1. Chapter 9
Audit Sampling: An Application to Substantive Tests of Account Balances
This presentation focuses (like my course) on MUS. It omits the effect of understatement misstatements (p. 325) It omits non-statistical sampling. It briefly discusses Advanced Module 1 on Classical Variables Sampling.

2. Substantive Tests of Details of Account Balances
LO# 1
Substantive Tests of Details of Account Balances
Sometime, auditors use Monetary Unit Sampling (MUS), sometimes Variables (aka Classical Variables) Sampling, and sometimes other statistical methods.
Our text discusses only MUS in the main part of the chapter. MUS is also known as dollar-unit sampling or probability-proportional-to-size sampling. Thus, our focus of study in Chapter 9 is MUS. It is used the most and thus the most important statistical method. Assume I am referring to MUS throughout this presentation unless I state otherwise.
9-2

3. Substantive Tests of Details of Account Balances
LO# 1
Some statistical concepts in Chapter 8 also apply to Chapter 9. In fact, when using the textbook to determine the right sample size, we use Table Take a look now at Table 8-5:
Desired confidence level – similar to Ch. 8
Tolerable Misstatement – somewhat similar to Tolerable Deviation Rate of Ch. 8
Estimated misstatement – somewhat similar to Expected Population Deviation Rate of Ch. 8
However, there are some things very different in Ch. 9. A fourth factor is very important for determining the right sample size:
4. Population – number of dollars in an account balance
9-3

4. Illustration of the MUS approach
The next slide explains what the text authors on p. 310 (of the 9th edition of your text) are trying to get across re MUS.

5. My explanation of the example on page 310
LO# 1
My explanation of the example on page 310
First, note that we examine a sample, but we want to learn about the population.
You have in this example a $2000 misstatement in the sample. You have to add an allowance for sampling risk. Then you will have the Upper Misstatement Limit (UML). If the UML is > the Tolerable Misstatement then the account is materially incorrect. What is the UML in this example? We need more info to determine what it is.
9-5

6. Monetary-Unit Sampling (MUS)
LO# 2
Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to express a conclusion in dollar amounts instead of the rate of occurrence that was the conclusion in Ch.8. It is commonly used by auditors to test accounts such as accounts receivable, loans receivable, investment securities, and inventory.
9-6

7. Monetary-Unit Sampling (MUS)
LO# 2
Advantages of MUS
When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling.
When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample.
MUS does not require the user to make assumptions about the distribution of misstatements.
9-7

8. Monetary-Unit Sampling (MUS)
LO# 2
Monetary-Unit Sampling (MUS)
Disadvantages of MUS
The selection of zero or negative balances generally requires special design consideration.
The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100%.
When more than one or two misstatements are detected, the sample results calculations may overstate the allowance for sampling risk.
9-8

9. Terms for MUS determination of right sample size: Text vs. ACL
Monetary Unit Sampling
ACL calls this Monetary
Desired Confidence Level
ACL calls this Confidence
Tolerable Misstatement (%)
ACL calls this Materiality
Expected Misstatement (%)
ACL calls this Expected Total Errors
Sampling Interval
ACL calls this Interval

10. Steps in MUS
LO# 2
9-10

11. LO# 2
Steps in MUS
MUS is used to test whether the dollar amount is materially correct.
9-11

12. LO# 2
Steps in MUS
For MUS the population is defined as the number of dollars in an account balance, such as accounts receivable, investment securities, or inventory.
9-12

13. Steps in MUS An individual dollar represents the sampling unit. 9-13
LO# 2
Steps in MUS
An individual dollar represents
the sampling unit.
9-13

14. LO# 2
Steps in MUS
A misstatement is the difference between monetary amounts in the company’s records and amounts supported by audit evidence.
For example, the company records that a customer owes it $10,000 as of the fiscal year end; the auditor reviews the support documentation and determines only $6000 was owed. That would be a $4000 misstatement.
9-14

15. LO# 2
Steps in MUS
9-15

16. LO# 2
Sample Selection
The auditor selects a sample for MUS by using probability-proportional-to-size selection. This requires (either manually or by having software like ACL do it) calculation of the sampling interval. Manual calculation of the sampling interval is book value (pre-audit recorded amount of the account or population) divided by the sample size.
9-16

17. Sample Selection (continued)
Each dollar in the population has an equal chance of being selected and items or “logical units” greater than the interval will always be selected.
However, no item will be selected more than once.
Consequently, the number of items selected, which is the actual size of the sample, almost always is smaller than the theoretical sample size.

18. 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:
9-18

19. LO# 2
Steps in MUS
After the sample items have been selected, the auditor conducts the planned audit procedures on the logical units containing the selected dollar sampling units.
9-19

20. LO# 2
Steps in MUS
The misstatements detected in the sample must be “projected to the population,” which means determining the allowance for sampling risk.
The process for determining the allowance for sampling risk is more complex for MUS than it was in Ch. 8. It involves two components:
Basic Precision: general sampling risk; and
Sampling risk associated with each misstatement found where the item was (pre-audit) less than the sample interval.
9-20

21. Comparison of textbook terms vs. ACL terms for MUS results evaluation
Monetary Unit Sampling
ACL: Monetary
Sampling Interval
ACL: Interval
Misstatements or Differences
ACL: Errors
Upper Misstatement Limit (the analog to Ch. 8’s CUDR)
ACL: Upper Error Limit

22. Evaluation of the results in MUS
The next slide discusses, using the example below, Basic Precision. Subsequent slides show the allowance for sampling risk related to specific misstatements found where the item misstated was (pre-audit or book value) less than the sampling interval, and then show all the information put together.

23. 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.
$26,882 × 3.0 = $80,646 upper misstatement limit
9-23

24. LO# 3
Steps in MUS
Misstatements Detected In the sample of 93 items, the following misstatements were found:
Because the Axa balance of $32,549 is greater than 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 specifically associated with large accounts.
$3,284 ÷ $21,893 = 15%
9-24

25. LO# 3
Steps in MUS
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.
(0.15 × $26,882 × 1.4 = $5,645)
9-25

26. LO# 3
Steps in MUS
In our example, the final decision is whether the accounts receivable balance is materially misstated or not.
Compare Tolerable Misstatement to the Upper Misstatement Limit. If the Upper Misstatement Limit is greater than the Tolerable Misstatement, we conclude that the balance is materially misstated.
9-26

27. 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:
Increase the sample size.
Perform other substantive procedures.
Request the client adjust the accounts receivable balance.
If the client refuses to adjust the account balance, the auditor would consider issuing a qualified or an adverse opinion.
9-27

28. Classical Variables Sampling
LO# 5
Classical Variables Sampling
There are some situations where MUS does not work well. Thus, auditors turn to other statistical methods. The most common method they turn to is classical variables sampling (also called variable sampling).
9-28

29. Classical Variables Sampling
LO# 5
Classical Variables Sampling
Advantages
When the auditor expects a large number of misstatements or differences between book and audited values, this method will normally result in smaller sample size than MUS.
The techniques are effective for both overstatements and understatements.
The selection of zero balances generally does not require special sample design considerations.
9-29

30. Classical Variables Sampling
LO# 5
Classical Variables Sampling
Disadvantages
Does not work well when little or no misstatement is expected in the population.
To determine sample size, the auditor must estimate the standard deviation of the audit differences. If the estimate is sufficiently wrong, the statistical results could be completely wrong.
9-30

31. End of Chapter 9
9-31