Using Benford on Expense Reports

1. Using Benford on Expense Reports ACL Users Group Wednesday, June 17, 2009 Richmond, Virginia Charles R. Gauntt BENFORD

2. Expense Report Audit • Annual Audit Required by Board • Now Conducted Quarterly • Personnel notified by E-Mail of Exceptions • Dramatic Improvement in Procedures during Early Stages • Need Ground Rules for Complex or Sensitive Internal Control Situations BENFORD

3. Expense Controls • Corporate Reports • Retail Location Reports • Wholesale Location Reports • Expense Report Form • May be filed electronically via e-mail but signed approved copy must be faxed. • All items require Receipt • Non Travel items often paid using Expense Reports BENFORD

4. Feed Plants Population Farm & Home GEAC Accounts Payable Retail Fertilizer Corporate and Field Support • Corporate and Field Support by Entity – includes more potential classification exceptions • Feed, Farm & Home, Fertilizer, and Retail by entity and account number – fewer potential classification issues. BENFORD

5. Sampling Strategy Using ACL • Benford • High Dollar Block • Excessive Frequency • Monetary Unit - Rejected • Random - Rejected • Stratified Random • Duplicates - Rejected • Excessive Frequency More than 52 • Whole Numbers - Rejected BENFORD

6. Why Benford? • Identified Duplicates • Identified Whole Numbers • Identified Recurring Expenses • Identified Anomalies • Coupled with high dollar and stratified random sample BENFORD

7. Benford Yields Interesting Information • The focus is not just fraud, but identifying unusual trends in the transactions that might represent control weaknesses or savings opportunities. • The Audit staff often finds that Benford items are more interesting to test. • Large classes of items can be understood quickly and the test procedures adjusted. BENFORD

8. Benford’s Law of Leading Digits • Leading Digit Numbers do not occur randomly • Leading Digit Numbers do not occur normally • Leading Digits in multi-digit numbers resulting from the same phenomenon appear in a distribution pattern where lower numbers are more likely to appear • This distribution is closer to a logarithmic or Poisson distribution. BENFORD

9. Which Distribution Fits Your Population? Uniform Normal Benford • Inventory Variances – Normal • Feed Tons Per Hour - Uniform • Invoice Amounts – Benford BENFORD

10. Benford Steps in ACL Presentation • Stratify the Population • Analyze the Population Using Benford • Organize Population into groups by the number of leading digits. • Analyze Groups Using Benford • Store Benford Analysis into a Table and then extract high frequency digit combination using the z statistic and the variance between actual and expected occurrence. (exceptions) BENFORD

11. Creating a Continuous Auditing Application • Assign each Detailed record representing an expense report a Benford Index using the Integer Command • Use Z Statistic or “Actual – Expected occurrences” to match leading digits from Benford Exceptions against the Benford index to extract detailed expense report for additional testing. • Create a script for continuous execution. BENFORD

12. Analysis Script OPEN expenserptpop2009 STATISTICS ON Amount STD TO SCREEN NUMBER 5 STRATIFY ON Amount SUBTOTAL Amount MINIMUM 0 MAXIMUM 10000 INTERVALS 20 TO PRINT BENFORD ON Amount LEADING 1 TO PRINT BENFORD ON Amount LEADING 2 TO PRINT BENFORD ON Amount LEADING 3 TO PRINT BENFORD ON Amount LEADING 4 TO Benford4 OPEN benford4 STRATIFY ON ZSTAT SUBTOTAL ACTUAL_COUNT MINIMUM 0 MAXIMUM 50 INTERVALS 50 TO PRINT OPEN expenserptpop2009 BENFORD ON Amount LEADING 5 TO Benford5 OPEN benford5 STRATIFY ON ZSTAT SUBTOTAL ACTUAL_COUNT MINIMUM 0 MAXIMUM 50 INTERVALS 50 TO PRINT BENFORD

13. Indices Script for 3 Digit Match OPEN expenserptpop2009 DELETE Digits3 DELETE Bindex3 DEFINE FIELD Digits3 COMPUTED INT(Amount*100) If Amount > .99 and Amount < 10 INT(Amount*10) If Amount > 9.99 and Amount < 100 INT(Amount/10) IF Amount > 999.99 and Amount < 10000 INT(Amount/100) IF Amount > 9999.99 and Amount < 100000 INT(Amount) DEFINE FIELD Bindex3 COMPUTED STRING(DIGITS3,3) BENFORD

14. Matching Script OPEN bendford3 OPEN expenserptpop2009 SECONDARY JOIN PKEY DIGITS FIELDS ACTUAL_COUNT EXPECTED_COUNT ZSTAT DIGITS SKEY Bindex3 WITH Amount Date newvendorname newvendorno PO Vendorloc TO "benford3sample" OPEN PRESORT MANY SECSORT IF ZSTAT > 5 OPEN "benford3sample" DUPLICATES ON newvendorname DIGITS OTHER ACTUAL_COUNT Amount Date DIGITS EXPECTED_COUNT newvendorname newvendorno PO Vendorloc ZSTAT PRESORT OPEN TO "duplicatebendford.FIL" CLASSIFY ON newvendorname SUBTOTAL Amount TO "benfordexceptions.FIL" OPEN "benfordexceptions" BENFORD

15. Issues in the Approach • Benford on the whole population provided dramatic number groupings. • The whole population did introduce noise. For example, $25, $250, and 2500 dollar transactions were grouped together. The $25 expense reports always shows up as exceptions due to association meetings. We do not test them in detail. • However, make sure your alternate procedures give you comfort. We did try to review the $25 population to make sure an employee had no more more than 12 association meeting expenses. • Benford creates a file with a character field “digits” as the key. A character index to match against digits had to be created in the expense report file • Make sure you understand the logic of Benford and can explain it to Management. Benford sometimes is attacked as “Hocus Pocus”. BENFORD

16. 1 Digit The Three Digit Analysis Provided the most Dramatic Variances 3 Digit Variances 2 Digit BENFORD

17. Benford Noise – Direct Versus Indirect $25 and $250 mixed together $25 turned out to be meeting dues BENFORD

18. Step 1 – Benford on 3 Digits for all Items Greater than 1.00 • Leading Digits – In this case 3 • Actual Count – Number of Expense reports for this combination of leading digits in the population • Expected Count – Number of Expense Reports expected by Benford • ZSTAT – Likelihood of the actual count occurring in population. Higher the number the less likely the count and the more likely this group is unusual. In this case 250 and 260 are potential exceptions. BENFORD

19. Benford Index BENFORD

20. Make sure you understand the logic of Benford and can explain it to Management. Benford sometimes is attacked as “Hocus Pocus”. The following ACL Help Index is an example of the resources available. Performing Benford digital analysis • The Benford command allows you to generate digital analysis using the Benford formula. • This command counts the number of times each leading digit or digit combination occurs in a data set, and compares the actual count to the expected count. The expected count is calculated using the Benford formula. The command output can be sent to a graph. • To help you evaluate the significance of deviations between actual and expected counts, the command output includes the Z-statistic for each count. You can also use the Bounds option to help you identify digit frequencies that are significantly outside expectations. When more than one count column falls outside the bounds, the data represented by these columns may be anomalous. • For more information about digital analysis, see Digital Analysis Using Benford’s Law: Tests & Statistics for Auditors by Mark J. Nigrini, Ph.D., published by Global Audit Publications. • Digital analysis tools like the Benford command enable auditors and other data analysts to focus on possible anomalies in large data sets. They do not prove that error or fraud exist, but identify items that deserve further study on statistical grounds. Digital analysis complements existing analytical tools and techniques, and should not be used in isolation from them. BENFORD