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Monetary unit sampling: combining accounts for sampling to increase audit efficiency and effectiveness--when and how.

INTRODUCTION

In the early stages of independent auditing development, professional auditors commonly performed verification audits for all company procedures and transactions. With a growing economy and the rise of large multinational companies, this approach was abandoned (Whittington & Pany, 2010). The alternative procedure for an auditor to obtain reasonable assurance about a company's financial status is to sample procedures and records of the auditee. The American Institute of Certified Public Accountants (AICPA's) Auditing Standards Board promulgates Statements of Auditing Standards (SAS), which provide guidance to auditors in the conduct of financial statements audits. SAS No. 39 (Audit Sampling) provides guidance in the application and use of various sampling techniques. One of the sampling methods discussed is Monetary Unit Sampling (MUS), often referred to in the Guide as Dollar-Unit Sampling (DUS) (Wampler & McEacham, 2005). Guidance presented in Wampler and McEacham, (2005) and Schwartz, (1998) are used to program the Excel spreadsheet for this study.

The purpose of this study is to determine how audit effectiveness and efficiency is increased or decreased when sampling accounts collectively as compared to sampling accounts individually.

BACKGROUND OF THIS STUDY

The American Institute of Certified Public Accountants (AICPA) Auditing Standard Board (ASB) defines audit sampling in AU Section 350-01 as the application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions, for the purpose of evaluating specific characteristics of the entire balance or class (AICPA, 1983). Sampling is a critical step in the auditing process. Auditors use their judgment to select the desired level of reliability (assurance), but they mathematically determine the extent of testing necessary to achieve the desired level of reliability (AICPA, 1983). Non-sampling risk is caused by human error, whereas sampling risk is caused by chance. In AU Section 350.11, non-sampling risk is shown to occur when the auditor fails to recognize the errors in a document, or applies an inappropriate audit procedure to the audit objective. Moreover, non-sampling risk may occur when the auditor relies on incorrect information received from another party (AICPA, 1983). When sampling risk is subtracted from audit risk, the remainder is the non-sampling risk. That is:

Audit Risk - Sampling Risk = Non-Sampling Risk

Furthermore, when performing audit sampling in accordance with the Generally Accepted Auditing Standards (GAAS), auditors may use non-statistical sampling, statistical sampling, or both, as all methods provide sufficient and competent evidence. Indeed, the two methods may even be combined in their procedures (Guy, Carmichael & Whittington, 1998).

Prior to the publication of SAS No 39 in 1981, auditors referred to non-statistical sampling as "judgment sampling." However, because judgment must be exercised in both methods, SAS No. 39 does not define non-statistical sampling as judgment sampling. Accordingly, auditors do not assume that statistical sampling eliminates the need for professional judgment. When using non-statistical sampling, auditors use their judgment to determine the sample size, to select the sampled items, and to determine if the account balance is within tolerable limits (AICPA, 1983).

Thus, auditors may unknowingly use samples that are too large or too small to accurately represent the population. Nevertheless, there are situations when non-statistical sampling is more appropriate than statistical sampling. Accordingly, statistical sampling is not necessarily more desirable than non-statistical sampling. There are some factors that lead auditors to use non-statistical sampling, rather than statistical sampling. Some of these factors include additional costs in areas such as: training, sample selection, and sample evaluation. Moreover, properly designed non-statistical sampling can be as effective as statistical sampling (Guy, Carmichael & Whittington, 1998).

When using statistical sampling, auditors use the laws of probability to determine the sample size and to evaluate the sample result. Thus, statistical sampling must meet both of the following conditions (Guy, Carmichael, & Whittington, 1998):

1. The sample must have a known probability of selection (the sample must be representative).

2. The sample results must be quantitatively or mathematically evaluated.

Most importantly, statistical sampling enables auditors to quantify and control sampling risk. When using non-statistical sampling, auditors use their professional judgment to evaluate sampling risk. There are many acceptable sampling methods that auditors can use to test internal controls and/or account balances as long as all population items have an opportunity to be selected (AU Section 350.24). One of the methods auditors commonly use to test account balances is MUS. MUS is a statistical sampling technique developed specifically for use by auditors. MUS has the statistical simplicity of attributes sampling, yet provides a statistical result expressed in dollars (or any other currency). MUS is in the family of dollar unit sampling, cumulative monetary amount sampling, and sampling with probability, proportional to size (Wampler & McEacham, 2005).

For this study, the authors' posit two approaches to determine sample size: The first approach is referenced as "sampling accounts collectively," where accounts are combined and the sample is selected as if there was one account. The second approach is "sampling accounts individually," where sample size is determined by the parameters set for each account separately.

Theoretically, sampling accounts collectively and sampling accounts individually should produce the same degree of auditing effectiveness. Both approaches are considered acceptable sampling methods under GAAS. However, with regard to auditing efficiency, sampling accounts collectively should be more efficient than sampling accounts individually considering the additional cost and effort associated with sampling accounts individually.

METHODOLOGY

Sample and Data Collection

The sample for this study is one hundred publicly held corporations included in the Standard & Poor's 500 Index (S&P 500) that reported account receivable, inventory, and marketable securities in their annual consolidated balance sheets. Two hundred seventy nine companies from six industries comprise the population: information technology, consumer staples, consumer discretionary, industrials, and materials. These industries are included in the population because these industries normally have separate accounts for accounts receivable, inventory, and investment securities. From the 279 companies, one hundred were randomly selected for analysis. Five companies were replaced in the sample when it was discovered that the balance sheet did not have the three separate accounts. Table 1 and Table 2 present information relating to the 100 companies included in the sample

Procedures

Financial information for each company included in the sample was taken from the company's official website. Data were entered into a Microsoft Excel worksheet for analysis. Companies included in the study are listed by row. Each row includes a company's accounts receivable, inventory, marketable securities, net operating income, and net income. Sample sizes were calculated under the two approaches: sampling accounts collectively and sampling accounts individually. When sampling accounts collectively, each company's accounts receivable, inventory, and investment securities were summed.

Monetary Unit Sampling requires three variables to determine sample size:

A. Beta--Acceptable Risk of Incorrect Acceptance (ARIA). Choosing the appropriate (ARIA) is highly dependent on auditor judgment. ARIA is the maximum risk the auditor is willing to accept of incorrectly concluding that the population is not materially misstated when, in fact, the true misstatement in the population exceeds the tolerable misstatement. The value of ARIA may be affected by several factors, including the overall acceptable audit risk and the results of tests of controls and other substantive tests (e.g., analytical procedures) performed on the accounts. Determining ARIA requires significant auditor judgment. In this study, an ARIA of 10% is used.

B. Estimated Population Error Rate (EPER). EPER is the error rate anticipated to exist in the population. Similar to ARIA, determining the value of EPER requires auditor judgment. In making this estimate, the auditor might consider prior audit findings, recent changes in client personnel, or other information that might shed light on the likelihood of misstatements. However, because it is most appropriate to use MUS when few or no misstatements expected, normally the estimate of the population error rate for MUS is zero. 0 EPER is used in this study.

A. Allowable Precision Limit--Tolerable Misstatement (TM). TM is a variable that relies on auditor judgment and emanates directly from the auditor's preliminary judgment of materiality. Factors which may influence this rate include size of the balance relative to total assets, the adequacy of other testing procedures for these accounts, evaluation of the company's accounting personnel, experience with other audit clients, and the risk involved in accepting the balance(s) as correct when they are materially incorrect. Tolerable misstatement in this study is assumed to be 5% of net operating income (Arkin, 1982, 1984; Arens & Loebbecke, 1981).

According to sampling accounts individually, the tolerable misstatement (5% of each company's net operating income) was divided by the balances in: account receivables, inventory, and marketable securities separately. This resulted in three separate tolerable rates of deviation (TR). The three tolerable rates were then used to calculate the required sample sizes using ARIA = 10%, and EPER = 0%. For sampling accounts collectively, the tolerable misstatement (5% of each company's net operating income) was divided by the total of the balances in the three accounts, resulting in a tolerable rate of deviation (TR). Therefore, for each company analyzed in this study, two sample sizes are calculated: one under the accounts collectively approach and one under the accounts individually approach (sum of sample sizes for each account). The following function is used to determine sample size with EPER set to equal 0:

n = Log (Beta)/Log(1-TR), where n = sample size; Beta = ARIA; TR = tolerable rate.

To calculate sample size when EPER is not set to zero requires visual basic programming in Excel as presented in Appendix A.

Findings

Table 3 presents the total sample sizes with the sampling accounts collectively approach and total sample sizes for the accounts individually approach for each of the one hundred companies. The first finding suggests that total sample size with the sampling accounts individually approach is much higher than the sample size with sampling the accounts collectively approach. (8,721 total sample size with the sampling accounts collectively approach and 12,628 with the sampling accounts individually approach.)

Table 4 divides the companies into two groups: Group 1 includes those companies whose sample size collectively is greater than their sample size under the individual approach. Group 2 includes those companies whose sample size under the accounts individually approach exceeds their sample size under the collectively approach. There were no companies where the sample sizes under both approaches were equal.

Because the companies included in the study belong to five different industries, the results presented in Tables 3 and 4 are subcategorized as follows:

Tables 5 & 6: Information Technology Industry, Tables 7 & 8: Consumer Discretionary Industry, Tables 9 & 10: Industrials, Tables 11 & 12: Consumer Staples, and Tables 13 & 14: Materials Another important finding can be explained with the aid of Figure 1.

In Figure 1, it can be seen that when the sample size for accounts collectively is between 22 and 76, the sample size on accounts individually is generally in the same range. When the sample size for accounts collectively reaches 114 (see Appendix B), the sample size for accounts individually begin to fluctuate significantly. Apparently, because 114 is the maximum sample size that can be obtained under the 0 expected error rate and the 10% risk of overreliance 114 becomes a barrier for sample size for accounts collectively, while sample size for accounts individually may go higher. In other words, since sampling for accounts individually is a combination of three samples, the total sample size for accounts individually can go as high as 342 (114 X 3). The sample size for accounts collectively is one sample size and therefore cannot go beyond 114 (114 X1).

The fact that the sample size for accounts collectively equals 114 does not, by itself, mean that the total sample size on accounts individually will differ. As Figure 1 depicts, the total sample size for accounts individually can be approximately the same as the sample size on accounts collectively, even when the sample size for accounts collectively equals 114. To further evaluate the samples, a correlation was performed between the tolerable error rates and the sample sizes for the two approaches.

Figure 2 shows a wide difference in sample sizes between the two approaches at low tolerable rates. This relationship holds true until the tolerable error rate reaches approximately 1.5%. Only marginal benefits accrue to sampling accounts collectively over sampling accounts individually beyond the 1.5% tolerable rate.

LIMITATIONS

It is presumed that when using MUS, or any other method of sampling, the auditor has considered several factors. These factors should include prior audit findings, overall acceptable audit risk, results of tests of controls and substantive tests, audit personnel, and other information that leads the auditor to believe in the reliability of the method (Higgins & Nadram, 2009). The auditor must also consider these factors to appropriately estimate the ARIA and the EPER. In this study, none of these factors were considered. The MUS was calculated for companies under investigation with no consideration of whether such a method is appropriate. Moreover, the ARIA and the EPER were estimated without considering these factors.

Furthermore, because this study applies to companies that carry three separate accounts for accounts receivable, inventory, and marketable securities, industries that do not carry inventories in their ordinary course of business were excluded (for example, financial and banking industries). In addition, companies that combined their marketable securities with their cash accounts were also excluded from the study.

CONCLUSION

In this study, it was determined that sample sizes using sampling accounts collectively and sampling accounts individually may or may not differ depending on the auditor's tolerable rate of deviation (precision limit percentage). When the tolerable rate of deviation is less than 1.5%, it is more likely that the sample size on accounts individually will be higher than the sample size on accounts collectively. When the tolerable deviation rate percentage is more than 1.5% the two sample sizes will likely be in the same range and will not differ materially.

Therefore, it is recommended that auditors consider using sampling accounts collectively, rather than sampling accounts individually, when the tolerable deviation rate percentage applied is less than 1.5%, since the sample size will be much smaller with the same degree of reliability than is achieved had the sampling accounts individually approach been used. However, when the tolerable deviation rate percentage on sampling accounts collectively is greater than 1.5%, auditors should use either approach, since the sample sizes will be approximately the same.

Appendix A

BinomSample Visual Basic Function

Function BinomSample(risk As Double, pE As Double, pT As Double)
  Dim n As Double, k As Double
  If risk <= 0 Or risk >= 1 Or pE < 0 Or pE >= 1 Or pT <= 0 Or pT >=
     1 Then
     BinomSample = CVErr(xlErrNum)
  Else
     n = Application.WorksheetFunction.RoundUp(Log(risk) /
         Log(1-pT), 0)
     k = Application.WorksheetFunction.RoundUp(pE * n, 0)
  While Application.WorksheetFunction.BinomDist(k, n, pT, True) >
     risk And n <= 20000
     n = n + 1
     k = Application.WorksheetFunction.RoundUp(pE * n, 0)
  Wend
  BinomSample = IIf(Application.WorksheetFunction.BinomDist
(k, n, pT, True) <= risk, n,
CVErr(xlErrNA))

  End If
End Function

AICPA (2008). "Technical Notes on the AICPA Audit Guide: Audit
Sampling." New Edition as of May 1, 2008. Trevor R. Stewart,
Deloitte & Touche, LLP, Member of the 2008 Audit Sampling Guide
Task Force.


Appendix B

Table A
Statistical Sample Size 10% Risk of Overreliance

                               To erable Rate

Expected    2%   3%   4%   5%   6%   7%   8%   9%   10%  15%  20%
Population
Deviation
Rate

0.00%       114  76   57   45   38   32   28   25   22   15   11
0.25        194  129  96   77   64   55   48   42   38   25   18
0.50        194  129  96   77   64   55   48   42   38   25   18
0.75        265  176  96   77   64   55   48   42   38   25   18
1.00         *   221  96   77   64   55   48   42   38   25   18
1.25         *    *   132  77   64   55   48   42   38   25   18
1.50         *    *   132  105  64   55   48   42   38   25   18
1.75         *    *   166  105  88   55   48   42   38   25   18
2.00         *    *   198  132  88   75   48   42   38   25   18
2.25         *    *    *   132  88   75   65   42   38   25   18
2.50         *    *    *   166  110  75   65   58   38   25   18
2.75         *    *    *   198  132  94   65   58   52   25   18
3.00         *    *    *    *   132  94   65   58   52   25   18
3.25         *    *    *    *   153  113  82   58   52   25   18
3.50         *    *    *    *   194  113  82   73   52   25   18
3.75         *    *    *    *    *   131  98   73   52   25   18
4.00         *    *    *    *    *   149  98   73   65   25   18
5.00         *    *    *    *    *    *   160  115  78   34   18
6.00         *    *    *    *    *    *    *   182  116  43   25
7.00         *    *    *    *    *    *    *    *   199  52   25

Sample size is too large to be cost-effective for most audit
applications. *


REFERENCES

American Institute of Certified Public Accountants (AICPA) (1983). Audit Section 350 (supersedes Statements of Auditing Standards Nos. 39, 43 and 45).

American Institute of Certified Public Accountants (AICPA) (2008). Technical Notes on the AICPA Audit Guide: Audit Sampling. Trevor R. Stewart, Deloitte & Touche, LLP, Member of the 2008 Audit Sampling Guide Task Force.

Arens, A., Elder, R., & Beasley, M. (2010). Auditing and Assurance Services, An Integrated Approach. (13th edition). Upper Saddle River, New Jersey. Pearson Education, Inc (see chapter 17, problem 31).

Arens, A., & Loebbecke, J. (1981). Applications of Statistical Sampling to Auditing. Englewood Cliffs, NJ. Prentice-Hall, Inc.

Arkin, H. (1982). Sampling Methods for the Auditors: An Advanced Treatment. McGraw-Hill, Inc.

Arkin, H. (1984). Handbook of Sampling for Auditing and Accounting (3 edition). New York, New York, McGraw-Hill Publishing Company.

Guy, D. M., Carmichael, D. R., & Whittington, O. R. (1998). Audit Sampling: An Introduction 4th edition. John Wiley & Sons, Inc. New York, New York.

Higgins, H.N., & Nandram, B. (2009). Monetary Unit Sampling: Improving Estimation of the Total Audit Error, Advances in Accounting, Incorporating Advances in International Accounting.

Schwartz, D. A. (1998). Computerized Audit Sampling. The CPA Journal. 46 ( 68).

Wampler, B., & McEacharn, M. (2005). Monetary-Unit Sampling Using Microsoft Excel. The CPA Journal. 75,( 5).

Whittington, O. R., & Pany. K. (2010). Principles of Auditing & Other Assurance Services, 17/e. New York, New York, McGraw-Hill Publishing Company.

Gary G. Johnson

Ahmed Al Mohsen

Southeast Missouri State University

Gary G. Johnson is professor of accounting at SE Missouri State University. Dr. Johnson has published numerous articles in auditing, accounting and information systems.

Ahmed Al Mohsen holds an MBA with an accounting option from SE Missouri State University. Ahmed currently works for an investment banking firm as deputy chief financial officer in Riyadh, Saudi Arabia.

Table 1
Number of Companies in the Selected Industries

Industry                 Number of companies

Information technology           43
Consumer Discretionary           20
Industrials                      17
Consumer Staples                 12
Materials                         8

Total                            100

Table 2
Summary of Financial Information by Industry (averages)

                            Accounts          Inventory
                           Receivable

Information technology   79,034,227,000    37,064,672,000
Consumer Discretionary   138,723,728,000   54,567,102,000
Industrials              49,156,765,000    35,362,103,000
Consumer Staples         24,309,420,000    33,064,606,000
Materials                16,421,065,000    15,926,922,000

Total                    307,645,205,000   175,985,405,000

                           Marketable       Net Operating
                           Securities          Income

Information technology   69,620,121,000    84,941,619,000
Consumer Discretionary   12,557,083,000    25,792,030,000
Industrials              53,293,184,000    52,801,003,000
Consumer Staples          4,470,382,000    44,780,534,000
Materials                 1,291,454,000    13,417,204,000

Total                    141,232,224,000   221,732,390,000

                           Net income

Information technology   69,746,482,711
Consumer Discretionary   -21,193,058,000
Industrials              44,184,325,000
Consumer Staples         31,453,901,000
Materials                 7,531,875,000

Total                    131,723,525,711

Table 3
Sample Sizes of Accounts Collectively and of Accounts Individually

Total sample size of all companies collectively    8,721
Total sample size of all companies individually    12,628

Table 4
Detailed Results--Total Sample

                       Number of      Total          Total
                       Companies   Sample Size    Sample Size
                                   Collectively   Individually

Sample size               14          1,387          1,312
collectively > total
sample size
individually

Sample size               86          7,334          11,316
collectively < total
sample size
individually

Sample size                0            0              0
collectively = total
sample size
individually

                          Highest         Lowest
                        Difference      Difference

Sample size                 14               1
collectively > total    (1 company)    (4 companies)
sample size
individually

Sample size                 228              2
collectively < total   (3 companies)   (2 companies)
sample size
individually

Sample size                  0               0
collectively = total
sample size
individually

Table 5
Information Technology Industry (43 companies)

Total sample size of all companies collectively    4,065
Total sample size of all companies individually    6,690

Table 6
Detailed Results--Information Technology

                       Number of      Total       Total Sample
                       Companies   Sample Size,      Size,
                                     Accounts       Accounts
                                   Collectively   Individually

Sample size                5           532            503
collectively > total
sample size
individually

Sample size               38          3,533          6,187
collectively < total
sample size
individually

Sample size                0            0              0
collectively =
total sample size
individually

                          Highest        Lowest
                        Difference     Difference

Sample size                  8              1
collectively > total   (2 companies)   (1 company)
sample size
individually

Sample size                 228             3
collectively < total   (2 companies)   (1 company)
sample size
individually

Sample size                  0              0
collectively =
total sample size
individually

Table 7
Consumer Discretionary Industry (20 companies)

Total sample size collectively    1,518
Total sample size individually    2,094

Table 8
Detailed Results--Consumer Discretionary

                    Number of      Total          Total
                    Companies   Sample Size,   Sample Size,
                                  Accounts       Account
                                Collectively   Individually

Sample size             1           114            113
collectively >
total sample size
individually

Sample size            19          1,404          1,981
collectively <
total sample size
individually

Sample size             0            0              0
collectively =
total sample size
individually

                      Highest        Lowest
                    Difference     Difference

Sample size              1              1
collectively >      (1 company)    (1 company)
total sample size
individually

Sample size             171             3
collectively <      (1 company)   (2 companies)
total sample size
individually

Sample size              0              0
collectively =
total sample size
individually

Table 9
Industrials Industry (17 companies)

Total sample size collectively    1,529
Total sample size individually    1.792

Table 10
Detailed Results--Industrials

                    Number of      Total       Total Sample
                    Companies   Sample Size,      Size,
                                  Accounts       Accounts
                                Collectively   Individually

Sample size             3           342            312
collectively >
total sample size
individually

Sample size            14          1,187          1,480
collectively <
total sample size
individually

Sample size             0            0              0
collectively =
total sample size
individually

                      Highest        Lowest
                    Difference     Difference

Sample size             14              8
collectively >      (1 company)   (2 companies)
total sample size
individually

Sample size             76              2
collectively <      (1 company)   (2 companies)
total sample size
individually

Sample size              0              0
collectively =
total sample size
individually

Table 11
Consumer Staples Industry (12 companies)

Total sample size collectively     868
Total sample size individually    1,227

Table 12
Detailed Results--Consumer Staples

                    Number of   Total Sample   Total Sample
                    Companies      Size,          Size,
                                  Accounts       Accounts
                                Collectively   Individually

Sample size             2           133            129
collectively >
total sample size
individually

Sample size            10           735           1,098
collectively <
total sample size
individually

Sample size             0            0              0
collectively =
total sample size
individually

                      Highest       Lowest
                    Difference    Difference

Sample size              3             1
collectively >      (1 company)   (1 company)
total sample size
individually

Sample size             228            2
collectively <      (1 company)   (1 company)
total sample size
individually

Sample size              0             0
collectively =
total sample size
individually

Table 13
Materials Industry (8 companies)

Total sample size collectively   741
Total sample size individually   825

Table 14
Detailed Results--Materials

                    Number of      Total       Total Sample
                    Companies   Sample Size,      Size,
                                  Accounts       Accounts
                                Collectively   Individually

Sample size             3           266            255
collectively >
total sample size
individually

Sample size             5           475            570
collectively <
total sample size
individually

Sample size             0            0              0
collectively =
total sample size
individually

                       Highest        Lowest
                     Difference     Difference

Sample size               5              1
collectively >      (2 companies)   (1 company)
total sample size
individually

Sample size              30             10
collectively <      (2 companies)   (1 company)
total sample size
individually

Sample size               0              0
collectively =
total sample size
individually
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Author:Johnson, Gary G.; Mohsen, Ahmed Al
Publication:International Journal of Business, Accounting and Finance (IJBAF)
Geographic Code:1USA
Date:Mar 22, 2013
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