Lesson A2.1 · 1 of 5 · Creative accounting
The Beneish M-score: the 8 ratios, the formula and Enron worked out
The Beneish M-score combines 8 indices from the balance sheet, income statement and cash flow statement, weighted as Messod Beneish estimated, to show how closely a company’s figures resemble those of firms that inflated their profits. Above -1.78 the company is flagged: a reason to dig deeper, not proof.
Terms in this lesson
- Beneish M-score
- A statistical test that looks for patterns of aggressive accounting.
- Balance sheet
- What the company owns, what it owes and what is left for shareholders, on a given date.
- Income statement
- How much the company sold over a period, what it spent and how much profit was left.
- Cash flow statement
- The money that actually came into and went out of the bank account over a period.
What is the Beneish M-score and how is it calculated
Definition
Where does the score come from?
M = -4.84 + 0.920 DSRI + 0.528 GMI + 0.404 AQI + 0.892 SGI + 0.115 DEPI - 0.172 SGAI + 4.679 TATA - 0.327 LVGI
Messod Beneish, a professor at Indiana University, published the model in 1999 in the Financial Analysts Journal. He built it on companies that had reported misleading figures: most had been charged with accounting fraud by the SEC, and others had publicly admitted they needed to restate. Seven of the indices compare this year with last year, so 1 means “no change”; TATA uses the current year only. The result comes from a statistical model (a probit): the higher M is, meaning the less negative, the higher the estimated probability of manipulation.
| Index | How it is calculated (t = this year) | What a rise points to |
|---|---|---|
| DSRI | (receivables ÷ sales) in t ÷ the same ratio in t-1 | Customers paying later, or sales booked too early |
| GMI | gross margin in t-1 ÷ gross margin in t | The gross margin has worsened |
| AQI | [1 - (current assets + PP&E) ÷ total assets] in t ÷ the same ratio in t-1 | More of the assets are hard to pin down, such as costs parked on the balance sheet |
| SGI | sales in t ÷ sales in t-1 | Fast growth, and pressure to keep it going |
| DEPI | depreciation rate in t-1 ÷ rate in t; rate = depreciation ÷ (depreciation + PP&E) | Depreciation has slowed |
| SGAI | (selling, general and admin costs ÷ sales) in t ÷ the same ratio in t-1 | Overheads rising relative to sales (negative weight) |
| TATA | (income from continuing operations - operating cash flow) ÷ total assets | Less and less cash behind the profit |
| LVGI | [(current liabilities + long-term debt) ÷ total assets] in t ÷ the same ratio in t-1 | Borrowing has gone up (negative weight) |
Formulas as given by M. D. Beneish in his AAII Journal interview, September 2023. PP&E = property, plant and equipment, net of depreciation.
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Create a free accountThe -1.78 cut-off and how often the score is wrong
The figures do not resemble those of firms that inflated profits.
The estimated probability of manipulation is above 3.75%.
Find out which ones rose and compare with earlier years and with a competitor.
Beneish explains the cut-off like this: on a normal distribution, -1.78 corresponds to a probability of 3.75%, while the average probability of manipulation in his sample was 0.69%. So a flagged company is more than five times as likely as average. The bar is set low on purpose: shares in companies caught manipulating their figures collapse, so missing one costs far more than checking an honest firm for nothing.
How many does it catch? In the abstract of the 1999 article, Beneish writes that the model identifies roughly half of the companies involved in earnings manipulation before it becomes public. A 2013 CFA Institute piece reports that, on the holdout sample, the model missed half of the manipulators and wrongly flagged 7.2% of the other firms. In a 2023 interview, Beneish says that out of 2,000 companies the score flags between 6% and 7.5%, and that 10 to 15 of them are actual frauds.
Worked example: Enron’s Beneish score for 2000
In a Form 8-K dated 27 February 2001, Enron filed its audited financial statements for 2000. In millions of dollars, 2000 against 1999: revenues 100,789 against 40,112; cost of gas, electricity, metals and other products 94,517 against 34,761; depreciation 855 against 870; net trade receivables 10,396 against 3,030; current assets 30,381 against 7,255; net PP&E 11,743 against 10,681; total assets 65,503 against 33,381; current liabilities 28,406 against 6,759; long-term debt 8,550 against 7,151. Income before the cumulative effect of accounting changes: 979; operating cash flow: 4,779. The income statement has no separate selling, general and admin line, so for SGAI we use operating expenses: 3,184 against 3,045.
Each index’s contribution to Enron’s Beneish M-score for 2000 (weight times index): DSRI 1.26, GMI 1.13, AQI 0.31, SGI 2.24, DEPI 0.13, SGAI -0.07, TATA -0.27, LVGI -0.44. With the constant of -4.84, the score is -0.56.
Add the eight contributions to the constant and M comes to -0.56, well above -1.78. On the figures published in February 2001, Enron was flagged nine months before its bankruptcy filing on 2 December 2001. But look at where the signal comes from: SGI (revenues up 2.5 times) and GMI (gross margin down from 13.3% to 6.2%) add 3.37 points between them. With those two indices at 1, the score would have been -2.51, below the cut-off. TATA, the profit-without-cash index, pulls the score down, because reported operating cash flow was almost five times the profit. The Enron lesson shows why even that cash was not what it seemed.
Real case
Enron’s Beneish M-score for 2000
Calculated from the 8 indices using the audited statements filed with the SEC. The signal came mostly from revenue growth and a thinner margin, not from the earnings-quality indices.
The limits of the Beneish score and what to do after a flag
Lessons are educational. They are not a recommendation to buy or sell. Investing involves risk and you can lose money. Sources: M. D. Beneish, “The Detection of Earnings Manipulation”, Financial Analysts Journal, vol. 55, no. 5, 1999 (abstract, CFA Institute); M. D. Beneish, interview in the AAII Journal, September 2023 (the formula, the indices, the -1.78 cut-off and 3.75% probability, the 0.69% average, the limits); D. McLeavey, CFA Institute, Enterprising Investor, 29 July 2013 (holdout sample results); Enron, Form 8-K of 27 February 2001 with the 2000 and 1999 financial statements (SEC EDGAR); our calculations.