1. APIPA 20091 STATISTICAL SAMPLING FOR AUDITORS Jeanne H. Yamamura CPA, MIM, PHD

2. APIPA 20092 OBJECTIVES  Review of sampling concepts  Types of sampling  Attribute sampling  Steps  Nonstatistical attribute sampling  Compliance auditing  Monetary unit sampling  Steps  Nonstatistical monetary unit sampling  Classical sampling  Ratio estimation  Difference estimation

3. APIPA 20093 AUDIT SAMPLING  Application of an audit procedure to less than 100% of the items in a population  Account balance  Class of transactions  Examination “on a test basis”  Key: Sample is intended to be representative of the population.

4. APIPA 20094 SAMPLING RISK  Possibility that the sample is NOT representative of the population  As a result, auditor will reach WRONG conclusion  Decision errors  Type I – Risk of incorrect rejection  Type II – Risk of incorrect acceptance

5. APIPA 20095 TYPE I – RISK OF INCORRECT REJECTION  Internal control: Risk that sample supports conclusion that control is NOT operating effectively when it really is  AKA – Risk of underreliance, risk of assessing control risk too high  Substantive testing: Risk that sample supports conclusion that balance is NOT properly stated when it really is

6. APIPA 20096 TYPE II – RISK OF INCORRECT ACCEPTANCE  Internal control: Risk that sample supports conclusion that control is operating effectively when it really isn’t  AKA – Risk of overreliance, risk of assessing control risk too low  Substantive testing: Risk that sample supports conclusion that balance is properly stated when it really isn’t

7. APIPA 20097 WHICH RISK POSES THE GREATER DANGER TO AN AUDITOR?  Risk of incorrect rejection  Efficiency  Risk of incorrect acceptance  Effectiveness  Auditor focus on Type II  Also provides coverage for Type I

8. APIPA 20098 NONSAMPLING RISK  Risk of auditor error  Sample wrong population  Fail to detect a misstatement when applying audit procedure  Misinterpret audit result  Controlled through  Adequate training  Proper planning  Effective supervision

9. APIPA 20099 SAMPLE SIZE FACTORS  Desired level of assurance (confidence level)  Acceptable defect rate (tolerable error)  Historical defect rate (expected error)

10. APIPA 200910 CONFIDENCE LEVEL  Complement of sampling risk  5% sampling risk, 95% confidence level  How much reliance will be placed on test results  The greater the reliance and the more severe the consequences of Type II error, the higher the confidence level needed  Sample size increases with confidence level (decreases with sampling risk)

11. APIPA 200911 TOLERABLE ERROR AND EXPECTED ERROR  “Precision” – the gap between tolerable error and expected error  AKA Allowance for sampling risk  Sample size increases as precision decreases

12. APIPA 200912 WHEN DO YOU SAMPLE?  Inspection of tangible assets, e.g., inventory observation  Inspection of records or documents, e.g., internal control testing  Reperformance, e.g., internal control testing  Confirmation, e.g., verification of AR balances

13. APIPA 200913 WHEN IS SAMPLING INAPPROPRIATE?  Selection of all items with a particular characteristic, e.g., all disbursements > $100,000  Testing only one or a few items, e.g., automated IT controls, walk throughs  Analytical procedures  Scanning  Inquiry  Observation

14. APIPA 200914 WALKTHROUGHS  Designed to provide evidence regarding the design and implementation of controls  Can provide some assurance of operating effectiveness BUT  Depends on nature of control (automated or manual)  Depends on nature of auditor’s procedures to test control (also includes inquiry and observation combined with strong control environment and adequate monitoring)  Walkthough = sample of 1

15. APIPA 200915 STATISTICAL VS NONSTATISTICAL SAMPLING  Statistical sampling  Statistical computation of sample size  Statistical evaluation of results  Nonstatistical sampling  Sample sizes should be approximately the same (AU 350.22)  Sample sizes must be sufficient to support reliance on controls and assertions being tested

16. APIPA 200916 WHEN IS SAMPLING NONSTATISTICAL?  If sample size determined judgmentally  If sample selected haphazardly  If sample results evaluated judgmentally

17. APIPA 200917 TYPES OF SAMPLING  Attribute sampling  Monetary unit sampling  Classical variables sampling

18. APIPA 200918 ATTRIBUTE SAMPLING  Used to estimate proportion of a population that possesses a specific characteristic  Most commonly used for T of C  Can also be used for dual purpose testing (T of C and Substantive T of T)

19. APIPA 200919 MONETARY-UNIT SAMPLING  AKA probability proportional to size (PPS) sampling, cumulative monetary unit sampling  Used to estimate dollar amount of misstatement

20. APIPA 200920 CLASSICAL VARIABLES SAMPLING  Uses normal distribution theory to identify amount of misstatement  Useful when large number of differences expected  Smaller sample size than MUS  Effective for both overstatements and understatements  Can easily incorporate zero balances

21. APIPA 200921 IN-CLASS EXERCISE NO. 1

22. APIPA 200922 IN-CLASS EXERCISE NO. 1 Test Involves Sampling? Attribute / Variable / MUS / NA 1Yes Attribute (ST of T) 2NoNA 3Yes Attribute (T of C) 4NoNA 5No NA (Could be MUS if large population) 6NoNA

23. APIPA 200923 IN-CLASS EXERCISE NO. 1 Test Involves Sampling? Attribute / Variable / MUS / NA 7Yes Attribute (T of C) 8YesMUS 9NoNA 10Yes Attribute (T of C/ST of T) 11NoNA

24. APIPA 200924 STEPS IN STATISTICAL ATTRIBUTE SAMPLING APPLICATION  Planning 1.Determine the test objectives 2.Define the population characteristics 3.Determine the sample size  Performance 4.Select sample items 5.Perform the auditing procedures  Evaluation 6.Calculate the results 7.Draw conclusions

25. APIPA 200925 STEP 1: DETERMINE THE TEST OBJECTIVES  Objective for T of C: To determine the operating effectiveness of the internal control  Support control risk assessment below maximum  Identify controls to be tested and understand why they are to be tested

26. APIPA 200926 TESTS OF CONTROLS  Concerned primarily with  Were the necessary controls performed?  How were they performed?  By whom were they performed?  Appropriate when documentary evidence of performance exists

27. APIPA 200927 STEP 2: DEFINE THE POPULATION CHARACTERISTICS  Define the sampling population  Assertion  Completeness  Define the sampling unit  Determined by available records  Define the control deviation conditions

28. APIPA 200928 STEP 3: DETERMINE THE SAMPLE SIZE  Determine factors  Desired confidence level (direct)  Tolerable deviation rate (inverse)  Expected population deviation rate (direct)  Desired confidence level  If planning to rely on controls, would be 90 to 95%  Significance of account and importance of assertion affected by control being tested

29. APIPA 200929 STEP 3: DETERMINE THE SAMPLE SIZE  Tolerable deviation rate  Maximum deviation rate that auditor willing to accept and still consider control effective  Control would be relied upon  Why any errors acceptable?  Control deviation = Misstatement Assessed importance of control Tolerable deviation rate Highly important 3-5% Moderately important 6-10%

30. APIPA 200930 STEP 3: DETERMINE THE SAMPLE SIZE  Expected population deviation rate  Rate expected to exist in population  Based on prior years’ results or pilot sample  If expected population deviation rate > tolerable rate, DO NOT TEST  SAMPLE SIZE TABLES

31. APIPA 200931 STEP 3: DETERMINE THE SAMPLE SIZE  Testing multiple attributes on the same sample  Select largest sample size and audit all of them for all attributes  Result is some overauditing BUT may take less time than trying to remember which sample items need to be tested for which attribute

32. APIPA 200932 FINITE POPULATION CORRECTION FACTOR  When population size < 500  Apply finite population correction factor  √ 1-(n/N)  Where n = sample size from table and N = number of units in population

33. APIPA 200933 STEP 4: SELECT THE SAMPLE ITEMS  Sample must be selected to be representative of the population  Each item must have an equal opportunity of being selected

34. APIPA 200934 STEP 4: SELECT THE SAMPLE ITEMS  Random number selection  Unrestricted random sampling without replacement (once selected cannot be selected again)

35. APIPA 200935 STEP 4: SELECT THE SAMPLE ITEMS  Random number table  Need to document  Correspondence: relationship between population and random number table  Route: selection path, e.g., up or down columns, and right to left (must be consistent)  Starting point: starting row, column, digit  Stopping point: to enable adding more sample items if needed

36. APIPA 200936 RANDOM NUMBER TABLE ILLUSTRATION  Select a sample of 4 items from prenumbered canceled checks numbered from 1 to 500. Start at row 5, column 1, digit starting position 1. Select three-digit numbers. Items selected are:  145 (sample item #1)  516 (discard because checks numbers do not exceed 500)  032 (sample item #2)  246 (sample item #3)  840 (discard)181 (sample item #4)

37. APIPA 200937 RANDOM NUMBER TABLE ILLUSTRATION  To minimize discards, table numbers > 500 can be reduced by 500 to produce a sample item within the population boundary of 1 to 500. The four sample items selected are:  145 (sample item #1)  016 (sample item #2 = 516 – 500 = 016)  032 (sample item #2)  246 (sample item #3)  340 (sample item #4 = 840 – 500 = 340)

38. APIPA 200938 RANDOM NUMBER TABLE ILLUSTRATION  Select 4 sales invoices numbered from 5000 to 12000. Start at row 21, column 2, digit starting point 1. Rather than use a 5-digit number, which produces a large number of discards, add a constant to get a population with 4 digits. If a constant of 3000 is used, the usable numbers selected from 2000 to 9000 are:  6,043 (sample item #1 = 3043 + 3000)  10,120 (sample item #2 = 7120 + 3000)  10,212 (sample item #3 = 7212 + 3000)  5,259 (sample item #4 = 2259 + 3000)

39. APIPA 200939 STEP 4: SELECT THE SAMPLE ITEMS - EXCEL  Excel  Select Tools  Select Data Analysis  Select Sampling

40. APIPA 200940 STEP 4: SELECT THE SAMPLE ITEMS - EXCEL

41. APIPA 200941 STEP 4: SELECT THE SAMPLE ITEMS  Input Range  Enter the references for the range of data that contains the population of values you want to sample. Microsoft Excel draws samples from the first column, then the second column, and so on.  Labels  Select if the first row or column of your input range contains labels. Clear if your input range has no labels; Excel generates appropriate data labels for the output table.  Sampling Method  Click Periodic or Random to indicate the sampling interval you want.  Period  Enter the periodic interval at which you want sampling to take place. The period-th value in the input range and every period-th value thereafter is copied to the output column. Sampling stops when the end of the input range is reached.

42. APIPA 200942 STEP 4: SELECT THE SAMPLE ITEMS  Number of Samples  Enter the number of random values you want in the output column. Each value is drawn from a random position in the input range, and any number can be selected more than once.  Output Range  Enter the reference for the upper-left cell of the output table. Data is written in a single column below the cell. If you select Periodic, the number of values in the output table is equal to the number of values in the input range, divided by the sampling rate. If you select Random, the number of values in the output table is equal to the number of samples.

43. APIPA 200943 STEP 4: SELECT THE SAMPLE ITEMS  Systematic selection  Determine sampling interval = Population / Sample Size  Ensure population is in random order  Select random starting number (within first interval)  Better to use multiple random starting points to reduce risk of missing systematic deviations  Select every nth item  Continue sample selection until population is exhausted  (Last sample selected + sampling interval) > Last item in population  In other words, don’t stop when desired sample size reached

44. APIPA 200944 STEP 5: PERFORM THE AUDITING PROCEDURES  Conduct planned audit procedures  What if?  Voided documents - if properly voided, not a deviation; replace with new sample item  Unused or inapplicable documents – replace with new sample item  Inability to examine sample item – deviation  Stopping test before completion – large number of deviations detected

45. APIPA 200945 STEP 5: PERFORM THE AUDITING PROCEDURES  Deviations observed  Investigate nature, cause, and consequence of every exception  Unintentional error? Or fraud?  Monetary misstatement resulted?  Cause – misunderstanding of instructions? Carelessness?  Effect on other areas?

46. APIPA 200946 STEP 6: CALCULATE RESULTS  Summarize deviations for each control  Calculate sample deviation rate and computed upper deviation rate  Sample deviation rate + Allowance for sampling risk = Computed upper deviation rate  Statistical sampling results evaluation tables

47. APIPA 200947 STEP 7: DRAW CONCLUSIONS  If Computed Upper Deviation Rate > Tolerable Rate, control is ineffective and cannot be relied upon.  If Computed Upper Deviation Rate < Tolerable Rate, control is effective

48. APIPA 200948 EVALUATION OF EXPOSURE  In a sample of 25 manual control operations from a population of 3,000 control operations, 1 deviation was identified. The sample was designed with an expectation that 0 deviations would be found.  Looking up the results (in 90% confidence level table): Computed upper error limit = 14.7%

49. APIPA 200949 EVALUATION OF EXPOSURE  The sample did not meet its design criteria, so there is a higher than desired risk that the control will fail to prevent or detect a misstatement.  To assess the magnitude of the exposure:  Identify the gross exposure of the account or process. This is based on the volume of dollars processed through the control.  The upper limit on the control deviations was 14.7%.  The adjusted exposure is $735,000 (14.7% * $5,000,000).  The $735,000 exposure may assist the auditor in evaluating the severity of the control deficiency.

50. APIPA 200950 IN-CLASS EXERCISES NO. 2 & NO. 3

51. APIPA 200951 IN-CLASS EXERCISE NO. 2 Problem 1: Prenumbered sales invoices where the lowest invoice number is 1 and the highest is 6211. Sampling unit Sales invoice Population numbering system 1 to 6211 Random number table correspondence Use 4 digits with random start at 0029-05 going down and then right First 5 items in sample 3553 0081 4429 0484 4881

52. APIPA 200952 IN-CLASS EXERCISE NO. 2 Problem 2: Prenumbered bills of lading where the lowest document number is 21926 and the highest is 28511. Sampling unit Bill of lading Population numbering system 21926 to 28511 Random number table correspondence Use last 4 digits with random start at 0005-07 First 5 items in sample 7744 7632 8120 3736 4091

53. APIPA 200953 IN-CLASS EXERCISE NO. 2 Problem 3: Accounts Receivable on 10 pages with 60 lines per page except the last page, which has only 36 full lines. Each line has a customer name and an amount receivable. Sampling unit Each line Population numbering system 9 * 60 = 540 + 36 = 576 lines Add 2000 (2001 to 2576) Random number table correspondence Use last 4 digits with random start at 00040-01 going down and then right First 5 items in sample 2240 2055 2094 2087 2608

54. APIPA 200954 IN-CLASS EXERCISE NO. 2 Problem 4: Prenumbered invoices in a sales journal where each month starts over with number 1. (Invoices for each month are designated by the month and document number.) There is a maximum of 20 pages per month with a total of 185 pages for the year. All pages have 75 invoices except for the last page for each month. Sampling unit Page of invoices Population numbering system Starting with January, first page is 1 (up to 185) Random number table correspondence Random start at 0008-03 going down then right, subtract random number from next 1000 First 5 items in sample 4000 – 3982 = 18; 7000 – 6847 = 153; 5000 - 4956 = 44; 6000 – 5985 = 15; 5000 – 4941 = 59

55. APIPA 200955 IN-CLASS EXERCISE NO. 3 For which of these auditing procedures can attribute sampling be conveniently used? 1No 2No 3No 4Yes 5aYes 5bYes

56. APIPA 200956 IN-CLASS EXERCISE NO. 3 For which of these auditing procedures can attribute sampling be conveniently used? 5cYes 5dYes 5eYes 6Yes

57. APIPA 200957 IN-CLASS EXERCISE NO. 3 2. Considering the audit procedures to be performed, what is the most appropriate sampling unit for conducting most of the audit sampling tests? Sales invoice

58. APIPA 200958 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 4. Existence of the sales invoice number in the sales journal No record of the sales invoice number in the sales journal 5a. Amount and other data in MF agree with the sales journal entry The amount recorded in the MF differs from the amount recorded in the sales journal.

59. APIPA 200959 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 5b. Amount and other data on the duplicate sales invoice agree with the sales journal entry Customer name and account number on the invoice differ from the information recorded in the sales journal

60. APIPA 200960 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 5b. Evidence that pricing, extensions, and footings are checked (initials and correct amounts). Lack of initials indicating verification of pricing, extensions, and footings.

61. APIPA 200961 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 5c. Quantity and other data on the bill of lading agree with the duplicate sales invoice and sales journal Quantity of goods shipped differs from quantity on sales invoice

62. APIPA 200962 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 5d. Quantity and other data on the sales order agree with the duplicate sales invoice Quantity on the sales order differs from quantity on the duplicate sales invoice 5e. Quantity and other data on the customer order agree with the duplicate sales invoice Product number and description on the customer order differ from information on the duplicate sales invoice

63. APIPA 200963 IN-CLASS EXERCISE NO. 3 For each T of C or ST of T, identify the attribute being tested and the exception condition. Attribute Exception Condition 5e. Credit is approved Lack of initials indicating credit approval 6. For recorded sales in the sales journal, the file of supporting documents includes a duplicate sales invoice, BL, sales order, and customer order. BL is not attached to the duplicate sales invoice and the customer order.

64. APIPA 200964 IN-CLASS EXERCISE NO. 3 See Solution

65. APIPA 200965 STEPS IN NONSTATISTICAL ATTRIBUTE SAMPLING APPLICATION  Planning 1.Determine the test objectives 2.Define the population characteristics 3.Determine the sample size  Performance 4.Select sample items 5.Perform the auditing procedures  Evaluation 6.Calculate the results 7.Draw conclusions

66. APIPA 200966 STEP 3: DETERMINE THE SAMPLE SIZE  Consider desired confidence level, tolerable deviation rate, and expected population deviation rate  Judgmentally determine sample size  NOTE: Check against statistical sample size tables to verify adequacy

67. APIPA 200967 STEP 3: DETERMINE THE SAMPLE SIZE  Guidelines for nonstatistical sample sizes for tests of controls  If any errors found, increase sample size or increase control risk Desired level of controls reliance Sample size Low15-20 Moderate25-35 High40-60

68. APIPA 200968 STEP 4: SELECT SAMPLE ITEMS  Random sample  Systematic sample (with random start)  Haphazard selection  Still desire representative sample  Avoid unusual, large, first or last

69. APIPA 200969 STEP 6: CALCULATE THE RESULTS  No computed upper deviation rate  If sample deviation rate > expected population deviation rate, control not effective

70. APIPA 200970 COMPLIANCE AUDITING  Performance of auditing procedures to determine whether an entity is complying with specific requirements of laws, regulations, or agreements  Governmental entities and other recipients of governmental financial assistance  Compliance with laws and regulations that materially affect each major federal assistance program

71. APIPA 200971 COMPLIANCE AUDITING OF FEDERAL ASSISTANCE PROGRAMS  Definition of population for testing of an internal control procedure that applies to more than one program  Define items from each major program as a separate population, OR  Define all items to which control is applicable as a single population  Second choice usually more efficient

72. APIPA 200972 COMPLIANCE AUDITING - EXAMPLE  Federal financial assistance for Island City  Three major federal financial assistance programs  Four nonmajor programs  Control: Transaction review to ensure that only legally allowable costs are charged to each program

73. APIPA 200973 COMPLIANCE AUDITING - EXAMPLE  More efficient to select one sample from population of all transactions (major and nonmajor programs)  Confidence level = 95%  Tolerable deviation rate = 9%  Expected population deviation rate = 1%  Sample size: 51  1 allowable deviation

74. APIPA 200974 SMALL POPULATIONS AND INFREQUENTLY OPERATING CONTROLS Small Population Sample Size Table Control Frequency and Population Size Sample Size Quarterly (4) 2 Monthly (12) 2-4 Semimonthly (24) 3-8 Weekly (52) 5-9

75. APIPA 200975 IN-CLASS EXERCISE NO. 4

76. APIPA 200976 IN-CLASS EXERCISE NO. 4 Selected Payroll T of C 1. Examine the time card for approval of a supervisor Moderately critical – affects E/O of S& W 2. Account for a sequence of payroll checks in the payroll journal Very critical – affects E/O of S&W 3. Recompute hours on the time card Moderately critical – affects V of S&W

77. APIPA 200977 IN-CLASS EXERCISE NO. 4 4. Compare the employee name in the payroll journal to personnel records Very critical – affects E/O - affects E/O of S& W; also an area subject to fraud 5. Review OT charges for approval of a supervisor Moderately critical – affects E/O and V of S&W

78. APIPA 200978 IN-CLASS EXERCISE NO. 4 Selected Cash Disbursement T of C 6. Examine voucher for supporting invoices, receiving reports, etc. Very critical – affects E/O of purchase transactions 7. Examine supporting documents for evidence of cancellation (“paid”) Moderately critical – affects validity of purchase transactions and relates to double payment

79. APIPA 200979 IN-CLASS EXERCISE NO. 4 Selected Cash Disbursement T of C 8. Ascertain whether cash discounts were taken Least critical – affects V of purchase transactions; amounts usually minor 9. Review voucher for clerical accuracy Moderately critical – affects V of purchase transactions

80. APIPA 200980 IN-CLASS EXERCISE NO. 4 Selected Cash Disbursement T of C 10. Agree purchase order price to invoice Moderately critical – affects V of purchase transactions

81. APIPA 200981 MONETARY UNIT SAMPLING  Uses attribute sampling theory to express conclusions in dollar amounts  Estimates the percentage of monetary units in a population that might be misstated  Multiples the percentage by an estimate of how much the dollars are misstated  Developed by auditors  Assumes little or no misstatements  Designed primarily to test for overstatements

82. APIPA 200982 ADVANTAGES  When no misstatements expected, results in smaller (more efficient) sample size than classical variables sampling  No need to compute/identify standard deviation  Automatically stratifies sample

83. APIPA 200983 DISADVANTAGES  Zero or negative balances must be tested separately  Assumes audited amount of sample items is not in error by more than 100%  When more than 1 or 2 misstatements found, allowance for sampling risk may be overstated  Auditor more likely to reject balance and overaudit

84. APIPA 200984 STEPS IN MONETARY UNIT SAMPLING APPLICATION  Planning 1.Determine the test objectives 2.Define the population characteristics 3.Determine the sample size  Performance 4.Select sample items 5.Perform the auditing procedures  Evaluation 6.Calculate the results 7.Draw conclusions

85. APIPA 200985 STEP 1: DETERMINE THE TEST OBJECTIVES  Substantive testing: To test the reasonableness of an amount, i.e., that an amount is fairly stated  To test the assertion that no material misstatements exist in an account balance, class of transactions, or disclosure component of the financial statements

86. APIPA 200986 STEP 2: DEFINE THE POPULATION CHARACTERISTICS  Define the sampling population  Monetary value of an account balance  Verify completeness of population  Define the sampling unit - Each individual dollar  Define the logical unit - The account or transaction that contains the sampling units  Define a misstatement – The difference between the book value and the audited value

87. APIPA 200987 STEP 3: DETERMINE THE SAMPLE SIZE  Determine factors (effect on sample size)  Desired confidence level (direct)  To increase confidence, more work is required! (larger sample size)  Tolerable misstatement (inverse)  Expected misstatement (direct)  Population size (direct)

88. APIPA 200988 STEP 3: DETERMINE THE SAMPLE SIZE  Computing sample sizes using the attribute sampling tables  Select desired confidence level  Compute tolerable misstatement as percentage of book value  Compute expected misstatement as percentage of book value  Look up sample size in attribute sampling table

89. APIPA 200989 STEP 4: SELECT THE SAMPLE ITEMS  Systematic selection approach called probability proportional to size (PPS)  Calculate sampling interval  Book value / sample size  From random start (within first interval), select every nth dollar  Logical unit included only once even if includes more than one sample unit

90. APIPA 200990 STEP 5: PERFORM THE AUDITING PROCEDURES  Conduct planned audit procedures on logical units  What if?  Missing document – consider to be a misstatement

91. APIPA 200991 STEP 6: CALCULATE RESULTS  Projected misstatement: Projection of the errors to the population  Upper limit on misstatement: Adds an allowance for sampling risk to the projected misstatement

92. APIPA 200992 STEP 6: CALCULATE RESULTS  Sort misstatements into two groups  Group 1: Logical unit equal to or greater than the sampling interval  Group 2: Logical unit less than the sampling interval  For Group 2, compute the tainting factor for each misstatement  Tainting factor = Book value – Audit value Book value

93. APIPA 200993 STEP 6: CALCULATE RESULTS  Place the Group 2 items in rank order by tainting factor (from largest to smallest)  Compute the projected misstatement  Calculate the upper limit increments (using the Monetary Unit Sampling – Confidence Factors for Sample Evaluation table)  Calculate upper misstatement for each Group 2 item  Add differences for Group 1  Total = Upper misstatement limit

94. APIPA 200994 STEP 6: CALCULATE RESULTS - EXAMPLE  Book value = $3,100,000  Tolerable misstatement = $150,000  Expected misstatement = $25,000  Desired confidence level = 95%  Tolerable misstatement rate = 4.8%,round to 5%  Expected misstatement rate =.8%, round to 1%

95. APIPA 200995 STEP 6: CALCULATE RESULTS - EXAMPLE  Sample size = 93  Sampling interval = $33,333  Expected misstatement = $25,000

96. APIPA 200996 STEP 6: CALCULATE RESULTS - EXAMPLE Item Book Value Audited Value Difference Item 112,0003,1208,880 Item 235,00032,0003,000 Item 31,4000 Item 445,20041,0004,200 Item 5740555185

97. APIPA 200997 STEP 6: CALCULATE RESULTS - EXAMPLE Item Book Value Audited Value Difference Group 1: BV > SI (33,333) Item 235,00032,0003,000 Item 445,20041,0004,200 7,200

98. APIPA 200998 STEP 6: CALCULATE RESULTS - EXAMPLE ItemDifference Book Value Tainting Factor Group 2: BV < SI (33,333) Item 18,88012,000.74 Item 31,400 1.0 Item 5185740.25

99. APIPA 200999 STEP 6: CALCULATE RESULTS - EXAMPLE Item Tainting Factor Sampling Interval Projected Misstatement (Tainting Factor * SI) Item 31.033,333 Item 1.7433,33324,666 Item 5.2533,3338,333

100. APIPA 2009100 STEP 6: CALCULATE RESULTS - EXAMPLE Item Projected Misstatement 95% Upper Limit Increment Upper Misstatement Item 333,3333.099,999 Item 124,6661.741,932 Item 58,3331.512,500 154,431

101. APIPA 2009101 STEP 6: CALCULATE RESULTS - EXAMPLE Item Projected Misstatement 95% Upper Limit Increment Upper Misstatement Group 2154,431 Group 17,200 Upper Misstatement Limit161,631

102. APIPA 2009102 STEP 7: DRAW CONCLUSIONS  If Upper Misstatement Limit > Tolerable Misstatement, balance is materially misstated.  If Upper Misstatement Limit > Tolerable Misstatement, balance is not materially misstated

103. APIPA 2009103 IN-CLASS EXERCISES NO. 5 TO NO. 6

104. APIPA 2009104 IN-CLASS EXERCISE NO. 5 1.Sampling interval: 746,237 / 10 = 74,624 Loan # Recorded Amount 1141,100 366,600 510,230 114,350 2016,530 242,950 26131,200 2750,370 325,900

105. APIPA 2009105 IN-CLASS EXERCISE NO. 5 2.Sampling items always included: The loans > the sampling interval Loan #1 – 141,100 Loan #26 – 131,200

106. APIPA 2009106 IN-CLASS EXERCISE NO. 6 Recorded amount of accounts receivable = $400,000  Tolerable misstatement: $20,000; 20,000 / 400,000 = 5%  Risk of incorrect acceptance: 5%  Expected misstatements: 0  Sample size = 59  Sampling interval = 400,000 / 59 = 6,780

107. APIPA 2009107 IN-CLASS EXERCISE NO. 6 Error Recorded Amount Audit Amount Difference Tainting % 14003208020% 25000500100% 37,0006,500500NA

108. APIPA 2009108 IN-CLASS EXERCISE NO. 6 Error Tainting % Sampling Interval Projected Misstate- ment Upper Limit Increment Upper Limit Misstate- ment Logical unit BV < Sampling Interval 21006,7806,7801.711,526 1206,7801,3561.52,034

109. APIPA 2009109 IN-CLASS EXERCISE NO. 6 Error Tainting % Sampling Interval Projected Misstate- ment Upper Limit Increment Upper Limit Misstate- ment Logical unit BV > Sampling Interval 3NANA500NA500 Basic Precision: 3.0 * 6,780 = 20,340

110. APIPA 2009110 IN-CLASS EXERCISE NO. 6 Error Tainting % Sampling Interval Projected Misstate- ment Upper Limit Increment Upper Limit Misstate- ment Logical unit BV < Sampling Interval 13,560 Logical unit BV > Sampling Interval 500 Basic Precision 20,340 Upper Misstatement Limit 34,400 Conclusion: The account is materially misstated. The upper misstatement limit of 34,400 exceeds the tolerable misstatement of 20,000.

111. APIPA 2009111 NONSTATISTICAL SAMPLING – BALANCE TESTING  Differences in  Identifying individually significant items  Determining sample size  Selecting sample items  Calculating sample results

112. APIPA 2009112 IDENTIFYING INDIVIDUALLY SIGNIFICANT ITEMS  Selected due to large size  Tested 100%  Results similar to PPS selection  For example, selecting all items > $100,000

113. APIPA 2009113 DETERMINING SAMPLE SIZE  Sample size = Sampling Population BV * Assurance (Tolerable – Expected Factor Misstatement) Misstatement) where Sampling Population BV excludes individually significant items where Sampling Population BV excludes individually significant items

114. APIPA 2009114 DETERMINING SAMPLE SIZE Assessment of RMM Desired Level of Confidence – Assurance Factors Maximum Slightly below maximum ModerateLow Maximum 3.02.72.32.0 Slightly below maximum 2.72.42.01.6 Moderate 2.32.11.61.2 Low 2.01.61.21.0

115. APIPA 2009115 DETERMINING SAMPLE SIZE - EXAMPLE  Book value = $3,100,000  Individually significant items = $1,500,000  Tolerable misstatement = $150,000  Expected misstatement = $25,000  Desired confidence level = Maximum  Risk of MM = Maximum  Sample size = 1,600,000 * 3.0 (150,000 – 25,000) (150,000 – 25,000) = 38.4, round to 39 = 38.4, round to 39

116. APIPA 2009116 SELECTING SAMPLE ITEMS  Random selection  Systematic selection  Haphazard selection

117. APIPA 2009117 CALCULATING SAMPLE RESULTS  Sample misstatement MUST be projected to population  Two acceptable methods  Apply sample misstatement ratio to population (ratio estimation)  Apply average misstatement $ of each item in sample to all items in population (difference estimation)

118. APIPA 2009118 CLASSICAL SAMPLING  Ratio estimation  Difference estimation

119. APIPA 2009119 RATIO ESTIMATION  Sample misstatements = $19,000  Sample book value = $175,000  Sample error rate = 10.9%, round to 11%  Total population BV = $1,840,000  Projected misstatement = $1,840,000 * 11% = $202,400  Compare projected misstatement to tolerable misstatement

120. APIPA 2009120 DIFFERENCE ESTIMATION  Sample misstatements = $19,000  # of sample items with misstatements = 5  Average misstatement per sample item = $3,800  # items in population = 256  Projected misstatement = $3,800 * 256 = $972,800  Compare projected misstatement to tolerable misstatement

121. APIPA 2009121 IN-CLASS EXERCISE NO. 7

122. APIPA 2009122 IN-CLASS EXERCISE NO. 7 Nonstatistical Sample Results:  Errors in accounts > $10,000 33,000  Errors in accounts < $10,000:  Total errors $ 4,350  Sample BV $81,500  Error rate 5.34%  Applied to population:  2,760,000  (465,000)  2,295,000 * 5.34%122,553  Total estimated error155,553  Tolerable misstatement 81,500  Conclusion: Account materially misstated

123. APIPA 2009123 IN-CLASS EXERCISE NO. 7 - PPS PPS Sample Results:  Accounts receivable recorded balance: $2,760,000 balance: $2,760,000  Accounts > $10,000 (tested separately) (465,000) separately) (465,000)  Accounts receivable population – PPS$2,295,000 – PPS$2,295,000  Tolerable misstatement$ 81,500

124. APIPA 2009124 IN-CLASS EXERCISE NO. 7 - PPS Sample and sampling interval: Tolerable rate: 81,500 / 2,295,000 = 3.55%, round to 4% Expected rate: 0 5% risk of overreliance (since IR and CR are both high) Sample size: 74 Sampling interval: 2,295,000 / 74 = 31,014

125. APIPA 2009125 IN-CLASS EXERCISE NO. 7 - PPS Recorded Value Audited Value DifferenceTainting % Item 125,1204,8203005.85 Item 1948538510020.6 Item 331,2502501,00080 Item 353,9753,87510025.2 Item 511,8501,825251.4 Item 594,2003,78042010 Item 742,4050 100

126. APIPA 2009126 IN-CLASS EXERCISE NO. 7 - PPS # of Overstatement Misstatements 5%Upper Limit Increment 03.00 14.751.75 26.301.55 37.761.46 49.161.40 510.521.36 611.851.33 713.151.30

127. APIPA 2009127 IN-CLASS EXERCISE NO. 7 - PPS Tainting % Sampling Interval Projected Misstatement Upper Limit Factor Upper Misstatement Item 74 10031,014 1.7554,275 Item 33 8031,01424,8111.5538,457 Item 35 25.231,0147,8161.4611,411 Item 19 20.631,0146,3891.408,944 Item 59 1031,0143,1011.364,218 Item 12 5.8531,0141,8141.332,413 Item 51 1.431,0144341.30564 120,282

128. APIPA 2009128 IN-CLASS EXERCISE NO. 7 - PPS  Items < Sampling Interval:120,282  Items > Sampling Interval: None  Basic precision: 3.0 * 31,014 = 93,042  Upper misstatement limit = 213,324  Conclusion: Account is materially misstated. Upper misstatement limit 213,324 > tolerable misstatement 81,500

129. APIPA 2009129 RESOURCES  Audit Sampling: An Introduction, 3 rd Edition, Guy, Carmichael & Whittington  Audit Guide: Audit Sampling, New Edition as of May 1, 2008, AICPA  Auditing & Assurance Services, 6 th Edition, Messier, Glover, & Prawitt  Auditing & Assurance Services, 12 th Edition, Arens, Elder & Beasley

130. APIPA 2009130 THE END!