value investing

Frank Voisin is the author of the popular value focused website Frankly Speaking, found at

In the late 1960s, NYU professor Edward Altman published a formula to assess the probability that a firm will go bankrupt within two years. The objective was to measure financial distress along a number of objective metrics, standardizing the assessment of credit risk. He called this the Z-Score and it includes five easily derived business ratios, weighted by coefficients. Given its simplicity and accuracy, it is a common calculation used by investors and plays a relatively easy addition to an investment checklist.

Though Altman’s research has been added upon in later years as new coefficients were created for more accuracy in various industries (as well as for firms in emerging markets and private firms), the original formula, widely applicable is this:

Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 +0.99X5.


Factor Ratio Objective
X1 = Working Capital / Total Assets Measure the liquidity of the company’s asset base
X2 = Retained Earnings / Total Assets Measure cumulative profitability relative to firm size
X3 = EBIT / Total Assets Measure how efficiently the company uses its assets to generate earnings from operations
X4 = Market Value of Equity / Book Value of Total Liabilities Consideration of the market’s view of the company relative to its liabilities
X5 = Sales / Total Assets Measure asset turnover

To interpret the resultant Z-Score, we place it in one of three categories:

  1. Firms with a Z-Score greater than 2.99 are considered to be safe and thus have a relatively remote risk of bankruptcy.
  2. Firms with a Z-Score between 1.81 and 2.99 are less clear, existing in a grey area where a clear statement cannot be made.
  3. Firms with a Z-Score less than 1.81 are considered to be in distress and thus at higher risk of bankruptcy.

According to Wikipedia:

In its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years prior to the event, with a Type II error (false positives) of 6% (Altman, 1968). In a series of subsequent tests covering three different time periods over the next 31 years (up until 1999), the model was found to be approximately 80–90% accurate in predicting bankruptcy one year prior to the event, with a Type II error (classifying the firm as bankrupt when it does not go bankrupt) of approximately 15–20% (Altman, 2000).

You can read Altman’s initial paper from 1968, Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy, here [PDF] and his updated paper from 2000, Predicting Financial Distress of Companies: Revisiting the Z-Score and Zeta Models, here [PDF].

So how should you use this? I recommend incorporating it into your investment analysis spreadsheet and calculating the Z-Score over time for any firm you are analyzing. It is also helpful to compare a firm’s Z-Score to others in its industry, as there may be some industry specific effects that are important to consider. Given how easy it is to calculate the Z-Score and its accuracy over time, there really is no excuse for not considering it.

How do you incorporate the Altman Z-Score into your analysis?