Audit Sampling Using ACL
ACL may be used for attributes sampling and probability-proportional-to size sampling (presented in Appendix A of Chapter 9). It does not have a utility for the classical variables methods (mean-per-unit, difference, and ratio).
To use ACL for sampling, one must have a “project” open. Unless you wish to actually select a sample (which is not done in Chapter 9), that project need have nothing to do with the specific sampling problem you are addressing. If you have used ACL prior to Chapter 9 in your auditing course, open any project you have worked on. If this is your first experience with ACL, use the following approach to open a project after you have installed ACL on your computer:
· Double click on the ACL Icon on your desktop.
· Under ACL Projects, click “Open an existing project.”
· Double click “Metaphor Employee Data” on the far left.
· Double click “Agents_Metaphor” on the far left.
· Select “Sampling” on the top of the screen.
You are now able to use ACL for sampling purposes. As indicated, the project you have open (here, Metaphor Employee Data” and the table you have open (Agents_Metaphor) need not relate to the calculations you will have ACL perform.
The approach you should use for ACL is to first read the related chapter material on attribute and/or probability proportional-to-size sampling to obtain an understanding of the concepts involved. Then, work through the following material to help you get started with sampling with ACL.
Using ACL For Attributes Sampling (Calculate Sample Size in ACL)
We will use an example similar to that in the text, but with an upper error limit of 9 percent and an expected error rate of 2 percent.[1] You must first align the terminology used in the text (as well as by the AICPA) with the ACL terminology. The following summarizes the differences:
AICPA and Text Terminology / ACL TerminologyAttributes sampling / Record Sampling
Risk of assessing control risk too low= 5% / Confidence = 1.00 – risk of assessing CR too low
= 1 - .05 = .95 = 95 (key in whole
numbers for all
inputs)
Population size (we don't use) / Population = number in population. This should be 3,653.
Tolerable Deviation Rate= 9% / Upper Error Limit = 9
Expected Population Deviation Rate = 2% / Expected Error Rate = 2
We will use ACL to determine the sample size and to evaluate results—the procedures performed manually in the text.
Determining the Sample Size
After clicking on “Calculate Sample Size” and using the inputs from the earlier table for “Record” sampling, we click we obtain a sample size of 71 (2). This corresponds to the sample size of 68 one may obtain from Figure 9.4 Again, small differences are to be expected. Also, we do not use the “Interval” information.
Evaluating Results (Evaluate in ACL)
Example a: Assume you find no deviations:
1. Approach 1: Using the text’s first approach of simply determining whether more or less than 2 deviations are identified, we are able to accept this population since no deviations were identified.
2. Approach 2: Using the text’s second approach, we use the results obtained in “Evaluate Error” (Sampling à Evaluate Error) as follows:
Record
Confidence = 95
Sample size = 71
Number of errors = 0
ACL generates 4.23%.
ACL generates an upper error limit frequency of 4.23. Following is the ACL Printout of the results:
As of: 03/11/2007 09:47:14
Produced with ACL by: ACL Educational Edition - Not For Commercial Use
Command: EVALUATE RECORD CONFIDENCE 95 SIZE 71 ERRORLIMIT 0 TO SCREEN
Confidence: 95, Sample Size: 71, Number of Errors: 0
Example b: Assume you find 3 deviations
1. Approach 1: Because you found more than 2 deviations, you have not met your audit objective. Accordingly the auditors conclude that the achieved upper deviation rate is greater than 9 percent.
“The achieved upper deviation rate is higher than 9 percent.” The planned assessed level of control risk is not achieved. You need to consider increasing the assessed level of control risk above the planned assessed level.
2. Approach 2:
Use ACL "Evaluate"
Record
Confidence = 95
Sample size = 71
Number of errors = 3
Using this second approach, the achieved upper deviation rate is 10.93.
ACL Printout of the results
As of: 03/11/2007 09:48:06
Produced with ACL by: ACL Educational Edition - Not For Commercial Use
Command: EVALUATE RECORD CONFIDENCE 95 SIZE 71 ERRORLIMIT 3 TO SCREEN
Confidence: 95, Sample Size: 71, Number of Errors: 3
Using ACL For Probability-Proportional-to Size Sampling
For PPS sampling we provide an example with the same parameters as that in the text—in this case in Appendix 9A.
The following summarizes differences in terminology for PPS Sampling:
AICPA (text) terminology / ACL TerminologyPPS sampling / Monetary Sampling
Risk of incorrect acceptance / Confidence = 1 – risk of incorrect acceptance = 1 - .05 = 95 (key in whole numbers for all inputs)
Book Value = $6,250,000 / Population = 6250000 (no commas)
Tolerable Misstatement= $364,000 / Materiality = 364000
Expected Misstatement = $50,000 / Expected Total Errors = 50000
Determining the Sample Size (Calculate Sample Size in ACL)
Inputting the information in the above table we obtain the following:
ACL arrives at a sample size of 67, with a sampling interval of $92,166.66. The text’s sample establishes a sample size of 66, and a sampling interval of $95,000. This small difference is again due to small differences in underlying statistical assumptions. While in practice we would certainly use ACL’s numbers, to better tie to the text in this one presentation, we will now assume the text’s sampling interval of $95,000. We do not use the “Maximum Tolerable Taintings (%) generated by ACL.
Evaluating Results (Evaluate in ACL)
We will use the text’s results presented in the "Illustration of PPS Sampling" section, in which the following three misstatements were identified.
Book Value Audited Value
$ 100 $ 90
2,000 1,900
102,000 102
Inputting the appropriate information we obtain the following:
Following is the ACL Printout of the results
As of: 03/11/2007 09:38:50
Produced with ACL by: ACL Educational Edition - Not For Commercial Use
Command: EVALUATE MONETARY CONFIDENCE 95 ERRORLIMIT 100, 10,2000,100,102000, 101898 INTERVAL 95000 TO SCREEN
Confidence: 95, Interval: 95000
Item / Error / Most Likely Error / Upper Error LimitBasic Precision / 285,000.00
100.00 / 10.00 / 9,500.00 / 16,625.00
2,000.00 / 100.00 / 4,750.00 / 7,362.50
102,000.00 / 101,898.00 / 101,898.00 / 101,898.00
Totals / 116,148.00 / 410,885.50
To summarize the results:
· Most likely error ($116,148) is the text’s Projected misstatement
· Basic Precision ($285,000) is the text’s Basic Precision.
· Upper Error Limit ($410,885.50) is within .50 of the text’s rounded total of $410,886.
· The incremental allowance is not explicitly printed out by ACL. One may obtain it by using the upper limit on misstatement formula:
Upper Limit on Projected
Misstatements = Misstatement + Basic precision + Incremental Allowance
(SWITCHING
TO ACL TERMS)
Upper Error Limit = Most likely Error + Basic Precision + Incremental Allowance
Upper Error Limit - Most Likely Error -Basic Precision: = Incremental Allowance
$410,888 - - $116,148 - $285,000 = Incremental Allowance.
$9,740 = Incremental Allowance.
Using ACL for Audit Sampling, Page 2 of 8
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[1]The ACL software uses several differences in assumptions as compared to the text (which uses those of the AICPA). Accordingly, sample sizes (and allowable deviations) may differ, ordinarily by small amounts.