# Modified Jones Discretionary Accrual Model

`D18-F04-A13` · Fundamental Analysis and Valuation → Quality and Distress · archetype `record-transform` · difficulty 4/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/fundamental-analysis-and-valuation/quality-and-distress/modified-jones-discretionary-accrual-model/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { modifiedJonesDiscretionaryAccrualModel } from "fintech-algorithms/fundamental-analysis-and-valuation/quality-and-distress/modified-jones-discretionary-accrual-model";
```

## Signature

```ts
modifiedJonesDiscretionaryAccrualModel(data)
```

Fits the modified Jones accrual model on an industry-year peer group, excluding the target firm, then applies the fitted coefficients to the target to split its scaled total accruals into non-discretionary and discretionary parts.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `data` | `{ target_id: string; industry_year_sample: { entity_id: string; prior_total_assets: number; total_accruals: number; revenue_change: number; receivables_change: number; net_ppe: number }[] }` | yes | `target_id` names the firm being measured and must be a non-empty string present in the sample. `industry_year_sample` must be an array of at least five records with unique `entity_id` values. Each record supplies `prior_total_assets` as the scaler, `total_accruals` as the regressand, and `revenue_change`, `receivables_change` and `net_ppe` as the regressors. |

## Returns

`{ state: string; method: string; target_id: string; estimation_count: number; coefficients: { inverse_assets: number; revenue_less_receivables: number; net_ppe: number }; peer_residuals: number[]; scaled_total_accruals: number; nondiscretionary_accruals: number; discretionary_accruals: number; absolute_discretionary_accruals: number; interpretation: string }`

`estimation_count` is the number of peers used, which is the sample size less the target. `coefficients` holds the three fitted slopes on inverse prior assets, revenue change net of receivables change, and net PPE, all scaled by prior assets. `peer_residuals` are the estimation-sample residuals. `scaled_total_accruals` is the target's accruals over its prior assets, `nondiscretionary_accruals` is the fitted value and `discretionary_accruals` is the difference, with `absolute_discretionary_accruals` its magnitude. `interpretation` notes that the result is a signed residual with no universal cutoff. `method` is `modified-jones-1995-peer-estimation` and `state` is `calculated`.

## Errors

- When data is not a plain object — throws TypeError
- When target_id is missing, not a string, or empty — throws TypeError
- When any numeric field read is missing or not a finite number — throws TypeError
- When industry_year_sample is not an array, holds fewer than five records, or contains a non-object entry — throws RangeError
- When entity_id values are not unique, or none of them equals target_id — throws RangeError
- When prior_total_assets on any record used is zero or negative — throws RangeError
- When the peer regression has no more observations than predictors, or its design matrix is singular — throws RangeError

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

### Input

`data`:

```json
{
  "target_id": "TARGET",
  "industry_year_sample": [
    {
      "entity_id": "TARGET",
      "prior_total_assets": 900,
      "total_accruals": 48,
      "revenue_change": 130,
      "receivables_change": 35,
      "net_ppe": 390
    },
    {
      "entity_id": "P1",
      "prior_total_assets": 700,
      "total_accruals": 25,
      "revenue_change": 80,
      "receivables_change": 12,
      "net_ppe": 260
    },
    {
      "entity_id": "P2",
      "prior_total_assets": 820,
      "total_accruals": 34,
      "revenue_change": 110,
      "receivables_change": 18,
      "net_ppe": 330
    }
  ]
}
```

### Call

```ts
modifiedJonesDiscretionaryAccrualModel(data)
```

### Returns

object with 11 fields: state, method, target_id, estimation_count, coefficients, peer_residuals, scaled_total_accruals, nondiscretionary_accruals, …

```json
{
  "state": "calculated",
  "method": "modified-jones-1995-peer-estimation",
  "target_id": "TARGET",
  "estimation_count": 7,
  "coefficients": {
    "inverse_assets": -0.5874747557833828,
    "revenue_less_receivables": 0.22667306767603043,
    "net_ppe": 0.033894017127085604
  },
  "peer_residuals": [
    0.0019446595725300733,
    0.0031079596068906493,
    0.002200572287491008,
    -0.0015260908118726463,
    -0.002277193589259173,
    -0.0029399533725206935
  ],
  "scaled_total_accruals": 0.05333333333333334,
  "nondiscretionary_accruals": 0.03796125928111433,
  "discretionary_accruals": 0.015372074052219006,
  "absolute_discretionary_accruals": 0.015372074052219006,
  "interpretation": "signed residual; no universal manipulation cutoff"
}
```

## Other exports

`calculate`, `altmanZScore`, `piotroskiFScore`, `beneishMScore`, `sloanAccrualMeasure`, `ohlsonOScore`, `zmijewskiXScore`, `springateSScore`, `tafflerZScore`, `fulmerHScore`, `groverGScore`, `dechowFScoreForMisstatementRisk`, `dechowDichevAccrualQuality`. Every module additionally exports `run` as an alias of its primary
function, and a `meta` object carrying its catalog id, domain, family, shape and article URL.

## Verification and provenance

Tier: **verified** (via D).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/fundamental-analysis-and-valuation/quality-and-distress/modified-jones-discretionary-accrual-model/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/fundamental-analysis-and-valuation/quality-and-distress/modified-jones-discretionary-accrual-model/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/fundamental-analysis-and-valuation/llms.txt