visiting the shopping complex seem to treat Chinese and Thai food as close
substitutes and have a slight preference for Thai food over Chinese. Consequently, if the firm
establishes both restaurants, the Chinese restaurant‟s cash flows are likely to be adversely affected
which may mean negative net present value for the Chinese restaurant. In this situation, the success
of the Chinese restaurant project will depend on the decision to reject the Thai restaurant proposal.
Since they are close substitutes, the rejection of one project will definitely affect boost the cash flows
of the other. Contingent projects should therefore be analyzed by taking into account all the projects.
- 10 -
1.10 Terminologies
a) Make or Buy decision: Make or buy decision is no longer a short run operating decision and it
becomes a problem of capital expenditure which necessitates consideration of required rate of return. A
company has to take this decision, when it has to face the following choice buy certain part or sub-
assemblies from outside suppliers; or use available capacity to produce the item within the factory. In
this decision, the following are major considerations:
i. Costs that will be incurred under both alternatives are not relevant to the analysis.
ii. Potential uses of available capacity should be considered.
iii. Pertinent quantitative factors must be evaluated in the decision process. These considerations
include price stability from suppliers, reliability of delivery and quality specifications of
materials or components involved.
Example 1 — Make or Buy Decision
You have the option to manufacture your own parts or purchase them from outside suppliers. If we purchase
the parts, it will cost Kshs 50.00 per part. Our factory is operating at 70% of capacity and our total cost to
manufacture parts is:
Direct Materials Kshs 15.00 / part
Direct Labor Kshs 19.00 / part
Overhead - Variable Kshs 14.00 / part
Overhead - Fixed Kshs 12.00 / part
Total Costs Kshs 60.00 / part
Since we are operating at 70% capacity, we do not expect an increase in fixed overhead; this is a sunk cost.
We would manufacture the parts since it is Kshs 2.00 / part cheaper: Purchase Kshs 50.00 vs. Manufacture
Kshs 48.00 (Kshs 15.00 + Kshs 19.00 + Kshs 14.00)
a) Unlimited funds: Is a financial situation in which an organization is able to accept all independent
projects that provide an acceptable return ( capital budgeting decision are simply a decision of
whether or not the project clears the hurdle rate)
b) Capital rationing: Is the financial situation in which the organization has only a fixed number of
cash (shillings) to allocate among competing capital expenditures. A further decision as to which of
the projects that meet the minimum requirement is to invest in has to be taken.
- 11 -
c) Conventional cash flows: Consist of an initial outflow (outlay) followed by only a series of inflows
( For example a firm spends KES 6 Million and expects to receive equal annual cash inflows of KES
2 Million in each year for the next 4 years)
d) Non- Conventional cash flows: Is a cash flow pattern in which an initial outlay is not only followed
by a series of inflows, but also cash flows (at least one). For example, the purchase of a machine may
require KES 10 million (as initial outlay) and may thereafter generate cash inflows of KES 2 million
for 5 years after which in the 6th year an overhaul costing of KES 6 million may be required. The
machine would then generate KES 2 million for the following 5 years
Evaluating projects with unconventional patterns poses challenges that require an analyst‟s special
attention.
e) Relevant cash flows: To evaluate capital expenditure alternatives, the organization must determine
the relevant cash flows which are the incremental after-tax initial cash flow and the resulting
subsequent inflows associated with the proposed capital expenditure.
Example 2 — Calculate Relevant Cash Flows for Capital Project
We plan on purchasing a new assembly machine for Kshs 25,000. It will cost Kshs 2,000 to have the
new machine installed and we expect a Kshs 1,000 net increase in working capital. By making the
investment, we will reduce our annual operating costs by Kshs 7,000 and we expect to save Kshs 500
a year in maintenance. The new machine will require Kshs 750 each year for technical support. We
will depreciate the machine over 5 years under the straight-line method of depreciation with an
expected salvage value of Kshs 5,000. The effective tax rate is 35%.
Annual Savings in Operating Costs Kshs 7,000
Annual Savings in Maintenance Kshs500
Annual Costs for Technical Support Kshs(750)
Annual Depreciation Kshs (4,000) *
Revenues Kshs 2,750
Taxes @ 35% Kshs(962)
Net Project Income Kshs1,788
- 12 -
Add Back Depreciation (noncash item) Kshs4,000
Relevant Project Cash Flow Kshs 5,788
* Kshs 25,000 - Kshs 5,000 / 5 years = Kshs 4,000
We will receive Kshs 5,788 of cash flow each year by investing in this new assembly machine.
Since we have a salvage value, we have a terminal cash flow associated with this project.
f) Incremental cash flows: Represent the additional cash flows (inflows and outflows) expected to
result from a proposed capital expenditure.
g) Sunk Costs: Are cash outlays that have already been made (past outlays) and therefore have no
effect on the cash flows relevant to a current decision. Therefore, sunk costs should not be included
in a project‟s incremented cash flows.
h) Opportunity Costs: Are cash flows that could be realized from the best alternative use of an owned
asset. They represent cash flows that can therefore not be realized, by employing that asset in the
proposed project. Therefore, any opportunity cost should be included as a cash outflow when
determining a project‟s incremental cash outflow
1.8 Capital Budgeting Process
Capital budgeting as a process can be divided into four major stages; identification and development of
investment proposals; financial evaluation of projects; implementation of projects; and project review. The
financial evaluation portion has a number of tools to determine the wealth that a project can create for the
organization; these methods can be split into accounting based concepts and economic based concepts
(Northcott, 1992)
Capital budgeting is a multi-faceted activity with several sequential stages as indicated above. For typical
investment proposals of a large corporation, the distinctive stages in the capital budgeting process are
depicted in the form of a highly simplified flow chart
Strategic Planning
The key components of 'strategic planning' include an understanding of the firm's vision, mission, values and
strategies. It is the grand design of the firm and clearly identifies the business the firm is in and where it
intends to position itself in the future. Strategic planning translates the firm‟s corporate goals in to specific
- 13 -
policies and directions, sets priorities, specifies the strategic and tactical areas of business development and
guides the planning process in the pursuit of solid objectives. The vision and mission are often captured in a
Vision Statement and Mission Statement.
Vision: outlines what the organization wants to be, or how it wants the world in which it operates to
be (an "idealized" view of the world). It is a long-term view and concentrates on the future. It can be
emotive and is a source of inspiration. For example, a charity working with the poor might have a
vision statement which reads "A World without Poverty."
Mission: Defines the fundamental purpose of an organization or an enterprise, succinctly describing
why it exists and what it does to achieve its vision. For example, the charity above might have a
mission statement as "providing jobs for the homeless and unemployed".
Values: Beliefs that are shared among the stakeholders of an organization. Values drive an
organization's culture and priorities and provide a framework in which decisions are made. For
example, "Knowledge and skills are the keys to success" or "give a man, bread and feed him for a
day, but teach him to farm and feed him for life". These example values may set the priorities of self
-sufficiency over shelter.
Strategy: Strategy, narrowly defined, means "the art of the general." A combination of the ends
(goals) for which the firm is striving and the means (policies) by which it is seeking to get there. A
strategy is sometimes called a roadmap which is the path chosen to plow towards the end vision. The
most important part of implementing the strategy is ensuring the company is going in the right
direction which is towards the end vision.
Proposal Generation
Identification of investment opportunities and generation of investment project proposals is an important
step in capital budgeting process. The investment opportunities have to fit in with the organization‟s
corporate goals, vision, mission and long-term strategic plan. Moreover, if an excellent investment
opportunity presents itself, it is prudent to change the corporate vision and strategy to accommodate the
change(s). Thus, there is a two-way traffic between strategic planning and investment opportunities.
Some investments are however mandatory for instance, those required to satisfy particular regulatory, health
or safety requirements- and they are essential for an organization to remain in business. Other investments
are discretionary and are generated by growth opportunities. , competition, cost reduction opportunities and
so on. These discretionary investments form the basis of the business of the organization.
- 14 -
A profitable investment proposal is not just born; someone has to suggest it. The organization should ensure
that it has searched and identified potentially lucrative investment opportunities and proposals. There should
be a mechanism such that investment suggestion coming from inside the organization, such as from its
employees, or outside the organization, such as from advisors to the organization. Some organizations have
research and development (R&D) divisions constantly searching for and researching into new products,
services and processes and identifying attractive investment opportunities. Sometimes, excellent investment
suggestions come through informal processes.
Preliminary Screening of Projects
Generally, in an organization, there will be many potential investment proposal generated. Obviously, they
cannot all go through rigorous project analysis process. Therefore, the identified investment opportunities
have to be subjected to a preliminary screening process by the management to isolate the marginal sound
proposals. This may involve some preliminary quantitative analysis and judgments based on intuitive feeling
and experience.
Review and Analysis
Projects that pass through the preliminary screening process become candidates for rigorous financial
appraisal to ascertain if they would add value to the firm. This stage is also the quantitative analysis,
economic and financial appraisal, project evaluation or simply project analysis.
Capital Expenditure proposals are formally reviewed for two reasons; First, to assess their appropriateness in
light of the organization‟s overall objectives, strategies and plans and secondly, to evaluate their economic
viability.
Review of proposed project(s) may involve lengthy discussions between senior management and those
members of staff at the division and plant level who will be involved in the implementation if adopted.
Benefits and costs are estimated and converted into a series of cash flows and various capital budgeting
techniques applied to assess economic viability. The risks associated with the projects are also evaluated
Qualitative Factors in Project Evaluation
When a projects passes through the quantitative analysis test; it has to be further evaluated taking into
account qualitative factors. Qualitative factors are those which will have an impact on the project, but which
are virtually impossible to evaluate accurately in monetary terms. These are:
a) Societal impact of an increase or decrease in employee numbers
- 15 -
b) Environmental impact of the project
c) Possible positive or negative governmental political attitudes towards the project
d) Strategic consequences of consumption of scarce raw materials
e) Positive or negative relationships with labour unions about the project
f) Possible legal difficulties with respect to the use of patents, copyrights and trade or brand names
g) Impact on the organization‟s image if the project is socially questionable
Some of the mentioned items may or may not affect the value of the organization. The organization can
address these issues during project analysis by means of discussion and consultation with various parties, but
these process is considerably lengthy and outcomes often unpredictable. It requires considerable
management experience and judgmental skills to incorporate the outcomes of these processes into the project
analysis.
Making Decision (Accept/ Reject)
NPV results from the quantitative analysis combined with qualitative factors from the basis of the decision
support information. The analysis relays this information to management with appropriate recommendations.
Management considers this information and other relevant prior knowledge using their routine information
sources, experience, expertise, “gut feeling‟ and of course, judgment to make a major decision – to accept or
reject the proposed investment project
Implementation and Monitoring
Once investment projects have vetted, then they have to be implemented. During this phase of
implementation, various divisions of an organization are likely to be involved. An integral part of project
implementation being the monitoring of project‟s progress with a view to identifying potential bottlenecks
thus allowing early intervention. Deviations from the estimated cash flows need to be monitored on a regular
basis with a view to taking corrective action(s) when need be.
Post- Implementation Audit
Post-implementation audit does not relate to the current decision support process of the project; it deals with
a post-mortem of the performance of already implemented projects. An evaluation of the performance of
past decisions, however, can attribute greatly to the improvement of current investment decision making by
analyzing the past “rights‟ and „wrongs‟.
The post-implementation audit can also provide useful feedback to project appraisal or strategy formulation.
It therefore helps pin-point sectors in the organization‟s activities that may warrant further financial
- 16 -
commitment; or may call for retreat if a particular project becomes unprofitable. The outcome of an
investment also reflects on the performance of those members of the management involved with it. Finally,
past errors and successes provide clues on the strengths and weaknesses of the capital budgeting process
itself.
1.9 Capital budgeting techniques
Capital budgeting process involves investment decisions in long term assets. Capital budgeting techniques
are used to evaluate the acceptability of each project in order to make accept or reject decisions and ranking
decisions.
The success of any business can be determined through its capacity to generate positive cash flows.
Therefore, cash inflow or outflow is considered one of the most essential elements which give us an idea
about the continued existence of a business in the future. The shareholders focus on two things while
investing in business: first, how does business generate funds and second, where does the business invest
those funds for generating more. The process involves three basic steps: -
a) Identifying potential investments
b) Analyzing investment opportunities, isolating those that will create shareholders‟ value and
prioritizing them, and;
c) Implementing and monitoring the investment project selected in step 2 (Megginson, Smart &Gitman,
2007).
Bringham and Besley (2000) identified several basic methods used by businesses to evaluate projects and to
decide whether they should be accepted for inclusion in the capital budget. These methods are; Payback
period, net present value and internal rate of return. The payback period method is a non-discounting
technique since it does not consider the time value of money. NPV and IRR are referred to as discounting
techniques since they take into account time value of money.
Relevant cash flows
The relevant cash flows include;
a) An initial investment – relevant cash outflow for a proposed project at time zero.
Example3 — Calculate Initial Investment
Referring back to Example 2on calculation of relevant cash flows, we can calculate our Net Investment.
We will also assume that an existing machine can be sold for Kshs 6,000.
- 17 -
Acquisition Costs Kshs 25,000
Installation Costs Kshs2,000
Increase in Working Capital Kshs1,000
Proceeds from Sale Kshs 6,000
Less Taxes @ 35% Kshs(2,100)
Net Proceeds from Sale Kshs(3,900)
Net Initial Investment Kshs24,100
b) Operating cash inflows –the incremental after-tax cash inflows resulting from execution of a project
during its life.
c) Terminal cash flow- the after-tax non-operating cash flow occurring in the final year of the project.
It is usually attributable to liquidation of the project.
- 18 -
CHAPTER TWO
2.0 CAPITAL BUDGETING TECHNIQUES
Capital budgeting techniques are categorized into two;
Non Discounted Cash Flow Techniques
a) Payback period (PBP)
b) Accounting Rate of Return (AROR)
Discounted Cash Flow Techniques
a) Net Present Value (NPV)
b) Internal Rate of Return (IRR)
c) Profitability Index (PI)
Most large companies according to Ryan (2002) utilize all, one or more of these methods when evaluating
capital projects. Cadbury Schweppes, as previously mentioned, utilizes three of these, namely: Payback
period, internal rate of return and profitability index when evaluating capital projects.
2.1 Pay Back Period (PBP)
Brigham and Besley (2000) define payback period as the number of years required to recover the original
investment. It‟s the simplest and the oldest formal method used to evaluate capital budgeting method. Using
the pay back to make capital budgeting decisions is based on the concept that it‟s better to recover the cost of
a project sooner rather than later. As a general rule a project is considered acceptable if its payback period is
less than the maximum cost recovery time established by the firm. The major limitations of this method are
the failure to recognize the time value of money and cash flows beyond the payback period.
To compute the payback period for a project using this technique, compute the present value of all future
cash flows expected to be generated and then subtract its initial investment to find the net benefit the firm
will realize from investing in the project. If the net benefit computed on a present value basis is positive,
then the project is considered an acceptable investment, (Brigham & Besley, 2000). The shorter the payback
period, the sooner the company recovers its investment.
Payback (Even Cash Flows)= Initial Investment
Annual Cash Inflow
- 19 -
For uneven cash flows, sum cash flows and get a moving balance. The PBP is then computed using the
formulae below;
PB = Year before full recovery + Cash flows remaining to full recovery
Cash flow the following year
Example 6- Payback Period (Even Cash Flows)
A project requires an outlay of Kshs 50,000 and yields annual cash inflows of Kshs 12,500 for 7 years. The
payback period for the project is:
PB= Kshs 50,000
Kshs 12,500
= 4 years
Example 7- Payback Period (Uneven Cash Flows)
If the Turtles Co. has a project with a cost of $150,000, and net annual cash inflows for the first seven years
of the project are: $30,000 in year one, $50,000 in year two, $55,000 in year three, $60,000 in year four,
$60,000 in year five, $60,000 in year six, and $40,000 in year seven, then its cash payback period would be
3.25 years. See the example that follows.
The Payback period has the following merits:
a) Easy to calculate
b) It is the simplest capital budgeting tool used for decision making
c) It provides a crude way of dealing with risk. The risk of a project can be tackled by having a shorter
standard payback period as it may ensure guarantee against loss.
d) It emphasizes liquidity
- 20 -
In spite of its simplicity and widespread use, the Payback Period technique suffers the following limitations:
a) It ignores cash flows that are received after the cut-off period. This leads to discrimination against
projects which generate substantial cash inflows in later years.
b) It is the measure of a project‟s capital recovery, not its profitability. Though it measures a project‟s
liquidity, it does not indicate the liquidity position of the firm as a whole, which is more important.
c) It ignores the time value of money. In the payback calculation, cash inflows are simply added
without suitable discounting. This violates the most basic principle of financial analysis, which
stipulates that cash flows occurring at different points of time can be added or subtracted only after
suitable compounding or discounting.
2.2 Accounting Rate of Return (ARR)
The Accounting Rate of Return (ARR) is defined as an investment‟s average net income divided by its
average book value. Simply put, it can be defined using the below equation:
ARR = Profit after tax
Book value of the investment
The numerator of this ratio is the average annual post-tax profit over the life of the investment; the
denominator is the average book value of investment committed to the project.Traditionally, a popular
investment appraisal criterion, the Accounting Rate of Return has the following advantages:
a) It is simple to calculate.
b) It is based on accounting information which is readily available and familiar to the businessman.
c) It considers benefits over the life of the project.
Despite these merits the ARR also has the following disadvantages:
a) It is based on accounting profits not cash flows, and
b) It does not take into account the time value of money.
The acceptance rule using the Accounting Rate of Return technique in capital budgeting is that a project is
acceptable if its accounting rate of return exceeds a target average accounting return. However, this rule has
some limitations:
a) ARR ignores the time value of money. In using average figures that occur at different times, the near
future and the distant future are treated in the same way.
- 21 -
b) ARR uses net income and book value instead of looking at the cash flows and market values. As a
result, the ARR does not provide information on what the effect on share price will be for
undertaking an investment.
c) ARR lacks an objective cut-off period. That is, a calculated ARR is really not comparable to a market
return, the target ARR must somehow be specified. There is no generally agreed way to do this.
2.3 Net Present Value (NPV)
(Bringham & Besley, 2000), defines NPV as a method of evaluating capital investment proposals by finding
the present value of future net cash flows discounted at a rate of return required by the firm. To implement
this approach, we find the present value of all future cash flows a project is expected to generate and then
subtract its initial investment to find the net benefit the firm will realize from investing in the project. If the
net benefit computed on a present value basis is positive, then the project is considered acceptable
investment.
Formula for calculating the NPV is as follows:
NPV=CFo+CF1/ (1+r) 1
} + {CF2/ (1+r) 2
} + …………. + {CF/ (1+r) n
}
Where:
CFOxis the initial cost of investment
CFi is the expected net cash inflow at time t, (t>0)
ris the project‟s opportunity cost of capital
nis the expected life of the project
It is assumed that the cost of capital is constant
The NPV decision rules for selecting or rejecting a project are as follows:
Independent projects:
If NPV>0: Accept the project
If NPV<0: Reject the project
If NPV=0: The project may be accepted
- 22 -
Example4— Calculate Net Present Value
The Cottage Gang is considering the purchase of $150,000 of equipment for its boat rentals. The equipment
is expected to last seven years and has a $5,000 salvage value at the end of its life. The annual cash inflows
are expected to be $250,000 and the annual cash outflows are estimated to be $200,000. Assuming a
required rate of return of 12%, the net present value is $80,452. It is calculated by discounting the annual net
cash flows and salvage value using the 12% discount factors. The Cottage Gang has equal net cash flows of
$50,000 ($250,000 cash receipt minus $200,000 operating costs) so the present value of the net cash flows is
computed by using the present value of an annuity for seven periods. Using a 12% discount rate, the factor is
4.5638 and the present value of the net cash flows is $228,190. The salvage value is received only once, at
the end of the seven years (the asset's life), so its present value of $2,262 is computed using the Present
Value of the table factor for seven periods and 12% discount rate factor of .4523 times the $5,000 salvage
value. The investment of $150,000 does not need to be discounted because it is already in today's dollars (a
factor value of 1.0000). To calculate the net present value (NPV), the investment is subtracted from the
present value of the total cash inflows of $230,452. See the examples that follow. Because the net present
value (NPV) is positive, the required rate of return has been met.
Mutually exclusive projects
Accept the project with the highest NPV.
If no project has positive NPV, then reject all projects
Brigham and Earnhardt (2011) referred to the NPV generally as the best screening criterion which has the
following merits:
a) It is the true measure of an investment profitability in that it provides the most acceptable investment
rules;
b) It recognizes the time value of money;
c) It uses all cash flows occurring over the life of the project in calculating its worth;
d) It is consistent with value additivity principle; NPV of different projects can be summed up to arrive
at the overall increase/ decrease in firm value as a result of investing in different projects;
e) It relies on the discount rates rather any arbitrary assumptions, and
f) It is consistent with the objectives of shareholders value maximization.
Limitations of NPV Method
a) It is difficult to obtain the estimates of cash flows due to uncertainty;
- 23 -
b) It is difficult to precisely measure the discount rate;
c) It does not incorporate managerial flexibility in calculating the NPV;
d) Caution needs to be taken when using NPV method to evaluate mutually exclusive projects with
unequal lives, or when there are fund constraints.
e) The ranking of projects is not independent of discount rates under NPV.
2.4 Profitability Index (PI)
The profitability index (PI) shows the relative profitability of any project or the present value per dollar of
initial cost. Pike & Neale (2009) defined the PI as the ratio of the present value of project cash flows to the
present value of its initial cost. The PI is the ratio of investment to payoff of a suggested project. It is a
useful capital budgeting technique for grading projects because it measures the value created by per unit of
investment made by the investor.
This technique is also known as profit investment ratio (PIR), benefit-cost ratio, and value investment ratio
(VIR). The PI can be calculated as follows:
PI = Present Value of Cash Inflows
Initial Cash Outlay
Example5- Profitability Index
The initial outlay of a project is Kshs 100,000 and it can generate cash inflow of Kshs 40,000, Kshs 30,000,
Kshs 50,000 and Kshs 20,000 in year 1 through to 4. Assume a 10% rate of discount. The PV of cash
inflows at 10% discount rate is:
NPV= Kshs 112,350-Kshs 100,000= Kshs 12,350
PI= Kshs 112,350
Kshs 100,000
= 1.1235
Decision Rule for PI Technique
If the PI for a project is greater than one, then accept the project; if the PI of a project is less than one, then
reject the project; if the PI of the project is equal to 1 the project may be accepted.
The PI and the NPV techniques are closely related. If a project has a positive NPV, the present value of the
future cash flows must be bigger than the initial investment and the PI for such project would therefore be
bigger than one. On the other hand, a project with a negative NPV will have a PI less than one.
- 24 -
The PI technique enjoys some advantages which include:
a) It recognizes the time value of money
b) It is consistent with value maximization. A project with a PI greater than 1 when accepted will
increase shareholders‟ wealth. The PI measures the value created per dollar.
c) It gives a relative measure of project profitability.
2.5 Internal Rate of Return (IRR)
IRR is the discount rate that forces the present value of a project‟s expected cash flows to equal its initial
cost. As long as the project‟s IRR, which is its expected return, is greater than the rate of return required by
the firm for such an investment, the project is accepted.
If the return is greater than the cash outlay for the project, then the difference is a bonus to shareholders
which causes share price to rise. If the return is less than the cash invested for the project, then shareholders
will have to make up for the shortfall, a situation that hurts the stock price (Brigham &Earnhardt, 2010).
IRR is computed as follows:
( ) + + + ………. + = 0
NPV = = 0
The decision rules for accepting or rejecting project based on the IRR technique are as follows:
Independent Project
a) If IRR is greater than the opportunity cost of capital (IRR>k), then accept the project
b) If IRR is less than the opportunity cost of capital (IRR<k), then reject the project
c) If IRR is equal to the opportunity cost of capital (IRR=k), then decision makers may accept.
Mutually Exclusive Projects
a) Accept project with the highest IRR provided that its IRR is greater than the opportunity cost of
capital (IRR>k).
b) Reject if IRR is less than the opportunity cost of capital (IRR<k)
- 25 -
Example 8- Calculate Internal Rate of Return
Referring back Example2 on calculation of relevant cash flow for projects, we would solve for IRR as
follows:
Kshs 5,788 x discount factor = Kshs 24,100 or Kshs 24,100 / Kshs 5,788 = 4.164.If we look in the Present
Value Tables for n = 5 years, we want to find apresent value factor nearest to 4.164. By referring to
published presentvalue tables, we find the following:
At 6%, n = 5 4.2124 4.2124
As Calculated 4.1640
At 7%, n = 5 4.1002
Difference .0484 .1122
.06 + (.0484 / .1122) x (.07 - .06) = .0643
Internal Rate of Return = 6.43%
The IRR faces the following setbacks:
a) Problems with the IRR may arise when cash flows are not conventional or when two or more
mutually exclusive projects are under consideration for investment.
b) It gives unrealistic rate of return. In the case of a mutually exclusive project in which firms are faced
with take-it-or-leave-it projects, the decision rule is that the firm should choose the one that add most
to shareholders‟ wealth. That is choosing the project with the highest NPV. It would also be
misleading to choose the one with the highest rate of return, according to the return rule.
c) In comparing projects with the same life but different outlays, the IRR may mistakenly favour small
projects with high rates of return but low NPVs (Brealey, Myers & Marcus, 2009).
The IRR method also poses a multiple rates of return problem. This occur when there are two discount rates
or two IRRs that equate the present value equal to the initial investment or a rate that makes the NPV equal
to zero. Hence the question that arises is which of these rates is correct. The answer is both or neither. More
precisely, there is no unambiguously correct answer. Purpose of this question is not to resolve the cases
where there are different IRRs. The purpose is to let you know that the IRR method, despite its popularity in
the business world, entails more problems than a practitioner may think. This multiple rates problem
indicates that despite the widely used IRR technique amongst firms in the business world it still contains
- 26 -
some little problems than we think. Unless the calculated IRR is a reasonable rate for reinvestment of future
cash flows, it should not be used as a yardstick to accept or reject a project.
2.6 Modified Internal Rate of Return (MIRR)
Bringham & Besley (2000) define MIRR as the discount rate at which the present value of a project‟s cost is
equal to the present value of its terminal value, in which the terminal value is found as the sum of the future
values of the cash flows, compounded at the firm‟s required rate of return. The use of the technique helps
overcome the IRRs limitation resulting from the reinvestment rate assumption.
The MIRR has two advantages over the IRR which makes it theoretically superior to the IRR. The MIRR
assumes that cash flows from each project are reinvested at the firm‟s cost of capital or some explicit rate. It
is an indicator of a project true profitability. Secondly, it eliminates the multiple IRRs problem: there is only
one MIRR for a project; it can be compared to the cost of capital when deciding to accept or reject (Brigham
&Ehrhardt, 2010). Despite these advantages over the IRR, it is not as widely used as the IRR. The MIRR can
be computed as follows:
PV (Costs) = PV (Terminal value)
=
Here, COF refers to cash outflows, or the cost of the project, and CIF refers to cash inflows. The left term is
the PV of the investment outlays when discounted at the cost of capital, and the numerator of the right term
is the compounded value of the inflows, assuming that the cash inflows are reinvested at the cost of capital.
The compounded value of the cash inflows is also called the terminal value. The MIRR is the discount rate
that forces the PV of the terminal value to equal the PV of the costs.
2.7 Discounted Payback Period
One of the limitations in using the payback period is that it does not take into account the time value of
money. Thus, the future cash inflows are not discounted or adjusted for debt/equity used to undertake the
project, inflation, etc. However, the discounted payback period solves this problem. It considers the time
value of money; it shows the breakeven after covering such costs. This technique is similar to payback
period except that the expected future cash flows are discounted for computing payback period. Discounted
payback period is how long an investment‟s cash flows, discounted at the project‟s cost of capital, will take
to cover the initial cost of the project. In the approach, the present values of the future cash inflows are
cumulated up to the time they cover the initial cost of the project. Discounted payback period is generally
- 27 -
higher than payback period because it is money you will get in the future and will be less valuable than
money today.
Example 9— Calculate Discounted Payback Period
Referring back to Example 2, we can calculate the discounted paybackperiod as follows:
Year Cash Flow x P.V. Factor = P.V. Cash Flow Total to Date
1 Kshs 5,788 .893 Kshs 5,169 Kshs 5,169
2 5,788 .797 4,613 9,782
3 5,788 .712 4,121 13,903
4 5,788 .636 3,681 17,584
5 5,788 .567 3,282 20,866
6 3,250 .567 1,843 22,709
Under the Discounted Payback Period, we would never receive a payback on our project; i.e. the total to date
present cash flows never reached Kshs 24,100 (net investment). If we had relied on the regular payback
calculation, we would falsely assume that this project does payback inthe fourth year.
2.1 Methods of calculating the overall cost of capital
a) Weighted Average Cost of Capital (WACC.),
b) Capital Asset Pricing Model (CAPM)
c) Arbitrage Pricing Theory (APT)
a. Weighted Average Cost of Capital (WACC)
The weighted average cost of capital (WACC) according to Bierman and Smidt (1980:258) represents the
average cost of funds to an organization and as such represents the sources of capital and their uses. WACC
for a given capital structure reflects the characteristics of organization‟s assets and in particular, their
average risk as well as the timing of expected cash proceeds. WACC represents an averaging of all the
financial risks of an organization.
The calculation of the weighted average cost of capital (WACC) according to Northcott (1992:77) has
several steps:
- 28 -
a) The identification of the ranges of the sources of long-term capital.
b) The determination of the cost of the capital sources.
c) The determination of the market value of the capital sources.
d) The calculation of the WACC.
Four sources of long-term capital exist; (a) long-term debt, (b) preferred shares, (c) common shares, and (d)
retained earnings (Gitman, 2003: 472; Lovemore, 1996: 87). The cost of each of the above mentioned sources
of capital can be calculated; this is not being explored in this text but is extensively covered in management
accounting texts.
It is sufficient to note for the purpose of this text that the cost of long-term debt is a function of the interest
payable, the tax rate, any issuing expenses and the market value of the debt. The cost of equity capital sources
(ordinary or preference shares) for listed organizations depends on dividend payable, the cost of issuing equity
and the market price of shares. Retained earnings are usually a less expensive source of capital than issuing
new shares, due to the fact that they do not incur the transaction costs associated with the public offering of
shares (Gitman, 2003: 473; Bierman&Smidt, 1980:245-251).
The weightings given to each source of funds in the WACC calculation are based on the market value of the
debt, ordinary shares and preference shares and are impacted on by the relative proportions employed of each
capital source (Nortcott: 1992:78).
The literature identifies two problems with the use of WACC for all projects, namely (Lovemore, 1996: 87-
89; Northcott, 1992:79; Bierman&Smidt, 1980: 258):
i. WACC is a reflection of the current cost of a pool of funds used for financing the current investments
of the organization. An investment outside of the normal activity of an organization should have a
different risk profile and hence the current WACC rate will not sufficiently allow for that risk profile.
ii. If the investment is large enough, it might alter the WACC rate by its implementation, for example, a
large loan might have to be incurred that could then alter the weighting of the long term debt and
hence the WACC rate. As WACC does not consider unique risk, it could lead to the acceptance of a
high return but overly high-risk projects (Brealey& Myers, 1991). A model suggested by the
literature that considers a project‟s unique risk is the capital asset pricing model (CAPM).
- 29 -
b. Capital Asset Pricing Model (CAPM)
According to Samuels, Wilkes and Brayshaw (1990), the CAPM assess risk by showing the connection
between individual project returns and the market for risky assets as a whole. The CAPM evaluates the
project‟s unique risk against its own returns and not the return that an investor could earn from the
organization‟s cost of capital (Samuels et al, 1990).Risk, as viewed by investors, needs better definition to
allow for a better understanding of the CAPM model and hence is briefly discussed. Northcott (1992) defines
risk as the unpredictability of returns from an investment. Gitman (2003) breaks risk down into two
components (a) diversifiable risk and (b) non-diversifiable risk.
Diversifiable risk or unsystematic risk is considered by Gitman (2003) to be the portion of an investment‟s
risk that can be associated with random causes and that can be eliminated by the use of diversification.
Examples of organizational specific diversifiable risks are: strikes, lawsuits and loss of a key account (Gitman,
2003).
Non- diversifiable risk or systematic risk according to Gitman (2003) is that portion of an investment‟s risk
that is attributable to market forces, affects all organizations in that market place, and as such cannot be
eliminated by diversification. Examples of systematic risks are war, inflation, international incidents and
political events (Gitman, 2003).
Investors are able to establish a portfolio of investments that can eliminate diversifiable risks but are unable to
eliminate non-diversifiable risks, hence non-diversifiable risk is the only important risk and as such, the
measurement of non-diversifiable risks in the selection of investments with the best risk return characteristics
is the most important (Gitman, 2003). The CAPM model links non-diversifiable risk and the return for all
assets. A measure of non-diversifiable risk is the beta coefficient.
c. Arbitrage Pricing Theory
In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected
return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical
market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient.
The model-derived rate of return will then be used to price the asset correctly - the asset price should equal the
expected end of period price discounted at the rate implied by the model. If the price diverges,arbitrage should
bring it back into line.The theory was proposed by the economist Stephen Ross in 1976.
- 30 -
Riskyassetreturns are said to follow a factor structure if theycanbeexpressed as:
where
is a constant for asset
is a systematic factor
is the sensitivity of the th asset to factor , also called factor loading,
and is the risky asset's idiosyncratic random shock with mean zero.
The APT states that if asset returns follow a factor structure then the following relation exists between
expected returns and the factor sensitivities:
where
is the risk premium of the factor,
is the risk-free rate,
That is, the expected return of an asset j is a linear function of the assets sensitivities to the n factors.
Note that there are some assumptions and requirementsthat have to befulfilled for the latter to be correct: There
must be perfect competition in the market, and the total number of factorsmayneversurpass the total number of
assets (in order to avoid the problem of matrix singularity).
- 31 -
CHAPTER THREE
1.10 3.0 THEORIES OF CAPITAL BUDGETING AND EMPIRICAL EVIDENCE
3.1 Theories of Capital Budgeting
1.11 3.1.1 Real Options theories
In the works of Black, Scholes, and Merton (1973) we are provided with a standard pricing model for
financial options. Together with Stewart Myers of Massachusetts Institute of Technology (MIT), they
recognized that option-pricing theory could be applied to real assets and non-financial investments. To
differentiate the options on real assets from the financial options traded in the market, Myers coined the term
“real options”, which has been widely accepted in academic and industry world. Unlike the standard
corporate resource allocation approaches, the real options approach acknowledges the importance of
managerial flexibility and strategic adaptability. Its superiority over other capital budgeting methods like
discounted cash flow analysis has been widely recognized in analyzing the strategic investment decision
under uncertainties (Luehrman, 1998).
Traditional approaches to capital budgeting, such as discounted cash-flows (DCF), cannot capture entirely
the project value, for different reasons: it is assumed that investment decision is irreversible, interactions
between decisions today and future decisions are not considered, and investment in assets seems to be a
passive one i.e. management doesn‟t interfere during the life of the project. Managerial flexibility generates
supplementary value for an investment opportunity because of managerial capacity to respond when new
information arises, while the project is operated. Investment in real assets includes a set of real options that
management can exercise in order to increase assets value (under favorable circumstances) or limit loses
(under unfavorable situations). Managerial flexibility in decision-making process introduces an asymmetry
for probability distribution of net present value (NPV) for a project. An investment opportunity value is
dependent on future uncertain events, so it will be greater than forecasted value in the situation of passive
management. From this perspective, a project has a standard value, determined through traditional
techniques (DCF, which does not capture adaptability and strategic value), but also a supplementary value,
coming from operational and strategic real options held by an active management (Vintila, 2007).
- 32 -
The real options in capital budgeting decisions include the following:
i) Option to Expand (Growth Options)
This occurs when managers accept investment projects that have negative or insignificant NPV but may
enable companies to find greater opportunities in the future that add considerable profitability and value to
the firm.
ii) Timing Option (Option to Wait/ defer)
This gives management an option to choose an investment timing now or later. If the project turns out to be a
winner project, then invest in it now; if the project turns out to be a loser project with negative NPV now,
then it may pay to wait and get a better fix on the likely demand. This usually occurs in the oil and other
extractive industries.
iii) Option to Abandon
If a project does not perform favorably and there is little promise for improvement, the firm can consider the
exit options. The firm needs not continue with an uneconomically vibrant project indefinitely. An
abandonment or exit option, like a shut- down option, reduces the downside risk of the project.
iv) Flexible Production Facilities
Apart from the options that naturally exist in most projects, managers can incorporate flexibility in designing
the project. The designed–in options may take the form of input flexibility options, and output flexibility
options.
An input flexibility option allows a firm to switch between alternative inputs. For example, an electric power
plant may go for a flexible dual –fuel boiler which can switch between gas or oil as fuel, depending on
which source of energy is cheaper at a given point of time.
An output flexibility option allows a firm to alter the product mix. Oil refineries are typically designed with
this flexibility. This permits them to switch from one product mix to another, depending on which product
mix is the most profitable at a given point in time (Pandey, 2010).
v) Time-to-Build (Staged Investment)
- 33 -
When investment costs occur in stages, management has an option to abandon the next stage of investment if
expectations become unfavorable. Therefore, each stage becomes an option of the subsequent stages.
vi) Shut Down Option
A project may temporarily shut down if it is economical to do so. For example, an iron ore mining project
may be closed for a while if the output price of the iron ore is depressed. In general, shut down options are
more valuable when the variable costs are high. A shut down option reduces the downside risk of the project.
vii) Option to Alter Operating Scale (e.g. to Expand; to Contract; to Shut Down)
If market conditions are more favorable than expected, the firm can expand the scale of production or
accelerate resource utilization. Conversely, if conditions are less favorable than expected, it can reduce the
scale of the operations. Examples of this real option can be found in natural-resource industries (mining),
consumer goods and commercial real estate.
Among the above options, option to wait and option to abandon are recognized as the most important real
options which are embedded in most investment opportunities.
3.1.2 MMs capital budgeting theory
MM pursues value maximization to increase the combined market values of debt and equity. In MMs theory
the two sources of financing used are permanent and equity is a form of permanent financing. Since
permanent financing is employed, the payment of principal is unnecessary so unlike in normal capital
budgeting depreciation is set aside each year to replace the obsolete capital and investors do not recover the
initial investment at all. According to MM the cost of capital is the weighted average cost of capital. To sum
up MM theory, the value of a levered firm is the after –tax cash flows for the stockholders discounted at the
cost of equity plus the after tax flows from bondholders discounted at the cost of debt or identically its value
is the NOI discounted at the WACC. Therefore MM maximized the combined value of equity and debt or
equivalently the combined wealth of the stockholders and bond holders.
3.1.3 Contemporary capital budgeting theory
Contemporary capital budgeting theory is deeply rooted in MM's theory which was discussed in the previous
section. Slight differences abide, though, because, contrary to MM's permanent cash flows, investment
projects have limited useful lives in the real world. In making capital budgeting decisions, five important
elements are to be considered: the initial investment, the operating cash flow, the useful life of the project,
the salvage value, and the cost of capital. Since the limited project life creates discrepancies between MM's
- 34 -
and contemporary theory, it is discussed before the other four components. In most major textbooks, a fixed
serviceable life is assumed, so the project will be in place for a few years, and, after that period, it will be
closed. See Block and Hirt (1994), Brigham and Gapenski (1993), Kolband Rodriguez (1992), Van Home
(1992), and Weston and Brigham (1993). The implication is that, upon the close of the project, the venture is
to be dissolved, so the company must pay back the par value of bonds to bondholders and the par value of
common shares to stockholders. Therefore, unlike in MM, depreciation is not accumulated from year to year
to replace the capital asset. Instead it is added back to the NOI to increase the operating cash flow for the
investors. The initial investment is the amount of capital required upfront to start a project which includes,
but is not limited to, the purchase price of the capital asset, sales taxes, transportation cost, installation cost,
and the working capital needs. In MM, the investors never recapture the initial investment because the
project will go on forever; in current theory this amount is recovered through the operating cash flows from
the project. The operating cash flow in current theory is the cash inflow to the investors from the project.
MM's cash flow is the NOI given by equation (1), but the operating cash flow in today's capital budgeting
(OCF, hereafter) is MM's NOI less the tax shield benefit of interest payment plus depreciation.
1.12 Empirical Evidence
(Njiru, 2008): A survey of capital investment appraisal techniques used by commercial parastatal in Nairobi.
The study‟s objective was to identify the most commonly used capital investment appraisal technique by commercial parastatals
and determine the factors that influence the choice of capital investment appraisal technique used by commercial parastatals. It
covered all commercial parastatals with headquarters in Nairobi and was for the period of 5 years between 2003 and 2008. The
researcher used the survey method. He asked questions about capital investment appraisal technique used in the organizations
andexplored factors considered by the parastatals in making these decisions. He used questionnaires consisting of both closed
and open-ended questions.
Interpretation and analysis of data was done using the statistical package for social science (SPSS). Out of the 30 parastatals
targeted, only 20 responded which was a response rate of 67%. Descriptive statistics, in particular, arithmetic mean and standard
deviation were used to interpret responses to the questionnaires. The analysis revealed that on average, the annual size of capital
budget is 1.4% of thetotal asset base of the organizations studied. This implies a low intensive capital investment during the study
period (2003-2008). The study also found that all the parastatals had a capital investment policy.
The results showed that incorporating risk, determination of the appropriate discount rateand incorporating inflation in the capital
investment analysis were the three main challenges that parastatals faced in the capital investment appraisal process.
According to the study, the three main capital investment appraisal techniques used by commercial parastatals are IRR (65%),
NPV (25%) and pay-back period technique (10%). The amount of funds required for the capital investment, size of the
- 35 -
organization, government policy and industrial practices are the main factors that influence the choice of the capital investment
appraisal technique. Further the study found that 75% of the respondents preferred discounted cash flow (DCF), 10% non-
discounted cash flow (DCF) technique whereas 15% did not respond.
(Kadondi, 2002) A survey of Capital Budgeting Techniques used by companies listed at the Nairobi Securities
Exchange (NSE)-Previously Nairobi Stock Exchange
In her study, Kadondi (2002) carried out a survey on capital budgeting techniques used by companies listed at Nairobi Securities
Exchange (NSE). The objectives were to document the capital budgeting techniques used in investment appraisal by
corporations in Kenya, to determine whether the techniques used conform to theory and practices of organizations in developed
countries and to determine how firms and CEO characteristics influence the use of a particular technique.
She intended to conduct the study on 54 Companies listed at the NSE but the analysis included only 43 Companies whose
annual reports and accounts were available. Of these, only 28 Companies responded of which 50% were small companies and
50% large companies. Data was collected through questionnaires.
Data was analyzed using SPSS and was put into frequency distribution tables. Chi-square test was used to test relationships
between techniques and firm characteristics. The findings of the study were that 31% of the companies used Payback Period
method, 27% use NPV while 23% uses IRR. According 71% of respondents, their companies considered capital budgeting
process a strategy for achieving competitive advantage. Another finding of the study was that small companies use IRR and
Payback Methods while large Companies with high net profit margins use NPV, IRR and Payback Period methods.
This study is consistent with the survey done by (Graham & Harvey, 2002) who found that large firms favored the sophisticated
techniques of capital budgeting while the smaller firms favored the traditional methods of payback and ARR. The issue of
capital budgeting techniques being used as a strategic tool for benchmarking and gaining competitive edge was imminent in the
study and we concur with the findings.
(Grinstein &Tolkowsky, 2004)): The Role of the Board of Directors in the Capital Budgeting Process - Evidence from
S&P 500 Firms
Grinstein and Tolkowsky (2004) carried out a Survey to determine the role of the board of directors in capital budgeting process.
The study was carried out in the United States of America. The sample consisted of “S&P 500” firms and covered the period
from 1995to 2000. Their final sample consisted of 2,262 firms after excluding financial institutions due to their special
governance regulations and requirements and a further 292 firms for whose proxy statement information was not obtained. They
used several financial and governance variables to characterize what determines theestablishment of the capital budgeting
committees which included firm size, boardstructure and the ratio of number of independent directors to total number of
directors. They used both univariate and multivariate data analysis methods in their survey. The findings were that 17% of the
boards of directors of the sampled firms disclosed that they establish committees that have a capital budgeting role. The study
- 36 -
revealed that boards of directors have four main roles in capital budgeting. These roles include reviewing of; annual budgets,
large capital expenditure requests, merger and acquisition proposals and performance of approved projects. They found that
committees that review budgets and capital expenditure requests perform a monitoring role which is consistent with existing
theories.
They also found that boards are more likely to establish special committees to perform these tasks where the auditing costs are
low and when the overinvestment problem is severe. Some committees have an advisory role in capital budgeting process. The
main finding of the study was that boards of directors have a dual role in capital budgeting process, that is the disciplinary role
and the advisory role.
In our opinion, the findings of this study are very relevant, and the role of the board and that of management should be clearly
spelt out in the capital budgeting process of most firms. It is evident that to reduce agency conflict, the board needs to play a more
active role of major capital projects.
(Pradeep & Quesada, 2008): The use of Capital Budgeting Techniques in Business a perspective from the Western
Cape.
Pradeep and Quesada (2008), in a study on the use of capital budgeting techniques in businesses in the Western Cape Province
of South Africa, investigated a number of variables and associations relating to capital budgeting practices. The sample consisted
of 600 firms but only 211 interviews were conducted successfully giving a response rate of 35%.A descriptive approach to the
research finding was adopted. Chi-square test technique was used to measure association between variables. Data analysis was
carried out using SPSS software. The results revealed that payback period followed by NPV appear to be the most used method
across the different sizes and sectors of businesses. 39% of respondents used Payback period technique while 36% used NPV.
28% of respondents used internal rate of return and profitability index. 22% of respondents used Accounting rate of return
while10% did not use any capital budgeting technique. The study also revealed that 64% of the business surveyed used only one
method of capitalbudgeting while 32% used between two and three different techniques to evaluate capital budgeting decisions.
The more complicated methods such as NPV and IRR were favored by large businesses compared to small businesses.
The findings of this study are contrary to earlier studies by (Graham and Harvey, 2001).The finding that most firms prefer
Payback period to NPV is a pointer to other behavioral factors like use of intuition, fear of failure and resistant to change.
(Robichek& Van Horne, 1967): Abandonment Value and Capital Budgeting
In their study, Robichek and Van Horne (1967) noted that routine consideration of the abandonment option reduces the potential
for down side movement in value. Using the option-pricing they have shown that an asset payoff is bonded from below when
the abandonment option is explicitly considered. Their approach emphasizes the reduction of the potential losses as opposed to
risk and the increase in firm value implied by the abandonment option is more obvious. According to them, the abandonment
value is the value of the abandonment option and its worth should be included in the calculation of the present value of the future
- 37 -
cash inflows. The calculations of the present value at time zero (PVO), provide the market valuation at such a point in time. As
time passes, conditions, either endogenous or exogenous to the firm, will change the present value of an asset. Thus the present
value of future cash flows of the same asset will be different at any given point in time. The question of whether to abandon and
the decision process of the optimal timing of abandonment have been considered. They suggest that a policy of abandoning an
asset one period after abandonment value becomes greater than the present value (AV>PV) would benefit the firm.
They considered investment in a mine when mothballing can occur by incurring maintenance cost and costless abandonment of
the mine is possible. They found that it‟s optimal to close the mine only when the output price has fallen considerably below
production cost, and conversely, it‟s not optimal to re-open a mothballed mine even when the output rises, well above the
production costs. Thus, there is a range of value of output prices over which it is optimal to produce. This phenomenon, that is a
consequence of the interaction of sunk costs and uncertainty, is referred to in economic literature as hysteresis.
(Myers& Majd, 1990): Abandonment Value and Project Life. Advances in Futures and Options Research, 4, 1-21
Intheir paper, Myers and Majd (1990) presented a general procedure for estimating the abandonment value of a capital
investment project. To develop their model, they equated an investment project to an American put-option on a dividend paying
stock. They equated the exercise price of the put to the salvage value of the project; the cash flows from the project to the
dividend payments on the stock and assumed the project can be abandoned at any time during its life. They showed that, other
things held constant, the value of the abandonment option increases with salvage value (the exercise price), project volatility, and
project life (maturity) while it decreases with project value, as predicted by put-option pricing theory.
(Graham& Harvey, 2002): How Do CFOs Make Capital Budgeting and Capital Structure Decisions?
In their survey, Graham and Harvey (2002) sought to find out how chief finance officers (CFOs) make capital budgeting
decisions and identify areas where theory and practice are consistent. They asked CFOs to rate how frequently they used
different capital budgeting techniques on a scale. The sample consisted of 4,440 US firms. A total of 392 CFOs responded to the
survey giving a response rate of 9%. Though low, the rate was consistent with the response rate for the quarterly FEI-Duke
survey whose response rate is usually 8-10%, given the length (three pages) and depth (approximately 100 questions) of the
survey. They reported results by summarizing the percentage of CFOs who said that they always or almost always used a
particular capital budgeting evaluation technique.
The study found that NPV and IRR were the most frequently used capital budgeting techniques, 74.9% of CFOs always or
almost always used NPV, 75.7% almost or always used IRR while 56.9% of CFOs used hurdle rate. They also found out that
companies that pay dividends were significantly more likely to use NPV and IRR than firms that do not pay dividends
regardless of firm size. Public companies were found to be more likely to use NPV and IRR than private companies. Other than
NPV, IRR and the hurdle rate, the payback period was the most frequently used capital budgeting technique (56.7% always or
almost used use this technique). This was found surprising because finance textbooks have lamented shortcomings of payback
- 38 -
criterion for decades. The choice of evaluation technique was found to be linked to firm size and executive characteristics. They
also observed that payback period method is used by less sophisticated, older managers without MBAs.
(Holmén& Pramborg, 2009): Capital Budgeting and Political Risk-Empirical Evidence
In their work, Holmén and Pramborg (2009) investigated Swedish firms‟ use of capital budgeting techniques for foreign direct
investments (FDI). Questionnaires were sent to the CFOs of the Swedish firms that had responded to a survey from the Swedish
central bank (Riksbanken) in the spring of 2003, regarding how much FDI the firm had invested as of December 2002. A total
of 497 firms met the criteria and 200 responded.
They surveyed to what extent firms actually use pre-investment strategies to manage political risks. They focused the analysis on
whether firms were more likely to use the Payback method instead of the theoretically correct NPV method when the risk of
expropriation was perceived to be high.
For data analysis they used Spearman rank correlation and cross-sectional regressions. The study found that the expropriation
risk index was quite skewed and most countries (31 countries out of 61) had the lowest possible ranking of „„1‟‟. Only a few
countries had an index value larger than „„2‟‟.
They concluded that in the presence of political risks, managers are reluctant to rely on the traditional NPV method and suggest
this is due to the fact that they find it difficult to take such risks into account. This is consistent with managers being bounded
rational decision makers, using simple rules of thumb when the deliberation cost is high. Further, the results are consistent with
the notion that the rules of thumb are adjusted to proxy optimal decision as far as possible.
(Block, 2005): Are There Differences in Capital Budgeting Procedures Between Industries?
Block (2005) carried out a study on the use of capital budgeting procedures between industries. He stated that while it is easy to
state that the use of capital budgeting analysis has become more sophisticated over the decades, the question remains as to
whether different industries have followed the same pattern. He conducted a survey comprising of three hundred and two
Fortune 1,000 companies and organized them along industry lines. Chi-square independence of classification tests indicated that
a null hypothesis of no significant relationship between industry classification and capital budgeting procedures could be rejected
in a number of decision-making areas including goal setting, rates of return, and portfolio considerations. This emphasized the
point that, just as industry patterns affects financing decisions; they also affect capital budgeting decisions.
(Uddin& Chowdhury, 2009): Do We Need to Think More about Small Business Capital Budgeting?
Uddin and Chowdhury (2009) sought to find out whether the capital budgeting theory of large business is well applicable for the
small businesses or not. He suggested that if it is not, then further development of theory becomes necessary. He found that out
that there is no well accepted standard definition of small business in the literature that can be used to create the basis of applying
- 39 -
the theory of capital budgeting. It is possible to say that the theory of capital budgeting, which is constructed under assumptions
related to large incorporated businesses, is not fully applicable for small businesses. He argued that NPV however is the
ultimately suggested method of capital budgeting that involves estimation of cash flows, and the market determined discount
rate. Both of these two tasks require expertise and relevant knowledge. Decision-makers in small businesses may lack this
knowledge or may find it cost ineffective to hire that kind of expertise.
Moreover, market determined discount rate is not possible to find since the market for small business‟s capital is not liquid,
which does not allow thinking about separation of investment and financing decision. Also, the effect of agency conflict, when it
is present, on the investment decision, is different for small businesses because of lack of separating ownership and control. Size
and availability of capital as well as investment opportunities are also among some other factors contributing to this conclusion.
He found that the reasons for the inapplicability were: - lack of knowledge, cost of hiring outside consultants, low priority of
planning, size and availability of capital, size and availability of investment opportunities, tendency of high reliance on easy
techniques like payback period, short operating history, credit constraints, difficulties in quantifying future cash flow, and limited
discretionary alternatives for investments.
Stein C. Jeremy and Scharfstein S. David (1997): The Dark Side of Internal Capital Markets: Divisional Rent-Seeking
and Inefficient Investment
Stein and Scharfstein (1997) developed a two-tiered agency model that shows how rent-seeking behaviour on the part of
division managers can subvert the workings of an internal capital market. By rent-seeking, division managers can raise their
bargaining power and extract greater overall compensation from the CEO. And because the CEO is herself an agent of outside
investors, this extra compensation may take the form not of cash wages, but rather of preferential capital budgeting allocations.
One interesting feature of his model is that it implies a kind of “socialism” in internal capital allocation, whereby weaker
divisions get subsidized by stronger ones.
- 40 -
Summary of unresolved issues:
a) Researchers have not been able to conclude studies on the relationship between the firm‟s investment risk characteristics and
the right capital budgeting technique.
b) The evaluation of project success against capital investment appraisal method used is yet to be studied.
c) An investigation to determine the existence of a relationship between capital budgeting method used by the firms and
profitability is another area that is yet to be fully explored.
4.0 CONCLUSION
A capital expenditure budget is one of the components that make up the financial budget. Each of the budget components has its
own unique contribution to make toward effective planning and control of business operations. Capital budgeting is the process
of identifying, evaluating planning and financing major investment projects of an organization.
For a single conventional, independent projects, the IRR, NPV and PI methods lead us to make similar accept/ reject decision.
Various types of circumstances and projects differences can cause ranking difficulties. Four situations that could cause include;
when funds are limited necessitating capital rationing, when ranking two or more projects proposals with varied lives, when
ranking two or more projects with different Investment scales and when projects have opposite cash flow patterns.
Although the area of capital budgeting has been studied widely and various recommendations made on the most preferable
methods, there is still a lot that needs to be done. The area of real options in capital budgeting, though explored quite widely, has
not been studied locally and this will form very good grounds for a local study. In their study, Li and Johnson (2002) concluded
that although some recent studies recognized the potential of real options theory in evaluating strategic IT investment
opportunities, they believed that the applicability of various real options models should be scrutinized under different scenarios.
Standard real options models assuming symmetric uncertainty in future investment payoffs cannot be directly applied to the
shared opportunities because of the competitive erosion.
With the presence of potential competitive entry, real options analysis should balance the strategic benefit of preemptive
investment and the value of the option to wait. IT switching cost is another important factor that must be considered when
conducting real option analysis. As high IT switching cost or technology locking is very common in the digital economy,
decision makers should pay more attention to the technology uncertainties. Since the dynamics of the technology competition
and standardization play an important role in IT investment decision, more studies should be done to incorporate it into the real
options based decision-making process. Further real options analyses should be conducted to explore the functions of open
standard and technology interoperability in fostering IT investment. According to Grinstein &Tolkowsky (2004) most studies on
the role of the board of directors in capital budgeting have focused on the disciplinary or monitory role of the board of directors.
- 41 -
The advisory role of the board of directors is under explored. Studying capital budgeting mechanisms that have both features is
an important topic for future research.
- 42 -
REFERENCES
Arnold, G. (2005). Corporate Financial Management, (5th ed.). New York: Financial Times/Prentice Hall.
Brealey, R. A. & Myers, S. C. (2000). Principles of corporate finance, (4th ed.) . New York
Brigham, E.F., & Houston, J.F. (2008). Fundamentals of Financial Management, (6th ed.). Ohio: Leap Publishing Services, inc.
Gitman, L. & Vandenberg, P. (2002). “Cost of Capital Techniques Used by Major U.S. Firms: 1997 vs. 1980”, Financial
Practice and Education, 10 (2), 53-68.
Gitman, L.J. (2003). Principles of Managerial Finance (10th ed.). Boston: Pearson Education.
Kadondi, E. A. (2002). A Survey of Capital Budgeting Techniques Used by CompaniesListed at The Nairobi Stock Exchange.
MBA, Project Paper, University of Nairobi
Shim, J.K. & Siegel, J.G. (2008). Financial Management, (3rd ed.). New York: Barron‟s Educational Series, inc.
Shim, J.K. & Siegel, J.G. (1994). Budgeting basics & beyond: A complete step-by-step guide for non financial managers. New
Jersey: Englewood Cliffs.
Njiru, B. M. (2008). A Survey of Capital Investment Appraisal Techniques Used by Commercial Parastatals in Nairobi. MBA
Project, University of Nairobi
Northcott, D. (1992). Capital Investment Decision-Making. London: Academic Press.
Pandey, I. M. (2010). Financial Management. New Delhi: Vikas Publishing House Pvt Ltd.
Pradeep, B., & Quesada, L. (2008). The Use of Capital Budgeting Techniques inBusinesses: A Perspective from the Western
Cape. 21st Australasian Finance and Banking Conference. http://ssrn.com/abstract=1259636
Rundolf, W.W., Bradford, D.J., & Stephen, A.R. (1998). Principles of Corporate Finance, (4th ed.). New York: Irwin
McGraw-Hill.
Ryan, G. P. (2002). Capital budgeting practices of the fortune 1000: How have things changed. Journal of Business and
Management, (8)4, 355-364.
Scott, B. & Eugene F. B. (2000). Essential of Managerial Finance, (12th ed.). The Dryden Press.
- 43 -
Stein, C. J. &Scharfstein, S.D. (1997). The Dark Side of Internal Capital Markets: Divisional Rent-Seeking and Inefficient
Investment
Uddin, M.. & Chowdhury, R. (2009). Do We Need to Think More about Small Business Capital Budgeting? International
Journal of Business and Management, 4(1).
Van Horne, James C. (1980) "An Application of the CAPM to Divisional Required Returns", Financial Management 9, 14-1.