Altman Z-score

The idea. Edward Altman ("Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy," Journal of Finance, 1968) took 33 bankrupt US manufacturers and 33 matched survivors (1946 to 1965). He used multiple discriminant analysis to find the weighted combination of ratios that best separated them. The result, the Z-Score, is the oldest quantitative screen still in daily use. Its method matters more than its vintage: five ratios, each an axis of survival, combined into one number.

Altman Z-score formula and zones

The five inputs (know what each measures):

• X1 = Working capital / Total assets: liquidity cushion relative to size (WC = CA − CL).
• X2 = Retained earnings / Total assets: cumulative reinvested profitability and, implicitly, age. Serial losers and young firms score low.
• X3 = EBIT / Total assets: raw earning power of the asset base, the heaviest-weighted input.
• X4 = Market value of equity / Book value of total liabilities: the market's equity cushion over creditors' claims (the one market input).
• X5 = Sales / Total assets: asset turnover.

The original public-manufacturer model (memorize):

Z = 1.2·X1 + 1.4·X2 + 3.3·X3 + 0.6·X4 + 1.0·X5

Zones: Z > 2.99 safe · 1.81 to 2.99 grey ("zone of ignorance") · Z < 1.81 distress. In-sample the model classified ~95% of firms correctly one year before bankruptcy, falling to ~72% two years out. Out-of-sample accuracy is lower still. It's a screen, and it doesn't pretend to be a rating. (A nuance from the paper worth knowing. Altman's original printing scaled X1 to X4 as percentages, with coefficients 0.012, 0.014, 0.033, 0.006 and 0.999. The decimal-proportion form above is the standard restatement. If a source you meet shows "0.012·X1," it's the same model. That's one of many reasons for the rule: check coefficients against the original papers, not blogs.)

Which Altman Z-score variant should you use?

Z′, private manufacturers (Altman, 1983). No market price exists, so X4 becomes book equity / total liabilities, and the whole model was re-estimated:

Z′ = 0.717·X1 + 0.847·X2 + 3.107·X3 + 0.420·X4(book) + 0.998·X5
Zones: > 2.90 safe · 1.23 – 2.90 grey · < 1.23 distress

Z″, non-manufacturers and emerging markets (Altman, Hartzell & Peck, 1995; Altman 2005). Asset turnover (X5) varies so much by industry that it drowns the signal outside manufacturing. So X5 is dropped and the rest re-estimated, with X4 at book value:

Z″ = 6.56·X1 + 3.26·X2 + 6.72·X3 + 1.05·X4(book)
Zones: > 2.60 safe · 1.10 – 2.60 grey · < 1.10 distress

For emerging-market credits Altman adds a constant: Z″(EM) = 3.25 + Z″, calibrated so scores map onto US bond-rating equivalents (the "EM scoring" bands in his papers). A standing instruction: the Z′ and Z″ coefficients above are widely reproduced with typos and unlabeled variants. So pull Altman's originals and confirm before you rely on them professionally. That means the 1968 paper, the 1983 Corporate Financial Distress, the free 2000 NYU working paper "Predicting Financial Distress of Companies: Revisiting the Z-Score and ZETA Models" (which restates all three models), and the 2005 Emerging Markets Review article. The zones are model-specific: never read a Z′ against Z zones.

Choosing the variant. A listed manufacturer gets Z. A private manufacturer gets Z′. Anything non-manufacturing (services, retail, tech), or an EM credit where you distrust market prices, gets Z″. Financial companies get none, because leverage is their business model and the model would flag every bank on earth. Cyclicals at the trough dip into grey zones as designed. Z is telling you distress risk rose, and that's all it's telling you. Pair it with cost-curve position before you conclude anything.

Worked example: all three variants

Worked computation: Kavery (Year 2). Here are all three variants.

Inputs: WC = 660 − 376 = 284; TA = 1,400; RE = 470; EBIT (reported, incl. the ₹25 crore gain via other income) = 228; MVE = 2,100; TL = 1,400 − 824 = 576; book equity = 824; Sales = 1,300.

X1 = 284/1,400 = 0.203 · X2 = 470/1,400 = 0.336 · X3 = 228/1,400 = 0.163 · X4(mkt) = 2,100/576 = 3.646 · X4(book) = 824/576 = 1.431 · X5 = 1,300/1,400 = 0.929

Z  = 1.2(0.203) + 1.4(0.336) + 3.3(0.163) + 0.6(3.646) + 1.0(0.929)
   = 0.243 + 0.470 + 0.537 + 2.188 + 0.929 = 4.37   → safe (> 2.99)

Z′ = 0.717(0.203) + 0.847(0.336) + 3.107(0.163) + 0.420(1.431) + 0.998(0.929)
   = 0.145 + 0.284 + 0.506 + 0.601 + 0.927 = 2.46   → grey (1.23–2.90)

Z″ = 6.56(0.203) + 3.26(0.336) + 6.72(0.163) + 1.05(1.431)
   = 1.331 + 1.094 + 1.094 + 1.502 = 5.02            → safe (> 2.60); EM version 3.25 + 5.02 = 8.27

Three lessons in one table. First, Kavery is not a distress candidate. A rich market multiple and decent earning power see to that, even though the Beneish M-score flagged its earnings quality. M and Z answer different questions. One asks whether the accounting is clean, the other whether the company will live, and a company can fail one while acing the other. Most manipulators are solvent for years, and most distressed firms keep clean books. Second, Z′ lands in the grey zone while Z is comfortably safe. The variants are different estimated models, and you can't convert between them like units. The market-price input carries a lot of weight in Z, which is worth remembering when the market itself is euphoric: X4 imports Mr. Market's mood into your "objective" screen. Third, you chose reported EBIT including a one-time gain. Normalized EBIT of 203 gives Z = 4.31. Screens inherit your input hygiene, so normalize before every screen.