Univariate Ratio Analysis Development

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Prior to Poor’s publishing of assets, liabilities, and earnings information in the American Railroad Journals of 1849, credit-worthiness was assessed using qualitative data. Poor’s publications were the first instances of quantitative data being used to assess the risk of commercial lending. This continued until the early 1930’s when the first academic studies were carried out to assess the quantitative differences in financial ratios between well performing and failing businesses (Altman 1968).

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Univariate Ratio analysis development

Between 1930 and 1968, financial ratios were analysed using univariate methodology to establish differences between failing and non-failing companies. This methodology analysed many ratios but individually. However the model could not find relationships between multiple ratios. An example of this was The Bureau of Business Research’s study (1930). It used 24 ratios to analyse 29 failing manufacturing companies. The results were compared to look for similar financial ratio characteristics in the sample. This showed that failing firms had common financial ratio characteristics which meant that it was possible to see potential failure of a firm before bankruptcy occurred. The research found that decline in the following ratios suggested potential future bankruptcy. Working Capital to Total Assets Surplus and Reserves to Total Assets Net Worth to Fixed Assets Fixed Assets to Total Assets Current Ratio Net Worth to Total Assets Sales to Total Assets Cash to Total Assets (BBR, 1930) The key weakness of the BBR model was that only failing companies had been compared. There was now a need to compare companies that had failed against companies that were trading successfully in order to see a true difference in ratio performance. Fitzpatrick chose 13 ratios to compare 19 failed and 19 successful companies in order to established a benchmark for average performance. Subjects whose ratios were better than average were deemed successful and those that were below average were deemed unsuccessful. This gave more meaningful results than the BBR study as it made a comparison between failed and non-failed companies rather than comparing failing companies only. Fitzpatrick suggested the most significant ratios were Net Worth to Debt and Net Worth to Net Profits. (Fitzpatrick, 1932) In 1935 BBR’s study was repeated using a larger sample. 183 bankrupt companies from numerous industries were sampled. This increased the model’s generalisability. The research suggested that the Working Capital to Total Assets ratio was most significant when predicting bankruptcy and the key trend was that the Current Assets to Total Assets ratio fell when companies were failing. (Smith and Wanakor, 1935) These studies were useful for differentiating between bankrupt and non-bankrupt firms and suggested common financial trends of a failing businesses; but they could not predict how soon bankruptcy was likely to occur. However Merwin suggested that trends of reducing Net-Working Capital to Total Assets, Current ratio, and Net Worth to Total Debt could predict company weakness up to five years before bankruptcy (Merwin,1942). The majority of bankruptcy prediction research up to 1946 suggested that the Working Capital to Total Assets ratio and the Current ratios were the most significant indicators of financial distress (Bellovary et al, 2007). However Chudson suggested that bankruptcy prediction models developed for multiple industry types gave greater generalisability but were less accurate than an industry specific model when predicting the bankruptcy timeframe (Chudson, 1945).

Multiple Discriminant Analysis Model Development

By 1968 the financial academics decided that univariate analysis models were not as accurate at predicting bankruptcy as required and considered the use of statistical evidence of past company performance would be a viable replacement. While academics agreed liquidity, solvency, and profitability were effective, they could not agree on their order of significance. The main issue was that a company could have low profitability but have good liquidity. In this instance a univariate model might give an ambiguous result. (Altman 1968) To address these issues Altman developed a model that established the most significant ratios and gave a weighting to each one so that they could be multiplied together. This created one formula that categorized companies into bankrupt and non-bankrupt entities. The model linked five different ratios into one formula that classified its sample into two groupings according to their characteristics. This technique is known multiple discriminant analysis or MDA. Altman called it the Z-Score model (Altman 1968).

Altman’s Z-Score Development Methodology

33 bankrupt companies and 33 non-bankrupt companies were chosen from the U.S.A. manufacturing industry. The bankrupt companies had all filed under chapter 10 of the National Bankruptcy Act between 1946 and 1965. To ensure reliability, validity, and generalisability the non-bankrupt companies were chosen using paired sampling and stratified random techniques. They were stratified by asset size and industry. To ensure comparability between samples, non-bankrupt companies were chosen that had continuous trading results for the same time period as the bankrupts (Altman 1968). Altman classified the 22 most common ratios used to indicate financial stress into five categories. They were liquidity, leverage, solvency, profitability, and activity. Out of the 22 ratios, five were chosen for their statistical significance in each category. Computer analysis was then used to establish the most accurate weighting for each ratio (Altman 1968).

Ratio Weighting

Working Capital to Total Assets (X1) 0.012

Retained Earnings to Total Assets (X2) 0.014

Earnings before interest and tax to Total Assets (X3) 0.033

Market Value of Equity to Book value of total debt (X4) 0.006

Sales to total Assets (X5) 0.999

Z score function formula = 0.012(X1) + 0.014(X2) + 0.033(X3) + 0.006(X4) +0.999(X5)

The following financial ratios were selected to create the Z-Score formula:

The Significance of the five selected ratios

X1, working capital / total assets ratio measures liquidity.

The working capital is calculated by taking away the current liabilities from the current assets. If a company continually makes an operating loss, its current assets will be depleting in relation to its total assets, thus reducing liquidity. This was in agreement of Merwin, 1942 who suggested this was the strongest indicator of potential bankruptcy. (Altman 1968)

X2, Retained Earnings / Total Assets

This measures the company’s accumulated profitability. By definition new companies will have less retained earnings than older companies; therefore they are more at risk of failure. Statistics have shown that younger companies are more likely to fail than older companies in real world situations, hence the significance of the ratio. (Altman 1968)

X3, Earnings before Interest and Taxes / Total Assets.

This ratio measures the company’s asset productivity. It eliminates all tax and leverage so that the true earning potential of the company’s assets can be measured. Assets are valued by their earning power, and since bankruptcy is defined as when total liabilities are in excess of valued assets, this ratio is of great importance. (Altman 1968)

X4, Market value of Equity / Book value of total debt.

This is in essence a debt to equity ratio, though it includes the current market value of all the company’s shares inclusive of regular and preference shares. The debt part of the ratio includes both long term and current liabilities. This ratio is used to measure how much asset value can be depleted before the company becomes insolvent. Altman has added the market value element to the ratio where previous studies have not. He suggests that this is more effective at predicting bankruptcy than the univariate analysis of net worth to total debt ratio which had been the most commonly used prior to his study. (Altman 1968)

X5, Sales / Total Assets

This is the capital turnover ratio which measures the company’s ability to generate sales from its assets. Individually it is of least significance; however its discriminate ability contribution is ranked second out of the five ratios used so is of great importance to the formula. (Altman 1968)

Z-score Meanings

After much research and modelling, Altman concluded that if a company’s Z-score was above 2.99 it could be classed as definitively non-bankrupt. However if its Z-score was below1.81then it could be classed as definitively bankrupt. However if its Z-score fell between these two figures then it could not be definitively classed as being in either category. This was known as the “grey area” or “zone of ignorance”. Altman found that companies who scored within this grey area were open to mis-classification. He suggested that it was difficult to predict bankruptcy in a company who’s Z-score fell within the “grey area”, particularly those that had recently started trading. To address this he developed guidelines for the classification of companies that Z-scored within this area.

Eliminating the “grey area”

Altman selected all the companies from his first sample that had fallen into the “grey area” and classified them by six Z-score ranges between 1.81 and 2.99. The results showed that as the Z-score increased from 1.8, the number of companies who’s Z-score falls in each sub range decreases to two companies at 2.67 – 2.68 and then increases again as it reaches 2.99. Altman suggested that this shows the mid range of the “grey area” to be 2.67 – 2.68. Therefore 2.675 is the optimum Z-score value that discriminates between Bankrupt and Non-bankrupt companies. (Altman, 1968)

The Z-Scores Accuracy at Predicting Bankruptcy

Altman tested his Z-score model accuracy to five years too. The results showed the following:

Year Prior to Bankruptcy Accuracy (%)

1 95% 2 72% 3 48% 4 29% 5 36%

Altman suggested that on the basis of these results, his Z-score model was accurate at predicting bankruptcy up to two years before the company was bankrupt. However after the second year Altman suggests that the model is unreliable. The reason being that in year three there is less than a 50/50 chance of accurate prediction.

Altman’s Conclusions

Altman concluded that as the companies came closer to bankruptcy, the ratios X1 to X5 showed increasing deterioration. Moreover there was massive deterioration during years three and two before eventual bankruptcy. Hence the Z-score also deteriorates as the company gets closer to bankruptcy. As all samples were from the manufacturing sector the model is most accurate when predicting bankruptcy in companies from this sector.

Strengths and weaknesses of the Z-score model

Before the Z-score model was developed, bankruptcy prediction models were univariate and not industry specific. Altman revolutionised bankruptcy prediction modelling and from 1968 MDA became the industry standard methodology. Altman’s Z-score model has proven to be reliable and valid. He also developed other variations on the Z-Score model including one for non PLC manufacturing companies. On this basis the model is very versatile for predicting bankruptcy in numerous applications. However when developing the private company Z-Score model, Altman used unadjusted financial data the sample was small giving rise to reliability issues. Another possible problem is that the Z-score, was developed using American company data, so there may be generalisability issues when Z-scoring non U.S. companies. https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1025&context=account_fac https://www.exceluser.com/tools/zscore.htm However Mandru et al suggest that Z-score models are not suitable in modern credit risk analysis. They suggest that it does not consider the economic and business cycle impact and should consider qualitative variables as well as market trends, market share, and the quality of the company’s products and management. Ultimately these variables are reflected in the companies’ share prices; hence why modern commercial credit risk analysts such as Moodys use this data within their computer modelling systems. https://www.wseas.us/e-library/conferences/2010/Cambridge/AIKED/AIKED-12.pdf

Bankruptcy Prediction Model development after Altman

Logit & Probit Models

Bankruptcy prediction modellers continued to use MDA through to the late 1980’s. As MDA was being phased out, Logit and Probit analysis models were becoming more popular. They are both regression type analyses that use both univariate and multivariate techniques. The Logit analysis model estimates the probability of an event occurring. It uses a set of independant variables i.e. the financial ratios, and predicts an outcome in the form of a 1 (bankrupt positive) or a 0 (non-bankrupt). Probit analysis models produce a threshold level where if the company’s score exceeds it, it is classed as bankrupt. https://www.iasri.res.in/ebook/EBADAT/6-Other%20Useful%20Techniques/5-Logit%20and%20Probit%20Analysis%20Lecture.pdf

Neural Network Analysis

The Neural network analysis for bankruptcy prediction has been developed since the late 1980’s. It is an advanced version of the Logit and Probit regression analyses. Using computer simulation, the model acts like a human brain, creating neural pathways to remember previous events of bankruptcy. The programme then processes the company’s data and compares it to the previous bankruptcy events. The result is a statistical probability of the company failing. Thus a quantitative credit risk value can be applied. An example of this type of analysis is a Back-Propagation neural network which can recognise patterns of business behaviour. The downside is that it requires an immense amount of data to be entered in order to train the system to successfully establish the ratio weightings. It also has seven parameters which makes it a complex task to ascertain the correct model structure to gain a meaningful outcome (Shin et al, 2005). https://www.iasri.res.in/ebook/EBADAT/6-Other%20Useful%20Techniques/5-Logit%20and%20Probit%20Analysis%20Lecture.pdf

Support Vector Machines

Support Vector Machines are another form of artificial intelligent bankruptcy prediction computer programme. They are closely related to the back-propagation neural network but can be used in a more generalised setting. Shin et al suggest they are better than the back-propagation neural networks because they only need two parameters and a much smaller data set to train the system to generate accurate predictions. Hence the SVM is more accurate and gives better generalisability than the BPN. (Shin et al, 2005)

Merton’s Expected Default Frequency Model

However in 1974 Merton developed a new way of calculating credit risk. The emphasis here is placed on predicting when the borrower is likely to default on a repayment loan as opposed to the likelihood of bankruptcy. Though bankruptcy prediction is of utmost importance when calculating credit risk, a company is more likely to default on a loan before ultimate bankruptcy. So in the case of the lender, the risk of default could be construed as more important than the company’s risk of bankruptcy; hence the development of the EDF model otherwise known as the Expected Default Frequency. EDF measures three values: The company’s current market value (calculated by the market value of total assets) The level of liability in the company (risk to default before further lending) The current market value and its vulnerability to large changes form the external environment. (How volatile are the company’s assets?) This was the first time that qualitative and quantitative data had been used to assess credit risk in one model. An improvement over Altman’s Z-score and other previous models that used quantitative data only. In 1990 Kealhofer et al, co-founders of KMV the credit ratings agency bought the rights to use this model and called it the KMV-EDF model. Moody’s analytics bought KMV in 2002 and the EDF model became the most widely accepted credit default model used today. It is now known as the Moody’s KMV RISKCALC with updated versions being developed continuously. (Dwyer et al, 2004)

Summing up

A key issue with bankruptcy prediction models is the difficulty in comparing models. Karels and Prakesh, 1987 suggest that some studies define financial failure as an “inability to pay financial obligations”, whereas others define financial failure as filing for official bankruptcy. If this hasn’t been defined properly throughout the research topic it is difficult to tell which model it is best to use in which circumstances. Accuracy is essential when predicting bankruptcy. If a company heading for bankruptcy is declared to be healthy there are many implications for the ratings agency such as lawsuits and loss of future clients. In terms of accuracy ratings the neural networks developed 100% accuracy at their peak of development and MDA models did not improve much further than Altman in 1968 at 95%. Although neural networks are 100% accurate, complex computer programmes are needed to run such prediction models. The reason Altman’s Z-score model is still so popular is that an accountant can reliably predict bankruptcy to the same degree of accuracy using only an excel spreadsheet. There is a general consensus throughout the literature that a model that can accurately predict bankruptcy at the earliest stage is the most valuable. There is a trend of models becoming less accurate as they predict further into the future. There is also a theme throughout the literature regarding the limitations of bankruptcy prediction models. The industry sector and time frame of the test subjects must be the same as the samples used to develop the model. If this rule is not kept to, the reliability of the model reduces. (Grice and Dugan, 2001) There have been over 150 bankruptcy prediction models developed with optimal accuracy. It has been suggested that new uses for existing models should be found and that new research should use existing models to be tested on real life situations, such as studying individual industries. https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1025&context=account_fac

The gap in the research

The literature suggests that prior to Moody’s RiskCalc 3.1; MDA and neural network analysis have proven to be the most accurate ways to predict the risk of credit default. However, due to the limitations of this study’s scope and relevant resources; the use of Riskcalc 3.1 and neural network analysis is inappropriate. Therefore MDA will be used to analyse the risk of bankruptcy in the automotive industry, ranking firms in order of risk. As Altman revolutionized bankruptcy prediction by becoming the first developer to use MDA methodology, and that the accuracy of this model type did not improve greatly after this time, the Z-score model is most appropriate to analyse the risk of bankruptcy in my chosen industry. Another reason to use Altman’s Z-score model is that Moody’s riskcalc 3.1 expected default frequency value is derived from the company’s share price and most recent financial statements. By using Altman 1968 we can eliminate the influence of the stock market and compare the real financial performance within the automotive industry and rank them according to risk of bankruptcy on the basis of their published financial accounts only. The advantage of Altman’s Z-score models is that accountants can use them to advise potential investors which companies within an individual industry are safest to invest in. Moreover they can accurately predict in ranked order how soon each company will become bankrupt. This information is most valuable in times of recession and global financial instability. With the current economic uncertainty and global financial market crisis, this information will prove invaluable to creditors and investors.

Automotive Industry relevance

During the recent global economic downturn, with exception to the banking industry, the largest global industry affected was the automotive industry. Hardest hit was General Motors which was nationalised by the United States federal government after chapter 11 bankruptcy. In 2010 this industry produced in excess of 60 million vehicles. Parts manufacturers situated in almost every country worldwide rely heavily on this industry for their livelihood. Many support industries are also reliant on the global automotive industry too. KPMG’s 2010 global automotive industry study suggests that the industry is running at almost 40% over capacity and little is being done to address the problem. Worst affected is North America followed by Western Europe and Japan. The problem is being made worse by existing manufacturers moving into the emerging markets in Brazil, Russia, India, and China. It is predicted that these markets will become overcapacities within 5 years, with China becoming 20% over built by 2015. The current industry over capacity is unsustainable. The potential financial and human cost if car manufacturers started defaulting on liability repayments could be as catastrophic as the recent banking crisis. Bankruptcy risk assessment in this industry is extremely important to the lives of people worldwide. If we can rank this industry by Altman’s Z-score we take away the influence of share trading, thus showing each company’s true quantitative financial position and risk of bankruptcy with a high degree of accuracy and will be able to rank each manufacturer accordingly. (KPMG, 2011)

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Univariate ratio analysis development. (2017, Jun 26). Retrieved December 7, 2022 , from

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