If the Piotroski F-Score is a fitness check, the Altman Z-Score is a medical scan. It was built for one specific question — "is this company likely to file for bankruptcy in the next two years?" — and it's been shockingly accurate at answering it for over 50 years.
This guide covers the exact formula, what each input means, how to read the number, which version to use for which type of company, and a worked example so you can run it yourself.
TL;DR
- The Z-Score is a weighted sum of 5 financial ratios. You plug numbers from the balance sheet and income statement into a formula and get a single number.
- Z > 3.0 = safe zone. Bankruptcy in the next 2 years is very unlikely.
- 1.8 ≤ Z ≤ 3.0 = grey zone. Some risk, worth watching.
- Z < 1.8 = distress zone. Historically ~75% of firms in this zone went bankrupt within 2 years.
- There are 3 versions: classic (public manufacturers), Z'-Score (private manufacturers), Z''-Score (non-manufacturers and emerging markets). Using the wrong one gives misleading numbers.
- Built by Edward Altman at NYU Stern in 1968 using linear discriminant analysis on 66 companies (half bankrupt, half healthy). Accuracy on out-of-sample data: ~95% for 1-year-out prediction, ~72% for 2-year-out.
The classic formula (public manufacturers)
Z = 1.2·X₁ + 1.4·X₂ + 3.3·X₃ + 0.6·X₄ + 1.0·X₅
The 5 inputs are:
X₁ = Working Capital / Total Assets What it measures: short-term liquidity relative to size. Working capital is current assets minus current liabilities — the cushion the company has to pay bills over the next year. Why it's in the model: companies drown in the short term long before they fail long-term. Negative working capital often precedes bankruptcy by 12–18 months.
X₂ = Retained Earnings / Total Assets What it measures: how much cumulative profit the company has kept over its entire history, scaled to its size. Why it's in the model: this is Altman's brilliant age proxy. Young companies have low retained earnings because they haven't had time to accumulate; they also fail more often. Retained earnings captures maturity and historical profitability in one ratio.
X₃ = EBIT / Total Assets What it measures: operating profitability before financing decisions. How much operating profit does each dollar of assets generate? Why it's in the model: this is the "is the business model actually working" test. A company can be temporarily unprofitable from interest expense (X₃ strips that out) but still have a viable operation. Negative X₃ = the core business loses money before you've even paid a dollar of interest.
X₄ = Market Value of Equity / Total Liabilities What it measures: how much equity cushion exists relative to debt, at market prices. Why it's in the model: equity is the buffer that absorbs losses before creditors take a hit. When this ratio falls below 1, the market is saying the debt exceeds the equity — creditors are next in line. Uses market value (not book) because the market often knows something the balance sheet doesn't.
X₅ = Sales / Total Assets What it measures: asset turnover. How many dollars of revenue does each dollar of assets generate? Why it's in the model: low turnover means assets are sitting idle. Combined with the other ratios, it catches companies that look financially okay but can't actually monetize their asset base.
Reading the score
The thresholds from Altman's original paper:
| Score | Zone | What it means |
|---|---|---|
| Z > 3.00 | Safe | Low probability of bankruptcy within 2 years |
| 1.81 ≤ Z ≤ 3.00 | Grey | Caution zone — model is uncertain |
| Z < 1.81 | Distress | High probability of bankruptcy within 2 years |
One important thing: the thresholds are probabilistic, not deterministic. A score of 1.5 doesn't mean the company will go bankrupt — it means, historically, ~75% of companies in that zone did. Some survive. Some at Z = 4.0 also fail (rare, but happens — model misses ~5% of 1-year failures).
Which version should I use?
Altman later built two variants for cases where the classic Z breaks down:
Z'-Score — Private Manufacturers (1983)
Private companies don't have a market cap, so X₄ uses book value of equity instead of market value. The coefficients are re-estimated:
Z' = 0.717·X₁ + 0.847·X₂ + 3.107·X₃ + 0.420·X₄ + 0.998·X₅
Thresholds: distress < 1.23, grey 1.23–2.90, safe > 2.90.
Z''-Score — Non-Manufacturers & Emerging Markets (1995)
Service companies, tech firms, retailers and emerging market companies have totally different asset bases. Altman dropped X₅ (asset turnover doesn't mean the same thing for them) and rescaled the weights:
Z'' = 3.25 + 6.56·X₁ + 3.26·X₂ + 6.72·X₃ + 1.05·X₄
Thresholds: distress < 1.1, grey 1.1–2.6, safe > 2.6.
The constant 3.25 is there to make the thresholds more comparable to the original Z — it's just a re-centering.
Practical rule of thumb:
- Public manufacturer (Ford, Boeing, Caterpillar) → classic Z
- Private manufacturer → Z'
- Public tech/retail/services (Apple, Microsoft, Walmart) → Z''
- Emerging market company of any kind → Z''
- Bank, insurance, or financial services → don't use any of them. Z-Score doesn't work on financials; their balance sheet structure violates the model's assumptions. Use specialized models (CAMEL, Merton's distance-to-default).
A live example: a healthy company
Let's run Z''-Score on Apple, since it's a non-manufacturer by classification.
Using the most recent fiscal year (simplified):
- Current assets ≈ $143B, current liabilities ≈ $163B → Working capital = -$20B
- Total assets ≈ $353B
- Retained earnings ≈ $(-18)B (negative because of massive buyback programs returning capital to shareholders)
- EBIT ≈ $123B
- Market cap ≈ $3,400B
- Total liabilities ≈ $290B
Computing the inputs:
- X₁ = -20 / 353 = -0.057
- X₂ = -18 / 353 = -0.051
- X₃ = 123 / 353 = 0.348
- X₄ = 3,400 / 290 = 11.72
Z'' = 3.25 + (6.56 × -0.057) + (3.26 × -0.051) + (6.72 × 0.348) + (1.05 × 11.72) Z'' = 3.25 - 0.374 - 0.166 + 2.339 + 12.306 = 17.36
Verdict: way above the 2.6 safe threshold. Bankruptcy risk is essentially zero.
Notice something weird though: X₁ and X₂ are both negative for Apple. A textbook reading would say "warning signs." But X₄ completely dominates the equation because Apple's market cap is enormous relative to its debt — 12× coverage. This is exactly why Z-Score uses market value: the market is implicitly saying "we don't care that Apple runs negative working capital, we see $3.4 trillion of enterprise value here." The model correctly weights that into a safe verdict.
A live example: a distressed company
For contrast, consider a company that was actually approaching bankruptcy — WeWork in 2019 before its failed IPO. Approximate numbers:
- Working capital ≈ $-2B (heavy short-term lease obligations)
- Total assets ≈ $47B (inflated by right-of-use lease assets)
- Retained earnings ≈ $-7B (accumulated losses)
- EBIT ≈ $-3.5B (operating loss)
- Private at that moment (failed IPO), so use book equity ≈ $-7B (negative shareholders' equity)
- Total liabilities ≈ $54B
This is clearly a Z' case (private). Computing:
- X₁ = -2 / 47 = -0.043
- X₂ = -7 / 47 = -0.149
- X₃ = -3.5 / 47 = -0.074
- X₄ = -7 / 54 = -0.130 (negative!)
- X₅ ≈ 0.075 (revenue $3.5B / assets $47B)
Z' = (0.717 × -0.043) + (0.847 × -0.149) + (3.107 × -0.074) + (0.420 × -0.130) + (0.998 × 0.075) Z' = -0.031 - 0.126 - 0.230 - 0.055 + 0.075 = -0.367
Verdict: deeply in the distress zone. Every term except revenue turnover is negative. WeWork filed Chapter 11 in November 2023 — the model would have flagged it 4 years earlier.
How to use Z-Score in practice
1. Use it as a filter, not a conclusion. Z-Score tells you bankruptcy probability, not whether a stock is a good investment. Many companies in the grey zone are interesting turnaround stories at the right price.
2. Pair it with F-Score. Piotroski F-Score tells you if fundamentals are improving. Altman Z-Score tells you how close to the edge the company is. A company that was in distress last year (Z = 1.2) and is now in grey (Z = 2.4) with an F-Score of 8 is a legitimate recovery candidate. A company going the other way is a warning.
3. Watch trend, not just level. A Z-Score that drops from 5.0 to 3.2 over 3 years is a more concerning signal than a Z-Score that has been stable at 2.5 for a decade. The rate of change is the story.
4. Normalize across industries before comparing. Z-Scores vary by industry baseline. A Z'' of 3.0 is strong for a grocery chain (thin-margin business) but weak for a SaaS company (where Z'' above 10 is common). Compare within sectors.
5. Don't use on financials. Don't use on REITs. The model was fit on industrial and retail firms. Banks have leverage ratios that look terrifying by Z-Score standards because that's how banks work. REITs have asset-heavy balance sheets that distort X₅. Use domain-specific models for these.
Limitations to keep in mind
- Linear model. Altman used linear discriminant analysis in 1968 because that's what was available. Modern machine learning models (Merton's distance-to-default, KMV, Kealhofer-McQuown) outperform Z-Score on pure accuracy. But Z-Score is interpretable, free, and you can compute it by hand — which is why it's still the industry default for back-of-envelope checks.
- Accounting quality assumed. The model assumes the financials are honest. Enron had great Z-Scores until the day before it collapsed because the accounting was fraudulent. No quantitative model catches fraud.
- Crisis regimes break it. During 2008, 2020, even healthy companies saw Z-Scores fluctuate wildly due to market-value volatility in X₄. The model works best on "ordinary" conditions, not tail events.
- No forward-looking information. Z-Score reads the balance sheet as of the last reporting date. If a company just announced a transformative acquisition or lost a major customer, the score lags.
Try both F-Score and Z-Score on any company
Computing Z-Score by hand takes about 5 minutes if you know the formula and which version to use. Doing it for a watchlist of 30 companies, every quarter, is 15 hours a year.
Sentinellis runs both F-Score and Altman Z-Score automatically on any public company, using the correct version based on industry classification, alongside ROIC-vs-WACC, 90+ other fundamental metrics, and plain-English explanations of every signal. Three reports are free.
Related reading
- Piotroski F-Score Explained — the 9-point fundamentals checklist that pairs naturally with Z-Score
- ROIC vs WACC: are they actually creating value? (coming soon)
- How to read a 10-K in 15 minutes (coming soon)
This article is for educational purposes only and is not investment advice. Sentinellis doesn't recommend individual stocks.