Reestimation and comparisons of alternative accounting based bankruptcy prediction models for Indian companies
 Bhanu Pratap Singh^{1}Email author and
 Alok Kumar Mishra^{1}Email author
DOI: 10.1186/s4085401600269
© The Author(s). 2016
Received: 9 January 2016
Accepted: 27 May 2016
Published: 9 June 2016
Abstract
Background
The suitability and performance of the bankruptcy prediction models is an empirical question. The aim of this paper is to develop a bankruptcy prediction model for Indian manufacturing companies on a sample of 208 companies consisting of an equal number of defaulted and nondefaulted firms. Out of 208 companies, 130 are used for estimation sample, and 78 are holdout for model validation. The study reestimates the accounting based models such as Altman EI (Journal of Finance 23: 19189–209, 1968) ZScore, Ohlson JA (Journal of Accounting Research 18:109–131, 1980) YScore and Zmijewski ME (Journal of Accounting Research 22:59–82, 1984) XScore model. The paper compares original and reestimated models to explore the sensitivity of these models towards the change in time periods and financial conditions.
Methods
Multiple Discriminant Analysis (MDA) and Probit techniques are employed in the estimation of ZScore and XScore models, whereas Logit technique is employed in the estimation of YScore and the newly proposed models. The performance of all the original, reestimated and new proposed models are assessed by predictive accuracy, significance of parameters, longrange accuracy, secondary sample and Receiver Operating Characteristic (ROC) tests.
Results
The major findings of the study reveal that the overall predictive accuracy of all the three models improves on estimation and holdout sample when the coefficients are reestimated. Amongst the contesting models, the new bankruptcy prediction model outperforms other models.
Conclusions
The industry specific model should be developed with the new combinations of financial ratios to predict bankruptcy of the firms in a particular country. The study further suggests the coefficients of the models are sensitive to time periods and financial condition. Hence, researchers should be cautioned while choosing the models for bankruptcy prediction to recalculate the models by looking at the recent data in order to get higher predictive accuracy.
Keywords
Bankruptcy prediction Indian manufacturing companies MDA Logit Probit Unstable coefficient Predictive accuracy Receiver operating characteristic Long range accuracyJEL Classification Codes
G 33Background
The World Economy at the start of 21^{st} century begin with the financial crisis, which led to shift emphasis on modeling and evaluation of credit risk. The factors behind the shift in the trend are the rapid growth of the credit derivative market, rise in the bankruptcy and developing credit risk literature. The failure of rating agencies (Moody’s, Standard and Poor’s) to predict the fall of giant manufacturing companies like Chrysler, GM, LyondellBasell Industries, Excide Technologies alarmed the need to revisit risk management framework worldwide.
The current study proposes a new bankruptcy prediction model for Indian manufacturing companies. Since Beaver (1966), a substantial literature on bankruptcy prediction is developed to assess the financial health of companies. These models were based upon different theoretical approaches and types of information to model bankruptcy. Three notable and most cited accounting based bankruptcy models in the literature of accounting research are Altman (1968), Ohlson (1980) and Zmijewski (1984) (Grice and Dugan, 2001). The suitability and performance of these models in the new era is an empirical question due to change in time periods and financial conditions in which it was originally developed. The study reestimates and compares these models with the newly proposed model.
In the bankruptcy prediction literature academician and accounting, practitioners have differed in the opinion on the power of these models to address the sensitivity of time periods and financial condition (crosscountry heterogeneity, market structure, business cycle, etc.).
Begley et al. (1996) reestimates and compares performance of original Altman’s and Ohlson’s models using US 1980’s data. The major finding of the study suggests Altman’s and Ohlson’s model outperforms reestimated model. Both the reestimated model have higher classification errors. Out of four contesting models, Ohlson’s original model outperforms other three contesting models. In line with Begley, Boritz et al. (2007) studying bankruptcy in Canada founds predictive accuracy of Altman’s and Ohlson’s original models are higher than reestimated model. They also compared the accuracy of models developed for Canadian firms, namely, Springate (1978), Altman and Levallee (1980), and Legault and Veronneau (1986). The study concludes the Canadian models are being simpler and requiring less data. All models have stronger performance with the original coefficients than the reestimated coefficients.
On the contrary, there are ample of studies questioning construct validity of the models to original models towards the change in time periods and financial conditions. Grice and Ingram (2001) analysed the sensitivity of Altman’s Zscore model for US companies. The study suggests the coefficients of the models are sensitive to the change in the financial environment and time period. The reestimated model with the most recent information give better predictive accuracy. Grice and Dugan (2001) conducted study on US companies founds predictive accuracy of reestimated Altman’s and Ohlson’s model is higher than the original models. Timmermans (2014) analysed the sensitivity of Altman’s, Ohlson’s and Zmijewski’s models on US companies. The major finding of the study suggests the reestimated model have a higher predictive accuracy than the original models. Avenhuis (2013) conducted study on Dutch companies. The study reestimates and compares performance of Altman’s, Ohlson’s and Zmijewski’s original models. The major finding of the study suggests reestimation of model with specific and bigger sample give better predictive accuracy.
According to Platt and Platt (1990) the economic environment of two periods may change because of three reasons: First, change in the relationship between bankruptcy (dependent variable) and financial ratios. Second, change in the range of financial ratios (independent variables). And third, change in the relationship among financial ratios. They also suggested these changes attribute to bring change in the corporate strategy, the competitive nature of market, business cycle and technology. In the Indian market Bandyopadhyay (2006), Bhumia and Sarkar, (2011) and Shetty et al. (2012) developed Industry specific models for Indian corporate bond, pharmaceutical, and Information Technology/Information Technology Enabled Services (IT/ITES) industry respectively. Chudson (1945) mentions industry specific models are more appropriate than general models. The similar evidence is also found in the study of Avenhuis (2013).
In the light of above discussion the major aim of the paper is threefold: First, to develop a new bankruptcy prediction model for Indian manufacturing companies on Indian sample. Second, to revisits and reestimate Altman (1968), Ohlson (1980) and Zmijewski (1984) models to examine the sensitivity of these models towards change in financial conditions and time periods. Finally, to choose the best model for prediction of financial distress of Indian manufacturing companies. The current study differs from prior study in three perspectives: Firstly, the study uses larger data set sampled over a longer period (Sample size 208) than in previous studies on Indian market which increases statistical power of the model. Second, the new bankruptcy prediction model is proposed with a unique combination of financial ratios measuring leverage, profitability and turnover of Indian manufacturing companies. Third, in the Indian market, there is no attempt is made to compare the sensitivity of Altman’s, Ohlson’s and Zmijewski’s models together towards change in time period and financial conditions.
The major findings of the study reveal that the overall predictive accuracy of all the three models improves on estimation and holdout sample when the coefficients are reestimated. Amongst the contesting models, the new proposed model outperforms while predicting bankruptcy for Indian manufacturing companies. The study further suggests the coefficients of the models are sensitive to time periods and financial conditions. The relation between financial ratios and bankruptcy and the comparative importance of the financial ratios are also not constant over the time periods. The findings are in line with past studies of Grice and Ingram (2001), Grice and Dugan (2001), Timmermans (2014) and Avenhuis (2013). Hence, researchers should be cautioned while choosing the models for bankruptcy prediction to recalculate the models by looking at the recent data in order to get higher predictive accuracy. The remainder of this paper is organized as follows. Survey of literature is covered in section 2. Section 3 discusses considered models for the study. Section 4 deals with sample and development of new bankruptcy prediction models for Indian manufacturing companies. Reestimations of models, results and discussion and evaluation of the model is done in section 5. The study concludes with section 6 which discusses the implications of those findings for users of the models.
Survey of literature
 1.
Parametric Models (Accounting and marketbased models) and
 2.
Nonparametric Models (Artificial Neural Networks (ANN), Hazard models, Fuzzy Models, Genetic Algorithms (GA) and Hybrid models, or models in which several of the former models are combined)
Parametric models
The parametric models could be univariate and multivariate in nature which uses mainly financial ratios and focuses on the symptoms of bankruptcy (Andan & Dar, 2006). Sometimes these models uses nonfinancial information (Ohlson, 1980; Bandyopadhyay, 2006). Balcaen and Ooghe (2004) and Bellovary et al. (2007) are the most cited paper in literature of bankruptcy prediction. Both the papers focused on the problems of parametric models. These problems are related to assumptions on the dichotomous variable, the sampling method, stationarity assumptions, data instability, selection of independent variables, use of accounting information and the time dimension (Balcaen & Ooghe, 2004). Further, parametric models can be classified into two categories: accounting based and marketbased models. Marketbased models are again divided into two parts structural and reduced form models.
Accounting based models
Beaver (1966) with his univariate default prediction study on US firms revolutionize the practice of credit risk assessment. The study compares the mean values of 30 financial ratios of 79 failed and 79 nonfailed firms in 38 industries. Further, the study tests the ability of individual financial ratios to classify between bankrupt and nonbankrupt firms. Four financial ratios were found to have highest classification power, namely, net income to total debt (92 %), net income to net worth (91 %), cash flow to total debt (90 %), and cash flow to total assets (90 %). For future research, the study suggested multiple ratios considered simultaneously may have higher predictive ability than single ratios which created a platform for multiple ratio models.
Altman (1968) developed a first multivariate discriminant model for default prediction for US companies. The model uses five financial ratios to predict bankruptcy of the firms. The model can predict bankruptcy with 95 % of accuracy for the initial sample one year prior to bankruptcy. Altman et al. (1977) developed a model for US manufacturing and retailers, which had the effective classifying ability from 5 years prior to default. Since Altman (1968), discriminant analysis is used by many researchers by making changes in financial ratios, study sample, and change in business culture. Some of the notable studies are Deakin (1972), Blum (1974), Springate (1978) and Fulmer (1984).
The limitations of discriminant analysis created space for the development of logit model. Ohlson (1980) introduced a logit model in the literature of bankruptcy prediction. The assumptions of logit model were different from Zscore models. Ohlson identified nine independent variables (financial and nonfinancial) based upon their frequent use in the bankruptcy prediction literature. The model was developed with the sample of 2163 companies (105 defaulted and 2058 nondefaulted) for the period 19701976. In line with Ohlson, Abdullah et al. (2008), applied the logistic model to foretell corporate failure of Malaysian firms. Further, Zmijewski (1984) applied probit technique using data of 40 bankrupt and 8000 nonbankrupt US firms for the period 19701978.
After logit and probit models, the number of studies attempted making comparison between logit, probit, and MDA analysis. In case of Thailand, Pongsatat et al. (2004) examines predictive capabilities of Ohlson’s and Altman’s models. The study concludes Altman model outperforms Ohlson model on the basis of predictive accuracy. Likewise, Ugurlu and Aksoy (2006) developed bankruptcy prediction model for Turkish firms using Altman’s (1968) and Ohlson’s (1980) statistical techniques. Further, Gu (2002) develops MDA model for estimating the failure of USA restaurant firms. In the Indian market, Bandyopadhyay (2006) develops a bankruptcy prediction model for the Indian corporate bond sector using MDA and logistic technique. Bhumia and Sarkar, (2011) developed a corporate failure model for the Indian pharmaceutical company based upon MDA technique. Ramkrishnan (2005) used discriminant and logistic model to foretell bankruptcy for Indian companies.
Marketbased models
The marketbased models are classified into structural (Merton 1974; Agarwal and Taffler 2008; Wu, Gaunt and Gray 2010; Hillegeist et al. (2004) and Bharath and Shumway 2008) and reduced (Jarrow and Turnbull 1995; Duffie and Singleton 1999 and Lando 1994) form models.
Black and Scholes (1973) option pricing theory which was extended by Metron (1974) is applied to model default in structural based models. In these models firms can default on its debt obligation only at the time of maturity. Later, some models were developed by extension to allow a default to occur before the date of maturity. These models were familiarized by Black and Cox (1976), Lonfstaff and Schwartz (1995), Leland and Toft (1996). On the other hand, reduced form models focus over modeling default explicitly as an intensity or compensator process. Some of the notable marketbased studies in the Indian market based upon Board of Industrial and Financial Reconstruction (BIFR) reference are Varma and Raghunathan (2000), Kulkarni et al. (2005).
Nonparametric models
The nonparametric models are heavily dependent on computer technology and mainly multivariate in nature (Andan & Dar, 2006). Some of the wellknown nonparametric models are artificial neural networks (ANN), hazard models, fuzzy models, genetic algorithms (GA) and hybrid models, or models in which several of the former models are combined.
The ANN models can learn and adapt, from a data set, and they have the ability to capture nonlinear relationships between variables which are also advantages of these models. The main shortcomings of the model are that they fail to explain causal relationships among their variables which restricts their application to practical management problems (Lee & Choi, 2013). Kirkos (2015) in a survey paper on credit risk, which focuses mainly on artificial intelligence models published between 2009 and 2011. The information technology revolution in the 1990’s helped artificial intelligence and managerial systems to grow and develop. This led to the development of a new set of bankruptcy prediction models known as neural networks. The study of Messier and Hansen (1988) is linked to the use of neural networks in bankruptcy prediction. This is followed by number of studies (Bellovary et al. 2007) such as Raghupathi et al. (1991), Coats and Fant (1993), Guan (1993), Tsukuda and Baba (1994), and Altman, Marco, and Varetto (1994).
Apart from neural network, there are other nonparametric models, namely, hybrid model. The hybrid models are use of two models either parametric or nonparametric (Lee et al. 1996). Genetic algorithm is also one of the prominent other nonparametric models which work as a stochastic search technique to find out a company goes bankrupt or not (Varetto, 1998). Other widely used nonparametric models are: genetic programming (Etemadi et al., 2009), models based on “rough test” theory (Dimitrias et al. 1999), Bayesian, Fuzzy, Hazard and Data Envelopment Analysis (DEA).
After 2005, the artificial intelligencebased models became more famous and widely used. Premachandra et al. (2009) compares LR and DEA models and concluded DEA models have a better predictive accuracy to predict bankrupt firms (between 84 % and 89 %), but the LR is more accurate in predicting healthy firms (between 69.3 % and 99.47 %). Verikas et al. (2010) conducted a study which reviews hybrid models and ensemblebased soft computing techniques applied in default prediction. Fuzzy logic approach is used by Korol and Korodi (2011). The model is based upon the financial data of 132 companies (107 nonbankrupt and 25 bankrupt). Gupta et al. (2014) conducted study which uses discretetime hazard model on the data base of 385,733 nonbankrupt and 8,162 bankrupt SMEs. The study develops three hazard models for micro, small, and mediumsized firms. The study further suggests the financial reports do not provide sufficient information about the default of the microfirms.
Shetty et al. (2012) develops early warning system for Indian IT/ITES using Data Envelopment Analysis (DEA). Kumar and Rao (2015) develops nonlinear new Zscore model based upon Person Type3 distribution for Indian companies.
Methods
Considered models
Summary of Empirical Models Employed and Variables Employed
Models  Formula  Variables  Descriptions 

Altman (1968) Multiple Discriminant Analysis  Z = β ^{ I } X Where Z is the MDA score and X represent the variables listed. Cutoff value: Z ≥ 2.675, classified as nonbankrupt Z < 2.675, classified as bankrupt  WCTA RETA EBITA MVEBVD SLTA  = Net Working Capital/Total Assets = Retained earnings/Total Assets = Earnings before interest and taxes/Total assets = Market value of equity/Book value of total liabilities = Sales/Total Assets 
Ohlson (1980) Logit Model  P = (1 + exp {β ^{ I } X})^{−1} Where P is the probability of bankruptcy and X represents the variables listed. The logit function maps the value of β ^{ I } X to a probability bounded between 0 and 1. Cutoff value: Y > 0.5, classified as defaulted otherwise nondefaulted.  SIZE TLTA WCTA CLCA OENEG NITA FUTL INTWO CHIN  = Log (Total assets/GNP pricelevel index). Index with a base 100 for 1968. = Total liabilities/Total Assets = Working capital/Total Assets= Current Liabilities/Current Assets = 1 If total liabilities exceed total assets, 0 otherwise. = Net income/Total assets = Funds provided by operations (income from operation after depreciation) divided by total liabilities. = 1 If net income was negative for the last 2 years, 0 otherwise. = (NI _{ t } − NI _{ t − 1})/(NI _{ t } + NI _{ t − 1}) where, NI _{ t } is net income for the most recent period. The denominator acts as a level indicator. The variable is thus intended to measure the relative change in net income. 
Zmijewski (1984) Probit model  P = ɸ (β ^{ I } X) Where, P is the probability of bankruptcy and X represents the variables listed, and ɸ (.) represents the cumulative normal distribution function. The probit function maps the value β ^{ I }X to a probability bounded between 0 and 1. Cutoff value: X > 0.5, classified as bankrupt, otherwise nonbankrupt.  NITL TLTA CACL  = Net income divided by total liabilities. = Total liabilities divided by total assets. = Current assets divided by current liabilities. 
Where, Y is the overall index based upon logistic function which determine the probability of firms’ membership in default or nondefault group. Based upon total error minimization^{1} criterion for the given data firm with Y > 0.5 is classified defaulted firm otherwise nondefaulted (Ohlson 1980, page 120). The description of variables is provided in Table 1.
Where, X is the overall index based upon probit function which determines the probability of firms’ membership in bankrupt and nonbankrupt group. Again based upon total error minimization criterion firm with X > 0.5 is classified bankrupt firm otherwise nondefaulted (Zmijewski 1984, page 72). NITL, TLTA, and CACL are the variables used in the model which details are provided in Table 1.
The new bankruptcy prediction model for indian manufacturing companies
This section covers the development of new bankruptcy prediction model for Indian manufacturing companies. The new bankruptcy prediction model is developed on sample of 208 equal numbers of defaulted and nondefaulted Indian manufacturing firms for the period 20062014. Out of 208 companies 130 used for estimation sample and 78 holdout for model validation.
Sample
Distribution of Firms as per NIC Classification 2008
NIC Code  Sector  Estimation Sample  Holdout Sample  Total 

107  Manufacturer of other food products  14  6  20 
131  Spinning, weaving and finishing of textiles  34  16  50 
170  Manufacturer of paper and paper products  4  10  14 
201  Manufacturer of basic chemicals, fertilizer and nitrogen compounds, plastics, synthetic rubber in primary form  18  6  24 
210  Manufacturer of pharmaceuticals, medicinal chemical and botanical products  6  2  8 
221  Manufacturer of rubber products  4  4  8 
231  Manufacturer of glass and glass products  4  2  6 
239  Manufacturer of nonmetallic mineral products n.e.c.  2  2  
243  Casting of metals  16  6  22 
261  Manufacturer of electronic components  6  16  22 
271  Manufacturer of electric motors, generators, transformers and electricity distribution and control apparatus  4  4  
291  Manufacturer of motor vehicles  8  6  14 
310  Manufacturer of furniture  4  4  
492  Other land transport  6  4  10 
Total  130  78  208 
Selection of financial ratios
There is extensive literature on the use of financial ratios to predict bankruptcy of the firms. Since Beaver (1966), various financial ratios were tried to foretell bankruptcy, and they can be broadly classified into four categories, which measures firm’s leverage, liquidity, profitability and turnover. Bellovary et al. (2007), in a survey paper on bankruptcy prediction list 42 financial ratios which is used in more than five financial studies on bankruptcy prediction.
In the Indian market, Bandyopadhyay (2006) develops bankruptcy prediction model based upon MDA and logistic technique for Indian corporate bond sector. The ratios used in his study measures liquidity, leverage, productivity, turnover and other financial variables which measures age, group ownership, ISO Quality Certification and interindustry effects of the firms. Bhumia and Sarkar (2011) in other study on Indian pharmaceutical industry developed model for corporate failure using MDA technique. The study chooses 16 financial ratios based upon past empirical literature measuring profitability, solvency, liquidity and efficiency of the firms. Shetty et al. (2012) develops early warning system for Indian IT/ITES using Data Envelopment Analysis (DEA). Based upon the past empirical studies ten financial ratios measuring firm’s liquidity, leverage, productivity, and turnover. Kumar and Rao (2015) develops nonlinear new Zscore model based upon Person Type3 distribution for Indian companies. In addition to Altman (1968) variables, the study uses two other nonfinancial variables measuring industry effects and rating of the companies. Based upon the past empirical literature and our own analytical judgment, we have chosen 25 financial ratios measuring firm’s leverage, liquidity, profitability, and turnover. In most of studies on global or Indian market, they found leverage, liquidity, profitability and turnover are the major financial ratio which predicts corporate failure.
Out of four major financial ratio leverage is considered to be one of the important ratios to assess financial position of the firms. According to Argenti (1976) in his study, he founds high indebtedness of the firms is one of the major reason leading a firm to bankruptcy. Similarly, Jensen (1989) argues leverage is an invitation to bankruptcy, and high debt ratios are not good for firms. In the Indian market Bandyopadhyay (2006), Bhumia and Sarkar (2011), Shetty et al. (2012) and Kumar and Rao (2015) acknowledges the importance of leverage ratio and uses different leverage indicators to assess bankruptcy. Except Bhumia and Sarkar (2011) all other studies (Bandyopadhyay (2006), Shetty et al. (2012) and Kumar and Rao (2015)) on Indian market have taken market value of equity to book value of total debt as ratio measuring leverage of the firms. In lieu of past empirical literature and importance of the indicators including market value of equity to book value of total debt, 11 leverage ratios are chosen out of 25 financial ratios.
Liquidity is also considered to be one of the important ratio to assess credit worthiness of firms. Beaver (1966) in his study found the firms with lower liquid assets are more prone to bankruptcy. In line with Beaver (1966), Altman, Haldeman and Narayana (1977), Charalambrus, Charitiu and Kaourou (2000) and Platt and Platt (2002) also gets the similar findings. In the Indian market Bandyopadhyay (2006), Bhumia and Sarkar (2011), Shetty et al. (2012) and Kumar and Rao (2015) all have used liquidity indicator including working capital to total assets as a common liquidity indicator used in all the four empirical studies. In the current study including working capital to total assets, four liquidity indicators are used out of 25 financial ratios.
Profitability ratios measures the performance of the firms. The ratio explains how efficient and effective utilization of its assets and management of its expenditure to produce adequate earnings for its shareholders. According to Gu (2002), unprofitable firms are more likely to default. Izan (1984), Maricca and Georgeta (2012) also got similar findings in their respective studies. In the Indian context Bandyopadhyay (2006) uses operating profits to total assets as the proxy for profitability indicator. Kumar and Rao (2015) and Bhumia and Sarkar (2011) uses retained earnings to total assets as a proxy for profitability indicator. In the current study out of 25 financial ratio, 7 profitability ratios are chosen.
Profile of Financial Ratios
Sl No.  Financial Ratio  Calculations 

Leverage Ratios  
1  TDTA  Total Debt/Total Assets 
2  BVEBVD  Book Value of Equity/Book Value of Total Debt 
3  CFOTA  Cash Flow from Operations/Total Assets 
4  CLTA  Current Liabilities/Total Assets 
5  CFTD  Cash Flow from Operations/Total Debt 
6  LTDTA  Longterm Debt/Total Assets 
7  NWTA  Net Worth/Total Assets 
8  TDNW  Total Debt/Net Worth 
9  TLNW  Total Liabilities/Net Worth 
10  TLTA  Total Liabilities/Total Assets 
11  FUTL  Fund Provided by Operations to Total Liabilities 
Liquidity  
12  CACL  Current Assets/Current Liabilities 
13  WCTA  Working Capital/Total Assets 
14  CATA  Current Assets/Total Assets 
15  CLCA  Current Liabilities/Current Assets 
Profitability  
16  NITA  Net Income/Total Assets 
17  RETA  Retained Earnings/Total Assets 
18  EBITA  Earnings Before Interest and Taxes/Total Assets 
19  NINW  Net Income/Net Worth 
20  CASL  Current Assets/Sales 
12  NISL  Net Income/Sales 
22  NITL  Net Income/Total Liabilities 
Turnover  
23  SLTA  Sales/Total Assets 
24  WCSL  Working Capital/Sales 
25  WCNW  Working Capital/Net Worth 

StepI: Analysis of Variables: We have chosen 25 financial ratios on the basis of past empirical literatures on Indian market. Analyses on these ratios are carried out in two broad steps. First, mean and standard deviation of bankrupt and nonbankrupt firms are analysed. Second, Ttest for equality in means of bankrupt and nonbankrupt groups are analysed.

StepII: Stepwise regression: Forward logistic selection and backward elimination methods are applied and different combinations of the ratios which are significantly different in mean by Ttest are tested and the final set of ratio are selected on the basis of the statistical significance of the estimated parameters, the sign of each variable’s coefficient and the model’s classification results.

StepIII: Inclusion of industry dummy: In the next step along with four financial ratios 14 industrial dummies were included in the model but none of them are found to be significant. This is also tested trough through stepwise regression model. However, the results are unchanged.

StepIV: Final profile of the ratios: Finally, all the financial ratios which are found to be statistically significant chosen for the model.
Analysis of variables
Descriptive Statistics of the Financial Ratios
Sample  Statistic  NITA  CACL  WCTA  RETA  EBITA  SLTA  TDTA  CATA  NINW 

Distressed  Mean  −0.290  2.519  0.215  −0.295  −0.100  0.984  1.151  0.714  2.257 
SD  0.321  3.951  0.538  0.322  0.26  1.041  0.651  0.833  3.946  
NonDistressed  Mean  0.044  3.496  0.553  0.034  0.152  2.013  0.723  0.961  0.054 
SD  0.094  6.428  0.788  0.08  0.14  2.966  0.627  1.058  0.185  
PValue  0.000  0.299  0.005  0.000  0.000  0.009  0.000  0.142  0.000  
Sample  Statistic  MVEBVD  CFOTA  CLTA  CFTD  CASL  NISL  LTDTA  NWTA  TDNW 
Distressed  Mean  −0.157  −0.159  0.499  −0.205  39.016  −23.170  1.151  −0.287  −14.589 
SD  0.200  0.262  0.571  0.409  250.959  114.765  0.651  0.485  40.268  
NonDistressed  Mean  0.481  0.104  0.407  0.132  0.861  0.012  0.723  0.48  1.858 
SD  0.300  0.128  0.436  0.999  1.830  0.447  0.627  0.420  1.835  
PValue  0.000  0.000  0.307  0.013  0.223  0.106  0.000  0.000  0.001  
Sample  Statistic  TLNW  WCSL  WCNW  TLTA  CLCA  FUTL  NITL  
Distressed  Mean  −23.578  −41.127  −5.685  1.681  0.821  −0.091  −0.191  
SD  76.339  342.421  29.01  0.982  0.693  0.116  0.230  
NonDistressed  Mean  2.859  0.305  1.094  1.150  0.560  0.129  0.360  
SD  2.451  1.060  0.932  0.873  0.427  0.371  2.586  
PValue  0.006  0.331  0.062  0.001  0.011  0.000  0.089 
Ttest for equality in means for defaulted and nondefaulted groups shows out of 25 financial ratios chosen for the model, 19 ratios have statistically different in mean between defaulted and nondefaulted groups.
Stepwise regression
In a stepwise regression, logistic forward selection and backward elimination methods were applied and different combinations of the ratios (19 ratios) which had significantly different in their respective means are tested. The selections of the final set of the variables are based upon statistical significance and sign of the each of the variable coefficients. The model classification power also took into consideration. The similar method is also used by Neophytou et al. (2001) conducting study for Netherland firms. The final set of ratios and their statistical significance is reported in third column (Model 2) of Table 7. From Table 7 all the set of financial ratios are significant at 1 % to 10 % level of significance, and LR ratio shows the overall significance of the model.
Inclusion of industry dummy
Industry Dummies for Sample Companies
Industry Dummy  Industry Type  No of Firms 

D1  Manufacturer of other food products  14 
D2  Spinning, weaving and finishing of textiles  34 
D3  Manufacturer of paper and paper products  4 
D4  Manufacturer of basic chemicals, fertilizer and nitrogen compounds, plastics, synthetic rubber in primary form  18 
D5  Manufacturer of pharmaceuticals, medicinal chemical, and botanical products  6 
D6  Manufacturer of rubber products  4 
D7  Manufacturer of glass and glass products  4 
D8  Manufacturer of nonmetallic mineral products n.e.c.  2 
D9  Casting of metals  16 
D10  Manufacturer of electronic components  6 
D11  Manufacturer of electric motors, generators, transformers and electricity distribution and control apparatus  4 
D12  Manufacturer of motor vehicles  8 
D13  Manufacturer of furniture  4 
D14  Other land transport  6 
Total  130 
Final profile of the ratios

BVEBVD (Book Value of Equity/Book value of Total Liabilities): This indicator measures leverage of the firms. The similar ratio is also used in the study of Altman (1968) on US manufacturing companies. In the current study market value of equity is replaced by book value of equity. The current study uses data of both publicly and privately held firms. In order to calculate market value of equity, stock price data (Altman, 1993) is required. The same principle is employed while reestimating Altman’s model. The ratio is found to be most effective predictor of bankruptcy than a similar, more commonly used ratio: net worth/total book value of debt. The indicator explains how much the firm’s asset can decline in value before the liabilities exceed the assets, and the firm becomes bankrupt. In the Indian case of India, Bandyopadhyay (2006), Shetty et al. (2012) and Kumar and Rao (2015) uses this indicator to predict bankruptcy.

SLTA (Sales/Total Assets): It is one of the widely used turnover ratio of firms. It measures efficiency and effectiveness of the firm’s assets to generate profit. This is a key variable for the measurement of the size of the firm. The capitalturnover ratio is a standard financial ratio illustrating the sales generating ability of the firm’s assets. It is one measure of management’s capability in dealing with competitive conditions. It is used in the study of Altman (1968) and Bandyopadhyay (2006) and Kumar and Rao (2015), used in the Indian market.

NITA (Net Income/Total Assets): It is the ratio of net income to total assets which is a measure of performance of the firms. It measures profitability and also used in the study of Ohlson (1980) on US manufacturing companies.

NITL (Net Income/Total Liabilities): It is the ratio of net income to total liabilities. The ratio measures return on asset which is the measure of firm’s performance and profitability. The ratio is also used in the study of Zmijewski (1984).
Broadly all the ratios used in the current study are from the studies of Altman (1968), Ohlson (1980) and Zmijewski (1984). The first two ratio’s BVEBVD and SLTA measuring leverage and turnover of the firms are also used in the Study of Altman (1968). Third ratio NITA measures profitability of the firms is used in the study of Ohlson (1980), and fourth NITL measures profitability of firm is also applied in the study of Zmijewski (1984). The new bankruptcy prediction model uses ratios measuring leverage, profitability, and turnover of the firms. The model is also considered to be comprehensive model because it uses variables from all three major accounting based bankruptcy prediction model mentioned above. By ‘Common Sense’ and past studies all the variables are expected to have negative sign (Ohlson 1980, page 119).
Descriptive Statistics of the Final Profile of the Financial Ratios
Sample  Statistic  BVEBVD  SLTA  NITA  NITL 

Estimation  
Distressed (N = 65)  Mean  −0.157  0.984  −0.289  −0.191 
SD  0.200  1.040  0.321  0.230  
NonDistressed (N = 65)  Mean  0.481  2.013  0.044  0.360 
SD  0.299  2.965  0.094  2.586  
Holdout  
Distressed (N = 39)  Mean  −0.157  1.521  −0.843  −0.192 
SD  0.264  1.919  1.863  0.602  
NonDistressed (N = 39)  Mean  3.359  2.522  0.110  0.094 
SD  7.173  3.111  0.169  0.160 
Logit model: estimation procedure
The logistic regression method is used to investigate the relationship between binary response variable (1 for bankrupt and 0 for nonbankrupt groups) and financial ratios (explanatory variables). The Maximum Likelihood Estimation (MLE) procedure is applied to estimate parameters. The objective of the logit regression is to evaluate the role of accounting variables in predicting bankruptcy for Indian manufacturing firms and also to arrive at an estimate of probability of default for a firm using them.
Logit model
Where, Pi represents probability, X _{ i } represents various financial ratios of the firms and Y is the dependent variable. Y = 1 means the firm is failed. β _{1} and β _{2} are slope coefficients.
Where F is cumulative density function.
In the context of default prediction study, the logit model is used to classify whether a company is defaulted or nondefaulted by using accountingbased financial ratios.
Estimation results
Results of Logit Model 1 and 2
Model 1  Model 2  

Variables  Coefficients  Coefficients 
MVEBVD  −39.907  −13.8597^{a} 
SLTA  −4.488  −1.11303^{c} 
NITA  −72.776  −18.760^{b} 
NITL  −107.685  −34.354^{b} 
C  −7.012  −0.604 
D1  13.256  
D2  6.277  
D3  −14.496  
D4  Dropped  
D5  −2.311  
D6  8.592  
D7  10.97  
D8  Dropped  
D9  3.865  
D10  15.956  
D11  Dropped  
D12  −1.563  
D13  Dropped  
D14  7.767  
LR Ratio  172.219  164.956 
pValue  0.000  0.000 
LR ratio tests the overall significance of the model. In case of final model (Model 2) the LR ratio is found to be 164.956 and statistically significant at 1 % level of significance. The Model 2 can be directly used to find PDs of firms to assess credit risk.
Model reestimations
This section covers reestimation of Altman, Ohlson and Zmijewski models using estimation sample of 130 Indian firms consisting equal numbers of defaulted and nondefaulted firms. The statistical methodologies are the same used in the original models and discussed in section 2. The stability of the coefficients of original models is tested by comparing it from reestimated models. The original and reestimated coefficients are reported in Table 11. The coefficients of original and reestimated models are compared to test the stability of coefficients to the time periods and change in the financial conditions. The overall predictive accuracy of model is tested on estimation and holdout sample to test whether change in coefficients (reestimated) with recent data set improves the predictive accuracy of the model. The newly proposed model is compared with original and reestimated models. By overall predictive accuracy, ROC, longrange accuracy test and the method to model bankruptcy, it is summarised that the newly proposed model for Indian manufacturing sectors outperforms other competitive models.
Descriptive statistics
Descriptive Statistics for Altman Model
Sample  Statistic  WCTA  RETA  EBITA  BVEBVD  SLTA 

Estimation  
Distressed (N = 65)  Mean  0.215  −0.295  −0.100  −0.157  0.984 
SD  0.538  0.322  0.260  0.200  1.041  
NonDistressed (N = 65)  Mean  0.553  0.034  0.152  0.481  2.013 
SD  0.788  0.080  0.140  0.299  2.966  
Holdout  
Distressed (N = 39)  Mean  0.634  −0.843  −0.550  −0.157  1.521 
SD  1.917  1.863  1.405  0.264  1.919  
NonDistressed (N = 39)  Mean  1.089  0.086  0.214  3.359  2.522 
SD  1.406  0.136  0.230  7.173  3.111 
Descriptive Statistics for Ohlson Model
Sample  Statistic  SIZE  TLTA  WCTA  CLCA  OENEG  NITA  FUTL  INTWO  CHIN 

Estimation  
Distressed (N = 65)  Mean  0.615  1.681  0.215  0.821  0.938  −0.289  −0.091  0.615  −0.117 
SD  1.289  0.982  0.538  0.693  0.242  0.321  0.116  0.490  0.627  
NonDistressed (N = 65)  Mean  0.638  1.150  0.553  0.560  0.338  0.044  0.129  0.077  0.057 
SD  1.121  0.873  0.788  0.427  0.477  0.094  0.371  0.269  0.503  
Holdout  
Distressed (N = 39)  Mean  −0.587  3.145  0.634  1.116  0.949  −0.843  −0.153  0.590  −0.236 
SD  1.219  3.282  1.917  1.197  0.223  1.863  0.209  0.498  0.682  
NonDistressed (N = 39)  Mean  −0.501  1.113  1.089  0.796  0.385  0.110  0.183  0.128  0.048 
SD  1.343  1.200  1.406  2.685  0.493  0.169  0.516  0.339  0.476 
Descriptive Statistics for Zmijewski Model
Sample  Statistic  NITL  TLTA  CACL 

Estimation  
Distressed (N = 65)  Mean  −0.191  1.649  2.519 
SD  0.230  0.958  3.980  
NonDistressed (N = 65)  Mean  0.360  1.131  3.496 
SD  2.586  0.861  6.428  
Holdout  
Distressed (N = 390  Mean  −0.192  3.054  2.603 
SD  0.602  3.173  2.925  
NonDistressed (N = 39)  Mean  0.094  1.043  4.693 
SD  0.160  1.205  6.526 
Table 8 shows the profile of variables used in Altman model on estimation and holdout sample. WCTA measures the liquidity of the firm; the mean WCTA for nondistressed group is higher than distressed group in both the sample. RETA measures the earned surplus of the firm. The average RETA for distressed group on both estimation (0.295) and holdout sample (0.843) is found to be negative whereas for nondistressed group it is positive on both estimation (0.034) and holdout sample (0.086) respectively.
EBITA measures the true productivity of the firm assets. For defaulted group the mean EBITA is negative for both estimation (0.100) and holdout (0.550) and positive for nondefaulted group. BVEBVD is measure of the leverage of the firm. The mean BVEBVD for nondefaulted group for both estimation (0.481) and holdout (3.359) sample is found to be positive for nondefaulted and negative for defaulted groups. SLTA measures the firms’ market size. For nondefaulted groups, the size is larger on both estimation (2.013) and holdout (2.522) whereas for defaulted groups its value is smaller on both estimation (0.984) and (1.521) holdout sample respectively.
Table 9 reports the descriptive statistics of the variable used in Ohlson model. SIZE is defined as log of total assets to GNP pricelevel index. The year 201112 is taken 100 as a base value. The mean SIZE for defaulted (0.615) and nondefaulted (0.638) groups is positive and not significantly different on estimation sample. Similarly, mean SIZE for defaulted (0.587) and nondefaulted (0.501) is negative and not significantly different from estimation sample. TLTA measures the leverage of firm. For the distressed companies the ratio is higher on both estimation (1.681) and holdout (3.145) sample as compare to nondistressed companies which have lower ratio on both estimation (1.150) and holdout (1.113) sample respectively. The higher ratio for defaulted groups indicates higher leverage.
WCTA is a measure of the current liquidity of the firm. The ratio deteriorates for distressed firms on both estimation (0.215) and holdout (0.634) sample as compare to nondefaulted firms’ ratio on estimation (0.553) and holdout sample (1.089) respectively. CLCA is also measure of firm current liquidity. As expected the ratio is higher for defaulted firms on both estimation (0.821) and holdout (1.116) sample as compare to nondefaulted firm which have lower ratio on both estimation (0.560) and holdout (0.796) sample respectively. The defaulted firms always expected to have higher ratio because their current liabilities will be always higher than current assets. OENEG is a dummy used for discontinuity correction for TLTA. It takes value 1 if total liabilities exceed total assets, 0 otherwise. NITA is a ratio which measures firms’ performance. The ratio deteriorates and found to be negative for bankrupt companies on estimation (0.289) and holdout (0.843) sample, whereas it is positive for nonbankrupt firms. FUTL measures the performance of firms’. The result is similar to NITA. The ratio deteriorates and found to be negative for bankrupt companies on estimation (0.091) and holdout (0.153) sample where as it is positive for non bankrupt firms. INTWO is a dummy which takes value 1, if net income was negative for the last two years, 0 otherwise. CHIN measures the change in the net income of the firm. The CHIN is negative for defaulted groups on both estimation (0.117) and holdout (0.236) sample, whereas it is found to be positive for nondefaulted groups on both estimation (0.057) and holdout (0.048) sample respectively.
Table 10 reports descriptive statistics of the variable used in Zmijewski model. NITL in the Table 10 measures return on asset which is measure of firm performance. For defaulted groups it is negative on both estimation (0.191) and holdout (0.192) sample, whereas the ratio is found to be positive for nonbankrupt firm on both estimation (0.360) and holdout (0.094) sample respectively. TLTA is the debt ratio which measures the leverage of the firms. The distressed firms have higher leverage on both estimation (1.649) and holdout sample (3.054) respectively. CACL measures the liquidity of the firms. The nondistressed firm have higher liquidity ratio on both (3.496) and holdout (4.693) sample as compared to distressed groups.
The profile analysis of the samples used in all the three models shows there is significant difference in the mean ratios of the defaulted and nondefaulted groups. The ratios deteriorates for bankrupt groups as compared to nonbankrupt groups.
Results and Discussion
This section analyzed the findings of the original, reestimated and newly proposed models on estimation and holdout samples. The stability of their coefficients and their predictive accuracies are also tested. This section also evaluates out of three models which outperforms in the Indian setting.
Unstable coefficients
Coefficient Comparison of Different Models
Statistic  Altman (1968) Model  Reestimated Model  Ohlson (1980) Model  Reestimated Model  Zmijewski (1984) Model  Reestimated Model  New Model 

WCTA  1.2^{a}  0.076^{a}  −1.4^{b}  −5.216^{c}  
RETA  1.4^{a}  1.464^{a}  
EBITA  3.3^{a}  −0.63^{a}  
BVEBVD  0.6^{a}  3.474^{a}  −13.86^{a}  
SLTA  0.99  0.028^{a}  −1.113^{c}  
SIZE  −0.4^{a}  0.079  
TLTA  6.03^{a}  1.623  5.7^{a}  0.586^{a}  
CLCA  0.1^{b}  −2.973^{b}  
OENEG  −2.4^{a}  2.836^{b}  
NITA  −1.8^{b}  −29.676^{a}  −18.76^{b}  
FUTL  0.3^{a}  −2.559  
INTWO  −1.7  0.337  
CHIN  −0.5^{a}  1.73^{c}  
NITL  −4.5^{a}  −13.797^{a}  −34.354^{b}  
CACL  0.004^{b}  0.01  
Constant  −0.425  −1.3  −2.454^{c}  −4.3^{a}  −1.522^{a}  −0.604  
LR  0.839^{d}  −15.952  203.78  −33.296  164.956  
Pvalue  0.000  0.000  0.000  0.000  0.000 
The result shows there is significant difference in the coefficients of original and reestimated model except RETA. In case of RETA the original (1.4) and reestimated (1.464) coefficients is found to be very close. For WCTA original coefficient was 1.2, and it ranks third with respect to relative importance of the variable to contribute in the overall index. In the reestimated model the coefficient (0.076) significantly changes but still its ranks third in term of its relative importance in the overall index. In the original model EBITA, coefficient was 3.3, and it ranks first to contribute in the overall index, whereas reestimated coefficient (.063) becomes negative and ranks fifth. In case of BVEBVD, the original coefficient was 0.6 and reestimated coefficient is 3.474 which is significantly different. For SLTA, the original coefficient was 0.99 and reestimated coefficient is 0.028. The * indicates the statistical significance of Fstatistic in the difference of mean. For both the Altman original and reestimated models, the Fstatistics is significant, meaning that both the groups defaulted and nondefaulted have significantly different means. The finding suggests the coefficients of Altman (1968) model are not stable, and they are sensitive to time periods.
The results of Ohlson original and reestimated models are also reported in Table 11. In the original model, all the variables were significant except CLCA, INTWO and constant whereas in the reestimated model all the variables are significant except SIZE, TLTA, FUTL and INTWO. The coefficients which are significant in both the original and reestimated models are WCTA, OENEG, NITA, and CHIN. In case of WCTA, the original coefficient was 1.43 and reestimated coefficient is 5.216 which is significantly different. For OENEG the original coefficient was 1.72 and reestimated coefficient is 2.836 which is different in value as well as in sign. There is huge difference in the value of NITA coefficient for original (2.37) and reestimated (29.676) model. In case of CHIN, the original (0.5) and reestimated (1.73) coefficient are not only different in value but also in sign. The result shows the coefficients of Ohlson (1980) model is sensitive to time period and not stable.
Finally, the result of Zmijewski model is again reported in Table 11. In the original model, all the coefficients are significant whereas in the reestimated model all the variables are significant except CACL (Current assets to current liabilities). Rest other coefficients preserve similar sign but different in the magnitude. In case of TLTA, the original coefficients were 5.7 and reestimated is 0.586 which is significantly different in magnitude. For NITL the original coefficients was 4.5 and reestimated coefficient is 13.797. The constant term in both the original (4.3) and reestimated (1.222) is different in values. The result shows the coefficients of Zmijewski (1984) model is sensitive to time period and not stable. The results of newly proposed model are reported in the last column of Table 11. All the variables are significant except intercept.
The results reported in Table 11 shows coefficient of all the three accounting based models are not similar. They are unstable and sensitive to time period. The findings are in line with the studies of Grice and Ingram (2001), Grice and Dugan (2001), Timmermans (2014) and Avenhuis (2013). Empirically it is found in the context of Indian manufacturing sector the coefficients are unstable and sensitive to time periods.
Predictive accuracy
Comparison of Predictive Accuracy of the Models
PanelA (Estimation Sample)  
Original model Accuracy  Reestimated model Accuracy  
Model  Overall  Distressed  NonDistressed  Overall  Distressed  NonDistressed 
Altman  67.692  92.308  43.077  96.923  98.462  95.385 
Ohlson  48.462  95.385  1.538  95.385  96.923  93.846 
Zmijewski  71.538  98.462  44.615  89.231  87.692  90.769 
New Model  98.460  98.460  98.460  NA  NA  NA 
PanelB (Holdout Sample)  
Original model Accuracy  Reestimated model Accuracy  
Overall  Distressed  NonDistressed  Overall  Distressed  NonDistressed  
Altman  61.538  25.641  97.436  88.462  87.179  89.744 
Ohlson  64.103  97.436  30.769  89.744  87.179  92.308 
Zmijewski  79.487  97.436  61.538  76.923  61.538  92.308 
New Model  87.179  82.051  92.308  NA  NA  NA 
PanelA of the Table 12 reports the predictive accuracy of original, reestimated and newly proposed models on estimation sample. The predictive accuracy of original Altman model on estimation sample is 67.692 % which correctly classify 92.308 % of distressed and 43.077 % of nondistressed firm. The Type II error is very high in case of Altman original model on estimation sample. The overall accuracy of Altman reestimated model on estimation sample is 96.923 which correctly classify 98.462 % of distressed and 95.385 % of nondistressed firms. For Ohlson original model the overall predictive accuracy is 48.462 % on estimation sample which correctly classifies 95.385 % of distressed firms and 1.538 % of nondistressed firms. The Type II error in the case of Ohlson original model on estimation sample is close to 100 %. On the other hand, overall predictive accuracy of reestimated Ohlson model is 95.385 which correctly classifies 96.923 % of defaulted and 93.846 % of nondefaulted firms. In case of Zmijewski original model, the overall predictive accuracy is 71.538 %. The model correctly classify 98.462 % of distressed and 44.615 % of nondistressed firms. The overall predictive accuracy of reestimated Zmijewski model on estimation sample is found to be 89.231 which correctly classify 87.692 % of defaulted and 90.769 % of nondefaulted firms. In case of newly proposed model, the predictive accuracy on estimation sample is found to be 98.46 which correctly classify 98.46 % of distressed and 98.46 % of nondistressed firm. The Type I and Type II error in case of new model is found to be equal. PanelA of Table 12 shows predictive accuracy of reestimated models is higher than original model on estimation sample. The newly proposed model have highest (98.46) predictive accuracy with minimum and equal Type I and Type II errors. Type II error is found to be more than 50 % in all the three original models. In case of original Ohlson model, the Type II error is close to 100 %. All the three reestimated models have higher predictive accuracy and low Type I and Type II errors compared to original models.
PanelB of Table 12 reports the predictive accuracy of original, reestimated and newly proposed models on holdout sample. The overall accuracy on holdout sample also constitutes diagnostic test for the estimated models. The overall accuracy of Altman original model on holdout sample is 61.538 % which correctly classifies 25.641 % of defaulted and 97.436 % of nondefaulted firms. The Type I error in case of Altman original model on holdout sample is very high and close to 75 %. On the other hand, overall predictive accuracy of Altman reestimated model is 88.462 % which correctly classifies 87.179 % of defaulted and 89.744 % of nondefaulted firms. In case of Ohlson original model, the overall predictive accuracy is found to be 64.103 % which correctly classify 97.436 % of distressed and 30.769 % of nondistressed firms. The Type II error in the case of Ohlson original model on holdout sample is close to 70 %. On reestimated Ohlson model, the overall predictive accuracy is 89.744 % which correctly classifies 87.179 % of defaulted and 92.308 nondefaulted firms. The predictive accuracy of Zmijewski original model on holdout sample is 79.487 % which correctly classifies 97.436 % of distressed and 61.538 % of nondistressed firms. The Type II error in case of original Zmijewski model on holdout sample is close to 40 %. The overall predictive accuracy of reestimated Zmijewski model on holdout sample is 79.487 % which correctly classifies 97.436 % of distressed and 61.538 % of nondistressed firms. On holdout sample, the Type II error is again high for original models except Altman model. The Type II error in case of both Ohlson and Zmijewski original model is more than 50 %. In case of all the reestimated models both the Type I and Type II errors are minimum except Zmijewski model. In case of new model the overall predictive accuracy on holdout sample is found to be 87.179 % which correctly classifies 82.051 % of defaulted and 92.307 % of nondefaulted firms. The Type I error in case of new model is found to be 18 % and Type II error close to 8 %.
From the results reported in PanelA and B of Table 12 on estimation and holdout sample, it can be summarized that the predictive accuracy of reestimated models are significantly higher than original models on both estimation and holdout sample. Except Altman model the Type II error is very high for all the original models on both estimation and holdout sample. The result shows the model applied on the recent data set gives higher predictive accuracy on both estimation and holdout sample. Out of contesting accounting based models, the new model outperforms regarding its predictive accuracy on estimation sample and fairly good accuracy on holdout sample for Indian manufacturing firms. The overall predictive accuracy of reestimated Ohlson model is 95.385 and 89.385 on estimation and holdout sample respectively. The overall predictive accuracy of Altman reestimated model is also close to new model, but new model is better than Altman model because it gives direct probability estimates and model bankruptcy in a nonlinear fashion which is in line with local and global regulatory framework. In the next section, we will apply other diagnostic check to check the stability of Ohlson reestimated model. The results are in line with the studies of Grice and Ingram (2001), Grice and Dugan (2001), Timmermans (2014) and Avenhuis (2013). Empirically it is found in the context of Indian manufacturing sector that the coefficients are unstable and sensitive to time periods.
Diagnostics check for the New Model
This section deals with two diagnostics tests for newly proposed model, ROC and longrange accuracy test.
The ROC (Hanley and McNeil, 1982) is one of the important and widely used test to assess the performance of a binary classifier. The Area Under the Curve (AUC) summarizes the performance of a model in a single number. The accuracy of the test depends upon how well it classifies between the groups. In the present context, it is between bankrupt and nonbankrupt. The model ROC with AUC 1 shows the perfect test whereas the model with AUC 0.5 shows worthless test. As compare to a simple metric of misclassification rate, ROC visualizes all possible classification thresholds.
In the ROC test the sensitivity or positive predictive value (PPV) is defined as the proportion of firms for whom the outcome is positive that are correctly identified. Similarly, the specificity or negative predictive value (NPV) is the probability that a firm has a negative outcome given that they have a negative test result.
The ROC is the graph of specificity against 1senstivity by which the impact of choice is understood. A fairly excellent test have good balance between sensitivity and specificity. The decision to set the classification threshold to predict outofsample data depends upon the business decision.
Longrange Accuracy of Newly Proposed Model
Years before distress  Estimation sample  Holdout Sample 

1  98.460  89.743 
2  86.923  70.513 
The long range accuracy results are fairly good and satisfactory. The result shows the predictive accuracy of new model decreases as we go more backward from the year of distress. Hence, the most recent information is helpful in predicting default with higher accuracy.
Conclusion
The paper proposed a new model to predict the bankruptcy of Indian manufacturing sector and also examines the sensitivity of Altman’s (1968), Ohlson’s (1980) and Zmijewski’s (1984) models to the sample of 208 equal numbers of defaulted and nondefaulted firms for the period 2006 to 2014 in the Indian context. The result shows the overall accuracy of the model improves when the coefficients are reestimated. The overall accuracy of Altman (1968), Ohlson (1980) and Zmijewski (1984) original models in the estimation sample are 67.692, 48.462 and 71.538 % respectively. When all the models are reestimated the accuracy improves to 96.923, 95.385 and 89.231 % respectively. On holdout sample, the overall accuracy of Altman’s (1968), Ohlson’s (1980) and Zmijewski’s (1984) original models are 61.538, 64.103 and 79.487 % respectively. The accuracy improves to 88.462, 89.744 and 76.923 when the models are reestimated. The predictive accuracy of new model on estimation and holdout sample is found to be 98.46 and 87.179 respectively. Therefore, the new model is found to be a more robust model in comparison to Altman’s, Ohlson’s and Zmijewski’s models. The major finding of the study suggests the coefficients of the Altman’s (1968), Ohlson’s (1980) and Zmijewski’s (1984) models are sensitive to time periods and financial condition. The predictive accuracy of the models increases when more recent data are used in the estimation samples. The change in the financial environment leads to change in the relation between financial distress and financial ratios. This also alters the comparative importance of the ratios to predict default. Hence, researchers should reestimate the original models to get higher predictive accuracy. In case of Indian manufacturing companies, out of all competitive accounting based models, the new model outperforms regarding predictive accuracy, ROC, and longrange accuracy test.
The major limitation of the study is that it can be applied to only manufacturing firms and excludes financial firms. The study can also use larger data set applying various other parametric and nonparametric models to check validity of the model, robustness and stability of the parameters. Though, the results of BlackScholesMerton (BSM) model can’t be directly compared with the proposed model but using Indian manufacturing data the same approach can be applied to develop model for Indian manufacturing companies.
The total error minimization principle is applied to obtain cutoff value. Various cutoff values are tested and the final cutoff value is decided where the sum of Type I and Type II errors are minimized. Type I errors occur when a model incorrectly classifies a distressed company as nondistressed, while Type II errors occur when a model incorrectly classifies a nondistressed company as distressed.
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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