Beaver (1966) tested ratios one at a time and found cash flow to total debt was the best single predictor of failure, beating the current ratio. Altman (1968) combined five ratios with discriminant analysis. The Z-score remains a common first screen.
Altman Z-score
Sources: Z from Altman (1968). Z″ weights from Altman, Hartzell, and Peck (1995) and Altman (2000); Z″ zone cutoffs as presented in Altman and Hotchkiss (2006).
All inputs in $ millions ($M). Enter 28 for $28,000,000.
Score
Zone
| Term | Ratio | Calculation | Weight | Contribution |
|---|
Where the numbers come from
The literature, in order
Filter by strand. Each model answered a weakness in the one before it.
- 1966BeaverUnivariate tests on failed firms. Cash flow to total debt was the best single predictor, ahead of the current ratio.
- 1968AltmanMultiple discriminant analysis produces the Z-score. Five ratios, still the default first screen.
- 1974MertonEquity as a call option on firm assets; default when assets fall below debt. Basis of the KMV distance-to-default.
- 1980OhlsonLogit replaces discriminant analysis. The O-score gives a probability of default; the Z-score gives a zone.
- 1984Myers and MajlufInformation asymmetry makes internal cash the cheapest capital. Foundation of the pecking order.
- 1986JensenFree cash flow as an agency cost. Managers with surplus cash overinvest; debt disciplines them.
- 1988Fazzari, Hubbard, and PetersenInvestment sensitivity to cash flow as a signal of financing constraints.
- 1996SloanMarkets overweight accruals, which persist less than cash earnings. High-accrual firms underperform.
- 1997Kaplan and ZingalesChallenge FHP: investment and cash flow sensitivity does not rise monotonically with constraints.
- 1999BeneishThe M-score. Eight ratios, including a DSO index and accruals, flag likely earnings manipulation.
- 1999Opler et al.Firms with riskier cash flows and better growth options hold more cash. The precautionary motive.
- 2001ShumwayStatic models are biased. Discrete-time hazard models with market variables predict better.
- 2002Dechow and DichevAccrual quality measured by how well accruals map to past, present and future cash flows.
- 2004Almeida, Campello, and WeisbachCash flow sensitivity of cash: constrained firms save more of each dollar of cash flow.
- 2008Campbell, Hilscher, and SzilagyiRicher hazard model; distressed stocks earn lower returns, the distress anomaly.
- 2008Bharath and ShumwayA naive distance-to-default predicts nearly as well as the full Merton solution.
- 2009Bates, Kahle, and StulzU.S. cash holdings roughly doubled from 1980 to 2006, driven by riskier cash flows.
The frontier
Cash flow at risk applies value-at-risk logic to operating drivers, answering how bad next year's cash flow gets at the 5th percentile (Stein et al. 2001). Machine learning models (gradient boosting, neural networks) now outperform traditional statistical models on bankruptcy prediction out of sample (Barboza, Kimura, and Altman 2017). The gains are real, and lenders and regulators still need to explain each decision, which favors simpler models. The investment and cash flow sensitivity debate that began in 1988 remains unresolved (Fazzari, Hubbard, and Petersen 1988; Kaplan and Zingales 1997).
References
Sources cited on this rung and in the glossary, in Chicago author-date style. The summaries above are our own descriptions of each work. None are quotations.
- Almeida, Heitor, Murillo Campello, and Michael S. Weisbach. 2004. “The Cash Flow Sensitivity of Cash.” Journal of Finance 59 (4): 1777–1804. https://doi.org/10.1111/j.1540-6261.2004.00679.x
- Altman, Edward I. 1968. “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy.” Journal of Finance 23 (4): 589–609. https://doi.org/10.1111/j.1540-6261.1968.tb00843.x
- Altman, Edward I. 2000. “Predicting Financial Distress of Companies: Revisiting the Z-Score and ZETA Models.” Working paper, Stern School of Business, New York University.
- Altman, Edward I., John Hartzell, and Matthew Peck. 1995. Emerging Markets Corporate Bonds: A Scoring System. New York: Salomon Brothers.
- Altman, Edward I., and Edith Hotchkiss. 2006. Corporate Financial Distress and Bankruptcy. 3rd ed. Hoboken, NJ: John Wiley & Sons.
- Barboza, Flavio, Herbert Kimura, and Edward Altman. 2017. “Machine Learning Models and Bankruptcy Prediction.” Expert Systems with Applications 83: 405–17.
- Bates, Thomas W., Kathleen M. Kahle, and René M. Stulz. 2009. “Why Do U.S. Firms Hold So Much More Cash than They Used To?” Journal of Finance 64 (5): 1985–2021. https://doi.org/10.1111/j.1540-6261.2009.01492.x
- Beaver, William H. 1966. “Financial Ratios as Predictors of Failure.” Journal of Accounting Research 4 (Empirical Research in Accounting: Selected Studies 1966): 71–111. https://doi.org/10.2307/2490171
- Beneish, Messod D. 1999. “The Detection of Earnings Manipulation.” Financial Analysts Journal 55 (5): 24–36. https://doi.org/10.2469/faj.v55.n5.2296
- Bharath, Sreedhar T., and Tyler Shumway. 2008. “Forecasting Default with the Merton Distance to Default Model.” Review of Financial Studies 21 (3): 1339–69. https://doi.org/10.1093/rfs/hhn044
- Campbell, John Y., Jens Hilscher, and Jan Szilagyi. 2008. “In Search of Distress Risk.” Journal of Finance 63 (6): 2899–2939. https://doi.org/10.1111/j.1540-6261.2008.01416.x
- Dechow, Patricia M., and Ilia D. Dichev. 2002. “The Quality of Accruals and Earnings: The Role of Accrual Estimation Errors.” Accounting Review 77 (Supplement): 35–59. https://doi.org/10.2308/accr.2002.77.s-1.35
- Fazzari, Steven M., R. Glenn Hubbard, and Bruce C. Petersen. 1988. “Financing Constraints and Corporate Investment.” Brookings Papers on Economic Activity 1988 (1): 141–206. https://doi.org/10.2307/2534426
- Jensen, Michael C. 1986. “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers.” American Economic Review 76 (2): 323–29.
- Kaplan, Steven N., and Luigi Zingales. 1997. “Do Investment-Cash Flow Sensitivities Provide Useful Measures of Financing Constraints?” Quarterly Journal of Economics 112 (1): 169–215. https://doi.org/10.1162/003355397555163
- Merton, Robert C. 1974. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance 29 (2): 449–70. https://doi.org/10.1111/j.1540-6261.1974.tb03058.x
- Myers, Stewart C., and Nicholas S. Majluf. 1984. “Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have.” Journal of Financial Economics 13 (2): 187–221. https://doi.org/10.1016/0304-405X(84)90023-0
- Ohlson, James A. 1980. “Financial Ratios and the Probabilistic Prediction of Bankruptcy.” Journal of Accounting Research 18 (1): 109–31. https://doi.org/10.2307/2490395
- Opler, Tim, Lee Pinkowitz, René Stulz, and Rohan Williamson. 1999. “The Determinants and Implications of Corporate Cash Holdings.” Journal of Financial Economics 52 (1): 3–46. https://doi.org/10.1016/S0304-405X(99)00003-3
- Shumway, Tyler. 2001. “Forecasting Bankruptcy More Accurately: A Simple Hazard Model.” Journal of Business 74 (1): 101–24. https://doi.org/10.1086/209665
- Sloan, Richard G. 1996. “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows about Future Earnings?” Accounting Review 71 (3): 289–315.
- Stein, Jeremy C., Stephen E. Usher, Daniel LaGattuta, and Jeff Youngen. 2001. “A Comparables Approach to Measuring Cashflow-at-Risk for Non-Financial Firms.” Journal of Applied Corporate Finance 13 (4): 100–109.