The ‘Relative Size Factor’ can unearth various frauds
Accounting manipulations stemming from intelligent planning can be easily camouflaged in vast data populations, and, even if noticed, can be explained as errors. Such manipulations are more often than not revealed by accident. However, there are certain tools which facilitate detection of such frauds and one of them is a mathematical tool called ‘Relative Size Factor’ (RSF).
The RSF is simple to understand: In a group of any given transactions, it is a ratio of the highest value divided by the second highest value. For instance, a vendors statement of account had these invoice values: Rs 10,000, Rs 12,000, Rs 3,400, Rs 7,600, Rs 15,000. The RSF is the ratio of the highest value 15,000 divided by the second highest 12,000 i.e. 5/4 or 1.25. If the RSF exceeds 10, then a very strong possibility exists of something being wrong and further inquiry is necessitated. For example, if the vendor’s highest bill was Rs 12.000 (Instead of Rs 15,000), the ratio of 10:1 is obviously inconsistent. Of course, this RSF is meaningful only where volumes of transactions are high because in essence, what the investigator attempts in finding out is the extraordinary. This example is one such case where the RSF revealed manipulation of a staggering value.
In an electronics company, there were several regional offices country-wide that had huge inventories of finished stocks, tools and spares. Since inventories at each regional office were huge, the company management insisted upon monthly-summarised region-wise inventory reports. Its internal auditors also verified stocks on a quarterly basis. In a regional office, a fire gutted every item of stock, documents and accounting records. An insurance claim was lodged, and the insurance company appointed surveyors to assess it. The claim was made on the basis of the previous month’s inventory adjusted with current month’s sales, purchases, issues and dispatches reported to the head office as per records available there. The internal auditors had back up data on a floppy of the last inventory valuation carried about a month, ago. Taking a copy of this data from the auditors with a management consent, the surveyor applied a series of tests on the inventory data, which had details of quantities and rates at about 5,000 items. He then applied the RSF test on the rates of items of the inventory. Using digital techniques he could filter out 176 items which had RSF 10:1 or more. He saw something unusual; all the 176 items had RSF either of 10:1 or 100:1. On further scrutiny, he found that all these were relatively small value items. A 50 paise item had its decimal place shifted by 2 zeroes making it at Rs 50. In certain cases, the decimal place was shifted by 1 zero. For instance, an item of Rs 4 was made Rs 40. The effect was to inflate the rate and the overall inventory value. He verified the rates of these items by obtaining quotations from other vendors. The results confirmed that the values were grossly overrated. By applying realistic rates, the inventory value came down by 1,3 crore. A meeting with the top management was held to appraise them of the reduced value of the claim. A detailed investigation showed that the regional office under a particular sales zonal manager had huge shortages of certain finished gods, which had been clandestinely sold in cash. Such shortages were camouflaged in the management inventory reports. This was because a fall in the inventory value would be noticed and questioned, To be able to show a sufficiently large inventory value, the zonal manager had to contend with the internal auditors who were frequently physically verifying the stocks as well. How was the manipulation done? Since physical quantities were short, and auditors verified the physical stocks of high value items, the only other way was to manipulate the rates. Accordingly, small priced ‘C’ category items were selected where quantities were high, and the decimal places in their rates were moved to inflate the inventory value and to offset the shortfall in stocks of finished goods. It was a calculated risk. The auditors would not verify these rates because the items affected were the miscellaneous ‘C’ category items. Even if any of these were queried, the manager would feign ignorance and rectify that particular item rate and pass it off as a data entry error. It was later revealed that even the fire was not an accident. However the point here is the manipulated rates, which went unnoticed from a population of 5000 items. It might have been revealed as an error but not as a fraud, except for the RSF.
The RSF is, therefore, an important tool now used by not only the auditors but also by management in order to highlight inconsistent data patterns to reveal manipulations.