Altman Z-Score
Overview
Altman Z-Score is a linear discriminant model predicting bankruptcy probability from five financial ratios. Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + 1.0X₅. Zones: Z > 2.99 (safe), 1.81-2.99 (grey), Z < 1.81 (distress). Originally for public manufacturing firms; variants exist for private and non-manufacturing.
When to Use
Trigger conditions:
- Screening companies for bankruptcy risk
- Quick credit assessment using publicly available financials
- Monitoring portfolio companies for financial distress signals
When NOT to use:
- For financial institutions (banks, insurers) — different capital structures
- When detailed credit scoring is needed (use logistic regression credit models)
Algorithm
IRON LAW: Z-Score Was Calibrated for PUBLIC MANUFACTURING Firms
Applying the original formula to private firms, service companies, or
emerging markets WITHOUT using the appropriate variant produces
misleading results. Use Z'-Score for private firms, Z''-Score for
non-manufacturing and emerging markets.Phase 1: Input Validation
Extract from financial statements: working capital, retained earnings, EBIT, market cap (or book equity for private), total assets, total liabilities, sales. Gate: All five inputs available, from same reporting period.
Phase 1.5: Variant Selection (MANDATORY)
Before touching any formula, pick the right variant — this is the single most common mistake when applying Altman Z.
| Firm description | Variant | Script flag |
|---|---|---|
| Public manufacturing firm | Original Z | --variant original |
| Private manufacturing firm (no market cap) | Z' | --variant private |
| Non-manufacturing — SaaS, services, retail, tech, finance-light | Z'' | --variant non_manufacturing |
| Emerging-market firm of any kind | Z'' | --variant non_manufacturing |
If the user description contains any of these tags: "SaaS", "cloud", "software", "services", "retail", "e-commerce", "platform", "tech", "emerging market", "BRICS", "non-manufacturing" → use Z''. Do not default to the original Z just because that's the "classic" formula.
Full formulas and zone thresholds for each variant live in references/z-score-variants.md. Coefficients, X₄ definition (market cap vs book equity), and the X₅ treatment all differ between variants — they are not small tweaks to the original.
Phase 2: Core Algorithm
- X₁ = Working Capital / Total Assets (liquidity)
- X₂ = Retained Earnings / Total Assets (cumulative profitability)
- X₃ = EBIT / Total Assets (operating efficiency)
- X₄ = Market Value of Equity / Total Liabilities (leverage)
- X₅ = Sales / Total Assets (asset turnover)
- Z = 1.2X₁ + 1.4X₂ + 3.3X₃ + 0.6X₄ + 1.0X₅
Phase 3: Verification
Check: all ratios in plausible ranges. Compare Z-score against industry peers and historical trend. Gate: Z-score computed, zone classification assigned.
Phase 4: Output
Return Z-score with component breakdown and zone classification.
Output Format
{
"z_score": 2.45,
"zone": "grey",
"components": {"X1": 0.12, "X2": 0.25, "X3": 0.08, "X4": 1.5, "X5": 0.9},
"metadata": {"model": "original", "company": "...", "period": "2024-Q4"}
}Examples
Sample I/O
Input: WC=200M, RE=500M, EBIT=150M, MktCap=2B, TL=1B, TA=3B, Sales=2.5B Expected: X1=0.067, X2=0.167, X3=0.05, X4=2.0, X5=0.833. Z=1.2(0.067)+1.4(0.167)+3.3(0.05)+0.6(2.0)+1.0(0.833)=2.53 → Grey zone.
Edge Cases
| Input | Expected | Why |
|---|---|---|
| Negative retained earnings | Low X₂, likely distress | Accumulated losses are a strong distress signal |
| Startup with no revenue | X₅ near zero | Z-score not designed for pre-revenue companies |
| Asset-light tech firm | Misleading X₅ | High revenue/low assets inflates turnover |
Gotchas
- Model age: Calibrated in 1968 on 1946-1965 data. Business models, accounting standards, and capital structures have changed. Use as one signal, not sole determinant.
- Accounting manipulation: Z-score uses reported financials. Creative accounting (off-balance-sheet debt, revenue recognition games) can mask distress.
- Industry differences: Capital-intensive industries naturally have lower asset turnover (X₅). Compare within industry, not across.
- Trend matters more than level: A company moving from Z=3.5 to Z=2.1 over two years is concerning even though 2.1 is still in the grey zone.
- Private firm variant (Z'): replaces X₄ with Book Equity / Total Liabilities and re-weights:
Z' = 0.717X₁ + 0.847X₂ + 3.107X₃ + 0.420X₄ + 0.998X₅. Zone thresholds shift to 2.9 / 1.23. - Non-manufacturing variant (Z''): drops X₅ entirely and re-estimates the rest:
Z'' = 6.56X₁ + 3.26X₂ + 6.72X₃ + 1.05X₄. Zone thresholds shift to 2.6 / 1.1. Using original Z on a SaaS / services firm inflates the score via X₅ and can mis-zone a distressed firm as safe.
Scripts
| Script | Description | Usage |
|---|---|---|
scripts/altman_z.py | Compute Altman Z-Score and classify zone | python scripts/altman_z.py --help |
Run python scripts/altman_z.py --verify to execute built-in sanity tests.
References
references/z-score-variants.md— Z / Z' / Z'' full formulas, zone thresholds, variant-selection rules, and a worked tech-firm example.