Bao et al. 2020, Journal of Accounting Research 58 (1), page 199

Checcini et al. 2010, Management Science 56 (7), page 1146.

The standard warning in this book applies: Beware of models. Playing with mirrors? In particular, ask how well they work out of the estimation period in real time. How often do they fail to predict bankruptcy or default (a Type I error)? How often do they predict bankruptcy when it does not occur (a Type II error)? Understand the fundamentals underlying the business and keep a book on liquidity.

Altman Z-score:

Altman, E. 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy.  Journal of Finance 23: 589–609.

Olson O-score:

Ohlson, J.  1980.  Financial ratios and the probabilistic prediction of bankruptcy.  Journal of Accounting Research 19: 109–131.

A review of these and other models are in

Beaver, W., M. Correia, and M. McNichols. 2010. Financial statement analysis and the prediction of financial distress. Foundations and Trends in Accounting 5: 99-173.

See also a review of bankruptcy prediction models at

https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1025&context=account_fac

Some models employ market price data for prediction with the insight that a firm’s equity can be viewed as a call option on its debt. See, for example, the KMV-Merton model at

Unlike other measures, this is comprehensive; it leaves nothing out. Further, it is not something that has to be calculated: Once you have reformulated balance sheets and income statements as all good value investors have, it just falls out from the OI number and beginning and ending NOA for the period.

An alternative calculation through the financing activities is:

That also drops out from reformulated statements.

• Firms can delay payments to generate cash flow
• Firms can sell receivables to generate cash flow
• Firms can reduce advertising expenditures to generate cash flow
• Firms can reduce R & D expenditures to generate cash flow
• Non-cash transactions are not in reported cash flows
• Structured financing can make borrowing look like cash from operations
• Capitalization policy shifts cash outflows from cash from operations to cash investment

• Investment in acquisitions paid for by issuing shares
• Assets acquired in asset exchanges
• Assets acquired by issuing debt
• Assets leased: The cash flow occurs later with lease payments

You can see that the firm, while generating positive net income, generated negative cash flow from operations in 1999. Its operations are absorbing cash, not generating cash; it has potential liquidity problem. At the same time, it is liquidating a net $682 million in debt assets by $682 million to meet the shortfall. But this is treated as a reduction in cash investment in operations. That makes free cash flow lower than it should be, so seemingly operations are using less cash. In 1998 and 1997, it goes the other way.

In 2023, Meta Platforms (Facebook) spent $27.7 billion investing in its business but sold off debt assets for a net $3.2 billion to make the investments. The latter was included in cash investment to report a total of $24.5 billion rather than the $27.7 billion.

In its December 2024 quarter, Apple Inc. reported a positive number, $1,927 million for cash investment in operations, looking as if investing activities were generating cash rather than using it. However, the cash investment section of the cash flow statement included a net $4,603 million from liquidating debt assets. The actual cash expenditure in operations was $2,676 million. As these and other firms invest heavily AI, watch the cash investment number: They might be liquidating their big debt asset holdings to do so.

If a firm uses the direct method in the U.S., it must report the indirect reconciliation in footnotes.