Beneish Model

Quick Summary
1. Calculate the eight variables of the Beneish model
2. Determine the M-score and avoid companies with values greater than -1.78

One quantitative tool for detecting earnings manipulation is the Beneish model. The model uses eight variables based on accounting information to assess the likelihood of misreporting. These variables are designed to capture the effects of either manipulation itself or the preconditions that may prompt firms to artificially increase revenues or deflate expenses. The estimation period of the study is 1982 to 1992 and consists of 50 manipulators and 1,708 control companies. The model serves as a useful screening device for investors.

1. Calculate the Variables

  • Days Sales in Receivables Index (DSRI): DSRI represents the ratio of receivables as a percentage of sales in the current year relative to the corresponding measure in the previous year. A disproportionate increase in receivables across two consecutive years may suggest that the firm is inappropriately inflating revenue. Earnings are likely overstated as a consequence.


  • Gross Margin Index (GMI): GMI is the ratio of gross margin in the year prior to the gross margin in the current year. A GMI greater than 1.0 indicates that gross margins have deteriorated. This may signal that the firm faces poor future prospects and therefore has a greater incentive to engage in earnings manipulation.


  • Asset Quality Index (AQI): AQI measures the ratio of non-current assets (CA), other than property plan and equipment (PPE), to total assets (TA). A value greater than 1.0 indicates that the firm has potentially increased its propensity to defer costs. The most likely culprit is excessive capitalization. In instances where a firms assets consist exclusively of current assets and PPE, it is recommended to set the value to one (its neutral value) rather than treat the observation as missing.


  • Sales Growth Index (SGI): SGI is the ratio of sales in the current year to sales in the previous year. While growth does not necessarily imply manipulation, it does put increased pressure on managers to achieve earnings targets. At the first hint of slowdown, managers at growth firms face greater incentives to manipulate earnings. A more general concern is that controls and reporting quality tend to slacken in periods of high growth.


  • Depreciation Index (DEPI): DEPI represents the rate of depreciation in the prior year compared to the corresponding rate in the current year. A ratio greater than 1.0 is evidence that the rate at which assets are depreciated has slowed. This raises the possibility that depreciation is understated. As the results of the final study show, DEPI does not represent a particularly useful variable in identifying manipulators. After all, a change from accelerated depreciation to straight line would also cause a higher depreciation index.


  • Sales, General, and Administrative Expenses Index (SGAI): SGAI represents the ratio of SGA-to-sales in the current year relative to the corresponding measure in the year prior. A ratio greater than 1.0 may suggest decreasing administrative and marketing efficiency. Since this is generally interpreted as a negative signal about the firm’s future prospects, companies may be predisposed to manipulation. In the end, the variable is not particularly significant.


  • Leverage Index (LVGI): LVGI is the ratio of debt and current liabilities to assets in year t relative to the corresponding ratio in year t-1. A ratio greater than 1.0 indicates an increase in leverage. In order to comply with debt covenants, some firms may be pressured to manipulate earnings when they take on greater leverage. The coefficient is not ultimately very significant. This is likely because the cost of not complying with debt covenants is small. The incentive to induce earnings manipulation is therefore more modest.


  • Total Accruals to Total Assets (TATA): TATA is the ratio of total accruals to total assets. It serves as a proxy for the extent to which cash underlies accounting income. Greater accruals (i.e. less cash) can indicate a higher likelihood of earnings manipulation. The most straightforward way to calculate accruals – and the method used in the CFA curriculum – is the difference between net income and operating cash flows. This can be further refined by excluding extraordinary times from net income. Another common method is Δassets – Δcash – Δliabilities. The actual calculation used by Beneish is Δcurrent assets – Δcash – Δcurrent liabilities –depreciation & amortization.


2. Determine the M-score
The estimation results confirm that accounting data is in fact useful in detecting manipulation. The probability of manipulation is estimated using a probit model where the output is an M-score. (M is a dichotomous variable coded 1 for manipulators and 0 otherwise). Investors should avoid firms with an M-score exceeding -1.78 as the probability of earnings manipulation becomes statistically significant after that point.

M-score = –4.840 + 0.920 (DSRI) + 0.528 (GMI) + 0.404 (AQI) + 0.892 (SGI) + 0.115 (DEPI) – 0.172 (SGAI) + 4.670 (TATA) – 0.327 (LEVI)

Concluding Thoughts
The model can make two types of errors. It can classify a firm as a non-manipulator when it manipulates (type I error) or it can classify a firm as a manipulator when it does not manipulate (type II error). Based on the sample dataset, the model misclassified 26% of the manipulators (type II error) and 14% of the non-manipulators (type I error). Given that the typical manipulator loses on average 40% of its market value in the quarter of the manipulation discovery, a type I error is decidedly more costly. Investors should always investigate the results of the screen to determine whether the distortions in the financial statements are truly driven by earnings manipulation or have another root cause.

The estimation results demonstrate that the Beneish model is a useful screen in avoiding manipulators. Earnings manipulators however are aware of such quantitative models and have consequently increased their sophistication in committing fraud. The predictive power of the model has declined over time as a result.

Suggested Reading
Messod Beneish. The Detection of Earnings Manipulation.




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