### Chapter 9x

```Chapter 9
Audit Sampling:
An Application to
Substantive Tests
of Account
Balances
McGraw-Hill/Irwin
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.
9-2
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%)
9-3
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.
9-4
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.
9-5
Steps in MUS
LO# 2
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:
• 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 and analyze any misstatements observed.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
9-6
LO# 2
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.
9-7
LO# 2
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.
9-8
LO# 2
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.
9-9
LO# 2
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 client’s records and
amounts supported by audit evidence.
9-10
LO# 2
Steps in MUS
Steps in MUS 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
9-11
LO# 2
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 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.
9-12
LO# 2
Steps in MUS
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, so 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
Cumulative
Dollars
\$
2,350
17,845
18,790
40,683
44,651
77,200
79,446
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)
9-13
LO# 2
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.
9-14
LO# 2
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:
New 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
9-15
LO# 3
Steps in MUS
Misstatements Detected
In the sample of 93 items, the following misstatements
were found:
Customer
Good Hospital Corp.
Marva Medical Supply
Learn Heart Centers
Axa Corp.
Book Value
\$
21,893
6,705
15,000
32,549
Audit Value
\$
18,609
4,023
0
30,049
Difference
\$
3,284
2,682
15,000
2,500
Tainting
Factor
Diff/BV
0.15
0.40
1.00
NA
Because the Axa balance of\$3,284
\$32,549
greater =than
÷is\$21,893
15%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.
9-16
LO# 3
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.
Tainting
Factor
1.00
1.00
0.40
0.15
Customer
Basic Precision
Learn Heart Centers
Marva Medical
Good Hospital
than the sampling interval:
Axa Corp.
NA
Sample
Interval
\$ 26,882
26,882
26,882
26,882
Projected
Misstatement
NA
26,882
10,753
4,032
26,882
2,500
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
9-17
LO# 3
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 but we would still want to add an
allowance for sampling risk.
Number of
Errors
0
1
2
3
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
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
\$26,882 × 3.0 = \$80,646 upper misstatement limit
9-18
LO# 3
Steps in MUS
Steps in MUS 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.
9-19
LO# 3
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 client adjust the accounts receivable balance.
4. If the client refuses to adjust the account balance, the
auditor would consider issuing a qualified or an adverse
opinion.
9-20
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
9-21
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)
9-22
```