Winter Accounting Dissertation Assistance

Winter Accounting Dissertation Assistance
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Winter Accounting Dissertation Assistance

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1. (Objectives 15-5, 15-7) The questions below relate to determining the CUER in audit sampling for...
(Objectives 15-5, 15-7) The questions below relate to determining the CUER in audit sampling for tests of controls, using the following table:

a. Using nonstatistical sampling, calculate TER – SER for each of columns 1 through 8 and evaluate whether or not sampling error is large enough to accept the population. Assume that TER is 5% for each column.
b. For each of the columns 1 through 8, determine CUER using attributes sampling from the appropriate table.
c. Using your understanding of the relationship between the four preceding factors and the CUER, state the effect on the CUER (increase or decrease) of changing each of the following factors while the other three are held constant:
(1) A decrease in the ARACR
(2) A decrease in the population size
(3) A decrease in the sample size
(4) A decrease in the number of exceptions in the sample
d. Compare your answers in part c with the results you determined in part a (non - statistical sampling) or part b (attributes sampling). Which of the factors appears to have the greatest effect on the CUER? Which one appears to have the least effect?
e. Why is it necessary to compare the CUER with the TER?
(Objective 15-5)
APPLICATION OF NONSTATISTICAL AUDIT SAMPLING
We will now examine the application of nonstatistical audit sampling in testing transactions for control deviations and monetary misstatements. Statistical sampling is examined later in this chapter. Before doing so, key terminology are defined and summarized in Table 15-1. The same terminology is used for statistical sampling.

Auditors use 14 well-defined steps to apply audit sampling to tests of controls and substantive tests of transactions. These steps are divided into the three phases described earlier. Auditors should follow these steps carefully to ensure proper application of both the auditing and sampling requirements. We use the example audit of Hillsburg Hardware Co. to illustrate the steps in the following discussion. Plan the Sample
1. State the objectives of the audit test.
2. Decide whether audit sampling applies.
3. Define attributes and exception conditions.
4. Define the population.
5. Define the sampling unit.
6. Specify the tolerable exception rate.
7. Specify acceptable risk of assessing control risk too low.
8. Estimate the population exception rate.
9. Determine the initial sample size.
Select the Sample and Perform the Audit Procedures
10. Select the sample.
11. Perform the audit procedures.
Evaluate the Results
12. Generalize from the sample to the population.
13. Analyze exceptions.
14. Decide the acceptability of the population.
The objectives of the test must be stated in terms of the transaction cycle being tested. Typically, auditors define the objectives of tests of controls and substantive tests of transactions:
• Test the operating effectiveness of controls
• Determine whether the transactions contain monetary misstatements The objectives of these tests in the sales and collection cycle are usually to test the effectiveness of internal controls over sales and cash receipts and to determine whether sales and cash receipts transactions contain monetary misstatements. Auditors normally define these objectives as a part of designing the audit program, which was discussed for the sales and collection cycle in Chapter 14. You can find the audit program for the sales and collection cycle for Hillsburg Hardware in Figure 14-6 (p. 462). Audit sampling applies whenever the auditor plans to reach conclusions about a population based on a sample. The auditor should examine the audit program and select those audit procedures where audit sampling applies. To illustrate, assume the following partial audit program:
1. Review sales transactions for large and unusual amounts (analytical procedure).
2. Observe whether the duties of the accounts receivable clerk are separate from handling cash (test of control).
3. Examine a sample of duplicate sales invoices for
a. credit approval by the credit manager (test of control).
b. existence of an attached shipping document (test of control).
c. inclusion of a chart of accounts number (test of control).
4. Select a sample of shipping documents and trace each to related duplicate sales invoices (test of control).
5. Compare the quantity on each duplicate sales invoice with the quantity on related shipping documents (substantive test of transactions). Audit sampling does not apply for the first two procedures in this audit program. The first is an analytical procedure for which sampling is inappropriate. The second is

an observation procedure for which no documentation exists to perform audit sampling. Audit sampling can be used for the remaining three procedures. Table 15-2 indicates the audit procedures for the sales cycle for Hillsburg Hardware Co. where audit sampling is appropriate. When audit sampling is used, auditors must carefully define the characteristics (attri - butes) being tested and the exception conditions. Unless they carefully define each attribute in advance, the staff person who performs the audit procedures will have no guidelines to identify exceptions. Attributes of interest and exception conditions for audit sampling are taken directly from the auditor’s audit procedures. Table 15-3 (p. 488) shows nine attributes

of interest and exception conditions taken from audit procedures 12 through 14 in the audit of Hillsburg’s billing function. Samples of sales invoices will be used to verify these attributes. The absence of the attribute for any sample item will be an exception for that attribute. Both missing documents and immaterial misstatements result in exceptions unless the auditor specifically states otherwise in the exception conditions. The population is those items about which the auditor wishes to generalize. Auditors can define the population to include any items they want, but when they select the sample, it must be selected from the entire population as it has been defined. The auditor should test the population for completeness and detail tie-in before a sample is selected to ensure that all population items are subjected to sample selection. The auditor may generalize only about that population that has been sampled. For example, when performing tests of controls and substantive tests of sales transactions, the auditor generally defines the population as all recorded sales invoices for the year. If the auditor samples from only one month’s transactions, it is invalid to draw con - clusions about the invoices for the entire year. The auditor must carefully define the population in advance, consistent with the objectives of the audit tests. In some cases, it may be necessary to define separate populations for different audit procedures. For example, in the audit of the sales and collection cycle for Hillsburg Hardware Co., the direction of testing in audit procedures 12 through 14 (in Table 15-2 on p. 487) proceeds from sales invoices in the sales journal to source documentation. In contrast, the direction of testing for audit procedures 10 and 11 proceeds from the shipping documents to the sales journal. Thus, the auditor defines two populations—a population of sales invoices in the sales journal and a population of shipping documents. The sampling unit is defined by the auditor based on the definition of the population and objective of the audit test. The sampling unit is the physical unit that corresponds to the random numbers the auditor generates. It is often helpful to think of the sampling unit as the starting point for doing the audit tests. For the sales and collection cycle, the sampling unit is typically a sales invoice or shipping document number. For example, if the auditor wants to test the occurrence of sales, the appropriate sampling unit is sales invoices recorded in the sales journal. If the objective is to determine whether the quantity of the goods described on the customer’s order is accurately shipped and billed, the auditor can define the sampling unit as the customer’s order, the shipping document, or the duplicate sales invoice, because the direction of the audit test doesn’t matter for this audit procedure. Audit procedure 14 in Table 15-2 is a test for the occurrence of recorded sales. What is the appropriate sampling unit? It is the duplicate sales invoice. Is the appropriate sampling unit for audit procedure 11 the shipping document? Yes, because this tests that existing sales are recorded (completeness). Either the duplicate sales invoice or the shipping document is appropriate for audit procedures 13a through 13e because these are all nondirectional tests. To perform audit procedures 12 through 14, the auditor will define the sampling unit as the duplicate sales invoice. Audit procedures 10 and 11 will have to be tested separately using a sample of shipping documents. Establishing the tolerable exception rate (TER) for each attribute requires an auditor’s professional judgment. TER represents the highest exception rate the auditor will permit in the control being tested and still be willing to conclude the control is operating effectively (and/or the rate of monetary misstatements in the transactions is acceptable). For example, assume that the auditor decides that TER for attribute 8 in Table 15-3 is 9 percent. That means that the auditor has decided that even if 9 percent of the duplicate sales invoices are not approved for credit, the credit approval control is still effective in terms of the assessed control risk included in the audit plan. The suitable TER is a question of materiality and is therefore affected by both the definition and the importance of the attribute in the audit plan. If only one internal control is used to support a low control risk assessment for an objective, TER will be lower for the attribute than if multiple controls are used to support a low control risk assessment for the same objective. TER will normally be lower for tests of controls in the audit of an accelerated filer public company because the results of the tests of controls provide the basis for the auditor’s report on internal control over financial reporting. TER can have a significant impact on sample size. A larger sample size is needed for a low TER than for a high TER. For example, a larger sample size is needed for the test of credit approval (attribute 8) if the TER is decreased from 9 percent to 6 percent. Since a lower TER is used for significant account balances, the auditor requires a larger sample size to gather sufficient evidence about the effectiveness of the control or absence of monetary misstatements. Most auditors use some type of template to document each sampling application. Figure 15-2 (p. 490) shows one example of a commonly used form. Notice that the top part of the form includes a definition of the objective, the population, and the sampling unit. Auditors determine the TER for each attribute being tested in audit procedures 12 through 14 in Table 15-3 by deciding what exception rate is material. As Figure 15-2, indicates:
(Objective 15-7)
APPLICATION OF ATTRIBUTES SAMPLING
While the 14 steps discussed for nonstatistical sampling are equally applicable to attributes sampling, in this section, we’ll focus on the differences between the two. Plan the Sample
1. State the objectives of the audit test. Same for attributes and nonstatistical sampling.
2. Decide whether audit sampling applies. Same for attributes and nonstatistical sampling.
3. Define attributes and exception conditions. Same for attributes and nonstatis - tical sampling.
4. Define the population. Same for attributes and nonstatistical sampling.
5. Define the sampling unit. Same for attributes and nonstatistical sampling.
6. Specify the tolerable exception rate. Same for attributes and nonstatistical sampling.
7. Specify acceptable risk of assessing control risk too low. The concepts of specifying this risk are the same for both statistical and nonstatistical sampling, but the method of quantification is usually different. For nonstatistical sampling, most auditors use low, medium, or high acceptable risk, whereas auditors using attri - butes sampling assign a specific amount, such as 10 percent or 5 percent risk. The methods differ because auditors need to evaluate results statistically.
8. Estimate the population exception rate. Same for attributes and nonstatistical sampling.
9. Determine the initial sample size. Four factors determine the initial sample size for both statistical and nonstatistical sampling: population size, TER, ARACR, and EPER. In attributes sampling, auditors determine sample size by using computer programs or tables developed from statistical formulas. The two tables in Table 15-8 (p. 504) come from the AICPA Audit Sampling Guide. The top one shows sample sizes for a 5 percent ARACR, while the bottom one is for a 10 percent ARACR. Use of the Tables When auditors use the tables to determine initial sample size, they follow these four steps:
i. Select the table corresponding to the ARACR.
ii. Locate the TER at the top of the table.
iii. Locate the EPER in the far left column.
iv. Read down the appropriate TER column until it intersects with the appropriate EPER row. The number at the intersection is the initial sample size.
Using the Hillsburg Hardware Co. example, assume that an auditor is willing to reduce assessed control risk for the agreement between sales orders and invoices if the number of exceptions in the population (attribute 6 in Table 15-3 on page 488) does not exceed 7 percent (TER), at a 5 percent ARACR. On the basis of past experience, the auditor sets EPER at 1 percent. On the 5 percent ARACR table, locate the 7 percent TER column, and read down the column until it intersects with the 1 percent EPER row. The initial sample size is 66. Is 66 a large enough sample size for this audit? It is not possible to decide until after the tests have been performed. If the actual exception rate in the sample turns out to be greater than 1 percent, the auditor will be unsure of the effectiveness of the control. The reasons will become apparent in the following sections. Effect of Population Size In the preceding discussion, auditors ignored the size of the population in determining the initial sample size. Statistical theory shows that in populations where attributes sampling applies, population size is a minor considera - tion in determining sample size. Because most auditors use attributes sampling for reasonably large populations, the reduction of sample size for smaller populations is ignored here. Select the Sample and Perform the Audit Procedures
10. Select the sample. The only difference in sample selection for statistical and nonstatistical sampling is the requirement that probabilistic methods must be used for statistical sampling. Either simple random or systematic sampling is used for attributes sampling.
11. Perform the audit procedures. Same for attributes and nonstatistical sampling. Evaluate the Results 12. Generalize from the sample to the population. For attributes sampling, the auditor calculates an upper precision limit (CUER) at a specified ARACR, again using special computer programs or tables developed from statistical formulas. The calculations are illustrated in tables like Table 15-9 (p. 505). These are “one-sided tables,” meaning they represent the upper exception rate for a given ARACR. Use of the Tables Use of tables to compute CUER involves four steps:
i. Select the table corresponding to the auditor’s ARACR. This ARACR should be the same as the ARACR used for determining the initial sample size.
ii. Locate the actual number of exceptions found in the audit tests at the top of the table.
iii. Locate the actual sample size in the far left column.

iv. Read down the appropriate actual number of exceptions column until it inter - sects with the appropriate sample size row. The number at the intersection is the CUER. To use the evaluation table for Hillsburg Hardware, assume an actual sample size of 70 and one exception in attribute 6. Using an ARACR of 5 percent, CUER equals 6.6 percent. In other words, the CUER for attribute 6 is 6.6 percent at a 5 percent ARACR. Does this mean that if 100 percent of the population were tested, the true exception


percent, there is a 95 percent probability that the conclusion is right and a 5 percent chance that it is wrong. It is possible to have a sample size that is not equal to those provided for in the attributes sampling evaluation tables. When this occurs, it is common for auditors to interpolate to estimate the data points that fall between those listed in the table. These tables assume a very large (infinite) population size, which results in a more conservative CUER than for smaller populations. As with sample size, the effect of population size on CUER is typically very small, so it is ignored.
13. Analyze exceptions. Same for attributes and nonstatistical sampling.
14. Decide the acceptability of the population. The methodology for deciding the acceptability of the population is essentially the same for attributes and nonsta - tistical sampling. For attributes sampling, the auditor compares CUER with TER for each attribute. Before the population can be considered acceptable, the CUER determined on the basis of the actual sample results must be less than or equal to TER when both are based on the same ARACR. In our example, when the auditor specified a TER of 7 percent at a 5 percent ARACR and the CUER was 6.6 percent, the requirements of the sample have been met. In this case, the control being tested can be used to reduce assessed control risk as planned, provided a careful analysis of the cause of exceptions does not indicate the possibility of a significant problem in an aspect of the control not previously considered. When the CUER is greater than the TER, it is necessary to take specific action. The four courses of action discussed for nonstatistical sampling are equally applicable to attributes sampling. Figure 15-8 illustrates the sampling documentation completed for the tests of attributes 1 through 9 in Table 15-3 (p. 488) for Hillsburg Hardware Co. using attri - butes sampling. Notice that much of the information in Figure 15-8 is consistent with information presented in the nonstatistical sampling example illustrated in Figure 15- 4 (p. 496). The key differences between Figures 15-4 and 15-8 are the auditor’s judgment about ARACR and the initial sample size determined when planning the audit, and the calculation of CUER using the actual test results. Notice that the ARACR judgment is numerical (5 percent) in the attributes sampling appli cation (Figure 15-8). The numerical judgment about ARACR is considered along with the assessments of EPER and TER to determine the initial sample sizes for each attribute using Table 15-8 (p. 504). The CUER in Figure 15-8 is determined using Table 15-9 (p. 505) based on the sample exceptions identified and the actual sample size tested. A criticism occasionally leveled against statistical sampling is that it reduces the auditor’s use of professional judgment. A comparison of the 14 steps discussed in this chapter for nonstatistical and attributes sampling shows that this criticism is unwarranted. For proper application, attributes sampling requires auditors to use professional judgment in most of the steps. To select the initial sample size, auditors depend primarily on TER and ARACR, which require a high level of professional judgment, as well as EPER, which requires a careful estimate. Similarly, the final evaluation of the adequacy of the entire application of attributes sampling, including the adequacy of the sample size, must also be based on high-level professional judgment