Solution Manual for Auditing and Assurance Services A
Systematic Approach 9th Edition Messier Glover Prawitt 0077862333 9780077862336
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CHAPTER 8
AUDIT SAMPLING: AN OVERVIEW AND APPLICATION TO TESTS OF CONTROLS
Answers to Review Questions
8-1 Audit sampling is the application of audit procedures to less than 100 percent of the items in a population of audit relevance selected in such a way that the auditor expects the sample to be representative of the population and thus likely to provide a reasonable basis for conclusions about the population. When the number of items or transactions in these populations is large and the items cannot be tested via computer assisted audit techniques (e.g., physical examination, confirmations), it is not economical for auditors to test 100 percent for the population; instead they use sampling to gather sufficient audit evidence. The justification for accepting some uncertainty from sampling is due to the trade-off between the cost to examine all of the data and the cost of making an incorrect decision based on a sample of the data.
8-2 Type I and Type II errors are the two types of decision errors an auditor can make when deciding that sample evidencesupportsordoes not support atest of controls orasubstantive test based on a sampling application.
In reference to test of controls, Type I and Type II errors are:
Risk of incorrect rejection (Type I): the risk that the assessed level of control risk based on the sample is greater than the true operating effectiveness of the control. Also commonly referred to as the risk of assessing control risk too high or the risk of underreliance.
Risk of incorrect acceptance (Type II): the risk that the assessed level of control risk based on the sample is less than the true operating effectiveness of the control. Also commonlyreferred as the riskofassessingcontrol risktoolow ortheriskofoverreliance.
In reference to substantive tests, Type I and Type II errors are as follows:
Risk of incorrect rejection (Type I): the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated.
Risk of incorrect acceptance (Type II): 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 relates to the efficiency of the audit because such errors can result in the auditor’s conducting more audit work than necessary in order to reach the correct conclusion. The risk of incorrect acceptance relates to the effectiveness of the audit because such errors can result in the auditor failing to detect a material misstatement in the financial statements. This can lead to litigation against the auditor by parties who relied on the financial statements.
8-3 Audit evidence types that do not involve audit sampling include:
Analytical procedures
Scanning
Inquiry
Observation
Examples of situations where audit sampling would not be used include:
Procedures applied to every item in the account or population (typically due to a small number of large items)
Classes of transactions or account balances not tested
Tests of automated information technology controls
8-4 Nonstatistical sampling is an approach in which the auditor uses a haphazard selection technique or uses judgment in any or all of the following steps:
Determining the sample size
Select the sample
Calculating the computed upper deviation rate
Nonstatistical sampling doesn’t require the use of statistical theoryto determine sample size or in the evaluation of sampling risk. Statistical sampling, on the other hand, uses the laws of probability to determine sample size, randomly select sampling units, and evaluate the results of an audit sample. The use of statistical theory permits the auditor to quantify the sampling risk for the purpose of reaching a conclusion about the population.
The major advantages of a statistical sampling application are that it helps the auditor (1) design an efficient sample, (2) measure the sufficiency of evidence obtained, and (3) quantify sampling risk. The disadvantages of statistical sampling include the additional costs of (1) training auditors in the proper use of sampling technique, (2) added complexity in designing and conducting the sampling application, and (3) lack of consistent application across audit teams due to the complexity of the underlying concepts.
8-5 Attribute sampling is used to estimate the proportion of a population that possesses a specified characteristic. For tests of controls, the auditor wants to measure the deviation rate to determine whether the control procedure can be relied upon to properly process accounting transactions and therefore support the auditor’s assessed level of control risk.
8-6 The timing of testing often will determine the period to be covered by the test. For example, interim testing mayinvolve testing transactions from the first nine months of the year. After the population has been defined, (1) the auditor must determine that the physical representation of the population is complete, and (2) if the testing was conducted at an interim date, whether to conduct additional tests in the remaining period.
8-7 The four factors that enter into the sample size decision and their relationship with sample size are:
Factor Relationship to Sample Size
Desired confidence level Direct
Tolerable deviation rate
Inverse
Expected population deviation rate Direct
Population size
Decreases sample size only when population size is small (<500 items)
8-8 In conducting the audit procedures for tests of controls, the auditor may encounter voided documents, inapplicable documents, or missing documents. The auditor may also stop the test before completion. Each of these situations should be handled in the following manner for an attribute-sampling application:
Voided documents: If the transaction has been properly voided, it does not represent a deviation. The item should be replaced with a new sample item.
Unused or inapplicable documents: Sometimes a selected item is not appropriate for the definition of the control. In such a case, the item is not a deviation and the auditor would simply replace the item with another purchase transaction.
Missing documents: If the auditor is unable to examine a document or use an alternative procedure to test whether the control was adequately performed, the sample item is a deviation for purposes of evaluating the sample results.
Stopping the test before completion: If a large number of deviations are detected early in the tests of controls, the auditor should consider stopping the test as soon as it is clear that the results of the test will not support the planned assessed level of control risk. The client should be informed and the exceptions would be considered a control deficiency unless remediation and retesting are successful.
8-9 Theauditor’spurposesinevaluatingthequalitativeaspectsofdeviationsinperformingerror analysis involves considering (1) the nature of the deviations and their causes and (2) how these deviations may impact the other phases of the audit.
8-10 An auditor using nonstatistical sampling uses judgment to consider the allowance for sampling risk. For example, when the rate of deviation from the prescribed control exceeds the expected rate used to plan the sample, the auditor usually concludes that there is unacceptably high sampling risk and he or she typically would increase the assessed level of control risk or consider further whether to rely at all on the control.
Answers to Multiple-Choice Questions
Solutions to Problems
8-21
a. The auditor’s justification for accepting the uncertainties that are inherent in the sampling process are based upon the premise that (1) the cost of examining all of the financial data would usually outweigh the benefit of the added reliability of a complete (100%) examination and (2) the time required to examine all of the financial data would usually preclude issuance of a timely auditor’s report.
b. The uncertainties inherent in applying auditing procedures are collectively referred to as audit risk. Auditriskistheriskthattheauditormayunknowinglyfailto appropriately modify the opinion on financial statements that are materially misstated. Audit risk can be controlled through the scope of the auditor’s test procedures with the audit risk model providing a framework to follow. Detection risk, which is a component of the audit risk model, is composed of two risks or uncertainties: sampling risk and nonsampling risk.
c. Sampling risk arises from the possibility that, when a test of controls or a substantive test is restricted to a sample, the auditor’s conclusions may be different from the conclusions he or she would reach if the test were applied in the same way to all items in the population.
Nonsampling risk includes all the aspects of audit risk that are not due to sampling and can occur because the auditor used an inappropriate audit procedure, failed to detect amisstatement when applyinganappropriate audit procedure, ormisinterpretedan audit result.
When performing a test of controls, the auditor can commit two types of decision errors: (1) the risk of incorrect rejection or of assessing control risk too high, which is the risk that the assessed level of control risk based on the sample is greater than the true operating effectiveness of the control and (2) the risk of incorrect acceptance or of assessing control risk too low, which is the risk that the assessed level of control risk based on the sample is less than the true operating effectiveness of the control.
When performing substantive tests, the related decision errors are: (1) the risk of incorrect rejection, which is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated and (2) the risk of incorrect acceptance, which is the risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated.
8-22 a 6, b 5, c 7, d 1, e 4, f 2, g 3
8-23 1. In this scenario, the stratum of loans greater than $1 million is tested in total. Since the entire population is tested, it does not involve sampling. Sampling is involved in the second strata because the auditor is only examining 15 of the 450 loans in the strata.
2. If the analytical procedures used do not include statistical techniques (e.g., regression analysis), then the use of analytical procedures does not involve sampling.
3. Since the auditor has haphazardly selected less than 100% of the population’s transactions, sampling is involved in such a test.
4. In this case, the auditor has decided not to audit the account because it is immaterial. This approach does not involve sampling.
8-24 a. The text includes Jenny’s step 3 within the second step of attributes sampling. The remaining steps of attribute sampling are as follows:
1. Define remaining population characteristics define the control deviation conditions.
2 Determine sample size, using the following inputs.
Determine the desired confidence level.
Determine the tolerable deviation rate.
Determine the expected population deviation rate.
Determine the population size (if < 500).
3. Select sample items.
4 Perform the audit procedures understand and analyze any deviations observed.
5. Calculate the sample deviation and computed upper deviation rates.
6. Draw final conclusions.
b. The advantages of using a statistical sampling methodology are that it helps the auditor
(1) design an efficient sample, (2) measure the sufficiency of the evidence obtained, and
(3) quantifysampling risk. Byusing a statistical sampling methodology, the auditor can limit sampling risk to an acceptable level.
8-25 The sample size for each control procedure is:
8-26 The computed upper deviation rate and the auditor’s decision for each control procedure are:
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
8-27 The sample size for each control procedure is:
8-28 The computed upper deviation rate and the auditor’s decision for each control procedure are:
Results using Tables
* It appears that the computed upper deviation rate exceeds the tolerable deviation rate for both procedures 2 and 4. However, these results are obtained because the evaluation tables do not include evaluations for sample sizes of 88 and 76, and when rounded down to sample sizes of80and 70, respectively, thecomputedupperdeviation rateof7.7%and 3.3%exceed the tolerable deviation rate. In reality, because a statistically derived sample size was determined in problem 8-27 and because the allowed number of deviations was found (see the number in parentheses in tables 8-5 and 8-6), the auditor is guaranteed that the results are acceptable. Note that when using ACL, rounding is not a potential source for auditor error.
Using the ACL, the upper error limit frequency and the auditor’s decision for each control procedure are:
The evaluation using ACL does lead to different upper error limit frequencies and leads to clearer conclusions that control procedures 2 and 4 are acceptable. Because the tables require auditors to round sample size, the computed upper deviation rates derived from the tables seem to initially suggest that 2 and 4 are not acceptable (see note above). ACL provides the advantage that exact sample sizes can be evaluated.
8-29 Austen’s conclusion on each item would be as follows:
1. The sample deviation rate is 1.3% (1 75). Since the sample deviation rate is less than the expected population deviation rate of 2%, the control can be relied upon.
2. The sample deviation rate is 3.3% (1 30). Since the sample deviation rate exceeds the expected population deviation rate of 2.5%, the control cannot be relied upon.
8-30 a. The allowance for sampling risk in this situation is the difference between the sample deviation rate 4% (6/150) and the computed upper deviation rate of 7.8%. Therefore, the allowance for sampling risk included in the computed upper deviation rate is 3.8% (7.8% - 4%). We can determine that the desired level of confidence for Nathan’s tests must have been 95% because we find an upper deviation rate of 7.8% associated with a sample size of 150 and 6 deviations in Table 8-8.
b. (1) The tolerable deviation rate, 6%, is greater than the sample deviation rate, but is less than the computed upper deviation rate, 7.8%. Therefore, Mathews could increase the samplesizeandreevaluatetheresultsbasedonthelargersamplesizebeforedetermining whether to adjust the preliminary control risk assessment.
(2) Mathews could increase control risk because the upper deviation rate exceeds the tolerable deviation rate and the sample deviation rate exceeds the expected deviation rate.
(3) Mathews could justify not adjusting the preliminary assessment because, even thoughtheupperdeviationrateexceedsthetolerablerate,thesampledeviationratefrom a relatively large sample is less than the tolerable rate and, upon further consideration, Mathews may determine that he can accept a higher tolerable rate than planned. However, he must recognize that this approach does not leave the allowance for sampling risk he originally planned. Looking at Table 8-5, we see that the original sample size should have been 195 based on a tolerable deviation rate of 6% and an
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
expected population deviation rate of 3%.
8-31 Iceberge’s conclusion on each item would be as follows:
1. The sample deviation rate is 2.0% (1 50). Since the sample deviation rate is less than the expected population deviation rate of 3%, the control can be relied upon.
2. The sample deviation rate is 4.0% (2 50). Since the sample deviation rate exceeds the expected population deviation rate of 3%, the control cannot be relied upon.
Solution to Discussion Case
8-32 The following are the incorrect assumptions and statements and inappropriate applications of attribute sampling in Baker’s procedures:
Statistical sampling does not eliminate the need for professional judgment.
The computed upper deviation rate is too high (20%) if Baker plans to assess control risk at a low level.
The increase in the population size has little or no effect on determining sample size.
Baker failed to consider the risk of assessing control risk too low in determining the sample size.
The population from which the sample was chosen (invoices) was an incorrect population.
The sample was not randomly selected.
Baker failed to consider the difference of an immaterial amount to be an error.
The allowance for sampling risk was incorrectly calculated.
Baker’s reasoningconcerning the decision that the sample supported a low assessed level of control risk was erroneous.
