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Chapter 17

Audit Sampling for Tests of Details of Balances

The approach to covering audit sampling for tests of details of balances in Chapter 17 is similar to the approach for audit sampling for tests of controls and substantive tests of transactions in Chapter 15. Nonstatistical sampling is covered early in the chapter, followed by discussions of monetary unit sampling and variables sampling (statistical sampling methods).

We believe that the format of Chapter 17 will provide you with maximum flexibility in deciding how you wish to approach the topic of audit sampling for tests of details of balances. The chapter is built around the fourteen steps of audit sampling, which were first introduced in Chapter 15. All fourteen steps apply to both nonstatistical and statistical sampling. Each step is covered in detail during the discussion of nonstatistical sampling on pages 567-575. The discussions of

monetary unit sampling (pages 576-586) and variables sampling (pages 586-592) use these same fourteen steps, but focus on the differences between how the steps are applied under these statistical methods compared to nonstatistical sampling.

Before assigning Chapter 17, you must decide how you want to approach the topic of audit sampling for tests of details of balances. There are four possible approaches for covering Chapter 17:

Cover nonstatistical sampling only

Cover nonstatistical sampling, followed by monetary unit sampling

Cover nonstatistical sampling, followed by variables sampling

Cover nonstatistical sampling, followed by both monetary unit sampling and variables sampling (this approach is not recommended unless you have extra time in your course schedule)

Note that it is not feasible to cover either monetary unit sampling (MUS) or variables sampling without first covering nonstatistical sampling. This is because the MUS and variables sampling portions of the chapter revolve around the fourteen steps outlined during the nonstatistical sampling discussion.

The following are the primary topical areas that we suggest you cover:

Chapter opening vignette

Comparisons of audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions Nonstatistical sampling

Monetary unit sampling [ignore this section if using approach (1) or (3) discussed earlier ]

Variables sampling [ignore this section if using approach (1) or (2) discussed earlier ]

Instructor Note: Statistical sampling is a highly complex subject to which justice cannot always be done in an introductory auditing course. There is certainly strong justification for skipping the topic entirely in the introductory course. We recommend this be done when an advanced auditing course is included in the auditing curriculum.

Chapter Opening Vignette - “ Both Statistical and Nonstatistical Sampling are Acceptable Under GAAS, But Whichever is Used, It Must be Done Right ”

The fundamental point of this vignette in one sense is that statistical sampling requires a greater level of expertise than nonstatistical sampling. However, nonstatistical sampling also requires expertise. Ascertaining how much sampling error to attribute to a nonstatistical sample is not an easy problem.

In the vignette, an "expert" was brought in for part of the statistical task, but did not complete it. The staff auditor who completed the statistical evaluation made an error in the calculations. This case highlights the complexity of statistical calculations, and the need for the auditor to thoroughly understand the requirements of any audit task, regardless of time constraints.

Since the auditor did not understand the statistical method, it is questionable whether a statistical evaluation should have been performed. However, the sample was selected based on the original audit plan, which called for a statistical evaluation.

The vignette offers an opportunity to discuss the relative merits of statistical and nonstatistical sampling, and what requirements exist for both to “do it right.

Comparisons of Audit Sampling for Tests of Details of Balances and for Tests of Controls and Substantive Tests of Transactions (page 566)

We introduce the topic of audit sampling for tests of details of balances using the summary of the audit process in Figure 13-9 (page 426). We then point out to students that Chapter 17 deals with audit sampling for tests of details of balances.

(See Figure 13-9)

Next, we discuss the fact that audit sampling for tests of details of balances focuses on dollar misstatements in account balances. You should compare this to determining an exception rate for tests of controls and the rate of monetary misstatements for substantive tests of transactions (Chapter 15). Review Questions 17-1 and 17-7 can be covered during this discussion.

Nonstatistical Sampling (page 567)

We suggest that you begin your discussion of nonstatistical sampling for tests of details of balances by referring back to the fourteen steps of audit sampling for tests of controls and substantive tests of transactions, which were introduced in Chapter 15. You can then use T-17-1 to show how these fourteen steps compare between audit sampling for tests of details of balances (Chapter 17) and for tests of controls and substantive tests of transactions (Chapter 15).

(See T-17-1)

Next, we cover each of the fourteen steps in detail. The following comments, beyond what the book discusses, are useful.

State the objectives of the audit test (page 567). The purpose of tests of details of balances is to determine whether the account balance being audited is fairly stated.

Decide whether audit sampling applies (page 567). No additional comments.

Define a misstatement (page 568). Stress that any misstatement found in a sample is defined as a misstatement condition.

Define the population (page 568). The population is defined as the recorded dollar population. During this discussion, we usually introduce the concept of stratified sampling. The first table on T-17-2 is a useful way to illustrate the concept of stratified sampling, using the example from page 568 and the accounts receivable population in Table 17-1 (page 568).

(See T-17-2)

(See Table 17-1)

Define the sampling unit (page 569). No additional comments.

Specify tolerable misstatement (page 569). Refer students back to Chapter 9 for a discussion of tolerable misstatement.

Specify acceptable risk of incorrect acceptance (ARIA) (page 569). Compare ARIA to the acceptable risk of assessing control risk too low, which applies to audit sampling for tests of controls and substantive tests of transactions. You can also discuss how ARIA affects sample size and the resulting evidence accumulation. Figure 17-1 (page 569) and Table 17-2 (page 570) are helpful here. Review Questions 17-10 and 17-11 also deal with ARIA.

(See Figure 17-1)

(See Table 17-2)

Estimate misstatements in the population (page 571). No additional comments.

Determine the initial sample size (page 571). Table 17-3 (page 571) is a good summary of the factors that determine initial sample size. Problem 17-27 part a can be used here.

(See Table 17-3)

Select the sample (page 572). We refer students back to Chapter 15 and stress that any of the sampling methods discussed in Chapter 15 can be used for nonstatistical sampling. Problem 17-27 part c is helpful during this discussion.

Perform the audit procedures (page 572). The second table on T-17-2 shows the results of performing the audit procedures for the example on page 573.

(See T-17-2)

Generalize from the sample to the population (page 526). We refer students back to the discussion of a point estimate in Chapter 9. The third table on T-17-2 illustrates the calculation of a point estimate for the example on page 573.

(See T-17-2)

Review Question 17-3 can be used here.

Analyze the misstatements (page 574). The mid-chapter vignette on page 572 provides a great example of the importance of analyzing the misstatements noted in the sample and the critically evaluating client explanations for noted exceptions.

Decide the acceptability of the population (page 574). We explain that for nonstatistical sampling, the auditor calculates the difference between the point estimate and tolerable misstatement (sampling error). This can be related back to Chapter 15's discussion of SER - TER, which also results in sampling error. We then discuss determining the sufficiency of sampling error in order to determine the acceptability of the population.

Problem 17-27 part d is helpful here. Case 17-35 part a gives students practice in evaluating the results of a nonstatistical sample.

Finally, we discuss the auditor ' s options when a population is rejected (see page 574).

Monetary Unit Sampling (page 576)

Note: You should skip this section if you decide to use approach (1) or (3) discussed on 1 . To provide continuity, the text discussion of monetary unit sampling (MUS) refers to the same fourteen steps discussed during the nonstatistical sampling portion of the chapter. We focus on the differences between how these fourteen steps are applied for MUS compared to nonstatistical sampling. Following are the most important differences that we suggest that you cover (see pages 576-

578 for detailed discussion):

The sampling unit is an individual dollar.

The population size is the recorded dollar population.

Preliminary judgment of materiality is used instead of tolerable misstatement.

Sample size is determined by statistical formula.

A formal decision rule is used for deciding the acceptability of the population.

Sample selection is done using probability proportional to size (PPS).

MUS techniques are used to generalize from the sample to the population.

We suggest using T-17-1 as a frame of reference for discussing how the fourteen steps are applied using MUS.

(See T-17-1)

Next, we discuss the concept of monetary unit sampling and discuss its advantages and disadvantages. We consider it optional to show how to select a sample for monetary unit sampling. Problem 17-28 is a good one to use for demonstrating how such a sample is selected.

Evaluating a sample using monetary unit sampling can be demonstrated by using Problem 17-29. In doing so we go over the terminology from SAS 39 (AU 350) plus additional terms needed for monetary unit sampling. As a part of discussing this material it is essential to refer to Chapter 9, discussing both materiality and the different risks.

(See T-17-3 through T-17-6)

If you want to show how to calculate a sample size for monetary unit sampling, we recommend Review Question 17-14.

Variables Sampling (page 586)

Note: You should skip this section if you decide to use approach (1) or (2) discussed on 1 . We typically spend little time on this material. The remainder of the material in this chapter is intended for those who prefer to emphasize variables sampling in their study of audit sampling. If you plan to emphasize variables sampling, we suggest that you also cover the illustration using difference estimation (pages 592-598). Problem 17-32 provides students with practice in applying difference estimation.

(See T-17-7 to T-17-11)

17-6

CHAPTER 17

CROSS-REFERENCE OF LEARNING OBJECTIVES AND PROBLEM MATERIAL

Learning Objectives

Review Questions

Multiple

Choice

Questions

Discussion

Questions and Problems

Cases

17-1

Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions.

17-1, 17-6, 17-7

17-26

17-2

Apply nonstatistical sampling to tests of details of balances.

17-2, 17-3,

17-4, 17-6, 17-7, 17-10, 17-12, 17-18

17-25, 17-26

17-27, 17-31

17-35

17-3

Apply monetary unit sampling.

17-5, 17-6,

17-8, 17-9,

17-13, 17-14,

17-16, 17-21,

17-24

17-28, 17-29, 17-30, 17-31

17-34, 17-35

17-4

Describe variables sampling.

17-6, 17-11,

17-19, 17-21,

17-22, 17-23, 17-24

17-31

17-5

Use difference estimation in tests of details of balances.

17-15, 17-17, 17-20

17-31, 17-32, 17-33

AUDIT SAMPLING FOR TESTS OF DETAILS OF BALANCES

Plan the Sample

State the objectives of the audit test.

Decide whether audit sampling applies.

Define a misstatement.

Define the population.

Define the sampling unit.

Specify tolerable misstatement.

Specify acceptable risk of incorrect acceptance.

Estimate misstatements in the population.

Determine the initial sample size.

Select the Sample and Perform the Audit Procedures

Select the sample.

Perform the audit procedures.

Evaluate the Results

Generalize from the sample to the population.

Analyze the misstatements.

Decide the acceptability of the population.

AUDIT SAMPLING FOR TESTS OF CONTROLS AND SUBSTANTIVE TESTS OF TRANSACTIONS

Plan the Sample

State the objectives of the audit test.

Decide whether audit sampling applies.

Define attributes and exception conditions.

Define the population.

Define the sampling unit.

Specify tolerable exception rate.

Specify acceptable risk of assessing control risk too low.

Estimate the population exception rate.

Determine the initial sample size.

Select the Sample and Perform the Audit Procedures

Select the sample.

Perform the audit procedures.

Evaluate the Results

Generalize from the sample to the population.

Analyze the exceptions.

Decide the acceptability of the population.

SAMPLING ILLUSTRATION

Stratum

Stratum Criteria

No. in Population

Dollars in

Population

1

> $15,000

3

$ 88,955

2

$5,000-$15,000

10

71,235

3

< $5,000

27

47,105

40

$207,295

Dollars Audited

Sample

Recorded

Audited

Client

Stratum

Size

Value

Value

Misstatement

1

3

$ 88,955

$ 91,695

$(2,740)

2

7

43,995

43,024

971

3

6

13,105

10,947

2,158

16

$146,055

$145,666

$ 389

Client

Recorded

Point

Misstatement /

x Book Value =

Estimate

Recorded Value

for the

of

Stratum

of the Sample

Stratum

Misstatement

1

$(2,740)/$88,955

$88,955

$ (2,740)

2

$ 971 /$43,995

71,235

1,572

3

$ 2,158 /$13,105

47,105

7,757

Total

$6,589

UPPER MISSTATEMENT BOUND

No. of Misstatements

Recorded

Value x

CUER Portion x

Misstatement %

Assumption =

Misstatement Bound

0

$1,975,000

.023

1.000

$45,425

1

1,975,000

.016

.694

21,930

2

1,975,000

.014

.084

2,323

Initial overstatement bound

$69,678

Understatement Amounts

TOC \o "1-5" \h \z .892

.030

(18,684)$50,994.^24

(18,684)

$50,994

.946 / 100 x 1,975,000 =

Adjusted overstatement bound

LOWER MISSTATEMENT BOUND

No. of

Misstate-

Misstate-

Misstate-

Recorded

CUER

ment %

ment

ments

Value x

Portion x

Assumption =

Bound

0

$1,975,000

.023

1.000

$45,425

1

1,975,000

.016

.892

28,187

2

1,975,000

.014

.030

830

3

1,975,000

.013

.024

616

Initial understatement bound $75,058

Overstatement Amounts

.694

.084

.778 / 100 x 1,975,000 = (15,366)

Adjusted understatement bound $59,692

DECISION

-50,000 Materiality +50,000

-59,692 Adjusted 50,994

Misstatement Bounds

POPULATION IS NOT ACCEPTABLE

Available Options

Increase the sample size

Segregate a specific type of misstatement and test it separately. The sample would then not include the specified type of misstatement since it is being tested separately.

Adjust the account balance.

Request the client to correct the population.

Consider qualifying the opinion.

Expand other areas in the audit of accounts receivable.

Recalculate misstatement bounds, assuming elimination of items 3 and 5. The cutoff problem would be investigated separately.

REVISED UPPER MISSTATEMENT BOUND

No. of

Misstate-

Misstate-

Misstate-

Recorded

CUER

ment %

ment

Ments

Value x

Portion x

Assumption =

Bound

0

$1,975,000

.023

1.000

$45,425

1

1,975,000

.016

.084

2,654

Initial overstatement bound

$48,079

REVISED LOWER MISSTATEMENT BOUND

No. of MisstateMents

Recorded

Value x

CUER Portion x

Misstatement % Assumption =

Misstatement Bound

0

$1,975,000

.023

1.000

$45,425

1

1,975,000

.016

.030

948

2

1,975,000

.014

.024

664

Initial understatement bound

$47,037

NOTE: Bounds need not be adjusted since both upper and lower bounds are now within materiality limits.

Point Estimate

e = 1840 - 173.69 = 3994.87

80

COMPUTED PRECISION INTERVAL

CPI = 1840 ? 1.64 ?CPI = 4,718.46

CPI = 1840 ? 1.64 ?

CPI = 4,718.46

I N - n

14.3 1 §40 =80

而 N 1840

STANDARD DEVIATION

STANDARD DEVIATION

SD =￡(q)2 - n(6)2

n - 1SD =SD =(

SD =

￡(q)2 - n(6)2

n - 1

SD =

SD =

(173.69 V

80 一 1

14.3

_e_i_ $(72.00) 65.70

41.10

36.10

51.80

(.12) 30.00 2111

80

_(e_￡ $ 5,184.00

4,316.49

1,689.21

1,303.21

2,683.24 .01 900.00 445 63

$173.69$16,521.79

$173.69

$16,521.79

CONFIDENCE LIMITS

UCL = e + CPI

UCL = 3,994.87 + 4,718.46 = 8,713.33

LCL = e - CPI

LCL = 3,994.87 - 4,718.46 = -723.59

DECISION

TOC \o "1-5" \h \z -TM + TM

-6000 +6000

LCL UCL

-724 +8,713

IN GENERAL

-TM Y + TM

LCL E UCL

DECISION RULE - If both confidence limits are within -TM and +TM accept; otherwise reject.

ADJUSTMENT OF BALANCE

TEST - Is CPI greater than tolerable misstatement? If so, no adjustment is possible.

IDEAL ADJUSTMENT - reduce book value $3,995

MINIMUM ADJUSTMENT -

UPL $8,713

Tolerable misstatement $6,000

Reduce book value $2,713

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