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Financial reforms in capital budgeting application
of goal programming approach
Rupina Popli
Advisor, Lloyds Bank, London, UK
G.S. Popli
Delhi School of Professional Studies and Research, Delhi, India
Keywords
Capital Budgeting, Goal Programming, Mathematical Programming, Risk and Return,
Project Management
Abstract
Capital Budgeting is an important aspect of finance which an executive and management
utilises to optimize the investment. In every organization there are different priorities for investment.
Risk and return are two vital aspects to be considered at the time of finalizing an investment option.
There are organizations which pay more attention towards the return while reducing the risk whereas
few organizations do not hesitate to take risk if more returns are expected from the investment. But
the fact remains that there should be a proper balance between the risk and return in any investment
decision.
There is a new dimension to this investment criteria, nowadays, the organizations are
focusing more on applying mathematical programming models for the management systems. There
are several approaches being practiced in this context. Here is a research paper where computing the
maximum return for accepting or rejecting a project is decided with the help of fundamental
programming model by prioritizing the goals. A new approach of computing capital budgeting is
implemented with the help of goal programming. For example, Mobiru proposed the model of Goal
Programming for allocating time and cost in Project Management by using the case in the project of a
construction company.
The basic objective of this research paper is to present a clear picture on how quality can be
brought into finance for getting more precise and better results in the field of capital budgeting. This
research paper has provided a critical review of the Capital Budgeting and an attempt to re-counsel it
with the ground level reality that a finance manager and management faces and which only can be
justified in relation to the earning for the objectives and goals of the organization.
Introduction
Capital Budgeting is a process to determine Institution’s long term investments such as new
projects, purchase of new machines, and change of machinery. This is the process of analyzing investment
opportunities and deciding which project to accept out of many options available. Basically, it deals with
selecting or rejecting a particular project. There are many stake-holders in an organization who are
concerned and effected, willing to invest their funds in any project which is ready to accept certain
amount of risk involved in order to earn a good return. To choose a specific project out of various
opportunities available is really very difficult and tedious work. It is not just only a single project
available all the times; but there remain situations where they have to deal with the multiple projects
available at one time. It is very difficult for a financial executive to choose the right project at the right
time failing which there are chances of collapsing even of a fundamentally sound organization.
The financial executives and the academicians have started using the Goal Programming
Approach in their decision making process, especially in Project Management. The main reason for this is
that there are multiple goals and objectives in project selections viz. budget management, material costs,
completion time and labour related issues. The financial executive is required to accommodate all
relevant matters by optimizing the overall return from the project. Though, the management always
prefer to maximize the returns and minimize the cost, but they have to accommodate the multiple aspects
and views from various stake holders such as regulators, workforce and society at large by setting
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different goals such as product quality, employment stability, industrial and labour relations and CSR etc.
Under these circumstances, a different kind of approach is required to accommodate the interests of
various stake holders and to optimize the multiple goals and objectives associated with a project. That is
the reason that a new technique known as Goal Programming Approach for financial decision making is
evolved.
Purpose of this Paper
The purpose of this research paper is to identify the applications of goal programming technique
of capital budgeting and the methodological aspects for the management and the financial executives and
to generate interest in academicians and researchers. It will motivate and will be very helpful to the
financial executives and the top management to choose a right project for investment by accommodating
all the goals and objectives of stake holders of an organization.
Literature Review
There have been various studies relating to the application of goal programming approach in
capital budgeting, some are mentioned below:
Arthur & Lawrence (1985) developed a model to analyse the make or buy decision. Their approach has
taken into account the multi-product environment, over-time levels and capital utilization effects.
Balachandern & Steuer (1982) developed an interactive model to assist a certified public accounting firm
in audit staff planning. The multiple objectives included such items as maximizing profit, accommodating
bookings, avoiding unnecessary audit staff increases and decreases, minimizing underutilization of staff,
and achieving professional developmental goals.
Callahan (1973) illustrated one goal programming investment planning model with profit and risk or
safety goals.
Charnes, Cooper, & Ijiri (1963), in the area of capital budgeting. They used the goal programming
formulation to show the Balance Sheet extension of break-even analysis.
Fabiane, Neida, & Carlos (2003) applied goal programming to a Brazilian forest problem. The goal
programming model was used seeking to reach the following goals :
Wood Harvest (Pine)
Wood Harvest (auraucaria),
Eva-mate Harvest,
Tourism,
Employees,
Diversity of flora, and
Diversity of Fauna
Gyu & John (2000) applied a goal programming model for project selection and resource planning. The
decision model used is 0-1 goal programming model, which is validated by applying it to case study from
the Woodward Governor Company.
Hawkins & Adams (1974) gave an illustration of goal programming applied to capital budgeting, which
directly incorporated the existence of multiple conflicting goals. Their example model included net
present value, sales and man-hour employment goals.
Hollis (1979) presented a single-period, multicounty goal programming model for centralized corporate
planning utilizing a cash-pooling center, with emphasis on short term investing and financing.
Hong (1981) used a goal programming model including on goals of local finance mix of the firm, earnings
per share, average rate of return, limit on debt financing and legal or other restrictions.
Jagetia & Nelson (1976) gave one example of a goal programming formulation for hospital budgeting
with goals of profit and number of patient days.
Keown & Taylor (1978) presented a general capital budgeting goal programming model for the firm.
Their example has the following goals : net present value, overall sales growth, profit, market share,
public service image, product innovation, limitation of risky ventures, limitation of the degree of
reliability on general economy, management depth and budget expense.
Klock & Lee (1974) suggested a goal programming model for property liability insurance with profit,
current asset returns, and legal bounded goals.
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Kumar & Philippatos (1979) applied goal programming to the investment decision of dual-purpose
funds. An empirical demonstration is provided to show that dual purpose funds managers can improve
their investment selection and subsequent performance by the use of goal programming methodology.
Kombluth (1986) extended that research to show how a “preference” variance could be introduced into
an accounting scheme using goal programming. The preference variance measures the proportion of the
total variance that could or should be attributed to changes in management preference.
Lawrance, Koch, & Burbridge (1976) illustrated an acquisition investment problem in terms of the
following constraints: maximum budget, minimum total earnings and the minimum cash flow. These
have the following goals and priorities: present worth of firm’s goal level of internal rate of return on all
acquisition investments, present worth of firm’s future revenue growth potential, amount of debt
financing for acquisition investments, and amount of assets-to-liability ratio for all acquisition
investments.
Lee and Kim (2000) suggest in their study an improved information system project selection
methodology, which reflects interdependencies among evaluation criteria and candidate projects, by
using network process within 0-1 goal programming model.
Liang (2009) focuses on developing a two-phase fuzzy mathematical programming approach for solving
the multi-objective project management decision problems in a fuzzy environment. The model designed
minimizes simultaneously total project costs, total completion time and cashing costs with reference to
direct costs, indirect costs, contractual penalty, costs, duration of activities, and the constraints of available
budget.
In a sequence of papers, Muhlemann, Lockell, & Gear (1978), Muhlemann & Lockett (1980) and
Harrington and Fischer (1980) examined the problem of multi objective project selection. They developed
a stochastic integer programme with recourse that includes as the objective function weighted linear
combinations of deviations from set values for two goals.
Mubiru (2010) proposed a goal programming model for allocating time and cost in project management.
A construction company case was utilized to illustrate his model.
Masood, Donald, & Dona (2001) developed a project selection model for which service institutions that
incorporated research and development, investment plans, capital budgeting etc. The decision model
used is 0-1 goal programming model, which is validated by applying it to a real project selection data.
Mukherjee & Bera (1995) examined the project selection decision by using the technique of goal
programming. The model was applied to Indian Coal Mining Industry. The model identifies five goals :
Capital Investment Goal
Cost of Production Goal
Profit Goal
Manpower Goal
Demand Goal
O’ Leary and O’Leary (1981) developed a goal programming model for the cash management problem.
Their model extended the basic single-objective cash management formulations to include multiple
objectives.
Sheshai, Harwood, & Hennanson (1977) assumed a piecewise linear variable cost function and a step
function for fixed cost. They used zero-one integer programming to compute break-even point for a two-
product example with a no-priority goal situation.
Sealey (1977), (1978), developed a goal programming bank financial planning model with the following
goals: profit, capital adequacy ratio. This model also has the following constraints: capacity adequacy,
diversification, required reserves and balance sheet.
Trennepohl (1975) showed an application of goal programming to bank asset management with the
following goals in the same priorities: meet Federal Banking Regulations, achieve adequate safety in the
bank’s investments, achieve adequate liquidity in the bank’s assets, achieve certain characteristics of the
loan portfolio, achieve certain characteristics of the securities portfolio and obtain a certain level of
earnings from the investments.
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Practices in Capital Budgeting
At present the financial executives have been applying various undernoted techniques to choose
one project out of various options available to the organisation. The most common practice among all is
by applying the Net Present Value technique of Capital Budgeting. With the help of this technique, the
financial executives decide upon accepting or rejecting a particular project. However, there are also
various techniques available to a finance manager for choosing a particular project. Here, we will discuss
in brief the various techniques of capital budgeting.
Capital Budgeting Tools
Net Present Value (NPV)
Pay Back Period
Internal Rate of Return (IRR)
Average Rate of Return (ARR)
Profitability Index (PI)
Net Present Value (NPV)
Every technique of Capital Budgeting is involved with cash outflows and cash inflows. This is the
latest and modern method of evaluating capital investment proposal. In this method, the time value of
money is calculated by taking into account the present value of future cash inflows and deducting from
this the net cash outflows. It helps in finding out the exact amount of return from a project. In simple
terms, the net present of all inflows and outflows of cash during the entire life of the project is calculated
separately for each year by discounting all the inflows by the organization’s cost of capital. Some
organizations consider NPV as the best way of choosing a particular project for investment. The thumb
rule for this approach is to find out whether the NPV is positive or negative. If it is positive, accept the
proposal for investment otherwise reject it out rightly.
Pay Back Period
In this method the finance executives focus on the duration or the period by which the
organization will get back their full cost of the initial cash outflows or the capital expenditure incurred for
a particular project. This method is based on the premise of capital expenditure pays itself back over a
number of years. Here, the organisation sets a certain target period during which they must receive their
money invested in the project back. If a particular project depicts the payback period less than the period
set out by the organization, then it is accepted otherwise rejected then and there only. If there is an option
of more than one project available to the organisation, then the project with less payback period will be
preferred but this is not the sole criteria of choosing any project. The return of the project is also calculated
for consideration. However, in practice it depends upon organization to organization to choose a project
having more payback period as per the organizations capability to bear the burden.
Internal Rate of Return (IRR)
The IRR technique is considered as the best technique by majority of the finance executives. As
per this technique the company fixes a rate for the project and if the rate of return on investment is more
than this rate, then they go for the project. In simple terms, the rate at which the sum of discounted cash
inflows equals the sum of discounted cash outflows is known as the internal rate of return. For
computing this internal rate, the present value of the cash inflows is equated with the present value of
cash outflows then the interest rate is calculated. This interest rate is applied with the benchmark rate/the
expected rate of the organization. The assumption under this technique is that intermediate cash inflows
generated by a particular project are reinvested at the rate of internal return. If this rate is more than or
equals to what company has anticipated, then they select the project otherwise it is rejected.
Average/Accounting Rate of Return (ARR)
This technique computes the average of averages i.e. average income/average investment. This
method is popularly known as Accounting Rate of Return as the accounting statements are used under
this technique to measure the profitability level of the projects. Various proposals available with the
organisation are ranked in order to their earnings. The project of higher rate of return is selected. The
decision rule using this technique is same as that of IRR. The Average Rate of Return should be more than
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the rate set by the company and for mutually exclusive projects, the one having more ARR should be
preferred. However, this technique leads to a lot of vague figures as such the ARR is considered quite
obsolete and not being taken serious and practiced by most of the finance executives nowadays.
Profitability Index (PI)
This method is upgraded version of the Net Present Value technique of Capital Budgeting and
also known as the Benefit Cost Ratio. It computes the ratio between present values of each cash inflows to
cash outflows. If the PI is greater or equal to 1 then, the project is accepted otherwise rejected. If there are
more than one project available with the organisation (mutually exclusive project) they should go for the
project having greater PI.
In all the methods discussed above in brief, the present value is computed at a discount rate. This
discount rate is also known as hurdle rate in accounting circle. The NPV of a project depends a lot on this
discount rate decided by the company. The discount rate is computed as per the prevailing market
conditions perceived by the financial executives and the top management. This discount rate should also
take into account and measure the risk involved and the volatility of the market. The hurdle rate is
sometimes referred to as cost of capital or cost of debt or cost of equity. A finance executive applies
various methods for computing this rate as the CAPM or APT and WACC. The choosing of right rate is
very important for any organisation failing which they will have to incur huge loss. Therefore, it is very
important to choose the right rate at the time of selecting any project.
Problems in Current Tools of Capital Budgeting
There are many problems being faced by the practioners in the application of current techniques
of Capital Budgeting. The major problem is that an organization using more than one parameter in
selecting a project ultimately ends up in getting itself confused instead of getting a proper solution. The
various techniques of capital budgeting mentioned above is that all focus on the different aspects of a
project. As such, the financial executives have to select and go as per only one technique of capital
budgeting. While doing this, they have to sacrifice the results derived from some other tool of capital
budgeting. The techniques applied by the finance executive deals only with limited parameters. That is,
it only computes the whole project as per the given rate of an organization’s expectation and some
additional measures or criteria or they fix a higher or lower limit, then the available tools of capital
budgeting are not able to provide the solution of the goals of the organization. For example, if there are
two different shares of companies which an organization intends to buy but both the shares are associated
with different amount of risk as well as returns attached with it. Suppose, the objective of a company is to
attain a minimum amount of return cannot satisfy their goal as it has restricted itself from taking the risk
beyond a minimum amount of risk as well as returns from it. In such a scenario, there would be several
combinations possible for choosing these shares. Here, the methods suggested for above mentioned
scenario will definitely not satisfy the goals of the company.
Further, there is much beyond just risk and return concepts associated with the project of an
organization. Nowadays some projects are undertaken for improving the brand image of an organization.
As such, in this case the method mentioned above will not be able to satisfy the required objective while
selecting the best project which will satisfy the overall criteria according to priority of the organisation.
The available techniques of capital budgeting will create a lot of conflicts at the time of choosing a project.
These methods are supposed to be handled with a lot of care and precautions as NPV and IRR sometime
depict different opinions about a project which may ultimately result in confusion for a finance manager.
There are also problems, if an organization intends to attach some more criteria in selecting a right project.
There may be several other objectives an organization intends to achieve, to be incorporated while
selecting a project which cannot be computed with the prevailing techniques of capital budgeting. As
such, the new approach of goal programming has been derived to provide solution to all the problems
discussed above.
Development of New approach Goal Programming
The Goal Programming Approach of Capital Budgeting is an advanced linear programming
technique used for providing a solution for the problems related to multi criteria decision making system.
Each of these criteria measures is provided a goal or target value which is expected from the project.
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Unwanted deviations from the process of target values are minimized or maximized in an achievement
function. This can be a vector or a weighted sum dependent on the goal programming variant used by
the financial executive.
Steps Involved in Goal Programming Approach
Step 1 : Identify the goals and constraints that may create hurdles in achieving the goals.
Step 2 : Determine the priority level of each goal with P1 is very important, P2 is next most important
and so on.
Step 3 : Define the decision variables.
Step 4 : Formulate the constraints using LP procedure.
Step 5 : Develop goal equation for each goal with right hand side specifying the target goal. Deviation
Variables d 1 + d 1 are included in each goal equation to reflect possible deviations from the
Target values i.e. above or below.
Step 6 : Write the objective function in terms of minimizing or maximizing a prioritized function of the
Deviation variables.
Goal Programming Approach for Capital Budgeting
We can accommodate and solve the problems related to various goals and objectives desired by
the stake-holders of an organization. The way we can develop this model is by first set various goals and
objectives for selecting a project out of various options available with the organization. We can divide our
discussions in two parts i.e. the first one dealing with clubbing of all the capital budgeting tools through
goal programming and second one by dealing with new parameters to select a project using goal
programming approach. Let’s discuss each part of this model in brief.
Inclusion of New parameters into Goal Programming Model
We can understand this model with the help of an example. Suppose, the process of selecting
projects in an organization is based upon certain parameters such as, the risk associated with the project,
returns expected from it, Pay Back Period of the project and the extent of social service presumed to be
performed through this project. Here, we have four goals and objectives expected to be fulfilled from a
particular project. We will now have to accord our priority to the goals decided by an organization, after
consultation with all the stake-holders. Now, let’s presume that the risk is on the top of priorities fixed by
this organisation, then the returns from this project, third is Pay Back Period and the last one is related to
the level of social work expected from this project.
Suppose, the organisation has six projects in hand to select from, then we can choose the best one
by applying various combinations. In Goal Programming, the goals with higher priority are expressed as
priority level 1 goal, i.e. risk, and the secondary goal as priority level 2 goal i.e. returns and so on. This
type of prioritizing procedure is known as pre-emptive priorities because the decision maker will not
sacrifice any portion of target of the priority level 1 for priority level 2. In goal programming with pre-
emptive priorities, trade-offs between higher and lower level goals are never permitted.
Then after prioritizing of the objectives and the goals of an organisation, goal equations and
constraints are developed by the financial executive. This is done just like as is done in linear
programming. The difference is just that here we form equation of the priority based upon the deviations.
For example, if we are talking about the level 1 goal i.e. risk, then deviations will be d1+, d1-, where :
d1+ = The amount by which the portfolio/ project risk index exceeds the target.
d2- = The amount by which the portfolio/project risk index is less than the target.
Now, after finding the deviations, these will be converted into equations. If risk associated with
each of the six projects are 0.50, 0.25, 0.75, 0.60, 0.40 and 0.10 and suppose the risk index is 1000, then the
goal equation will be subject to following constraints :-
0.50A + 0.25B + 0.75C + 0.60D + 0.40E + 0.10F - d1+ +d1- = 1,000
Where, A, B, C, D, E and F are various projects.
The objective function will be minimizing the deviation that exceeds the risk. Thus, our objective
function would be represented as :
Minimise d1-
This is just an example to express the goal equation formulated as level one, likewise other level
goals are written in each kind of equation and then total of all the equations are merged by forming a
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unique equation for the whole project. To complete the formulation of the model, we must develop a goal
equation for each goal. Thus, for the above mentioned example, our objective function will be as under
Minimise P1(d1) + P2(d2) + P3(d3) + P4(d4)
Where, P1, P2, P3 and P4 represent goals and objectives of the organisation at priority level 1, 2, 3
and 4 respectively. As mentioned above d implies positive and negative deviations from the goal at
various levels. By solving the equation, we can easily come to a point for selecting projects and this is
very helpful in solving the equations. We can easily come to a point for selecting projects and this is very
helpful in Portfolio Management. These equations can be easily solved by using excel and specially
developed software package.
Application of Goal ProgrammingModel
The goal programming approach of capital budgeting can be utilized effectively in many areas of
financial management as mentioned below :-
Corporate Budgeting and Financial Planning
Working Capital Management
Capital Budgeting
Financing Decisions
Mergers, Acquisitions and Divestitures
Investment Planning / Portfolio Selection
Commercial Bank Management
Insurance Management and Pension Fund Management
Scheduling Financing Staff
Interest Rates and Risk
Government and Public Firms
Accounting Control
Research work on Goal Programming Applications by Basic Application Areas *
S.No.
Application Area
Author
1.
Corporate Budgeting and
Financial Planning
Charnes et al (1983), Turk and Seliman (1981), Guerad and Lawrence (1987), Hindelang and
Krishnamurthy (1985), Jagetia and Nelson (1976), Kvanli (1980), Kvanil and Buckley (1986),
Lawrence et al (1981), Mulvey (1987), Nunamaker and Truilt (1987), Shashei et al (1977).
2.
Working Capital
Management
Cos (1981), Hollis (1979),Keown and Martin (1977), O’Leary and O’Leary (1981),
Phililippatos and Christofi 91984), Rakes and Franz (1985), Sartoris and Spruill (1974).
3.
Capital Budgeting
Bernhard (1980), Bhasker (1979), (1980), Bhasker and McNance (1983), Chateu (1975),
Gonzales et al (1987), Hawkins and Adams (1974), Ignizio (1976), Keown and Taylor (1978),
Lin (1976), Mervile and Tavis (1974), Spahr et al (1987), Thanassoulis (1985).
4.
Financing Decisions
Arther and Lawrance (1985), Ashron (1985), (1986), Jones (1979), Maimon and Porter (1987).
5.
Mergers, Acquisitions and
Divestitures
Charnes et al (1988), Fowler and Schnniederjans (1987), Lawrence et al (1976).
6.
Investment Planning/
Portfolio Selection
Callahan (1973), Harrington and Fisher (1980, Kumar and Phillapattos (1979), Kumar et al
(1978), Lee and Chesser (1980), Lee and Lerro (1973, (1978), Muhlemann (1978), Mulhemann
and Lickett (1980), Shar and Musser (1986), Stone and Reback (1975).
7.
Commercial Bank
Management
Booth and Dash (1977), Fortson and Dince (1977), Keown (1978), Lam and Karwan (1978),
Lee et al (1971), Sealey (1977), Sealey (1977), (1978), Tremepohi (1975), Turshen and Nolley
(1987).
8.
Insurance Management
and Pension Fund
Management
Drudell (1977), Gleason and Lilly (1977), Klick and Lee (1974), O’Leary and O;Leary (1987).
9.
Scheduling Financial Staff
Balachandran and Seauer (1982).
10.
Interest Rates and Risk
Booth and Ressier (1989), Boquist and Moore (1983), Gressis et al (1985), Hong (1981).
11.
Government and Public
Firms
Channes et al (1988), Gueard and Buell (1984), Jackman (1973), Joiner and Drake 91983),
Keown and Martin (1976), (1978), O’Leary and O’Leary (1982), O’Leary (1990), Olive (1981),
Taguchi et al (1983), Trivedi (1981), Wacht and Whatford (1976), Wallenius et al (1978).
12.
Accounting Control
Kaornbluth (1985), (1986), Lee (1979), (1986).
(Taken from Research Paper on Goal Programming Application by Basic Application Area by Lin &
O’Leary, 1993)
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Clubbing Current Capital Parameters into a Goal Programming Model
The major problem with the current techniques of capital budgeting was that the Finance
Executive used to get confused at the time of using more than one tool. This issue now can be easily
handled and resolved by applying this model as he can now apply easily, all the techniques of capital
budgeting for finding the best project out of all the projects available with the organisation. Suppose, we
want to consider a project by considering NPV, IRR, Pay Back Period, ARR and Profitability Index and
our priority remains as per ascending order i.e. NPV, IRR, Pay Back Period, Profitability Index and ARR.
Then our objective function of Goal Programming Model will be as follows :-
Minimise P1(d1-) + P1(d2-) + P3(d3+) + P4(d4-) + P5(d5-)ere,
P1, P2, P3, P4 and P5 represent goals at priority level 1,2,3,4 and 5 respectively.
d1- = The amount by which project is having a present value of each cash inflows less cash out follows.
d2- = The amount by which the project is having IRR less than the hurdle value.
d3+ = The amount by which project is having Pay Back Period greater than the required period.
d4- = The amount by which project is having P1 less than the desired index.
d5- = The amount by which project is having ARR less than the hurdle rate or discount rate.
Now, the whole problem in finding the best project can be solved by the finance executive by using this
equation under Goal Programming. We can arrive at the best project that will optimize the objective
function. We have already discussed above about how to solve this equation.
Note : In the above cases, we have shown you the objective function by minimizing the deviations
that reduces from attaining maximum profits. The same thing can be done to maximize the deviation that
helps in achieving our goal. The whole objective function can be formulated so as to maximize the
deviations accordingly.
Advantages of Goal Programming Model
The major advantage of this Goal Programming approach is that it also takes into consideration
all other aspects of the projects/ investments/portfolios. Such as the extent of benefits expected from the
project for public welfare, branding the project and economically soundness etc. There is yet another
major benefit using this model that is it prioritises the goals as per the expectations of various stake
holders who help in selecting the project, without any conflict. The prioritization is done purely on the
basis of each stake holder, which helps in producing the desired results through customization. This
customization will solve the major problems of the organization in selecting the projects which they used
to face at the time of using IRR and NPV methods of capital budgeting.
Conclusion
Use of Goal Programming Approach over the conventional methods of capital budgeting will
prove to be very useful for organizations having multiple objectives to handle at the time of selecting the
best suited project out of various options available. It is quite easy to apply, once this method is
understood properly. This model provides an opportunity to the finance executives and the management
to prioritize the risk and return as per their requirement which helps in solving the problems being faced
by them because of various compulsions in the organisation.
The Goal Programming Model appears to be an appropriate, powerful and flexible tool for
decision making for a modern decision maker who is burdened with achieving multiple conflicting goals
under complex environmental constraints. This approach does not attempt to maximize or minimize the
objective function directly, as in the case of Linear Programming technique but focuses on
accommodating the goals and objectives of all the stake holders of an organization. This new approach of
capital budgeting tries to minimize the deviations observed between the desired goals and the actual
results to be achieved as per the assigned priorities in an organization.
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Multiple Objectives. Accounting Review, 57(1), pp. 125-139.
Callahan, J. (1973). An Introduction to Financial Planning through Goal Programming. Cost and Management, pp. 7-12.
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