To Your Credit

Note: _t = current year & _{t – 1} = prior year LTD = long term debt; PP&E = property, plant & equipment

Days’ sales in receivables index:

DSRI = Receivables_t / Sales_t
               Receivables_t-1 / Sales_t-1

This variable gauges whether receivables and revenues are in or out of balance in two consecutive years. A large increase in days’ sales in receivables could be the result of a change in credit policy to spur sales in the face of increased competition, but disproportionate increases in receivables relative to sales could also suggest revenue inflation..

Gross margin index:

GMI = (Sales_t-1 – Cost of goods sold_t-1/Sales_t-1
(Sales_t – Cost of goods sold_t)/Sales_t

A GMI greater than 1 represents deterioration in gross margins.    

Asset quality index:
AQI = 1 - (Current assets_t + PP&E)/Total assets_t
         1 - (Current assets_t-1 +  PP&E_t-1)/Total assets_t-1

A greater than 1 AQI infers that the company has potentially increased its involvement in cost deferral.  The AQI index measures the proportion of total assets for which future returns are not certain.    

Sales growth index:
SGI = Sales_t
         Sales_t-1

Although sales growth is a desirable occurrence within a company, some professionals are of the opinion that high growth companies are “more likely than other companies to commit financial statement fraud”.

Depreciation index:

DEPI = Depreciation_t-1/(Depreciation_t-1 + PP&E_t-1)
 Depreciation_t /(Depreciation_t + PP&E_t)

A DEPI greater than 1 indicates that the rate at which assets are being depreciated has slowed.  This may imply that the lives of assets have been extended or the company has changed its method of calculating depreciation.  The net effect of decreasing depreciation is inevitably an increase in income when other income statement variables remain constant. 

Sales, general, and administrative expenses index:

SGAI = Sales, general, and administrative expenset/Sales_t
                Sales, general, and administrative expense_t-1 /Sales_t-1)

A disproportionate relative increase in sales may suggest uncertainties about a company’s future prospects.

Leverage index:

LVGI = (LTD_t + Current liabilities_t)/Sales_t
                (LTD_t-1 + Current liabilities_t-1)/Sales_t-1

An LVGI greater than 1 indicates an increase in leverage.

Total accruals to total assets:

ΔCurrent assets_t – ΔCash_t – (ΔCurrent liabilities_t                                                                                                                
                    - Δcurrent maturities of LTD_t – ΔIncome tax payable_t)
                                      – Depreciation and amortization_t
TATA =________________________________________________
Total assets

Total accruals are calculated as the change in working capital accounts other than cash less depreciation.  Positive accruals suggest that there is less cash behind accounting income.

As you will see in the illustration that follows, Pr. Beneish has used the 8 variables described above to show that there existed some distortions in the financials that Enron, Lucent and Sunbeam had filed prior to the discovery of the accounting scandals associated with these companies.   

Illustration of the two types of variables in Beneish’s earnings manipulation detection model "The Detection of Earnings Manipulation" in the Financial Analysts’ Journal, 1999, 55(5): 24-36], by MD Beneish

1. Variables designed to capture financial statement distortions:

Days’ sales in receivables index and Accrual to Total Assets are responsible for flagging Lucent and Sunbeam as potential earnings manipulators.  Days’ sales in receivables index is computed as the ratio of days sales in receivables in two consecutive years.   Absent a change in credit policy to spur sales in the face of increased competition, days sales in receivables in two consecutive years should be the approximately the same and the index variable would have an expected value of one. 

As you can see below, Lucent‘s computation shows an unusual accumulation in receivables, with the latter growing at a rate 17% faster than sales.  Such a disproportionate increase in receivables relative to sales is suggestive of revenue inflation.  A similar pattern appears for Sunbeam when I apply the model to their originally reported data, but the index variable is very close to its expected value of 1, once the firm has been forced to restate their previously inflated revenues.  The variable Accruals to Total Assets also contributes to flagging these firms: positive accruals suggest that there is less cash behind accounting income—on average accruals tend to be negative in the range of -4 to -5%.   

	Lucent	Sunbeam 1997
Variables	1999	As reported	As restated
Day Sales in Receivables Index	1.170	1.167	0.999
Gross Margin Index	0.976	0.300	0.393
Asset Quality Index	0.960	0.928	0.907
Sales Growth Index	1.204	1.187	1.090
Depreciation  Index	0.952	1.284	1.247
SG&A  Index	1.018	0.516	0.632
Accruals to Total Assets	0.088	0.105	0.042
Leverage Index	0.908	0.795	0.966
Model Score	-1.736	-1.884	-2.460
Model Estimated Probability	0.041	0.030	0.007

2. Variables that suggest propitious conditions for the occurrence of manipulation

Two variables contribute to identifying Enron as a potential manipulator as early as 1998 are:  A value greater than 1 for the Gross Margin Index suggests that gross margins have deteriorated, a signal that poorer prospects provides greater incentives to manipulate. A large value for the Sales Growth Index does not imply manipulation, except that manipulators tend to be young, high growth firms. 

	Enron
Variables	1997
Day Sales in Receivables Index	0.625
Gross Margin Index	1.448
Asset Quality Index	1.308
Sales Growth Index	1.526
Depreciation  Index	1.017
SG&A  Index	0.649
Accruals to Total Assets	0.012
Leverage Index	1.041
Model Score	-1.890
Model Estimated Probability	0.029

The analysis above received much attention subsequent to the Enron scandal because a group of Cornell MBA students had prepared a report applying various techniques including my model as part of their involvement, in 1998, with a student run fund. 

In order to have a better appreciation of the professor’s work, the readers are encouraged to consult the paper in its totality as published in the Financial Analysts Journal.  A review written by Joseph T. Wells on the professor’s work can also be found at http://www.aicpa.org/pubs/jofa/aug2001/wells.htm.