# Beneish M-score

The Beneish model is a statistical model that uses financial ratios calculated with accounting data of a specific company in order to check if it is likely (high probability) that the reported earnings of the company have been manipulated.

## How to calculate

The Beneish M-score is calculated using 8 variables (financial ratios):
* Days Sales in Receivables Index
(DSRI) DSRI = (Net Receivables$_t$ / Sales$_t$) / (Net Receivables$_{t-1}$ / Sales$_{t-1}$)
* Gross Margin Index (GMI)
GMI = [(Sales$_{t-1}$ - COGS$_{t-1}$) / Sales$_{t-1}$] / [(Sales$_t$ - COGS$_t$) / Sales$_t$]
* Asset Quality Index (AQI)
AQI = [1 - (Current Assets$_t$ + PP&E$_t$ + Securities$_t$) / Total Assets$_t$] / [1 - ((Current Assets$_{t-1}$ + PP&E$_{t-1}$ + Securities$_{t-1}$) / Total Assets$_{t-1}$)]
* Sales Growth Index (SGI)
SGI = Sales$_t$ / Sales$_{t-1}$
* Depreciation Index (DEPI)
DEPI = (Depreciation$_{t-1}$/ (PP&E$_{t-1}$ + Depreciation$_{t-1}$)) / (Depreciation$_t$ / (PP&E$_t$ + Depreciation$_t$))
* Sales General and Administrative Expenses Index (SGAI)
SGAI = (SG&A Expense$_t$ / Sales$_t$) / (SG&A Expense$_{t-1}$ / Sales$_{t-1}$)
* Leverage Index (LVGI)
LVGI = [(Current Liabilities$_t$ + Total Long Term Debt$_t$) / Total Assets$_t$] / [(Current Liabilities$_{t-1}$ + Total Long Term Debt$_{t-1}$) / Total Assets$_{t-1}$]
* Total Accruals to Total Assets (TATA)
TATA = (Income from Continuing Operations$_t$ - Cash Flows from Operations$_t$) / Total Assets$_t$
The formula to calculate the M-score is:
    M-score = −4.84 + 0.92 × DSRI + 0.528 × GMI + 0.404 × AQI + 0.892 × SGI + 0.115 × DEPI −0.172 × SGAI + 4.679 × TATA − 0.327 × LVGI

## How to interpret

The threshold value is -1.78 for the model whose coefficients are reported above. (see Beneish 1999, Beneish, Lee, and Nichols 2013, and Beneish and Vorst 2020).
* If M-score is less than -1.78, the company is unlikely to be a manipulator. For example, an M-score value of -2.50 suggests a low likelihood of manipulation.
* If M-score is greater than −1.780, the company is likely to be a manipulator. For example, an M-score value of -1.50 suggests a high likelihood of manipulation.

### Aggregate recession predictor

A 2023 research paper uses an aggregate score of many companies to predict recessions. It finds that the score in early 2023 is the highest in some 40 years.

## Important notices

* Beneish M-score is a probabilistic model, so it cannot detect companies that manipulate their earnings with 100% accuracy.
* Financial institutions were excluded from the sample in Beneish paper when calculating M-score since these institutions make money through different routes. Sales and receivables which are two main ingredients that go into the Beneish formula are not used when analyzing a financial institution.

## Example of successful application

Enron Corporation was correctly identified 1998 as an earnings manipulator by students from Cornell University using M-score Noticeably, Wall Street financial analysts were still recommending to buy Enron shares at that point in time..

## Further reading on financial statement manipulation

* A sequence of articles on Alpha Architect blog.
* An article on Investopedia about different types of financial statement manipulation ("smoke and mirrors", "elder abuse", "fleeing town", and others).