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CHAPTER 13 AUDIT SAMPLING Learning Check 13-1. No. Audit sampling is applicable to both tests of controls and substantive tests. However, it is not equally applicable to all auditing procedures. For example, it is widely used in vouching, confirming, and tracing, but it is ordinarily not used in inquiring, observing, and analytical procedures. 13-2. a. Sampling risk relates to the possibility that a properly drawn sample may not be representative of the population from which it is drawn. Nonsampling risk refers to the portion of audit risk that is not due to examining only a portion of the data. b. There are two types of sampling risks for tests of controls and two for substantive tests. The types of sampling risk and their potential effects on the audit are: Tests of controls: The risk of assessing control risk too low is the risk that the assessed level of control risk based on the sample supports the planned assessed level of control risk when the true operating effectiveness of the control structure policy or procedure, if known, would not be considered adequate to support the planned assessed level. The risk of assessing control risk too high is the risk that the assessed level of control risk based on the sample does not support the planned assessed level of control risk when the true operating effectiveness of the control structure policy or procedure, if known, would be considered adequate to support the planned assessed level. Substantive tests: The risk of incorrect acceptance is the risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated. The risk of incorrect rejection is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated. The risk of assessing control risk too low and the risk of incorrect acceptance relate to audit effectiveness. The risk of assessing control risk too high and the risk of incorrect rejection relate to the efficiency of the audit. 13-3. a. Both nonstatistical and statistical sampling (1) require the exercise of judgment, (2) can provide sufficient evidential matter required by the third standard of field work, and (3) are subject to some sampling and nonsampling risk. The critical difference is that the laws of probability are used to measure and control sampling risk in statistical sampling. b. Statistical sampling benefits the auditor in (1) designing an efficient sample, (2) measuring the sufficiency of the evidence obtained, (3) evaluating sample results, and (4) quantifying and controlling sampling risk. 13-4. a. The types of statistical sampling techniques used in auditing are attribute sampling and variables sampling. b. Attribute sampling is used in tests of controls to estimate the rate of deviations from prescribed controls in a population. Variables sampling is used in substantive tests to estimate the total dollar amount of a population or the dollar amount of error in a population. 13-5. a. The primary purpose of a test of controls is to estimate the rate of deviations from prescribed controls in a population. For example, the auditor wants to estimate the percentage of the time that a specific internal controls fails to function as designed. b. The primary purpose of a substantive test is to estimate the total dollar amount of a population or the dollar amount of error in a population. For example, the auditor wants to estimate the amount by which total accounts receivable might be misstated and determine whether the potential misstatement is material to the financial statements. 13-6. The concepts associated with audit sampling does not apply to the following tests of controls: Tests that rely primarily on inquiry and observation. (e.g., many tests of the control environment, tests of segregation of duties, or observation of physical controls). Tests of computer application controls because they can test a programmed decision point with only two elements of test data (one test to determine that the control appropriately accepts transactions that meet the control criteria and one to see that it appropriately rejects transactions that fail to meet control criteria). Tests of computer application controls that may show exceptions on a computer screen and prevent further processing of a transaction (Tested with inquiry and observation, and by submitting transactions that may generate expected error messages). 13-7. a. Five types of control procedures where the auditor is likely to use some form of nonstatistical sampling for tests of controls include: (1) programmed control procedures, (2) computer general control procedures, (3) manual follow-up of exceptions identified by programmed controls, (4) management performance reviews, and (5) controls over management discretion in financial reporting. Other examples might include controls over management’s use of spreadsheets in the financial reporting process, or tests of the control environment. b. When testing programmed control procedures the auditor usually want to know that the key aspect of the program (1) processed transactions that met that criteria of the control procedures and should be processed and (2) rejected transactions that did not meet the criteria of the control procedures and should not be processed. When using CAATs, such as test data, it is sufficient to test each condition. c. If the auditor wants to assess control risk as low based on a programmed control procedure the auditor will usually (1) directly test the programmed control procedures using CAATS, (2) test computer general control procedures to gain assurance that the programmed control functioned effectively over time, and (3) test the effectiveness of manual follow-up of exceptions identified by the programmed control procedure. 13-8. The following table outlines the steps in a nonstatistical sampling plan for tests of controls and identifies the professional judgment(s) involved in each step. Step Professional Judgment 1. Determine the objectives of the test of controls Determine audit objectives and how the objectives of the test relate to financial statement assertions. 2. Determine procedures to evaluate internal controls The determination of procedures is a matter of professional judgment that provides evidence about the effective design and operation of internal controls. 3. Make a decision about the audit sampling The choice of using statistical or nonstatistical technique. sampling is a matter of professional judgment. 4. Define the population and sampling unit. The population depends on the control being tested. In many cases, there may be several ways to identify different sampling units for the same control (e.g., each report or each item on a report). 5. Use professional judgment to determine sample Sample size is a function of a variety of factors. The size. auditor uses professional judgment to make a decision about each judgment that influences sample size. If the auditor uses nonstatistical sampling the auditor also uses professional judgment to determine the sample size used. 6. Select a representative sample. The auditor uses professional judgment in determining the technique used to select a representative sample from the population. 7. Apply audit procedure. In step 2 the auditor used professional judgment to determine the procedures to be performed. Now the auditor uses judgment to apply those procedures to each sampling unit. Judgment is necessary to determine if evidence supports a control deviation or whether the control functioned effectively. 8. Evaluate the sample results. The auditor uses professional judgment to sum the sample results and project the sample results on the population, particularly in a nonstatistical sample. 9. Document conclusions Professional judgment is an integral part of documenting the audit conclusions about effective operation of a control based on sample results. 13-9. The following discussion explains each factor that influences sample size. 1. The nature of the control. Management’s review of weekly expenditure reports is a manual control and should be tested more extensively than an automated control. 2. The frequency of operation of the control. The control operates weekly and would be tested less extensively than controls that operate daily or on every transaction. 3. The importance of the control. If management’s review of weekly expenditure reports is critical to the audit strategy, it needs to be tested more extensively than if the control is only tangential to the audit strategy. 4. The risk of assessing control risk too low. The smaller the amount of sampling risk the larger the sample size. 5. Tolerable deviation rate. The smaller the rate of deviation (inappropriate or inadequate review of weekly reports) from the proscribed control procedure that the auditor can tolerate, the larger the sample size. 6. Expected population deviation rate. The closer the tolerable deviation rate and the expected deviation rate are to each other, the larger the sample size. 7. Population size. For small population sizes, such as a weekly control activity, sample size decrease as the population size decreases. 13-10. In a few instances the logic behind audit sampling does not apply to substantive tests. For example, audit sampling does not apply to: Initial procedures, Substantive analytical procedures, Many tests of details of accounting estimates, and Many tests of details of disclosures. 13-11. The following table outlines the steps in a nonstatistical or statistical sampling plan for substantive tests and identifies the professional judgment(s) involved in each step. Step Professional Judgment 1. Determine the objectives of the substantive test Determine audit objectives and the objectives of the test relate to financial statement assertions. 2. Determine substantive audit procedure to perform The determination of substantive audit procedures is a matter of professional judgment that provides evidence about the potential amount of misstatement in an account. 3. Make a decision about the audit sampling The choice of using statistical or nonstatistical technique. sampling is a matter of professional judgment. 4. Define the population and sampling unit. The population depends on the account balance being evaluated. In many cases, there may be several ways to identify different sampling units for the same account balance (e.g., each customer or each sales invoice receivable from a customer). 5. Use professional judgment to determine sample Sample size is a function of a variety of factors. The size. auditor uses professional judgment to make a decision about each judgment that influences sample size. If the auditor uses nonstatistical sampling the auditor also uses professional judgment to determine the sample size used. 6. Select a representative sample. The auditor uses professional judgment in determining the technique used to select a representative sample from the population. 7. Apply audit procedures. In step 2 the auditor used professional judgment to determine the procedures to be performed. Now the auditor uses judgment to apply those procedures to each sampling unit. Judgment is necessary to determine if evidence is present of a misstatement in the amount of the balance or transaction tested. 8. Evaluate the sample results. The auditor uses professional judgment to sum the sample results and project the sample results on the population, particularly in a nonstatistical sample. 9. Document conclusions Professional judgment is an integral part of documenting the audit conclusions about the potential for material misstatement in the financial statements. 13-12. a. The inventory population can be defined as (1) all inventory irrespective of location, or (2) all inventory in the warehouse and then all inventory at retail locations, or (3) each location may be treated as a separate population. b. The sampling unit could be defined as each stock number (irrespective of location), or each stock number at each location, or it could be defined in terms of physical location, such as bin number, or rack in a retail store. 13-13. The AICPA’s Audit Sampling Guide (pp. 68–69) identifies several advantages and disadvantages of PPS sampling. The advantages of PPS sampling are: It is generally easier to use than classical variables sampling because the auditor can calculate sample sizes and evaluate sample results by hand or with the assistance of tables. The size of a PPS sample is not based on any measure of the estimated variation of audit values. PPS sampling automatically results in a stratified sample because items are selected in proportion to their dollar values. PPS systematic sample selection automatically identifies any item that is individually significant if its value exceeds an upper monetary cutoff. If the auditor expects no misstatements, PPS sampling will usually result in a smaller sample size than under classical variables sampling. A PPS sample can be designed more easily, and sample selection may begin before the complete population is available. In contrast, PPS sampling has the following disadvantages: It includes an assumption that the audit value of a sampling unit should not be less than zero or greater than book value. When understatements or audit values of less than zero are anticipated, special design considerations may be required. If understatements are identified in the sample, the evaluation of the sample may require special considerations. The selection of zero balances or balances of a different sign (e.g. credit balances) requires special consideration. PPS evaluation may overstate the ASR when misstatements are found in the sample. As a result, the auditor may be more likely to reject an acceptable book value for the population. As the expected number of misstatements increases, the appropriate sample size increases. Thus, a larger sample size may result than under classical variables sampling. Professional judgment should be exercised by the auditor in determining the appropriateness of this approach in a given audit circumstance. 13-14. a. The sampling unit in a PPS sample is the individual dollar (the population is considered to be a number of dollars equal to the dollar amount o the population). The logical sampling unit is the account, document, transaction, etc., with which an individual dollar unit selected for inclusion in the sample is associated. b. Since the individual dollar is the sampling unit in PPS sampling, the more dollars associated with a logical sampling unit the greater its chance of selection. Conversely, logical units with zero balances have no chance of selection. Therefore, they should be treated separately when using PPS sampling. In testing accounts with credit balances, such as liabilities, the auditor is usually primarily concerned with understatement. Since PPS sampling results in selection proportional to size. The more an item is understated, the less its chance of selection. Accordingly, the approach is incompatible with the objective. 13-15. a. The formula for calculating sample size in a PPS sample is: BV x RF n TM ( AM x EF ) b. Explanations of the factors in the above formula and their effect on sample size are: Relationship to Factor Explanation Sample Size BV Book value of Direct population tested RF Reliability factor for Direct (1) specified risk of incorrect acceptance TM Tolerable misstatement Inverse AM Anticipated misstatement Direct (2) EF Expansion factor for anticipated Direct misstatement (1) Note that while the relationship between RF and n is direct, the relationship between the risk of incorrect acceptance (which is controlled through the RF factor) and n is inverse. (2) Note that while the relationship between AM and n is direct, the relationship between the risk of incorrect rejection (which is controlled through the AM factor) and n is inverse. 13-16. The specification of anticipated misstatement provides the auditor with a means to control the risk of incorrect rejection. The auditor uses prior experience and knowledge of the client and professional judgment in determining an amount for anticipated misstatement, bearing in mind that an excessively high anticipated misstatement will unnecessarily increase sample size while too low an estimate will result in a high risk of incorrect rejection. 13-17. The three factors considered in evaluating the result of a PPS sample are (a) the projected misstatement determined from the sample, (b) the allowance for sampling risk, and (c) the upper misstatement limit. 13-18. The two components of the allowance for sampling risk for PPS samples are (a) basic precision and (b) an incremental allowance resulting from any misstatements found. 13-19. A tainting percentage and projected understatement are calculated for each logical unit with a book value less than the sampling interval that contains a misstatement. The tainting percentage is calculated by dividing the difference between the book and audit values by the book value. The tainting percentage is then multiplied by the sampling interval to project the degree to which a logical unit is tainted with misstatement to all of the dollars in the sampling interval it represents. For each logical sampling unit with a book value greater than or equal to the sampling interval, projected misstatement is simply the difference between the book value and the audit value. Appendix A 13A-1. a. The factors that influence sample size for tests of controls using statistical attribute sampling are: Risk of assessing control risk too low Tolerable deviation rate Expected population deviation rate Population size when auditing small populations (fewer than 5,000 units). b. Some auditors use the same risk of assessing control risk too low for all statistical tests of controls. Other auditors vary the risk of assessing control risk too low depending on the planned assessed level of control risk, such that the lower the planned assessed level of control risk, the lower the risk of assessing control risk too low. c. If the auditor plans a “low” assessed level of control risk, the auditor should set tolerable deviation rates between 2% and 7%. d. When using a statistical attribute sample the auditor can get a sample size of 59 with a 5% risk of assessing control risk too low, a 5 percent tolerable deviation rate, and a 0% expected deviation rate (assuming a large population size). 13A-2. a. The three steps involved in quantitatively evaluating sample results for a statistical test of controls are (1) calculating the sample deviation rate, (2) determining the upper deviation limit, and (3) determining the allowance for sampling risk. b. The steps involved in using the sample evaluation tables are: 1. Select the table that corresponds to the risk of assessing control risk too low. 2. Locate the column that contains the actual number of deviations (not the deviation rate) found in the sample. 3. Locate the row that contains the sample size used. 4. Read the upper deviation limit from the intersection of the column and row determined in steps two and three. c. With a sample size of 59 and one deviation, the auditor can conclude that he or she is 95% confident that the maximum deviation rate in the population is not more than 7.7%. 13A-3. a. When evaluating qualitative factor the auditor will want to consider whether there is evidence of management override of controls, collusion, or fraud. b. When the sample results do not support the planned assessed level of control risk the auditor should increase the final assessed level of control risk to a level supported by the sample and decrease the level of detection risk associated with substantive tests of details accordingly. Appendix B 13B-1. a. The formula for determining sample size in mean-per-unit sampling is: 2 N U R S xj n A When the relationship between n and N is greater than .05, a finite correction factor is recommended resulting in an adjusted sample size (n') calculated as follows: n n n 1 N b. The elements in the formula for n given above represent the following: N = Population size UR = The standard normal deviate for the desired risk of incorrect rejection Sxj = Estimated population standard deviation A = Planned allowance for sampling risk c. The formula differs for difference and ratio estimation only in the term for the estimated standard deviation. In difference estimation, Sdj (the estimated standard deviation of the differences) is substituted for Sxj. In ratio estimation, Srj (the estimated standard deviation of the ratios) is substituted for Sxj. 13B-2. a. The risk of incorrect acceptance is controlled in classical variables sampling plans by specifying the planned allowance for sampling risk (A) in the sample size formula. (A) is determined by multiplying the auditor's specified tolerable misstatement (TM) by a ratio (R) of planned allowance for sampling risk to tolerable misstatement. The ratio is determined from a table based on the auditor's specified risks of incomplete rejection and acceptance. b. Three ways of estimating the standard deviation for a mean-per-unit sampling plan are: (1) in a recurring engagement, the standard deviation found in the preceding audit may be used, (2) it may be estimated from available book values in the current year, and (3) it may be based on the audit values found in a presample of 30 to 50 items selected from the current year's population. 13B-3. a. Planned allowance for sampling risk in a classical variables sampling plan provides the means by which the risk of incorrect acceptance is controlled. It is found by multiplying the auditor's specified tolerable misstatement by a ratio determined from a table based on the specified risks of incorrect rejection and acceptance. b. The achieved allowance for sampling risk is calculated from the sample. When the achieved allowance is not greater than the planned allowance used to determine sample size, it is used to calculate a range, plus and minus, about the estimated total population value, if the recorded book value falls within this range, the sample results support the conclusion that the book value is not materially misstated at a risk of incorrect acceptance not exceeding that specified in designing the sample. c. An adjusted achieved allowance for sampling risk is calculated from a sample when the achieved allowance is greater than the planned allowance. This adjustment is required so that the risk of incorrect acceptance associated with the range calculated for the estimated total population value will not exceed that originally specified by the auditor. 13B-4. When sample results do not support the book value, the auditor must use professional judgment in deciding on an appropriate course of action. If the auditor believes the sample is not representative of the population, he or she may expand the sample and reevaluate. Also, if the auditor believes the achieved allowance is larger than the planned allowance because the sample size was too small (e.g., because the population standard deviation used to determine sample size was underestimated), he or she may expand the sample and reevaluate. If the auditor believes the population book value may be reinstated by more than tolerable misstatement, he or she may have the client investigate, and, if warranted, adjust the book value. The auditor would then reevaluate the sample results relative to the adjusted book value. Appendix C 13C-1. Consideration of the same factors in nonstatistical samples as in statistical samples may help to produce more efficient and effective samples. However, in nonstatistical samples the factors need not be explicitly quantified. The factors to be considered are: (1) book value of the population, (2) variation in the population, (3) tolerable misstatement, and (4) risk of incorrect acceptance. 13C-2. Two acceptable methods for projecting the misstatement found in nonstatistical samples to the population are: (1) the ratio method which divides the total dollar amount of misstatement in the sample by the fraction of total dollars from the strata of the population included in the sample; (2) the difference method which multiplies the average difference between audit and book values for sample items by the number of units in the strata of the population. In either case the results of each strata should be added together to determine a estimated misstatement for the population. 13C-3. In nonstatistical samples, the difference between the auditor's total projected misstatement and tolerable misstatement may be viewed as an allowance for sampling risk. Comprehensive Questions 13-20. (Estimated Time – 20 minutes) a. 1. In determining an acceptable level of risk of assessing control risk too low, an auditor should consider the importance of the control to be tested in determining the extent to which substantive tests will be restricted and the planned control risk. 2. In determining the tolerable deviation rate, an auditor should consider the planned control risk and how materially the financial statements would be affected if the control does not function properly. 3. In determining the expected population deviation rate, an auditor should consider the results of prior years' test, the overall control environment, or utilize a preliminary sample. b. 1. There is a decrease in sample size if the acceptable level of risk assessing control risk too low is increased. 2. There is a decrease in sample size if the tolerable deviation rate is increased. 3. There is an increase in sample size if the population deviation rate is increased. c. For a low risk of assessing control risk too low, it is generally appropriate to reconsider the planned control risk as the calculated estimate of the population deviation rate identified in the sample (7%) approaches the tolerable deviation rate (8%). This is because there may be an unacceptably high sampling risk that these sample results could have occurred with an actual population deviation rate higher than the tolerable deviation rate. d. If statistical sampling is used, an allowance for sampling risk can be calculated. If the calculated estimate of the population deviation rate plus the allowance for sampling risk is greater than the tolerable deviation rate, the sample results should be interpreted as not supporting the planned control risk. 13-23. (Estimated time - 30 minutes) a. Areas where judgment may be exercised by a CPA in planning a statistical test include: Determining the objectives of the plan. The CPA must identify the controls that are of interest and relate the controls to relevant financial statement assertions. Selecting the sampling method to be used. The CPA may choose from among several methods including attribute and discovery sampling. Defining the population and sampling unit. The CPA must give consideration to the appropriateness of the population to the objectives of the plan, the population's homogeneity with respect to control procedures to be tested, multiple client locations, changes in control procedures during the year, and population size. In defining the sampling unit, the CPA must consider compatibility with the objective of the test and audit efficiency. Specifying the attributes of interest. In attribute sampling, the CPA must identify attributes that relate to the effectiveness of the controls being tested. Determining sample size. The CPA must specify the acceptable level of risk of assessing control risk too low, tolerable deviation rate, expected population deviation rate, and population size. Determining the sample selection method. The CPA must decide which sampling selection method to use (e.g., random number sampling or systematic sampling). b. The CPA must consider the qualitative aspects of the deviations as well as the number of deviations. Deviations that directly affect the financial statements or appear to be irregularities have greater audit significance. When the sample results do not support the planned control risk, the nature, extent, or timing of substantive tests are ordinarily modified, or, if applicable, tests may be made of other compensating controls. c. Two techniques for selecting a nonstratified sample of 80 accounts payable vouchers are: Random number sampling. Use a table of random numbers or a computer program that generates random numbers to identify 80 four digit numbers that can be uniquely related to items in the population. When a table of random numbers is used, the starting point in the table should be selected randomly and the path to be followed through the table should be determined in advance and followed consistently. Systematic sampling. Select every 40th voucher (3200 - 80) after selecting the initial voucher (from 1-40) randomly. If the CPA is concerned that there may be a cyclical pattern in the population, he or she may use multiple random starts, multiplying the skip interval for a single random start (40) by the number of multiple starts. o (Estimated Time: 25 minutes) 13-27 a. Sample Size = 66 b. The sampling interval = $44,455 c. 1. Projected misstatement = $97,727.27 2. The incremental allowance for sampling risk = $48,704.55 3. The upper misstatement limit = $251,431.82 d. The auditor is 90% confident that the maximum overstatement in the population is $251,431.82. This is exceeds tolerable misstatement of $150,000. The know errors are immaterial, so there is a risk that he auditor is incorrectly rejecting the population. The auditor might consider increasing the sample size. Alternatively, the client might further investigate the errors and choose to adjust the book value of accounts receivable. Note: This solution is supported by an excel worksheet labeled Problem 13-27. 13-31. (Estimated Time – 20 Minutes) a. The pricing test is a substantive test that relates to the detection risk component of audit risk. b. Factors that should influence sample size are: Population size Variation in the population Tolerable misstatement Risk of incorrect acceptance c. The sampling unit is stock items appearing on the computer printout. The items may be selected by any of the following methods: (1) simple random, (2) systematic random, (3) haphazard, and (4) block sampling. The method used should provide a representative sample. Use of a single block is generally not acceptable. Accordingly, when this method is used, several blocks should be selected. d. In interpreting the results, Wheeler and Jones should (1) project the misstatement found in the sample to the population and (2) consider the sampling risk. 'The projected misstatement can be calculated in either of the following ways:

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Interval Intersection for Invoice Formula in Excel document sample

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