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Financial Statement Auditing: A Risk-Based Approach, 11e
Solutions for Chapter 8
Answers to “Test Your Basic Knowledge” Questions
8-1 T
8-2 T
8-3 a
8-4 c
8-5 T
8-6 F
8-7 e
8-8 a
8-9 F
8-10 F
8-11 e
8-12 c
8-13 T
8-14 F
8-15 b
8-16 a
8-17 T
8-18 F
8-19 a
8-20 e
8-21 F
8-22 T
8-23 c
8-24 c
8-25 F
8-26 T
8-27 e
8-28 c
8-29 T
8-30 T
8-31 b
8-32 d
8-33 F
8-34 F
8-35 a
8-36 e
8-37 F
8-38 T
8-39 b
8-40 e
Review Questions and Short Cases
8-1
Auditor use sampling in testing both controls and account balances and assertions. Sampling
involves looking at less than 100% of the transactions that occurred during the period under
audit. Sampling techniques would be appropriate when an auditor wants to perform procedures
such as examining documents, reperforming calculations, or sending confirmations.
Data analytics tools are techniques and processes that auditors use to enhance their productivity
and effectiveness; auditors use these tools to extract, categorize, identify, and analyze patterns or
trends in the data; data analytics tool vary according to auditor objectives.
8-2
See Exhibit 8.1.
8-3

Sampling units refer to the individual items to be tested. The sampling units make up the
population. The population is a group of transactions or the items that make up an account
balance for which the auditor wants to estimate some characteristic, such as the effectiveness of a
control procedure or the extent of misstatement in an account.
8-4
The auditor needs to answer four questions when sampling:
1. Which population and sampling unit should be tested, and what characteristics should
be examined (population)?
2. How many items should be selected for audit testing (sample size)?
3. Which items should be included in the sample (selection)?
4. What inferences can be made about the overall population from the sample
(evaluation)?
8-5
Sampling risk is the risk that the auditor’s conclusion based on a sample might be different from
the conclusion he or she would reach if the test were applied in the same way to the entire
population. Nonsampling risk is the risk that the auditor reaches an erroneous conclusion for any
reason not related to sampling risk.
8-6
a.
Risk of incorrect acceptance of internal control reliability The risk that the auditor will
conclude that the state of internal controls is effective when internal controls are
actually not effective (also referred to as the risk of assessing control risk too
low).
Risk of incorrect rejection of internal control reliability The risk that the auditor will
conclude that the state of internal controls is not effective when internal controls
are actually effective (also referred to as the risk of assessing control risk too
high).
Risk of incorrect acceptance of book value The risk that the auditor will conclude that
the account balance does not contain a material misstatement when the account
balance actually does contain a material misstatement.
Risk of incorrect rejection of book value The risk that the auditor will conclude that
the account balance contains a material misstatement when the account balance
actually does not contain a material misstatement.

b. The auditor should be most concerned about the risk of incorrect acceptance of either
internal control reliability or of book value because these lead to audit ineffectiveness.
While the auditor will certainly not want to be inefficient, ineffectiveness is a greater risk.
8-7
See Exhibit 8.4.
8-8
Attributes sampling is a statistical sampling method used to estimate the rate of control procedure
failures based on selecting a sample and performing the appropriate audit procedure. An attribute
is a characteristic of the population of interest to the auditor.
An example of an attribute of interest to an auditor would be evidence that the client has matched
vendor invoice details with the purchase order and receiving report before payment approval, and
noting that they match before authorizing a payment for the goods received.
An example of a control failure would be if the appropriate client employee failed to seek credit
approval for a new account, even though doing so is required by company policy.
8-9
In defining the population, the auditor should address:
• The period to be covered by the test; for example, the year when evaluating controls
• The sampling unit; for example, an item that would indicate the operation of a control
• The completeness of the population
8-10
The AICPA’s 2012 Audit Sampling formally defines the tolerable rate of deviation as a rate of
deviation set by the auditor in respect of which the auditor seeks to obtain an appropriate level of
assurance that the rate of deviation set by the auditor is not exceeded by the actual rate of
deviation in the population. This term is sometimes referred to as the tolerable failure rate. In
more practical terms, the auditor’s tolerate rate of deviation is the level at which the control’s
failure to operate would cause the auditor to conclude that the control is not effective and would
likely change the auditor’s planned assessment of control risk in performing tests of account
balances.
8-11
Risk of
Overreliance
Tolerable Rate of
Deviation
Expected
Population
Sample Size
(Expected Errors)

Deviation Rate
a. 5% 2% 1% 590 (6)
b. 5% 6% 5% 1,580 (79)
c. 5% 10% 8% 649 (52)
d. 10% 2% 1% 398 (4)
e. 10% 6% 5% 1,019 (51)
f. 10% 10% 8% 424 (34)
8-12
Risk of
Overreliance
Tolerable Rate of
Deviation
Expected
Population
Deviation Rate
Sample Size
a. 10% 20% 0% 11
b. 5% 20% 0% 14
c. 5% 20% 0.25% 22
d. 5% 10% 0% 29
e. 10% 10% 0.25% 38
f. 10% 15% 7% 52
g. These assumptions imply that in order to justify these relatively small sample sizes, the
auditor will have to accept a relatively high tolerable rate of deviation, while expecting a
relatively low expected population deviation rate; these assumptions may be unrealistic,
thus calling into question very low sample sizes.
8-13
a. An increase in sampling risk results in a smaller sample because the auditor is willing to
accept more risk of the audit conclusion being in error. As a general sampling rule, the
more risk the auditor is willing to take of being wrong, the smaller will be the sample
size.
b. An increase in the tolerable rate of deviation results in a smaller sample because the
sample does not have to be as precise – there is a bigger range between the tolerable
failure rate and expected failure rate. Additionally, this increase likely means the auditor
has concluded the control is less important – also resulting in a smaller sample size.
c. An increase in the expected population deviation rate results in a larger sample result
because the sample has to be more precise – there is a smaller range between the tolerable
failure rate and expected failure rate.
d. Increase in population size normally does not affect the sample size unless the population
size is relatively small; then a larger sample would be required, but not in proportion to
the increase in population size.

8-14
a. Simple random sampling. Selecting a random sample by matching random numbers
generated by a computer or selected from a random-number table with, for example,
document numbers such as an invoice or a purchase order.
b. Systematic sampling. A statistical sampling method that involves dividing the number of
physical units in the population by the sample size to determine a uniform interval; a
random starting point is selected in the first interval, and one item is selected throughout
the population at each of the uniform intervals after the starting point.
c. Systematic random sampling. This sampling technique involves systematic sampling in
which the first item is selected randomly from the interval.
d. Haphazard sampling. A nonstatistical sample selection method that attempts to
approximate a random selection by selecting sampling units without any conscious bias
or special reason for including or omitting certain items from the sample.
e. Block sampling. A sampling technique that involves selecting a sample that consists of
contiguous population items, such as selecting transactions by day or week.
8-15
Risk of
Overreliance
Sample Size Number of
Deviations
Upper Limit of
Deviations
a. 5% 20 0 14.0%
The upper limit is
greater than 0, even
though there were
no deviations,
because the sample
size is very low; so
there is a strong
possibility that even
though the auditor
detected no
deviations in the
sample of 20 items,
there exist
deviations that the
auditor failed to
detect.

b. 5% 75 5 13.6%
c. 5% 150 10 11.1%
d. 10% 20 0 10.9%
The upper limit is
greater than 0, even
though there were
no deviations in the
sample, because the
sample size is very
low; so there is a
strong possibility
that even though
the auditor detected
no deviations in the
sample of 20 items,
there exist
deviations that the
auditor failed to
detect.
e. 10% 75 5 12.1%
f. 10% 150 10 10.1%
Interpretations:
a. The auditor is 95% confident that that the upper limit of the real deviation rate in the
population does not exceed 14.0%. Stated another way, it means that there is a 5% chance
that the real deviation rate exceeds 14.0%. Because the tolerable deviation rate is 12%,
the auditor concludes that the control is not operating effectively.
b. The auditor is 95% confident that that the upper limit of the real deviation rate in the
the auditor concludes that the control is not operating effectively.
c. The auditor is 95% confident that that the upper limit of the real deviation rate in the

the auditor concludes that the control is operating effectively.
d. The auditor is 90% confident that that the upper limit of the real deviation rate in the
population does not exceed 10.9%. Stated another way, it means that there is a 10%
chance that the real deviation rate exceeds 10.9%. Because the tolerable deviation rate is
12%, the auditor concludes that the control is operating effectively.
e. The auditor is 90% confident that that the upper limit of the real deviation rate in the
12%, the auditor concludes that the control is not operating effectively. However, given
how close the upper limit is to the tolerable rate, the auditor might consider increasing the
sample size a bit to be more certain about this conclusion.
f. The auditor is 90% confident that that the upper limit of the real deviation rate in the
12%, the auditor concludes that the control is operating effectively.
8-16
In any sampling application, there exists sampling risk. The upper limit considers sampling risk
and is the best indicator of the maximum deviation rate in the population; the auditor should
compare it to the tolerable failure rate.
The alternative courses of action are:
• A compensating control procedure could be identified and tested. The decision to test the
compensating control procedure will depend on the perceived effectiveness of the control
and the additional cost to test the control procedure.
• A larger sample could be taken, but this is not likely to be cost-beneficial unless the
auditor has reason to believe the original sample was not representative.
• The assessment of control risk can be set higher than originally planned and the nature,
timing, and/or the extent of the related substantive tests can be modified. If the upper
limit of the population deviation rate does not exceed the tolerable failure rate by very
much, this modification could be very slight. For example, if the upper limit was 5.4%
and the tolerable rate was 5%, very little modification is needed.
• The auditor will analyze the nature of the control deviations and determine the
implications on the type of misstatements, or causes of misstatements, that might occur in
the financial statements and adjust the nature, timing, and/or extent of the planned
substantive testing.
8-17
a.
Control Upper Limit of Control Failures

1 The upper limit is 3%.
2 Since the control calls for credit approval to be noted on the customer
orders, there are five deviations (the auditor must conclude there was no
credit approval for the two sales for which no customer order could be
found). The upper limit is 10.3%.
3 The upper limit is 7.6%.
6 The upper limit is 6.2%.
7 There are 6 deviations. The upper limit is 11.5%.
b. The upper limit of deviation for all controls tested except 1 (sales manager approval of
sales over $10,000) and 5 (proper pricing) exceeded the tolerable deviation rate. Thus,
there are problems with proper credit approval, lack of supporting shipping documents
and customer orders, premature recording of sales, and billing for larger quantities that
customers ordered. These deficiencies in internal controls would probably result in an
adverse opinion on internal controls because they are likely to cause the auditor to
conclude that there is a reasonable possibility that a material misstatement could exist.
Certainly, the pattern of errors suggests pervasive internal control problems related to
revenue and accounts receivable.
Control c. Potential Misstatements d. Substantive Audit Procedure
2 & 6
3
4
7
The allowance for doubtful accounts
may be understated because of the lack
of proper credit approval.
The lack of customer orders for two
recorded sales could mean that the sales
were not ordered by customers,
resulting in artificially inflated sales.
The lack of shipping documents could
indicate misplaced documents or that
the sales did not take place. The auditor
should be professionally skeptical and
assume the worst – the sales did not take
place.
Sales being recorded prior to shipment
could be an honest mistake due to the
temporary employee. However, this
may result in sales recorded in the
current year that should be recorded
next year.
Billing for more quantities than
• Carefully review the aging of the
year-end receivables.
• Increase coverage of confirmations
and subsequent collections.
• Increase the extent of cutoff testing,
particularly for sales recorded just
prior to year-end.
• Review the extent of subsequent
sales returns to determine if they are
more than normal. This may require
estimating sales returns and
allowances as of year-end to match
with the sales.
• Heightened alertness to other
approaches management may use to
manage its earnings, particularly in
the area of accounts based on
estimates.

Control c. Potential Misstatements d. Substantive Audit Procedure
customers ordered results in inflated
sales and receivables.
8-18
a. Misstatement. A dollar amount of misstatement, either intentional or unintentional, that
exists in a transaction or financial statement account balance. For substantive sampling
purposes, a misstatement involves differences between recorded values and audited
values.
b. Factual misstatement. A misstatement that has been specifically identified and about
which there is no doubt. Also referred to as a known misstatement.
c. Projected misstatement. The best estimate of the actual amount of dollar misstatements in
the population based on projecting the sample results to the population. The projected
misstatement is calculated as the sampling interval multiplied by the tainting percentage.
Also referred to as likely misstatement or most likely misstatement.
d. Tolerable misstatement. A monetary amount set by the auditor in respect of which the
auditor seeks to obtain an appropriate level of assurance that the monetary amount set by
the auditor is not exceeded by the actual misstatement in the population. In practical
terms, a tolerable misstatement is the maximum amount of misstatement the auditor can
accept in the population without requiring an audit adjustment or a qualified audit
opinion.
e. Expected misstatement. The level of misstatement that the auditor expects to detect, and it
is based on projected misstatements in prior-year audits, results of other substantive tests,
professional judgment, and knowledge of changes in personnel and the accounting
system.
8-19
The sampling unit when gathering evidence about misstatements in account balances and
associated assertions is the individual auditable items that make up individual account balances.
Examples in the context of accounts receivables include the customer’s balance, individual
unpaid invoices, or a combination of these two.
8-20
Stratification involves the division of a population into two or more sub-groups. Top-stratum
items are those that are large-value items exceeding the sampling interval. All items in the top
stratum are audited. In contrast, lower-stratum items are lower-value items that are less than the
sampling interval. These items are sampled.
8-21

When using nonstatistical sampling, the auditor must use judgment in determining the sample
size, selecting the sample, and evaluating the sample results:
a. In determining the sample size, the auditor should test all significant items. The auditor
should select all items over a specific dollar amount, and then, depending on audit
objectives, select items with other characteristics, such as items billed in the last week or
billed to specific parties.
b. The auditor should select the sample in a manner that increases the likelihood that the
sample is representative of the population. The auditor may obtain a representative
sample using a random-based method.
c. As with statistical sampling, the auditor should project the sample to the population and
compare with tolerable misstatement. The auditor should also consider whether there is
an adequate allowance for sampling risk.
8-22
a. Lower-stratum projected misstatement: ($600 ÷ $185,000)  $1,500,000 = $4,864.86
Plus top-stratum misstatement 1,000.00
Total projected misstatement $5,864.86
b. Tolerable misstatement has been set at $25,000, so the projected misstatement is
significantly less than tolerable misstatement. No further work needs to be performed.
c. When the total estimated misstatement exceeds the tolerable misstatement, the auditor
has available several possible courses of action. The auditor can:
Ask the client to correct the factual misstatements. If this is done, the total estimated
misstatement can be adjusted for those corrections but not for the projection of
misstatements associated with those items. In some cases, simply correcting the factual
misstatement can bring the total estimated misstatement below the auditor’s tolerable
misstatement level.
Analyze the detected misstatements for common problem(s). When misstatements are
discovered, the auditor should look beyond the quantitative aspects of the misstatements
to understand the nature and cause of the misstatements—especially to determine if there
is a systematic pattern to the misstatements. If a systematic pattern is found, the client can
be asked to investigate and make an estimate of the correction needed. The auditor can
review and test this estimate. Furthermore, the auditor can recommend improvements to
prevent such errors in the future. For example, assume several confirmation replies
indicate that merchandise was returned prior to year-end but credit was not recorded until
the subsequent year. A careful review of receiving reports related to merchandise returned
prior to year-end and of credits recorded in the subsequent year will provide evidence
regarding the extent of the needed correction. The auditor should also consider the

relationship of the misstatements to other phases of the audit—problems in recording
receivables may also reveal problems in the accuracy of recorded sales.
Design an alternative audit strategy. Discovering more misstatements than expected in
the planning stage of the audit suggests that the planning assumptions may have been in
error and internal controls were not as effective as originally assessed. In such cases, the
auditor should plan the rest of the audit accordingly. For public companies, significant
problems with internal control will cause the auditor to consider whether it is necessary to
express an adverse opinion on the effectiveness of the client’s internal controls over
financial reporting.
Expand the sample. The auditor can increase the sample size. Although, this approach
may not be very useful if the first sample is representative of the population.
Change the audit objective to estimating the correct value. In cases where material
misstatements are likely, it may be necessary to change from an objective of testing
details to an objective of estimating the correct population value. A lower detection risk
and a smaller tolerable misstatement should be used because the auditor is no longer
testing the balance but estimating the correct population value from the sample. The
auditor will expect the client to adjust the book value to the estimated value. A larger
sample size will normally be required.
8-23
Strengths of MUS include:
• MUS is generally easier to apply than other statistical sampling approaches.
• MUS automatically selects a sample in proportion to an item’s dollar amount,
thus providing automatic stratification of the sample.
• If the auditor expects (and finds) no misstatements, MUS usually results in a
highly efficient sample size.
Examples of the circumstances in which the auditor might use MUS include:
• Accounts receivable confirmations (when credit balances are not significant).
• Loans receivable confirmations (e.g., real estate mortgage loans, commercial
loans, and installment loans).
• Inventory price tests in which the auditor anticipates relatively few misstatements
and the population is not expected to contain a significant number of large
understatements.
• Fixed-asset additions tests where existence is the relevant assertion.
8-24
The auditor should also be aware of difficulties in using MUS:

• MUS is not designed to test for the understatement of a population.
• If an auditor identifies understatements in a MUS sample, evaluation of the
sample requires special considerations.
• Selection of zero or negative balances requires special design considerations.
8-25
The sample size of a MUS sample is a function of the following factors: (1) the risk of incorrect
acceptance, (2) the ratio of expected misstatement to tolerable misstatement, and (3) the ratio of
tolerable misstatement to the population.
8-26
Risk of Incorrect
Acceptance
Ratio of Expected
to Tolerable
Misstatement
Ratio of Tolerable
Misstatement to
Population
Sample Size
a. 5% 0.20 50% 10
b. 10% 0.20 30% 12
c. 15% 0.30 8% 43
d. 20% 0.30 5% 56
e. 25% 0.40 4% 73
f. 30% 0.40 3% 80
g. 35% 0.50 2% 169
h. 50% 0.50 1% 170
8-27
a. $8,500,000 ÷ 10 = $850,000; no need to round down
b. $8,500,000 ÷ 12 = 708,333 rounded down to 700,000
c. $8,500,000 ÷ 43 = $197,674 rounded down to $195,000
d. $8,500,000 ÷ 56 = $151,786 rounded down to $150,000
e. $8,500,000 ÷ 73 = $116,438 rounded down to $115,000
f. $8,500,000 ÷ 80 = $106,250 rounded down to $105,000
g. $8,500,000 ÷ 169 = $50,296 rounded down to $50,000
h. $8,500,000 ÷ 170 = $50,000; no need to round down

8-28
a. From Exhibit 8.7, the sample size is 54.
b. The sampling interval = $5,643,200 ÷ 54 = 104,689
c. $104,689 unless you round the interval down to the next $1,000 or $10,000. If you
rounded down to $100,000, then the largest number for a random start would be
$100,000.
d. Using a sampling interval of $100,000, items 4, 6, 10, and 14 would be included in the
sample:
Item Book Value
Cumulative
Book
Cumulative
Book Plus
Random
Start
Included in
Sample –
Selection
Amount
0 0 25,000
1 3,900 3,900 28,900
2 26,000 29,900 54,900
3 5,000 34,900 59,900
4 130,000 164,900 189,900 Yes,
100,000
5 2,000 166,900 191,900
6 260,000 426,900 451,900 Yes,
200,300 &
400,000
7 100 427,000 452,000
8 25,000 452,000 477,000
9 19,000 471,000 496,000
10 10,000 481,000 506,000 Yes,
500,000
11 9,000 490,000 515,000
12 2,500 492,500 517,500
13 65,000 557,500 582,500

e. The probability of selecting each item is as follows:
Item
Book
Value Probability of Selection
1 3,900 3.9% = 3,900 ÷ 100,000
2 26,000 26.0% = 26,000 ÷ 100,000
4 130,000 100.0% = 130,000 ÷ 100,000
6 360,000 100.0%
f. Because logical units with recorded amounts greater than the sampling interval might be
selected more than once, the actual number of logical units selected for the sample might
be less than the computed sample size.
8-29
a. The audit conclusion if no misstatements are found in the sample is that the auditor is 70
percent confident that accounts receivable are not overstated by more than $121,000 (the
basic precision = 1.21  $100,000). Because this is less than the tolerable misstatement
of $200,000, the auditor can conclude that the account balance is not materially
overstated.
b. The audit evaluation of the sample results is as follows:
Confidence
Factor*
Tainting
Percent
Sampling
Interval
Conclusion
Factual misstatement in
top stratum
Basic precision
Projected misstatement:
1.21  100,000 =
2,000
121,000
First largest tainting % 750 ÷ 15,000 5%
14 110,000 667,500 692,500 Yes,
600,000
15 6,992 674,492 699,492

=
Second largest tainting % 90 ÷ 9000 = 1%
6%  100,000 = 6,000
Incremental allowance for sampling risk 1,330**
Total Estimated Misstatement: 130,330
*Confidence factors come from the 30% column in Exhibit 8.9.
** See below for the calculation of this value.
Projected Misstatement Incremental Changes in
Confidence Factor
(Step 2)
Projected Misstatement 
Factor (Step 3)
5,000 + 2.44 – 1.21 = 1.23 6,150 +
1,000 3.62 – 2.44 = 1.18 1,180
6,000 (Step 1) 7,330 (Step 4)
Incremental allowance for sampling risk: 7,330 – 6,000 = 1,330 (Step 5)
c. These results are acceptable because the total estimated misstatement ($130,330) is less
than tolerable misstatement ($175,000).
d. When the total estimated misstatement exceeds the tolerable misstatement, the auditor
has available several possible courses of action. The auditor can:
o Ask the client to correct the factual misstatements. If this is done, the total estimated
misstatements associated with those items. In some cases, simply correcting the
factual misstatement can bring the total estimated misstatement below the auditor’s
tolerable misstatement level.

o Analyze the detected misstatements for common problem(s). When misstatements are
discovered, the auditor should look beyond the quantitative aspects of the
misstatements to understand the nature and cause of the misstatements—especially to
determine if there is a systematic pattern to the misstatements. If a systematic pattern
is found, the client can be asked to investigate and make an estimate of the correction
needed. The auditor can review and test this estimate. Furthermore, the auditor can
recommend improvements to prevent such errors in the future. For example, assume
several confirmation replies indicate that merchandise was returned prior to year-end
but credit was not recorded until the subsequent year. A careful review of receiving
reports related to merchandise returned prior to year-end and of credits recorded in
the subsequent year will provide evidence regarding the extent of the needed
correction. The auditor should also consider the relationship of the misstatements to
other phases of the audit—problems in recording receivables may also reveal
problems in the accuracy of recorded sales.
o Design an alternative audit strategy. Discovering more misstatements than expected
in the planning stage of the audit suggests that the planning assumptions may have
been in error and internal controls were not as effective as originally assessed. In such
cases, the auditor should plan the rest of the audit accordingly. For public companies,
significant problems with internal control will cause the auditor to consider whether it
is necessary to express an adverse opinion on the effectiveness of the client’s internal
controls over financial reporting.
o Expand the sample. The auditor can increase the sample size. However, this approach
may not be very useful if the first sample is representative of the population.
o Change the audit objective to estimating the correct value. In cases where material
details to an objective of estimating the correct population value. A lower detection
risk and a smaller tolerable misstatement should be used because the auditor is no
longer testing the balance but estimating the correct population value from the
sample. The auditor will expect the client to adjust the book value to the estimated
value. A larger sample size will normally be required.
8-30
a. Round the ratio of expected to tolerable misstatement up to 30%, and round the ratio of
the tolerable misstatement to the population book value down to 4%. From Exhibit 8.7,
the sample size is 109. The student can find this by looking in the 10% row, the 0.30 row,
and the 4% column.
Sampling interval = population size ÷ sample size, so:
Sampling interval = $8,124,999 ÷ 109 = $74,541, which would likely be rounded down
to $70,000.

b. The total estimated misstatement is calculated as follows:
Confidence
Factor*
Tainting
Percent
Sampling
Interval
Conclusion
Factual misstatement in
top stratum
Basic precision
Projected misstatement in
lower stratum:
2.31  70,000 =
2,000
161,700
First largest tainting % 11.93%
11.93%  70,000 = 8,352
Incremental allowance for sampling risk
in lower stratum
4,844**
Total Estimated Misstatement: 176,896
** See below and Exhibit 8.12 for the calculation of this value.
First largest tainting % = $41,906.45 – $36,906.45 = $5,000 ÷ $41,906.45 = 0.119313
Confidence Factor
(Step 2)
Projected Misstatement 
Factor (Step 3)
8,352 (Step 1) 3.89 – 2.31 = 1.58 13,196 (Step 4)
c. The statistical conclusion is that the auditor is 90% confident that this population is not
overstated by more than $176,896. Because the total estimated misstatement is less than the

tolerable misstatement ($275,000), the auditor can conclude that, at the desired level of risk
of incorrect acceptance, the population does not contain a material amount of overstatement.
8-31
a. Round the ratio of the tolerable misstatement to the population book value down to 2%.
From Exhibit 8.7, the sample size is 171. You can find this by looking in the 10% row,
the 0.20 row, and the 2% column.
Sampling interval = population size ÷ sample size, so:
Sampling interval = $8,425,000 ÷ 171 = $49,269, which would likely be rounded down
to $45,000.
b.
Item Dollar / Percent Misstatement Problem
1. $0 / 0% Account balance is correct, just
posted to wrong customer.
2. $20,000; 50%; Lower stratum Credit memo problem.
3. $75,000; Top stratum Cost overrun.
4. $5,000; Top stratum Cost overrun
5. $122; 100%; Lower stratum Credit memo problem.
c. The total estimated misstatement is calculated as follows:
Confidence
Factor*
Tainting
Percent
Sampling
Interval
Conclusion
Factual misstatement in top
stratum ($75K + $5K) =
Basic precision
Projected misstatement in
the lower stratum:
2.31  45,000 =
$80,000
103,950
First largest tainting %
Second largest tainting %
100%
50%
150%  45,000 = 67,500

Incremental allowance for sampling risk in lower
stratum 36,000**
Total Estimated Misstatement: $287,450
** See below and Exhibit 8.12 for the calculation of this value.
First largest tainting % = $122 – 0 = 122 ÷ $122 = 100%
Second largest tainting % = $40,000 – $20,000 = $20,000 ÷ $40,000 = 50%
Confidence Factor
(Step 2)
Projected Misstatement  Factor (Step
3)
45,000 + 3.89 – 2.31 = 1.58 71,100 +
22,500 5.33 – 3.89 = 1.44 32,400
67,500 (Step 1) 103,500 (Step 4)
The statistical conclusion is that the auditor is 90% confident that this population is not
overstated by more than $287,450. Because the total estimated misstatement is more than
the tolerable misstatement ($200,000), the auditor can conclude that, at the desired level
of risk of incorrect acceptance, the population does contain a material amount of
overstatement.
d. The auditor would expand audit tests on the account balance. Two types of misstatement
patterns should concern the auditor. First, there appears to be a problem with timely
issuance of credit memos. The auditor should find out more about the causes of the credit
memo problems and examine the process of issuing credit memos further. Second, there
is a pattern of cost overruns on large projects. The auditor would want to expand audit
work to examine a number of other large contracts to determine whether cost overruns
were applicable to other contracts, including those that had been closed during the period
(sales may be overstated even if there is a zero accounts receivable balance).
8-32

When the total estimated misstatement exceeds the tolerable misstatement, the auditor has
available several possible courses of action. The auditor can:
• Ask the client to correct the factual misstatements. If this is done, the total estimated
misstatements associated with those items. In some cases, simply correcting the factual
misstatement can bring the total estimated misstatement below the auditor’s tolerable
misstatement level.
• Analyze the detected misstatements for common problem(s). When misstatements are
discovered, the auditor should look beyond the quantitative aspects of the misstatements
to understand the nature and cause of the misstatements—especially to determine if there
is a systematic pattern to the misstatements. If a systematic pattern is found, the client can
be asked to investigate and make an estimate of the correction needed. The auditor can
review and test this estimate. Furthermore, the auditor can recommend improvements to
prevent such errors in the future. For example, assume several confirmation replies
indicate that merchandise was returned prior to year-end but credit was not recorded until
the subsequent year. A careful review of receiving reports related to merchandise
returned prior to year-end and of credits recorded in the subsequent year will provide
evidence regarding the extent of the needed correction. The auditor should also consider
the relationship of the misstatements to other phases of the audit—problems in recording
receivables may also reveal problems in the accuracy of recorded sales.
• Design an alternative audit strategy. Discovering more misstatements than expected in
the planning stage of the audit suggests that the planning assumptions may have been in
error and internal controls were not as effective as originally assessed. In such cases, the
auditor should plan the rest of the audit accordingly. For public companies, significant
problems with internal control will cause the auditor to consider whether it is necessary to
express an adverse opinion on the effectiveness of the client’s internal controls over
financial reporting.
• Expand the sample. The auditor can calculate the additional sample size needed by
substituting the most likely misstatement from the sample evaluation for the original
expected misstatement in the sample interval formula and determine a new interval and
total sample size based on the new expectations. The number of additional sample items
can then be determined by subtracting the original sample size from the new sample size.
The new sampling interval can be used for selection of items not already included in the
sample.
• Change the audit objective to estimating the correct value. In cases where material
details to an objective of estimating the correct population value. A lower detection risk
and a smaller tolerable misstatement should be used because the auditor is no longer
testing the balance but estimating the correct population value from the sample. The
auditor will expect the client to adjust the book value to the estimated value. A larger
sample size will normally be required.
8-33

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