The business of forensic accounting is — most of the time — a very precise, highly detailed process. It might surprise you then to learn that one of the tricks of the trade forensic accountants use in fraud investigation stems from the very inexact science of probabilities, specifically, Benford’s Law.
“Frank Benford was a physicist in the 1930s who essentially proved an earlier hypotheses by astronomer Simon Newcomb in the 1880s that numbers starting with 1 occurred more frequently than other numbers,” explained David Anderson, a Philadelphia forensic accountant and principal of David Anderson & Associates, a Philadelphia forensic accounting firm that provides a full range of fraud investigation and fraud deterrence programs in the Delaware Valley. “Newcomb had noticed that when he looked up logarithm tables in a book he shared with colleagues, the earlier pages (which contained numbers that started with 1) were much more worn than the other pages. Benford tested and expanded that work and the phenomenon was named after him.”
Benford’s Law, also known as the First Digit Law, states that the lower the first digit, the higher the probability that it will occur more often than higher numbers, Anderson said. Studies have confirmed the concept by showing that the number 1 occurs as a first digit more than 30% of the time, the number 2 occurs as a first digit about 18% of the time, and so on, according to Anderson, a Philadelphia forensic accountant who also is a Certified Fraud Examiner in Philadelphia. The number 9 occurs as a first digit the least – less than 5% of the time, Anderson added.
Benford’s Law is one of the tricks of the trade that forensic accountants use in analyzing financial transactions during fraud investigations, Anderson said. If the results of the financial analysis show a mismatch with Benford’s Law, it is a red flag to forensic accountants that fraud may be present.
In one case, Anderson said, senior management engaged him to determine if any of their divisions were circumventing spending authorization limits.
“The company had a policy that required higher levels of approval for expenditures in excess of $100,000,” according to Anderson, a forensic accounting expert in Philadelphia with experience in conducting fraud investigations and establishing comprehensive fraud deterrence programs in the Delaware Valley. “I analyzed all transactions between $10,000 and $100,000 for each division and found that three divisions had a higher incidence of transactions between $90,000 and $99,999 than would be expected. Two divisions exceeded 10%, while the third division exceeded 8%.”
Anderson’s findings for the three divisions were out of sync with Benford’s Law and a further analysis of the transactions between $90,000 and $99,000 revealed that the three divisions were “splitting” vendor invoices that exceeded $100,000 so as to avoid having to obtain higher level approval, explained Anderson, a Certified Fraud Examiner in Philadelphia.
In another case, Anderson said, management had a policy that employees did not have to submit copies of receipts for meal expenditures under $25. When a senior sales representative submitted six months of travel reimbursement requests at once, the corporate controller noted that more than 50% of his meal charges in more than 17 different cities were for the same amount – $24.73 – regardless of whether they were for breakfast, lunch or dinner.
As a result, senior management engaged Anderson to analyze travel reimbursement requests for all employees. Anderson, a Philadelphia forensic accountant whose firm provides a full range of forensic accounting services in Philadelphia and the Delaware Valley, found that more than 70% of all employee reimbursement requests for meals were for between $24.00 and $24.99. But under Benford’s Law, more than 70% of all employee meals with a stated cost of under $25.00 should have been less than $20.00, he said.
“The resulting conclusion was that employees were likely abusing the company’s policy,” explained Anderson, a forensic accounting expert in Philadelphia. “Management changed its policy to reimburse employees at the equivalent federal per diem rates. The only exceptions to this were for business meals at which customers or prospects were entertained. In these cases, the employee was required to provide a receipt.”
Two years later, management analyzed its travel meal reimbursements, and found that it was actually spending less than it had prior to the policy change, Anderson said. In this case, the fraudulent behavior was stopped, and the company realized material expense savings, he said.
This blog is the first in a series of four posts that will examine the so-called tricks of the trade that forensic accountants use when conducting fraud investigations.
If you require the services of a Certified Fraud Examiner in Philadelphia or any other forensic accounting services in Philadelphia and the Delaware Valley, please contact the Philadelphia forensic accounting firm of David Anderson & Associates by calling David Anderson at 267-207-3597 or emailing him at firstname.lastname@example.org.
About David Anderson & Associates
David Anderson & Associates is a Philadelphia forensic accounting firm that provides a full range of forensic accounting services in Philadelphia and the Delaware Valley. The experienced professionals at David Anderson & Associates provide forensic accounting, business valuation, fraud investigation, fraud deterrence, litigation support, economic damage analysis, business consulting and outsourced CFO services. Company principal David Anderson is a forensic accounting expert in Philadelphia who has more than 30 years of experience in financial and operational leadership positions and is a Certified Public Accountant, a Certified Valuation Analyst and a Certified Fraud Examiner in Philadelphia.