LECTURE_8_Module_9_Sampling_S2_2008 - LECTURE 8 Module 9 Audit Sampling Learning Objectives xDefine audit sampling and discuss its applicability

LECTURE_8_Module_9_Sampling_S2_2008 - LECTURE 8 Module 9...

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Unformatted text preview: LECTURE 8 Module 9 Audit Sampling Learning Objectives xDefine audit sampling and discuss its applicability xDistinguish between sampling and non-sampling risk xDistinguish between statistical and non-statistical sampling Learning Objectives xExplain the steps in planning to select a sample xIndicate the factors that affect sample size xDescribe the methods of selecting a sample Learning Objectives xExplain the steps in testing a sample and evaluating the results xDescribe the principal methods of statistical sampling used in auditing Key Terms & Concepts xAttribute sampling xPPS Sampling xDeviation rate xSampling risk xNon-sampling risk Basic Concepts of Audit Sampling xAs defined in AUASB glossary: the application of audit procedures to less than 100% of the items within a population to obtain audit evidence about a particular characteristic of the population Auditing Standards (ASA 530) and Audit Sampling xRequirement for reasonable basis in arriving at opinion allows for some degree of uncertainty xUncertainty involves judgement as to consequences of erroneous opinion (audit risk) versus cost and time of extra audit effort Auditing Standards and Audit Sampling xAudit sampling relates to: Assessment Quantifying of control risk and controlling detection risk Sampling and Non-sampling Risk xSampling risk Properly drawn sample may not be representative of the population For tests of controls there is a −Risk of over-reliance −Risk of under-reliance Sampling and Non-sampling Risk xSampling risk for is a substantive tests of details there −Risk of incorrect acceptance −Risk of incorrect rejection this will impact on audit efficiency & effectiveness Sampling and Non-sampling Risk xNon-sampling risk Other audit failures e.g. human mistakes, misinterpreting the results of the sample Cannot be quantitatively assessed Risk can be controlled by planning, supervision and adherence to quality control standards which will reduce non-sampling risk to a negligible level Audit Sampling x Statistical and non-statistical sampling Current practice in Australia − Random − Probability Proportional to Size (PPS) − Systematic − Haphazard − Block x Other types of testing Selecting all items Selecting specific items Audit sampling: statistical and non-statistical (continued on next slide) Determine objective of test Determine procedures to meet objective How How many items? All items A sample Statistical Type of sampling Non-statistical Statistical Type of sampling Non-statistical Determine sample size from model explicitly recognising relevant factors Judgementally determine sample size implicitly recognising relevant factors Randomly select Randomly representative sample Judgementally select representative sample Apply audit procedures Apply audit procedures Evaluate test results statistically and judgementally Evaluate results judgementally Document conclusions Statistical Sampling Plans Sampling technique Type of test Purpose attribute sampling test of control estimate rate of deviations from prescribed controls in the population PPS sampling substantive estimate total $ amount of error in the population Statistical Sampling Techniques xChoice of statistical sampling method Attribute PPS Sampling for Tests of Control Sampling for Substantive Procedures Use of Samples for Audit Tests x 1. Planning the sample involves the following steps 1. Determining the objectives of the test − Test of control and/or − Substantive tests of details 2. Defining errors or deviations being sought 3. Identifying the population and sampling unit 4. Deciding the size of the sample 2. Calculating Sample Size n = RF / TDR Where x n = Sample Size x RF = Reliability Factor x TDR = Tolerable Deviation Rate Sample Testing Attribute Testing of Controls x Once sample selected perform audit procedures to check for errors applying appropriate audit procedures to ensure achievement of the audit objective x Rate/number of errors found in the sample is inferred to population by calculating the Upper Error / Deviation Limit or UEL Upper Error / Deviation Limit (UEL) x The maximum amount of deviations from controls that could exist in the population based on sample results UEL = RF / n x Where n = Sample Size x RF = Reliability Factor based on the number of errors / deviations actually found after testing the sample 3. Evaluate Sample Results x Quantitative Evaluation 1. Compare Upper Error / Deviation Limit against the Tolerable Deviation Rate x Qualitative Evaluation 1. Each deviation should be analysed to determine its Nature & Cause 2. Consider whether the deviation has a direct effect on the financial statements x May necessitate the revision of the planned nature, timing & extent of substantive testing Use of Samples for Audit Tests xSelecting the sample Random selection Systematic selection Haphazard selection xTesting the sample Use of Samples for Audit Tests xEvaluating the results Qualitative aspects of errors or deviations Projecting the error to the population − Tests of control − Substantive tests Probability-Proportional to Size (PPS) Sampling for Substantive Testing x Also called Dollar-Unit Sampling x Focus is on estimation of dollar balances based on sample x Evaluate reasonableness of monetary values and whether they are fairly stated x Each dollar is a sampling unit and PPS sampling tests whether it is correctly stated x Sample error rates are then projected to the total amount in the account balance (the population) to provide an indication whether the account balance is materially misstated Defining the Population & Sampling Unit x A sampling unit is the individual dollar x The population is the number of dollars equal to the total dollar amount of the population x Each dollar is given an equal chance of being selected x Auditor does not examine individual dollars x Dollar is used to ‘snag’ an account x Snagged account is known as the ‘Logical Sampling unit’ x The more dollars associated with a logical unit, the greater the chance of being snagged PPS Practical Example PPS Practical Example Details Accounts receivable balance $ 1,500,000 Tolerable Error Confidence level required $ 70,000 90% Determine Sample Size Determine Sample Size n = (PV / TE) x RF Where n = Sample Size PV = Population Value TE = Tolerable Error RF = Reliability Factor ­ determined from table 9.1 (as for Attribute Sampling) Calculate Sample Size Calculate Sample Size From Example PV = $ 1,500,000 TE = $ 70,000 RF = 9.28 (from table 9.1) Sample Size = 1,500,000 x 9.28 70,000 = 198.85 or 199 Calculate Sampling Interval Calculate Sampling Interval The interval between successive sampling units selected for testing where systematic sample selection is being applied SI = PV / n Where SI = Sampling Interval PV = Population Value n = Sample Size Calculate Sampling Interval Calculate Sampling Interval From Example PV = $ 1,500,000 n = 199 SI = 1,500,000 / 199 SI = 7537.69 or $7538 Use a random number generator for start value between $1 & $ 7538 & then select every $7538 until sample size has been obtained Selecting The Sample Selecting The Sample Most common method is systematic selection Pick a starting random number & then select (snag) ‘logical units’ by adding on the sampling interval Continue this process until you have selected the number of subsidiary accounts to fill the required sample size Substantive Testing on Substantive Testing on Selected Sample After selecting the sample, carry out the audit procedures From Example the auditor would send confirmation requests to those debtors who’s balance was selected as an item in the sample Test of details of accounts receivables balance Document individual errors identified Assume that you detect four Assume that you detect four overstatement errors as follows: Error No 1 Book Audit Value Value 10,000 6,000 2 20,000 18,000 3 6,000 4 35,000 28,000 0 MUST CALCULATE UEL MUST CALCULATE UEL UEL IS THE UPPER ERROR LIMIT THIS IS THE MAXIMUM AMOUNT OF OVERSTATEMENT ERROR, BASED ON THE SAMPLE RESULTS, THAT COULD EXIST IN THE POPULATION. STEPS IN CALCULATION STEPS IN CALCULATION OF UEL 1. 2. 3. 4. 5. CALCULATE PROJECTED POPULATION ERROR CALCULATE BASIC PRECISION/ERROR CALCULATE PRECISION GAP WIDENING CALCULATE THE TOTAL UEL APPLY DECISION RULES 1. Calculate Projected Error 1. Calculate Projected Error Error No 1 Book Audit Tainting Sampling Projected Value Value Interval Error 10,000 6,000 NA NA 4,000 2 20,000 18,000 3 6,000 4 35,000 28,000 0 N/A N/A 2,000 100% 7,538 7,538 NA N/A 7,000 Total Projected Error $20,538 Tainting Tainting The need to estimate the degree of error in the remainder of the sampling interval where the book value is lower than the sampling interval. In this way we are projecting the error for that particular sampling interval NOTE: When book value is less than sampling interval value the projected error = tainting x sampling interval (100% x SI) When book value is greater than sampling interval PE = actual error amount Projected Population Error Projected Population Error Projected Population error based on the projection of the error rate found in the sample Total Projection Error = The sum of the projection errors for individual errors identified in the sample Calculate Upper Error Limit Calculate Upper Error Limit (consists of 3 conponents) UEL = PE + BP + PGW Where UEL = Upper Error Limit PE = Projected Error BP = Basic Precision PGW = Precision Gap Widening Basic Precision/Error Basic Precision/Error Basic Precision is the Upper Error Limit when zero errors are estimated in the sample The sampling risk or the risk associated with not testing 100% 2. Basic Precision/Error 2. Basic Precision/Error BP = RF x SI Where BP = Basic Precision RF = Reliability Factor ­ from Table 9.1 for zero errors at desired level of confidence Basic Precision Basic Precision From Example SI = $7538 RF at 90% Confidence Level & Zero Errors = 2.31 BP = 7538 x 2.31 BP = 17412.78 or $17413 3. Precision Gap Widening 3. Precision Gap Widening Also called Projection Risk The risk associated with projecting the degree of overstatement in the sampling interval using tainting process Is only calculated therefore for the projection errors where tainting is applied Is the sum of {(the projected errors) x (the incremental change in the reliability factor – 1)} Precision Gap Widening Incremental change in reliability factors are given in table 9.2 in the study guide. When performing calculation select those individual projection errors where tainting has been applied in order from largest to smallest with the largest error being error one Precision Gap Widening Precision Gap Widening Error Number Projected Error Incremental Precision Change ­ 1 Gap Widening 1 7,538 0.58 4,372 4. Calculate Upper Error Limit 4. Calculate Upper Error Limit UEL = BP + PE + PGW BP = $ 17,413 PE = $ 20,538 PGW = $ 4,372 UEL = $17,413 + $20,538 + $4,372 UEL = $ 42,323 5.Decision Rules (PPS Sampling) 5.Decision Rules ( 1. 2. Compare calculated Upper Error Limit with the Tolerable Error If UEL > TE then it is likely that the account balance is materially misstated – the account balance is not value (fairly) stated If UEL < TE then no likely material misstatement in the account balance – the account balance is fairly (value) stated 5. Decision Rules (PPS Sampling) 5. Decision Rules Example $ 42,323 < $70,000 therefore the accounts receivable balance is fairly stated The auditor can be 90% confident that no material misstatement exists in this account balance There is only a 10% chance that accounts receivables balance is materially misstated (risk of incorrect acceptance) Non-statistical Sampling Techniques xWhy use non-statistical sampling? Low cost Straightforward xUsing informal non-statistical sampling approaches can be: Inconsistent Cause incorrect evaluation of sampling Summary 1. The Usefulness of Sampling 2. The Risks associated with Sampling 3. Basic concepts of Audit Sampling 4. Attribute Sampling for Tests of Control (compliance testing) 5. PPS Sampling for Substantive Tests You will only be given tables in the examination; therefore you must memorise the appropriate formulae & procedures. ...
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