Thursday, December 8, 2011

DIGITAL ANALYSIS IN INTERNAL AUDIT


DIGITAL ANALYSIS IN INTERNAL AUDIT

         Digits can do wonders. Analysis of Digits can do more wonders. It is a methodology  to find abnormal duplications of specific digits, combinations of digits, specific  numbers in corporate data.  Enthusiastic internal auditors and external auditors  may likely to use Digital Analysis which bring value added services to their corporates  and clients. The purpose of this paper submission is to enrich the auditors in the most effective use of digital analysis, based on  Benford’s  Law.
Benfords  Law :
         Similar to the experience of an apple fell on the head of  Sir Isaac Newton,  Frank Benford, a physicist at the GE Research Laboratories  also had a unique experience. In the year, 1920   while at his work spot, Frank Benford noticed that his log table books were more worn at the first few pages than at the last few pages. The first pages give the logarithms of numbers with low first digits. The first digit in a number is the left most digit. For example, the first digit of 1,18,020 is 1 and the third digit is  8. The first and second digit of 7,840 is 7 and 8 respectively. Benford  hypothesized  that he was looking up the logs of numbers with low first digits more often, because there were more numbers with low first digits than with high first digits.
 Origin :
          In 1881, Simon Newcomb, an astronomer and mathematician, published the first known article describing what has become known as Benford’s Law in the American Journal of Mathematics. He observed that library copies of books of logarithms were considerably more damaged  in the starting pages which dealt with low digits and comparitively less damaged on the pages dealing with higher digits. He himself inferred from this pattern that fellow scientists used those tables to look up numbers which started with the numeral one more often than those starting with two, three and so on. The obvious conclusion was that more numbers exist which begin with the numeral one than with the large numbers. Newcomb calculated that the probability that a number has any particular non-zero first digit is:
                  P(d) = Log10(1+1/d)
          Where d is a  number 1..2...3................9... and  P is the probability.
           Using Newcomb’s formula, the probability that the first digit of a number is one is about 30% while the probability of the first digit a nine is only 4.6 percent. The following table shows the expected frequencies for all digits starting from 0 to 9 in each of the first two places in any number.
Expected Frequencies based on Benford’s Law
               DIGIT
FIRST PLACE
SECOND PLACE
         0
           ---
         0.11968
         1
     0.30103
         0.11389
         2
     0.17609
         0.10882
         3
     0.12494
         0.10433
         4
     0.09691
         0.10031
         5
     0.07918
         0.09668
         6
     0.06695
         0.09337
         7
     0.05799
         0.09035
         8
     0.05115
         0.08757
         9
     0.04576
         0.08500
  
                     In a nutshell, we may say that Benford’s  law is based on a peculiar observation that lower digits appear more frequently than higher digits in data sets. Hitherto,  we focused  on sample, which is now switched over to population!   
           Let us see how this phenomenon applied to Auditing and Accounting.   
Benford’s Law applied to Internal Audit:
            Not all data sets are expected to have the digit frequencies of Benford’s Law: therefore the guidelines for deciding whether a data set would comply are that:
1.   The numbers in the data set should describe the sizes of the elements in the data set;
2.   There should be no built-in maximum or minimum to the numbers. A maximum or minimum that occurs often would cause many numbers to have the digital patterns of the maximum or minimum;
3.   The numbers should not be assigned. Assigned numbers are those given to objects to identify them. Examples are social security, bank account and telephone numbers, and cheque numbers. 
Benford’s  Law gives auditors the expected frequencies of the digits in tabulated data.The premise is that we would expect authentic, and un manipulated data to exhibit these patterns. If a data set does not follow these patterns,  however a few possible reasons exist to explain this phenomenon.
1.   The data set did not meet the three tests noted above, and/or;
2.   The data set includes invented numbers, biased numbers
or errors.
If a data set follows Benford Law, auditors might conclude that the data have passed a reasonableness. This does not mean that all the numbers are correct, but rather that any errors or manipulations were not significant enough to distort the digit patterns. Auditors would still have to combine Digital Analysis with other analytical procedures and possible statistical sampling procedures.
Audit tests:
         The first and second digit tests are used as high level tests of reasonableness. Experience has shown that large accounts payable files have followed Benford’s Law quite closely. Also the extended values of the Inventory follows Benford’s Law closely. The third, more focused test is to verify the frequencies of the first two digits. The formula for the expected first two digit frequencies under Benford’s Law is :
Expected First Two Digit frequency=log(1+1/FTD)
         The fourth, still more focused test is the number duplication test. Here, the frequencies of the actual numbers in the audit data set are tabulated. The list begins with the most frequently occurring number and ends with the least frequently occurring number. Auditors generally direct their attention to
1.   Numbers that have occurred abnormally often relative to
other numbers;
2.   Odd numbers that have occurred abnormally often;
3.   Round numbers that have occurred abnormally often;


Exemptions :
         Some populations of accounting- related data do not conform to a Benford  distribution. For example, assigned numbers such as cheque numbers, purchase order numbers or numbers that are influenced by human thought , for example, the price of a pair of shoes is 199.99 or ATM withdrawals do not follow Benford’s Law. Assigned numbers should follow a uniform distribution rather than a Benford distribution.
     In addition to an auditor’s perception  in determining which populations fit a Benford distribution, there exist some tests that reveal whether or not Benford’s Law applies to a particular data set. Wallace suggests that if the mean of a particular set of numbers is larger than the median and the skewness value is positive, the data set likely follows a Benford distribution. It follows that the larger the ratio of the mean divided by the median, the more closely the set will follow Benford’s Law. This is true since observations from a Benford distribution have a predominance of small values. The difficulty in relying only on such tests as a screening process, before applying digital analysis, is that if an account contains sufficient bogus observations it could fail the tests; thus, digital analysis would not be applied when, in fact, it should.
Conclusion:
     We conclude that Benford’s analysis, when used correctly, is a useful tool for identifying suspect accounts for further analysis. Because of its usefulness, digital analysis tools based on Benford’s Law are now being included in many popular software packages like ACL and CaseWare 2002.The goal of this paper has been to help auditors more appropriately apply Benford’s law-based analysis to increase their ability to detect ubnormal  transactions or fraud. Benford  analysis is a particularly useful analytical tool because it does not use aggregated data, rather it is conducted on specific accounts using all the data available. It can be very useful in identifying specific accounts for further analysis and investigation.
 References :
1.   Mark J Nigrini  Ph.D, Institute of Internal Auditors
247, Maitland Avenue, Altamonte Sprins, Florida.
2.   “ The effective use of Benford’s Law to assist in detecting fraud in Accounting Data” – M/s Cindy Durtschi, William Hillison & Carl Pacini.  
3.   Chartered Accountant Magazine November 2011 issue.           
      

Friday, October 1, 2010

Winners gain Everything......

In a 2x2 game, one wins and another looses. To elaborate, we should find that how much the winner is going to gain in the game and how much the loser is going to loose. The charisma is not in the winning but in the techniques and methods, one applied in winning!
Everything is in Boolean phenomenon. In one side, (that is,internal) we have resource,power,capital,police and what not and in the other side of the coin(perhaps external) we have application,work done,ploughing back of capital,riots etc..etc.. Inject less resource and gain more output from the resource applied.Like that lesser police personnel (comparing to the requirement) is to be deployed to control anti social elements in a vulnerable territory.That is the sucess of a good Administration!
Put less strain to win a big battle!
It is interesting to note that one side is within our control and the other is beyond our control. The success lies in how we apply.
In a market, for a business house, the supply is internal (controllable) and the demand is external (beyond our control). A sucessful businessman forecasts his demand and adjusts his supply accordingly. Thereby the pricing wizard is in his hands
We can apply this principle in Management techniques also. When a Boss exercises more power than the required, he becomes powerless in the long run.
Keep it in mind that resources are always in scarce and we should apply them justifiably!
And so,
Accelerate Less !
Gain More momentum !!!

Monday, May 10, 2010

Where Both Ends will meet ?


Sometimes a company recruits Artisans and Direct workers after a long gap,
due to some expansion programme. The ultimate result is there exists the problem of inter-personal relationships. When there is a gradual increase of recruitment in anticipation of
superannuation and labour turnover, the relationship between the existing employees
and the new recruits is coridal and there is a good understanding of both class of employees.
Moreover, there exists a brotherhood relationship among the employees and it will be adjusted in the short run.

On the other hand, when there is recruitment ban and after a time gap of roughly twenty years, it is lifted and new recruits are peeped in, there comes the problem. There exist a mis-match between existing workers and new recruits. Here, the relationship is like a fatherhood relationship. Nodoubt in fatherhood relationship, the generation gap prevails which leads to strained relationship. Usually, the older employees want to retain their position at any cost and the new recruits want to establish their technological competance over the existing elderly workers. There may be a chance of rivalry between themselves. When the rivalry developed, the first casualty is communication. When there is no clear communication, in the long run the peril will quash the very mission of the corporate entity it self. Imagine in a shift , the partners in a Lathe is in different age group?

On the other hand, it is interesting to see that in the Top level , there is no vast diffence in ages. Unstructred decions are taken by the Strategic Leaders in the same age-group it self?
Then why there is a long age gap among operational level people?
Let us anticipate the Problems :
1. Psychological fear among Old Employees.
2. Their productivity will be decreased.
3. Working Environment will be disturbed.
4. Mis-match between Older and New recruits.
5. Strained Relationship.
6. Poor Communication.
7. Value added per Worker reduced.
8. Low Turn-over.

In the present scenario, World Class Companies switch over the focus from Customer to their Working force. How we can escape?
Can anybody guess how the panecea will be overcome?
Your valuable ideas are very much solicited.

Friday, February 26, 2010

BE INNOVATIVE !!!!


BUSINESS IS EQUAL TO WARFARE . TO QUOTE A PERSON A WINNER, THERE ARE SO MANY POINTS TO BE CONSIDERED. HOW HE WINS, HOW MUCH IT COSTS HIM TO WIN, TIME , RETENTION ETC. WHEN THE COST OF A WAR COMES TO 1 BILLION DOLLAR FOR A WINNER AND IT IS 0.5 BILLION DOLLAR FOR A LOSER , WHO IS THE REAL WINNER AND WHO IS THE LOSER! MOREOVER RETENTION IS A REAL PROBLEM FOR A WINNER . FOR A LOSER, HE JUST BENCHMARKS WHAT THE WINNER DOES! AND SO,HIS STRAINS ARE COMPARITIVELY LESSER THAN THAT OF A WINNER! IT IS RIGHTLY SAID THAT WINNERS GAIN NOTHING!!!
JUST LIKE THAT IN BUSINESS ALSO, FOR A PRODUCT ONE PERSON IS A MARKET LEADER. IN THAT FIELD, SO MANY ARE THE FOLLOWERS. THERE IS A TUG OF WA R BETWEEN NO.1 AND NO.2. THE MARKET LEADER EXERCISES DEFENSIVE APPROACH. HE ALWAYS WANTS TO RETAIN HIS POSITION.HIS ALL ACTIONS ARE FOCUSED TO THAT ONLY, WHEREAS THE NO.2 EXERCISES OFFENSIVE APPROACH, AND HE DETERMINES TO DO ANYTHING (SOMETIMES UNETHICAL ALSO) TO CAPTURE THE MARKET.IT IS NOT AS MUCH AS A HARD TASK LIKE THAT OF A NO.1.
HOWEVER ONE BELIEVES THAT HARD WORK, CUSTOMER FOCUS,LONG RANGE PLANNING, STRATEGICAL APPROACH MAY WIN THE RACE. BUT A PERSON WITH INNOVATIVE APPROACH WILL LEAD THE RACE!
OF COURSE, LEADERS DO NOT DO DIFFERENT THINGS. THEY DO THE THINGS DIFFERENTLY!!!