Chapter 17 Audit Sampling for Tests of Details of Balances
Chapter 17Audit 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 SamplingIII. Alternative Procedures When a
Population is ProjectedIV. 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 BalancesStep 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 BalancesStep 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 BalancesStep 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 ofTransactions would be: Define attributes and exception conditions.
Audit Sampling for Tests of Details of BalancesStep 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 BalancesStep 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 BalancesStep 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 ofTransactions would be: Specify the tolerable exception rate.
Audit Sampling for Tests of Details of BalancesStep 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 ofTransactions would be: Specify acceptable risk of assessing control
risk too low.
Audit Sampling for Tests of Details of BalancesStep 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 ofTransactions would be: Estimate the population exception rate.
Audit Sampling for Tests of Details of BalancesStep 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 BalancesStep 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 BalancesStep 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 BalancesStep 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 ofTransactions 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.
RECORDEDITEM
VALUE
AUDITEDITEM
VALUEMISSTATEMENT
2073 6,200 6,100 1005111 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.
RECORDEDITEM
VALUE
AUDITEDITEM
VALUEMISSTATEMENT
MISSTATEMENT / RECORDED ITEM VALUE
2073 6,200 6,100 100 .0165111 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.
OVER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
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
UNDER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
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).
OVER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
UPPER PRECISION
LIMIT PORTION*
0 1,200,000 1.0 .0301 1,200,000 .671 .017
2 1,200,000 .07 .015
3 1,200,000 .016 .014
4 1,200,000 .0002 .014
UNDER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
UPPER PRECISION
LIMIT PORTION*
0 1,200,000 1.0 .0301 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.
OVER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
UPPER PRECISION
LIMIT PORTION
MISSTATE-MENT
BOUND
0 1,200,000 1.0 .030 36,0001 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
UNDER-STATEMENTS
RECORDEDPOPULATION
VALUE
MISSTATEMENTPERCENTAGEASSUMPTION
UPPER PRECISION
LIMIT PORTION
MISSTATE-MENT
BOUND
0 1,200,000 1.0 .030 36,0001 1,200,000 .03 .017 612
Totals .090 51,220
Totals .047 36,612
Monetary Unit Sampling (MUS) Step 6: Calculate point estimate for
overstatements and understatements.Sum of Unit
Misstatement Assumptions
Sample SizeX
Recorded Population
Value=
Point Estimate
Overstatement Point Estimate:
( .671 +.07 +.016 + .0002 )
100X 1,200,000 = 9,086
Understatement Point Estimate:
.03
100X 1,200,000 = 360
Initial understatement bound 36,612Less overstatement point estimate (9,086)Adjusted understatement bound 27,526
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 overstatement bound 51,220Less understatement point estimate (360)Adjusted overstatement bound 50,860
Reject
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
($40,000)
Tolerable misstatement
$40,000
($27,526)
LMB
($50,860)
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 AreasC. Increase the Sample Size
D. Adjust the Account BalanceE. 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 PopulationARACR and ARIA