Equity Valuation & Forensic Accounting
Sloan Accrual Anomaly & Cash-ROA Persistence Formula
Decompose Return on Assets into Cash-Flow ROA (CFO / Avg_Assets) and Operating Accrual Ratio ((NI - CFO) / Avg_Assets) to forecast next-year ROA under Richard Sloan’s (1996) differential persistence model.
Why two firms with 12% ROA diverge sharply when one relies on working-capital accruals!
Richard Sloan (1996) uncovered one of empirical accounting’s landmark findings: investors fixate on headline Return on Assets ROA_t = Net_Income / Avg_Assets as if a dollar of accounting accruals persisted just as reliably as a dollar of free operating cash flow! Decomposing ROA_t = Cash_ROA_t + Accrual_ROA_t where Cash_ROA_t = CFO / Avg_Assets and Accrual_ROA_t = (Net_Income - CFO) / Avg_Assets, Sloan proved that next-year earnings follow ROA_{t+1} = alpha_0 + gamma_cash * Cash_ROA_t + gamma_acc * Accrual_ROA_t with gamma_cash > gamma_acc because inventory/receivable write-ups mean-revert!
Verify on Net_Income NI = 120 ($M, B2), Operating_Cash_Flow CFO = 70 ($M, B3), Average_Total_Assets = 1,000 ($M, B4), Intercept alpha_0 = 0.0100 (B5), Cash_Persistence gamma_cash = 0.85 (B6), and Accrual_Persistence gamma_acc = 0.70 (B7): Headline ROA_t is 120 / 1,000 = 0.1200 (12.00%), composed of Cash_ROA = 0.0700 (7.00%) and Operating Accrual Ratio = +0.0500 (+5.00% bloat), yielding Expected Next-Year ROA_{t+1} = 0.0100 + 0.85 * 0.0700 + 0.70 * 0.0500 = 0.1045 (10.45%)! Now compare a cash-backed peer with identical 12.00% Headline ROA (NI = 120, CFO = 150 -> Accrual_ROA = -0.0300): Expected Next-Year ROA_{t+1} rises to 0.0100 + 0.85 * 0.1500 + 0.70 * (-0.0300) = 0.1165 (11.65% — +120 bps higher earnings persistence)!
| Sloan (1996) Earnings Quality Metric (NI=120, CFO=70, Assets=1,000) | Formula | Verified Output |
|---|---|---|
| Headline Return on Assets (ROA_t) | Net_Income / Avg_Assets | 0.1200 (12.00%) |
| Operating Accrual Ratio (Sloan Bloat) | (Net_Income - CFO) / Avg_Assets | +0.0500 (+5.00% Accruals) |
| Sloan Forecast Next-Year ROA_{t+1} | alpha_0 + gamma_cash*Cash_ROA + gamma_acc*Acc_ROA | 0.1045 (10.45%) |
| Cash-Rich Peer Comparison (CFO = 150) | Accrual_ROA = -0.0300 | 0.1165 (+120 bps Higher) |
Sloan Operating Accrual Ratio & Differential Persistence Forecast Formula
Validate Avg_Assets > 0 and persistence ordering 0 <= gamma_acc < gamma_cash <= 1!
=LET(ni_yr, B2, cf_op, B3, as_av, B4, al_in, B5, gm_cs, B6, gm_ac, B7, IF(OR(as_av <= 0, gm_ac < 0, gm_cs <= gm_ac, gm_cs > 1), "Invalid Sloan Input", LET(ro_cs, cf_op / as_av, ro_ac, (ni_yr - cf_op) / as_av, ROUND(al_in + gm_cs * ro_cs + gm_ac * ro_ac, 4))))Earnings Quality Signal Classification Formula
Flag high positive operating accruals (> +5% of assets) as "Aggressive Accrual Bloat (Short Signal)" and cash-backed negative accruals (CFO > NI) as "High Cash Conversion Quality"!
=IF(ISTEXT(E4), E4, IF(E3 >= 0.05, "High Accrual Bloat (Mean-Reversion Risk)", IF(E3 < 0, "High Cash Conversion Quality (CFO > NI)", "Moderate Working-Capital Accruals")))Try the example
Use the original values or change them to test your understanding.