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Variety in fraud investigation techniques: application of Vedic Mathematics It is variety that makes life interesting and enjoyable. Virtually in every walk of life, we crave for variety. Take for instance our daily meals. Each meal we try to eat something different to make each meal more enjoyable. We try different kinds of breads, soups, vegetables, and fruits. We can actually survive just as well even if we have exactly the same items to eat everyday, but that would make our meals monotonous. Film makers make different kinds of films only because we would get bored of the same story over and over again. A cricket match would become absolutely boring if a batsman were to play each shot in the same identical manner. A popular batsman is one who has a range of different strokes and shots. Thus it has been correctly stated that variety is the spice of life.
Audit, investigation and forensic accounting are no exception to this maxim. It is very possible that if an auditor or an investigator approached every investigation with the same routine steps in a lackadaisical manner, a wrongdoer would be able to take suitable counter measures to ensure that he is protected and safe. Therefore it is absolutely essential to keep trying new methods, hitherto untried techniques and tools, and use a surprise element to get the best results. Research of algorithms, vedic scriptures can be extremely useful in this context. Many audits and investigations end at a dead end, or sometimes reach wrong conclusions, only because of the lack of application of imaginative and innovative methods.
The following is a case study where a chartered accountant was an advisor in an acquisition by a fruit juice manufacturing company. Initially by applying the standard auditing techniques, he felt that there was nothing serious to stop his client from acquiring a company owning a couple of mango farms based on details and information given. It was only after he looked at data differently, using ‘visual mathematics’ and an application of vedic mathematics that he was able to detect a sinister fraud.
Case Study: Fraud in mango farm sale
A fruit juice manufacturing company ABC was looking for more and more orchards and fruit plantations for expansion. In this hunt, they came across a proposal from a mango grower PQR in Maharashtra for sale of two mango farms. PQR had been growing mangoes and exporting them and seemed to have had a fairly good crop in the last season. The substantial part of the acquisition value was for the two fertile farms. The two mango farms commanded a rich premium because of their fertility and huge potential for growing mangoes in bulk. ABC had asked its CA to conduct a review of its financials and operating results for the last couple of years. Some extracts of the financial information given to him were as follows:
1. Farm A had 4 acres and Farm B was 6.3 acres in size. The potential for much greater crop of mangoes was huge and PQR had not been able to tap it because of its lack of resources. ABC realized that with more resources and better techniques the mango crop could be tripled.
2. Plucking and packing activity was performed over two days. The mangoes would be plucked and packed on the last two days of each month. On day 1, there would only be plucking activity and the mangoes would be stacked neatly. On day 2, the mangoes plucked the previous day would be washed and cleaned of all pesticide and then packed in boxes of one dozen each.
3. The packed mangoes from both the farms would be sent to the main godown where they would be counted and kept ready for export.
4. Costs of plucking and packaging for farm B were greater than farm A because it was further in the interior part of the district and labourers charged more to work at farm B
5. Costs of plucking and packaging during each month also varied based on demand supply of skilled labour in season time. Usually in May the cost would be the highest
The details of plucking and packaging costs per dozen are given in the table below
Conventional Audit checks did not throw up any adverse results.
The number of mangoes packed for each farm individually were not available, but the total mangoes packed for both farms for each month were physically verified by the management, as follows: March 720 mangoes, April, 2400 mangoes, and May 4800 mangoes. Though the CA was not conducting any investigation, he did have the responsibility of carrying out a special penetrative audit of the financial information given by PQR because ABC was going to invest a huge amount only based on the CA’s assessment. Therefore the CA applied all the conventional audit checks and tests. The bills for labourer’s payments were available in the form of wage sheets which prima facie looked satisfactory and his audit did have some routine queries but nothing serious.
The sales and collections audits and verifications using walk through tests also did not raise any alarm bells. These were also well documented. A decent price was earned by PQR for the sale of mangoes per reasonable market inquiries. In most respects, based on his routine audit techniques, the CA seemed to have derived a comfort in the financial information given. Under normal circumstances he would have given a ‘go ahead’ green signal to his client for acquisition of PQR.
How vedic mathematics helped the CA to spot a fraud by a mere visual look at the numbers.
The information given by PQR was incomplete in one important respect. The numbers of mangoes plucked and packaged in each farm for each month. This was important to determine the crop size and fertility of each farm. How could one find this? Actually applying mathematics using knowledge of algebra by solving simultaneous equations for each month it is possible. But that is a tedious task.
To illustrate, for the month of March, to find out how many mangoes were plucked and packaged, one would have to use algebra by using variables ‘x’ and ‘y’ to represent mangoes plucked and packed in farms A and B respectively. Then the cost information given above can be simply converted into a simultaneous equation in the conventional form as follows.
20x + 40y = 1200
70x + 85y = 4200
But solving such equations would be slightly tedious. However, through vedic mathematics, in one look, the viewer will be able to state that y = 0 in the above equations. How is this possible? Actually it is very simple.
A sutra of vedic mathematics called Anurupye Shunyamanayat’ states that if the co-efficients of one of the variables in a simultaneous equation are in the same ratio as the resulting values of each equation, then the other variable MUST BE ZERO
Thus in our above simultaneous equation of mangoes plucked and packaged in March
20x + 40y = 1200
70x + 85y = 4200
The coefficients of x are 20 and 70. Their ratio is therefore 2/7. The resulting values of each equation are 1200 and 4200. Their ratio is also 2/7. Since these two ratios are the same, the other variable, ‘y’ as per sutra 6 of vedic mathematics, anuraupye shunyamanayat, MUST be zero.
THUS THERE WERE ‘0’ MANGOES GROWN IN MARCH IN FARM B. BY USING THE SAME VEDIC MATHEMATICS APPROACH THERE WERE ‘0’ MANGOES GROWN IN FARM B FOR THE OTHER MONTHS AS WELL. THE COST FIGURES WERE IMAGINARY AND FICTITIOUS FOR FARM B.
In other words, Farm B was not producing any mangoes at all.
The fraud was a simple deception by PQR by claiming that mangoes were indeed being grown on farm B, even though it had no fertility to grow any mango at all.
Though it was the larger farm, since it was not a fertile plot, the price being demanded by PQR was an atrocious exponential value of its actual worth. ABC would obviously never be interested in purchasing such a farm. PQR’s labour costs were therefore nil for farm B and PQR was deceiving ABC by stating that mangoes were being plucked and packed in farm B. The CA then advised the client ABC not to go ahead with this acquisition.
What is important in this case study is that the CA always strived to upgrade his knowledge and he was always eager to learn new techniques and methods useful in his profession. He had recently been studying vedic mathematics. Vedic mathematics has some amazing solutions for certain types of mathematical problems. As we all know India discovered ‘0’ and a lot of vedic mathematics sutras are based on, or revolve around ‘0’. Among them, one of the sutras, sutra no 6 is ‘Anurupye Shunyamanayat’.
Vedic mathematics itself may be useful in a rare assignment, but what counted was the fact the CA was trying new things and different things every time to get better results. That, friends is the measure of life and true success.
Editor’s note: Fraud investigation and detection are an important area of practice for a chartered accountant. This involves acquisition of specialised knowledge. The law now casts an important duty in regard to reporting fraud on the auditor. Public expectations have now found statutory recognition. We have therefore thought it necessary to carry a series of articles by Mr. Chetan Dalal an expert on the subject. These will appear in the journal at intervals, that is probably in each alternate month. We hope readers will find this series useful.
