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Section 2a. The Use of Audit Sampling Test of Balances. Statistical Tests of Balances. Monetary Unit Sampling (MUS) or (PPS) Involves the same previously seen 14 steps.

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Section 2a

Section 2a

The Use of Audit Sampling

Test of Balances


Statistical tests of balances
Statistical Tests of Balances

  • Monetary Unit Sampling (MUS) or (PPS)

  • Involves the same previously seen 14 steps


An auditor has been assigned the responsibility of auditing the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

Athens Corporation Case


  • Must relate to the audit procedure the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

  • What would be the assertion in this example?

1. Determine the Objective of MUS Sampling


  • Decide if audit sampling applies the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

    • Why would sampling apply here?

  • 3. Define attributes and error conditions

    • What is the attribute here?

    • Error condition?


4. the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.Define the population

  • What is the population in this case?

  • 5. Define the sampling unit

  • The sampling unit is ?

  • Logical sampling unit


Summary: the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

For Athens Corporation, the population is all 800 customer accounts with debit balances, and the recorded book value of the accounts is $2,400,000. The audit manager decided that customers' accounts rather than individual invoices are to be confirmed. Accounts receivable has 2,400,000 sampling units and 800 logical sampling units.

  • Specify Tolerable Misstatement (TM)

    • The auditor’s planned level of materiality for the account

    • Thus TM is


DR the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

7. Specify the reliability factor (RF) for acceptable risk of incorrect acceptance (ARIA)

  • Can eliminate the acceptable risk of incorrect acceptance by auditing the entire population

  • Recall the audit risk model

  • AR = IR x CR x AP x ARIA

  • ARIA =


RF the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

Always used

Reliability Factors for Misstatements of Overstatements


8. the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.Specify Anticipated Misstatement (AM) and Expansion Factor (EF)

  • Anticipated misstatement

    • For Athens Corporation?


  • The expansion factor (EF) the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

  • What is the expansion factor for anticipated misstatement and why?


Sample size the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

(n)

=

Book value (BV)

x

Reliability factor (RF) for risk of overstatement

Tolerable misstatement (TM)

-

Anticipated Misstatement (AM)

x

Expansion factor for anticipated misstatement (EF)

n =

x

-

x

9. Determine the sample size

  • Auditors can use the following formula:

n =


  • Change in a component of sample size the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.


Sampling Interval the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

=

Book value of the population (BV) Sample size (n)

10. Select Sample

  • Sampling interval

  • Systematic sampling


  • What is the sampling interval? the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

  • BV/n =

  • Must now identify customer account numbers

    • Also called logical sampling units

  • The auditor decides to use systematic sampling


  • Assume auditor selects 9832 with a random stab the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

    • From where?

  • Which account balance should we select?

  • What is the sampling interval?

  • Thus what is the next account?


11. Perform the audit procedures the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

  • Appropriate procedures that are appropriate for the circumstances

  • What is the appropriate procedure?


Allowance for sampling risk the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

Upper misstatement limit

Projected misstatement

Basic precision

Incremental allowance

=

+

+

  • Upper misstatement limit

12. Generalize from the sample to the population


(a) Computing Projected Misstatements the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

  • What is projected misstatement?

  • The tainting percentage


Tainting percentage the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

Book value – Audited value

Sampling interval

Project misstatement for each audited item

x

=

Book value

  • For logical sampling units less than the sampling interval

  • For logical sampling units greater than or equal to the sampling interval

Book value – Audited value = Projected misstatement for each audited item



(b) Computing Allowance for Sampling Risk Customer accounts 1491 and 1794 have book values less than the sampling interval, and customer account 1225 is larger than the sampling unit

  • What is this allowance?

  • Two components

    • Basic precision

      • BP = RF x SI


  • Auditor must use reliability factors



Allowance for sampling risk identified as including misstatements less than the sampling interval.

Upper misstatement limit

Projected misstatement

Basic precision

Incremental allowance

=

+

+

Thus upper misstatement limit (UML) is

UML =


13. Evaluating results

  • From the results, the auditor for Athens Corporation may conclude with a 5% risk that the $2,400,000 book value is not overstated by more than $94,176.

  • What was the tolerable misstatement?

  • What is the final evaluation?


  • What does this mean to valuation?

  • If the sample has no misstatements

    • UML = PM + BP + IA


    • Reaching a conclusion misstatement

    • Have to also look at qualitative aspects

    • Must evaluate whether misstatements are errors or irregularities

    14. Decide the acceptability of the population


    • Population is not acceptable

  • Some possible courses of action


  • 2. Consider whether the sample is representative of the population.



    Advantages the accounts

    1. Increases likelihood of including high-dollar value items

    2. Easy to use

    Advantages and Disadvantages of MUS Sampling


    Disadvantages the accounts

    1. Assumption is that the audited value of a sampling unit is neither less than zero nor greater then book value.

    2. Upper misstatement limit.

    3. Enables auditor to state a conclusion


    Problem 16. MUS Sampling. the accounts Edwards has decided to use MUS sampling in the audit of a client’s accounts receivable balance. Few, if any, overstatements of account balance are expected. Edwards plans to use the following MUS sampling table:

    Reliability Factors for Overstatement

    • Required:

    • Calculate the sampling interval and the sampling size Edwards should use, given the following information:

      • Tolerable misstatement $15,000

      • Risk of incorrect acceptance 5%

      • Number of misstatements allowed 0

      • Recorded amount of accounts receivable $300,000



    • Problem 2. three misstatements were discovered in a MUS sample:MUS Sampling. Tim Dolan plans to use MUS sampling in auditing the Repairs and Maintenance account for Daco International to determine whether the accounts includes items that should be capitalized rather than expensed. Daco has recorded 2,000 invoices in arriving at the $800,000 expense for the year. Tim has decided to use $4,000 as the anticipated misstatement, and $50,000 as tolerable misstatement. After reviewing Tim’s work, the audit manager agreed with him that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 2 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 50 percent.

    • Required:

      • Determine the required sample size and sampling interval.

      • Calculate the upper misstatement limit, assuming that the auditor tested the sample and discovered the following misstatements.

        • Voucher Number Book Value Audited Value

        • 0220-01 $ 2,400 $ 0

        • 0615-31 50 48

        • 0714-09 3,600 2,400

        • 1119-22 15,000 14,000


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