1. Audit Sampling Chapter 9

2. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-2 What is Audit Sampling?  Applying a procedure to less than 100% of a population  To estimate some characteristic of the population Qualitative Quantitative

3. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-3 Advantages of Statistical Sampling  Design efficient samples  Measure sufficiency of evidence  Objectively evaluate sample results

4. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-4 Selection of Random Sample  Random number tables  Random number generators  Systematic selection

5. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-5 Random Number Table

6. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-6 Types of Statistical Sampling Plans  Attributes sampling  Discovery sampling  Classical variables sampling  Probability-proportional-to-size sampling

7. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-7 Requirements of Audit Sampling Plans  When planning the sample consider: The relationship of the sample to the relevant audit objective Materiality or the maximum tolerable misstatement or deviation rate Allowable sampling risk Characteristics of the population  Select sample items in such a manner that they can be expected to be representative of the population  Sample results should be projected to the population  Items that cannot be audited should be treated as misstatements or deviations in evaluating the sample results  Nature and cause of misstatements or deviations should be evaluated

8. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-8 Actual Extent of Operating Effectiveness of the Control Procedure is Adequate Inadequate The Test of Controls Sample Indicates: Extent of Operating Effectiveness is Adequate Extent of Operating Effectiveness Inadequate Sampling Risks--Tests of Controls Correct Decision Incorrect Decision (Risk of Assessing Control Risk Too High) Incorrect Decision (Risk of Assessing Control Risk Too Low) Correct Decision

9. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-9 Audit Sampling for Tests of Controls  Determine the objective of the test  Define the attributes and deviation conditions  Define the population to be sampled  Specify: The risk of assessing control risk too low The tolerable deviation rate  Estimate the population deviation rate  Determine the sample size  Select the sample  Test the sample items  Evaluate the sample results  Document the sampling procedure

10. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-10 Sampling Risks--Substantive Tests The Population Actually is Not MateriallyMaterially MisstatedMisstated The Substantive Procedure Sample Indicates Misstatement in Account Exceeds Tolerable Amount Misstatement in Account Is Less Than Tolerable Amount Correct Decision Incorrect Decision (Risk of Incorrect Rejection) Incorrect Decision (Risk of Incorrect Acceptance) Correct Decision

11. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-11 Audit Sampling for Substantive Tests  Determine the objective of the test  Define the population and sampling unit  Choose an audit sampling technique  Determine the sample size  Select the sample  Test the sample items  Evaluate the sample results  Document the sampling procedure

12. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-12 Population Variability—Why it Matters Item Population APopulation B 1 2,100 8,000 2 2,100 25 3 2,1002,000 4 2,100 400 5 2,100 75 Mean 2,1002,100 Standard deviation -0- 3,395  The variability determines how much information each of the items in the population tells you about the other items in the population.

13. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-13 Factors Affecting Sample Size

14. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-14 Determining Sample Size--MPU Sample size = 2

15. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-15 Determining Sample Size--MPU Sampling Planned allowance for sampling risk = Tolerable misstatement ______________________ 1 + Incorrect acceptance coef. Incorrect rejection coef.

16. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-16 Adjusted allowance for sampling risk = Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size  This formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level. Variables Sampling Illustration--MPU

17. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-17 Variables Sampling Illustration--MPU Using the text example with a standard deviation of audited values of $16 Adjusted allowance for sampling risk = Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size = $364,000 _ ($100,000 * 1.64 * $16) 225 = $189,067  We would still “accept” the book balance because the $6,250,000 (book value) falls within this interval Estimate of total + Adjusted allowance audited value for sampling risk $6,100,000 + $189,067 [$5,910,933 to $6,289,067]

18. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-18 Acceptance Interval Figure 9-12

19. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-19 Nonstatistical Variables Sampling Illustration  Plan Sample: Population: Size = 363 items Book value = $200,000 Tolerable misstatement = $10,000 Risk assessments: Inherent and control risk = Slightly below maximum Other substantive tests = Moderate

20. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-20 Nonstatistical Sampling-- Determination of Sample Size Sample size = Population book value X Reliability factor Tolerable misstatement = $200,000 X 2.0 = 40 items $10,000

21. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-21 Nonstatistical Sampling--Evaluation of Sample Results  Sample results: 40 accounts in sample $350 net overstatement $60,000 book value of sample items  Projected misstatement: = [Sample net misstatement] X Book value of population [ Book value of sample ] = [ $350 ] X $200,000 [$60,000] = $1,167 Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.

22. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-22 PPS Sampling Illustration  Population book value = $6,250,000  Other Information: Tolerable misstatement = $364,000 Sampling risk--Incorrect acceptance = 5% Expected misstatement = $50,000  Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor.”

23. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-23 PPS Sample Size Computation  Sample size = Recorded amount of population * Reliability factor Tolerable misstatement - (Expected misstatement * Expansion factor) = $6,250,000 * 3.0 = 66 $364,000 - ($50,000 * 1.6) Sampling interval = Book value of the population Sample size = $6,250,000 = $95,000 (approximately) 66

24. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-24 PPS Evaluation of Results Upper Limit on misstatement = Projected misstatement + Basic precision (Rel. factor x interval) + Incremental allowance

25. McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. 9-25 Calculation of Upper Limit on Misstatement