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Topic 11: Fieldwork â Audit Sampling for Tests of Details of Balances

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### Topic 11: Fieldwork ― Audit Sampling for Tests of Details of Balances

Auditing

Arens Ch. 17 (should avoid textbook for this topic)

James J. McKinney

jmckinney@rhsmith.umd.edu

See US ASB AU–C 530 and AICPA Audit Guide: Audit Sampling

Through All Audit Phases

Topic 1: Overview

Topic 2: Accounting Information System

Topic 18: Legal Liability

Fraud Detection

IT Auditing

Other Engagements – NOT AUDITING!

Planning

Fieldwork

Audit Completion

Topic 11: Sampling - Tests of Details of Balances

(these topics affect fieldwork and

completion)

Topic 3: Cycles

Topic 4: Management Assertions

and Audit Objectives

Topic 5: Evidence

Topic 6: Materiality

Topic 7: Audit Risk

Topic 8: Test Types and

Audit Plan

Topic 9: Sampling in Tests of

Controls and Substantive

Tests of Transactions

Topic 10: Tests of Controls

Topic 11: Sampling - Tests of Details

of Balances

Topic 12: Sales and Collections Cycle

Topic 13: Inventory and Warehousing

Cycle

Topic 14: Acquisition and Payment

Cycle

Topic 15: Cash

Topic 16: Audit Completion

Topic 17: Reporting

Overview of a Financial Statement Audit

Audit Work Papers

Planning

Fieldwork

Audit

Completion

- Substantive Testing:
- Substantive Tests of Transactions
- Analytical Procedures
- Tests of Details of Balances

Test of Controls and Reassessment of Control Risk

- Perform:
- Pre-Acceptance Client Review
- Understand Business
- Business Risk
- Initial Analytical Procedures
- Engagement Letter
- Preliminarily Determine and Assess:
- Controls
- Materiality
- Audit Risk
- Risk of Material Misstatement
- Detection Risk
- Determine audit procedures based on previous assessments and:
- Management Assertions
- Audit Objectives
- Evidence Availability, Persuasiveness, and Cost
- Prepare:
- Audit Plan
- Audit Program

- Complete the Audit:
- Contingent Liabilities
- Subsequent Events
- Reassess:
- Risk
- Materiality
- Evidence
- Final Analytical Procedures
- Management Representation Letter
- Issue:
- Audit Report on Financial Statements
- Audit Report on Internal Controls (issuers)
- Management Letters (SAS 115)

balance testing

not usually

analytical procedures

Opening Balances

Sampling

Audit sampling for tests

of details of balances

Audit sampling for tests of

controls and substantive

tests of transactions

1

State the objectives

of the audit test.

2

Decide whether audit

sampling applies.

3

Define misstatement

conditions.

Define attributes and

exception conditions.

4

Define the population.

5

Define the sampling unit.

!

Comparison of the 14 Steps Between TOC/STOT and TDB SamplingComparison of the 14 Steps Between TOC/STOT and TDB Sampling

Step

Audit sampling for tests

of details of balances

Audit sampling for tests of

controls and substantive

tests of transactions

6

Specify Tolerable

Misstatement.

Specify the Tolerable

Deviation Rate.

7

Specify Risk

of Incorrect Acceptance.

Specify Risk

of Assessing Control

Risk Too Low.

8

Estimate Anticipated

Misstatement in the pop.

Estimate the Estimated

Pop. Deviation Rate.

9

Determine the initial

sample size.

Audit sampling for tests

of details of balances

Audit sampling for tests of

controls and substantive

tests of transactions

10

Select the sample.

11

Perform the audit

procedures.

12

Generalize from the

sample to the population.

13

Analyze the

misstatements.

Analyze the

deviations.

14

Decide the acceptability

of the population.

!

Comparison of the 14 Steps Between TOC/STOT and TDB SamplingSampling Risk - Substantive Testing

Conclusion Based on Entire Population

Accept Balance as Fairly Stated

Believe Balance is Unacceptably Misstated

- Note: Whereas with RACRTL, failure had only a potential for audit failure since insufficient substantive testing was done, RIA implies that a balance is misstated and therefore more likely to result in audit failure.
- RIR results in loss of efficiency but could lead to improperly issuing a qualified opinion.

Accept Balance as Fairly Stated

CORRECT

Risk of Incorrect Acceptance

Beta or Type II Error

Conclusion Based on Sample

Risk of Incorrect Rejection

Alpha or Type I Error

Believe Balance is Unacceptably Misstated

CORRECT

- One way to think of determining RIA is to modify the Audit Risk model from:
- AAR=IRxCRxPDR to
- AAR=IRxCRx(PDRSTOTxPDRAP x PDROther TDB x RIA)
- New definitions:
- PDRSTOT: Risk that substantive tests of transactions would not detect the misstatements not prevented by internal controls.
- PDRAP: Risk that analytical procedures would not detect the misstatements not prevented by internal controls.
- PDROther TDB : Risk that other tests of details of balances (beside the sampling test being performed) would not detect the misstatements not prevented by internal controls.
- Think of RIA as PDRSample, the risk that your sample would not detect the misstatements not prevented by internal controls or detected by other test.
- We can rewrite the formula as:
- RIA=AR/(IRxCRxPDRSTOTxPDRAPxPDROther TDB)
- This implies that as we rely on other substantive testing that RIA increases causing a smaller sample size.

Terminology with Test of Controls Comparison

- RIA (Risk of Incorrect Acceptance):
- AKA Acceptable Risk of Incorrect Acceptance – Similar to RACRTL for TOC (Need for PPS and CVS) [In ACL Confidence Level = One minus RIA]
- RIR (Risk of Incorrect Rejection):
- Similar to RACRTH for TOC (Need for CVS only)
- AM (Anticipated Misstatement [$] Rate [%]):
- AKA Expected Error or Expected Misstatement – rates are determined by dividing AM by population $ – Similar to EDR for TOC [In ACL is called Expected Total Errors]
- TM (Tolerable Misstatement [$] Rate [%]):
- similar to Performance Materiality or Tolerable Error – Similar to TDR for TOC [In ACL is called Materiality]
- PM (Projected Misstatement):
- Our best estimate of misstatement. Similar to Sample Deviation Rate for TOC [In ACL is called Most Likely Error]
- ULM (Upper Limit on Misstatement):
- Our statistical upper bound. AKA Worst Case Error, Upper Misstatement Limit, or Misstatement Bounds – Similar to UPL for TOC [In ACL is called Upper Error Limit]

See Topic 9 to compare similar terms

Impact on Sample Sizes

- RIA ↓ SS↑
- AM ↓ SS↓
- TM ↓ SS↑
- RIR ↓ SS↑
- Population Variability ↓ SS↓

Only used for CVS

Only used for CVS

- Probability-Proportional-to-Size Sampling (PPS)
- Monetary-Unit Sampling (MUS)
- Dollar-Unit Sampling (DUS)
- Cumulative Monetary Amount (CMA)
- Sampling-Proportional-to-Size (SPS)

- In Test of Controls - document was the sample item.
- When testing a control on a document, a control was 100% not working (a deviation) or working.
- In PPS, think of each $ being the item to be selected and tested.
- However if a $ is selected within a $4,000 dollar invoice, which is your selected $? If we cannot isolate the $ then we test the entire invoice. If we find a misstatement, then we consider the misstatement to be proportionately spread throughout the invoice's $s. For example if you find a $1,000 misstatement, then assume that each $ in the invoice is misstated by 25 cents ($1,000/$4,000). Thus say if you selected dollar 200 in the $4,000, invoice, you conclude that $ is misstated by 25 cents.
- This $ is considered to have a 25% tainting (note you can sum tainting %’s unlike regular %’s).

- Note: In past exams we determined sample size and evaluated samples using tables similar to those used for test of controls. This method is valid but other sources emphasize the approach below. Required: only RIA, AM, TM, and Table.
- SS=(population book value x RF0) / (TM- (AM x EF) )
- RF is the reliability factor for 0 misstatements and the appropriate RIA (see following page)
- EF is the expansion factor for the appropriate RIA (see following page)
- SS = ($500,000 x 3.0) / ($15,000 - ($3,000 x 1.6)) = 147.05
- RIA=5%
- TM for test = $15,000
- AM=$3,000
- Population book value=$500,000
- Note: ACL does not round when computing SS. You should round up to nearest whole number.
- The sample size may not equal the number of items actually tested. SS here actually equals the number of intervals selected. Amounts over the interval might actually consist of one or more intervals from the SS. See examples on pages that follow.

Reliability and Expansion Factors

Reliability Factors for Misstatements

Risk of Incorrect Acceptance

1%

5%

10%

20%

25%

50%

0

4.61

3.00

2.31

1.61

1.39

.70

1

6.64

4.75

3.89

3.00

2.70

1.68

2

8.41

6.30

5.33

4.28

3.93

2.68

3

10.05

7.76

6.69

5.52

5.11

3.68

Number of Misstatements

4

11.61

9.16

8.00

6.73

6.28

4.68

5

13.11

10.52

9.28

7.91

7.43

5.68

6

14.57

11.85

10.54

9.08

8.56

6.67

7

16.00

13.15

11.78

10.24

9.69

7.67

8

17.41

14.44

13.00

11.38

10.81

8.67

Expansion Factors for Anticipated Misstatements

Risk of Incorrect Acceptance

1%

5%

10%

20%

25%

50%

1.9

1.6

1.5

1.3

1.25

1.0

- AICPA, Audit and Accounting Guide: Audit Sampling

PPS Selection

- To evaluate statistically, you need a random sample. Could select random $'s throughout, however traditionally firms have selected PPS samples using systematic random selection. This avoids having an invoice less than the interval being selected twice.
- Easy way: Set up a list of cumulative $. Should exclude zero and negative balances.
- Next determine the interval: Population $ divided by sample size. Round down if necessary (forces sample size to be higher). If you have to estimate population $, estimate higher amount to avoid redoing sample.
- Pick a random $ from .01 up to and including the interval amount. This is your random start or random seed.
- You will skip through the cumulative $ until you find that random start.
- Add the interval to the random start and find that $. Add the interval again a find that $. Keep adding intervals until you have gone through the entire population.

PPS Selection - Example

- Population = $5,050 with only 6 items (to make it easy)
- Sample Size =5
- Thus interval is? Round down to $1,000 – (note it is unacceptable to round for tests or projects unless directed to do so).
- Determine that random start is $499.

- Note: that #2,#3,#4 and #6 were selected.
- Note any amount that is greater than the interval will always be selected once.
- Our Original Population is 6 items totaling $5,050.
- 100% Examined Items is the 1 item totaling $2,100. Items selected regardless of random start.
- Sample Population is the original population minus 100% examined items - in this case 5 items totaling $2,950 (or $5050-2100).
- Our sample selection would have 3 invoices related to the Sample Population with 1 additional invoice tested 100%.

PPS Selection - Example

Invoice 1

$300

$499

($499 cumulative $)

Invoice 2

$700

Invoice 3

$900

$499

($1,499 cumulative $)

$499

($2,499 cumulative $)

Invoice 4

$2,100

$499

($3,499 cumulative $)

Invoice 5

$400

$499

($4,499 cumulative $)

Invoice 6

$650

$1,000

$50

$1,000

$1,000

$1,000

$1,000

EVALUATION

- Resolve and document misstatements just as you did for deviations in Test of controls.
- Compute misstatement amount (in testing for existence or performing vouching it would be book - audited and in testing for completeness or performing tracing it would be audited - book). This assumes misstatements n PPS are all typically overstatements or understatements.
- Segregate items inOriginal Populationover the interval or100% Examined Items. These items are tested completely. For these items: misstatement found=PM=ULM.
- For items in theSample Population(Original Populationitems< interval):
- Compute tainting %'s for all misstatements in Sample Population (in testing for existence or performing vouching it would be misstatement / book and in testing for completeness or performing tracing it would be misstatement / audited). Individual taintings should range fro m 0%-100%. Example if book amount is $5,000, audited amount is $3,750 (and you are testing existence), then misstatement is? $1,250. Tainting % is? ($1,250/$5,000=25% or .25).
- Rank misstatements from largest tainting % in magnitude to smallest %.
- Compute PM by multiplying tainting %'s by the interval. Summing the products to compute PM for the Sample Population.
- For the number of misstatements obtain the reliability factors for the given RIA.
- Compute the factor differences. Multiply the differences by the respective PM to compute ULM's.
- Sum the products and add the reliability factor for zero misstatements x the SI, this is the ULM for the Sample Population.
- Misstatement <= PM (= if 0$ misstatement found) < ULM .

EVALUATION

Should add PM from the Sample Population and misstatement amounts from 100% Examined Items (items over the interval) to determine overall PM (projected misstatement) for the Original Population.

Should add ULM from Sample Population and misstatement amounts from 100% Examined Items (items over the interval) to determine overall ULM(upper limit on misstatement) for the Original Population.

Allowance for sampling risk (ASR) or precision = ULM - PM.

Decision rule if ULM>TM then reject population, if ULM <TM then accept.

Note that PM is the point estimate like sample mean, ULM is like the confidence bound.

- Original Population - The one on which we want to draw a conclusion
- RIA=25%, Original Population=$600,000, AM=$6,500,TM=$36,000 RF=1.39, EF=1.25 S.S. = ($600,000 x 1.39) / ($36,000 - ($6,500 x 1.25)) = 29.92 will round up to 30. Note these are intervals. We will test for existence.
- $600,000 / 30 = $20,000 interval.
- Select all 30 intervals regardless if over interval ($20,000) or not - for this example assume 20 invoices< interval and 4 > interval the 4 invoices total $200,000.
- Perform testing
- Segregate population into two groups (only when doing final evaluation)

Sample Population (Less than Interval ) - $400,000

100% Examined Items - $200,000

(For this class we mean over Interval)

Assume only one 100% item misstatement found totaled $3000.

$8,000

PM

(.20+.15+.05) x $20,000 interval = $4,000 + $3,000 + $1,000= $8,000. Note sorting of tainting %’s.

$37,910

ULM

[$4,000x(2.70-1.39) + $3,000x(3.93-2.70) + $1,000x(5.11-3.93)] + [1.39x$20,000] = $5,240+$3,690 + $1,180+$27,800 = $37,910

$1,000

Sample Misstatement

Tested 20 items, found 3 misstatements totaling $1,000. Misstatement taintings are 5%, 20%, and 15%.

0$

$29,910

ASR or Precision

- Then total misstatement for test would by $1,000+$3,000=$4,000. PM $8,000+$3,000=$11,000. ULM $37,910+$3,000=$40,910.
- ULM ($40,910) > TM [36,000] would fail test.
- What happens to PM if doubled sample size Interval should decrease in half, Tainting sum double No change
- What happens as SS ↑ Sample Miss. ↑ PM (no change) ULM ↓ Tainting Sum ↑Interval ↓ Precision ↓
- So if increase SS here, need precision to go down to $36,000-$11,000=$25,000 in order to pass. Might make sense to do.
- What if TM was $12,000, need precision to get to $1,000 - does not make sense to do.

ULM > TM, Now What?

(assuming you think results may be incorrect and the population is not actually misstated – i.e., you thought the sample was non-representative)

- Increase sample size. Your PM will be more precise even though your best estimate is that it would remain unchanged. If there is lot of precision (large ASR), and it is the precision that is causing you to fail, increasing SS will reduce ASR. Using systematic random sampling would have to double SS. Using unrestricted random (if population entered on computer then not a problem) then could pick smaller S.S. Still may be impossible. Could be a problem of turn-around if doing confirms or can't extend sample if doing a physical inventory selection.
- Segregate misstatements based on a qualitative difference - example particular clerk makes a series of misstatements.
- Expand other substantive procedures within cycle.

(assuming you think results are correct and the population is misstated)

- Have client go through entire population and correct all potential problems and then reperform test with new sample. Usually impractical, have issues similar to increasing sample size
- Make AJE for PM (leaving precision) [or in rare cases ULM – put this may lead to a distortion itself]. E.g., debit: sales returns and credit A/R (unspecified customer). As find actual misstatements in A/R, then credit customer A/R and debit unallocated A/R. If recording PM, ASR must be less than TM.
- Allocate materiality from other cycles – only if difference between ULM and TM is small.
- Issue a qualified or adverse opinion – if client does not make adjustment.

You usually need to choose one logical choice that will depend on your population and sample results.

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