Beneish M-score

The idea. Messod Beneish ("The Detection of Earnings Manipulation," Financial Analysts Journal, 1999; free on SSRN, read it) asked a simple question. Compare companies later charged with earnings manipulation against clean peers: which statement signals separated them in the manipulation year? His answer became an eight-variable probit model. Five variables capture distortion, the residue you learned to spot with the earnings games: receivables outrunning sales, margins slipping, asset quality softening, depreciation slowing, accruals bulging. Three capture incentive and pressure: growth that must be fed, rising SG&A, rising leverage. The model was estimated on 74 identified manipulators against ~2,300 controls from 1982 to 1992 COMPUSTAT data. Remember that vintage when you interpret it.

What are the eight Beneish indices?

The eight indices. Subscript t = current year, t−1 = prior year. Unless stated, use year-end balance-sheet values and full-year flows. "Index" means this year's ratio divided by last year's, so the model reads change, the deterioration from one year to the next.

1. DSRI (Days Sales in Receivables Index) = (Receivables_t / Sales_t) / (Receivables_{t−1} / Sales_{t−1}). Receivables growing faster than sales (DSRI > 1) is the classic residue of premature or fictitious revenue.
2. GMI (Gross Margin Index) = GrossMargin_{t−1} / GrossMargin_t, where GrossMargin = (Sales − COGS)/Sales. Note the inversion: GMI > 1 means margin deteriorated. That's a pressure signal, since deteriorating firms are likelier to manipulate.
3. AQI (Asset Quality Index) = [1 − (CA_t + PPE_t)/TA_t] / [1 − (CA_{t−1} + PPE_{t−1})/TA_{t−1}], where CA = current assets, PPE = net property/plant/equipment, TA = total assets. The bracketed term is the share of "soft" assets: everything that's neither current nor hard PP&E (capitalized costs, intangibles, goodwill, "other assets"). AQI > 1 means the balance sheet is softening, and that's cost parked territory from the earnings games. (Beneish's later work also nets long-term securities out of soft assets. The original 1999 definition is as given. Say which you use.)
4. SGI (Sales Growth Index) = Sales_t / Sales_{t−1}. Growth isn't manipulation. But growth companies face the treadmill (see financial shenanigans) and dominate the manipulator sample. This variable is why the M-Score throws false positives on real compounders. More on that below.
5. DEPI (Depreciation Index) = DepRate_{t−1} / DepRate_t, where DepRate = Depreciation / (Depreciation + Net PPE) (depreciation excluding amortization, per the original). DEPI > 1 means depreciation slowed: lives lengthened or methods softened, the second lever of cost parked.
6. SGAI (SG&A Index) = (SGA_t / Sales_t) / (SGA_{t−1} / Sales_{t−1}). Rising SG&A intensity as a pressure proxy.
7. LVGI (Leverage Index) = [(LTD_t + CL_t)/TA_t] / [(LTD_{t−1} + CL_{t−1})/TA_{t−1}], LTD = long-term debt, CL = current liabilities. Rising leverage brings covenant pressure (see earnings management).
8. TATA (Total Accruals to Total Assets) = (Income from continuing operations − CFO) / TA_t. It's the one level variable in the set, the accrual wedge itself. (Beneish's original 1999 paper computed total accruals from balance-sheet changes, the Sloan-style working-capital construction you'll meet in the accruals ratio. His own later implementations and common practice use NI − CFO. State your method. The coefficient was estimated on the balance-sheet version, so tiny differences are inherent.)

Beneish M-score formula, and where it falls short

The model (published coefficients, memorize them):

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

Flag threshold: M > −1.78, meaning the company resembles the manipulator sample. M is a probit score, so the implied manipulation probability is the standard normal CDF at M. At −1.78 that's about 3.8%. Beneish recommended that cutoff once you weigh the cost of missing a manipulator against the cost of investigating an innocent (his cost-ratio analysis, and the paper reports the alternatives). Some practitioners screen wider at M > −2.22 (≈1.3% implied probability) to cast a bigger net for shorting or audit triage. Both cutoffs come from the same model. Pick per your error preference and say which you used.

Three footnotes before the worked example, because a world-class analyst knows where the model's seams are:

• The workhorses are DSRI, GMI, AQI, SGI and TATA, the last with its huge 4.679 weight. DEPI is marginal. SGAI and LVGI came out insignificant, with signs opposite the fraud intuition: their negative coefficients mean higher SGAI or LVGI lowers M slightly. Beneish kept them. A reduced five-variable version of the model exists. The paper covers it, as does the 2013 work by Beneish with Lee and Nichols. Both give variants and coefficients, and you shouldn't mix versions.
• Benchmarks from the paper are manipulator against non-manipulator sample means, as reported. Pull the paper to verify before you rely on them: DSRI 1.465 vs 1.031, GMI 1.193 vs 1.014, AQI 1.254 vs 1.039, SGI 1.607 vs 1.134, DEPI 1.077 vs 1.001, TATA 0.031 vs 0.018. Once you know the typical clean value is ≈1.0 for each index, you can read the eight numbers directly, before the weighted sum.
• False positives come with the design. A high-growth company shows SGI ≫ 1 by definition. It shows DSRI > 1 whenever new customers pay on normal terms from a standing start, AQI > 1 whenever it invests in intangibles or acquires, and high TATA whenever growth consumes working capital. So fast compounders and young companies live near the threshold. For firms like these, the M-Score is an earnings-quality triage and nothing more. Flag, then read. (A mature, slow-growth firm clearing −1.78 is a much louder alarm, because nothing mechanical explains it.)

Worked example: Kavery Precision Engineering (synthetic)

Complete worked computation: Kavery Precision Engineering Ltd (synthetic Indian mid-cap manufacturer; ₹ crore; two fiscal years). The same statement set comes back in the accruals ratio, Altman Z-score and Piotroski F-score pages, so you can watch all four screens interrogate one company.

Income statement:

Balance sheet:

Extras you'll need: CFO Year 2 = ₹25 crore (indirect: 130 NI + 44 dep − 25 gain − 121 ΔAR − 70 ΔInv − 34 ΔOCA + 55 ΔAP + 4 ΔTaxes + 42 ΔOCL = 25). Total assets at the start of Year 1 = ₹900 crore. No dividends. A ₹94 crore QIP was raised in Year 2, so a capital-raising window gave management an incentive. Market cap ≈ ₹2,100 crore. Retained earnings Y2 = ₹470 crore. All figures synthetic.

The eight indices, every number shown:

The score:

M = −4.84 + 0.920(1.333) + 0.528(1.053) + 0.404(1.238) + 0.892(1.300)
        + 0.115(1.083) − 0.172(0.950) + 4.679(0.075) − 0.327(1.029)
  = −4.84 + 1.227 + 0.556 + 0.500 + 1.160 + 0.125 − 0.163 + 0.351 − 0.336
  = −1.42

M = −1.42 > −1.78, so flagged. Read the indices as well as the score. Receivables far outran a 30% sales surge (DSRI 1.33). Soft assets swelled (AQI 1.24), and that ₹110 crore jump in "other non-current assets" wants a footnote. Margins slipped while depreciation slowed, and the accrual wedge is enormous (TATA 0.075: NI of 130 against CFO of 25). That's the profile of the channel-stuffer from the earnings games. Or of a clean company having a growth year hungry for working capital, one that also capitalized a product-development program and banked a land-sale gain. The screen has done its job. You now know which five notes to read.