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Chapter 9 Audit Sampling: An Application to Substantive Tests of Account Balances Note: this presentation focuses on MUS. It omits nonstatistical sampling and only briefly discusses Advanced Module 1 on Classical Variables Sampling. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. LO# 1 Substantive Tests of Details of Account Balances Sometime, auditors use Monetary Unit Sampling (MUS), sometimes Variables (or Classical Variables) Sampling, and sometimes other methods of statistical inference. Our text discusses only MUS in the main part of the chapter. MUS is also known as dollar-unit sampling or probability-proportional-to-size sampling. Classical Variables Sampling is discussed in Module 1 (which we do not study in depth). Thus, our focus of study in Chapter 9 is MUS. It is arguably the most important method. Assume I am referring to MUS throughout this presentation unless I state otherwise. 9-2 LO# 1 Substantive Tests of Details of Account Balances Some statistical concepts in Chapter 8 also apply to Chapter 9. In fact, when using the textbook to determine the right sample size, we use Table 8-5. Take a look now at Table 8-5: 1. Desired confidence level – similar to Ch. 8 2. Tolerable Misstatement – analogous to Tolerable Deviation Rate of Ch. 8 3. Estimated misstatement – analogous to Expected Population Deviation Rate of Ch. 8 However, there are some things very different in Ch. 9. A fourth factor is very important for determining the right sample size: 4. Population – number of dollars in an account balance 9-3 Illustration of the MUS approach The next 2 slides demonstrate (as does p. 312 of the 8th edition of your text) the MUS approach They do not demonstrate correct MUS They merely demonstrate an approach somewhat like MUS LO# 1 Illustration slide 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%) 9-5 LO# 1 Illustration slide 2: 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. 9-6 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. 9-7 LO# 2 Monetary-Unit Sampling (MUS) MUS estimates the percentage of monetary units in a population that might be misstated and then multiplies this percentage by an estimate of how much the dollars are misstated. 9-8 LO# 2 Monetary-Unit Sampling (MUS) Advantages of MUS 1. When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling. 2. When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample. 3. MUS does not require the user to make assumptions about the distribution of misstatements. 9-9 LO# 2 Monetary-Unit Sampling (MUS) Disadvantages of MUS 1. The selection of zero or negative balances generally requires special design consideration. 2. The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100%. 3. When more than one or two misstatements are detected, the sample results calculations may overstate the allowance for sampling risk. 9-10 Terms for MUS determination of right sample size: Text vs. ACL Monetary Unit Sampling – The ACL GUI calls this Monetary Desired Confidence Level – ACL calls this Confidence Tolerable Misstatement (%) – ACL calls this Materiality Expected Misstatement (%) – ACL calls this Expected Total Errors Sampling Interval – ACL calls this Interval 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. 9-12 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. MUS is usually used to test the reasonableness of assertions about a financial statement amount (i.e., is the dollar amount materially correct). 9-13 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 number of dollars in an account balance, such as accounts receivable, investment securities, or inventory. 9-14 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. 9-15 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 the difference between monetary amounts in the company’s records and amounts supported by audit evidence. For example, the company records that a customer owes it $10,000 as of the fiscal year end; the auditor reviews the support documentation and determines only $6000 was owed. That would be a $4000 misstatement. 9-16 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 9-17 LO# 2 Sample Selection 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 probability-proportional-to-size selection. This requires (either manually or by having software like ACL do it) calculation of the sampling interval. Manual calculation of the sampling interval is book value (pre-audit recorded amount of the account or population) divided by the sample size. 9-18 Sample Selection (continued) Each dollar in the population has an equal chance of being selected and items or “logical units” greater than the interval will always be selected. However, no item will be selected more than once. – Consequently, the number of items selected, which is the actual size of the sample, almost always is smaller than the formal sample size. 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) 9-20 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. 9-21 LO# 2 Steps in MUS 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,” which means determining the allowance for sampling risk. The process for determining the allowance for sampling risk is more complex for MUS than it was in Ch. 8. It involves two components: Basic Precision: general sampling risk; and Sampling risk associated with each misstatement found where the item was (pre-audit) less than the sample interval. 9-22 Comparison of textbook terms vs. ACL terms for MUS results evaluation Monetary Unit Sampling – ACL: Monetary Sampling Interval – ACL: Interval Misstatements or Differences – ACL: Errors Upper Misstatement Limit (the analog to Ch. 8’s CUDR) – ACL: Upper Error Limit Evaluation of the results in MUS The next slide discusses, using the example below, Basic Precision. Subsequent slides show the allowance for sampling risk related to specific misstatements found where the item misstated was (pre-audit or book value) less than the sampling interval, and then show all the information put together. 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 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. 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 9-25 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 specifically associated with large accounts. 9-26 LO# 3 Steps in MUS 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 9-27 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. Compare Tolerable Misstatement to the Upper Misstatement Limit. If the Upper Misstatement Limit is greater than the Tolerable Misstatement, we conclude that the balance is materially misstated. 9-28 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. 9-29 LO# 5 Classical Variables Sampling There are some situations where MUS does not work well. Thus, auditors turn to other statistical methods. The most common method they turn to is classical variables sampling (also called variable sampling). 9-30 LO# 5 Classical Variables Sampling Advantages 1. When the auditor expects a large number of misstatements or differences between book and audited values, this method will normally result in smaller sample size than MUS. 2. The techniques are effective for both overstatements and understatements. 3. The selection of zero balances generally does not require special sample design considerations. 9-31 LO# 5 Classical Variables Sampling Disadvantages 1. Does not work well when little or no misstatement is expected in the population. 2. To determine sample size, the auditor must estimate the standard deviation of the audit differences. If the estimate is sufficiently wrong, the statistical results could be completely wrong. 9-32 End of Chapter 9 9-33