1. Chapter 9
Audit Sampling: An Application to Substantive Tests of Account Balances
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Substantive Tests of Details of Account Balances
LO# 1
Substantive Tests of Details of Account Balances
The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important determinants of sample size are
Desired confidence level.
Tolerable misstatement.
Estimated misstatement.
Population plays a bigger role in some of the sampling techniques used for substantive testing.
Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk.
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3. Substantive Tests of Details of Account Balances
LO# 1
Substantive Tests of Details of Account Balances
Consider the following information about the inventory account balance of an audit client:
The ratio of misstatement in the sample is 2% ($2,000 ÷ $100,000)
Applying the ratio to the entire population produces a best estimate of misstatement of inventory of $60,000. ($3,000,000 × 2%)
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4. Substantive Tests of Details of Account Balances
LO# 1
Substantive Tests of Details of Account Balances
The results of our audit test depend upon the tolerable misstatement associated with the inventory account. If the tolerable misstatement is $50,000, we cannot conclude that the account is fairly stated because our best estimate of the projected misstatement is greater than the tolerable misstatement.
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5. Monetary-Unit Sampling (MUS)
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Monetary-Unit Sampling (MUS)
MUS uses attribute-sampling theory to express a conclusion in dollar amounts rather than as a rate of occurrence. It is commonly used by auditors to test accounts such as accounts receivable, loans receivable, investment securities, and inventory.
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6. Steps in MUS
LO# 2
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7. Steps in MUS Sampling may be used for substantive testing to:
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Steps in MUS
Sampling may be used for substantive testing to:
Test the reasonableness of assertions about a financial statement amount (i.e., accuracy, existence). This is the most common use of sampling for substantive testing.
Develop an estimate of some amount.
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8. LO# 2
Steps in MUS
For MUS the population is defined as the monetary value of an account balance, such as accounts receivable, investment securities, or inventory.
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9. Steps in MUS An individual dollar represents the sampling unit. 9-9
LO# 2
Steps in MUS
An individual dollar represents the sampling unit.
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10. LO# 2
Steps in MUS
A misstatement is defined as the difference between monetary amounts in the client’s records and amounts supported by audit evidence.
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11. LO# 2
Steps in MUS
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12. LO# 2
Steps in MUS
The auditor selects a sample for MUS by using a systematic selection approach called probability-proportional-to-size selection. The sampling interval can be determined by dividing the book value of the population by the sample size. Each individual dollar in the population has an equal chance of being selected and items or “logical units” greater than the interval will always be selected.
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13. 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:
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14. 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.
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15. LO# 2
Steps in MUS
The misstatements detected in the sample must be projected to the population. Let’s look at the following example:
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16. 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 associated with large accounts.
$3,284 ÷ $21,893 = 15%
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17. LO# 3
Steps in MUS
Computed 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)
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18. 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 but we would still want to add an allowance for sampling risk.
$26,882 × 3.0 = $80,646 upper misstatement limit
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19. LO# 3
Steps in MUS
In our example, the final decision is whether the accounts receivable balance is materially misstated or not.
We compare the tolerable misstatement to the upper misstatement limit. If the upper misstatement limit is less than or equal to the tolerable misstatement, we conclude that the balance is not materially misstated.
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20. 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.
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21. Risk When Evaluating Account Balances
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Risk When Evaluating Account Balances
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22. Effect of Understatement Misstatements
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Effect of Understatement Misstatements
MUS is not particularly effective at detecting understatements. An understated account is less likely to be selected than an overstated account.
The most likely error will be reduced by $2,688 (– 0.10 × $26,882)
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