Problem DC 10-2, Page 547 What is K? The confidence factor. 1 2 3 4 5 The following are auditor judgments and audit sampling results for six populations. Assume large population sizes. 1 2 3 4 5 6 TER (in percentage) 8 20 15 ARACR (in percentage) 10 Actual sample size 100 60 Actual number of exceptions in the sample REQUIRED For each population, did the auditor select a smaller sample size than is indicated by using attribute sampling tables for determining sample size? (Assume K=0 in sample size planning). Evaluate, selecting either a larger or smaller size than those determined in the tables. Calculate Sample Deviation Rate (SDR) and Upper Error Limit (UEL) for each population. For which of the six populations should the sample results be considered unacceptable? What options are available to the auditor? Why is analysis of the exceptions necessary even when the populations are considered acceptable? For the following terms, identify which is an audit decision, which is a non-statistical estimate made by the auditor, which is a sample result, and which is a statistical conclusion about the population. Estimated population deviation rate. Tolerable deviation rate. Acceptable risk of overreliance on internal control. Actual sample size. Actual number of deviations in the sample. Sample deviation rate. Achieved P or UEL What is K? The confidence factor.

Confidence Factors for MUS Sample Size Design (ARIA in brackets) Same Table 11-8, Page 355 – for calculating K Number of Errors Confidence Factors for MUS Sample Size Design (ARIA in brackets) 99% (1%) 97.5% (2.5%) 95% (5%) 90% (10%) 85% (15%) 80% (20%) 75% (25%) 4.51 3.69 3.00 2.31 1.90 1.61 1.39 1 6.64 5.58 4.75 3.89 3.38 2.70 2 8.41 7.23 6.30 5.33 4.73 4.28 3.93 3 10.05 8.77 7.76 6.69 6.02 5.52 5.11 4 11.61 10.25 9.16 8.00 7.27 6.73 6.28 5 13.11 11.67 10.52 9.28 8.50 7.91 7.43 6 14.58 13.06 11.85 10.54 9.71 9.08 8.56 7 16.00 14.43 13.15 11.78 10.90 10.24 9.69 8 17.41 15.77 14.44 13.00 12.08 11.38 10.81 9 18.79 17.09 15.71 14.21 13.25 12.52 11.92 10 20.15 18.40 16.97 15.41 14.42 13.66 13.03 In this example K will either be 3.00, or 2.31, depending on the value of ARIA

ACTUAL NUMBER OF DEVIATIONS FOUND Sample size ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10 5 PERCENT RISK OF OVER RELIANCE (RIA or Beta Risk) 20 14.0 21.7 28.3 34.4 40.2 45.6 50.8 55.9 60.7 65.4 69.9 25 11.3 17.7 23.2 28.2 33.0 37.6 42.0 46.3 50.4 54.4 58.4 30 9.6 14.9 19.6 23.9 28.0 31.9 35.8 39.4 43.0 46.6 50.0 35 8.3 12.9 17.0 20.7 24.3 27.8 31.1 37.5 40.6 43.7 40 7.3 11.4 15.0 18.3 21.5 24.6 27.5 30.4 33.3 36.0 38.8 45 6.5 10.2 13.4 16.4 19.2 22.0 24.7 27.3 29.8 32.4 34.8 50 5.9 9.2 12.1 14.8 17.4 19.9 22.4 27.1 29.4 31.6 55 5.4 8.4 11.1 13.5 15.9 18.2 20.5 22.6 24.8 26.9 28.9 60 4.9 7.7 12.5 14.7 16.8 18.8 20.8 22.8 26.7 65 4.6 7.1 9.4 11.5 13.6 15.5 17.5 19.3 21.2 23.0 70 4.2 6.6 8.8 10.8 12.7 14.5 16.3 18.0 19.7 21.4 23.1 75 4.0 6.2 8.2 10.1 11.8 15.2 16.9 18.5 20.1 21.6 80 3.7 5.8 9.5 14.3 18.9 20.3 90 3.3 5.2 6.9 9.9 12.8 14.2 100 3.0 4.7 7.6 9.0 10.3 125 2.4 3.8 5.0 6.1 7.2 9.3 12.3 13.2 150 2.0 3.2 5.1 6.0 7.8 8.6 200 1.5 3.9 300 1.0 1.6 2.1 2.6 3.1 3.5 4.4 4.8 5.6 400 0.8 1.2 2.3 2.7 3.6 4.3 500 0.6 1.3 1.9 2.9 3.4

ACTUAL NUMBER OF DEVIATIONS FOUND Sample size ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10 10 % Risk of Incorrect Acceptance (RIA or Beta Risk) 20 10.9 18.1 24.5 30.5 36.1 41.5 46.8 51.9 56.8 61.6 66.2 25 8.8 14.7 20.0 24.9 29.5 34.0 38.4 42.6 50.8 54.8 30 7.4 12.4 16.8 21.0 28.8 32.5 36.2 39.7 43.2 46.7 35 6.4 10.7 14.5 18.2 21.6 28.2 31.4 34.5 37.6 40.6 40 5.6 9.4 12.8 16.0 19.0 22.0 27.7 33.2 35.9 45 5.0 8.4 11.4 14.3 17.0 19.7 22.3 24.8 27.3 29.8 32.2 50 4.6 7.6 10.3 12.9 15.4 17.8 20.2 22.5 24.7 27.0 29.2 55 4.2 6.9 11.8 14.1 16.3 18.4 20.5 22.6 24.6 26.7 60 3.8 8.7 10.8 15.0 16.9 18.9 20.8 22.7 65 3.5 5.9 8.0 10.0 12.0 13.9 15.7 17.5 19.3 22.8 70 3.3 5.5 7.5 9.3 11.1 14.6 18.0 19.6 21.2 75 3.1 5.1 7.0 10.4 12.1 13.7 15.2 18.3 19.8 80 2.9 4.8 6.6 8.2 9.8 11.3 15.8 17.2 18.7 90 2.6 4.3 7.3 10.1 11.5 16.7 100 2.3 3.9 5.3 7.9 9.1 12.7 125 1.9 6.3 8.3 10.2 11.2 150 1.6 3.6 4.4 6.1 7.8 8.6 200 1.2 2.0 2.7 3.4 4.0 6.5 7.1 300 0.8 1.3 1.8 4.7 400 0.6 1.0 1.4 1.7 2.4 3.0 500 0.5 1.1 2.1

Solution to DC 10-2 Note: K = the number of expected errors, and P = TER. See table on the next page. Case 1: K = 3, and P = 6%. Thus n = 3/0.06 = 50 Case 2: K = 3, and P = 3%. Thus n = 3/0,03 = 100 Case 3: K = 2.31, and P = 8%. Thus n = 2.31/0.08 = 29 Case 4: K = 3, and P = 5%. Thus n = 3/0.05 = 60 Case 5: K = 2.31, and P = 20%. Thus n = 2.31/.2 = 12 Case 6: K = 2.31,and P = 15%. Thus n = 2.31/.15 = 16 Anything larger than these discovery sample sizes reduces efficiency risk, while effectiveness risk (1 – confidence level) remains constant. i.e. the auditor is doing to much work. Not being efficient. Anything smaller than a discovery sample size means that the auditor has more effectiveness risk than planned. i.e. the auditor is not being effective.

Using the tables from the following two pages: Case 1: Actual sample size = 100, number of deviations = 2, and ARACR = 5%. SDR = 2/100 = 2%, From the table - UEL = 0.062 Case 2: Actual sample size = 100, number of deviations = 0, and ARACR = 5%. SDR = 0, UEL = 0.030 Case 3: Actual sample size = 60, number of deviations = 1, and ARACR = 10%. SDR = 1/60 = 1.7%, UEL = 0.064 Case 4: Actual sample size = 100, number of deviations = 4, and ARACR = 5%. SDR = 4/100 = 4%, UEL = 0.090 Case 5: Actual sample size = 20, number of deviations = 1, and ARACR = 10%. SDR = 1/20 = 5%, UEL = 0.181 Case 6: Actual sample size = 60, number of deviations = 8, and ARACR = 10%. SDR = 8/60 = 13.3%, UEL = 0.208

The population results are unacceptable for cases 1, 4, and 6 The population results are unacceptable for cases 1, 4, and 6. . In each of those cases, the UEL exceeds TER. The auditor’s options are to; change tolerable exception rate or ARACR increase the sample size or perform other substantive tests to determine whether there are actually material errors in the population   Sources of error helps auditor asses whether error is intentional or unintentional, and to assess qualitative aspects of internal control (for example, whether a particular individual, department, or time period is affected). 1. auditor estimate 2. auditor decision 3. auditor decision 4. auditor decision, or by formula 5. sample result 6. sample result 7. sample result: achieved P or UEL is the maximum error rate at the stated confidence level.

Problem DC 11-4, Page 612 Control Weakness: Shipping and Billing: Ajax Inc. recently implemented a new accounting system to process the shipping, billing, and accounts receivable records more efficiently. During the interim work of Ajax’s auditors an assistant completed the review of the accounting system and the internal controls. The assistant determined the following information concerning the computer systems and the processing and control of shipping notices and customer invoices. The computer system documentation consists of the following items: program listings, error listings, logs, and database dictionaries. The system and documentation are maintained by the IT administrator. To increase efficiency, batch totals, and processing controls are not used in the system. Ajax ships its product directly from two warehouses, which forward shipping invoices to general accounting. There, the billing clerk enters the price of the item and accounts for the numerical sequence of the shipping notices. The billing clerk also manually prepares daily adding machines tapes of the units shipped and the sales amounts. The computer processing output consists of the following: A three-copy invoice that is forwarded to the billing clerk A daily sales register showing the aggregate total of units shipped and sales amounts that the billing clerk compares with the adding machine tapes The billing clerk mails two copies of each invoice to the customer and retains the third copy in an open invoice file that serves as detailed accounts receivable record. Required: Prepare a list of weaknesses in internal control (manual and computer), and for ,each weakness make one or more recommendations. Suggest how Ajax’s computer processing over shipping and billing could be improved through the use of remote terminals to enter shipping notices. Describe appropriate controls for such an online data entry system.

a) Weaknesses Recommendations Lack of segregation of duties   Recommendations Lack of segregation of duties The billing clerk both enters sales data and checks the output. There is a risk that errors will not be detected when a person is checking his or her own work. There is an opportunity for shipper and billing clerk to cover up unauthorized shipments since no one but the billing clerk checks that valid invoices are issued for every shipment. Deficient documentation Need documentation of flowcharts, program changes, systems software, testing. Lack of control totals Error-checking validations need control totals for effective operation. No computer price list For manual entry process, clerk should not need to enter the sales price. It should be in a database. Numerical sequence The computer should be used to check numerical sequence. Control total The billing clerk’s control total of sales should be used to compare to total sales processed by the computer. Customer accounts The computer system should be used to maintain customer accounts instead of using a manual open invoice file.

Shipping clerks could enter the date, customer identification, shipment quantities, and product identification numbers in a terminal. Then the computer system could automatically produce a sales invoice. Controls include:   Autoclock date checking Self-checking customer identification numbers Self-checking product identification numbers Terminal batch hash total of customer ID numbers Automatic numbering of sales invoices Authorized price list in database Control total comparison of hash ID numbers in run-to-run totals