In this article, I will demonstrate how to use the Beneish M-Score, a mathematical model developed by Professor Messod Beneish to detect potential earnings manipulation and fraud in financial statements. The M-Score employs a set of financial variables to identify red flags and inconsistencies that may suggest a company is manipulating its reported earnings. By learning how to calculate and interpret the M-Score, investors can better assess the reliability of a company's financial reporting and make more informed investment decisions.

This article will explore both the original 5-variable model, introduced in 1997, and the more comprehensive 8-variable model, presented in 1999. It will detail how these versions work, how to calculate them, and how to interpret the results. We'll also provide a real-world example, a free Excel template, and discuss the research behind the model's effectiveness in identifying earnings manipulation. Lastly, we'll discuss the model's limitations and practical considerations for its application.

## Beneish M-Score Explained

The **Beneish M-Score** is a mathematical model that uses a set of financial variables to identify whether a company has manipulated its earnings. Developed by Messod Beneish, an accounting professor at Indiana University Kelley School of Business, the model was first presented in his 1997 paper "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," and later expanded in his 1999 paper "The Detection of Earnings Manipulation."

The model is well-known partially because a group of Cornell University business students used it in 1998 to predict that Enron Corporation (which concealed debts and inflated profits through accounting loopholes) was manipulating its earnings while the stock was trading at about half its eventual peak price. Despite their warning, Wall Street did not heed their advice, and Enron's stock continued to climb before its dramatic fall into bankruptcy a few years later in 2001.

Today, many investors use the Beneish M-Score to identify companies that may be manipulating their earnings, which helps them decide which firms to further scrutinize or avoid investing in altogether.

### Beneish M-Score Evolution

Beneish's research focused on identifying the characteristics of firms that engage in earnings manipulation and developing models to detect such behavior. He argued that by using financial statement data, one could construct variables that capture the effects of manipulation or preconditions that may prompt companies to engage in such activity.

In his two seminal papers, Beneish developed and refined the following models:

**1997 Paper**: Beneish developed the original M-Score model using a sample of**64 companies**that violated Generally Accepted Accounting Principles (GAAP) and a control sample of firms with "extreme" financial performance**between 1982 and 1992**. This initial model included**five variables**and was designed to evaluate the probability of earnings manipulation among companies with large discretionary accruals (accruals that are subject to management's discretion).**1999 Paper**: Building upon his previous work, Beneish expanded the model to include**eight variables**, creating a more comprehensive approach to detecting earnings manipulation. This updated model was based on a sample of**74 companies**that manipulated their earnings and were subject to enforcement actions by the Securities and Exchange Commission (SEC)**between 1982 and 1992**. Beneish used this sample to identify the unique characteristics of manipulators and refine the model.

Key differences between the 1997 and 1999 models include the number of variables (5 vs. 8), the samples used (64 GAAP violators vs. 74 earnings manipulators), and the control samples (firms with extreme financial performance vs. industry-matched firms). The 1999 model is generally considered the standard version of the M-Score and is more widely used in practice due to its comprehensive approach and refined methodology. Therefore, we'll primarily focus on the 8-variable Beneish M-Score model in this article.

### Beneish M-Score Effectiveness

Regarding the M-Score's effectiveness, out-of-sample tests (evaluations using data not involved in model creation) conducted by Beneish revealed that the M-Score correctly identified **~76%** of the manipulators in the holdout sample, but it also incorrectly identified non-manipulators **17.5%** of the time.

Furthermore, Beneish's method has stood the test of time and remains one of the most reliable. In his 2020 paper "The Cost of Fraud Prediction Errors," Beneish showed that his approach had a better balance between correctly identifying manipulators and avoiding false accusations compared to other techniques, except for a newly developed machine learning model.

Thus, although the M-Score is not a perfect model and has its limitations (as discussed towards the end of this article), its persistence and accuracy make it a useful tool for investors seeking to detect earnings manipulation.

## 5-Variable Beneish M-Score

The **5-variable Beneish M-Score**, introduced in the 1997 paper "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," is a model designed to assess the likelihood of earnings manipulation among firms with large discretionary accruals. The model was developed using a sample of **64 firms that violated GAAP** and a control sample of firms with extreme financial performance **between 1982 and 1992**.

### 5 Variables Explained

The 5 variables in the original Beneish M-Score are described below:

**Days Sales in Receivables Index (DSRI)**: Measures the ratio of days sales in receivables in the current year compared to the previous year.**Gross Margin Index (GMI)**: Measures the deterioration of the gross margin compared to the previous year.**Asset Quality Index (AQI)**: Measures the proportion of total assets for which future benefits are potentially less certain.**Sales Growth Index (SGI)**: Measures the growth in sales compared to the previous year.**Total Accruals to Total Assets (TATA)**: Measures the extent to which cash underlies reported earnings.

These five variables, their formulas, and interpretations are further described in the discussion of the 8-variable Beneish M-Score.

### 5-Variable Beneish M-Score Formula

After defining the five variables included in the model, Beneish used a weighted combination of these variables to arrive at an overall score (known as the M-Score), which indicates the likelihood of earnings manipulation.

The weights for each variable were determined through a "probit regression analysis," which is a statistical technique used to estimate the probability of a binary outcome (in this case, whether a company is a manipulator or not) based on a set of predictor variables.

The resulting 5-variable Beneish M-Score formula is as follows:

5-Variable Beneish M-Score = -6.065 + (0.823 Ã— DSRI) + (0.906 Ã— GMI) + (0.593 Ã— AQI) + (0.717 Ã— SGI) + (0.107 Ã— TATA)

These variables were selected to capture the effects of manipulation or preconditions that may prompt firms to engage in such activity. The model also includes variables that have implications for the specification of accrual models, such as lagged total accruals and a measure of past price performance, as detailed in the following section.

In the original 5-variable model, Beneish suggested an M-Score **greater than -2.22** as a cutoff for classifying a company as a potential manipulator. This means that companies with an M-Score above -2.22 are considered more likely to be engaging in earnings manipulation, while those with scores below this threshold are less likely to be manipulating their earnings.

### 5-Variable Beneish M-Score Findings

In his 1997 paper, Beneish emphasizes the significance of the 5-variable M-Score model in identifying potential earnings manipulators among firms with large discretionary accruals.

"**Discretionary accruals**" are the portion of accruals that are subject to managerial discretion and are often used as a proxy for earnings management. However, large discretionary accruals can also result from factors unrelated to earnings manipulation, such as a company's business strategy or external influences on its performance. The M-Score model helps distinguish between these possibilities:

"First, the model presented in this paper provides a means of assessing the likelihood of opportunistic reporting among firms with large discretionary accruals. This is of interest because large discretionary accruals could result not only from earnings management but also from exogenous influences on firms' performance or from the effects of strategic operating decisions that are not motivated by a desire to artificially increase reported earnings."

- Messod D. Beneish in "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," pg. 273

To evaluate the model's effectiveness, Beneish tested it on two samples: (1) an estimation sample used to develop the model and (2) a holdout sample to validate its performance. In the estimation sample, the model accurately identified **56.8% of the GAAP violators** (companies that manipulated their earnings) when assuming a 20:1 ratio of Type I to Type II error costs:

**Type I Errors**: Occur when the model incorrectly identifies a non-manipulator as a manipulator.**Type II Errors**: Occur when the model fails to identify a manipulator.

Notably, the model outperformed the "modified Jones accrual model," a commonly used method for detecting earnings management, by consistently showing lower expected misclassification costs.

Moreover, Beneish's research suggests that the accuracy of discretionary accrual models, like the modified Jones model, could be improved by including two additional factors: (1) lagged total accruals (accruals from the previous year) and (2) a measure of the company's past stock price performance:

"Second, the findings have implications for the specification of accrual models. The evidence indicates that researchers seeking a residual metric to study firms with extreme performance, should consider augmenting the modified Jones model with lagged total accruals and a measure of past price performance."

- Messod D. Beneish in "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," pg. 299

The decision to include these variables in the M-Score model is supported by Beneish's analysis of real-world cases of earnings manipulation. This analysis suggests that accrual models that take into account managers' incentives to manipulate earnings and the tendency for discretionary accruals to reverse over time are more likely to detect earnings manipulation successfully.

Thus, the 5-variable Beneish M-Score is purported to be useful for assessing the probability of earnings manipulation among companies with large discretionary accruals, especially in situations where a company's extreme financial performance makes traditional accrual models less reliable.

## 8-Variable Beneish M-Score

Building upon the foundation of the 5-variable model, Beneish introduced the 8-variable Beneish M-Score in his 1999 paper "The Detection of Earnings Manipulation." This expanded model incorporates additional financial ratios and variables to provide a more comprehensive approach to detecting earnings manipulation. The 8-variable model was developed using a sample of **74 firms that manipulated their earnings **and were subject to SEC enforcement actions **between 1982 and 1992**.

### 8 Variables Explained

The 8 variables, along with their academic formulas, interpretations, and nuances, are discussed in the sections below. It's important to note that for the formulas, the year "t" refers to the first year in which earnings manipulation occurs.

#### Variable #1: Days Sales in Receivables Index (DSRI)

The **Days Sales in Receivables Index (DSRI)** is a financial ratio that compares the proportion of receivables to sales in the current year to the same proportion in the previous year.

The formula for calculating DSRI is shown below:

Days Sales in Receivables Index (DSRI) = (Net Receivables_{t} / Sales_{t}) / Net Receivables_{t-1} / Sales_{t-1})

A DSRI greater than 1 suggests that the company's receivables are growing faster than its sales, which could indicate aggressive accounting tactics, such as recognizing revenue prematurely, or a deterioration in the company's economic conditions. It may also be a sign that the company is offering more generous credit terms to customers to boost sales.

On the other hand, a DSRI below 1 implies that the company's receivables are decreasing relative to its sales. While this may seem positive, it could also be a warning sign, indicating that the company is resorting to desperate measures to increase sales, such as extending credit to customers with poor credit histories or engaging in "channel stuffing."

When evaluating a company's DSRI, it's also important to be aware that certain practices, such as factoring or securitizing receivables, can distort the ratio's usefulness. In these cases, it may be necessary to adjust the data to account for these practices and gain a more accurate understanding of the company's financial situation.

#### Variable #2: Gross Margin Index (GMI)

The **Gross Margin Index (GMI)** is a financial ratio that compares a company's gross margin in the current year to the gross margin in the previous year.

The formula for calculating GMI is shown below:

Gross Margin Index (GMI) = ((Sales_{t-1} - COGS_{t-1}) / Sales_{t-1}) / ((Sales_{t} - COGS_{t}) / Sales_{t})

A GMI greater than 1 indicates that the company's gross margins have decreased compared to the previous year, which could be a warning sign, suggesting that the company is facing challenges in maintaining its profitability. This deterioration in gross margin may be due to the company struggling to control its costs or maintain its pricing power in the market.

On the other hand, a GMI significantly lower than 1 implies that the company's gross margins are increasing dramatically. While this may seem positive at first glance, it can also be a cause for concern, as it may indicate that the company is engaging in manipulative practices to inflate its financial performance.

Companies with declining or rapidly increasing gross margins may be more likely to engage in earnings manipulation to make their financial performance appear better than it actually is. Therefore, the GMI is included in the Beneish model to help identify potential red flags in a company's financial statements.

#### Variable #3: Asset Quality Index (AQI)

The **Asset Quality Index (AQI)** is a financial ratio that measures the proportion of a company's total assets composed of assets with potentially uncertain future benefits.

The formula for calculating AQI is shown below:

Asset Quality Index (AQI) = (1 - ((Current Assets_{t} + PP&E_{t}) / Total Assets_{t})) / (1 - ((Current Assets_{t-1} + PP&E_{t-1}) / Total Assets_{t-1}))

An AQI greater than 1 indicates that the company's noncurrent assets, such as goodwill, intangibles, and other items with uncertain long-term value, are growing as a percentage of total assets compared to the previous year. This increase in the proportion of assets with uncertain future benefits may indicate a higher risk of earnings manipulation.

A higher AQI could be the result of excessive capitalization of expenses (meaning the recording of costs as assets on the balance sheet, delaying their impact on the income statement) or a sign of deteriorating fundamentals at the company. The further AQI is above 1, the more these intangible assets have grown compared to the more tangible current assets.

However, it's important to note that a high AQI could also be the result of substantial acquisitions (since acquisitions can increase non-current assets relative to total assets, raising the AQI), although Beneish points out that firms prone to manipulation usually engage in minimal acquisition activities:

"However, sample manipulators undertake few acquisitions and those are primarily stock-for-stock exchanges accounted for using

pooling of interests."- Messod D. Beneish in "The Detection of Earnings Manipulation," pg. 10

This means that firms known for financial manipulation rarely engage in acquisitions. When they do, they typically use their stock for transactions and adopt a "pooling of interests" method. This avoids revaluing assets and liabilities, helping to conceal financial weaknesses and reduce impacts on reported profits.

In essence, the AQI depends on the balance between current assets, net plant, and total assets. If one or two of these components change radically from one year to the next, it can be a significant warning sign that merits close consideration, even in the absence of reverse mergers and acquisitions.

#### Variable #4: Sales Growth Index (SGI)

The **Sales Growth Index (SGI)** is a financial ratio that measures the growth in a company's sales (or revenues) compared to the previous year.

The formula for calculating SGI is shown below:

Sales Growth Index (SGI) = Sales_{t} / Sales_{t-1}

An SGI greater than 1 indicates that the company's sales have increased compared to the previous year. The higher the SGI is above 1, the greater the growth in sales.

While sales growth is generally viewed as a positive by investors, high growth companies may be more likely to manipulate their earnings, especially if they're facing a potential slowdown. This is because their financial position and capital needs put pressure on managers to achieve earnings targets, and they may face large stock price losses at the first indication of a slowdown, creating greater incentives to manipulate earnings.

Therefore, when a company with high sales growth also scores poorly on other variables in the Beneish model, it could be a significant red flag for potential financial statement fraud. However, it's important to note that high sales growth alone does not necessarily imply manipulation; it's the combination of high growth and other warning signs that should raise concerns.

#### Variable #5: Depreciation Index (DEPI)

The **Depreciation Index (DEPI)** is a financial ratio that compares a company's depreciation rate in the current year to the rate in the previous year.

The formula for calculating DEPI is shown below:

Depreciation Index (DEPI) = (Depreciation_{t-1} / (Depreciation_{t-1} + PP&E_{t-1})) / (Depreciation_{t} / (Depreciation_{t} + PP&E_{t}))

A DEPI greater than 1 indicates that the company's depreciation rate has decreased compared to the previous year. The higher the DEPI is above 1, the more the depreciation rate has slowed down. This suggests that the company may have revised its estimates of assets' useful lives upwards or adopted a new depreciation method that results in higher reported income.

The DEPI is included in the Beneish model to capture potential manipulation of depreciation to inflate earnings. By increasing its estimates of asset useful lives or adopting a new income-increasing method, a company can slow down the recognition of expenses, potentially artificially boosting its reported income.

#### Variable #6: Sales, General, and Administrative Expenses Index (SGAI)

The **Sales, General, and Administrative Expenses Index (SGAI)** is a financial ratio that measures the change in a company's SG&A expenses as a percentage of sales compared to the previous year.

The formula for calculating SGAI is shown below:

Sales, General and Administrative Index (SGAI) = (SG&A Expense_{t} / Sales_{t}) / (SG&A Expense_{t-1} / Sales_{t-1})

An SGAI greater than 1 indicates that the company's SG&A expenses have increased as a percentage of sales compared to the previous year, which could be a sign of declining administrative and marketing efficiency. The higher the SGAI is above 1, the more SG&A expenses have grown relative to sales.

The SGAI is included in the Beneish model to capture potential manipulation of SG&A expenses to boost earnings. A disproportionate increase in sales compared to SG&A expenses (i.e., SGAI < 1) could be interpreted as a negative signal about a company's future prospects, as it may indicate that sales are overstated. Public companies facing deteriorating operational performance may be more likely to engage in earnings manipulation to mask their challenges.

On the other hand, a substantial increase in SG&A expenses without a corresponding increase in sales (i.e., SGAI > 1) could also be a warning sign, as it may suggest that managers are being paid excessively or that the company is experiencing declining administrative and marketing efficiency, which could motivate managers to manipulate earnings.

#### Variable #7: Leverage Index (LVGI)

The **Leverage Index (LVGI)** is a financial ratio that compares a company's total debt to total assets in the current year to the previous year.

The formula for calculating LVGI is shown below:

Leverage Index (LVGI) = ((Long-Term Debt_{t} + Current Liabilities_{t}) / Total Assets_{t}) / ((Long-Term Debt_{t-1} + Current Liabilities_{t-1}) / Total Assets_{t-1})

An LVGI greater than 1 indicates that the company has become more leveraged compared to the previous year. The higher the LVGI is above 1, the more the company's leverage has increased, suggesting that the company may be under pressure to meet debt covenants or raise additional capital.

The LVGI is included in the Beneish model because companies facing financial pressure may be more likely to manipulate their earnings. As a company becomes increasingly leveraged, it tightens its debt constraints and may be more predisposed to manipulate its earnings to meet obligations or maintain access to capital.

However, it's important to note that a decrease in the LVGI (i.e., LVGI < 1) could also be a warning sign. While a company with a declining LVGI might be paying off its debts, it could also be increasing its equity by selling a large number of shares. One of the most prevalent signs of a company engaging in fraudulent activities is the excessive sale of shares, which quality scores like the Piotroski F-Score capture.

#### Variable #8: Total Accruals to Total Assets (TATA)

The **Total Accruals to Total Assets (TATA)** ratio measures the extent to which a company's reported earnings are backed by cash.

"**Accruals**" represent the difference between a company's accounting profit (or loss) and its cash profit (or loss), which is then divided by total assets to make the variable comparable across companies of different sizes.

The TATA is included in the Beneish model because accruals are often used to manipulate earnings, and a higher level of accruals relative to assets could signal potential manipulation. Companies that generate large accruals (accounting profits without corresponding cash profits) are more likely to be engaging in earnings manipulation. Higher positive accruals (meaning less cash) indicate a greater likelihood of earnings manipulation.

In Beneish's 1997 paper, "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," the calculation of TATA was based on the balance sheet approach:

"Total accruals were calculated as the

change in current assets(COMPUSTAT item #4),minus the change in(#1),

cashminus changes in current liabilities(#5),plus the change in short-term debt(#34)- depreciation and(#14)

amortization expense- deferred tax on earnings(#50)+ equity in earnings(#55)."- Messod D. Beneish in "Detecting GAAP Violation: Implications for Assessing Earnings Management among Firms with Extreme Financial Performance," pg. 281

In Beneish's 1999 paper "The Detection of Earnings Manipulation," where he introduced three additional variables to the Beneish M-Score (DEPI, SGAI, and LVGI), Beneish also maintained a similar approach, and discussed calculating total accruals as follows:

"Total accruals are calculated as the

change in working capital accounts other than cash less depreciation."- Messod D. Beneish in "The Detection of Earnings Manipulation," pg. 12

For reference, here's how Beneish defined the TATA formula in his 1999 paper:

Total Accruals to Total Assets (TATA) [1999 Version] = ((Î”Current Assets_{t} - Î”Cash_{t}) - (Î”Current Liabilities_{t} - Î”Current Maturities of LTD_{t} - Î”Income Tax Payable_{t}) - Depreciation and Amortization_{t}) / Total Assets_{t}

However, in the 2013 paper "Earnings Manipulation and Expected Returns," Beneish, Lee, and Nichols switched to the more widely accepted cash flow statement approach to calculate total accruals. The updated formula for TATA using the cash flow statement approach is shown below:

Total Accruals to Total Assets (TATA) [2013 Version] = (Income Before Extraordinary Items_{t} - Cash From Operations_{t}) / Total Assets_{t}

Beneish elaborates on this difference in the TATA calculation in the 2013 paper:

"Beneish (1999a) used a total accruals variable that is computed slightly differently but yields similar results; before the current presentation of the statement of cash flows became effective (in 1987), few companies reported cash flow from operations. Our current implementation follows the evolution of this variable in the accruals literature."

- Messod D. Beneish, Charles M.C. Lee, and D. Craig Nichols in "Earnings Manipulation and Expected Returns," pg.76

Therefore, when applying the Beneish M-Score model, it's recommended to use the cash flow statement approach (2013 version) to calculate total accruals, as it has become the standard in the accruals literature and is widely accepted by researchers and practitioners. Additionally, this method provides a more direct and reliable measure of accruals by capturing the difference between a company's reported income and its actual cash flows from operations.

### 8-Variable Beneish M-Score Formula

The 8-variable Beneish M-Score formula, derived using a weighted probit regression analysis (like the 5-variable model), was developed using a sample of **74 companies** identified as earnings manipulators by the SEC and a control sample of **2,332 non-manipulators**.

The 8-variable Beneish M-Score is calculated using the following formula:

8-Variable Beneish M-Score = -4.84 + (0.92 Ã— DSRI) + (0.528 Ã— GMI) + (0.404 Ã— AQI) + (0.892 Ã— SGI) + (0.115 Ã— DEPI) - (0.172 Ã— SGAI) + (4.679 Ã— TATA) - (0.327 Ã— LVGI)

Here, the constant term (-4.84) and the coefficients for each variable were determined by the probit regression analysis to maximize the model's ability to distinguish between manipulators and non-manipulators in the sample.

Positive coefficients (DSRI, GMI, AQI, SGI, DEPI, TATA) indicate that an increase in the corresponding variable leads to a higher probability of earnings manipulation, while negative coefficients (SGAI, LVGI) suggest that an increase in the corresponding variable decreases the probability of earnings manipulation. The magnitude of each coefficient represents the relative importance of the corresponding variable in predicting earnings manipulation.

For example, the coefficient for TATA (4.679) is the largest in absolute value, indicating that total accruals to total assets is the most influential variable in the model. In contrast, the coefficient for DEPI (0.115) is relatively small, suggesting that the depreciation index has a lesser impact on the M-Score compared to other variables.

Lastly, it's important to note that while the 5-variable model uses a different set of coefficients and a different constant term, the interpretation of the coefficients and the overall approach to calculating the M-Score are similar to the 8-variable model.

## How to Interpret the Beneish M-Score

The Beneish M-Score is a relatively useful tool for detecting potential earnings manipulation. By calculating the M-Score using the 8-variable model, investors can assess the likelihood that a company has manipulated its financial statements.

The 8-variable Beneish M-Score model demonstrated improved performance in detecting earnings manipulators compared to the 5-variable model. As previously mentioned, in out-of-sample tests, the model correctly identified **~76% of the manipulators** in the holdout sample (vs. 56.8% with the 5-variable model, albeit under different control samples) when using a cut-off score of **-1.78**. However, it's important to note that the model inaccurately identifies a non-manipulator as a manipulator **17.5%** of the time.

### Individual Variable Interpretations

The interpretations of individual variables were explained prior, but you can also refer to the table below to examine whether each variable suggests that a company is a potential manipulator or not:

These values are based on the mean values reported in Table 2 of the 1999 paper for the estimation sample, which consists of **50 manipulators** and **1,708 non-manipulators**:

The table shows that, on average, manipulators have higher values for each of the eight indices compared to non-manipulators. Keep in mind that these are average values, and individual companies may have index values that deviate from these means.

### Beneish M-Score Interpretation

To interpret the final Beneish M-Score, the illustration below can be referenced:

In essence, when interpreting the M-Score, follow these guidelines:

**Likely Manipulator**: An M-Score**greater than -1.78**suggests that the company is likely engaging in earnings manipulation.**Possible Manipulator**: An M-Score**between -2.22 and -1.78**indicates a possible risk of manipulation, warranting further investigation.**Unlikely Manipulator**: An M-Score**less than -2.22**implies that the company is unlikely to be manipulating its earnings.

Note that the Beneish's calculator on the Indiana University Kelley School of Business (where the Beneish M-Score originated) uses -2.0 as the threshold, not -2.22. However, -2.22 is more conservative and reduces the likelihood of false positives, so it's applied in this context.

In closing, the 8-variable Beneish M-Score expands upon the 5-variable model by incorporating additional financial variables (DEPI, SGAI, and LVGI), resulting in improved performance in detecting earnings manipulation. By considering both the -2.22 and -1.78 thresholds, the model provides a more nuanced approach to assessing the likelihood of earnings manipulation, making it an even more valuable tool for investors to identify potential red flags and assess the reliability of a company's financial reporting.

## Beneish M-Score Calculation Example

To demonstrate the calculation of the Beneish M-Score, we'll use Boeing (BA), as our example, an American multinational corporation that designs, manufactures, and sells airplanes, rotorcraft, rockets, satellites, telecommunications equipment, and missiles worldwide, and also provides leasing and product support services.

We'll use the company's financial data from their 2022 and 2023 fiscal years to calculate the 5-variable and 8-variable Beneish M-Scores and assess the likelihood of earnings manipulation.

To apply the Beneish M-Score (both the 5-variable and 8-variable versions), investors can follow these steps:

- Gather the necessary financial data for the company, including the current and prior year's income statements, balance sheets, and cash flow statements.
- Calculate the relevant ratios/variables.
- Calculate the 5-variable and 8-variable Beneish M-Score formulas and interpret the results.

Investors can use the spreadsheet linked below and/or the web calculator on Beneish's webpage at the Indiana University Kelley School of Business to calculate the Beneish M-Score:

### Step #1: Gather Necessary Financial Data

To calculate the Beneish M-Score for any company, you'll need to gather relevant financial data from the income statement, balance sheet, and cash flow statement. Financial statements can be sourced from the company's 10-K annual report, which can be found via the SEC or the company's investor relations pages.

###### Income Statement

The income statement is a financial statement that summarizes a company's revenues, expenses, and profits (or losses) over a specific period.

From the income statement, you'll need to locate these four financials:

Here's Boeing's income statement with these four financials outlined:

Thus, in FY 2022, Boeing reported total revenues of $66,608M, COGS of $63,078M, and SG&A expenses of $4,187M.

In FY 2023, Boeing reported total revenues of $77,794M, COGS of $70,070M, SG&A expenses of $5,168M, and income before extraordinary items of -$2,242M.

Note that for the Beneish M-Score, "net loss" is used instead of "net loss attributable to Boeing shareholders" because it includes the entire company's losses, without excluding losses attributable to noncontrolling interests. This provides a complete view of financial performance for more accurate earnings manipulation analysis.

###### Balance Sheet

The balance sheet is a financial statement that provides a snapshot of a company's assets, liabilities, and shareholders' equity at a specific point in time.

From the balance sheet, you'll need to locate these six financials:

Here's Boeing's balance sheet with these six financials outlined:

Thus, in FY 2022, Boeing reported accounts receivable of $2,517M, total current assets of $109,523M, PP&E of $10,550M, total assets of $137,100M, total current liabilities of $90,052M, and long-term debt of $51,811M.

In FY 2023, Boeing reported accounts receivable of $2,649M, total current assets of $109,275M, PP&E of $10,661M, total assets of $137,012M, total current liabilities of $95,827M, and long-term debt of $47,103M.

###### Cash Flow Statement

The cash flow statement is a financial statement that shows the inflows and outflows of cash and cash equivalents during a specific period, categorized into operating, investing, and financing activities.

From the cash flow statement, you'll need to locate these two financials:

Here's Boeing's cash flow statement with these two financials outlined:

Thus, in FY 2022, Boeing reported D&A of $1,979M. In FY 2023, Boeing reported D&A of $1,861M and CFO of $5,960M.

Note that depreciation and amortization (D&A) from the cash flow statement can be used in the Beneish model because they represent the total non-cash charges from operating activities, clearly indicating the depreciation expense needed for detecting potential earnings manipulation.

However, for companies with large amortization costs, it's more accurate for the M-Score to use the actual depreciation expense, typically found in the "Notes to the Financial Statements" section of a 10-K annual report.

### Step #2: Calculate and Interpret the 8 Variables for the Beneish M-Score

Now that we've gathered the relevant financials for the 8-variable Beneish M-Score for FY 2022 and FY 2023, the next step is to calculate the ratios/variables necessary for completing the FY 2023 Beneish M-Score calculation.

###### Variable #1: Days Sales in Receivables Index (DSRI)

DSRI compares the ratio of accounts receivable to sales in the current year to the same ratio in the previous year. Here's Boeing's DSRI calculation for FY 2023:

DSRI [BA; FY 2023] = ($2,649M / $77,794M) / ($2,517M / $66,608M) --> **0.901**

A DSRI of **0.901** indicates that Boeing's receivables are growing slower than its sales compared to the previous year, which is generally a positive sign and suggests a lower likelihood of revenue manipulation.

###### Variable #2: Gross Margin Index (GMI)

GMI compares the gross margin (sales minus cost of goods sold) in the previous year to the gross margin in the current year. Here's Boeing's GMI calculation for FY 2023:

GMI [BA; FY 2023] = (($66,608M - $63,078M) / $66,608M) / (($77,794M - $70,070M) / $77,794M) --> **0.534**

A GMI of **0.534** suggests that Boeing's gross margin has improved compared to the previous year, which is a positive indicator and reduces the likelihood of earnings manipulation.

###### Variable #3: Asset Quality Index (AQI)

AQI compares the ratio of non-current assets (excluding property, plant, and equipment (PP&E)) to total assets in the current year to the same ratio in the previous year. Here's Boeing's AQI calculation for FY 2023:

AQI [BA; FY 2023] = (($137,012M - $109,275M - $10,661M) / $137,012M) / (($137,100M - $109,523M - $10,550M) / $137,100M) --> **1.004**

An AQI of **1.004** indicates a slight increase in the proportion of Boeing's assets with uncertain future benefits, which may suggest a marginally higher risk of asset realization and potential earnings manipulation.

###### Variable #4: Sales Growth Index (SGI)

SGI compares the sales in the current year to the sales in the previous year. Here's Boeing's SGI calculation for FY 2023:

SGI [BA; FY 2023] = $77,794M / $66,608M --> **1.168**

An SGI of **1.168** indicates that Boeing's sales have grown by 16.8% compared to the previous year, which is a positive sign but may also increase the pressure to maintain growth and potentially manipulate earnings.

###### Variable #5: Depreciation Index (DEPI)

DEPI compares the ratio of the depreciation rate (depreciation divided by depreciation plus property, plant, and equipment (PP&E)) in the previous year to the same ratio in the current year. Here's Boeing's DEPI calculation for FY 2023:

DEPI [BA; FY 2023] = ($1,979M / ($1,979M + $10,550M)) / ($1,861M / ($1,861M + $10,661M)) --> **1.063**

A DEPI of **1.063** suggests that Boeing's depreciation rate has slightly decreased compared to the previous year, which could indicate a minor risk of earnings manipulation through changes in depreciation policies.

###### Variable #6: Sales, General, and Administrative Expenses Index (SGAI)

SGAI compares the ratio of sales, general, and administrative (SG&A) expenses to sales in the current year to the same ratio in the previous year. Here's Boeing's SGAI calculation for FY 2023:

SGAI [BA; FY 2023] = ($5,168M / $77,794M) / ($4,187M / $66,608M) --> **1.057**

An SGAI of **1.057** indicates that Boeing's SG&A expenses have grown slightly faster than sales compared to the previous year, which may be a minor red flag for potential earnings manipulation.

###### Variable #7: Leverage Index (LVGI)

LVGI compares the ratio of total debt (current liabilities plus long-term debt) to total assets in the current year to the same ratio in the previous year. Here's Boeing's LVGI calculation for FY 2023:

LVGI [BA; FY 2023] = (($47,103M + $95,827M) / $137,012M) / (($51,811M + $90,052M) / $137,100M) --> **1.008**

An LVGI of **1.008** indicates a slight increase in Boeing's leverage compared to the previous year, which may suggest a marginally higher risk of financial pressure and potential earnings manipulation.

###### Variable #8: Total Accruals to Total Assets (TATA)

TATA calculates the difference between income before extraordinary items and cash flow from operations (CFO), then divides the result by total assets. Here's Boeing's TATA calculation for FY 2023:

TATA [BA; FY 2023] = (-$2,242M - $5,960M) / $137,012M --> **-0.060**

A TATA of **-0.060** suggests that Boeing's total accruals are negative, meaning that cash flows from operations exceed net income, which is generally a positive sign and reduces the likelihood of earnings manipulation.

###### Beneish M-Score Calculator Interpretation

Investors may find the analysis and assessment from the Beneish M-Score Calculator (on Beneish's Kelley School of Business website) useful for these variable-specific interpretations.

Here's the completed version for our Boeing FY 2023 example:

Based on these individual variable interpretations alone, according to the Beneish M-Score, Boeing's FY 2022 and FY 2023 financials do not suggest that it's an earnings manipulator.

### Step #3: Calculate and Interpret the Beneish M-Score

Now that we've gathered the relevant financials and calculated the ratios/variables needed for the Beneish M-Score, the final step is to calculate and interpret the 8-variable Beneish M-Score using the formula provided in his 1999 paper. For demonstration purposes, we'll also calculate the older 5-variable version as well (found in his 1997 paper).

First, here's the completed calculation for the 5-variable Beneish M-Score for Boeing in FY 2023

Beneish M-Score (5-Variable) [BA; FY 2023] = -6.025 + (0.823 Ã— 0.901) + (0.906 Ã— 0.534) + (0.593 Ã— 1.004) + (0.717 Ã— 1.168) + (0.107 Ã— -0.060) --> **-3.374**

A 5-variable Beneish M-Score of **-3.374** for Boeing's FY 2023, based on Beneish's 1997 paper, suggests that Boeing is unlikely to be manipulating its earnings. The 1997 paper considered an M-Score **greater than -2.22** as an indication of potential earnings manipulation. Boeing's score of -3.374 is well below this threshold, indicating a low likelihood of earnings manipulation.

Now, here's the completed calculation for the 8-variable Beneish M-Score for Boeing in FY 2023:

Beneish M-Score (8-Variable) [BA; FY 2023] = -4.84 + (0.92 Ã— 0.901) + (0.528 Ã— 0.534) + (0.404 Ã— 1.004) + (0.892 Ã— 1.168) + (0.115 Ã— 1.063) - (0.172 Ã— 1.057) + (4.679 Ã— -0.060) - (0.327 Ã— 1.008) --> **-2.951**

An 8-variable Beneish M-Score of **-2.951** for Boeing's FY 2023, based on Beneish's 1999 paper, also suggests that Boeing is unlikely to be manipulating its earnings. The 1999 paper considered an M-Score **greater than -1.78** as an indication of potential earnings manipulation and an M-Score **greater than -2.22** as a more conservative threshold for potential manipulation. Boeing's score of -2.951 is well below both thresholds, indicating a low likelihood of earnings manipulation.

For illustration purposes, the visual below displays Boeing's Beneish M-Scores from FY 2021 to FY 2023:

As you can see, Boeing has consistently been considered not an earnings manipulator based on the Beneish M-Score from FY 2021 to 2023.

## Limitations of the Beneish M-Score

The Beneish M-Score, particularly the 8-variable model, is a mathematical model that has proven valuable in detecting earnings manipulation. However, as with any mathematical model, its key limitations are centered around its inherent design and methodological constraints.

Here are the key limitations to consider when applying the model and interpreting its results:

**False Positives and False Negatives**: The model can generate false positives, identifying non-manipulative companies as potential manipulators, and false negatives, missing actual manipulators. Beneish reported that the model correctly identified approximately 76% of manipulators in his 1999 study, which implies that 24% were not detected. Furthermore, the model inaccurately identified non-manipulators as manipulators 17.5% of the time, as previously discussed.**Limited Scope**: Developed using a sample from U.S. public companies between 1982 and 1992, the model's applicability may be limited to similar contexts. It may not perform as well with companies outside the U.S., in different industries, or in varying economic conditions.**Reliance on Historical Data**: Since the model relies on historical financial data, it can only identify manipulation*after*it has occurred and is influenced by changes in accounting standards or business practices since its development.**Exclusion of Financial Services**: The M-Score does not apply to financial firms such as banks and insurance companies, as these were not included in Beneish's analysis.**Focus on Earnings Overstatement**: Designed primarily to detect earnings overstatement, the model may not effectively identify other forms of manipulation like earnings understatement or shifting income between periods.**Dependence on Accrual-Based Measures**: The M-Score heavily relies on accrual-based measures, which can be influenced by factors other than manipulation, such as changes in a company's business model or economic environment.**Potential for Gaming**: Companies that are aware of the Beneish M-Score might manipulate their ratios to meet the model's parameters, thus "gaming" the M-Score to avoid detection.**Lack of Contextual Information**: The model focuses solely on quantitative financial data and does not consider qualitative factors like management integrity or corporate governance, which can be necessary for a comprehensive evaluation.

Despite these limitations, the Beneish M-Score remains a relatively useful tool for investors when assessing the potential for earnings manipulation. However, it should be used as part of a detailed evaluation that includes both quantitative and qualitative factors, and its results should be interpreted with caution. Moreover, the M-Score should be viewed as a starting point for further investigation rather than a definitive indicator of earnings manipulation.

## The Bottom Line

The Beneish M-Score is a relatively useful tool investors can use to identify potential earnings manipulators. The model has two versions: a 5-variable model (1997) and an 8-variable model (1999), with the latter being more widely used. The M-Score uses a set of financial variables to assess the likelihood of earnings manipulation.

Beneish's research found that the 8-variable model correctly identified **76%** of manipulators in the holdout sample, while also inaccurately identifying non-manipulators as manipulators **17.5%** of the time. The model's variables capture both the effects of manipulation and the preconditions that may prompt companies to engage in such activities.

To calculate the M-Score, investors should gather data from financial statements, calculate the ratios and variables for each component, and input these values into the appropriate model formula. When interpreting the results, investors should consider three key ranges: (1) an M-Score **greater than -1.78** indicates a **likely manipulator**, (2) an M-Score **between -2.22 and -1.78** suggests a **possible manipulator**, and (3) an M-Score **less than -2.22** implies that the company is **unlikely to be a manipulator**.

However, the Beneish M-Score has limitations. As a probabilistic model, it may not capture all forms of earnings manipulation, and its accuracy may vary across different industries and time periods. Additionally, the model relies on historical data and cannot predict future manipulation. Moreover, as the model becomes more popular, its effectiveness may diminish if management becomes aware of the variables and takes steps to avoid detection.

In conclusion, investors can use the Beneish M-Score in two ways: (1) by subjecting companies with high M-Scores to further scrutiny or (2) by simply excluding them from their investment portfolio. The choice ultimately depends on the investor's risk tolerance and investment strategy.