audit sampling for tests of details of balances
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Audit Sampling for Tests of Details of Balances. Chapter 16. Learning Objective 1. Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions. Tests of Details of Balances, Controls, and Substantive Transactions. - PowerPoint PPT PresentationTRANSCRIPT
©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 16 - 1
Audit Sampling for Testsof Details of Balances
Chapter 16
©2003 Prentice Hall Business Publishing, Auditing and Assurance Services 9/e, Arens/Elder/Beasley 16 - 2
Learning Objective 1
Differentiate audit sampling for
tests of details of balances and for
tests of controls and substantive
tests of transactions.
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Tests of Details of Balances, Controls, and Substantive Transactions
Tests of Controls
Substantive tests of transactions
Sampling for tests of details of balances
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Learning Objective 2
Apply nonstatistical sampling
to tests of details of balances.
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Nonstatistical Sampling
There are 14 steps required in auditsampling for tests of details of balance.
These steps parallel the 14 steps usedfor sampling for tests of controls and
substantive tests of transactions.
There are a few differences becauseof the different objectives of the tests.
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Tests of Controls and Substantive
Tests of Transactions
Step 1 State the objectives of the audit test.
Step 2 Decide whether audit sampling applies.
Step 3 Define attributes and exception conditions.
Step 4 Define the population.
Step 5 Define the sampling unit.
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Audit Sampling for Tests
of Details of Balances
Step 1 State the objectives of the audit test.
Step 2 Decide whether audit sampling applies.
Step 3 Define misstatement conditions.
Step 4 Define the population.
Step 5 Define the sampling unit.
Difference
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Tests of Controls and Substantive
Tests of Transactions
Specify acceptable risk of assessingcontrol risk too low.
Estimate the population exception rate.
Determine the initial sample size.
Step 7
Step 8
Step 9
Specify the tolerable exception rate.Step 6
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Audit Sampling for Tests of Details of Balances
Specify acceptable risk of incorrectacceptance.
Estimate misstatements in thepopulation.
Determine the initial sample size.
Step 7
Step 8
Step 9
Specify tolerable misstatement.Step 6
Difference
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Tests of Controls and Substantive
Tests of Transactions
Select the sample.
Perform the audit procedures.
Step 10
Step 11
This is the same as in“Audit Sampling for Tests of Details of Balances.”
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Tests of Controls and Substantive
Tests of Transactions
Generalize from the sampleto the population.
Analyze the exceptions.
Decide the acceptability of the population.
Step 12
Step 13
Step 14
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Audit Sampling for Tests of Details of Balances
Generalize from the sampleto the population.
Analyze the misstatements.
Decide the acceptability of the population.
Step 12
Step 13
Step 14
Difference
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Action When aPopulation Is Rejected
• Take no action until tests of other audit areasare completed
• Perform expanded audit tests in specific areas • Increase the sample size• Adjust the account balance• Request the client to correct the population• Refuse to give an unqualified opinion
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Learning Objective 3
Apply monetary unit sampling.
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Monetary Unit Sampling
MUS is an innovation in statisticalsampling methodology that was
developed specifically foruse by auditors.
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Differences between MUS and Nonstatistical Sampling
The definition of the sampling unitis an individual dollar.
The population size is the recordeddollar population.
Preliminary judgment of materialityis used for each account instead of
tolerable misstatement.
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Differences between MUS and Nonstatistical Sampling
Sample size is determined usinga statistical formula.
A formal decision rule is usedfor deciding the acceptability
of the population.
Sample selection is done usingprobability proportional to size
sample selection (PPS).
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The Auditor Generalizes from theSample to the Population Using
MUS
Attributes sampling tables are used tocalculate the results.
The attributes results must be converted to dollars.
The auditor must make an assumption aboutthe percentage of misstatement for each
population item that is misstated.
The statistical results when MUS is usedare called misstatement bounds.
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Generalizing from theSample to the Population
Overstatement amounts equal 100 percent;understatement amounts equal 100 percent;
misstatement bounds at a 5 percent ARIA are:
Upper misstatement bound= $1,200,000 × 3% × 100% = $36,000
Lower misstatement bound= $1,200,000 × 3% × 100% = $36,000
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Generalizing from theSample to the Population
All amounts have to be overstatements.
All population items misstated have tobe 100 percent misstated.
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Generalizing from theSample to the Population
Overstatement amounts equal 10 percent;understatement amounts equal 10 percent;
misstatement bounds at a 5 percent ARIA are:
Upper misstatement bound= $1,200,000 × 3% × 10% = $3,600
Lower misstatement bound= $1,200,000 × 3% × 10% = $3,600
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Generalizing from theSample to the Population
Overstatement amounts equal 20 percent;understatement amounts equal 200 percent;
misstatement bounds at a 5 percent ARIA are:
Upper misstatement bound= $1,200,000 × 3% × 20% = $7,200
Lower misstatement bound= $1,200,000 × 3% × 200% = $72,000
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Appropriate Percent of Misstatement Assumption
The appropriate assumptionfor the overall percent of
misstatement in thosepopulation items containing
a misstatement is anauditor’s decision.
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Generalizing When Misstatements Are Found
1. Overstatement and understatement amountsare dealt with separately and then combined.
2. A different misstatement assumptionis made for each misstatement,
including the zero misstatements.
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Generalizing When Misstatements Are Found
3. The auditor must deal with layers of thecomputed upper exception rate (CUER)
from the attributes sampling table.
4. Misstatement assumptions must beassociated with each layer.
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Illustration of the Auditor’s Decision Rule for MUS
LMB
– TolerableMisstatement $0 Misstatement
+ TolerableMisstatement
UMB
LMB UMB#4
LMB UMB
LMB
LMB UMB
UMB
#5
#3
#2
#1
#2
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Determining Sample SizeUsing MUS
Materiality
Assumption of the average percent ofmisstatement for population items
that contain a misstatement
Acceptable risk of incorrect acceptance
Recorded population value
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Determining Sample SizeUsing MUS
Estimate of the population exception rate
Relationship of the audit risk modelto sample size for MUS
PDR = AAR ÷ (IR × CR)
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Learning Objective 4
Describe variables sampling.
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Frequency Distributionof Sample Means
Value of in dollarsxF
requ
ency
of
valu
esin
per
cent
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Sampling Distribution
A corollary is that the sample mean value with the highest frequency of occurrence
is also equal to the population mean.
The mean value of all the sample meansis equal to the population mean .(X)
(x)
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Sampling Distribution
The shape of the frequency distributionof the sample means is that of a normal
distribution (curve), as long as the samplesize is sufficiently large, regardless of the
distribution of the population.
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Sampling Distribution
The percentage of sample means betweenany two values of the sampling
distribution is measurable.
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Sampling Distribution fora Population Distribution
Value of in dollarsxF
requ
ency
of
valu
esin
per
cent
Sampling distribution –Normal
Population distribution –Skewed
Mean
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Variables Methods
Difference estimation
Ratio estimation
Mean-per-unit estimation
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Stratified Statistical Methods
All of the elements of the population aredivided into two or more subpopulations.
Each subpopulation is independently tested.
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Sampling Risks(ARIA and ARIR)
Conclude that the Correct conclusion Incorrect conclusion population is – no risk – risk is ARIR materially misstated
Conclude that the Incorrect conclusion Correct conclusion population is – risk is ARIA – no risk not materially misstated
Actual State of the Population Actual Audit Materially Not Materially
Decision Misstated Misstated
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Learning Objective 5
Use difference estimation in
tests of details of balances.
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Plan the Sample andCalculate the Sample Size
State the objectives of the audit test.
Decide whether audit sampling applies.
Define misstatement conditions.
Define the population.
Define the sampling unit.
Specify tolerable misstatement.
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Plan the Sample andCalculate the Sample Size
Specify acceptable risk.
ARIA ARIR
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Estimate Misstatementin the Population
Estimate an expected point estimate.
Make an advance population standard deviationestimate – variability of the population.
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Calculate the InitialSample Size
n = {[SD*(ZA + ZB)N] ÷ (TM – E*)}2
n = initial sample sizeSD* = advance estimate of the standard deviation ZA = confidence coefficient for ARIA ZB = confidence coefficient for ARIR N = population size TM = tolerable misstatement for the population (materially) E* = estimated point estimate of the population misstatement
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Select the Sample andPerform the Procedures
Select the sample.
Perform the audit procedures.
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Evaluate the Results
Compute the point estimateof the total misstatement.
Compute an estimate of thepopulation standard deviation.
Compute the precision interval.
Compute the confidence limits.
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Effect of Changing Factors
Effect on the ComputedType of Change Precision IntervalIncrease ARIA DecreaseIncrease the point estimate of the misstatements IncreaseIncrease the standard deviation IncreaseIncrease the sample size Decrease
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Analyze the Misstatements
The auditor must evaluate misstatements todetermine the cause of each misstatementand decide whether modification of the
audit risk model is needed.
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Auditor’s Decision Rule for Difference Estimation
LCL
– TolerableMisstatement $0 Misstatement
+ TolerableMisstatement
UCL
LCL UCL#4
LCL UCL
LCL
LCL UCL
UCL
#5
#3
#2
#1
#2
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End of Chapter 16