A goal programming approach to the study of optimal capital structure in the context of Indian corporate firms

International Journal of Management (IJM)
Volume 11, Issue 3, March 2020, pp. 193–207, Article ID: IJM_11_03_021
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A GOAL PROGRAMMING APPROACH TO THE
STUDY OF OPTIMAL CAPITAL STRUCTURE IN
THE CONTEXT OF INDIAN CORPORATE
FIRMS
Uma Charan Pati
Assistant Professor, School of Economics,
Gangadhar Meher University, Amruta Vihar, Sambalpur, Odisha, India &
Ph.D. Scholar in Sambalpur University, Sambalpur, Odisha, India
Sudhanshu Sekhar Rath
Former Vice Chancellor, Gangadhar Meher University,
AmrutaVihar, Sambalpur, Odisha, India
ABSTRACT
The capital structure controversy debate is still to die down even after five decades
of its birth from the seminal work by Modigliani and Miller in 1958. The irrelevance
theorem was proved wrong by many later day theorists/empiricists but many
postulated it otherwise. The existence of an optimal capital structure in the corporate
sector has been debated extensively and non-conclusively too. The present study has
been conducted to check the possible existence of an optimal capital structure in the
Indian corporate sector. Besides other descriptive statistical techniques, the linear
goal programming technique has been used to study whether the optimality objective
is achieved by the thirty companies selected from private, public and IT sectors. The
goal programming results show the non-existence of something called an optimal
capital structure and instead corporate firms are inclined towards achieving multiple

objectives/goals at a time and hence not optimizing rather satisfying level of
achievement at multiple ends is the goal in the present globalised era of fierce
competitions.
Keywords: Corporate Finance, Goal Programming, Satisfying Behavior, Multiobjective goal setting
Cite this Article: Uma Charan Pati and Sudhanshu Sekhar Rath, A Goal
Programming Approach to the Study of Optimal Capital Structure in the Context of
Indian Corporate Firms, International Journal of Management (IJM), 11 (3), 2020, pp.
193–207.
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A Goal Programming Approach to the Study of Optimal Capital Structure in the Context of Indian
Corporate Firms

1. INTRODUCTION
The entire financial management literature is dominated by the capital structure controversy
debate being initiated with the irrelevance theorem of Modigliani and Miller. A broad
theoretical review brings forth the idea that the debate has not yet got settled. Movement from
the MM hypothesis of capital structure irrelevance to the relevant MM hypothesis of 1963
followed by the trade-off theory and finally the pecking order theory reveals that the debate is
still going on.
Based on the whole analysis of the capital structure debate, in this study effort has been
made to explore the possibility of the existence of an optimal capital structure in the Indian
corporate sector. The whole study and analysis in this particular study has come down to the
point that there is no specific or targeted capital structure that firms do follow across different
sectors. However, there have been studies conducted to ascertain the possible impact of

capital structure on the performance of the corporate firms. Taking cues from those theories
and studies we have tried to explore the possible impacts of the capital structure of a company
on its performance by using different inferential statistical analysis including the technique of
Goal programming followed by the ANOVA and the F test.
If we move deep into the theoretical premises on capital structure principles we find that
almost all the theories have come to the conclusion that there is no concrete inference that can
be drawn as regards the existence of something called an optimal capital structure. It has been
proved by Nassar, S., (2016) , Marmara University, Institute of Social Science, Accounting
and Finance Department, Istanbul/Turkey in his research work titled “The impact of capital
structure on Financial Performance of the firms: Evidence From Borsa Istanbul” . By taking
136 Industries as a sample, and by using multivariate regression analysis including ” Return
on Asset (ROA), Return on Equity (ROE) and Earning per Share (EPS) as well as DebtEquity Ratio (DR) as capital structure variables, he has derived the conclusion that there is a
negative significant relationship between capital structure and firm performance.” Some other
studies have also confirmed the existence of this particular relationship.

1.1 Relationship between the Capital Structure and Firm’s Financial
Performance: A Theoretical Analysis
As has already been referred earlier, there is a great debate started with the MM Hypothesis
on the relevance of a capital structure and its impact on the financial performance of corporate
firms.
Right from the Modigliani and Miller Theory of 1958 and then 1963, followed by the
traditional theory, the trade-off theory and the Pecking Order theory upto the Managerial
Entrenchment theory, we find that there is no general rule or formula of an optimal capital
structure and for that matter there is no significant impact found in the relationship between
the capital structure and the firms‟ financial performance.
By basing our study on all the above mentioned theories and our own results where we
have found that most of the firms are more flexible towards equity instead of debt in their
capital structure and there is no target debt-equity ratio set out by any firm for that matter, we
have made use of different statistical techniques such as Goal programming, F statistics and
ANOVA to test a few hypotheses as regards the existence of such relationships.

1.2. Data Analysis & Interpretation
This section of the research deals with the data analysis and the interpretation of these data
with the help of various statistical methods. In this analysis section a total of eight hypotheses
have been tested. To test the hypotheses, we have collected financial information and these

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were categorized under different heads with the aim to test them. The data collected were all
from financial reports available in public domain. In this section the basic information
gathered were secondary in nature and their authenticity lies with the sources from where they
were collected. The data collected for the research are from audited balance sheets makes it
more reliable and authentic source of information on which our research is rested upon.

2. BACKGROUND TO STATISTICAL AND ECONOMETRIC
METHODS USED
In this research work three different methods of data analysis have been used. First one is Ftest, second one is OLS regression method and the third one is the Goal Programming
technique. The Goal Programming technique is an advanced method to prioritize the goals
that corporate firms aim at. It is a technique which ranks goals as per the priorities of the firm
and therefore it is a multi-objective goal determination technique based on satisfying behavior
of managers of corporate firms in the modern world.
In this regard the Goal programming is an extension of linear programming in which
targets are specified for a set of constraints. In goal programming technique there are two
basic models such as the Pre-emptive model (lexicographic) and the Archimedean model. In

the case of the pre-emptive model, goals are ordered according to their priorities. The goals at
a certain priority level are considered to be indefinitely more important than the goals at the
next level. In the pre-emptive case we try to meet as many goals as possible taking them in
priority order. In our study, we have used the pre-emptive Goal programming method in
which the goals are ranked from most to least important. At the beginning, we found the
optimal value of the first goal. Once we have found this value, we turn this objective
functions into a constraints such that its value does not differ from its optimal value by more
than certain amount.

3. THE USEFULNESS OF F-TEST
In this research study the simple F-test has been used when we want to test the equality of
variances of two nominal populations. In such a situation, the null hypothesis happens to be
H0:σ2p1= σ2p2, σ2p1 and σ2p2 represents the variances of two normal populations. This
hypothesis is tested on the basis of sample data and the test statistic F is found, using σ2s2 and
σ2s1. The F value can be obtained in the following way;

The objective of F-test is to test the hypothesis whether the two samples are from the same
normal population with equal variance or from two normal populations with equal variances.
The F-test was initially used to verify the hypothesis of equality between two variances, but is
now mostly used in the context of analysis of variance.

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4. ADOPTING THE GOAL PROGRAMMING METHOD
The Linear goal programming is one of many techniques for dealing with the modeling,
solution, and analysis of multiple and conflicting objectives linear problems. This type of
multi objective linear problems requiring a goal programming solution have been expanded
and defined considerably since Charnes and Cooper [1961] introduced the concept of „Goal
programming‟ specially used for solving multiple objective decision making problems
(MODMP). It has been studied by many researchers and successfully applied to many diverse,
real life problems. Now it has been accepted as a basic mathematical programming method
for solving multiple objective decision making problems (MODMP). Pre-emptive goal
programming is a special case of goal programming, in which the most important (upper
level) goals are optimized with before least important goals. In non-pre-emptive models, the
goals are assigned weights and considered simultaneously.
Decision makers sometimes set achievable goals even within the limits of available
resources. These problems are solved using objective programming methodology, where the
objective function is established in such a way that all of the objectives are to be achieved.
There are some other methods adopted in searching for multiple objectives like the constraint
method, weighted method, goal programming, and interactive methods. In the -constraint
method, the decision maker specifies acceptable levels of all but one objective function. The
restrictive approach in goal programming method specifies acceptable levels in all useful
activities except the decision maker; these values are used as constraints and the problem is
solved as a single criterion optimization problem. In the weighted method, the decision maker
specifies the relative weight for each of the objectives, and the problem is solved as a single
criterion problem. When developing targeted programming, decision-makers specify the
priority of objective tasks. The problem is first addressed to the highest priority, and then this
value is never eroded. The problem will be resolved for the next priority until it is resolved. In
an interactive way, the decision maker is not prioritized for one or more solutions at the same
time and asks him to choose one. If the decision maker is satisfied with the solution, the
process stops; otherwise, the decision maker specifies the desired changes in the value or
address of the objective functions and the problem is resolved. The decision maker does not
find any acceptable solution until the process continues and acceptable solution is reached.

The goal programming approach allows a simultaneous solution of a system of complex
objectives rather than a single objective. In other words, goal programming is a technique that
is capable of handling decision problems that deals with a single goal, with multiple sub
goals. In this research work the primary function is to find the result of the following
assumptions;
 Companies failed to become successful in minimizing the level of fixed cost over the
years.
 Companies failed to become successful in Maximizing the level of Earning After Tax
(EAT) over the years.
 Companies failed to become successful in minimizing the level of long term debt over
the years.

4.1. Usefulness of Weighted Goal Programming Model
A research Goal programming models were improved to more accurately reflect the decision
environment they were designed to model, complications inevitably arose. One complication
concerned the weighting of goals in the objective function. Ignizio [1976], the problem that
arose was finding a valid mean by which one calculates representative weightings. One
approach to avoid this difficulty is to eliminate the mathematical weighting from the model.

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With this approach, a goal programming problem becomes a lexicographic problem. The
goals in the lexicographic problem are not differentiated by a weighting system, but instead
are ordinals ranked in order of preference.

To solve the lexicographic goal programming problem, decision makers have a choice of
two approaches:
(1) The multi-phase simplex methods, or
(2) The sequential linear goal programming methods.
The two most common versions of the multi-phase simplex method are by Lee [1972] and
Ignizio [1976, 1982]. The sequential linear goal programming method's major feature is that it
allows goal programming problems to be run on conventional linear programming computer
programs. Kornbluth [1973] originally described the sequential linear goal programming
algorithm, while Arthur and Ravindran [1978] improved its efficacy, and Kwak and
Schniederjans [1985] gives an alternative solution.

4.2. Generic Weighted Goal Programming Model
The weighted goal programme variant allows for direct trade-offs between all unwanted
deviational variables by placing them in a weighted, normalized single achievement function.
Weighted goal programming is sometimes termed non pre-emptive goal programming in the
literature. If we assume linearity of the achievement function then we can represent the linear
weighted goal programme by the following formulation:

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4.3. Usefulness of Pre-emptive Goal Programming Model
A large number of real world decision-making and optimization problems are actually multiobjective. Even so, many important optimization models, such as linear programming models,
require that the decision maker express his/her wishes as one aggregate objective function that

is usually subjected to some constraints.
Goal programming (GP), generally applied to linear problems, deals with the achievement
of prescribed goals or targets. Both academicians and practitioners have embraced this
technique. The basic purpose of goal programming is to simultaneously satisfy several goals
relevant to the decision-making situation. To this end, a set of attributes to be considered in
the problem situation is established. Steps for the Pre-emptive Goal Programming algorithm
are provided in Table and Figure followed by the above table depicts the flow chart of the
overall algorithm.

4.4. Hypotheses Testing
Hypothesis: -1
Null Hypothesis (H0): EBIT do not have direct impact on EPS of the companies
Since this hypothesis discusses the relationship between two variables in which one variable
is dependent and the other is independent, it was observed that the EPS is the dependent
variable and the EBIT is the independent variable. To test this hypothesis, the following
equation was prepared.
Y=β+αxi+εi
(Eq.-1)
Table 1
Impact of EBIT on EPS
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Source: Secondary Compiled Data

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0.320956827

0.103013285
0.069791555
27.43920345
29

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Uma Charan Pati and Sudhanshu Sekhar Rath
Table 2

The above table 2 provides the information on the multiple R, which is the correlation
coefficient between two variables i.e. EBIT and EPS. It is observed from the above table that
there is the positive linear relationship exists but the relationship is very weak i.e. 32%. The R
squared value says that only 10% of the value falls on the regression line. In other words,
10% of the values fit the model.
Steps
1
2
3

4

5

Action
Embed the relevant data set. Set the first goal set as the current goal set.
Obtain a Linear Programming (LP) solution defining the current goal set as

the objective function.
If the current goal set is the final goal set, then set it equal to the LP objective
function value obtained in Step 2, and STOP. Otherwise, go to Step 4.
If the current goal set is achieved or overachieved a. set it equal to its
aspiration level and add the constraint to the constraint set, Go to Step 5. b.
Otherwise, if the value of the current goal set is underachieved, set the
aspiration level of the current goal equal to the LP objective function value
obtained in Step 2. Add this equation to the constraint set. Go to Step 5.
Set the next goal set of importance as the current goal set. Go to Step 2

From the ANOVA table it can be interpreted that the F value is more than the F critical
value (i.e.3.101>0.090).Thus it can be concluded that the alternate hypothesis can be accepted
and the null hypothesis is rejected i.e. EBIT do not have direct impact on EPS of the
companies is rejected. Thus it is to state that EBIT do have direct impact on EPS of the
companies.
In this research thesis it is to suggest that the combination weights method and preemptive method have been used to construct the model. These two methods or algorithms
convert multiple goals into a single objective function. This technique is known as the goal
programming technique (Taha, 2003). A goal programming model was developed in this
research to obtain the optimal solution of goals. Goal programming was to test the hypothesis
2, 3 and 4 and for this the goals and constraints must be involved to formulate the model.

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Table 3

The objective function of the weight goal programming model is a single objective
function of the weighted sum of the functions representing the goals of the problems. The
model is given as:
Minimize Z = ∑ (

)

(Eq.-2)

Where,

gi

∑

Here,
X k,

(Eq.-3)
≥0

Here the xk is the decision variable for k=1,2,3,4…m, αik represents the parameter of the
decision variable, w +¦i and w -¦i are weights for i=1,2,3,---n, the deviational variables are
represented by d +¦i while d -¦i and gi are the self-improving or aspirational value. Kwak et al.
in 1991 proved that the weighted lexicographic goal programming model is a combination of
weighted goal programming and pre-emptive goal programming methods, cited in Ekezie and
Onuohac, (2013) and the model is given as:
Minimize Z = ∑

Pi∑

Here,
Pi is the preference.

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Uma Charan Pati and Sudhanshu Sekhar Rath
Table 4
Summarised table for different financial parameters (in 1000 crore)
ITEMS
year
Average of
Average of
Average of
TOTAL
fixed cost
Long term debt
EAT
2004
1.17501
2.33097
1.30068
4.80666
2005
1.27837

2.48011
1.86045
5.61893
2006
1.50136
3.26631
1.16574
5.93341
2007
1.73873
4.22307
2.15585
8.11765
2008
2.04598
4.86209
2.37583
9.2839
2009
2.51333
4.40505
2.11337
9.03175
2010
2.97686
5.03901
2.68101
10.69688
2011
3.58847

8.00286
2.94792
14.53925
2012
3.97386
10.26757
3.08058
17.32201
2013
4.57059
11.36983
3.41727
19.35769
2014
5.35666
13.94381
3.54186
22.84233
2015
6.10339
14.94521
3.42497
24.47357
2016
6.76886
16.18484
3.01317
25.96687
2017
7.60411

15.44639
4.46642
27.51692
2018
8.56562
16.91827
4.99898
30.48287
TOTAL
59.7612
133.6854
42.5441
235.9907
Source: Secondary Compiled Data

The decision variables are:
X1= the amount of financial statement in year 2004
X2= the amount of financial statement in year 2005
X3= the amount of financial statement in year 2006
X4= the amount of financial statement in year 2007
X5= the amount of financial statement in year 2008
X6= the amount of financial statement in year 2009
X7= the amount of financial statement in year 2010
X8= the amount of financial statement in year 2011
X9= the amount of financial statement in year 2012
X10= the amount of financial statement in year 2013
X11= the amount of financial statement in year 2014
X12= the amount of financial statement in year 2015
X13= the amount of financial statement in year 2016
X14= the amount of financial statement in year 2017

X15= the amount of financial statement in year 2018
The Goal constraints:
1.17501X1+1.27837 X2+1.50136 X3+1.73873 X4+......+8.56562 X15 ≤ 59.7612 (Fixed cost
Constraint)
2.33097 X1+2.48011 X2+3.26631 X3+4.22307 X4+......+16.91827X15 ≤ 133.6854 (Long
term Debt Constraint)
1.30068 X1+1.86045 X2+1.16574 X3+2.15585 X4+......+42.5441X15 ≥42.5441 (EAT
Constraint)
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A Goal Programming Approach to the Study of Optimal Capital Structure in the Context of Indian
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X1,X2,X3,X4,----X15, d +¦1,d +¦2,d +¦3,d +¦4,------ d +¦15,d -¦1,d -¦2,d -¦3,d -¦4 ---- d -¦15
(non-negativity constraint)
Objective function:
Minimum:P1(d -¦1):maximize the EAT+P2(d +¦2): Minimize the Long term Debt + P3 (d
+¦3): Minimize the fixed cost
In all the below three cases, the LINGO Software version 12 was used to obtain the
optimal solutions. The findings of goal achievements are illustrated in the Table below.
Table 5
Goals achievement
Goals priority
Output value
P1
0

P2
0
P3
0
Source: Compiled data from goal programming results

Goals Achievement
Goals fully achieved
Goals fully achieved
Goals fully achieved

Hypothesis: -2
Null Hypothesis (H0): Companies failed to become successful in minimizing the level of
fixed cost over the years.
In this case we have taken the average of fixed cost of all the 30 companies even if they are
operating in different sectors to make the research more feasible and result oriented.
Since P3 =0 it can be interpreted that the alternative hypothesis is accepted and the null
hypothesis is rejected. It is in conformity of the results that we have derived for all the firms
across sectors that companies are more oriented towards equity funding than debt funding.
Hypothesis: -3
Null Hypothesis (H0): Companies failed to become successful in maximizing the level of
EAT over the years.
In this case we have taken the average of total liability of all 30 companies even if they are
operating in different sectors to make the research more feasible and result oriented
Since P1 =0 it can be interpreted that the alternative hypothesis is accepted and the null
hypothesis is rejected. It implies that companies have succeeded in maximizing the level of
EAT over the years.
Hypothesis: -4
Null Hypothesis (H0): Companies failed to become successful in minimizing the level of
long term debt over the years.

In this case we have taken the average of long term debt of all 30 companies even if they are
operating in different sectors to make the research more feasible and result oriented
Since P2 =0 it can be interpreted that the alternative hypothesis is accepted and the null
hypothesis is rejected. Thus, it is clear that companies have succeeded in minimizing the level
of long term debt over the years. Hence, the modern day firms have multiple goals to aspire
for due to the presence of bounded rationality and imperfections of various kinds in
association with asymmetric information.
Hypothesis: -5
Null Hypothesis (H0): There is no significant relationship exists between average Net sales
and EAT
It was observed that the EAT is the dependent variable and the average Net sales is the
independent variable. To test this hypothesis, the following equation was prepared.
Y=β+αxi+εi
(Eq.-2)
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Uma Charan Pati and Sudhanshu Sekhar Rath
Table 6
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Source:Compiled data

0.470131335
0.221023472
0.192172489
3462.865727
29

Table 7

The above table 6 provides the information of multiple R, which is the correlation
coefficient between two variables i.e. EAT and Net Sales. It is observed from the above table
that there is the positive linear relationship exists but the relationship is relatively weak i.e.
47%. The R squared value says that only 22% of the value falls on the regression line. In
other words, 22% of the values fit the model.
From the ANOVA table 7 it can be interpreted that the F value is more than the F critical
value (i.e. 7.661>0.010).Thus it can be concluded that the alternate hypothesis can be
accepted and the null hypothesis is rejected i.e. there is no significant relationship exists
between average Net sales and EAT. Thus it is to state that there is significant relationship
exists between average Net sales and EAT.
Hypothesis: -6
Null Hypothesis (H0): There is no significant relationship exists between EPS and ROE.
Table 8

Mean
Variance
Observations
Df
F
P(F<=f) one-tail
F Critical one-tail
Source:Complied data

F-Test Two-Sample for Variances
EPS
42.12964
924.288
30
29
1.73438
0.072022
1.860811

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ROE
18.18318
532.9213
30
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From the above F- table 8 it was observed that the calculated F value is smaller than
the Critical F value (1.734<1.860). Thus it can be concluded that the null hypothesis will be
accepted i.e. There is no significant relationship exists between EPS and ROE on the contrary
it says there is the rejection of the alternate hypothesis.

Hypothesis: -7
Null Hypothesis (H0): There is no significant association of EPS with the market
capitalization of the companies.
Table 9

From the above F- table 8 it was observed that the calculated F value is higher than the
Critical F value (1683.742>1.860). Thus it can be concluded that the null hypothesis will be
rejected i.e. there is no significant association exists between EPS and Market Capitalization.
On the contrary, it says that there is the acceptance of the alternate hypothesis i.e. there is a
significant relationship exists between EPS and Market Capitalization.
Hypothesis: -8
Null Hypothesis (H0): EAT do not have significant impact on the retained earnings
It was observed that the EAT is the dependent variable and the retained earnings is the
independent variable. To test this hypothesis, the following equation was prepared.
Y=β+αxk+εi
(Eq.-3)
Table 10

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Table 11

The above table 10 provides the information of multiple R, which is the correlation
coefficient between two variables i.e. EAT and Retained Earnings. It is observed from the
above table that there is the positive linear relationship exists and the relationship is very

strong i.e. 86%. The R squared value says that 75% of the value falls on the regression line. In
other words, 75% of the values fit the model.
From the ANOVA table 11 it can be interpreted that the F value is more than the F critical
value (i.e. 78.043>0.000).Thus it can be concluded that the alternate hypothesis can be
accepted and the null hypothesis is rejected i.e. EAT do not have significant impact on the
retained earnings is rejected. Thus it can be concluded that the EAT have significant impact
on the retained earnings of the firm.

5. CONCLUSION
There were total three different methods used to test all the Eight (08) hypotheses. The use of
hypothesis testing methods is based on the nature of research and the requirements. Taking
this into account two statistical methods and one quantitative method were used
Table 12
SL. No
Hypothesis
1
Hypothesis-1
2
Hypothesis-2
3
Hypothesis-3
4
Hypothesis-4
5
Hypothesis-5
6
Hypothesis-6
7
Hypothesis-7
8

Hypothesis-8
Source: Compiled data

Null Hypothesis
Rejected
Rejected
Rejected
Rejected
Rejected
Accepted
Rejected
Rejected

Alternate Hypothesis
Accepted
Accepted
Accepted
Accepted
Accepted
Rejected
Accepted
Accepted

To test the hypothesis 6 and 7 statistical F test was used. To test hypothesis 2, 3 and 4
quantitative analysis with the use of goal programming was adopted and to test the hypothesis
1, 5 and 8 regression analysis was used. The summary of hypothesis testing was expressed in
the tabular form as provided in the above table.

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5.1. Bounded Rationality and Satisfying Behavior on the part of Finance
Managers
There is no denying the fact that the standard model of rationality in the neo-classical tradition
of economics is essentially a decision-making model which claims to be both descriptive and
normative. The term „rationality‟ in Economics has a different meaning in contrast to the
meaning of the term in some other disciplines. When we refer to people acting rationally in
the everyday sense we usually mean that they are using reason but not by emotional factors or
by unconscious instinct.
There may be many reasons why we fail to judge what is in our „self-interest‟. We may
have incomplete knowledge, or we may have cognitive failures in terms of the processing of
information within given time constraints. These failures are often ascribed to „bounded
rationality‟, and behavior that fails to achieve self-interest because of bounded rationality is
therefore not irrational according to this criterion.
What we have derived in this chapter is the fact that firms or financial managers are
subjected not to economic rationality rather to bounded rationality due to constraints of
multiple types. As a result of this managers do not look for optimization of capital structure
rather they believe in the satisfying behavior.
Satisfying behavior based on bounded rationality exposes modern day managers to go for
multiple goal setting and achievement at the same given time. Our results from the application
of the goal programming technique have proved that modern firms believe in satisfactory
achievements of multiple goals at the same time. In our study firms have achieved three
objectives at the same time instead of just one objective of achieving a single objective of
optimal capital structure. The three objectives are being- (1) Minimization of fixed cost

components over time, (2) Maximization of the EAT over time and (3) Minimization of the
long term debt component over time.
Thus, it is proved that modern firms across sectors are subjected to bounded rationality
and they have satisfying tendency but not optimization objective.

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