Forensic Accounting & Earnings Quality
Modified Jones Discretionary Accruals Formula
Calculate Dechow, Sloan, and Sweeney’s (1995) Modified Jones Non-Discretionary Accruals NDA_t and Discretionary Accruals DA_t by subtracting credit-sales receivable growth from revenue growth.
Catch end-of-quarter credit-sales channel stuffing missed by the original Jones model!
Jennifer Jones (1991) estimated normal working-capital and depreciation accruals scaled by lagged assets A_{t-1} as NDA_Jones = a_1*(1 / A_{t-1}) + a_2*(Delta_Rev / A_{t-1}) + a_3*(PPE_t / A_{t-1}) — implicitly assuming ALL revenue growth Delta_Rev is non-discretionary! Patricia Dechow, Richard Sloan, and Amy Sweeney (1995) exposed the fatal blind spot: if management manipulates earnings by booking premature credit sales at year-end, both Delta_Rev and Accounts Receivable Delta_Rec jump together, tricking Original Jones into classifying manipulated receivables as "normal" accruals! The Modified Jones Model subtracts Delta_Rec inside evaluation: NDA_Mod = a_1*(1 / A_{t-1}) + a_2*((Delta_Rev - Delta_Rec) / A_{t-1}) + a_3*(PPE_t / A_{t-1}), isolating Discretionary Accruals DA_Mod = (TA_t / A_{t-1}) - NDA_Mod!
Verify on Lagged_Assets A_{t-1} = 1,000 ($M, B2), Total_Accruals TA_t = 40 ($M, B3 -> 4.00% of assets), Revenue_Change Delta_Rev = 150 ($M, B4), Receivable_Change Delta_Rec = 100 ($M, B5), Gross_PPE = 400 ($M, B6), and Industry_Coefficients a_1 = 2.0 (B7), a_2 = 0.12 (B8), a_3 = -0.05 (B9): Original Jones NDA is 2.0/1000 + 0.12*(150/1000) - 0.05*(400/1000) = 0.0020 + 0.0180 - 0.0200 = 0.0000 (Original DA = +0.0400), whereas Modified Jones NDA drops to 0.0020 + 0.12*((150 - 100)/1000) - 0.0200 = -0.0120, unmasking Modified Jones Discretionary Accruals DA_Mod = 0.0400 - (-0.0120) = +0.0520 (+5.20% of lagged assets, +120 bps hidden credit-sales manipulation)!
| Forensic Accrual Model Metric (A_{t-1}=1,000, TA=40, dRev=150, dRec=100) | Formula | Verified Output |
|---|---|---|
| Original Jones (1991) Normal Accruals | a_1/A + a_2*(dRev/A) + a_3*(PPE/A) | 0.0000 (DA_Jones = +0.0400) |
| Modified Jones (1995) Normal Accruals | a_1/A + a_2*((dRev - dRec)/A) + a_3*(PPE/A) | -0.0120 (-1.20% of Assets) |
| Modified Jones Discretionary Accruals | (TA_t / A_{t-1}) - NDA_Mod | +0.0520 (+5.20% of Assets) |
| Unmasked Credit-Sales Manipulation Wedge | DA_Mod - DA_Jones = a_2 * (dRec / A_{t-1}) | +0.0120 (+120 bps) |
Modified Jones (1995) Non-Discretionary & Discretionary Accruals Formula
Remember the Dechow-Sloan-Sweeney two-step subtlety: industry slopes (a_1, a_2, a_3) are estimated on unadjusted Delta_Rev in the clean estimation sample, and Delta_Rec is subtracted in the event/audit prediction step!
=LET(as_lg, B2, ta_cr, B3, dv_rv, B4, dv_rc, B5, pp_gr, B6, a_on, B7, a_tw, B8, a_th, B9, IF(OR(as_lg <= 0, pp_gr < 0), "Invalid Forensic Input", LET(nd_md, a_on * (1 / as_lg) + a_tw * ((dv_rv - dv_rc) / as_lg) + a_th * (pp_gr / as_lg), ROUND((ta_cr / as_lg) - nd_md, 4))))Original Jones Comparison & Receivable-Wedge Audit Formula
Set B5 = 0 (zero receivable growth) to verify that Modified Jones and Original Jones converge identically to +0.0400!
=IF(ISTEXT(E4), E4, ROUND(E4 - ((B3 / B2) - E2), 4))Try the example
Use the original values or change them to test your understanding.