A Brief Note On The Z-Score

Introduction
Forecasting a debtor’s ability to repay its financial obligations is a challenging task to credit analysts. Knowing how likely the borrowers are going to pay is central to the valuation and asset allocation of debt portfolios. The Z-Score, developed by Professor Edward Altman, is perhaps the most widely recognized and applied model for predicting financial distress using multiple discriminant analysis, Altman narrowed a list of 22 potentially significant ratios to five that, as a set, proved significant in predicting bankruptcy in his sample of 66 corporations (33 bankruptcies and 33 non-bankruptcies). As a junior credit analyst I have developed a model similar to Professor Altman z-score model using the same five ratios he used as a predicator of bankruptcy. The formula is a function of liquidity, balance sheet strength and earnings power. With the help of the Z- Score model, the bankruptcy likelihood could be predicted in advance.
Model description and comparison
The data sample for our study is taken from S&P US-listed firms for the year1990 and 2010. The data covers firms’ ratings and characteristics potentially relevant to credit risk.
Two models were developed using multiple regression based on the data provided for year 2010 and 1990, the dependent variable is the Z-score and the independent variables are working capital/TA ratio, retained earnings/TA ratio, EBIT/TA ratio, book value of equity/ Long term debt ratio and sales/ TA. The models for 2010 and 2009 are as follows;
Z (2010) =-0.364627195A+ 0.47580865B + 1.725750679C + 0.003153399D - 0.095720379E

Z (1990) =-0.4242A+ 1.033147B + 1.691825C + 0.005064D - 0.11272E

Altman Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E
Year
Intercept working capital/assets retained earnings/assets
EBIT/Assets
Book equity/Long term debt
Sales/Assets
Altman
-
1.2
1.4
3.3
0.6
1
1990
2.244
-0.424
1.033
1.692
0.005
-0.113
2010
2.186
-0.365
0.476
1.726
0.003
-0.096

When comparing the two predicted models to Professor Altman’s model few differences were found. First, the weights (coefficients) assigned to each variable in the two predicted models are different from Professor Altman model’s weights. The predicted scoring models for 2010 and 2009 relates the working capital/total assets ratio and the sales/total assets ratio negatively to the z-score which means the higher these two ratios are the lower the z-score. Moreover, the computed models assign lower weights to all the independent variables than Altman’s model, this indicates the lower significance of these factors in explaining the z-score of 1990 and 2010 models. It was also found, that the predicted models for 2010 and 1990 differed from each other. The models differ in weights assigned to each independent variable, in 2010 the EBIT/total assets, working capital/TA and sales/TA ratios had higher coefficients than 1990. Where in 1990 the weights assigned to retained earnings/assets and Book equity/Long term debt ratios were higher than 2010. The return on total assets ratio EBIT/TA had the highest weight in all the models, this indicates the high importance of this ratio in explaining the credit risk. The variation in weights given to each factor could be due to the different market conditions and company specific factors at of the sample data. Thus, we can see that one model cannot be used to explain the credit risk in different times for different firms, as the weights assigned to each variable changes through time and the relative importance of the factors or ratios in explaining the credit risk cannot be fixed.
Other factors
However, these five factors of Altman’s model don’t always capture anticipated credit risk. There are other financial and non-financial factors that could be used for signalling credit risk. Financial ratios such as the interest coverage ratio has a lot of importance for the creditors of the firm. This number tells how safe their investments are and how

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