Chapter 8 & 9 Lecture PDF

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Chapter 8 & 9 – Audit Sampling I.

II.

Primary purpose of sampling is to draw inferences about the whole population based on the results of testing only a subset of the population Four Key Terms: a. Audit Sampling b. Sampling Risk c. Confidence Level d. Tolerable Error and Expected Error

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Audit Sampling a. The selection and evaluation of 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 b. When do we test a sample? i. Inspection of tangible assets, inspection of records or documents, reperformance, recalculations, confirmations c. Auditors may test all items with a particular characteristic or test only one or a few items i. Example: class of transactions with very few, but large transactions or a routine transactions processed by automated information system

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Recall the audit risk model where AR = CR x DR x IR a. Detection risk is comprised of 2 types of risk: 1. Sampling risk – the possibility that the sample drawn is not representative of the population and that, as a result, the auditor will reach an incorrect conclusion about the account balance or class of transactions based on the sample 1. Representative sample – a sample where the evaluation of the sample results lead to the same conclusions that would be drawn if the same audit procedures were applied to the entire population 2. Nonsampling risk – the risk that the auditor reaches an erroneous conclusion for any reason not related to sampling risk 1. Examples – auditor error, testing the wrong population, failing to detect misstatement when applying an audit procedure, misinterpreting an audit result

V.

Two Types of Sampling Risk: (also known as Decision Errors) 1

Chapter 8 & 9 – Audit Sampling 1. Risk of incorrect rejection (Type I or Alpha) – risk that the sample supports a conclusion that the control (account balance) is not operating effectively (is materially misstated) when, in truth, it is operating effectively (is not materially misstated) i. Affects the efficiency of the audit – must perform more procedures 2. Risk of incorrect acceptance (Type II or Beta) – risk that the sample supports a conclusion that the control (account balance) is operating effectively (is not materially misstated) when, in truth, it is not operating effectively (materially misstated) ii. Affects the effectiveness of the audit – can results in audit failure

VI.

Nonstatistical vs statistical sampling a. Auditing standards recognize & permit both statistical and nonstatistical methods of audit sampling i. Auditors can use a combination of statistical and nonstatistical sampling techniques, depending on the account b. Statistical sampling – the auditor uses the laws of probability to compute sample size and evaluate the sample results

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Chapter 8 & 9 – Audit Sampling i. Advantages: design an efficient audit, measure the sufficiency of evidence obtained, quantify sampling risk ii. Disadvantages: training auditors in proper use, lack of consistent application across audit teams c. Nonstatistical sampling – the auditor uses professional judgment rather than laws of probability to compute sample size and evaluate the sample results

VII.

Types of Statistical Sampling Techniques a. Attribute Sampling – used to estimate the proportion of a population that possesses a specified characteristic i. Most common use is test of controls & determining deviation rate

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Chapter 8 & 9 – Audit Sampling ii. Example: control testing for approval of sales on credit (select sample of all credit sales to see if proper approval and sign-off was conducted after the employee checked credit worthiness of customer) b. Monetary-Unit Sampling (also known as Probability-Proportional-to-Size and Dollar-Unit Sampling i. Sampling technique where each dollar in a transaction or balance is a separate sampling unit. ii. Uses attribute sampling theory and technique iii. Most common use is substantive testing 1. Often used to test accounts such as A/R, loans receivable, investment securities and inventory iv. Advantage - Each dollar has an equal chance of being selected – therefore larger balances have a greater chance of being selected. v. Disadvantage - The selection of zero or negative balances generally requires special design consideration. VIII. IX.

Excel Example – Statistical vs. Nonstatistical Sampling and MUS Steps in Performing Sampling Procedures 1. Determine the test objectives a. Test of controls – evaluate the operating effectiveness of internal controls b. Substantive procedures – test the reasonableness of assertions about a financial statement amount (i.e., accuracy, existence) 2. Define the population characteristics a. Define the sampling population (e.g., fixed asset depreciation transaction) b. Define the sampling unit (e.g., depreciation journal entry) c. Define the deviation conditions 1. Test of controls – departure from adequate performance of the internal control (e.g., fixed asset clerk/manager signature) 2. Substantive procedures – a difference between monetary amounts in the client’s records and amounts supported by audit evidence (e.g., accuracy of calculation and proper journal entry) 3. Determine the sample size – in general, the larger the sample size, the more accurate the estimate a. Test of Controls (Attribute Sampling) a. Desired confidence level

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Chapter 8 & 9 – Audit Sampling 1. The desired level of assurance that the sample results are consistent with the overall population results 2. Confidence level is the complement of sampling risk (specifically, the risk of incorrect acceptance or a Type II error) a. Therefore, confidence level is related to the risk that the percentage of errors in the population is greater than the percentage found in your sample b. Example: If you set sampling risk at 5%, your confidence level is 95%. 3. As confidence level increases (and sampling risk decreases), sample size increases (direct relationship) b. Tolerable deviation rate 1. The maximum deviation rate that the auditor is willing to accept and still consider the control effective a. Example: tolerable deviation rate could be set to 10% (I can tolerate a 10% defect/error rate) 2. As the tolerable deviation rate increases, sample size decreases (inverse relationship) c. Expected population deviation rate 1. The rate the auditor expects to exist in the population a. Example: I expect the population deviation rate to be 6% 2. As the expected population deviation rate increases, sample size increases (direct relationship) 3. The closer the tolerable deviation rate and the expected population deviation rate are, the larger the sample size required d. ACL example of Record Sample (attribute sampling for tests of controls) i. Can also use tables like Tables 8-5 and 8-6 on page 286.

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Chapter 8 & 9 – Audit Sampling

b. Substantive Testing: a. Desired confidence level - the desired level of assurance that the sample results are consistent with the overall population results. i. As confidence level increases (and sampling risk decreases), sample size increases (direct relationship) b. Tolerable Misstatement (similar to tolerable deviation rate) – maximum amount by which the account can be misstated and still be acceptable as being fairly presented. i. As the tolerable misstatement increases, sample size decreases (inverse relationship) c. Expected Misstatement (similar to Expected population deviation rate) – dollar amount of misstatement the auditor believes exists in the population (based on inherent risk, prior years’ results, results of related substantive procedures) i. As the expected misstatement increases, sample size increases (direct relationship) d. Population – dollar amount of total population. Larger populations lead to larger sample size. ii. As population increases, sample size increases (direct relationship) e. ACL example of Monetary Sample (for test of details in substantive testing)

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Chapter 8 & 9 – Audit Sampling iii. Can also use tables like Tables 8-5 and 8-6 – but have to calculate: 1. tolerable misstatement = tolerable misstatement $ / book value of account 2. expected misstatement = expected misstatement $ / book value of account

4. Select sample items a. Should perform procedures such that every item in the population has the same probability of being selected b. Examples – random-number selection, systematic approach 5. Perform the audit procedures 6. Calculate the sample deviation and upper deviation rates a. The sample deviation rate = number of deviations identified in the sample divided by total sample a. = number of deviations / sample size b. Upper deviation rate = sample deviation rate + allowance for sampling risk 1. Because the sample may not represent the full population an allowance is added to the sample deviation rate to provide a range for the “true” population deviation rate 2. Upper deviation rate represents the highest possible value for the “true” population deviation rate based on your desired confidence level 3. ACL example – attribute testing

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Chapter 8 & 9 – Audit Sampling a. Can also use Tables 8-8 and 8-9 on page 294 7. Draw final conclusions a. If the tolerable deviation rate > upper deviation rate, accept the control as effective (account balance as fairly stated) a. Example: tolerable deviation rate = 10% which is greater than the upper deviation rate = 4.24% therefore accept control as effective b. If the tolerable deviation rate < upper deviation rate, consider the control to be ineffective (account balance materially misstated) 1. Test of controls response – increase sample size or deem control ineffective and update substantive testing strategy 2. Substantive procedures response – increase sample size, perform other substantive procedures, request an audit adjustment

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