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Chapter 9 Audit Sampling: An Application to Substantive Tests of Account Balances McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved Purpose To determine if a financial statement account is fairly stated. Sampling Techniques Statistical - Monetary Unit Sampling ( MUS) - Classical variable sampling Non-statistical 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. 9-4 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%) 9-5 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. 9-6 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 uses attribute-sampling theory (used primarily to test controls) to estimate 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. The calculation of the sample size and evaluation of the sample results are not based on the variation between items in the population. 3. When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample. 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 LO# 2 Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample 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 an alayzye any missstatements observed. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement. 7. Draw final conclusions. 9-11 LO# 2 Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample 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., is the amount fairly stated). This is the most common use of sampling for substantive testing. 2. Develop an estimate of some amount. 9-12 LO# 2 Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample 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. 9-13 LO# 2 Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement. An individual dollar represents the sampling unit. 9-14 LO# 2 Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample 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. 9-15 LO# 2 Steps in MUS Sampling Steps in MUS Sampling 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 9-16 LO# 2 Steps in MUS Sampling Steps in MUS Sampling 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. 9-17 LO# 3 Steps in MUS Sampling 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 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 Cumulatvie Dollars $ 2,350 17,845 18,780 40,673 44,641 77,190 79,436 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) 9-18 LO# 3 Steps in MUS Sampling Steps in MUS Sampling 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. 9-19 LO# 3 Steps in MUS Sampling Steps in MUS Sampling 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. 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 9-20 LO# 3 Steps in MUS Sampling Basic Precision using the Tables If no misstatements are found in the sample, the best estimate of the population misstatement would be zero dollars. Sample Size 65 70 85 80 90 100 125 Actual Number of Deviations Found 0 1 2 3 4.6 7.1 9.4 11.5 4.2 6.6 8.8 10.8 4.0 6.2 8.2 10.1 3.7 5.8 7.7 9.5 3.3 5.2 6.9 8.4 3.0 4.7 6.2 7.6 2.4 3.8 5.0 6.1 $26,882 × 3.0 = $80,646 upper misstatement limit 9-21 LO# 3 Steps in MUS Sampling Misstatements Detected In the sample of 93 items, the following misstatements were found: Customer Good Hospital Marva Medical Supply Axa Corp. Learn Heart Centers Book Value $ 21,893 6,705 32,549 15,000 Audit Value $ 18,609 4,023 30,049 - Difference $ 3,284 2,682 2,500 15,000 Tainting Factory 15% 40% NA 100% Because the Axa balance of$3,284 $32,549 is greater than the ÷ $21,893 = 15% 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. 9-22 LO# 3 Steps in MUS Sampling Computed Upper Misstatement Limit using Tables 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. Customer Basic Precision Learn Heart Centers Marva Medical Good Hospital Add misstatments greater that the sampling interval: Axa Corp. Tainting Factor 1.00 1.00 0.40 0.15 NA Sample Interval $ 26,882 26,882 26,882 26,882 Projected Misstatement NA (26,882) (10,753) (4,032) 26,882 NA 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 9-23 LO# 3 Steps in MUS Sampling Steps in MUS Sampling 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. 9-24 LO# 3 Steps in MUS Sampling 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 adverse opinion. 9-25 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 9-26 Why is the Sampling Interval Rather than the Sample Size Used in Evaluating MUS Results? LO# 3 Due to simplifying assumptions about accounting populations, the misstatement factors used in most MUS evaluation approaches are nearly identical to the misstatement factors associated with a sample size of 100, regardless of the actual sample size used by the auditor. Always use these factors: Number of Errors 0 1 2 3 4 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 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 9-27 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) 9-28 LO# 4 Nonstatistical Sampling for Tests of Account Balances The sampling unit for nonstatistical sampling is normally a customer account, an individual transaction, or a line item on a transactions. When using nonstatistical sampling, the following items must be considered: o Identifying individually significant items. o Determining the sample size. o Selecting sample items. o Calculating the sample results. 9-29 LO# 4 Identifying Individually Significant Items The items to be tested individually are items that may contain potential misstatements that individually exceed the tolerable misstatement. These items are tested 100% because the auditor is not willing to accept any sampling risk. 9-30 LO# 4 Determining the Sample Size Sampling Population book value Sample = Tolerable – Expected misstatement × Assurance factor Size Assessment of Risk of Material Misstatement Maximum Slightly below maximum Moderate Low Desired Level of Confidence Slightly Below Maximum Maximum Moderate 3.0 2.7 2.3 2.7 2.4 2.0 2.3 2.1 1.6 2.0 1.6 1.2 Low 2.0 1.6 1.2 1.0 9-31 LO# 4 Selecting Sample Items Auditing standards require that the sample items be selected in such a way that the sample can be expected to represent the population. 9-32 LO# 4 Calculating the Sample Results One way of projecting the sampling results to the population is to apply the misstatement ratio in the sample to the population. Assume the auditor finds $1,500 in misstatements in a sample of $15,000. The misstatement ratio is 10%. If the population total is $200,000, the projected misstatement would be $20,000 ($200,000 × 10%) 9-33 LO# 4 Calculating the Sample Results A second method is the difference estimation. This method projects the average misstatement of each item in the sample to all items in the population. Assume misstatements in a sample of 100 items total $300 (for average misstatement of $3), and the population contains 10,000 items. The projected misstatement would be $30,000 ($3 × 10,000). 9-34 LO# 4 Nonstatistical Sampling Example The auditor’s of Calabro Wireless Service have decided to use nonstatistical sampling to examine the accounts receivable balance. Calabro has a total of 11,800 (15 + 250 + 11,535) accounts with a balance of $3,717,900. The auditor’s stratify the accounts as follows: Number and Size of Accounts 15 accounts > $25,000 250 accounts > $3,000 11,535 accounts < $3,000 Total Book Value $ 550,000 850,500 2,317,400 $ 3,717,900 9-35 LO# 4 Nonstatistical Sampling Example The auditor’s decide . . . o There is a low assessment for inherent and control risk. o The tolerable misstatement is $40,000, and the expected misstatement is $15,000. o There is a moderate risk that other auditing procedures will fail to detect material misstatements. o All customer account balances greater than $25,000 are to be audited. 9-36 Nonstatistical Sampling Example LO# 4 Sampling population book value Sample = Tolerable - Estimated misstatement × Assurance factor Size $3,717,900 – $550,000 Sample = Size $3,167,900 $40,000 × 1.2 = 95 (rounded) $55,000 – $15,000 Combined Assessment of Inherent and Control Risk Maximum Slightly below maximum Moderate Low Risk That Other Substantive Procedures Fail to Detect Material Misstatement Slightly Below Maximum Maximum Moderate Low 3.0 2.7 2.3 2.0 2.7 2.4 2.0 1.6 2.3 2.1 1.6 1.2 2.0 1.6 1.2 1.0 9-37 Nonstatistical Sampling Example LO# 4 The auditor sent positive confirmations to each of the 110 (95 + 15) accounts selected. Either the confirmations were returned or alternative procedures were successfully used. Four customers indicated that their accounts were overstated and the auditors determined that the misstatements were the result of unintentional error by client personnel. Here are the results of the audit testing: Stratum >$25,000 >$3,000 <$3,000 Book Value $ 550,000 850,500 2,317,400 Book Value of Sample $ 550,000 425,000 92,000 Audit Value of Sample $ 549,500 423,000 91,750 Amount of OverStatement $ 500 2,000 250 9-38 Nonstatistical Sampling Example LO# 4 As a result of the audit procedures, the following projected misstatement was prepared: Amount of Ratio of Misstatement Stratum Misstatement in Stratum Tested >$25,000 $ 500 Not Applicable--100% Tested >$3,000 2,000 $2,000 ÷ 425,000 × $850,500 <$3,000 250 $250 ÷ 92,000 × $2,317,400 Total projected misstatement Projected Misstatement $ 500 4,002 6,298 $ 10,800 The total projected misstatement of $10,800 is less than the expected misstatement of $15,000, so the auditors may conclude that there is an acceptably low risk that the true misstatement exceeds the tolerable misstatement. 9-39 LO# 4 Why Did Statistical Sampling Fall Out Of Favor? 1.Firms found that some auditors were over relying on statistical sampling techniques to the exclusion of good judgment. 2.There appears to be poor linkage between the applied audit setting and traditional statistical sampling applications. 9-40 LO# 5 Classical Variable Sampling Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data. Auditors most commonly use classical variables sampling to estimate the size of misstatement. Sampling distributions are formed by plotting the projected misstatements yielded by an infinite number of audit samples of the same size taken from the same underlying population. 9-41 LO# 5 Classical Variables Sampling A sampling distribution is useful because it allows us to estimate the probability of observing any single sample result. 9-42 LO# 5 Classical Variables Sampling In classical variables sampling, the sample mean is the best estimate of the population mean. 9-43 LO# 5 Classical Variables Sampling Advantages 1. When the auditor expects a large number of differences between book and audited values, this method will 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. 9-44 LO# 5 Classical Variables Sampling Disadvantages 1. Does not work well when little or not misstatement is expected in the population. 2. To determine sample size, the auditor must estimate the standard deviation of the audited value or differences. 3. If few misstatements are detected in the sample data, the true variance tends to be underestimated, and the resulting projection of the misstatements to the population is likely not to be reliable. 9-45 End of Chapter 9 9-46