Substantive Test Sampling CAS 500 – Audit evidence CAS 315 - Identifying and Assessing the Risks of Material Misstatement through Understanding the Entity and its Environment CAS 450 - Evaluation of Misstatements Identified during the Audit CAS 320 – Materiality in planning and performing an audit CAS 530 – Audit sampling

Substantive Procedures for Auditing Account Balances Substantive tests of details auditing is the performance of procedures to obtain direct evidence about the dollar amounts and disclosures in the financial statements. Substantive procedures include:

The Audit Risk Model Audit Risk = Inherent Risk x Control Risk x Detection Risk Audit risk Inherent risk Control Risk Detection risk

Risk Model Expansion Detection risk (DR) is actually a combination of two risks: Analytical procedures risk (APR) Risk of incorrect acceptance (RIA)

Risk Model Expansion AR RIA = IR x CR x APR Expanded risk model: AR = IR × CR × APR × RIA Only risk of incorrect acceptance can be controlled by the auditor. Solve the risk model for RIA: with AR, IR, and APR held constant RIA varies inversely with CR or control risk. RIA = AR IR x CR x APR

More About Sampling Risk In sampling for substantive procedures, the auditor faces two sampling risks. The risk of incorrect acceptance (RIA) (effectiveness risk, beta risk) The risk of incorrect rejection (RIR) (efficiency risk, alpha risk)

Which is considered the more important of the two. Incorrect acceptance leads to audit failure. Incorrect rejection leads to additional audit procedures to determine actual misstatement.

Sampling Steps for an Account Balance Audit Specify the audit objectives. Define the population. Choose an audit sampling method. Determine the sample size. Select the sample. Perform the substantive-purpose procedures. Evaluate the evidence.

Plan the Procedures – involves the first three steps The first three steps represent the problem-recognition phase. So what is being considered in the first three steps? Remember a key to the audit approach: Management’s Assertions lead to Audit Objectives lead to Audit Procedures

1. Specify the Audit Objectives Objective is to decide whether the client’s assertions about existence, rights, and valuation are materially accurate.

2. Define the Population Definition of population must match objectives. Examine individually significant items. Apply stratification to the remaining population.

3. Choose an Audit Sampling Method Auditor will decide whether to use statistical or judgmental sampling methods. Steps 4 to 6 represent the evidence-collection phase. Sample size determination requires consideration of several factors. It is important to get the sample size correct, and to avoid over-auditing or under-auditing.

4. Determine the Sample Size The sample size is based on the following: risk of incorrect acceptance (RIA), risk of incorrect rejection (RIR), material misstatement amount, expected dollar misstatement in the population, variability within the population, and size of the population.

5. Select the sample Random or non-random methods, as in sample selection for test of controls.

6. Perform the substantive purpose procedures. Substantive-purpose audit program produces evidence to support or refute management assertions. Remember the assertions.

7. Evaluate the Evidence Evaluate the evidence: Determine amount of known misstatement. Determine the likely misstatement. Project the misstatement found in the sample to the population.

7. Evaluate the Evidence Consider sampling risks: Auditor uses professional judgment and experience to consider these risks. Qualitative evaluation: Follow up on all differences uncovered to determine any misunderstanding of GAAP, simple mistakes, intentional irregularities, or management override of controls.

7. Evaluate the Evidence Evaluate the misstatement: Known misstatement and likely misstatement are combined and compared to materiality. Sample risk gives rise to “possible misstatements.”

Timing of Substantive Procedures Account balances can, in part, be audited at an interim date. Auditor will extend the interim date audit conclusions to balance sheet date. Audit work is performed at interim dates: Poor controls, or significant business risk may preclude performing procedures at interim.

Monetary Unit Sampling - How Does it Work? Auditors use monetary unit sampling, also called probability-proportional-to-size or dollar-unit sampling, to determine the accuracy of financial accounts. With monetary unit sampling, each dollar in a transaction is a separate sampling unit. A transaction for $40, for example, contains 40 sampling units. Auditors usually use monetary unit sampling to sample and test accounts receivable. Here’s an example of how monetary unit sampling works The audit client’s accounts receivable book value is $300,000, and the sample size is set at 96 records. Figure the sampling interval by dividing book value by sample size (300,000/96) = 3125 Arrange the client’s accounts receivable in an ordered list using some sort of ordering sequence. For example, you can arrange them alphabetically by customer name or numerically by customer number. Pick a random number between 1 and 3,125. For this method to work correctly, the random number has to be less than the sampling interval and greater than the smallest sampling unit. Auditors usually use a random-number-generator computer program to pick the random number. The sampling unit and sampling interval limits are programmed into the software before the task is run. In this case, say the software selects the random number 556. Monetary Unit Sampling Table Customer Name Customer Balance Cumulative Balance Sampling Item ABC Electric $435 Best Friend Cat Care $785 $1,220 (1) $556 Brandy’s Grill $1,510 $2,730 Buddy’s Gas Station $5,000 $7,730 (2) $556 + $3,125 = $3,681

First, pick the records to test: Take the alphabetically ordered list shown in the Customer Name column, which lists every customer balance by dollar amount, and count each dollar until getting to $556. The random number generator gives the number 556 in Step 3 in the previous slide. The cumulative dollar amount for ABC Electric is under $556. That shows that the first sampling item is Best Friend Cat Care, which at a cumulative total of $1,220 is the first customer in the list with a cumulative balance over $556. Best Friend Cat Care becomes the first customer in the sample. Secondly, select the next invoice to sample: Add the sampling interval of $3,125 to the random number of $556. This equals $3,681, which is the next sampled item dollar amount. Brandy’s Grill at $2,730 cumulatively is under $3,681, thus Brandy’s is skipped. Buddy’s Gas Station has the 3,681st dollar. To pick the next sampling item: Add the sampling interval of $3,125 to the prior sampling item of $3,681, which equals $6,806, and so on until the last name in the customer list is reached. This will give the total sample size of 96. When sampling, misstatements are being looked for. If a selected customers invoice should have been entered for $986, for example, and it was entered as $896, there is a misstatement. If the total misstatements exceed the tolerable level, there may be a material misstatement.

Example for Calculation of Sample Size for MUS This example uses materiality: Book Value of Population = 596,566 Acceptable risk of incorrect acceptance (RIA) = 10% Tolerable misstatement /materiality (a) = 40,000 Expected misstatements in the population (b) = 4,000 Ratio of expected to tolerable misstatements - b/a = .10 Confidence factor (R) – next page (c) = 2.77 Tolerable misstatement (P) as % of population (d) = 0.067 Sample size - c/d (n=R/P) = 42 (round up) We will use 40 for MUS.

MUS Confidence Factors (R Values) (RIA in brackets) Ratio of Expected to Tolerable Misstatement Confidence Level (Risk of Incorrect Acceptance) 95% (5%) 90% (10%) 85% (15%) 80% (20%) 75% (25%) 70% (30%) 65% (35%) 63% (37%) 50% (50%) 0.00 3.00 2.31 1.90 1.61 1.39 1.21 1.05 1.00 0.70 0.05 3.31 2.52 2.06 1.74 1.49 1.29 1.12 1.06 0.73 0.10 3.68 2.77 2.25 1.89 1.20 1.13 0.77 0.15 4.11 3.07 2.47 1.28 0.82 0.20 4.63 3.41 2.73 2.26 1.62 1.38 1.30 0.87 0.25 5.24 3.83 3.04 2.49 2.09 1.76 1.50 1.41 0.92 0.30 6.00 4.33 2.30 1.93 1.63 1.53 0.99 0.35 6.92 4.95 3.86 3.12 2.57 2.14 1.79 1.67 0.40 8.09 5.72 4.42 3.54 2.89 2.39 1.99 1.85 1.14 0.45 9.59 6.71 5.13 4.07 3.29 2.70 2.22 1.25 0.50 11.54 7.99 6.04 4.75 3.80 3.08 2.51 2.32 1.37 0.55 14.18 9.70 7.26 5.64 4.47 3.58 2.65 1.52 0.60 17.85 12.07 8.93 6.86 5.37 4.25 3.38 3.09 1.70

Problem DC 10-1, Page 547 When Marge Simpson, PA, audited the Candle Company inventory, a random sample of inventory types was chosen for physical observation and price testing. The sample size was 80 different types of candles and candle-making inventory. The entire inventory contained 1,740 types, and the amount in the inventory control account was $166,000. Simpson had already decided that a misstatement of as much as $6,000 in the account would not be material. The audit work revealed the following no errors in the sample of 80. This problem has been changed from the text to show no errors.

There are no misstatements in this sample. Assume the sample was chosen using Monetary Unit Sampling, and the sampling risk is 10%. Simpson also assumes that the Misstatement Assumption for zero misstatements is 50% for both over and under misstatements. Is the inventory materially misstated? Total Population = 166,000.00 Sample Size = 80 ARACR = 10.00% Upper Misstatement Unit Error Assumption 50.00% Lower Misstatement Unit Error Assumption Materiality 6,000 This part of the population is not in the sample. Thus zero misstatements have been found here because these items have not been examined. Sample There are no misstatements in this sample. The misstatements of the remaining part of the population are not known. Thus a misstatement assumption has to be made. E.g. they are 50% misstated. See next slide.

Overstatements Understatements Number of Misstatements (1) Upper Precision Limit Portion (2) Recorded Value (3) Misstatement Unit Error Assumption (4) Bound Portion 2x3x4 Overstatements 0.029 166,000 0.500 $2,407 Upper Precision Limit Initial Misstatement Bound Understatements Number of Misstatements (1) Upper Precision Limit Portion (2) Recorded Value (3) Misstatement Unit Error Assumption (4) Bound Portion 2x3x4 Understatements 0.029 166,000 0.500 $2,407 Upper Precision Limit Initial Misstatement Bound As the Upper Bound and Lower Bound are less than the materiality of $6,000, there is no material misstatement

ACTUAL NUMBER OF DEVIATIONS FOUND Sample size ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10 5 PERCENT RISK OF OVER RELIANCE (RIA or Beta Risk) 20 14.0 21.7 28.3 34.4 40.2 45.6 50.8 55.9 60.7 65.4 69.9 25 11.3 17.7 23.2 28.2 33.0 37.6 42.0 46.3 50.4 54.4 58.4 30 9.6 14.9 19.6 23.9 28.0 31.9 35.8 39.4 43.0 46.6 50.0 35 8.3 12.9 17.0 20.7 24.3 27.8 31.1 37.5 40.6 43.7 40 7.3 11.4 15.0 18.3 21.5 24.6 27.5 30.4 33.3 36.0 38.8 45 6.5 10.2 13.4 16.4 19.2 22.0 24.7 27.3 29.8 32.4 34.8 50 5.9 9.2 12.1 14.8 17.4 19.9 22.4 27.1 29.4 31.6 55 5.4 8.4 11.1 13.5 15.9 18.2 20.5 22.6 24.8 26.9 28.9 60 4.9 7.7 12.5 14.7 16.8 18.8 20.8 22.8 26.7 65 4.6 7.1 9.4 11.5 13.6 15.5 17.5 19.3 21.2 23.0 70 4.2 6.6 8.8 10.8 12.7 14.5 16.3 18.0 19.7 21.4 23.1 75 4.0 6.2 8.2 10.1 11.8 15.2 16.9 18.5 20.1 21.6 80 3.7 5.8 9.5 14.3 18.9 20.3 90 3.3 5.2 6.9 9.9 12.8 14.2 100 3.0 4.7 7.6 9.0 10.3 125 2.4 3.8 5.0 6.1 7.2 9.3 12.3 13.2 150 2.0 3.2 5.1 6.0 7.8 8.6 200 1.5 3.9 300 1.0 1.6 2.1 2.6 3.1 3.5 4.4 4.8 5.6 400 0.8 1.2 2.3 2.7 3.6 4.3 500 0.6 1.3 1.9 2.9 3.4

ACTUAL NUMBER OF DEVIATIONS FOUND Sample size ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10 10 PERCENT RISK OF OVER RELIANCE (RIA or Beta Risk) 20 10.9 18.1 24.5 30.5 36.1 41.5 46.8 51.9 56.8 61.6 66.2 25 8.8 14.7 20.0 24.9 29.5 34.0 38.4 42.6 50.8 54.8 30 7.4 12.4 16.8 21.0 28.8 32.5 36.2 39.7 43.2 46.7 35 6.4 10.7 14.5 18.2 21.6 28.2 31.4 34.5 37.6 40.6 40 5.6 9.4 12.8 16.0 19.0 22.0 27.7 33.2 35.9 45 5.0 8.4 11.4 14.3 17.0 19.7 22.3 24.8 27.3 29.8 32.2 50 4.6 7.6 10.3 12.9 15.4 17.8 20.2 22.5 24.7 27.0 29.2 55 4.2 6.9 11.8 14.1 16.3 18.4 20.5 22.6 24.6 26.7 60 3.8 8.7 10.8 15.0 16.9 18.9 20.8 22.7 65 3.5 5.9 8.0 10.0 12.0 13.9 15.7 17.5 19.3 22.8 70 3.3 5.5 7.5 9.3 11.1 14.6 18.0 19.6 21.2 75 3.1 5.1 7.0 10.4 12.1 13.7 15.2 18.3 19.8 80 2.9 4.8 6.6 8.2 9.8 11.3 15.8 17.2 18.7 90 2.6 4.3 7.3 10.1 11.5 16.7 100 2.3 3.9 5.3 7.9 9.1 12.7 125 1.9 6.3 8.3 10.2 11.2 150 1.6 3.6 4.4 6.1 7.8 8.6 200 1.2 2.0 2.7 3.4 4.0 6.5 7.1 300 0.8 1.3 1.8 4.7 400 0.6 1.0 1.4 1.7 2.4 3.0 500 0.5 1.1 2.1 The Upper and Lower Bounds must be determined. What do these mean? Obtain the Precision Limits from this table – 10% RIA

Problem DC 10-1, Page 547 When Marge Simpson, PA, audited the Candle Company inventory, a random sample of inventory types was chosen for physical observation and price testing. The sample size was 80 different types of candles and candle-making inventory. The entire inventory contained 1,740 types, and the amount in the inventory control account was $166,000. Simpson had already decided that a misstatement of as much as $6,000 in the account would not be material. The audit work revealed the following eight errors in the sample of 80. Book Value (a) Audit value Error Amount (b) % Misstatement b/a $600.00 $622.00 $(22.00) (0.037) 15.50 14.50 1.00 0.065 65.25 31.50 33.75 0.517 83.44 53.45 29.99 0.359 16.78 15.63 1.15 0.069 78.33 12.50 65.83 0.840 13.33 14.22 (0.89) (0.067) 93.87 39.87 54.00 0.575 $966.50 $803.67 $162.83

Assume the sample was chosen using Monetary Unit Sampling, and the sampling risk is 10%. Simpson also assumes that the Misstatement Assumption for zero misstatements is 50% for both over and under misstatements. Is the inventory materially misstated? Total Population = 166,000.00 Sample Size = 80 ARACR = 10.00% Upper Misstatement Unit Error Assumption 50.00% Lower Misstatement Unit Error Assumption Materiality 6,000 This part of the population is not in the sample. Thus zero misstatements have been found here because these items have not been examined. Sample The misstatements of the sample, as percentages, are known . See previous slide 39. The misstatements of the remaining part of the population are not known. Thus a misstatement assumption has to be made. E.g. they are 50% misstated. See next slide.

Overstatements Number of Misstatements (1) Upper Precision Limit Portion (2) Recorded Value (3) Misstatement Unit Error Assumption (4) Bound Portion 2x3x4 Overstatements 0.029 166,000 0.500 $2,407 1 0.019 0.840 2649 2 0.018 0.575 1718 3 0.016 0.517 1373 4 0.359 954 5 0.015 0.069 172 6 0.065 162 Upper Precision Limit 0.128 Initial Misstatement Bound $9,435

ACTUAL NUMBER OF DEVIATIONS FOUND Sample size ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10 10 PERCENT RISK OF OVER RELIANCE (RIA or Beta Risk) 20 10.9 18.1 24.5 30.5 36.1 41.5 46.8 51.9 56.8 61.6 66.2 25 8.8 14.7 20.0 24.9 29.5 34.0 38.4 42.6 50.8 54.8 30 7.4 12.4 16.8 21.0 28.8 32.5 36.2 39.7 43.2 46.7 35 6.4 10.7 14.5 18.2 21.6 28.2 31.4 34.5 37.6 40.6 40 5.6 9.4 12.8 16.0 19.0 22.0 27.7 33.2 35.9 45 5.0 8.4 11.4 14.3 17.0 19.7 22.3 24.8 27.3 29.8 32.2 50 4.6 7.6 10.3 12.9 15.4 17.8 20.2 22.5 24.7 27.0 29.2 55 4.2 6.9 11.8 14.1 16.3 18.4 20.5 22.6 24.6 26.7 60 3.8 8.7 10.8 15.0 16.9 18.9 20.8 22.7 65 3.5 5.9 8.0 10.0 12.0 13.9 15.7 17.5 19.3 22.8 70 3.3 5.5 7.5 9.3 11.1 14.6 18.0 19.6 21.2 75 3.1 5.1 7.0 10.4 12.1 13.7 15.2 18.3 19.8 80 2.9 4.8 6.6 8.2 9.8 11.3 15.8 17.2 18.7 90 2.6 4.3 7.3 10.1 11.5 16.7 100 2.3 3.9 5.3 7.9 9.1 12.7 125 1.9 6.3 8.3 10.2 11.2 150 1.6 3.6 4.4 6.1 7.8 8.6 200 1.2 2.0 2.7 3.4 4.0 6.5 7.1 300 0.8 1.3 1.8 4.7 400 0.6 1.0 1.4 1.7 2.4 3.0 500 0.5 1.1 2.1 1.9 1.8 1.6 1.6 1.5 1.9 The Upper and Lower Bounds must be determined. What do these mean? Obtain the Precision Limits from this table – 10% RIA

Understatements Number of Misstatements (1) Upper Precision Limit Portion (2) Recorded Value (3) Misstatement Unit Error Assumption (4) Bound Portion 2x3x4 Understatements 0.029 166,000 0.500 $2,407 1 0.019 0.067 211 2 0.018 0.037 111 Upper Precision Limit 0.066 Initial Misstatement Bound $2,729

Offsetting Adjustments Number of Misstatements Misstatement Unit Error Assumption (a) Sample Size (b) Recorded Population (c) Point Estimate a(c/b) Bounds Initial Overstatement Bound $9,435 Understatement Misstatements 1 0.067 80 166,000 139 (139) 2 0.037 77 (77) Total 0.104 216 (216) Adjusted Overstatement Bound 9,219 Initial Understatement Bound 2,729 Overstatement Misstatements 0.840 1743 (1743) 0.575 1193 (1193) 3 0.517 1073 (1073) 4 0.359 745 (745) 5 0.069 143 (143) 6 0.065 135 (135) 2.425 5032 (5032) Adjusted Understatement Bound -2303 As the Upper Bound is greater than the materiality of $6,000, there may be a material misstatement

Tolerable misstatement The Decision Rule Reject Tolerable misstatement ($6,000) $6,000 $2,303 LMB $9,219 UMB Problem Since materiality is $6,000, there may be material misstatement.

Problem EP 10-5, Page 546 – Point Estimate Assume the results shown below were obtained from a stratified sample. Required : Apply the ratio calculation method (Point Estimate) to each stratum to calculate the projected likely misstatement (PLM). What is the PLM for the entire sample? SAMPLE RESULTS Stratum Population Size Recorded Amount Sample Misstatement Amount PLM 1 6 $100,000 $(600) 2 80 75,068 23 21,700 (274) 3 168 75,008 22 9,476 (66) 4 342 75,412 4,692 (88) 5 910 74,512 1,973 Total 1,506 $400,000 96 $137,841 $(1,005)

Problem DC 10-1, Page 547 – The Difference Method Sample size is 80 Population consists of 1,740 types Book Value (a) Audit value Error Amount (b) % Misstatement b/a $600.00 $622.00 $(22.00) (0.037) 15.50 14.50 1.00 0.065 65.25 31.50 33.75 0.517 83.44 53.45 29.99 0.359 16.78 15.63 1.15 0.069 78.33 12.50 65.83 0.840 13.33 14.22 (0.89) (0.067) 93.87 39.87 54.00 0.575 $966.50 $803.67 $162.83