Forensic scores you can calculate: Beneish M-score, Altman Z-score, Sloan accruals and Piotroski F-score

What you will learn

• The Beneish M-score formula, inputs and threshold.
• The Altman Z-score for financial distress and its zones.
• Sloan accruals and the nine Piotroski F-score signals.
• The limits of each score.

Explanation

Forensic scores compress several red flags from lessons 4 to 6 into one number. Built on historical US data, they are screening tools, not verdicts. All inputs come from two consecutive annual reports.

Beneish M-score

Messod Beneish's model (1999) estimates the probability of earnings manipulation from eight indices, each this year ÷ last year unless stated:

• DSRI – days sales in receivables index: (receivables ÷ sales) this year ÷ last year.
• GMI – gross margin index: last year's gross margin ÷ this year's (falling margins give values above 1).
• AQI – asset quality index: share of non-current assets other than property, plant and equipment.
• SGI – sales growth index: sales this year ÷ last year.
• DEPI – depreciation index: last year's depreciation rate ÷ this year's.
• SGAI – selling, general and administrative expenses ÷ sales index.
• TATA – total accruals to total assets: (net income − operating cash flow) ÷ total assets.
• LVGI – leverage index: total debt ÷ total assets.

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

Beneish's original cut-off is −1.78; many practitioners use the more cautious −2.22. Scores above the cut-off indicate a higher likelihood of manipulation. The model does not work for banks and insurers, and fast but honest growth can push SGI and DSRI up.

Altman Z-score

Edward Altman's 1968 model predicts distress for listed manufacturers:

Z = 1.2·X1 + 1.4·X2 + 3.3·X3 + 0.6·X4 + 1.0·X5

where X1 = working capital ÷ total assets, X2 = retained earnings ÷ total assets, X3 = EBIT ÷ total assets, X4 = market value of equity ÷ total liabilities, X5 = sales ÷ total assets. Zones: below 1.81 distress, 1.81 to 2.99 grey, above 2.99 safe. For non-manufacturers and private companies Altman published variants (Z' and Z'') with different weights and zones. Like Beneish, it is unsuitable for financial companies.

Sloan accruals

Richard Sloan (1996) showed that companies with high accruals relative to total assets tend to have lower subsequent returns, because investors treat accrual-based profit as cash. His measure is close to the accruals ratio from lesson 4 and to TATA: (net income − operating cash flow) ÷ average total assets. Use it to rank companies; the highest-accrual tenth is where earnings most often disappoint.

Piotroski F-score

Joseph Piotroski (2000) designed nine yes/no tests, one point each. Profitability: (1) return on assets positive, (2) operating cash flow positive, (3) return on assets up, (4) operating cash flow greater than net income. Leverage and liquidity: (5) long-term debt ÷ assets down, (6) current ratio up, (7) no new shares issued. Efficiency: (8) gross margin up, (9) asset turnover up. Scores of 8–9 are strong, 0–2 weak. The course Factor Investing uses related quality definitions; here the score is a checklist of year-over-year improvement.

Worked example

Hypothetical example: the machinery maker from lessons 5 and 6 (€ million). Sales 800 → 880; receivables 100 → 150; gross margin 40% → 36%; net income 120; operating cash flow 60; total assets 1,200; AQI = 1.05, DEPI = 1.00, SGAI = 1.00, LVGI = 1.02. For the Z-score, a different company: working capital 150, retained earnings 300, EBIT 120, market value of equity 900, total liabilities 700, sales 1,500, total assets 1,200.

1. DSRI = (150 ÷ 880) ÷ (100 ÷ 800) = 0.1705 ÷ 0.125 ≈ 1.364.
2. GMI = 0.40 ÷ 0.36 ≈ 1.111. SGI = 880 ÷ 800 = 1.100. TATA = (120 − 60) ÷ 1,200 = 0.050.
3. M = −4.84 + 0.920 × 1.364 + 0.528 × 1.111 + 0.404 × 1.05 + 0.892 × 1.10 + 0.115 × 1.00 − 0.172 × 1.00 + 4.679 × 0.050 − 0.327 × 1.02
   = −4.84 + 1.255 + 0.587 + 0.424 + 0.981 + 0.115 − 0.172 + 0.234 − 0.334 ≈ −1.75.
4. −1.75 is above both −1.78 and −2.22: the company screens as a possible manipulator, driven by DSRI (receivables) and TATA (accruals), the lesson 5 and lesson 4 signals.
5. Z-score: X1 = 150 ÷ 1,200 = 0.125; X2 = 300 ÷ 1,200 = 0.25; X3 = 120 ÷ 1,200 = 0.10; X4 = 900 ÷ 700 ≈ 1.286; X5 = 1,500 ÷ 1,200 = 1.25. Z = 1.2 × 0.125 + 1.4 × 0.25 + 3.3 × 0.10 + 0.6 × 1.286 + 1.0 × 1.25 = 0.15 + 0.35 + 0.33 + 0.771 + 1.25 ≈ 2.85, in the grey zone just below the safe threshold of 2.99.

Values are rounded to three decimals.

Common mistake

Practice activity

On paper: compute the Altman Z-score for a company with working capital €60 million, retained earnings €90 million, EBIT €50 million, market value of equity €300 million, total liabilities €450 million, sales €700 million and total assets €600 million, and state the zone. Then score the Piotroski F-score from these facts: ROA 4% (last year 3%); CFO €40 million, net income €30 million; long-term debt ÷ assets 0.30 (last year 0.25); current ratio 1.4 (last year 1.5); shares outstanding unchanged; gross margin 32% (last year 30%); asset turnover 1.1 (last year 1.2).

Key takeaways

• Beneish M above −1.78 (or −2.22) flags possible earnings manipulation; receivables and accruals usually drive it.
• Altman Z below 1.81 signals distress, above 2.99 safety, with a grey zone in between; match the variant to the company type.
• Sloan accruals rank companies by the gap between profit and cash; high accruals predict disappointment.
• Piotroski's nine tests are a year-over-year improvement checklist; none of the scores works for banks or insurers.

Next step

Next you will redline risk factors and the management discussion year over year to find what changed and what quietly disappeared.