chapter 09 international
TRANSCRIPT
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9-1
Chapter Nine
Audit Sampling:
An Application to Substantive Tests
of Account Balances
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Substantive Tests of Details of Account
Balances
The statistical concepts we discussed in the last
chapter apply to this chapter as well. Three important
determinants of sample size are
1. Desired confidence level.
2. Tolerable misstatement (error).
3. Estimated misstatement (error).
Misstatements discovered in the audit sample mustbe projected to the population, and there must be an
allowance for sampling risk.
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Substantive Tests of Details of Account
Balances
Consider the following information about the inventory
account balance of an audit client:
The ratio of misstatement in the sample is 2%
(2,000 100,000)
Applying the ratio to the entire population produces a best
estimate of misstatement of inventory of60,000.(3,000,000 2%)
Book value of inventory account balance 3,000,000
Book value of items sampled 100,000Audited value of items sampled 98,000
Total amount of overstatement observed in audit sample 2,000
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Substantive Tests of Details of Account
Balances
The results of our audit test depend
upon the tolerable error associated with
the inventory account. If the tolerable
error is50,000, we cannot concludethat the account is fairly stated because
our best estimate of the projected error
is greater than the tolerable error.
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Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory toexpress a conclusion in monetary amounts
(e.g. in euros or other currency) rather than
as a rate of occurrence. It is commonly usedby auditors to test accounts such as
accounts receivable, loans receivable,
investment securities and inventory.
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Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to
estimate the percentage of monetary units in
a population that might be misstated and then
multiplies this percentage by an estimate ofhow much the euros are misstated.
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Monetary-Unit Sampling (MUS)
Advantages of MUS
1. When the auditor expects no misstatement, MUS
usually results in a smaller sample size than classical
variables sampling.
2. The calculation of the sample size and evaluation of
the sample results are not based on the variation
between items in the population.
3. When applied using the probability-proportional-to-size
procedure, MUS automatically results in a stratified
sample.
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Monetary-Unit Sampling (MUS)
Disadvantages of MUS
1. The selection of zero or negative balances generally
requires special design consideration.
2. The general approach to MUS assumes that the
audited amount of the sample item is not in error by
more than 100%.
3. When more than one or two misstatements aredetected, the sample results calculations may
overstate the allowance for sampling risk.
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Steps in MUS Sampling ApplicationSteps in MUS Sampling Application
Planning1. Determine the test objectives.
2. Define the population characteristics.
Define the population.
Define the sample unit.
Define a misstatement.
3. Determine the sample size, using the following inputs:
The desired confidence level or risk of incorrect acceptance.
The tolerable misstatement.
The expected population misstatement.
Population size.
Performance4. Select sample items.
5. Perform the auditing procedures.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. draw final conclusions.
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPlanning
1. Determine the test objectives.
2. Define the population characteristics.
Define the population.
Define the sample unit.
Define a misstatement.
Sampling may be used for substantive testing to:
1. Test the reasonableness of assertions about a
financial statement amount.
2. Develop an estimate of some amount.
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPlanning
1. Determine the test objectives.
2. Define the population characteristics.
Define the population.
Define the sample unit.
Define a misstatement.
For MUS the population is defined as the
monetary value of an account balance,
such as accounts receivable, investmentsecurities or inventory.
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPlanning
1. Determine the test objectives.
2. Define the population characteristics.
Define the population.
Define the sample unit.
Define a misstatement.
An individual euro represents the sampling unit.
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPlanning
1. Determine the test objectives.
2. Define the population characteristics.
Define the population.
Define the sample unit.
Define a misstatement.
A misstatement is defined as the difference between
monetary amounts in the clients records andamounts supported by audit evidence.
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Steps in MUS Sampling Application
Steps in MUS Sampling Application3. Determine the sample size, using the following inputs:
The desired confidence level or risk of incorrect acceptance.
The tolerable misstatement.
The expected population misstatement.
Population size.
Factor
Relationship
to Sample Size
Change
in Factor
Effect on
Sample
Lower Decrease
Higher Increase
Lower IncreaseHigher Decrease
Lower Decrease
Higher Increase
Lower Decrease
Higher Increase
Desired confidence level
Tolerable mistatement
Expected mistatement
Population size
Direct
Inverse
Direct
Direct
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPerformance
4. Select sample items.
5. Perform the auditing procedures.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
The auditor selects a sample for MUS by using a
systematic selection approach called probability-
proportionate-to-size selection. The sampling intervalcan be determined by dividing the book value of the
population by the sample size. Each individual euro in
the population has an equal chance of being selected.
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Steps in MUS Sampling Application
Assume a clients book value of accounts receivable is 2,500,000, and theauditor determined a sample size of 93. The sampling interval will be
26,882(2,500,000 93). The random number selected is 3,977theauditor would select the following items for testing:
Cumulative Sample
Account Balance Euros Item1001 Ace Emergency Center 2,350 2,350
1002 Admington Hospital 15,495 17,845 3,977 (1)
1003 Jess Base 945 18,780
1004 Good Hospital Corp. 21,893 40,673 30,859 (2)
1005 Jen Mara Corp. 3,968 44,641
1006 Axa Corp. 32,549 77,190 57,741 (3)
1007 Green River Mfg. 2,246 79,436
1008 Bead Hospital Centers 11,860 91,306 84,623 (4)
1213 Andrew Call Medical - 2,472,032
1214 Lilly Health 26,945 2,498,977 2,477,121 (93)
1215 Janyne Ann Corp. 1,023 2,500,000
Total Accounts Receivable 2,500,000
3,977
26,882
30,859
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationPerformance
4. Select sample items.
5. Perform the auditing procedures.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
After the sample items have been selected,
the auditor conducts the planned audit
procedures on the logical units containingthe selected euro sampling units.
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationEvaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
The misstatements detected in the sample
must be projected to the population.
Book value 2,500,000
Tolerable misstatement 125,000
Sample size 93Desired confidence level 5%
Expected amount of misstatement 25,000
Sampling interval 26,882
Example Information
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Steps in MUS Sampling Application
Basic PrecisionIf no misstatements are found in the sample,
the best estimate of the population
misstatement would be zero euros.
SampleSize 0 1 2 3
65 4.6 7.1 9.4 11.5
70 4.2 6.6 8.8 10.8
85 4.0 6.2 8.2 10.1
80 3.7 5.8 7.7 9.5
90 3.3 5.2 6.9 8.4100 3.0 4.7 6.2 7.6
125 2.4 3.8 5.0 6.1
Actual Number of Deviations Found
26,882 3.0 = 80,646upper misstatement limit
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Steps in MUS Sampling Application
Misstatements DetectedIn the sample of 93 items the following misstatements
were found:
3,284 21,893 = 15%Because the Axa balance of32,549 is greater than theinterval of26,882, no sampling risk is added. Since allthe euros in the large accounts are audited, there is no
sampling risk associated with large accounts.
Customer Book Value Audit Value Difference
Tainting
Factory
Good Hospital 21,893 18,609 3,284 15%Marva Medical Supply 6,705 4,023 2,682 40%
Axa Corp. 32,549 30,049 2,500 NA
Learn Heart Centers 15,000 - 15,000 100%
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Steps in MUS Sampling Application
Compute the Upper Misstatement LimitWe compute the upper misstatement limit by calculating basic
precision and ranking the detected misstatements based on
the size of the tainting factor from the largest to the smallest.
(0.15 26,882 1.4 =5,645)
Customer
Tainting
Factor
Sample
Interval
Projected
Misstatement
95% Upper
Limit
Upper
Misstatement
Basic Precision 1.00 26,882 NA 3.0 80,646
Learn Heart Centers 1.00 26,882 (26,882) 1.7 (4.7 - 3.0) 45,700
Marva Medical 0.40 26,882 (10,753) 1.5 (6.2 - 4.7) 16,130
Good Hospital 0.15 26,882 (4,032) 1.4 (7.6 - 6.2) 5,645
Add misstatments greater
that the sampling interval:
Axa Corp. NA 26,882 NA 2,500
Upper Misstatement Limit 150,621
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Steps in MUS Sampling Application
Steps in MUS Sampling ApplicationEvaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
We compare the tolerable misstatement to the upper
misstatement limit. If the upper misstatement limit is lessthan or equal to the tolerable misstatement, we conclude
that the balance is not materially misstated.
In our example, the final decision is
whether the accounts receivable balance
is materially misstated or not.
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Steps in MUS Sampling Application
In our example the upper misstatement limit of150,621is greater than the tolerable misstatement of125,000, so
the auditor concludes that the accounts receivable
balance is materially misstated.
When faced with this situation, the auditor may:
1. Increase the sample size.
2. Perform other substantive procedures.
3. Request the client adjust the accounts receivable balance.
4. If the client refuses to adjust the account balance, the
auditor would consider issuing a qualified or adverse
opinion.
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Risk When Evaluating Account Balances
Auditor's Decision Based
on Sample Evidence Not Materially Misstated Materially Misstated
Supports the fairness of
the account balanceCorrect decision
Risk of incorrect
acceptance (Type II)Does not support the
fairness of the account
balance
Risk of incorrect
rejection (Type I)
Correct Decision
True State of Financial Statement Account
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Effect of Understatement Misstatements
MUS is not particularly effective at detecting
understatements. An understated account is less likely to be
selected than an overstated account.
The most likely error will be reduced by2,688( 0.10 26,882)
CustomerBookValue
AuditValue Difference
TaintingFactor
Wayne County Medical 2,000 2,200 (200) -10%
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Identifying Individually Significant Items
The items to be tested individually are items that may
contain potential misstatements that individually exceed
the tolerable misstatement. These items are tested
100% because the auditor is not willing to accept any
sampling risk.
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Determining the Sample Size
Sample
Size=
Population book value
Tolerable misstatement Assurance factor
Combined Assessment of Slightly Below
Inherent and Control Risk Maximum Maximum Moderate LowMaximum 3.0 2.7 2.3 2.0
Slightly below maximum 2.7 2.4 2.0 1.6
Moderate 2.3 2.1 1.6 1.2
Low 2.0 1.6 1.2 1.0
Risk That Other Substantive Procedures Will Fail to
Detect Material Misstatements
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Selecting Sample Items
Auditing standards require that the sample items be
selected in such a way that the sample can be expected
to represent the population.
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Calculating the Sample Results
One way of projecting the sampling results to the
population is to apply the misstatement ratio in the
sample to the population.
If the population
total is200,000,the projected
misstatement would
be20,000(200,000 10%)
Assume the auditor
finds1,500 inmisstatements in a
sample of15,000.
The misstatementratio is 10%.
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Calculating the Sample Results
A second method is the difference estimation. This
method projects the average misstatement of each item
in the sample to all items in the population.
The projected
misstatement would
be30,000, (300
100 =3 10,000).
Assume
misstatements in a
sample of 100 items
total300, and the
population contains10,000 items.
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Non-statistical Sampling Example
The auditors of Calabro Paging Service have decidedto use non-statistical sampling to examine the accounts
receivable balance. Calabro has 11,800 accounts with
a balance of3,717,900. The auditors stratify theaccounts as follows:
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Non-statistical Sampling Example
The auditor sent positive confirmations to each of the 110
(95 + 15) accounts selected. Either the confirmations were
returned or alternative procedures were successfully
used. Four customers indicated that their accounts were
overstated and the auditors determined that themisstatements were the result of unintentional error by
client personnel. Here are the results of the audit testing:
Amount of
Book Value Audit Value Over-
Stratum Book Value of Sample of Sample Statement
>25,000 550,000 550,000 549,500 500
>3,000 850,500 425,000 423,000 2,000
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Non-statistical Sampling Example
As a result of the audit procedures, the following
projected misstatement was prepared:
The total projected misstatement of10,800 is less thanthe expected misstatement of15,000, so the auditors
may conclude that there is a low riskthat the true
misstatement exceeds the tolerable misstatement.
Amount of Projected
Stratum Misstatement Misstatement
>25,000 500 500
>3,000 2,000 4,002
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Why Did Statistical Sampling Fall Out Of
Favor?
1.Firms found that some auditors were
over relying on statistical sampling
techniques to the exclusion of good
judgment.
2.There appears to be poor linkage
between the applied audit setting and
traditional statistical sampling
applications.
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Classical Variable Sampling
Classical variables sampling uses normal distribution
theory to evaluate the characteristics of a population
based on sample data. Auditors most commonly use
classical variables sampling to estimate the size of
misstatement.
Sampling distributions are formed by plotting the
projected misstatements yielded by an infinite
number of audit samples of the same size takenfrom the same underlying population.
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Classical Variables Sampling
In classical variables sampling, the sample mean is
the best estimate of the population mean.
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Classical Variables Sampling
Advantages
1. When the auditor expects a large number of
differences between book and audited values, this
method will result in smaller sample size thanMUS.
2. The techniques are effective for both
overstatements and understatements.
3. The selection of zero balances generally does not
require special sample design considerations.
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Classical Variables Sampling
Disadvantages
1. To determine sample size, the auditor must
estimate the standard deviation of the audited
value or differences.
2. If few misstatements are detected in the sample
data, the true variance tends to be
underestimated, and the resulting projection of the
misstatements to the population is likely not to bereliable.
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Applying Classical Variables Sampling
Defining the Sampling Unit
The sampling unit can be a customer account,
an individual transaction, or a line item. In
auditing accounts receivable, the auditor candefine the sampling unit to be a customers
account balance or an individual sales invoice
included in the account balance.
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Applying Classical Variables Sampling
Determining the Sample Size
where
ZIA = One-tailed Z value for the specified
level of the risk of incorrect acceptance.SD = Estimated standard deviation.
Sample
Size
=Population size ZIA SD
Tolerable misstatement Estimated misstatement
2
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Applying Classical Variables Sampling
The risk of incorrect acceptance is the risk that the
auditor will mistakenly accept a population as fairly
stated when the true population misstatement is greater
than tolerable misstatement.
Risk of Incorrect
Acceptance Z Value
2.5% 1.96
5.0% 1.65
10.0% 1.2815.0% 1.04
20.0% 0.84
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Applying Classical Variables Sampling
The year-end balance for accounts receivable contains 5,500accounts with a book value of5,500,000. The tolerable
misstatement for accounts receivable is set at50,000. Theexpected misstatement has been judged to be20,000. The
risk of incorrect acceptance is 2.5%. Based on workcompleted last year, the auditor estimates the standard
deviation at31. Lets calculate sample size.
SampleSize 5,500 1.96 3150,00020,000
2
= = 125
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Applying Classical Variables Sampling
The mean misstatement must beprojected to the population.
= 5,500 2.65 =14,575
Population size Mean misstatementper sampling item
Projected
populationmisstatement
= (in sampling units)
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Applying Classical Variables Sampling
Point estimate of accounts receivable balance . . .
Accounts receivable
point estimate
Book
value
Projected population
misstatement=
= 5,500,00014,575 =5,485,425
The sum of the audited differences squared is
equal to36,018.32. We will use this value tocalculate the standard deviation.
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Applying Classical Variables Sampling
The formula for the standard deviation is . . .
Total audit
differences squared
Mean difference
per sampling item2
Sample
Size
Sample size 1
SD =
= 36,018.32 (125 2.652)124
=16.83
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Applying Classical Variables Sampling
Confidence
bound
Population
size ZIASD
Sample size =
= 5,500 1.96 16.83125 =16,228
Confidence
interval
Population
point estimate
Confidence
bound=
= 5,485,425 16,228
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Applying Classical Variables Sampling
Lowerbound5,469,197
Pointestimate5,485,425
Upperbound5,501,652
Book
value5,500,000
Confidence interval
If theprecision intervalincludes the book value, the
evidence supports the conclusion that the account is not
materially misstated.
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Applying Classical Variables
Sampling
Lowerbound5,469,197
Pointestimate5,485,425
Upperbound5,501,652
Book
value5,508,000
Confidence interval
When the evidence indicates that the account may be materially
misstated the auditor might consider(1) increasing sample size, (2)
performing additional substantive procedures, (3) adjusting the
account, or(4) issue a qualified or adverse opinion.
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End of Chapter 9