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Chapter 9 Audit Sampling: An Application to Substantive Tests of Account Balances McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. LO# 1 Substantive Tests of Details of Account Balances The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important determinants of sample size are 1. Desired confidence level. 2. Tolerable misstatement. 3. Estimated misstatement. Population plays a bigger role in some of the sampling techniques used for substantive testing. Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk. 9-2 LO# 1 Substantive Tests of Details of Account Balances Consider the following information about the inventory account balance of an audit client: Book value of inventory account balance Book value of items sampled Audited value of items sampled Total amount of overstatement observed in audit sample $ 3,000,000 $ 100,000 98,000 $ 2,000 The ratio of misstatement in the sample is 2% ($2,000 ÷ $100,000) Applying the ratio to the entire population produces a best estimate of misstatement of inventory of $60,000. ($3,000,000 × 2%) 9-3 LO# 1 Substantive Tests of Details of Account Balances The results of our audit test depend upon the tolerable misstatement associated with the inventory account. If the tolerable misstatement is $50,000, we cannot conclude that the account is fairly stated because our best estimate of the projected misstatement is greater than the tolerable misstatement. 9-4 LO# 2 Monetary-Unit Sampling (MUS) MUS uses attribute-sampling theory to express a conclusion in dollar amounts rather than as a rate of occurrence. It is commonly used by auditors to test accounts such as accounts receivable, loans receivable, investment securities, and inventory. 9-5 Steps in MUS LO# 2 Steps in MUS Application Planning 1. Determine the test objectives. 2. Define the population characteristics: • Define the population. • Define the sampling unit. • Define a misstatement. 3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable misstatement. • The expected population misstatement. • Population size. Performance 4. Select sample items. 5. Perform the auditing procedures. • Understand and analyze any misstatements observed. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement. 7. Draw final conclusions. 9-6 LO# 2 Steps in MUS Steps in MUS Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sampling unit. • Define a misstatement. Sampling may be used for substantive testing to: 1. Test the reasonableness of assertions about a financial statement amount (i.e., accuracy, existence). This is the most common use of sampling for substantive testing. 2. Develop an estimate of some amount. 9-7 LO# 2 Steps in MUS Steps in MUS Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sampling unit. • Define a misstatement. For MUS the population is defined as the monetary value of an account balance, such as accounts receivable, investment securities, or inventory. 9-8 LO# 2 Steps in MUS Steps in MUS Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sampling unit. • Define a misstatement. An individual dollar represents the sampling unit. 9-9 LO# 2 Steps in MUS Steps in MUS Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sampling unit. • Define a misstatement. A misstatement is defined as the difference between monetary amounts in the client’s records and amounts supported by audit evidence. 9-10 LO# 2 Steps in MUS Steps in MUS Application 3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable misstatement. • The expected population misstatement. • Population size. Factor Relationship to Sample Size Desired confidence level Direct Tolerable mistatement Inverse Expected mistatement Direct Population size Direct Change in Factor Lower Higher Lower Higher Lower Higher Lower Higher Effect on Sample Decrease Increase Increase Decrease Decrease Increase Decrease Increase 9-11 LO# 2 Steps in MUS Steps in MUS Application Performance 4. Select sample items. 5. Perform the auditing procedures. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement. 7. Draw final conclusions. The auditor selects a sample for MUS by using a systematic selection approach called probabilityproportional-to-size selection. The sampling interval can be determined by dividing the book value of the population by the sample size. Each individual dollar in the population has an equal chance of being selected and items or “logical units” greater than the interval will always be selected. 9-12 LO# 2 Steps in MUS Assume a client’s book value of accounts receivable is $2,500,000, and the auditor determined a sample size of 93. The sampling interval will be $26,882 ($2,500,000 ÷ 93). The random number selected is $3,977, so the auditor would select the following items for testing: Account 1001 Ace Emergency Center 1002 Admington Hospital 1003 Jess Base, Inc. 1004 Good Hospital Corp. 1005 Jen Mara Corp. 1006 Zippy Corp. 1007 Green River Mfg. 1008 Bead Hospital Centers • • 1213 Andrew Call Medical 1214 Lilly Heather, Inc. 1215 Janyne Ann Corp. Total Accounts Receivable Balance $ 2,350 15,495 945 21,893 3,968 32,549 2,246 11,860 • • 26,945 1,023 $ 2,500,000 Cumulative Dollars $ 2,350 17,845 18,790 40,683 44,651 77,200 79,446 91,306 • • 2,472,032 2,498,977 $ 2,500,000 Sample Item $ 3,977 (1) 30,859 (2) 57,741 (3) 84,623 • • (4) 2,477,121 $ 3,977 26,882 $ 30,859 (93) 9-13 LO# 2 Steps in MUS Steps in MUS Application Performance 4. Select sample items. 5. Perform the auditing procedures. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement. 7. Draw final conclusions. After the sample items have been selected, the auditor conducts the planned audit procedures on the logical units containing the selected dollar sampling units. 9-14 LO# 2 Steps in MUS Steps in MUS Application Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement. 7. Draw final conclusions. The misstatements detected in the sample must be projected to the population. Let’s look at the following example: New Example Information Book value Tolerable misstatement Sample size Desired confidence level Expected amount of misstatement Sampling interval $ 2,500,000 $ 125,000 93 95% $ 25,000 $ 26,882 9-15 LO# 3 Steps in MUS Misstatements Detected In the sample of 93 items, the following misstatements were found: Customer Good Hospital Corp. Marva Medical Supply Learn Heart Centers Axa Corp. Book Value $ 21,893 6,705 15,000 32,549 Audit Value $ 18,609 4,023 0 30,049 Difference $ 3,284 2,682 15,000 2,500 Tainting Factor Diff/BV 0.15 0.40 1.00 NA Because the Axa balance of$3,284 $32,549 greater =than ÷is$21,893 15%the interval of $26,882, no sampling risk is added. Since all the dollars in the large accounts are audited, there is no sampling risk associated with large accounts. 9-16 LO# 3 Steps in MUS Computed Upper Misstatement Limit We compute the upper misstatement limit by calculating basic precision and ranking the detected misstatements based on the size of the tainting factor from the largest to the smallest. Tainting Factor 1.00 1.00 0.40 0.15 Customer Basic Precision Learn Heart Centers Marva Medical Good Hospital Add misstatments greater than the sampling interval: Axa Corp. NA Sample Interval $ 26,882 26,882 26,882 26,882 Projected Misstatement NA 26,882 10,753 4,032 26,882 2,500 Upper Misstatement Limit (0.15 × $26,882 × 1.4 = $5,645) 95% Upper Limit 3.0 1.7 (4.7 - 3.0) 1.5 (6.2 - 4.7) 1.4 (7.6 - 6.2) Upper Misstatement $ 80,646 45,700 16,130 5,645 $ 2,500 150,621 9-17 LO# 3 Steps in MUS Basic Precision using the Table If no misstatements are found in the sample, the best estimate of the population misstatement would be zero dollars but we would still want to add an allowance for sampling risk. Number of Errors 0 1 2 3 4 90% Confidence Level Misstatement Incremental Factor Increase 2.3 3.9 1.6 5.3 1.4 6.6 1.3 7.9 1.3 95% Confidence Level Misstatement Incremental Factor Increase 3.0 4.7 1.7 6.2 1.5 7.6 1.4 9.0 1.4 $26,882 × 3.0 = $80,646 upper misstatement limit 9-18 LO# 3 Steps in MUS Steps in MUS Application Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement 7. Draw final conclusions. In our example, the final decision is whether the accounts receivable balance is materially misstated or not. We compare the tolerable misstatement to the upper misstatement limit. If the upper misstatement limit is less than or equal to the tolerable misstatement, we conclude that the balance is not materially misstated. 9-19 LO# 3 Steps in MUS In our example, the upper misstatement limit of $150,621 is greater than the tolerable misstatement of $125,000, so the auditor concludes that the accounts receivable balance is materially misstated. When faced with this situation, the auditor may: 1. Increase the sample size. 2. Perform other substantive procedures. 3. Request the client adjust the accounts receivable balance. 4. If the client refuses to adjust the account balance, the auditor would consider issuing a qualified or an adverse opinion. 9-20 LO# 3 Risk When Evaluating Account Balances True State of Financial Statement Account Auditor's Decision Based on Sample Evidence Supports the fairness of the account balance Does not support the fairness of the account balance Not Materially Misstated Correct decision Risk of incorrect rejection (Type I) Materially Misstated Risk of incorrect acceptance (Type II) Correct Decision 9-21 LO# 3 Effect of Understatement Misstatements MUS is not particularly effective at detecting understatements. An understated account is less likely to be selected than an overstated account. Customer Wayne County Medical Book Value $ 2,000 Audit Value $ 2,200 Difference $ (200) Tainting Factor -10% The most likely error will be reduced by $2,688 (– 0.10 × $26,882) 9-22