Audit Sampling - PowerPoint PPT Presentation

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Audit Sampling

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Audit Sampling Defined SAS No. 39 defines audit sampling as the application of an audit procedure to less than 100 percent of the items within an account balance or ... – PowerPoint PPT presentation

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Title: Audit Sampling


1
Audit Sampling
2
Audit Sampling Defined
  • SAS No. 39 defines audit sampling 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 some characteristic of the balance
    or class (AU 350.01).

3
Advantages of Statistical Sampling
  • Design efficient samples
  • Measure sufficiency of evidence
  • Objectively evaluate sample results

4
Requirements of Audit Sampling Plans
  • When planning the sample consider
  • The relationship of the sample to the relevant
    audit objective
  • Materiality or the maximum tolerable misstatement
    or deviation rate
  • Allowable sampling risk
  • Characteristics of the population
  • Select sample items in such a manner that they
    can be expected to be representative of the
    population
  • Sample results should be projected to the
    population
  • Items that cannot be audited should be treated as
    misstatements or deviations in evaluating the
    sample results
  • Nature and cause of misstatements or deviations
    should be evaluated

5
Selection of Random Sample
  • Random number tables
  • Random number generators
  • Systematic selection
  • Haphazard Selection
  • Note that these methods are often used in
    conjunction with a stratification process.

6
Terminology
  • Sampling risk
  • Risk of assessing CR too high / Risk of incorrect
    rejection
  • Risk of assessing CR too low / Risk of incorrect
    acceptance
  • Precision (allowance for sampling risk)

7
Types of Statistical Sampling Plans
  • Attributes sampling
  • Discovery sampling
  • Classical variables sampling
  • Probability-proportional-to-size sampling

8
Attribute Sampling Applied To Tests Of Controls
  • Attribute sampling is a statistical method used
    to estimate the proportion of a characteristic in
    a population.
  • The auditor is normally attempting to determine
    the operating effectiveness of a control
    procedure in terms of deviations from the
    prescribed internal control.

9
Sampling Risk for Tests of Controls
  • True State of Population
  • Deviation Rate Deviation Rate
    Exceeds
    Is Less Than
  • Auditors Conclusion Tolerable Rate
    Tolerable Rate
  • From the Sample Is
  • Deviation Rate
  • Exceeds
  • Tolerable Rate
  • Deviation Rate
  • Is Less Than
  • Tolerable Rate

Correct Decision
Incorrect Decision (Risk of Assessing Control
Risk Too High)
Incorrect Decision (Risk of Assessing Control
Risk Too Low)
Correct Decision
10
Attribute Sampling for Tests of Controls
  • Determine the objective of the test
  • Define the attributes and deviation conditions
  • Define the population to be sampled
  • Specify
  • The risk of assessing control risk too low
  • The tolerable deviation rate
  • The estimated population deviation rate
  • Determine the sample size
  • Select the sample
  • Test the sample items
  • Evaluate the sample results
  • Document the sampling procedure

Planning
Performance
Evaluation
Documentation
11
Discovery Sampling
  • A modified case of attributes sampling
  • Purpose is to detect at least one deviation (i.e.
    critical deviations)
  • Useful in fraud detection
  • Auditor risk and deviation assessments
  • Risk of assessing control risk too low (i.e. 5)
  • Tolerable rate (normally set very low, i.e. lt 2)
  • Expected deviation rate is generally set at 0

12
Nonstatistical Attributes Sampling
  • Determination of required sample size
  • Must consider risk of assessing control risk too
    low and tolerable deviation rate
  • Need not quantify the risks
  • Evaluation of results
  • Compare tolerable deviation rate to sample
    deviation rate. Assuming appropriate n
  • If SDR somewhat less than TDR, then conclude that
    risk of assessing control risk too low is set
    appropriately.
  • If SDR approaches TDR it becomes less likely that
    PDR lt TDR
  • Must use professional judgment

13
Audit Sampling for Substantive Tests
  • Determine the objective of the test
  • Define the population and sampling unit
  • Choose an audit sampling technique
  • Determine the sample size
  • Select the sample
  • Test the sample items
  • Evaluate the sample results
  • Document the sampling procedure

Planning
Performance
Evaluation
Documentation
14
Audit Sampling for Substantive Tests Sampling
Risk
  • True State of Population
  • Misstatement in
    Misstatement in
    Account Exceeds Account Is Less
  • Auditors Conclusion Tolerable Amount
    Than Tolerable
  • From the Sample Is
    Amount
  • Misstatement in
  • Account Exceeds
  • Tolerable Amount
  • Misstatement in
  • Account Is Less
  • Than Tolerable
  • Amount

Correct Decision
Incorrect Decision (Risk of Incorrect
Rejection)
Incorrect Decision (Risk of Incorrect Acceptance)
Correct Decision
15
Risk of Incorrect Acceptance (RIA)
  • Modification of audit risk model
  • AR IR x CR x DR
  • DR comprised of two types of substantive
    procedures, each with an associated type of risk
  • Risk associated with AP and other procedures that
    do not involve audit sampling (AP)
  • Risk associated with procedures involving audit
    sampling (RIA)
  • AR IR x CR x AP x RIA
  • RIA AR /(IR x CR x AP)

16
Classic Variables Sampling
  • Mean per-unit estimation
  • Difference and Ratio Estimation
  • Appropriate when differences between audited and
    book values are frequent
  • Difference estimation is most appropriate when
    the size of the misstatements does not vary
    significantly in comparison to book value
  • Ratio estimation is most appropriate when the
    size of misstatements is nearly proportional to
    the book values of the items.

17
Mean Per-unit (MPU) EstimationDetermining the
Sample Size
  • N population size
  • Ur incorrect rejection coefficient (Table 9-8)
  • SDE estimated population standard deviation
  • A planned allowance for sampling risk

18
Mean Per-unit (MPU) EstimationDetermining the
Sample Size
Standard deviation
Population SD
Sample SD
19
MPU Estimation Determining the Sample Size
  • Calculation of planned allowance for sampling
    risk (A)

TM tolerable misstatement Ua Incorrect
acceptance coefficient (Table 9-8) Ur incorrect
rejection coefficient (Table 9-8)
20
MPU Estimation Adjusted Allowance for Sampling
Risk
  • Calculation of adjusted allowance for sampling
    risk (A)
  • TM Tolerable misstatement
  • Ua Incorrect acceptance coefficient (Table 9-8)
  • SDC Sample (calculated) standard deviation
  • n sample size

21
MPU Estimation
  • Estimated total audited value
  • Mean audited value x Number of accounts
  • Acceptance interval
  • Estimated total audited value /- Adjusted
    allowance for sampling risk
  • Projected misstatement
  • Estimated total audited value Book value of
    population

22
Nonstatistical Variables Sampling
  • PBV population book value
  • RF reliability factor (based on auditors
    combined assessment of inherent and control risk
    and the risk that other substantive procedures
    will fail to detect misstatements) (Table 9-13).
  • TM tolerable misstatement

23
Nonstatistical Variables Sampling
PM projected misstatement SNM sample net
misstatement SBV sample book value PBV
population book value Test compare PM to TM.
Rule-of-thumb if PM exceeds 1/3 of TM, PM
becoming too high
24
Probability-proportional-to-size (PPS) Sampling
  • Applies the theory of attributes sampling to
    estimate the total dollar amount of misstatement
    in a population.
  • Population is defined by the individual dollars
    comprising the populations book value (1 1
    item).
  • Relatively easy to use and often results in
    smaller sample sizes than classical variables
    approaches.
  • Assumptions underlying PPS sampling
  • Expected misstatement rate in the population is
    small.
  • Amount of misstatement in physical unit should
    not exceed recorded BV of the item.
  • PPS focuses on overstatements.

25
PPS SamplingDetermination of Sample Size
PBV population book value RF reliability
factor (Table 9-14) TM tolerable
misstatement EM expected misstatement EF
expansion factor (Table 9-15)
26
PPS SamplingSample Selection
  • Systematic selection is generally used with PPS
    sampling

SI sampling interval PBV population book
value n sample size
27
PPS SamplingEvaluation of Sample Results
Allowance for sampling risk
ULM upper limit on misstatement PM projected
misstatement BP basic precision IA
incremental allowance
28
PPS SamplingEvaluation of Sample Results
  • Projected misstatement (PM)
  • If BV lt SI, PM TF x SI
  • TF tainting factor (BV AV) / BV
  • BV book value
  • AV audit value
  • If BV gt SI, PM actual misstatement

29
PPS SamplingEvaluation of Sample Results
  • Allowance for sampling risk
  • Basic precision SI x RF0
  • Incremental allowance
  • If no misstatements in sample found, IA 0
  • If misstatements found
  • For misstatements in which BV lt SI, rank order
    projected misstatements from largest to
    smallest, multiply by corresponding incremental
    factor (from Table 9-14) and sum to calculate
    IA.

30
PPS SamplingEvaluation of Sample Results
  • Compare ULM to TM
  • If ULM lt TM, conclude that population is not
    misstated by more than TM at the specified level
    of sampling risk.
  • If ULM gt TM, conclude that the sample results do
    not provide enough assurance that the population
    misstatement is less than the TM and balance
    adjustment may be warranted.
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