Calculates the Zmijewski Score, a financial metric used to predict the likelihood of a company going bankrupt. It is a simpler, three-variable model compared to both the Altman Z-Score and the Ohlson O-Score, and is commonly used as a robustness check when those two models disagree, since it is estimated on a different sample and with a different statistical technique (a probit model rather than discriminant analysis or logistic regression).

The formula is as follows:

\[\text{Net Income to Total Assets} = \text{Net Income} / \text{Total Assets}\] \[\text{Total Liabilities to Total Assets} = \text{Total Liabilities} / \text{Total Assets}\] \[\text{Current Assets to Current Liabilities} = \text{Current Assets} / \text{Current Liabilities}\] \[X = - 4.3 - 4.5 \cdot \text{Net Income to Total Assets} + 5.7 \cdot \text{Total Liabilities to Total Assets}\] \[0.004 \cdot \text{Current Assets to Current Liabilities}\] \[\text{Bankruptcy Probability} = \Phi(X),\;\; \text{the standard normal cumulative distribution function}\]

The Zmijewski Score can be interpreted as follows:

  • A higher X (and therefore a higher bankruptcy probability) indicates a higher likelihood of financial distress.

Also known as: Zmijewski Score, ZFC score, bankruptcy prediction, financial distress score.

No programming experience? With the Finance Toolkit MCP server, AI assistants such as Claude and ChatGPT can calculate the Zmijewski Score for you. Just ask in plain English.

Calculate the Zmijewski Score in Python

The Zmijewski Score is available in the Models module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_zmijewski_score as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AAPL", "MSFT"], api_key="FINANCIAL_MODELING_PREP_KEY")

zmijewski_score = toolkit.models.get_zmijewski_score()

zmijewski_score.loc["AAPL"]

Which returns:

  2020 2021 2022 2023
Net Income to Total Assets 0.1773 0.2697 0.2829 0.2751
Total Liabilities to Total Assets 0.7983 0.8203 0.8564 0.8237
Current Assets to Current Liabilities 1.3636 1.0746 0.8794 0.988
Zmijewski Score -0.553 -0.8427 -0.6955 -0.8466
Zmijewski Bankruptcy Probability 0.2901 0.1997 0.2434 0.1986

Parameters

get_zmijewski_score accepts the following parameters:

  • rounding (int, optional): The number of decimals to round the results to. Defaults to None.
  • growth (bool, optional): Whether to calculate the growth of the values. Defaults to False.
  • lag (int | list[int], optional): The lag to use for the growth calculation. Defaults to 1.
  • standardize (bool, optional): Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False.
  • trailing (int | None, optional): The trailing period to use for the calculation. Defaults to None.
  • show_columns (list[str] | None, optional): List of columns to show in the results. If None, all columns will be shown. Defaults to None.
Internal Growth Rate (IGR) Graham Number Free Cash Flow to Firm (FCFF) Free Cash Flow to Equity (FCFE) Two-Stage Dividend Discount Model Residual Income Market Value Added (MVA) Tobin's Q Ratio Ohlson O-Score Springate Score Grover Score Fulmer H-Score

The Models module page introduces the module, and the sidebar lists all of its functions.

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