Distress scores

In depth

Where the models came from

The original Z was fitted to manufacturers whose shares were traded, which is why it uses the market value of equity in $X_4$. Altman’s 1968 article wrote the first four ratios as percentages, so its published weights read 0.012, 0.014, 0.033 and 0.006 (and 0.999 on sales); his 2000 paper restates them as 1.2, 1.4, 3.3 and 0.6 for ratios written as decimals. Use the second set with decimals: mixing them is a classic error.

Most firms that borrow from banks have no share price. Altman re-estimated the model for private firms with book equity in $X_4$: that is Z′, whose weights and zones differ because book and market values differ. He then fitted Z″ without $X_5$, to reduce the industry effect that asset turnover brings: a retailer or café turns its assets over far faster than a steel mill, which would make it look safer than it is. Z″ was developed for non-manufacturers and for companies in emerging markets; in that use Altman added a constant of 3.25, so that a score of zero corresponds to a bond in default, and calibrated the scores to US bond ratings.

What the sources say about the zones

The constant matters when you read someone else’s analysis. Lantern’s 2027 Z″ is 0.24 without the constant and $0.24 + 3.25 = 3.49$ with it; both are in the distress zone of their own scale. Comparing 3.49 with the plain zones (1.10 and 2.60) would wrongly put Lantern in the safe zone. Altman (2000) also gives the average score with the constant for each US bond rating in 1994: 8.15 for AAA, 5.85 for BBB, 3.75 for B−, 3.20 for CCC+ and 0 for D. On that scale Lantern’s 2026 score of 9.72 is above the AAA average and its 2027 score of 3.49 lies between the CCC+ and B− averages. Those averages describe large rated companies in the mid-1990s, so treat them as a rough translation, not a rating.

Choosing the model changes the zone

The same business can land in different zones under different versions. Lantern’s 2027 Z′, which keeps sales ÷ total assets, is 2.16, in its grey zone: sales of $577,860 on $327,883 of assets add 1.76 points. That is the industry effect Z″ removes. For a café business, Z″ is the right model, and its answer is distress.

Harbourline Roasters, the fictional listed roaster from F00, shows the other side. A roaster turns green beans into roasted coffee, so it is a manufacturer, and it has a share price, so the original Z applies. F00 gives Harbourline’s total equity ($300 million) but not its split; for this lesson assume (a fictional assumption) that $180 million of it is retained earnings. With its market capitalisation of $765 million against liabilities of $360 million, Harbourline’s Z is 3.04, just inside the safe zone (above 2.99). That call rests on the assumption: between none and all of the $300 million being retained earnings, Z ranges from 2.66 to 3.30, and with less than about $156 million of retained earnings it would be grey. On book equity its Z′ is 1.90, in the grey zone, and its Z″ is 2.98, safe. The market thinks Harbourline’s equity is worth two and a half times its book value, and the original model gives that confidence weight.

Limits of the scores

• The samples. The original Z was fitted to 66 US manufacturers with between $1 million and $25 million of assets, half of which failed between 1946 and 1965; later versions to other samples. A two-year-old private café business is far from any of them, and accounting, financing and industries have changed since.
• Leases on the balance sheet. Since ASC 842 (from 2019 for public companies; from fiscal years beginning after 15 December 2021 for private ones) and IFRS 16, lessees record right-of-use assets and lease liabilities. The current part of the lease liability cuts working capital, the asset enlarges every denominator and the liability lowers equity ÷ liabilities. The models were fitted before that change.
• Part-year and first-year periods. Lantern’s 2026 EBIT covers ten months. Annualised, its 2026 Z″ would be about 7.01 rather than 6.47 (same zone). Young firms also have small retained earnings, which $X_2$ penalises by design.
• Book equity that isn’t a cushion. Some strong companies have negative book equity after years of buybacks and dividends. Their $X_2$ and $X_4$ go negative and the score says distress, which may say more about the balance sheet than about the risk.
• Quality of the inputs. The score takes EBIT and retained earnings at face value. Profit inflated by aggressive accounting raises the score, as the previous lesson showed it can.
• Not a forecast. The zones mark where Altman’s samples were classified with or without error; they are not probabilities. A score near a boundary is a reason to look closer, not a coin toss.

Leases show the second limit at its starkest. Remove the right-of-use asset and the lease liabilities from Lantern’s 2027 balance sheet, as under the rules before ASC 842 (the straight-line lease cost equals what the rent would have been, so EBIT and equity don’t change), and its Z″ rises from 0.24 to 2.27: grey, not distress. The cafés’ economics are the same; only the accounting moved.

Starbucks illustrates the fourth. At 29 September 2024 it reported a retained deficit of $7,343.8 million and total shareholders’ deficit of $7,441.6 million, after years of dividends and share repurchases ($2,585.0 million and $1,266.7 million in fiscal 2024 alone). Its Z″ from the FY2024 balance sheet is −0.27, deep in the distress zone, although in the same year its operations produced $6,095.6 million of cash and its operating income covered its interest expense $5{,}408.8 \div 562.0 = 9.62$ times. A model built on book equity misreads a company whose deficit comes from returning cash to shareholders.

Other approaches

Altman’s scores are the best known of many credit-scoring models. Ohlson’s O-score (1980) uses logistic regression on similar ratios and gives a probability of failure rather than a zone. Market-based models infer default risk from the share price and its volatility. Credit rating agencies combine financial ratios with judgement about the industry, management and the terms of the debt. Banks build their own scorecards from their loan histories, and Altman’s later work extends the approach to small and medium-sized firms. All of them start from the same evidence: liquidity, profitability, leverage and the quality of the figures.