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

The present study has been conducted to check the possible existence of an optimal capital structure in the Indian corporate sector.

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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, Multi-objective 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

http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=11&IType=3

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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 Debt-Equity 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 F-test, 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

multi-objective 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

Table 1

Impact of EBIT on EPS

Regression Statistics

Source: Secondary Compiled Data

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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

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 pre-emptive 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

1 Embed the relevant data set Set the first goal set as the current goal set

2 Obtain a Linear Programming (LP) solution defining the current goal set as

the objective function

3 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

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

5 Set the next goal set of importance as the current goal set Go to Step 2

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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:

Where,

gi ∑

Here,

Xk, ≥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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Table 4 Summarised table for different financial parameters (in 1000 crore)

year

ITEMS Average of

fixed cost

Average of Long term debt

Average of

Source: Secondary Compiled Data

The decision variables are:

X1= the amount of financial statement in year 2004

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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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

Source: Compiled data from goal programming results

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

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