**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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