Chapter 17
Audit Sampling for Tests of Details
of Balances
Presentation Outline
I.
The 14 Steps of Audit Sampling for Tests
of Details of Balances
II. The 7 Steps of Monetary Unit Sampling
III. Alternative Procedures When a
Population is Projected
IV. ARACR and ARIA
I. The 14 Steps of Audit
Sampling for Tests of Details of
Balances
The 14 steps required in audit sampling for tests of details of
balances parallel the 14 steps used for sampling for tests of
controls and substantive tests of transactions. Any differences
are noted on the following slides.
Audit Sampling for Tests of Details of Balances
Step 1: State the objectives of the audit test.
When auditors sample
for tests of details of
balances, the objective
is to determine
whether the account
balance being audited
is fairly stated.
Audit Sampling for Tests of Details of Balances
Step 2: Decide whether audit sampling applies
Audit sampling applies
whenever the auditor
plans to reach
conclusions about a
population based on a
sample.
Audit Sampling for Tests of Details of Balances
Step 3: Define Misstatement Conditions
Misstatement conditions
are any conditions that
represent a monetary
misstatement in a sample
item.
Step 3 for Tests of Controls and Substantive Tests of
Transactions would be: Define attributes and exception conditions.
Audit Sampling for Tests of Details of Balances
Step 4: Define the population
In testing for the existence
objective, the recorded
dollar population is the
population. If the
completeness objective is
a concern, the sample
should be selected from a
different source.
Audit Sampling for Tests of Details of Balances
Step 5: Define the Sampling Unit
 The sampling unit for
nonstatistical audit sampling in
tests of details of balances is
almost always the item making
up the account balance.
 Monetary unit sampling (MUS)
is a statistical technique in
which the sampling unit is the
individual dollars that make up
an account balance.
Audit Sampling for Tests of Details of Balances
Step 6: Specify Tolerable Misstatement
As discussed in Chapter 9,
the auditor starts with a
preliminary judgment
about materiality and
uses that total in
deciding tolerable
misstatement for each
account.
Step 6 for Tests of Controls and Substantive Tests of
Transactions would be: Specify the tolerable exception rate.
Audit Sampling for Tests of Details of Balances
Step 7: Specify Acceptable Risk of Incorrect
Acceptance (ARIA)
 There is an inverse
relationship between
ARIA and required
sample size.
 When internal controls
are effective, control risk
can be reduced,
permitting the auditor to
increase ARIA.
Step 7 for Tests of Controls and Substantive Tests of
Transactions would be: Specify acceptable risk of assessing control
risk too low.
Audit Sampling for Tests of Details of Balances
Step 8: Estimate Misstatements in the Population
 This estimate is based on
prior experience with the
client, inherent risk,
control risk, etc.
 Planned sample size
increases as the amount
of expected
misstatements in the
population increases.
Step 8 for Tests of Controls and Substantive Tests of
Transactions would be: Estimate the population exception rate.
Audit Sampling for Tests of Details of Balances
Step 9: Determine the Initial Sample Size
 Table 17-3 on page 525
summarizes the primary
factors that influence sample
size for nonstatistical
sampling.
 Figure 17-2 on page 525
presents a table for
computing sample size based
on the AICPA Audit Sampling
Auditing Guide.
 MUS uses a statistical
formula illustrated on page
538.
Audit Sampling for Tests of Details of Balances
Step 10: Select the Sample
 For nonstatistical
sampling, auditing
standards permit the
auditor to use any of the
selection methods
discussed in Chapter 15.
 MUS uses PPS sampling
that allows the physical
inclusion of an item
more than once in the
sample.
Audit Sampling for Tests of Details of Balances
Step 11: Perform the Audit Procedures
Auditor applies the
appropriate audit
procedures to each item
in the sample to
determine whether it is
correct or contains a
misstatement.
Audit Sampling for Tests of Details of Balances
Step 12: Generalize from the Sample to the
Population
 A common approach to is
assume that misstatement in
the population are
proportional to
misstatements in the sample.
(See pages 526-527).
 For MUS, the process
involves a four-step process.
(See page 533-534).
 Auditor must consider that
the true population
misstatement may be larger
due to sampling error.
Audit Sampling for Tests of Details of Balances
Step 13: Analyze the Misstatements
The reason for the
misstatement must be
considered. It could be
from an isolated error.
However, it could have
arisen from the
consistent misapplication
of accounting procedure.
Such causes could
represent a large effect
on the financial
statements.
Step 13 for Tests of Controls and Substantive Tests of
Transactions would be: Analyze the exceptions.
Audit Sampling for Tests of Details of Balances
Step 14: Decide the Acceptability of the
Population
 With nonstatistical
population the auditor
uses judgment to decide
if the potential
misstatement in the
population is greater
than tolerable
misstatement.
 MUS computes
misstatement bounds
that provide an objective
evaluation.
II. The 7 Steps of Monetary Unit
Sampling
Monetary unit sampling (MUS) is a statistical
method of sampling that is also called dollar unit
sampling, cumulative monetary amount sampling,
and sampling with probability proportional to size.
This section discusses the seven steps of MUS and
the MUS decision rule.
Note: The computation of the appropriate sample
size for MUS is illustrated on page 538.
Monetary Unit Sampling (MUS)
Step 1: Determine misstatements for each sample
item.
CUST.
No.
RECORDED
ITEM
VALUE
AUDITED
ITEM
VALUE
MISSTATEMENT
2073
6,200
6,100
100
5111
12,910
12,000
910
5206
4,322
4,450
(128)
7642
23,000
22,995
5
9816
8,947
2,947
6,000
Monetary Unit Sampling (MUS)
Step 2: Calculate misstatement per dollar unit in
each sample item.
CUST.
No.
RECORDED
ITEM
VALUE
AUDITED
ITEM
VALUE
MISSTATEMENT
MISSTATEMENT /
RECORDED ITEM
VALUE
2073
6,200
6,100
100
.016
5111
12,910
12,000
910
.07
5206
4,322
4,450
(128)
(.03)
7642
23,000
22,995
5
.0002
9816
8,947
2,947
6,000
.671
Monetary Unit Sampling (MUS)
Step 3: Layer misstatements per dollar unit from highest to lowest,
including the percent misstatement assumption for sample items not
misstated.
OVERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
0
1,200,000
1.0 *
1
1,200,000
.671
2
1,200,000
.07
3
1,200,000
.016
4
1,200,000
.0002
UNDERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
0
1,200,000
1.0 *
1
1,200,000
.03
* See Appropriate Percent of Misstatement Assumption on page 533.
Monetary Unit Sampling (MUS)
Step 4: Determine upper precision limit from attributes sampling table (Table 15-9
on page 470) and calculate the percent misstatement bound for each misstatement
(layer).
OVERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
UPPER
PRECISION
LIMIT
PORTION*
0
1,200,000
1.0
.030
1
1,200,000
.671
.017
2
1,200,000
.07
.015
3
1,200,000
.016
.014
4
1,200,000
.0002
.014
UNDERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
UPPER
PRECISION
LIMIT
PORTION*
0
1,200,000
1.0
.030
1
1,200,000
.03
.017
* ARIA OF 5%. Sample size of 100.
Monetary Unit Sampling (MUS)
Step 5: Calculate initial upper and lower misstatement bounds for each layer
and total.
OVERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
UPPER
PRECISION
LIMIT
PORTION
MISSTATEMENT
BOUND
0
1,200,000
1.0
.030
36,000
1
1,200,000
.671
.017
13,688
2
1,200,000
.07
.015
1,260
3
1,200,000
.016
.014
269
4
1,200,000
.0002
.014
3
.090
51,220
Totals
UNDERSTATEMENTS
RECORDED
POPULATION
VALUE
MISSTATEMENT
PERCENTAGE
ASSUMPTION
UPPER
PRECISION
LIMIT
PORTION
MISSTATEMENT
BOUND
0
1,200,000
1.0
.030
36,000
1
1,200,000
.03
.017
612
.047
36,612
Totals
Monetary Unit Sampling (MUS)
Step 6: Calculate point estimate for
overstatements and understatements.
Sum of Unit
Misstatement
Assumptions
X
Sample Size
Recorded
Population
Value
Point
Estimate
=
Overstatement Point Estimate:
( .671 +.07 +.016 + .0002 )
X 1,200,000
=
9,086
=
360
100
Understatement Point Estimate:
.03
100
X 1,200,000
Monetary Unit Sampling (MUS)
Step 7: Calculate adjusted upper and lower
misstatement bounds.
Most MUS users believe that the approach is overly
conservative when there are offsetting amounts. The
adjustment of bounds for offsetting amounts is made by
reducing each bound by the opposite point estimate.
Initial understatement bound
Less overstatement point estimate
Adjusted understatement bound
36,612
(9,086)
27,526
Initial overstatement bound
Less understatement point estimate
Adjusted overstatement bound
51,220
(360)
50,860
The MUS Decision Rule
If both the lower misstatement bound (LMB) and upper
misstatement bound (UMB) fall between the understatement
and overstatement tolerable misstatement amounts, accept
the conclusions that the book value is not misstated by a
material amount. Otherwise, conclude that the book value
is misstated by a material amount.
Tolerable misstatement
Tolerable misstatement
($40,000)
$40,000
Reject
($27,526)
($50,860)
LMB
UMB
III. Alternatives When a Population is Rejected
A. Take No Action Until Tests of Other Audit Areas
are Completed
B. Perform Expanded Audit Tests in Specific Areas
C. Increase the Sample Size
D. Adjust the Account Balance
E. Request the Client to Correct the Population
F. Refuse to Give an Unqualified Opinion
A. Take No Action Until Tests of Other Audit
Areas are Completed
Offsetting
misstatements in
other parts of the
audit may make a
balance acceptable.
B. Perform Expanded Audit Tests in Specific
Areas
After a problem area is
corrected, the remaining
misstatements may be
within an acceptable
range. May be effective
when errors are of a
specific type.
C. Increase the Sample Size
When the auditor increases
sample size, sampling error is
reduced if the rate of
misstatements in the expanded
sample, their dollar amount,
and their direction are similar
to those in the original sample.
This could satisfy the auditor’s
tolerable misstatement
requirements. May be helpful
when initial sample is not
representative of the
population.
D. Adjust the Account Balance
 When the auditor concludes
that an account balance is
materially misstated, the
client may be willing to
adjust the book value based
on the sample results.
 Even when the client adjusts
the book value the auditor
must consider whether
sampling error to exceed
tolerable misstatement.
 Appropriate when client
balance is misstated.
E. Request the Client to Correct the Population
When the client’s records
are filled with significant
misstatements, the
auditor may request the
client to correct the
population before an
effective audit process
can begin.
F. Refuse to Give an Unqualified Opinion
If the auditor believes that
there is a reasonable
chance that the financial
statements are
materially misstated, it
would be a serious
breach of auditing
standards to issue an
unqualified opinion.
The audit
process
must have
some teeth
in it!
IV. ARACR and ARIA
A lower control risk requires a
lower acceptable risk of
assessing control risk too low
(ARACR). This requires a
larger sample size for tests of
controls.
If tested controls are effective,
the auditor can increase
acceptable risk of incorrect
acceptance (ARIA). This
means that the auditor can use
smaller sample sizes for tests
of details of balances.
Summary
Steps of Audit Sampling for Tests of Details
of Balances
The Statistical Technique of Monetary Unit
Sampling
The Rejection of a Population
ARACR and ARIA