### Chapter 9

```Chapter 9
Audit Sampling: An Application to Substantive Tests of
Account Balances
McGraw-Hill/Irwin
Purpose
To determine if a financial statement
account is fairly stated.
Sampling Techniques
Statistical
- Monetary Unit Sampling ( MUS)
- Classical variable sampling
Non-statistical
LO# 1
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.
3. Estimated misstatement.
Population plays a bigger role in some of the sampling
techniques used for substantive testing.
Misstatements discovered in the audit sample must be
projected to the population, and there must be an
allowance for sampling risk.
9-4
LO# 1
Substantive Tests of Details of
Account Balances
Consider the following information about the inventory
account balance of an audit client:
Book value of inventory account balance
Book value of items sampled
Audited value of items sampled
Total amount of overstatement observed in audit sample
\$ 3,000,000
\$
100,000
98,000
\$
2,000
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 of \$60,000.
(\$3,000,000 × 2%)
9-5
LO# 1
Substantive Tests of Details of
Account Balances
The results of our audit test depend upon
the tolerable misstatement associated
with the inventory account. If the tolerable
misstatement is \$50,000, we cannot
conclude that the account is fairly stated
because our best estimate of the
projected misstatement is greater than
the tolerable misstatement.
9-6
LO# 2
Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to
express a conclusion in dollar amounts rather
than as a rate of occurrence. It is commonly
used by auditors to test accounts such as
accounts receivable, loans receivable,
investment securities, and inventory.
9-7
LO# 2
Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory (used
primarily to test controls) to estimate the
percentage of monetary units in a population
that might be misstated and then multiplies
this percentage by an estimate of how much
the dollars are misstated.
9-8
LO# 2
Monetary-Unit Sampling (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.
9-9
LO# 2
Monetary-Unit Sampling (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 are
detected, the sample results calculations may
overstate the allowance for sampling risk.
9-10
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Planning
1. 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.
Performance
4. Select sample items.
5. Perform the auditing procedures.
• Understand an alayzye any missstatements observed.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
9-11
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Planning
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 (i.e., is the amount fairly
stated). This is the most common use of sampling for
substantive testing.
2. Develop an estimate of some amount.
9-12
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Planning
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, investment
securities, or inventory.
9-13
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Planning
1. Determine the test objectives.
2. Define the population characteristics.
• Define the population.
• Define the sample unit.
• Define a misstatement.
An individual dollar represents the sampling unit.
9-14
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Planning
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 client’s records and
amounts supported by audit evidence.
9-15
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
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.
Factor
Relationship
to Sample Size
Desired confidence level
Direct
Tolerable mistatement
Inverse
Expected mistatement
Direct
Population size
Direct
Change
in Factor
Lower
Higher
Lower
Higher
Lower
Higher
Lower
Higher
Effect on
Sample
Decrease
Increase
Increase
Decrease
Decrease
Increase
Decrease
Increase
9-16
LO# 2
Steps in MUS Sampling
Steps in MUS Sampling Application
Performance
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 probabilityproportional-to-size selection. The sampling interval can
be determined by dividing the book value of the
population by the sample size. Each individual dollar in
the population has an equal chance of being selected
and items or “logical units” greater than the interval will
always be selected.
9-17
LO# 3
Steps in MUS Sampling
Assume a client’s book value of accounts receivable is \$2,500,000, and the
auditor determined a sample size of 93. The sampling interval will be
\$26,882 (\$2,500,000 ÷ 93). The random number selected is \$3,977 the
auditor would select the following items for testing:
Account
1001 Ace Emergency Center
1003 Jess Base, Inc.
1004 Good Hospital Corp.
1005 Jen Mara Corp.
1006 Zippy Corp.
1007 Green River Mfg.
•
•
1213 Andrew Call Medical
1214 Lilly Heather, Inc.
1215 Janyne Ann Corp.
Total Accounts Receivable
Balance
\$
2,350
15,495
945
21,893
3,968
32,549
2,246
11,860
•
•
26,945
1,023
\$ 2,500,000
Cumulatvie
Dollars
\$
2,350
17,845
18,780
40,673
44,641
77,190
79,436
91,306
•
•
2,472,032
2,498,977
\$ 2,500,000
Sample
Item
\$
3,977
(1)
30,859
(2)
57,741
(3)
84,623
•
•
(4)
2,477,121
\$ 3,977
26,882
\$ 30,859
(93)
9-18
LO# 3
Steps in MUS Sampling
Steps in MUS Sampling Application
Performance
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 containing
the selected dollar sampling units.
9-19
LO# 3
Steps in MUS Sampling
Steps in MUS Sampling Application
Evaluation
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.
Example Information
Book value
Tolerable misstatement
Sample size
Desired confidence level
Expected amount of misstatement
Sampling interval
\$ 2,500,000
\$ 125,000
93
95%
\$
25,000
\$
26,882
9-20
LO# 3
Steps in MUS Sampling
Basic Precision using the Tables
If no misstatements are found in the sample,
the best estimate of the population
misstatement would be zero dollars.
Sample
Size
65
70
85
80
90
100
125
Actual Number of Deviations Found
0
1
2
3
4.6
7.1
9.4
11.5
4.2
6.6
8.8
10.8
4.0
6.2
8.2
10.1
3.7
5.8
7.7
9.5
3.3
5.2
6.9
8.4
3.0
4.7
6.2
7.6
2.4
3.8
5.0
6.1
\$26,882 × 3.0 = \$80,646 upper misstatement limit
9-21
LO# 3
Steps in MUS Sampling
Misstatements Detected
In the sample of 93 items, the following misstatements
were found:
Customer
Good Hospital
Marva Medical Supply
Axa Corp.
Learn Heart Centers
Book Value
\$
21,893
6,705
32,549
15,000
Audit Value
\$
18,609
4,023
30,049
-
Difference
\$
3,284
2,682
2,500
15,000
Tainting
Factory
15%
40%
NA
100%
Because the Axa balance of\$3,284
\$32,549
is greater
than the
÷ \$21,893
= 15%
interval of \$26,882, no sampling risk is added. Since all
the dollars in the large accounts are audited, there is no
sampling risk associated with large accounts.
9-22
LO# 3
Steps in MUS Sampling
Computed Upper Misstatement Limit using Tables
We 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.
Customer
Basic Precision
Learn Heart Centers
Marva Medical
Good Hospital
that the sampling interval:
Axa Corp.
Tainting
Factor
1.00
1.00
0.40
0.15
NA
Sample
Interval
\$ 26,882
26,882
26,882
26,882
Projected
Misstatement
NA
(26,882)
(10,753)
(4,032)
26,882
NA
Upper Misstatement Limit
(0.15 × \$26,882 × 1.4 = \$5,645)
95% Upper
Limit
3.0
1.7 (4.7 - 3.0)
1.5 (6.2 - 4.7)
1.4 (7.6 - 6.2)
Upper
Misstatement
\$
80,646
45,700
16,130
5,645
\$
2,500
150,621
9-23
LO# 3
Steps in MUS Sampling
Steps in MUS Sampling Application
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
In our example, the final decision is
whether the accounts receivable balance
is materially misstated or not.
We compare the tolerable misstatement to the upper
misstatement limit. If the upper misstatement limit is less
than or equal to the tolerable misstatement, we conclude
that the balance is not materially misstated.
9-24
LO# 3
Steps in MUS Sampling
In our example, the upper misstatement limit of \$150,621
is greater than the tolerable misstatement of \$125,000, 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.
9-25
LO# 3
Risk When Evaluating Account
Balances
True State of Financial Statement Account
Auditor's Decision Based
on Sample Evidence
Supports the fairness of
the account balance
Does not support the
fairness of the account
balance
Not Materially Misstated
Correct decision
Risk of incorrect
rejection (Type I)
Materially Misstated
Risk of incorrect
acceptance (Type II)
Correct Decision
9-26
Why is the Sampling Interval
Rather than the Sample Size Used
in Evaluating MUS Results?
LO# 3
Due to simplifying assumptions about accounting populations,
the misstatement factors used in most MUS evaluation
approaches are nearly identical to the misstatement factors
associated with a sample size of 100, regardless of the actual
sample size used by the auditor. Always use these factors:
Number of
Errors
0
1
2
3
4
95% Confidence Level
Misstatement
Incremental
Factor
Increase
3.0
4.7
1.7
6.2
1.5
7.6
1.4
9.0
1.4
90% Confidence Level
Misstatement
Incremental
Factor
Increase
2.3
3.9
1.6
5.3
1.4
6.6
1.3
7.9
1.3
9-27
LO# 3
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.
Customer
Wayne County Medical
Book
Value
\$ 2,000
Audit
Value
\$ 2,200
Difference
\$
(200)
Tainting
Factor
-10%
The most likely error will be reduced by \$2,688
(– 0.10 × \$26,882)
9-28
LO# 4
Nonstatistical Sampling for Tests
of Account Balances
The sampling unit for nonstatistical sampling is normally a
customer account, an individual transaction, or a line item
on a transactions. When using nonstatistical sampling, the
following items must be considered:
o Identifying individually significant items.
o Determining the sample size.
o Selecting sample items.
o Calculating the sample results.
9-29
LO# 4
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.
9-30
LO# 4
Determining the Sample Size
Sampling Population book value
Sample
= Tolerable – Expected misstatement × Assurance factor
Size
Assessment of Risk of
Material Misstatement
Maximum
Slightly below maximum
Moderate
Low
Desired Level of Confidence
Slightly Below
Maximum
Maximum
Moderate
3.0
2.7
2.3
2.7
2.4
2.0
2.3
2.1
1.6
2.0
1.6
1.2
Low
2.0
1.6
1.2
1.0
9-31
LO# 4
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.
9-32
LO# 4
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.
Assume the auditor
finds \$1,500 in
misstatements in a
sample of \$15,000.
The misstatement
ratio is 10%.
If the population
total is \$200,000,
the projected
misstatement would
be \$20,000
(\$200,000 × 10%)
9-33
LO# 4
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.
Assume
misstatements in a
sample of 100 items
total \$300 (for
average
misstatement of \$3),
and the population
contains 10,000
items.
The projected
misstatement would be
\$30,000 (\$3 × 10,000).
9-34
LO# 4
Nonstatistical Sampling
Example
The auditor’s of Calabro Wireless Service have
decided to use nonstatistical sampling to examine the
accounts receivable balance. Calabro has a total of
11,800
(15 + 250 + 11,535) accounts with a
balance of \$3,717,900. The auditor’s stratify the
accounts as follows:
Number and Size
of Accounts
15 accounts > \$25,000
250 accounts > \$3,000
11,535 accounts < \$3,000
Total
Book
Value
\$ 550,000
850,500
2,317,400
\$ 3,717,900
9-35
LO# 4
Nonstatistical Sampling
Example
The auditor’s decide . . .
o There is a low assessment for inherent and control risk.
o The tolerable misstatement is \$40,000, and the expected
misstatement is \$15,000.
o There is a moderate risk that other auditing procedures
will fail to detect material misstatements.
o All customer account balances greater than \$25,000 are
to be audited.
9-36
Nonstatistical Sampling
Example
LO# 4
Sampling population book value
Sample
= Tolerable - Estimated misstatement × Assurance factor
Size
\$3,717,900 – \$550,000
Sample
=
Size
\$3,167,900
\$40,000
× 1.2 = 95 (rounded)
\$55,000 – \$15,000
Combined Assessment of
Inherent and Control Risk
Maximum
Slightly below maximum
Moderate
Low
Risk That Other Substantive Procedures Fail to
Detect Material Misstatement
Slightly Below
Maximum
Maximum
Moderate
Low
3.0
2.7
2.3
2.0
2.7
2.4
2.0
1.6
2.3
2.1
1.6
1.2
2.0
1.6
1.2
1.0
9-37
Nonstatistical Sampling
Example
LO# 4
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 the
misstatements were the result of unintentional error by
client personnel. Here are the results of the audit testing:
Stratum
>\$25,000
>\$3,000
<\$3,000
Book Value
\$
550,000
850,500
2,317,400
Book Value
of Sample
\$
550,000
425,000
92,000
Audit Value
of Sample
\$
549,500
423,000
91,750
Amount of
OverStatement
\$
500
2,000
250
9-38
Nonstatistical Sampling
Example
LO# 4
As a result of the audit procedures, the following
projected misstatement was prepared:
Amount of
Ratio of Misstatement
Stratum
Misstatement
in Stratum Tested
>\$25,000
\$
500 Not Applicable--100% Tested
>\$3,000
2,000
\$2,000 ÷ 425,000 × \$850,500
<\$3,000
250
\$250 ÷ 92,000 × \$2,317,400
Total projected misstatement
Projected
Misstatement
\$
500
4,002
6,298
\$
10,800
The total projected misstatement of \$10,800 is less than
the expected misstatement of \$15,000, so the auditors
may conclude that there is an acceptably low risk that
the true misstatement exceeds the tolerable
misstatement.
9-39
LO# 4
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
sampling applications.
9-40
LO# 5
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 taken
from the same underlying population.
9-41
LO# 5
Classical Variables Sampling
A sampling distribution is useful because it allows us
to estimate the probability of observing any single
sample result.
9-42
LO# 5
Classical Variables Sampling
In classical variables sampling, the sample mean is
the best estimate of the population mean.
9-43
LO# 5
Classical Variables Sampling
1. When the auditor expects a large number of
differences between book and audited values, this
method will result in smaller sample size than
MUS.
2. The techniques are effective for both
overstatements and understatements.
3. The selection of zero balances generally does not
require special sample design considerations.
9-44
LO# 5
Classical Variables Sampling
1. Does not work well when little or not misstatement
is expected in the population.
2. To determine sample size, the auditor must
estimate the standard deviation of the audited
value or differences.
3. 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 be
reliable.
9-45
End of Chapter 9
9-46
```