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Some objective methods for determining relative importance of financial ratios

Some objective methods for determining relative importance of financial ratios
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The aim of this study is to examine the efficiency of various financial ratios and identify their average weights through objective methods namely MLP of Artificial Neural Network, Entropy and Critic Methods.

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  1. International Journal of Management (IJM)
    Volume 10, Issue 4, July-August 2019, pp. 76–96, Article ID: IJM_10_04_008
    Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=10&IType=4
    Journal Impact Factor (2019): 9.6780 (Calculated by GISI) www.jifactor.com
    ISSN Print: 0976-6502 and ISSN Online: 0976-6510
    © IAEME Publication

    SOME OBJECTIVE METHODS FOR
    DETERMINING RELATIVE IMPORTANCE OF
    FINANCIAL RATIOS
    G. Anupama
    Part time PhD Scholar, Department of Mechanical Engineering,
    College of Engineering (A), Andhra University, Visakhapatnam, India

    V.V.S. Kesava Rao
    Professor, Department of Mechanical Engineering,
    College of Engineering (A), Andhra University, Visakhapatnam, India

    ABSTRACT
    The segregation of financial ratios into input and output ratios are useful to
    determine the business insolvency/failure and financial efficiency of the business
    organizations. A total of 18 software companies are considered with nine financial
    ratios. The aim of this study is to examine the efficiency of various financial ratios and
    identify their average weights through objective methods namely MLP of Artificial
    Neural Network, Entropy and Critic Methods.
    Key word: MLP, Entropy, Critic Methods.
    Cite this Article: G. Anupama and V.V.S. Kesava Rao, Some Objective Methods for
    Determining Relative Importance of Financial Ratios, International Journal of
    Management, 10 (4), 2019, pp. 76–96.
    http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=10&IType=4

    1. INTRODUCTION
    Financial ratio analysis is much popular among regulators due to its effectiveness in different
    countries including India, this method could not import the weights to the financial ratios to
    evaluate the performance of business organizations. Multi-criteria decision making methods
    consider the relative weights of financial ratios to evaluate the performance of business
    organizations.
    The weights of criteria are usually assigned by the DMs, based on their own experiences,
    knowledge and perception of the problem. However, the DMs involved in the decision process
    usually have different attitudes and can rarely reach an agreement on the relative importance of
    criteria. Another difficulty is the inconsistency problem in subjective weighting. These
    problems can be overcome by using an objective weighting process, which is carried out
    independently from the subjective preferences of the DMs. The logic behind such a weighting
    process is that each alternative is objectively described by its performance scores, and these
    scores in the performance matrix represent the sources of information provided to the DM.

    http://www.iaeme.com/IJM/index.asp 76 editor@iaeme.com

  2. Some Objective Methods for Determining Relative Importance of Financial Ratios

    In Entropy Method (EM), the criteria weights are obtained directly from the performance
    matrix, i.e., independently of the DM. This qualifies the entropy method (EM) as an unbiased
    evaluation procedure. In addition to the entropy method, any other method of measuring the
    divergence in performance ratings can be used to determine the objective weights. Diakoulaki
    et al. (1995) has proposed the CRITIC (CRiteria Importance Through Inter-criteria Correlation)
    method.
    One interesting area for the use of neural networks is in event prediction. This study
    develops a neural network model for determination of relative weights of predictor variables
    using financial data from the organizations. Relative importance of input variables in neural
    networks is computed as the sum of the product of raw input-hidden, hidden-output connection
    weights, proposed by Olden et al. 2004.

    1.1. Stockholders’ equity ratio (FR1)
    The ratio is expressed as a percentage and is calculated by dividing a company’s total
    shareholder equity by its total assets.

    1.2. Turnover rate of accounts receivable (Debtor Turnover Ratio) (FR2)
    Receivables turnover ratio can be calculated by dividing the net value of credit sales during a
    given period by the average accounts receivable during the same period = net value of credit
    sales/average accounts receivable Debtor turnover ratio is the relationship between net sales
    and average debtors.

    1.3. Turnover rate of inventory (FR3)
    The inventory turnover ratio is defined as ratio of cost goods sold to average inventory
    maintained.

    1.4. Return of stockholder equity (FR4)
    The return on equity ratio or ROE is a profitability ratio that measures the ability of a firm to
    generate profits from its shareholders investments in the company.

    1.5. Quick ratio (FR5)
    The quick ratio is an indicator of a company’s short-term liquidity position and measures a
    company’s ability to meet its short-term obligations with its most liquid assets.

    1.6. Operating income ratio (FR6)
    Operating income can be calculated by subtracting operating expenses, depreciation, and
    amortization from gross income or revenues, = Net profit (Results of Operations)/Revenue from
    operations.

    1.7. Ratio of cash flow (FR7)
    The operating cash flow ratio is a measure of the number of times a company can pay off current
    debts with cash generated within the same period Cash flow ratio = Operating cash flow /current
    liabilities

    1.8. Return of assets (FR8)
    Return on assets is displayed as a percentage and it’s calculated as: ROA = Net Income / Total
    Assets.

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  3. G. Anupama and V.V.S. Kesava Rao

    1.9. Market share (FR9)
    Market share is calculated by taking the company’s sales over the period and dividing it by the
    total sales of the industry over the same period. Market share = Company’s sales /Total
    industry’s sales

    2. PROBLEM STATEMENT
    There are some dimensionality reduction techniques and correlation methods used to group a
    range of financial ratios that characterizes business failure/success in IT companies. However
    these techniques have not addressed the financial efficiency. The financial efficiency of the
    MLP must be compared with Entropy measurement method and CRITIC method for cross
    validation.

    3. DATA SOURCE
    In this case, Data has been collected from 18 IT companies. Last 5 years financial data is
    considered for the analysis and subsequently these financial ratios are separated as 9 variables
    based on different parameters.

    4. LITERATURE REVIEW
    Hsiang-Hsi Liu et al. (2013) considered data envelopment analysis (DEA), three-stage DEA
    (3SDEA) and artificial neural network (ANN) are employed to measure the technical efficiency
    of 29 semi-conductor firms in Taiwan. Estimated results show that there are significant
    differences in efficiency scores among DEA, 3SDEA and ANN analysis. The advanced setting
    of the three stages mechanism of DEA does show some changes in the efficiency scores
    between DEA and ANN approaches.
    Krzysztof Piasecki and Aleksandra Wójcicka-Wójtowicz (2017) investigated the use of
    different structure NN and DA in the process of the classification of banks’ potential clients.
    The results of those different methods are juxtaposed and their performance compared.
    Nor Mazlina Abu Bakar and Izah Mohd Tahir (2009) made a study to predict bank
    performance using multiple linear regression and neural network. The study then evaluates the
    performance of the two techniques with a goal to find a powerful tool in predicting the bank
    performance. Data of thirteen banks for the period 2001-2006 was used in the study. The study
    concluded that artificial neural network is the more powerful tool in predicting bank
    performance.
    Ayan Mukhopadhyay et al. (2012) combined Data Envelopment Analysis and Multi-Layer
    Perceptron (MLP) to suggest a new method for prediction of bankruptcy that not only focusses
    on historical financial data of firms. The proposed method thus identifies firms that have a high
    chance of facing bankruptcy along with those that have filed for bankruptcy.
    Olanrewaju A Oludolapo et al. (2012) presented techniques based on the development of
    multilayer perceptron (MLP) and radial basis function (RBF) of artificial neural network (ANN)
    models, for calculating the energy consumption of South Africa’s industrial sector between
    1993 and 2000. The approach examines the energy consumption in relation to the gross
    domestic product. The results indicate a strong agreement between model predictions and
    observed values,
    Mehdi Alinezhad Sarokolaei et al. (2012) made a research to forecast the performance of
    10 Iranian banks using multi-linear regression method and artificial neural network and to
    compare these two methods. To do so, the financial data related to 10 Iranian banks during the
    years between 2006 and 2010 were collected from the most reliable resources.

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  4. Some Objective Methods for Determining Relative Importance of Financial Ratios

    Viju Raghupathi and Wullianallur Raghupathi (2015) deployed neural networks to examine
    the strategic association between hospitalization experience and treatment results. The
    healthcare data for the years 2009-2012 are downloaded from the Statewide Planning and
    Research Cooperative System (SPARCS) of the New York State Department of Health
    (NYSDOH).
    Mahmoud H. Al-Osaimy (1998) used neural networks for predicting Islamic banks
    performance. A data sample of twenty six Islamic banks has been collected for the period 1991-
    1993. Seven financial ratios were constructed from the data sample. Kohonen neural network
    was used first to group the Islamic banks into high and low performance groups using the seven
    financial ratios for the performance year (1993). The results of this network have assigned
    twelve banks to the high performance group and fourteen banks to the low performance group.
    Satish Sharma and Mikhail Shebalkov (2013) presented an application of neural network
    and simulation modeling to analyze and predict the performance of 883 Russian Banks over the
    period 2000-2010. Neural network was trained over the entire dataset, and then simulation
    modeling was performed generating values. Next, a combination of neural network and
    simulation modeling techniques was validated with the help of back-testing.
    Faruk Erinci and Serhat Duranay (2016) have been estimated future-oriented performance
    using 2457 input and 364 output normalized data of 28 deposit bank continuously operating
    during 2002-2014 in Turkish Banking Sector. The study is helpful in the banking sector to the
    decision-making experts to help with these parameters and for the visualization of prediction
    results for the future.

    5. METHODOLOGY TO BE ADOPTED:
    Entropy Measurement Method
    It is assumed that there is a set of m feasible alternatives, Ai (i = 1,2,…,m) and n evaluation
    criteria Cj (j = 1,2,…,n) in the problem.
    Step-1: The decision matrix X which shows the performance of different alternatives with
    respect to various criteria is formed.
     x11 x12  x1n 
    x x 22  x 2 n 
    X  [ x ij ]mn   21 (i = 1,2,…,m; j = 1,2,…,n) (1)
         
     
     x m1 x m2  x mn 
    xij presents the performance value of ith alternative on jth criterion.
    Step-2: The decision matrix is normalized. Beneficial (maximization) and non-beneficial
    (minimization) criteria are normalized by Eq.(2) and Eq.(3) respectively. To have the
    performance measures comparable and dimensionless, all the entries of the decision matrix are
    linear normalized using the following two equations:
    x ij  min( x ij )
    rij  i = 1,2,…,m and j = 1,2,…,n (2)
    max( x ij )  min( x ij )

    max( x ij )  x ij
    rij  i = 1,2,…,m and j = 1,2,…,n (3)
    max( x ij )  min( x ij )
    Step-3: Entropy values (ej) are determined for each criterion.

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  5. G. Anupama and V.V.S. Kesava Rao

    m

    f ij ln f ij
    ej  i 1
    i = 1,2,…,m and j = 1,2,…,n (4)
    ln m
    rij
    where f ij  m
    and 0 < ej < 1.
    r
    i 1
    ij

    If fij are all the same, then the entropy values of each criterion is the maximum (ej = 1). If fij is
    0, then fij ln fij is 0 (Wu et al., 2011).
    Step-4: Entropy weights (Wj) are calculated.
    1 ej n
    Wj  m
    where W j 1 (5)
    n  ej j1

    i 1

    (1 – ej) represents the inherent contrast intensity of each criterion. In other words it is the
    degree of divergence of the intrinsic information of each criterion. If (1 – ej) is normalized, then
    the final weights of each criterion can be obtained. The entropy weight is a parameter that
    describes the importance of the criterion. The smaller the value of the entropy, the larger the
    entropy-based weight, then the specific criterion provides more information and this criterion
    becomes more important than the other criteria in the decision making process (Wu et al., 2011).

    6. CRITIC METHOD
    It is based on analytical testing of the decision matrix in order to determine the information
    contained in the criteria by which variants are evaluated. For each criteria xij membership
    function rij which translates all the values of criteria fј into interval [0, 1], is defined
    x ij  x min
    rij 
    j

    x max
    j  x min
    j

    This transformation is based on the concept of an ideal point. In this way, the initial matrix
    is converted into a matrix with generic elements rij.
    Each vector rj is characterised by the standard deviation (sj), which quantifies the contrast
    intensity of the corresponding criterion. So, the standard deviation of rj is a measure of the value
    of that criterion to be considered in the decision-making process. Next, a symmetric matrix is
    constructed, with dimensions m x m and a generic element ljk, which is the linear correlation
    coefficient between the vectors rj and rk. It can be seen that the more discordant the scores of
    the alternatives in criteria j and k are, the lower is the value ljk. In this sense, Eq. (6) represents
    a measure of the conflict created by criterion j with respect to the decision situation defined by
    the rest of the criteria:
    m

     (1  l
    k 1
    jk ) (6)

    The amount of information Cj conveyed by the jth criterion can be determined by composing
    the measures which quantify the above 2 notions through the multiplicative aggregation formula
    (Eq. (7)).
    m
    C j   j  (1  lkj ) (7)
    k 1

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  6. Some Objective Methods for Determining Relative Importance of Financial Ratios

    The higher the value Cj is, the larger is the amount of information transmitted by the
    corresponding criterion and the higher is its relative importance for the decision-making
    process. Objective weights are derived by normalizing these values to unity (Eq. (18)).
    1
    m 
    w j  C j  C k  (8)
     k 1 
    Objective criteria weights are obtained by normalizing the values Cj:
    cj
    wj  m
    i1 ci
    7. RESULTS AND ANALYSIS
    Nine financial ratios of 18 software companies during five financial years as discussed. Relative
    weights of the financial ratios are determined through objective methods namely MLP of
    artificial neural network, entropy method and critic method. Finally average weights of the
    financial ratios are determined.
    In this study, FR1, FR2 and FR3 are considered as input financial ratios and FR4, FR5,
    FR6, FR7, FR8 and FR9 are considered as output ratios.
    CCR model of data envelopment analysis is used for determining the category of financial
    efficiency based on input and output financial ratios using LINGO 8.0 software.

    Table 1 Financial efficiency of software companies during 1st financial year
    Software Input Out puts Financial
    Financial
    Companies Efficiency
    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9 Efficiency
    (SWC) Group
    SWC1 0.1298 6.1418 981.2177 -0.6244 0.3774 0.0697 0.0404 -0.0811 0.0052 0.0622 NE
    SWC2 0.0047 6.3151 136.2825 46.4965 2.1518 0.2500 0.6807 0.2166 0.1274 1 E
    SWC3 0.0050 6.4964 3016.0000 37.2587 3.8368 0.2671 0.7710 0.1861 0.1988 0.6308 NE
    SWC4 0.0172 4.7198 1350.6822 6.7102 1.5198 0.1402 0.2634 0.1153 0.0107 0.474 NE
    SWC5 0.0147 6.9437 1299.9365 4.6751 2.5468 0.0976 0.4650 0.0687 0.0037 0.3568 NE
    SWC6 0.0199 5.7679 1301.4115 10.8106 3.8261 0.2012 0.7064 0.2147 0.0120 0.736 NE
    SWC7 0.0300 3.6304 1299.8089 1.4404 2.4361 0.1694 0.1465 0.0432 0.0103 1 E
    SWCS 0.0331 4.5276 417.7281 3.7979 2.7036 0.1537 0.2895 0.1256 0.0091 0.7176 NE
    SWC9 0.0043 5.3117 1307.6618 32.3109 9.2470 0.3740 0.7097 0.1398 0.0148 1 E
    SWC10 0.0257 6.0927 1300.9625 6.2320 3.4367 0.2482 0.8481 0.1601 0.0066 0.781 NE
    SWC11 0.0221 3.3705 1297.3562 1.7584 0.3089 0.3276 0.2878 0.0389 0.0099 1 E
    SWC12 0.0427 5.0058 146.0758 2.4187 3.9531 0.1166 0.6923 0.1034 0.0018 1 E
    SWC13 0.0160 8.9554 1466.2900 7.3926 2.2570 0.0636 0.4550 0.1180 0.0062 0.2488 NE
    SWC14 0.0029 5.0615 3116.4230 97.8397 3.2098 0.3075 0.8360 0.2854 0.3244 1 E
    SWC15 0.0792 5.3193 4098.0000 2.4120 1.8727 0.1773 0.7977 0.1911 0.0031 0.5258 NE
    SWC16 0.0146 6.2134 1405.6346 12.9713 1.9744 0.2225 0.2496 0.1900 0.0746 0.4126 NE
    SWC17 0.0099 5.3555 121.6289 16.1199 2.2232 0.2219 0.5476 0.1599 0.1722 1 E
    SWC18 0.0295 6.7336 16.9201 5.4265 1.9696 0.1534 0.5656 0.1598 0.0093 1 E
    Note: E- Efficient; NE- Not Efficient:

    From Table-1 it is observed that software companies namely: SWC2, SWC7, SWC9,
    SWC11, SWC12, SWC14, SWC17 and SWC 18 are grouped as efficient decision making units
    (Software companies). Remaining companies are arrived as Not-efficient organizations, during
    1st Financial Year.

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  7. G. Anupama and V.V.S. Kesava Rao

    Table 2 Financial efficiency of software companies during 2nd financial year
    Software Input Out puts
    Financial Financial
    Companies
    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9 Efficiency Efficiency
    (SWC)
    SWC1 0.1660 6.9077 836.6929 -1.6170 0.4026 0.1284 -0.0290 -0.2684 0.004693 0.1845 NE
    SWC2 0.0080 6.0060 201.6980 26.0209 2.4413 0.2309 0.5317 0.2073 0.128143 0.7296 NE
    SWC3 0.0086 5.9033 1301.0146 21.6294 3.4819 0.2791 0.5263 0.1857 0.186165 0.0622 NE
    SWC4 0.0165 4.3579 202.6233 6.3012 1.5730 0.1085 0.5998 0.1038 0.010439 1 E
    SWC5 0.0136 8.0919 1299.7027 1.5732 2.3440 0.0468 0.2834 0.0213 0.003535 0.2299 NE
    SWC6 0.0315 5.4938 1300.7675 6.4074 3.2675 0.1991 0.9353 0.2020 0.012436 0.6369 NE
    SWC7 0.0282 8.2604 1299.9875 3.2103 2.5911 0.1496 0.4397 0.0905 0.020233 0.2515 NE
    SWC8 0.0303 4.0544 297.3188 1.8688 2.2119 0.1391 0.3963 0.0566 0.008284 1 E
    SWC9 0.0067 6.0902 1299.1862 28.1806 1.8961 0.3974 0.3751 0.1901 0.013634 0.5616 NE
    SWC10 0.0444 5.7189 1301.0629 3.6329 3.5237 0.2064 0.7971 0.1614 0.006603 0.5479 NE
    SWC11 0.0191 3.4431 1297.4939 1.5197 0.4284 0.3517 0.2067 0.0290 0.012847 1 E
    SWC12 0.0382 5.2617 385.7953 5.6026 4.6112 -0.1447 1.7252 0.2139 0.001494 1 E
    SWC13 0.0130 6.4877 354.6815 12.7091 2.0666 0.0997 0.2163 0.1654 0.005873 0.4523 NE
    SWC14 0.0027 4.8954 4486.3619 101.3539 2.6936 0.2587 0.8544 0.2695 0.330468 1 E
    SWC15 0.0662 5.4860 4635.4483 3.3044 1.9887 0.2087 0.7669 0.2188 0.002966 0.3408 NE
    SWC16 0.0242 4.7352 1074.5364 5.4698 2.0811 0.1854 0.3548 0.1324 0.078983 0.7068 NE
    SWC17 0.0083 5.3047 102.6374 17.5428 2.1787 0.2194 0.5451 0.1459 0.163931 1 E
    SWC18 0.0253 6.5412 18.0122 5.9686 2.0244 0.1475 0.7641 0.1510 0.009273 1 E
    Note: E- Efficient; NE- Not Efficient:

    From Table-2 it is observed that software companies namely: SWC4, SWC8, SWC11,
    SWC12, SWC14, SWC14, SWC17 and SWC 18 are grouped as efficient decision making units
    (Software companies). Remaining companies are arrived as in Not-efficient organizations,
    during 2nd Financial Year.

    Table 3 Financial efficiency of software companies during 3rd financial year
    Software Input Out puts
    Financial Financial
    Companies
    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9 Efficiency Efficiency
    (SWC)
    SWC1 0.4034 6.2637 1689.2743 -0.8610 0.5238 -0.6959 0.3602 -0.3473 0.003574 0.0551 NE
    SWC2 0.0072 4.3669 116.0055 19.8611 2.4697 0.2137 0.3496 0.1421 0.098853 1 E
    SWC3 0.0152 5.9346 1302.2510 11.7911 4.5542 0.2735 0.7370 0.1790 0.198242 0.994 NE
    SWC4 0.0171 4.6595 91.6409 7.4767 1.9310 0.1348 0.7307 0.1279 0.010237 1 E
    SWC5 0.0269 4.5697 1300.8451 1.1948 3.3349 0.0287 0.2913 0.0321 0.001673 0.8169 NE
    SWC6 0.0506 5.5994 1299.7556 3.2926 2.3899 0.1757 0.4914 0.1666 0.014836 0.4921 NE
    SWC7 0.0295 9.5450 2545.3073 3.0045 4.3873 0.1419 0.9124 0.0885 0.019306 0.3932 NE
    SWC8 0.0263 4.4945 503.1328 4.4118 1.8866 0.1755 0.4832 0.1160 0.008534 0.7442 NE
    SWC9 0.0074 5.7670 1302.2844 24.7672 4.5831 0.3916 0.6701 0.1828 0.013116 1 E
    SWC10 0.0373 5.8828 1301.0457 3.4663 3.5089 0.1693 0.5257 0.1293 0.007341 0.621 NE
    SWC11 0.0172 2.3494 1297.4821 1.1296 0.4181 0.3021 0.2125 0.0194 0.012063 1 E
    SWC12 0.0278 5.8140 323.5205 11.6416 4.3087 0.0224 1.8110 0.3235 0.001534 1 E
    SWC13 0.0106 5.8396 201.6851 15.0751 1.6740 0.0989 0.4587 0.1599 0.006161 0.6341 NE
    SWC14 0.0022 4.8818 4862.4259 123.1980 4.2836 0.2824 1.0727 0.2723 0.344937 1 E
    SWC15 0.0514 5.8231 5706.8276 4.9714 2.2688 0.2304 0.5511 0.2557 0.003414 0.3571 NE
    SWC16 0.0193 4.8275 685.9136 6.8723 2.2918 0.1612 0.4568 0.1327 0.084116 0.6922 NE
    SWC17 0.0066 5.3613 79.0081 18.0285 2.0085 0.2107 0.4899 0.1191 0.162693 1 E
    SWC18 0.0233 5.9399 20.2269 6.4878 2.3456 0.1486 0.5056 0.1509 0.009372 1 E
    Note: E- Efficient; NE- Not Efficient:

    From Table-3 it is observed that software companies namely: SWC2, SWC4, SWC9,
    SWC11, SWC12, SWC14, SWC17 and SWC 18 are grouped as efficient decision making units
    (Software companies). Remaining companies are arrived as in not efficient organizations,
    during 3rd Financial Year.

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  8. Some Objective Methods for Determining Relative Importance of Financial Ratios

    Table 4 Financial efficiency of software companies during 4th financial year
    Software Input Out puts
    Financial Financial
    Companies
    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9 Efficiency Efficiency
    (SWC)
    SWC1 0.7223 5.2397 973.2874 0.0800 0.4050 0.1564 0.1149 0.0578 0.002826 0.1624 NE
    SWC2 0.0062 5.9378 137.5962 30.1965 2.3498 0.2183 0.7172 0.1868 0.133911 1 E
    SWC3 0.0136 5.7910 1302.3524 12.5463 4.6421 0.2717 0.7663 0.1708 0.192792 0.9407 NE
    SWC4 0.0148 4.5157 73.0530 6.3366 1.9498 0.1050 0.2847 0.0938 0.009346 0.7949 NE
    SWC5 0.0160 6.1482 1299.4242 2.7725 2.1025 0.0812 0.2177 0.0443 0.001577 0.2904 NE
    SWC6 0.0491 5.6034 1300.2779 2.4917 2.8430 0.1345 0.8781 0.1224 0.014741 0.5793 NE
    SWC7 0.0285 9.5181 2494.1024 3.7619 4.4497 0.1586 0.6872 0.1073 0.017106 0.388 NE
    SWC8 0.0247 5.2965 7740.3333 4.0733 2.0441 0.1713 0.6070 0.1004 0.007888 0.3356 NE
    SWC9 0.0070 5.7150 1299.1445 27.9112 1.8600 0.3908 0.4030 0.1961 0.012461 0.8823 NE
    SWC10 0.0338 6.3758 1301.5167 3.7684 3.9173 0.1583 0.6165 0.1274 0.008103 0.5113 NE
    SWC11 0.0156 1.9229 1297.6098 1.0150 0.5288 0.3044 -0.0278 0.0158 0.008952 1 E
    SWC12 0.0256 5.3704 337.9028 4.9497 5.8861 0.1069 0.2594 0.1266 0.001315 1 E
    SWC13 0.0087 5.4230 435.4106 15.0723 1.7774 0.0808 0.3342 0.1305 0.006674 0.5501 NE
    SWC14 0.0019 5.0532 4630.0000 133.4467 5.1366 0.2739 1.4336 0.2539 0.332091 1 E
    SWC15 0.0432 5.3794 1301.3368 5.6127 3.7613 0.2211 0.8859 0.2426 0.003483 0.8037 NE
    SWC16 0.0168 5.2467 492.2367 6.4104 2.0357 0.1436 0.4926 0.1079 0.082035 0.6019 NE
    SWC17 0.0059 5.7028 94.8469 17.4719 2.0497 0.2042 0.5785 0.1036 0.156095 1 E
    SWC18 0.0209 5.6944 22.4173 5.2345 2.5092 0.1250 0.5587 0.1092 0.008602 1 E
    Note: E- Efficient; NE- Not Efficient:

    From Table-4 it is observed that software companies namely: SWC2, SWC11, SWC12,
    SWC14, SWC17 and SWC 18 are grouped as efficient decision making units (Software
    companies). Remaining companies are arrived as not efficient organizations, during 4th
    Financial Year

    Table 5 Financial efficiency of software companies during 5th financial year
    Software Input Out puts
    Financial Financial
    Companies
    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9 Efficiency Efficiency
    (SWC)
    SWC1 0.9961 4.7757 874.7225 0.0436 0.5345 0.1572 0.1356 0.0434 0.002695 0.1607 NE
    SWC2 0.0058 5.6376 175.5491 31.3705 2.4869 0.2224 0.7369 0.1808 0.13749 1 E
    SWC3 0.0135 5.5390 1302.0376 14.7325 4.3691 0.2696 0.8507 0.1992 0.19174 1 E
    SWC4 0.0138 4.6083 97.9456 6.6715 2.0681 0.1013 0.6633 0.0923 0.009961 1 E
    SWC5 0.0141 7.4214 1299.6222 5.9038 2.2742 0.1220 0.2904 0.0833 0.002222 0.3276 NE
    SWC6 0.0433 5.7151 1300.1192 3.4783 2.7053 0.1356 0.7575 0.1505 0.014853 0.5989 NE
    SWC7 0.0276 9.0946 1300.8642 4.3333 3.3514 0.1622 0.6429 0.1194 0.017797 0.4101 NE
    SWC8 0.0228 5.6774 8298.0000 4.5561 1.9668 0.1678 0.4235 0.1038 0.008133 02613 NE
    SWC9 0.0071 5.2477 1301.6730 28.9909 4.0529 0.4000 0.9130 0.2070 0.01231 1 E
    SWC10 0.0300 6.3194 1301.5781 4.0386 3.9706 0.1545 0.7778 0.1210 0.008248 0.6438 NE
    SWC11 0.0145 2.0309 1297.6936 -0.6395 0.6016 0.2889 0.0303 -0.0092 0.007778 1 E
    SWC12 0.0232 6.4312 1303.9958 4.8171 6.0674 0.1381 0.6861 0.1120 0.001368 0.8937 NE
    SWC13 0.0084 5.3559 1299.2248 18.5482 1.9296 0.0941 0.5448 0.1561 0.006672 0.7028 NE
    SWC14 0.0018 5.1768 3854.8085 135.2147 4.4735 0.2641 1.2029 0.2430 0.334704 1 E
    SWC15 0.0655 5.0276 1301.6462 3.8542 4.0296 0.2513 0.9269 0.2524 0.003769 0.9091 NE
    SWC16 0.0145 5.2001 410.4457 8.6027 1.9674 0.1530 0.3862 0.1248 0.083667 0.6062 NE
    SWC17 0.0116 5.5646 121.0707 8.8448 1.9927 0.1906 0.5226 0.1027 0.148143 0.9341 NE
    SWC18 0.0193 5.2878 25.0863 5.3685 2.6411 0.1174 0.3182 0.1039 0.00845 1 E
    Note: E- Efficient; NE- Not Efficient:

    From Table-5 it is observed that software companies namely: SWC2, SWC3, SWC4,
    SWC9, SWC11, SWC14 and SWC 18 are grouped as efficient decision making units (Software
    companies). Remaining companies are arrived as not efficient organizations, during 5th
    Financial Year.

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  9. G. Anupama and V.V.S. Kesava Rao

    The efficiency groups obtained through DEA are considered as dependent variables in
    MLP.

    8. MLP METHOD
    The aim of this study was to examine relative importance of financial ratios through MLP neural
    networks by analyzing data obtained from the annual reports from 1st FY to 5th FY of the 18
    software companies. MLP of Neural networks is implemented to the case study using SPSS 17
    and the following outputs of the analysis are discussed in the following sections.

    8.1. MLP Network information
     Number of inputs = 9 Financial Ratios.
     Number of output units =1(financial Efficiency Group)
     Number of hidden units = 13
     Training dataset = 90% of the sample
     Testing dataset = 5% of the sample.
     Holdout dataset= 5% of the sample.
     Type of training = Batch training
     Optimizing Algorithm = scaled congregated method
     Training options, Initial λ = 0.0000005

    8.2. Case Processing Summary
    Table-6 gives information about the datasets used to build the ANN model. From the table it is
    observed that the training, testing and holdout dataset contains 90%, 5% and 5% of the sample
    respectively.

    Table 6 Case processing summary
    N Percent
    Sample Training 90 90
    Testing 5 5
    Holdout 5 5
    Valid 100 100
    Excluded 0
    Total 100
    Network Information: The Table-7 shows network information. The table shows the
    number of neurons in every layer. Input layer contains 9 factors (FR1, FR2,…,FR9). The
    Automatic architecture selection chose 13 nodes for the hidden layer, while the output layer
    had 2 nodes and the depended variable financial efficiency group. For the hidden layer the
    activation function was the hyperbolic tangent, while for the output layer also the softmax
    function is used.

    Table 7 Network information
    Input Layer Factors 1 FR1
    2 FR2
    3 FR3
    4 FR4
    5 FR5
    6 FR6
    7 FR7

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  10. Some Objective Methods for Determining Relative Importance of Financial Ratios

    8 FR8
    9 FR9
    Number of Unitsa 723
    Hidden Layer(s) Number of Hidden Layers 1
    Number of Units in Hidden Layer 1a 13
    Activation Function Hyperbolic tangent
    Output Layer Dependent Variables 1 GROUP
    Number of Units 2
    Activation Function Softmax
    Error Function Cross-entropy
    a.
    Excluding the bias unit
    Model Summary: The model summary is shown in Table-8.

    Table 8 Model Summary
    Training Cross entropy error 6.524E-5
    Percent incorrect predictions 0.0%
    Stopping rule used Training error ratio criterion (0.001)
    achieved
    Training time 0:00:00.28
    Testing Cross entropy error 1.255E-6
    Percent incorrect predictions 0.0%
    Holdout Percent incorrect predictions 0.0%
    Dependent variable: GROUP
    Table-8 provides information related to the results of training, testing and holdout samples.
    Cross entropy error is given for training, testing and holdout samples. The small value (6.524
    E-5) of this error of training set indicates the power of the model to predict financial efficiency.
    The cross entropy error (1.255 E-6) is also very less for the testing data set, meaning that the
    network model has not been over-fitted to the training data. The result justifies the role of testing
    sample which is to prevent overtraining. From the results, it is observed that, there are no
    incorrect predictions based on training and testing samples.
    Classification Summary: Table-9 displays classification for categorical dependent variable
    (financial efficiency).

    Table 9 Classification
    Predicted
    Sample Observed
    E NE Percent correct
    Training E 36 0 100.0
    NE 0 54 100.0
    Overall percent 40.0 60.0% 100.0
    Testing E 3 0 100.0
    NE 0 2 100.0
    Overall percent 60.0 40.0% 100.0
    Holdout E 2 0 100.0
    NE 0 3 100.0
    Overall percent 40.0 60.0% 100.0
    Dependent Variable: GROUP
    As can be seen, the MLP network correctly classified all 18 software companies out of 90
    observations, in the training sample in training and sample and two out of two in testing sample

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  11. G. Anupama and V.V.S. Kesava Rao

    were correctly classified. Overall 100.0% of the training cases and testing case were correctly
    classified.
    Importance Analysis: Table-10 gives the impact of each independent variable in the ANN
    model in terms of relative and normalized importance.

    Table-10 Independent variable importance
    Normalized
    Importance
    importance
    FR1 0.118 83.5%
    FR2 0.108 76.0%
    FR3 0.132 93.4%
    FR4 0.109 76.9%
    FR5 0.104 73.4%
    FR6 0.095 66.8%
    FR7 0.100 70.6%
    FR8 0.092 64.8%
    FR9 0.142 100.0%
    From the Table-10, it is apparent that the financial ratio FR9 has the greatest effect on
    financial efficiency since the relative importance of the variable is 0.142. FR8 has the lowest
    effect on the financial efficiency since the relative importance of the variable is 0.0928. The
    importance of the variables, i.e., how sensitive is the model is in the change of each input
    variable is depicted.
    The accuracy of prediction of overall financial performance measured by MLP is measured
    by the area under the ROC curve. An area of 1 represents a perfect test; an area of 0.5 represents
    a worthless test. A rough guide for classifying the accuracy of prediction is Excellent (0.9 to
    1.0), Good (0.8 to 0.9), Fair (0.7 to 0.8), Poor (0.6 to 0.7) and Fail (0.5 to 0.6). Excellent
    prediction of overall financial performance is obtained through the proposed MLP is obtained
    in this study, since the area under ROC for all groups is equal to 1.00.

    9. ENTROPY MEASUREMENT METHOD
    Decision matrix: The decision matrix shows the payoff eighteen software companies during 5
    financial years with respect to nine financial ratios. The decision matrix is shown in Tables A.1-
    A.5 of Appendix.
    Normalized Decision matrix: The normalized decision matrix is shown in Tables A.6-A.10
    of Appendix.
    Entropy values: Entropy values are shown in Table-11.
    Table 11 Entropy values
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    ej 0.4374 0.6638 0.5482 0.4907 0.6517 0.6427 0.6147 0.6649 0.4801
    Inherent contrast intensity (1-ej): Inherent contrast intensity is the degree of divergence of
    the intrinsic information of each criterion is determined Entropy Weight (wj): Entropy weight
    is determined The entropy weights are shown in Table-12. Entropy weight is a parameter that
    describes the importance of the criterion. Smaller the value of the entropy, the larger the entropy
    based weight.
    Table 12 Entropy weight
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9

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  12. Some Objective Methods for Determining Relative Importance of Financial Ratios

    wj 0.2345 0.0304 0.1225 0.1749 0.0544 0.0554 0.0556 0.0272 0.2451
    FR9 (Market Share) is the most important criterion with the highest entropy weight of
    0.2451. The contribution of FR8 (Return of Assets) is minimum (0.0272) for financial
    efficiency.

    10. CRITIC METHOD
    Standard Deviation: Standard deviations of FRs are determined as discussed in section 6.
    Standard deviation, of FRs represent the degree of deviation of variant values for a given criteria
    of a mean value. Standard Deviation of Financial Ratios are shown in Table-13

    Table 13 Standard Deviation of Financial Ratios
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    Standard deviation 0.1300 0.1662 0.1832 0.1971 0.1577 0.1147 0.1713 0.1414 0.2601
    From Table-13, it is observed that highest standard deviation is obtained with FR4 (Return
    of Stock Holder Equity). FR6 (Operating income ratio) is obtained low standard deviation. A
    high standard deviation implies that, on average, data points are all pretty far from the average.
    A low standard deviation means most points are very close to the average.
    Correlation Coefficient Matrix: Linear correlation coefficients between the financial ratios
    are determined as discussed in section 6. The correlation coefficient matrix is shown in Table-
    14.

    Table 14 Correlation coefficient of financial ratios
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    FR1 1.0000 -0.0166 -0.0255 -0.1713 -0.3145 -0.3023 -0.2540 -0.3880 -0.3880
    FR2 -0.0166 1.0000 0.0516 -0.0701 0.2870 -0.2432 0.1785 0.0315 -0.0706
    FR3 -0.0255 0.0516 1.0000 0.3784 0.1391 0.1518 0.2278 0.1986 0.2613
    FR4 -0.1713 -0.0701 0.3784 1.0000 0.3131 0.3204 0.4564 0.4725 0.8321
    FR5 -0.3145 0.2870 0.1391 0.3131 1.0000 0.1948 0.6336 0.5066 0.2326
    FR6 -0.3023 -0.2432 0.1518 0.3204 0.1948 1.0000 0.0537 0.5222 0.3197
    FR7 -0.2540 0.1785 0.2278 0.4564 0.6336 0.0537 1.0000 0.6619 0.3646
    FR8 -0.3880 0.0315 0.1986 0.4725 0.5066 0.5222 0.6619 1.0000 0.4088
    FR9 -0.1760 -0.0706 0.2613 0.8321 0.2326 0.3197 0.3646 0.4088 1.0000
    Correlation coefficients are used in statistics to measure how strong a relationship is
    between two variables. 1 indicates a strong positive relationship. –1 indicates a strong negative
    relationship. A result of zero indicates no relationship at all. From table 4.10 it is observed that
    FR1 is showing negative correlation with all other financial ratios. There is strong correlation
    of 0.3880 is observed between, FR1- FR8 and FR1-FR9.
    FR2 is showing negative correlation with FR1, FR4, and FR6 and FR9. There is strong
    correlation of 0.2870 is observed between, FR1 and FR5. FR3 is showing highest positive
    correlation (0.3784) with FR4. FR5 is showing highest positive correlation (0.6336) with FR7.
    FR6 is showing highest positive correlation (0.6619) with FR8. FR9 is showing highest positive
    correlation (0.8321) with FR4
    Measure of Conflict: Measure of conflict is determined as discussed in section 6 and shown in
    Table-15.

    Table 15 Measure of conflict
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    Measure of conflict 9.6483 7.8218 6.6168 5.4685 6.0077 6.9828 5.6776 5.5861 6.0395

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  13. G. Anupama and V.V.S. Kesava Rao

    From Table-4.3.3, it is observed that there is a high measure of conflict of 9.6483 with FR1
    and low measure of conflict of 5.4685 is obtained with FR4.
    Amount of information in the FRs: The amount of information contained in the FR is determined
    as discussed in section 6. The values of Amount of information in the FRs are shown in Table-
    16.

    Table 16 Information content of FRs
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    Cj 1.2539 1.3046 1.2123 1.0777 0.9472 0.8007 0.9726 0.7897 1.5706
    From Table-16, it is observed that, FR9 is obtained the highest value of Cj(1.5706). Hence
    FR9 transmits the largest information and it has the highest relative importance for the decision-
    making process.
    Relative weights of FRs: Relative weights of FRs is obtained as discussed in section 6 and
    the relative weights of FRS is show in Table-17.

    Table 17 Relative weights of FRs
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    wj 0.1263 0.1314 0.1221 0.1085 0.0954 0.0806 0.0979 0.0795 0.1582
    From Table-17, it is observed that highest weight of 0.1582 is obtained with FR9 and the
    lowest weight (0.0795) is obtained with FR8. The relative importance order of FRs is is
    presented below.
    Relative importance of FRs: FR9 > FR2 > FR1 > FR3 > FR4 > FR7 > FR5 > FR6 > FR8.

    11. COMPARISON OF RELATIVE WEIGHTS
    In this paper, three objective rating methods namely: MLP, EM and CRITIC methods are
    proposed for determination of relative weights of financial ratios in determining the financial
    efficiency of software manufacturing organizations. Comparison of relative weights obtained
    by the proposed methods are compared and presented in Table-18.

    Table 18 Comparison of relative weights
    Methods
    FRs
    MLP EM CRITIC
    FR1 0.118(III) 0.2345(II) 0.1263(III)
    FR2 0.108(V) 0.0304(VIII) 0.1314(II)
    FR3 0.132(II) 0.1125(IV) 0.1221 (IV)
    FR4 0.109(IV) 0.1749(III) 0.1085(V)
    FR5 0.104(VI) 0.0544(VII) 0.0954(VII)
    FR6 0.095(VIII) 0.0554(VI) 0.0806(VIII)
    FR7 0.1(VII) 0.0556(V) 0.0979(VI)
    FR8 0.092(IX) 0.0272(IX) 0.0795(IX)
    FR9 0.142(I) 0.2451(I) 0.1582(I)
    From the results shown in Table-18, it is observed that the proposed methods are consistent
    in prioritizing the FRs of FR9, FR8 in contributing the highest and lowest importance on the
    financial efficiency. Similar ranking is obtained based on relative importance of FRs on
    Financial efficiency for other financial ratios.

    12. CORRELATION OF THE METHODS
    Correlations between the three proposed in determining the relative weights methods are
    computed. Correlation coefficients are shown in Table-19.

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  14. Some Objective Methods for Determining Relative Importance of Financial Ratios

    From the correlations between objective weight methods, it is observed that there is high
    significant positive correlation ( 0.890) is existed between MLP and CRITIC methods. The p-
    values for the individual hypothesis tests of the correlations are being shown in brackets. Since
    all the p-values are less than or equal to 0.05, there is sufficient evidence at α = 0.05 that there
    exists significant correlation between the three methods.

    Table 19 Correlation coefficients
    Method MLP EM CRITIC
    MLP 1.000 0.761 (0.017) 0.890 (0.001)
    EM 0.761 (0.017) 1.000 0.696(0.037)
    CRITIC 0.890 (0.001) 0.696(0.037) 1.000

    13. AVERAGE RELATIVE WEIGHTS
    Average relative weights of financial ratios are obtained by taking the average of the weights
    obtained from the proposed methods. Average Relative weights of financial ratios based on the
    data on financial ratio from FY2013-14 to 2017-18 are determined and average relative weights
    of financial ratios are shown in Table-20.

    Table 20 Average relative weights of financial ratios
    FRs FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    Average relative
    0.1596 0.0899 0.1255 0.1308 0.0846 0.0770 0.0845 0.0663 0.1818
    weight
    Order of Average relative weights of FRs is presented below.
    Relative weights of FRs: FR9(0.1818) > FR1(0.1596) > FR4(0.1308) > FR3(0.1255) >
    FR2(0.0899) > FR5(0.0846) > FR7(0.0845) > FR6(0.0770).
    Relative weights of financial ratios obtained by the proposed methods and average relative
    weights are presented in Figure 1.
    Relative weight

    FR1 FR2 FR3 FR4 FR5 FR6 FR7 FR8 FR9
    RW_MLP 0.1180 0.1080 0.1320 0.1090 0.1040 0.0950 0.1000 0.0920 0.1420
    RW_EM 0.2345 0.0304 0.1225 0.1749 0.0544 0.0554 0.0556 0.0272 0.2451
    RW_CRITIC 0.1263 0.1314 0.1221 0.1085 0.0954 0.0806 0.0979 0.0795 0.1582
    Average 0.1596 0.0899 0.1255 0.1308 0.0846 0.0770 0.0845 0.0663 0.1818

    Figure 1 Average relative weights

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  15. G. Anupama and V.V.S. Kesava Rao

    14. CONCLUDING REMARKS
    The aim of this paper is to determine the relative weights of the financial ratios through MLP
    of artificial neural networks in predicting financial efficiency, based on financial ratios data
    collected from annual reports of eighteen software companies during 1st FY to 5th FY. Also, the
    results of the neural network analysis are compared with entropy measurement method and
    CRITIC method. Multilayer perceptron neural networks were trained, to predict financial
    efficiency also.
    The classification accuracy rate of multilayer perception was very high, with 100%. The
    results also showed that MLP of ANN is the most powerful predictors of financial efficiency.
    Although future work will need to validate these findings in larger and more diverse samples,
    there is strong evidence that the proposed model can be used effectively to predict financial
    efficiency of business organizations in general and software companies in particular and to help
    the management to design interventions that increase the financial efficiency.

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    APPENDIX
    Table-A.1 Data belonging to financial ratios for the 1st year
    Turnover
    rate of Return of Operatin
    Software Turnover Operatin Return
    Stockholder accounts stockholde Quick g cash Marke
    compan rate of g income of
    s equity receivable r equity Ratio flow ratio t Share
    y inventory ratio Assets
    ratio (FR1) s (FR4) (FR5) (FR7) (FR9)
    (FR3) (FR6) (FR8)
    (FR2)
    SWC1 0.1298 6.1418 981.2177 -0.6244 0.377 0.0697 0.0404 – 0.0052
    4 0.0811
    SWC2 0.0047 6.3151 136.2825 46.4965 2.151 0.2500 0.6807 0.2166 0.1274
    8
    SWC3 0.0050 6.4964 3016.000 37.2587 3.836 0.2671 0.7710 0.1861 0.1988
    0 8
    SWC4 0.0172 4.7198 1350.682 6.7102 1.519 0.1402 0.2634 0.1153 0.0107
    2 8
    SWC5 0.0147 6.9437 1299.936 4.6751 2.546 0.0976 0.4650 0.0687 0.0037
    5 8
    SWC6 0.0199 5.7679 1301.411 10.8106 3.826 0.2012 0.7064 0.2147 0.0120
    5 1
    SWC7 0.0300 3.6304 1299.808 1.4404 2.436 0.1694 0.1465 0.0432 0.0103
    9 1
    SWC8 0.0331 4.5276 417.7281 3.7979 2.703 0.1537 0.2895 0.1256 0.0091
    6
    SWC9 0.0043 5.3117 1307.661 32.3109 9.247 0.3740 0.7097 0.1398 0.0148
    8 0
    SWC10 0.0257 6.0927 1300.962 6.2320 3.436 0.2482 0.8481 0.1601 0.0066
    5 7
    SWC11 0.0221 3.3705 1297.356 1.7584 0.308 0.3276 0.2878 0.0389 0.0099
    2 9
    SWC12 0.0427 5.0058 146.0758 2.4187 3.953 0.1166 0.6923 0.1034 0.0018
    1
    SWC13 0.0160 8.9554 1466.290 7.3926 2.257 0.0636 0.4550 0.1180 0.0062
    0 0
    SWC14 0.0029 5.0615 3116.423 97.8397 3.209 0.3075 0.8360 0.2854 0.3244
    0 8
    SWC15 0.0792 5.3193 4098.000 2.4120 1.872 0.1773 0.7977 0.1911 0.0031
    0 7
    SWC16 0.0146 6.2134 1405.634 12.9713 1.974 0.2225 0.2496 0.1900 0.0746
    6 4
    SWC17 0.0099 5.3555 121.6289 16.1199 2.223 0.2219 0.5476 0.1599 0.1722
    2
    SWC18 0.0295 6.7336 16.9201 5.4265 1.969 0.1534 0.5656 0.1598 0.0093
    6

    Table-A.2 Data belonging to financial ratios for the 2nd year

    Softwar Turnover rate Return of Operati Operating
    Return
    e Stockholders of accounts Turnover rate stockholder Quick ng cash flow Market
    of
    compan equity ratio receivables of inventory equity Ratio income ratio Share
    Assets
    y (FR1) (FR2) (FR3) (FR4) (FR5) ratio (FR7) (FR9)
    (FR8)
    (FR6)
    SWC1 0.1660 6.9077 836.6929 -1.6170 0.4026 0.1284 -0.0290 -0.2684 0.004693

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  17. G. Anupama and V.V.S. Kesava Rao

    SWC2 0.0080 6.0060 201.6980 26.0209 2.4413 0.2309 0.5317 0.2073 0.128143
    SWC3 0.0086 5.9033 1301.0146 21.6294 3.4819 0.2791 0.5263 0.1857 0.186165
    SWC4 0.0165 4.3579 202.6233 6.3012 1.5730 0.1085 0.5998 0.1038 0.010439
    SWC5 0.0136 8.0919 1299.7027 1.5732 2.3440 0.0468 0.2834 0.0213 0.003535
    SWC6 0.0315 5.4938 1300.7675 6.4074 3.2675 0.1991 0.9353 0.2020 0.012436
    SWC7 0.0282 8.2604 1299.9875 3.2103 2.5911 0.1496 0.4397 0.0905 0.020233
    SWC8 0.0303 4.0544 297.3188 1.8688 2.2119 0.1391 0.3963 0.0566 0.008284
    SWC9 0.0067 6.0902 1299.1862 28.1806 1.8961 0.3974 0.3751 0.1901 0.013634
    SWC10 0.0444 5.7189 1301.0629 3.6329 3.5237 0.2064 0.7971 0.1614 0.006603
    SWC11 0.0191 3.4431 1297.4939 1.5197 0.4284 0.3517 0.2067 0.0290 0.012847
    SWC12 0.0382 5.2617 385.7953 5.6026 4.6112 -0.1447 1.7252 0.2139 0.001494
    SWC13 0.0130 6.4877 354.6815 12.7091 2.0666 0.0997 0.2163 0.1654 0.005873
    SWC14 0.0027 4.8954 4486.3619 101.3539 2.6936 0.2587 0.8544 0.2695 0.330468
    SWC15 0.0662 5.4860 4635.4483 3.3044 1.9887 0.2087 0.7669 0.2188 0.002966
    SWC16 0.0242 4.7352 1074.5364 5.4698 2.0811 0.1854 0.3548 0.1324 0.078983
    SWC17 0.0083 5.3047 102.6374 17.5428 2.1787 0.2194 0.5451 0.1459 0.163931
    SWC18 0.0253 6.5412 18.0122 5.9686 2.0244 0.1475 0.7641 0.1510 0.009273

    Table-A.3: Data belonging to financial ratios for the 3rd year

    Softwar Turnover rate Return of Operating
    Operating Return
    e Stockholders of accounts Turnover rate stockholde Quick cash flow Market
    income of
    compan equity ratio receivables of inventory r equity Ratio ratio Share
    ratio Assets
    y (FR1) (FR2) (FR3) (FR4) (FR5) (FR7) (FR9)
    (FR6) (FR8)
    SWC1 0.4034 6.2637 1689.2743 -0.8610 0.5238 -0.6959 0.3602 -0.3473 0.003574
    SWC2 0.0072 4.3669 116.0055 19.8611 2.4697 0.2137 0.3496 0.1421 0.098853
    SWC3 0.0152 5.9346 1302.2510 11.7911 4.5542 0.2735 0.7370 0.1790 0.198242
    SWC4 0.0171 4.6595 91.6409 7.4767 1.9310 0.1348 0.7307 0.1279 0.010237
    SWC5 0.0269 4.5697 1300.8451 1.1948 3.3349 0.0287 0.2913 0.0321 0.001673
    SWC6 0.0506 5.5994 1299.7556 3.2926 2.3899 0.1757 0.4914 0.1666 0.014836
    SWC7 0.0295 9.5450 2545.3073 3.0045 4.3873 0.1419 0.9124 0.0885 0.019306
    SWC8 0.0263 4.4945 503.1328 4.4118 1.8866 0.1755 0.4832 0.1160 0.008534
    SWC9 0.0074 5.7670 1302.2844 24.7672 4.5831 0.3916 0.6701 0.1828 0.013116
    SWC10 0.0373 5.8828 1301.0457 3.4663 3.5089 0.1693 0.5257 0.1293 0.007341
    SWC11 0.0172 2.3494 1297.4821 1.1296 0.4181 0.3021 0.2125 0.0194 0.012063
    SWC12 0.0278 5.8140 323.5205 11.6416 4.3087 0.0224 1.8110 0.3235 0.001534
    SWC13 0.0106 5.8396 201.6851 15.0751 1.6740 0.0989 0.4587 0.1599 0.006161
    SWC14 0.0022 4.8818 4862.4259 123.1980 4.2836 0.2824 1.0727 0.2723 0.344937
    SWC15 0.0514 5.8231 5706.8276 4.9714 2.2688 0.2304 0.5511 0.2557 0.003414
    SWC16 0.0193 4.8275 685.9136 6.8723 2.2918 0.1612 0.4568 0.1327 0.084116
    SWC17 0.0066 5.3613 79.0081 18.0285 2.0085 0.2107 0.4899 0.1191 0.162693
    SWC18 0.0233 5.9399 20.2269 6.4878 2.3456 0.1486 0.5056 0.1509 0.009372

    Table-A.4: Data belonging to financial ratios for the 4th year

    Softwar Turnover rate Return of Operating
    of accounts Operating cash flow Retur
    e Stockholders Turnover rate stockhold Quick income n of
    Market
    compan equity ratio receivables of inventory er equity Ratio ratio Share
    ratio Assets
    y (FR1) (FR2) (FR3) (FR4) (FR5) (FR7) (FR9)
    (FR6) (FR8)
    SWC1 0.7223 5.2397 973.2874 0.0800 0.4050 0.1564 0.1149 0.0578 0.002826
    SWC2 0.0062 5.9378 137.5962 30.1965 2.3498 0.2183 0.7172 0.1868 0.133911
    SWC3 0.0136 5.7910 1302.3524 12.5463 4.6421 0.2717 0.7663 0.1708 0.192792
    SWC4 0.0148 4.5157 73.0530 6.3366 1.9498 0.1050 0.2847 0.0938 0.009346
    SWC5 0.0160 6.1482 1299.4242 2.7725 2.1025 0.0812 0.2177 0.0443 0.001577
    SWC6 0.0491 5.6034 1300.2779 2.4917 2.8430 0.1345 0.8781 0.1224 0.014741
    SWC7 0.0285 9.5181 2494.1024 3.7619 4.4497 0.1586 0.6872 0.1073 0.017106
    SWC8 0.0247 5.2965 7740.3333 4.0733 2.0441 0.1713 0.6070 0.1004 0.007888
    SWC9 0.0070 5.7150 1299.1445 27.9112 1.8600 0.3908 0.4030 0.1961 0.012461
    SWC10 0.0338 6.3758 1301.5167 3.7684 3.9173 0.1583 0.6165 0.1274 0.008103
    SWC11 0.0156 1.9229 1297.6098 1.0150 0.5288 0.3044 -0.0278 0.0158 0.008952

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  18. Some Objective Methods for Determining Relative Importance of Financial Ratios

    SWC12 0.0256 5.3704 337.9028 4.9497 5.8861 0.1069 0.2594 0.1266 0.001315
    SWC13 0.0087 5.4230 435.4106 15.0723 1.7774 0.0808 0.3342 0.1305 0.006674
    SWC14 0.0019 5.0532 4630.0000 133.4467 5.1366 0.2739 1.4336 0.2539 0.332091
    SWC15 0.0432 5.3794 1301.3368 5.6127 3.7613 0.2211 0.8859 0.2426 0.003483
    SWC16 0.0168 5.2467 492.2367 6.4104 2.0357 0.1436 0.4926 0.1079 0.082035
    SWC17 0.0059 5.7028 94.8469 17.4719 2.0497 0.2042 0.5785 0.1036 0.156095
    SWC18 0.0209 5.6944 22.4173 5.2345 2.5092 0.1250 0.5587 0.1092 0.008602

    Table-A.5 Data belonging to financial ratios for the 5th year

    Softwar Turnover rate Return of Operati Operating
    Return
    e Stockholders of accounts Turnover rate stockholder Quick ng cash flow Market
    of
    compan equity ratio receivables of inventory equity Ratio income ratio Share
    Assets
    y (FR1) (FR2) (FR3) (FR4) (FR5) ratio (FR7) (FR9)
    (FR8)
    (FR6)
    SWC1 0.9961 4.7757 874.7225 0.0436 0.5345 0.1572 0.1356 0.0434 0.002695
    SWC2 0.0058 5.6376 175.5491 31.3705 2.4869 0.2224 0.7369 0.1808 0.13749
    SWC3 0.0135 5.5390 1302.0376 14.7325 4.3691 0.2696 0.8507 0.1992 0.19174
    SWC4 0.0138 4.6083 97.9456 6.6715 2.0681 0.1013 0.6633 0.0923 0.009961
    SWC5 0.0141 7.4214 1299.6222 5.9038 2.2742 0.1220 0.2904 0.0833 0.002222
    SWC6 0.0433 5.7151 1300.1192 3.4783 2.7053 0.1356 0.7575 0.1505 0.014853
    SWC7 0.0276 9.0946 1300.8642 4.3333 3.3514 0.1622 0.6429 0.1194 0.017797
    SWC8 0.0228 5.6774 8298.0000 4.5561 1.9668 0.1678 0.4235 0.1038 0.008133
    SWC9 0.0071 5.2477 1301.6730 28.9909 4.0529 0.4000 0.9130 0.2070 0.01231
    SWC10 0.0300 6.3194 1301.5781 4.0386 3.9706 0.1545 0.7778 0.1210 0.008248
    SWC11 0.0145 2.0309 1297.6936 -0.6395 0.6016 0.2889 0.0303 -0.0092 0.007778
    SWC12 0.0232 6.4312 1303.9958 4.8171 6.0674 0.1381 0.6861 0.1120 0.001368
    SWC13 0.0084 5.3559 1299.2248 18.5482 1.9296 0.0941 0.5448 0.1561 0.006672
    SWC14 0.0018 5.1768 3854.8085 135.2147 4.4735 0.2641 1.2029 0.2430 0.334704
    SWC15 0.0655 5.0276 1301.6462 3.8542 4.0296 0.2513 0.9269 0.2524 0.003769
    SWC16 0.0145 5.2001 410.4457 8.6027 1.9674 0.1530 0.3862 0.1248 0.083667
    SWC17 0.0116 5.5646 121.0707 8.8448 1.9927 0.1906 0.5226 0.1027 0.148143
    SWC18 0.0193 5.2878 25.0863 5.3685 2.6411 0.1174 0.3182 0.1039 0.00845

    Table-A.6:
    Turnover
    Softwar rate of Return of Opera Operatin
    Turnover Return Mark
    e Stockholde accounts stockhold Quick ting g cash
    rate of of et
    compan rs equity receivable er equity Ratio incom flow ratio
    inventory Assets Share
    y ratio (FR1) s (FR4) (FR5) e ratio (FR7)
    (FR3) (FR8) (FR9)
    (FR2) (FR6)
    SWC1 1.0000 0.4962 0.2363 0.0465 0.0077 0.0199 0.0000 0.0000 0.0104
    SWC2 0.0137 0.5272 0.0292 0.5028 0.2062 0.6004 0.7927 0.8123 0.3895
    SWC3 0.0164 0.5597 0.7349 0.4134 0.3947 0.6556 0.9045 0.7288 0.6106
    SWC4 0.1124 0.2416 0.3268 0.1175 0.1355 0.2468 0.2761 0.5357 0.0275
    SWC5 0.0928 0.6398 0.3144 0.0978 0.2504 0.1095 0.5257 0.4087 0.0057
    SWC6 0.1335 0.4293 0.3147 0.1572 0.3935 0.4434 0.8246 0.8071 0.0316
    SWC7 0.2134 0.0465 0.3144 0.0665 0.2380 0.3409 0.1315 0.3391 0.0263
    SWC8 0.2377 0.2072 0.0982 0.0893 0.2679 0.2902 0.3085 0.5640 0.0227
    SWC9 0.0111 0.3476 0.3163 0.3654 1.0000 1.0000 0.8287 0.6026 0.0404
    SWC10 0.1795 0.4874 0.3146 0.1129 0.3499 0.5947 1.0000 0.6581 0.0149
    SWC11 0.1515 0.0000 0.3137 0.0696 0.0000 0.8504 0.3064 0.3274 0.0251
    SWC12 0.3138 0.2928 0.0316 0.0760 0.4077 0.1708 0.8071 0.5033 0.0000
    SWC13 0.1028 1.0000 0.3551 0.1241 0.2180 0.0000 0.5133 0.5432 0.0136
    SWC14 0.0000 0.3028 0.7595 1.0000 0.3245 0.7856 0.9850 1.0000 1.0000
    SWC15 0.6014 0.3489 1.0000 0.0759 0.1750 0.3664 0.9377 0.7427 0.0039
    SWC16 0.0924 0.5090 0.3403 0.1782 0.1863 0.5120 0.2590 0.7396 0.2255
    SWC17 0.0552 0.3554 0.0257 0.2086 0.2142 0.5100 0.6279 0.6576 0.5282
    SWC18 0.2091 0.6022 0.0000 0.0000 0.1858 0.2893 0.6503 0.6573 0.0231

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  19. G. Anupama and V.V.S. Kesava Rao

    Table-A.7

    Return
    Oper
    Softwar Stockh Turnover rate of Operatin
    Turnover ating Retur
    e olders of accounts stockhol Quick g cash Marke
    rate of incom n of
    compan equity receivables der Ratio flow ratio t Share
    inventory e Assets
    y ratio (FR2) equity (FR5) (FR7) (FR9)
    (FR3) ratio (FR8)
    (FR1) (FR4)
    (FR6)
    0.503
    SWC1 1.0000 0.7192 0.1773 0.0000 0.0000 9 0.0000 0.0000 0.0097
    0.692
    SWC2 0.0325 0.5320 0.0398 0.2684 0.4844 8 0.3196 0.8844 0.3850
    0.781
    SWC3 0.0363 0.5107 0.2779 0.2258 0.7317 8 0.3166 0.8443 0.5614
    0.467
    SWC4 0.0846 0.1899 0.0400 0.0769 0.2781 1 0.3584 0.6920 0.0272
    0.353
    SWC5 0.0667 0.9650 0.2776 0.0310 0.4613 4 0.1781 0.5386 0.0062
    0.634
    SWC6 0.1767 0.4257 0.2778 0.0779 0.6807 2 0.5497 0.8745 0.0333
    0.542
    SWC7 0.1562 1.0000 0.2776 0.0469 0.5200 9 0.2672 0.6672 0.0570
    0.523
    SWC8 0.1690 0.1269 0.0605 0.0339 0.4299 5 0.2424 0.6041 0.0206
    1.000
    SWC9 0.0250 0.5495 0.2775 0.2894 0.3549 0 0.2304 0.8525 0.0369
    0.647
    SWC10 0.2557 0.4724 0.2779 0.0510 0.7416 7 0.4709 0.7990 0.0155
    0.915
    SWC11 0.1004 0.0000 0.2771 0.0305 0.0061 7 0.1344 0.5528 0.0345
    0.000
    SWC12 0.2174 0.3775 0.0797 0.0701 1.0000 0 1.0000 0.8966 0.0000
    0.450
    SWC13 0.0634 0.6320 0.0729 0.1391 0.3954 8 0.1399 0.8065 0.0133
    0.744
    SWC14 0.0000 0.3015 0.9677 1.0000 0.5444 1 0.5036 1.0000 1.0000
    0.651
    SWC15 0.3890 0.4241 1.0000 0.0478 0.3769 9 0.4537 0.9057 0.0045
    0.608
    SWC16 0.1319 0.2682 0.2288 0.0688 0.3988 9 0.2188 0.7451 0.2355
    0.671
    SWC17 0.0346 0.3865 0.0183 0.1861 0.4220 6 0.3273 0.7702 0.4938
    0.539
    SWC18 0.1386 0.6431 0.0000 0.0737 0.3854 0 0.4521 0.7797 0.0236

    Table-A.8
    Return
    Softwa Stockho Turnover rate of Operati Operatin
    Turnover Retur
    re lders of accounts stockhol Quick ng g cash Marke
    rate of n of
    compa equity receivables der Ratio income flow ratio t Share
    inventory Assets
    ny ratio (FR2) equity (FR5) ratio (FR7) (FR9)
    (FR3) (FR8)
    (FR1) (FR4) (FR6)
    SWC1 1.0000 0.5440 0.2935 0.0000 0.0254 0.0000 0.0924 0.0000 0.0059
    SWC2 0.0123 0.2804 0.0168 0.1670 0.4926 0.8364 0.0857 0.7296 0.2834
    SWC3 0.0323 0.4982 0.2254 0.1020 0.9930 0.8914 0.3281 0.7846 0.5728
    SWC4 0.0371 0.3210 0.0126 0.0672 0.3632 0.7639 0.3242 0.7084 0.0253
    SWC5 0.0615 0.3086 0.2252 0.0166 0.7003 0.6663 0.0493 0.5656 0.0004
    SWC6 0.1206 0.4517 0.2250 0.0335 0.4734 0.8014 0.1744 0.7661 0.0387
    SWC7 0.0679 1.0000 0.4440 0.0312 0.9530 0.7704 0.4378 0.6497 0.0518
    SWC8 0.0600 0.2981 0.0849 0.0425 0.3526 0.8012 0.1693 0.6906 0.0204

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  20. Some Objective Methods for Determining Relative Importance of Financial Ratios

    SWC9 0.0129 0.4750 0.2255 0.2066 1.0000 1.0000 0.2862 0.7903 0.0337
    SWC10 0.0875 0.4911 0.2252 0.0349 0.7421 0.7956 0.1959 0.7105 0.0169
    SWC11 0.0374 0.0000 0.2246 0.0160 0.0000 0.9176 0.0000 0.5467 0.0307
    SWC12 0.0638 0.4815 0.0533 0.1008 0.9341 0.6605 1.0000 1.0000 0.0000
    SWC13 0.0209 0.4850 0.0319 0.1285 0.3015 0.7308 0.1540 0.7561 0.0135
    SWC14 0.0000 0.3519 0.8515 1.0000 0.9281 0.8995 0.5381 0.9237 1.0000
    SWC15 0.1227 0.4828 1.0000 0.0470 0.4443 0.8517 0.2118 0.8990 0.0055
    SWC16 0.0426 0.3444 0.1171 0.0623 0.4499 0.7881 0.1528 0.7156 0.2405
    SWC17 0.0110 0.4186 0.0103 0.1523 0.3819 0.8336 0.1735 0.6954 0.4693
    SWC18 0.0525 0.4990 0.0000 0.0592 0.4628 0.7766 0.1833 0.7428 0.0228

    Table-A.9
    Return
    Softwa Stockho Turnover rate of Operati Operatin
    Turnover Return
    re lders of accounts stockhol Quick ng g cash Marke
    rate of of
    compa equity receivables der Ratio income flow ratio t Share
    inventory Assets
    ny ratio (FR2) equity (FR5) ratio (FR7) (FR9)
    (FR3) (FR8)
    (FR1) (FR4) (FR6)
    SWC1 1.0000 0.4367 0.1232 0.0000 0.0000 0.2440 0.0976 0.1763 0.0046
    SWC2 0.0059 0.5286 0.0149 0.2258 0.3548 0.4435 0.5098 0.7182 0.4009
    SWC3 0.0163 0.5093 0.1658 0.0935 0.7730 0.6156 0.5434 0.6511 0.5789
    SWC4 0.0179 0.3414 0.0066 0.0469 0.2818 0.0781 0.2138 0.3276 0.0243
    SWC5 0.0195 0.5563 0.1655 0.0202 0.3097 0.0012 0.1680 0.1196 0.0008
    SWC6 0.0655 0.4846 0.1656 0.0181 0.4448 0.1733 0.6199 0.4475 0.0406
    SWC7 0.0369 1.0000 0.3203 0.0276 0.7379 0.2508 0.4892 0.3841 0.0477
    SWC8 0.0316 0.4442 1.0000 0.0299 0.2990 0.2919 0.4344 0.3554 0.0199
    SWC9 0.0071 0.4993 0.1654 0.2087 0.2654 1.0000 0.2948 0.7575 0.0337
    SWC10 0.0443 0.5863 0.1657 0.0277 0.6408 0.2501 0.4409 0.4686 0.0205
    SWC11 0.0190 0.0000 0.1652 0.0070 0.0226 0.7214 0.0000 0.0000 0.0231
    SWC12 0.0329 0.4539 0.0409 0.0365 1.0000 0.0843 0.1965 0.4655 0.0000
    SWC13 0.0094 0.4608 0.0535 0.1124 0.2504 0.0000 0.2477 0.4817 0.0162
    SWC14 0.0000 0.4121 0.5970 1.0000 0.8633 0.6228 1.0000 1.0000 1.0000
    SWC15 0.0573 0.4551 0.1657 0.0415 0.6123 0.4526 0.6252 0.9525 0.0066
    SWC16 0.0207 0.4376 0.0609 0.0475 0.2975 0.2025 0.3561 0.3868 0.2440
    SWC17 0.0056 0.4977 0.0094 0.1304 0.3001 0.3979 0.4148 0.3689 0.4679
    SWC18 0.0263 0.4966 0.0000 0.0386 0.3839 0.1425 0.4013 0.3923 0.0220

    Table-A.10
    Return
    Softwa Stockho Turnover rate of Operati Operatin
    Turnover Retur
    re lders of accounts stockhol Quick ng g cash Market
    rate of n of
    compa equity receivables der Ratio income flow ratio Share
    inventory Assets
    ny ratio (FR2) equity (FR5) ratio (FR7) (FR9)
    (FR3) (FR8)
    (FR1) (FR4) (FR6)
    0.201
    SWC1 1.0000 0.3886 0.1027 0.0050 0.0000 0.2062 0.0898 2 0.0040
    0.726
    SWC2 0.0040 0.5106 0.0182 0.2356 0.3529 0.4193 0.6025 1 0.4084
    0.796
    SWC3 0.0118 0.4966 0.1544 0.1132 0.6930 0.5735 0.6996 7 0.5711
    0.387
    SWC4 0.0121 0.3649 0.0088 0.0538 0.2772 0.0236 0.5398 9 0.0258
    0.353
    SWC5 0.0124 0.7631 0.1541 0.0482 0.3144 0.0910 0.2218 6 0.0026
    0.610
    SWC6 0.0417 0.5216 0.1541 0.0303 0.3923 0.1354 0.6201 5 0.0405
    0.491
    SWC7 0.0259 1.0000 0.1542 0.0366 0.5091 0.2226 0.5224 8 0.0493
    0.432
    SWC8 0.0211 0.5162 1.0000 0.0382 0.2589 0.2409 0.3353 0 0.0203
    0.826
    SWC9 0.0054 0.4554 0.1543 0.2181 0.6359 1.0000 0.7527 6 0.0328

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