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

2. 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 The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important determinants of sample size are 1.Desired confidence level. 2.Tolerable misstatement. 3.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. Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk. The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important determinants of sample size are The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important determinants of sample size are 1.Desired confidence level. 2.Tolerable misstatement. 3.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. Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk. LO# 1 9-2

3. 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. LO# 2 MUS uses attribute-sampling theory (used primarily to test controls) to estimate the percentage of monetary units in a population that might be misstated and then multiplies this percentage by an estimate of how much the dollars are misstated. 9-3

4. Monetary-Unit Sampling (MUS) Advantages 1.When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling. 2.When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample. 3.MUS does not require the user to make assumptions about the distribution of misstatements. 1.When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling. 2.When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample. 3.MUS does not require the user to make assumptions about the distribution of misstatements. LO# 2 Disadvantages 1.The selection of zero or negative balances generally requires special design consideration. 2.The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100%. 3.When more than one or two misstatements are detected, the sample results calculations may overstate the allowance for sampling risk. 1.The selection of zero or negative balances generally requires special design consideration. 2.The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100%. 3.When more than one or two misstatements are detected, the sample results calculations may overstate the allowance for sampling risk. 9-4

5. Steps in MUS LO# 2 9-5

6. Steps in MUS If the upper misstatement limit is greater than the tolerable misstatement, the auditor concludes that the account balance is materially misstated. When faced with this situation, the auditor may: 1.Increase the sample size. 2.Perform other substantive procedures. 3.Request the client adjust the accounts receivable balance. 4.If the client refuses to adjust the account balance, the auditor would consider issuing a qualified or an adverse opinion. When faced with this situation, the auditor may: 1.Increase the sample size. 2.Perform other substantive procedures. 3.Request the client adjust the accounts receivable balance. 4.If the client refuses to adjust the account balance, the auditor would consider issuing a qualified or an adverse opinion. LO# 3 9-6

7. Risk When Evaluating Account Balances LO# 3 9-7

8. Nonstatistical Sampling for Tests of Account Balances The sampling unit for nonstatistical sampling is normally a customer account, an individual transaction, or a line item on a transaction. When using nonstatistical sampling, the following items must be considered: o Identifying individually significant items. o Determining the sample size. o Selecting sample items. o Calculating the sample results. o Identifying individually significant items. o Determining the sample size. o Selecting sample items. o Calculating the sample results. LO# 4 9-8

9. Why Did Statistical Sampling Fall Out Of Favor? 1.Firms found that some auditors were over relying on statistical sampling techniques to the exclusion of good judgment. 2.There appears to be poor linkage between the applied audit setting and traditional statistical sampling applications. LO# 4 9-9

10. Classical Variable Sampling Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data. Auditors most commonly use classical variables sampling to estimate the size of misstatement. Sampling distributions are formed by plotting the projected misstatements yielded by an infinite number of audit samples of the same size taken from the same underlying population. LO# 5 9-10

11. Classical Variables Sampling A sampling distribution is useful because it allows us to estimate the probability of observing any single sample result. LO# 5 In classical variables sampling, the sample mean is the best estimate of the population mean. 9-11

12. Classical Variables Sampling 1.When the auditor expects a relatively large number of differences between book and audited values, this method will normally result in smaller sample size than MUS. 2.The techniques are effective for both overstatements and understatements. 3.The selection of zero balances generally does not require special sample design considerations. 1.When the auditor expects a relatively large number of differences between book and audited values, this method will normally result in smaller sample size than MUS. 2.The techniques are effective for both overstatements and understatements. 3.The selection of zero balances generally does not require special sample design considerations. LO# 5 AdvantagesDisadvantages 1.Does not work well when little or no misstatement is expected in the population. 2.To determine sample size, the auditor must estimate the standard deviation of the audit differences. 3.If few misstatements are detected in the sample data, the true variance tends to be underestimated, and the resulting projection of the misstatements and the related confidence limits are not likely to be reliable. 1.Does not work well when little or no misstatement is expected in the population. 2.To determine sample size, the auditor must estimate the standard deviation of the audit differences. 3.If few misstatements are detected in the sample data, the true variance tends to be underestimated, and the resulting projection of the misstatements and the related confidence limits are not likely to be reliable. 9-12

13. Applying Classical Variables Sampling Defining the Sampling Unit The sampling unit can be a customer account, an individual transaction, or a line item. In auditing accounts receivable, the auditor can define the sampling unit to be a customer’s account balance or an individual sales invoice included in the account balance. LO# 6 9-13

14. Applying Classical Variables Sampling Determining the Sample Size where CC = Confidence coefficient SD = Estimated standard deviation Sample Size = Population size (in sampling units) × CC × SD Tolerable misstatement – Estimated misstatement 2 LO# 6 9-14

15. Applying Classical Variables Sampling Mean misstatement per sampling item = Total audit difference Sample size LO# 6 Population size × Mean misstatement per sampling item Projected population misstatement = (in sampling units) Total audit differences squared – Mean difference per sampling item 2 Sample Size × Sample size – 1 SD = Project the error and the SD: 9-15

16. Applying Classical Variables Sampling Confidence bound Population size CC SD Sample size × ×= Confidence interval Projected misstatement Confidence bound ± = LO# 6 9-16

17. Applying Classical Variables Sampling Lower limit ($1,653) Projected misstatement $14,575 Upper limit $30,803 If both limits are within the bounds of tolerable misstatement, the evidence supports the conclusion that the account is not materially misstated. LO# 6 ($50,000)$50,000$0 Tolerable Misstatement 9-17

18. End of Chapter 9 9-18