This document discusses audit sampling techniques for substantive tests of account balances, specifically monetary unit sampling (MUS). It outlines the steps in applying MUS, including: 1) planning by defining the population, sampling unit, and misstatements, 2) determining sample size based on desired confidence level, tolerable misstatement, expected population misstatement, and population size, 3) selecting the sample, 4) performing audit procedures on the sample, 5) calculating the projected misstatement and upper limit, and 6) drawing conclusions by comparing the upper limit to the tolerable misstatement. An example application of MUS to test accounts receivable is provided to illustrate these steps.

1. Chapter 9
Audit Sampling: An
Application to
Substantive Tests of
Account Balances
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2. Substantive Tests of Details of
Account Balances
Consider the following information about the inventory
account balance of an entity:
Book value of inventory account balance 3,000,000
$
Book value of items sampled 100,000
$
Audited value of items sampled 98,000
Total amount of overstatement observed in audit sample 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%)
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3. 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.
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4. Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to
express a monetary conclusion rather than a
rate of occurrence. It is commonly used by
auditors to test accounts such as accounts
receivable, loans receivable, investment
securities, and inventory.
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5. 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.
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6. Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics:
• Define the population.
• Define the sampling unit.
• Define a misstatement.
3. Determine the sample size, using the following inputs:
• Desired confidence level or risk of incorrect acceptance.
• Tolerable misstatement.
• Expected population misstatement.
• Population size.
Performance
4. Select sample items.
5. Perform the auditing procedures.
• Understand and analyze any misstatements observed.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
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7. Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics.
• Define the population.
• Define the sampling 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., accuracy,
existence). This is the most common use of sampling
for substantive testing.
2. Develop an estimate of some amount.
LO# 2
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8. Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics.
• Define the population.
• Define the sampling 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.
LO# 2
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9. Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics.
• Define the population.
• Define the sampling unit.
• Define a misstatement.
An individual dollar represents the sampling unit.
LO# 2
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10. Steps in MUS
Steps in MUS Application
Planning
1. Determine the test objectives.
2. Define the population characteristics.
• Define the population.
• Define the sampling unit.
• Define a misstatement.
A misstatement is defined as the difference between
monetary amounts in the entity’s records and
amounts supported by audit evidence.
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11. Steps in MUS
Steps in MUS Application
3. Determine the sample size, using the following inputs:
• Desired confidence level or risk of incorrect acceptance.
• Tolerable misstatement.
• Expected population misstatement.
• Population size.
Factor
Relationship
to Sample Size
Change
in Factor
Effect on
Sample
Lower Decrease
Higher Increase
Lower Increase
Higher 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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12. Steps in MUS
Steps in MUS 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 probability-
proportional-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.
LO# 2
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13. Steps in MUS
Assume an entity’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, so the
auditor would select the following items for testing:
Cumulative Sample
Account Balance Dollars Item
1001 Ace Emergency Center 2,350
$ 2,350
$
1002 Admington Hospital 15,495 17,845 3,977
$ (1)
1003 Jess Base, Inc. 945 18,790
1004 Good Hospital Corp. 21,893 40,683 30,859 (2)
1005 Jen Mara Corp. 3,968 44,651
1006 Zippy Corp. 32,549 77,200 57,741 (3)
1007 Green River Mfg. 2,246 79,446
1008 Bead Hospital Centers 11,860 91,306 84,623 (4)
• • • •
• • • •
1213 Andrew Call Medical - 2,472,032
1214 Lilly Heather, Inc. 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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14. Steps in MUS
Steps in MUS 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.
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15. Steps in MUS
Steps in MUS 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. Let’s
look at the following example:
Book value 2,500,000
$
Tolerable misstatement 125,000
$
Sample size 93
Desired confidence level 95%
Expected amount of misstatement 25,000
$
Sampling interval 26,882
$
New Example Information
LO# 2
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16. Number of Misstatement Incremental Misstatement Incremental
Errors Factor Increase Factor Increase
0 2.3 3.0
1 3.9 1.6 4.7 1.7
2 5.3 1.4 6.2 1.5
3 6.6 1.3 7.6 1.4
4 7.9 1.3 9.0 1.4
95% Confidence Level
90% Confidence Level
Steps in MUS
Basic Precision using the Table
If no misstatements are found in the sample,
the best estimate of the population
misstatement would be zero dollars.
$26,882 × 3.0 = $80,646 upper misstatement limit
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17. Steps in MUS
Misstatements Detected
In the sample of 93 items, the following misstatements
were found:
Customer Book Value Audit Value Difference
Tainting
Factor
Diff/BV
Good Hospital Corp. 21,893
$ 18,609
$ 3,284
$ 0.15
Marva Medical Supply 6,705 4,023 2,682 0.40
Learn Heart Centers 15,000 0 15,000 1.00
Axa Corp. 32,549 30,049 2,500 NA
$3,284 ÷ $21,893 = 15%
Because the Axa balance of $32,549 is greater than the
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.
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18. Steps in MUS
Computed Upper Misstatement Limit
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
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
than the sampling interval:
Axa Corp. NA 26,882 2,500 2,500
Total 44,167
$ 150,621
$
(0.15 × $26,882 × 1.4 = $5,645)
LO# 3
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19. Steps in MUS
Steps in MUS Application
Evaluation
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 less
than 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.
LO# 3
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20. Steps in MUS
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 entity adjust the accounts receivable balance.
4. If management refuses to adjust the account balance, the
auditor would consider issuing a qualified or an adverse
opinion.
LO# 3
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