The Analyst’s Course · Forensic Accounting
The Altman Z-Score, Coefficient by Coefficient
The construction
Altman (1968, Journal of Finance) ran multiple discriminant analysis on 66 manufacturing firms — 33 bankrupt within a year, 33 matched survivors — and extracted five ratios with weights: Z = 1.2·X₁ + 1.4·X₂ + 3.3·X₃ + 0.6·X₄ + 1.0·X₅, where X₁ = working capital/assets (short-term cushion), X₂ = retained earnings/assets (accumulated, reinvested history), X₃ = EBIT/assets (operating profitability), X₄ = market equity/total liabilities (the market's live vote on solvency), X₅ = sales/assets (asset productivity). Below 1.8 = distress, 1.8–3.0 = grey, above 3.0 = safe. Year-one classification accuracy: about 95%.
What each factor is really asking
X₁ asks: can you pay the next two quarters of bills without selling anything? X₂ asks: has this company ever actually made money and kept it — or is it structurally re-founding itself? X₃ asks: does the asset base produce operating profit at all? X₄ asks: what do shareholders, with real money, think solvency is worth relative to what creditors are owed (the leverage ratio that cannot be massaged, because the market sets it daily)? X₅ asks: how hard does every dollar of assets work? Notice the design: two balance-sheet cushions, one earnings engine, one market vote, one efficiency measure. No single accounting choice can move all five.
Flavors and honest limits
The original weights fit manufacturers with 1960s capital structures. Altman published re-estimated sets: private firms (0.717/0.847/3.107/0.42/0.998, cutoffs 1.23/2.9) and non-manufacturers (6.56/3.26/6.72/1.05, X₅ dropped because service firms carry few tangible assets). The panel auto-selects the flavor. Limits to respect: banks are structurally inapplicable (leverage is the business model), and a strong Z is a statement about probability, not destiny — healthy firms do file with sudden-fraud or sudden-liability events.
Z = 1.2·WC/A + 1.4·RE/A + 3.3·EBIT/A + 0.6·MktEq/TL + 1.0·Sales/A
Altman Z (public manufacturer) — Zones: <1.8 distress · 1.8–3.0 grey · >3.0 safe. Accuracy ~95% one year ahead in the 1968 sample.
Sears 2017 — the Z said it for years
Sears Holdings' Z-Score slid below the distress line years before the October 2018 Chapter 11: negative retained earnings from a decade of losses (X₂ deeply negative), shrinking sales per asset (X₅ falling), thinning working capital (X₁), while X₄ collapsed as equity value evaporated against mounting liabilities. The market kept repricing "real estate value" stories; the model kept answering with arithmetic. JCPenney traced the same path. The Z-Score's power is precisely its boringness — it cannot be talked into a story.
What you'll practise
Which Altman factor uses the stock market's own valuation rather than an accounting number?
3 graded checkpoints · certification exam at the end of the track
Sources
Altman (1968); Beneish (1999); Sloan (1996); company 10-K filings via SEC EDGAR
Learn content is for education only — not individualized financial advice, a recommendation, or a solicitation to buy or sell any security. Options involve substantial risk. Examples are simplified and historical patterns never guarantee future results.