About

Altman Z' Score (for Private Firms / Private Manufacturing Companies)

The original Z-score was formulated for public manufacturing companies. For private firms, the Altman Prime score was developed which essentially replaces the market value of equity with the book value of equity and revised co-efficients

The book value of equity is defined by Total Assets - Total Liabilities.

• Working Capital to Total Assets: Measures short-term liquidity.$$\mathrm{X1}=\frac{\mathrm{Working\; Capital}}{\mathrm{Total\; Assets}}$$
• Retained Earnings to Total assets: Measures profitability and accumulated earnings.$$\mathrm{X2}=\frac{\mathrm{Retained\; Earnings}}{\mathrm{Total\; Assets}}$$
• Earnings Before Interest and Tax To Total Assets : Measures operating profitability.$$\mathrm{X3}=\frac{\mathrm{Earnings\; Before\; Interest\; and\; Taxes}}{\mathrm{Total\; Assets}}$$
• Book Value of Equity to Total Liabilities: Measures leverage and market health.$$\mathrm{X4}=\frac{\mathrm{Market\; value\; of\; Equity}}{\mathrm{Total\; Liabilities}}$$
• Sales to Total Asset : Measures asset turnover/efficiency.$$\mathrm{X5}=\frac{\mathrm{Sales}}{\mathrm{Total\; Assets}}$$

Z' > 2.99: Safe zone (low bankruptcy risk).

1.23 < Z' < 2.99: Grey zone (caution).

Z' < 1.23: Distress zone (high bankruptcy risk).

Altman Z'' Score (also written as Z''-Score) is a four-variable variant of the Altman Z-Score model.

Edward Altman developed it specifically for private or public non-manufacturing companies (e.g., service, retail, wholesale, or general firms where asset turnover can vary significantly by industry).

Why Z'' Exists

• The original Z-Score and Z' (private manufacturing) include Sales / Total Assets (X5), which can be highly industry-sensitive.

• Removing this variable makes the model more robust across different non-manufacturing sectors.

• It uses Book Value of Equity (not market value), making it suitable for both private and public non-manufacturing firms.

• Working Capital to Total Assets: Measures short-term liquidity.$$\mathrm{X1}=\frac{\mathrm{Working\; Capital}}{\mathrm{Total\; Assets}}$$
• Retained Earnings to Total assets: Measures profitability and accumulated earnings.$$\mathrm{X2}=\frac{\mathrm{Retained\; Earnings}}{\mathrm{Total\; Assets}}$$
• Earnings Before Interest and Tax To Total Assets : Measures operating profitability.$$\mathrm{X3}=\frac{\mathrm{Earnings\; Before\; Interest\; and\; Taxes}}{\mathrm{Total\; Assets}}$$
• Book Value of Equity to Total Liabilities: Measures leverage and market health.$$\mathrm{X4}=\frac{\mathrm{Market\; value\; of\; Equity}}{\mathrm{Total\; Liabilities}}$$

Z'' > 2.6: Safe zone (low bankruptcy risk).

1.1 < Z'' < 2.6: Grey zone (caution).

Z'' < 1.1: Distress zone (high bankruptcy risk).

Ohlson O-Score (developed in 1980 by James Ohlson) is a logistic regression-based bankruptcy prediction model.

It serves as a strong alternative (and often more accurate) to the Altman Z-Score for forecasting the probability of corporate financial distress or bankruptcy within two years.

Key Advantages Over Altman Z-Score

• Uses 9 variables (more comprehensive).

• Based on a much larger sample (over 2,000 companies vs. Altman's ~66).

• Employs logit (logistic regression) rather than multiple discriminant analysis.

• Generally shows higher predictive accuracy for the 2-year horizon.

• Outputs a score that can be converted into a probability.

Required Financial Information

You need data from the current year (t) and previous year (t-1) for some variables:

• Total Assets (TA)

• Total Liabilities (TL)

• Current Assets (CA)

• GCurrent Liabilities (CL)

• Working Capital (WC) = Current Assets − Current Liabilities

• Net Income (NI) for current and prior year

• Funds from Operations (FFO) — typically Cash Flow from Operations

• GNP Price Index (for size adjustment; base year 1968 = 100). For modern use, people often use CPI or GDP deflator as a proxy, or omit/adjust the size variable in updated implementations.

• Dummy variables:OENEG (X): 1 if Total Liabilities > Total Assets (negative equity), else 0

• Dummy variables:INTWO (Y): 1 if Net Income was negative for the last two years, else 0

Ohlson O-Score Formula

Where CHIN (change in net income) is:

O-Score > 0.5: High probability of bankruptcy within 2 years.

O-Score < 0.5 (especially negative values): Lower risk / financially healthier.

The raw O-score can be converted to a probability using the logistic function:

Beneish M-Score (developed by Professor Messod Beneish in 1999) is a statistical model designed to detect earnings manipulation (financial statement fraud) rather than outright bankruptcy risk.

It identifies companies that are likely 'cooking the books' by inflating revenues, deferring expenses, or manipulating accruals.

• Uses 8 financial ratios (indices) derived from two consecutive years of financial statements.

• Based on a probit model from a sample of companies that were known manipulators.

• Outputs an M-Score that signals the probability of manipulation.

• Probabilistic tool: A high score indicates patterns consistent with manipulation, but it is not definitive proof.

• DSRI: Days Sales in Receivables Index. Detects aggressive revenue recognition / receivables inflation$$\frac{\frac{{\mathrm{Receivables}}_t}{{\mathrm{Sales}}_t}}{\frac{{\mathrm{Receivables}}_{t-1}}{{\mathrm{Sales}}_{t-1}}}$$
• GMI: Gross Margin Index

  Deteriorating gross margins (incentive to manipulate)

  $$\frac{{\mathrm{Gross\; Margin}}_{t-1}}{{\mathrm{Gross\; Margin}}_t}$$
• AQI: Capitalization of expenses / asset quality decline Measures provides a measure of the changing quality of assets $$\frac{\frac{{\mathrm{Current\; Assets}}_t+{\mathrm{PPE}}_t+{\mathrm{Securities}}_t}{{\mathrm{Total\; Assets}}_t}}{\frac{{\mathrm{Current\; Assets}}_{\mathrm{t-1}}+{\mathrm{PPE}}_{\mathrm{t-1}}+{\mathrm{Securities}}_{\mathrm{t-1}}}{{\mathrm{Total\; Assets}}_{\mathrm{t-1}}}}$$
• SGI: Sales Growth Index Detects high sales growth pressure $$\frac{{\mathrm{Sales}}_{t1}}{{\mathrm{Sales}}_{t-1}}$$
• DEPI: Depreciation Index Is a measure of slowing depreciation (as an indicator of extending asset life) $$\frac{{\mathrm{Depreciation\; Rate}}_{t-1}}{{\mathrm{Depreciation\; Rate}}_t}$$
• SGAI: SG&A Expense Index This is an indicator of rising selling/general/admin expenses$$\frac{\frac{{\mathrm{Selling/General/Admin\; Expenses}}_t}{{\mathrm{Sales}}_t}}{\frac{{\mathrm{Selling/General/Admin\; Expenses}}_{t-1}}{{\mathrm{Sales}}_{t-1}}}$$
• LVGI: Leverage Index Indicates increasing leverage/debt usage) $$\frac{\frac{{\mathrm{Total\; Liabilities}}_t}{{\mathrm{Total\; Assets}}_t}}{\frac{{\mathrm{Total\; Liabilities}}_{t-1}}{{\mathrm{Total\; Assets}}_{t-1}}}$$
• TATA: Total Accruals to Total Assets Indicates high levels of accruals (non-cash earnings) $$\frac{{\mathrm{Net\; Income}}_t-{\mathrm{Cash\; Flow\; From\; Operations}}_t}{{\mathrm{Total\; Assets}}_t}$$

The Beneish M-Score Formula (8 variable model)

The Beneish M-Score Formula applies factors to the indices calculated above to arrive at an M-Score

The interpretation thresholds of the M-Score are such that a score higher than -2.22 indicates a higher probability of earnings manipulation and an M-Score lower than -2.22 indicates manipulation of earnings is unlikely