James Balcom shook his head in frustration as he re-examined the preliminary financial statements for the year ending November 4, 1979. As the proprietor of the Bromleigh Avenue Mini-Market in Longborough, Leicestershire, England, Mr. Balcom was not surprised to see that the trading results for the market had shown a significant downturn since the previous fiscal year but he was surprised that the latest preliminary financial results were so bad. He was not sure that the business could continue without some major changes being made. There was, however, one mitigating circumstance; he knew that some of last year's revenues had been stolen by one of his employees. Perhaps these losses had been much greater than he first thought. He had little hard evidence to support his suspicions, however, and wondered how to use the limited information he did have to investigate this issue. The Bromleigh Avenue Business Mr. Balcom had first established his Mini-market in November, 1972. The shop carried a range of tobacco, newspapers, popular food and grocery lines and some specialty items, and had been successful through its early years of operation. The auditors' report, received by Mr. Balcom in mid-March, 1979, presented a very different picture. The quarter just ended had been a poor one. More ominously, the auditors believed that someone connected with the business was regularly stealing either cash or merchandise from the firm. Mr. Balcom took the auditors' concerns to heart, and began watching his employees for signs of dishonesty. Early in May, he noticed one of his shop assistants, Mrs. Ruth Faringham, ringing amounts of 1p and 2p into the cash register. Since the shop did not carry any items priced lower than 5p, Mr. Balcom was at once suspicious. He informed the police of his problem, and plain-clothes officers began making spot purchases in the shop. Mrs. Faringham was twice observed by the police to be understriking the purchase 1 This case was written by Professors Peter C. Bell and John S. Hulland for the sole purpose of providing material for class discussion. The authors acknowledge the assistance of Mr. David G. Johnson who provided much of the information that is used in this case. amount on the cash register. Understriking involved ringing a smaller amount into the register than the actual value of the purchase, followed by theft of the difference from the till at a later time. During the week ending June 16, 1979, Mrs. Faringham was arrested for theft. A court case followed. During the proceedings, Mrs. Faringham admitted to stealing 52 and 8 on the two occasions observed. She also admitted to having stolen a total of 250 from the business, starting in February, 1979, and ending when she was arrested. Based on the police testimony and her own confession, Mrs. Faringham was found guilty of theft of 250. Searching the Records Mr. Balcom found the outcome of the trial highly unsatisfactory since he suspected that the amount stolen was much greater than that admitted. Since opening the business in 1972, he had kept weekly records of the number of customers, the total value of sales rung up, and the difference between the register reading and the actual amount of money in the cash register till. He wondered if examination of these records for the past year might provide a more realistic estimate of the total amount stolen from the shop. In order to estimate the true magnitude of his losses, Mr. Balcom consulted an auditor with experience in the area of fraud detection. He discovered that while understriking that has been done carefully is often difficult to detect, there are four characteristic symptoms that may be in evidence. First, understriking is often disguised by ringing in a no sale or a small amount right after the incorrect sale. Customers seldom notice the incorrect entry. If this practice is employed, however, the average revenue per customer drops, since total revenue is being reduced at the same time as the number of customers is being increased. A second possible indication of understriking is, therefore, an inflation of the total number of customers. A third indicator of understriking follows from the first two. If no-sale entries are being used to conceal understriking with any regularity, then the total number of no-sales or small amounts will also be inflated. Finally, in large scale theft, money is often left in the till until no customers are around to watch its removal. The thief has to remember the amount by which sales were understruck on each occasion and keep track of the total owing from the till. It is quite easy for the thief to forget the exact amount stolen and there is a tendency for the thief to be overly cautious, removing less money from the till than the total which was actually understruck. Consequently, the till contains more money than is recorded on the till register, creating a positive till difference. Normally, one would expect the till differences due to routine errors to average out to zero over time, but consistent understriking often results in a consistently positive till difference. The weekly records collected for the year begun in November 1978 are given in Exhibit 1, with the revenue per customer figures already calculated. Mr. Balcom realized that the data would have to be adjusted to eliminate the effects of seasonality and inflation before any comparisons could be made. He calculated weekly seasonal indices, for both revenue per customer and the number of customers, using his records for the previous six years. He also obtained weekly inflation figures for the period in question, in order to further adjust the revenue data. These indices are presented week-by-week in Exhibit 2. The Magnitude of the Theft Armed with the information he had collected, Mr. Balcom wondered how to proceed. If he used Mrs. Faringham's confession to establish the period of theft, he should closely examine the data following February 24 [week 17] (when she claimed she had started stealing) through to June 16 [week 32] (when she was arrested). He was suspicious that some theft had occurred prior to February 24, but was unsure as to how to identify the real starting date. Nor did he have a clear idea as to how to go about estimating the full extent of his loss. His only certainty, as he sat down to examine the data again, was that he wanted to get some answers as quickly as possible. SUGGESTED ASSIGNMENTS3 1. Use the data to strengthen the theft case against Mrs. Faringham with respect to the 16 weeks starting February 24, 1979. 2. Examine the time series data. Can you identify when the stealing started? 3. Estimate the total amount of the theft. EXHIBIT 1 Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 REVENUE PER CUSTOMER 70 70 85 97 115 132 160 85 60 64 59 58 58 60 59 60 55 49 54 64 54 53 59 59 55 61 56 59 63 53 59 65 73 68 76 80 72 65 73 71 73 73 73 74 70 66 66 48 67 76 71 77 NUMBER OF CUSTOMERS 1 164 1 339 1 198 1 489 1 524 2 041 3 441 1 294 1 511 1 119 1 180 1 335 1 349 1 409 1 216 1 422 1 475 1 294 1 187 1 379 1 394 1 458 1 418 1 470 1 229 1 307 1 423 1 421 1 314 1 358 1 239 1 354 1 216 1 205 1 247 1 414 826 1 045 1 060 1 053 1 054 1 090 1 194 1 118 1 162 1 268 1 110 1 232 1 257 1 244 1 213 1 312 TILL DIFFERENCE 15 -183 -820 -438 463 -116 410 -538 -149 281 12 -185 57 230 24 72 158 395 223 19 333 -165 715 903 -159 -83 11 -8 167 -156 392 15 -117 -39 -1 8 494 -28 38 -52 -147 -225 -194 -183 237 -71 -169 -1 71 -34 -80 95 1. These records begin with the week ended November 11, 1978, and carry through an entire year