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评价公司运营状况的阿尔曼分析模型，对选择价值投资公司具有一定的帮助。然而，目前大多数会计教材和解释都对采用的表达式没有一个准确的定义。所得到的结果差异非常之大。本文希望对其数值的选择和加权数值给予进一步研究和定义。
Z=0.012×X1+0.014×X2+0.033×X3+0.006×X4+0.01×X5 这是一组系数；
其中:Z——判别函数值
X1——(营运资金÷资产总额)×100
X2——(留存收益÷资产总额)×100
X3——(息税前利润÷资产总额)×100
X4——(普通股优先股市场价值总额÷负债帐面价值总额)×100
X5——销售收入÷资产总额
在其它文章中还出现了另一组系数：
Z=0.012×X1+0.014×X2+0.033×X3+0.006×X4+0.999×X5；
首先X1描述的是描述能够用于运营的资金与企业总资产的比例或比率，其关键在于该值是百分比？还是简单比值？还有一种说法是：它等于经营现金净流量除以负债总额。这个比率越高，说明企业承担债务的能力越强。注意目前对于阿尔曼模型的有多种说法，包括对权重系数的表述不是很准确。
我查阅了原文《PREDICTING FINANCIAL DISTRESS OF COMPANIES:REVISITING THE Z-SCORE AND ZETA® MODELS》_Edward I. Altman (2000,7)，他是这么说的：
X1, Working Capital/Total Assets (WC/TA).
The working capital/total assets ratio, frequently found in studies of corporate problems,is a measure of the net liquid assets of the firm relative to the total capitalization. Working capital is defined as the difference between current assets and current liabilities. Liquidity and size characteristics are explicitly considered. Ordinarily, a firm experiencing consistent operating losses will have shrinking current assets in relation to total assets. Of the three liquidity ratios evaluated, this one proved to be the most valuable. Two other liquidity ratios tested were the current ratio and the quick ratio. There were found to be less helpful and subject to perverse trends for some failing firms.
X1 是企业流动资金与资产总额的比；流动资金定义为：流动资产（现金+库存）－ 流动负债（短期贷款）；
X2, Retained Earnings/Total Assets (RE/TA).
Retained earnings is the account which reports the total amount of reinvested earnings and/or losses of a firm over its entire life. The account is also referred to as earned surplus. It should be noted that the retained earnings account is subject to "manipulation" via corporate quasi-reorganizations and stock dividend declarations. While these occurrences are not evident in this study, it is conceivable that a bias would be created by a substantial reorganization or stock dividend and appropriate readjustments should be made to the accounts. This measure of cumulative profitability over time is what I referred to earlier as a “new” ratio. The age of a firm is implicitly considered in this ratio. For example, a relatively young firm will probably show a low RE/TA ratio because it has not had time to build up its cumulative profits. Therefore, it may be argued that the young firm is somewhat discriminated against in
this analysis, and its chance of being classified as bankrupt is relatively higher than that of another older firm, ceteris paribus. But, this is precisely the situation in the real world. The incidence of failure is much higher in a firm’s earlier years. In 1993, approximately 50% of all firms that failed did so in the first five years of their existence (Dun & Bradstreet, 1994).
In addition, the RE/TA ratio measures the leverage of a firm. Those firms with high RE, relative to TA, have financed their assets through retention of profits and have not utilized as much debt.
X2，未分配利润（未分配利润+资本公积）/资产总额；
X3, Earnings Before Interest and Taxes/Total Assets (EBIT/TA).
This ratio is a measure of the true productivity of the firm’s assets, independent of any tax or leverage factors. Since a firm’s ultimate existence is based on the earning power of its assets, this ratio appears to be particularly appropriate for studies dealing with corporate failure. Furthermore, insolvency in a bankrupt sense occurs when the total liabilities exceed a fair valuation of the firm’s assets with value determined by the earning power of the assets. As we will show, this ratio continually outperforms other profitability measures, including cash flow.
X3，税前和利息前收益/资产总额；
X4, Market Value of Equity/Book Value of Total Liabilities (MVE/TL).
Equity is measured by the combined market value of all shares of stock, preferred and common, while liabilities include both current and long term. The measure shows how much the firm’s assets can decline in value (measured by market value of equity plus debt) before the liabilities exceed the assets and the firm becomes insolvent. For example, a company with a market value of its equity of $1,000 and debt of $500 could experience a two-thirds drop in asset value before insolvency. However, the same firm with $250 equity will be insolvent if assets drop only one-third in value. This ratio adds a market value dimension which most other failure
studies did not consider. The reciprocal of X4 is a slightly modified version of one of the variables used effectively by Fisher (1959) in a study of corporate bond yield-spread differentials. It also appears to be a more effective predictor of bankruptcy than a similar, more
commonly used ratio; net worth/total debt (book values). At a later point, we will substitute the book value of net worth for the market value in order to derive a discriminant function for privately held firms (Z’) and for non-manufacturers (Z”). More recent models, such as the KMV approach, are essentially based on the market value of equity and its volatility. The equity market value serves as a proxy for the firm's asset values.
X4，市场价值（优先股+流通股）/总负债（短期负债+长期负债）
X5, Sales/Total Assets (S/TA).
The capital-turnover ratio is a standard financial ratio illustrating the sales generating ability of the firm’s assets. It is one measure of management’s capacity in dealing with competitive conditions. This final ratio is quite important because it is the least significant ratio
on an individual basis. In fact, based on the univariate statistical significance test, it would not have appeared at all. However, because of its unique relationship to other variables in the model, the sales/total assets ratio ranks second in its contribution to the overall discriminating ability of the model. Still, there is a wide variation among industries in asset turnover, and we will specify an alternative model (Z”), without X5 at a later point.
X5，销售收入/资产总额
A Clarification
The reader is cautioned to utilize the model in the appropriate manner. Due to the original computer format arrangement, variables X1 through X4 must be calculated as absolute percentage values. For instance, the firm whose net working capital to total assets (X1) is 10% should be included as 10.0% and not 0.10. Only variable X5 (sales to total assets) should be expressed in a different manner: that is, a S/TA ratio of 200% should be included as 2.0. The practical analyst may have been concerned by the extremely high relative discriminant coefficient of X5. This seeming irregularity is due to the format of the different variables. Table 1 illustrates the proper specification and form for each of the five independent variables. Over the years many individuals have found that a more convenient specification of the model is of the form: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5. Using this formula, one inserts the more commonly written percentage, for example, 0.10 for 10%, for the first four variables (X1-X4) and rounds the last coefficient off to equal 1.0 (from 0.99). The last variable continues to be written in terms of number of times. The scores for individual firms and related group classification and cutoff scores remain identical. We merely point this out and note that we have utilized this format in some practical application, for example, Altman and LaFleur (1981).
根据上述的描述，我们可以确切描述一下公式：
Z = 1.2×X1 + 1.4×X2 + 3.3×X3 + 0.6×X4 + 1.0×X5；
X1=（流动资产（现金+库存）－ 流动负债（短期贷款））÷ 资产总额；
X2= 未分配利润（未分配利润+资本公积）÷ 资产总额；
X3= 税前和利息前收益/资产总额；
X4= 市场价值（优先股+流通股）÷ 总负债（短期负债+长期负债）；
X5= 销售收入 ÷ 资产总额；
或者
Z = 0.012×X1 + 0.014×X2 + 0.033×X3 + 0.006×X4 + 1.0×X5；
X1=（流动资产（现金+库存）－ 流动负债（短期贷款））÷ 资产总额 × 100；
X2= 未分配利润（未分配利润+资本公积）÷ 资产总额 × 100；
X3= 税前和利息前收益 ÷ 资产总额 × 100；
X4= 市场价值（优先股+流通股）÷ 总负债（短期负债+长期负债）× 100；
X5= 销售收入 ÷ 资产总额；
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