# ARENS 17 2118 Audit Sampling for Test of Details of Balances by jyW1dSL

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```									      Chapter 17

Audit Sampling for
Tests of Details of Balances

Accounts Receivable

1
David

Tests of Controls

What do they measure

The operating effectiveness of
internal controls

2
The introduction

… when all the confirmation replies were
received or alternate procedures were
completed ….. Bob called Barbara to do
some statistical evaluation.

3
Julian

Substantive Tests of Balances

What do Substantive Tests measure

Whether the dollar amounts of account
balances are materially misstated

4
Sampling Methods

Non statistical sampling
Statistical sampling
monetary unit sampling
variables sampling (mean per unit)

5
Page 411   Test of Details - sampling
Objective
Define misstatement
population
sampling unit
Specify tolerable misstatement
risk of incorrect acceptance
Determine sample size
Select the sample
Perform the procedure
Project the sample results to the population

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Test of Details - sampling
Objective             evid inv not material overstated
Define misstatement          cost or quantity incorrect
population             items in parts inventory
sampling unit          SKU or part number
Specify tolerable misstatement             \$200,000
risk of incorrect acceptance       5%
Determine sample size                      387
Select the sample
Perform the procedure
Project the sample results to the population

7
Fabiola

what is the audit risk model ?

8
Audit Risk Model

AAR
AAR IR CRPDR        AR RoMM PDR        rearrange PDR 
RoMM

c
PDR  f (CR )          if PDR  high  limited Substantiv e Tests
CR
if PDR  low  extensive Substantiv e Tests

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Nicholas M
pretend GAAS requires AAR ≤ .05

Controls are effective, we assess CR as 0.03

Which audit approach will we take ?

10
Belen
pretend GAAS requires AAR ≤ .05

Controls are effective, we assess CR as 0.03

We will take the Reduced Level of Control Risk Approach
What is the required level of Detection Risk ?

11
Erynn
pretend GAAS requires AAR ≤ .05

Controls are effective, not great but effective
and we assess CR as 0.50

Which audit approach will we take?

12
Melissa O
pretend GAAS requires AAR ≤ .05

Controls are effective, not great but effective
and we assess CR as 0.50

We will take the RL of CR
What is the required level of Detection Risk ?

13
Andrew F

is Detection Risk

risk of incorrect rejection  Type I or  risk
risk of incorrect acceptance Type II or  risk

14
ately 10% of the \$1,965,560 balance. Statistical sampling cannot prove
t auditing standards do not require balances to be exact. Auditing
“obtain reasonable assurance about whether the financial statements are
” Auditing standards require auditors obtain “sufficient, appropriate
ments “present fairly, in all material respects.” Auditors are typically
, such as inventory, are overstated. If tolerable error is \$200,000, we need
ce of the parts inventory is greater than \$1,765,560.
he hypothetical mean \$1,036.74 (\$1,765,560 /
value \$1,154.17 (\$1,965,560 / 1,703) is
This will remain the same regardless of how
ha Risk and Beta Risk. The interval is
he upper portion of the hypothesis test and the
nterval. Together these two elements comprise

15
Andrew K
pretend GAAS requires AAR ≤ .05

Controls are ineffective, we assess CR as MAX

Which audit approach are we going to take ?

16
Gavin
pretend GAAS requires AAR ≤ .05

Controls are ineffective, we assess CR as MAX

We are taking the Primarily Substantive Approach
What is the required level of Detection Risk ?

17
        
type II   type I

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19
Test of Details - sampling

Project the sample results to the population

you must project sample results to the population
plus
appropriate consideration for sampling risk

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projected error + allowance for sampling risk

must be less than

tolerable error

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Accept

cv
22
\$1,110.32
C V

Accept

allowance for
sampling risk
BV
tolerable error

\$200,000 or
\$117.44                 23
24
Also notice that the critical value will change because it now 1.645 standard deviations to the
right of the hypothesized mean.

Later, during the audit we will select and audit a random sample of 387 inventory line items. If
everything goes exactly as planned and the sample mean of the audited values exceeds \$1,108.78, we
will accept the hypothesis that the parts inventory balance is not materially overstated.
The attached work sheet shows the results of our sample. We found two types of errors in our
sample. We observed instances where the actual quantity on hand differed from the quantity in the
client’s accounting records. We also observed on instance where the cost per the invoice was different
than the cost used to determine the inventory balance. The sum of the extended audited balances for
the 387 part lines in the sample came to \$441,567.00. The sample mean of \$1,141.00 lies in the
acceptance region. However, the standard deviation of the sample exceeded the standard deviation
used to calculate the original critical value.

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\$1,110.32
C V

Accept

allowance for
sampling risk
BV
tolerable error

\$200,000 or
\$117.44                 26
Test of Details - sampling

Project the sample results to the population

you must project sample results to the population
appropriate consideration for sampling risk
is the projected error too close to tolerable error

How close is too close?

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Applying what we know about Hypothesis Tests and Confidence Intervals

The risk of incorrectly concluding the book value of the inventory is incorrect when it is correct
is Alpha risk or a Type I error. This is the risk of incorrect rejection. The risk of incorrectly concluding
inventory is fairly presented when the book value is materially overstated is Beta risk or a Type II
error. This is the risk of incorrect acceptance.
In the previous examples the critical value of the hypothesis test and the lower limit of the
interval were arbitrarily set to equal to the midpoint between the hypothetical mean and the book
value. This will result in Alpha risk that is twice as large as Beta risk because the hypothesis test is a
one-tail test while intervals have two tails.
For planning purposes assume that tolerable error for the parts inventory has been set as
\$200,000, which is approximately 10% of the \$1,965,560 balance. Statistical sampling cannot prove
that the balance is correct. But auditing standards do not require balances to be exact. Auditing
standards require auditors to “obtain reasonable assurance about whether the financial statements are
free of material misstatement.” Auditing standards require auditors obtain “sufficient, appropriate
evidence” the financial statements “present fairly, in all material respects.” Auditors are typically
concerned that asset accounts, such as inventory, are overstated. If tolerable error is \$200,000, we need
evidence that the actual balance of the parts inventory is greater than \$1,765,560.
The interval between the hypothetical mean \$1,036.74 (\$1,765,560 /
1,703) and the average book value \$1,154.17 (\$1,965,560 / 1,703) is
\$117.44 (\$200,000 / 1,703). This will remain the same regardless of how
we allocate risk between Alpha Risk and Beta Risk. The interval is
comprised of two elements: the upper portion of the hypothesis test and the
lower tail of the confidence interval. Together these two elements comprise
the tolerable error.
28
\$1,110.32
C V

Accept

allowance for
sampling risk
BV
tolerable error

\$200,000 or
\$117.44                 29
n=     Mean       N=      Projection

Book value                             1,154.18    1703   1,965,560.03

Sample total      441,567.00     387   1,141.00    1703   1,943,123.00

overstatement                            13.18               22,437.03

Allowance for     Zβ for 0.05
sampling risk
1.645             73.59     1703     125,323.77

error plus allowance                     86.77              147,760.80

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Let’s assume the sample mean was \$1,094.09
What if the Sample Mean is less than the Critical Value?

Assume the sum of the 387 lines that were audited came to \$423,412.83; the standard deviation
of the sample was \$880.00 and the sample mean was \$1,094.09. The sample mean would not lie in the
acceptance region. However, the sample mean is larger than the hypothetical mean of \$1,036.74. The
projected balance would be \$1,863,235.27                                                . The
projected discrepancy is \$102,324.73 (\$1,965,560 - \$1,863,235) which is less than tolerable error.
The sample does not provide sufficient evidence to state that the parts inventory is not
materially overstated with 95% confidence. However, the sample does not provide evidence that the
parts inventory is materially overstated. We can modify the equation used to calculate the critical value
and determine the level of confidence the sample results do provide.

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\$1,110.32
C V

Accept

allowance for
sampling risk
BV
tolerable error

\$200,000 or
\$117.44                 32
n=     Mean       N=      Projection

Book value                             1,154.18    1703   1,965,560.03

Sample total      441,567.00     387   1,094.09    1703   1,863,235.27

overstatement                            60.09              102,324.76

Allowance for     Zβ for 0.05
sampling risk
1.645             73.59     1703     125,323.77

error plus allowance                    133.68              227,648.53

33
Nathan

Which assertions relate to Inventory and
Accounts Receivable?

34
35
Valuation & allocation

36
Valuation & allocation

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Page 436-437       V&T                                                                               what
we did
Sales Collection cycle
performed by:
date:
2/28/2006
Sales

nature of test Test of details of transactions
objective      The objective of this procedure is to determine if the sales account is overstated.
assertion(s)   Existence/Occurrence and Valuation

ship      sales                                      invoice       audited          difference
invoice                       customer
doc       order                                                    amount
amount
1      6523      4973     10153   Trusco Tank                         9,182.00       9,182.00            0.00
1      6526      4975     10155   San Luis Ready Mix                 22,546.00      22,546.00            0.00
1      6532      4981     10161   Copeland's Sports Superstoresds     4,188.00       4,188.00            0.00
1      6537      4985     10165   Standard Motor Co.                  4,538.00       4,538.00            0.00
1      6542      4990     10170   Airport Auto Center                12,664.00      12,664.00            0.00
1      6545                       Flora Design Studio                 3,432.00             0.00     (3,432.00)
1      6552      4998     10178   F. McLintocks                      18,908.00      18,908.00            0.00
1      6560      5006     10186   Foothill Cyclery                   12,446.00      11,572.00         (874.00)
1      6562      5008     10188   Sinsheimer, Schiebelhut & Baggett -PC
11,982.00      11,982.00            0.00
1      6565      5011     10191   Hind Inc.                          16,576.00             0.00    (16,576.00)

sample average                                   9,558.00
projected value                                430,110.00

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Page 436-437       Difference
Estimation
Sales Collection cycle                                              date:                          2/28/2011
Sales

nature of test Test of details of transactions
objective      The objective of this procedure is to determine if the sales account is overstated.
assertion(s)   Existence/Occurrence and Valuation

ship      sales                                      invoice       a udite d      diffe re nce
invoice                       customer
doc       order                                     a mount        a mount
1      6523      4973     10153   Trusco Tank                         9,182.00       9,182.00          0.00
1      6526      4975     10155   San Luis Ready Mix                 22,546.00      22,546.00          0.00
1      6532      4981     10161   Copeland's Sports Superstoresds     4,188.00       4,188.00          0.00
1      6537      4985     10165   Standard Motor Co.                  4,538.00       4,538.00          0.00
1      6542      4990     10170   Airport Auto Center                12,664.00      12,664.00          0.00
1      6545                       Flora Design Studio                 3,432.00           0.00     (3,432.00)
1      6552      4998     10178   F. McLintocks                      18,908.00      18,908.00          0.00
1      6560      5006     10186   Foothill Cyclery                   12,446.00      11,572.00       (874.00)
1      6562      5008     10188   Sinsheimer, Schiebelhut & Baggett -PC
11,982.00      11,982.00          0.00
1      6565      5011     10191   Hind Inc.                          16,576.00           0.00    (16,576.00)

sample average                                                  -2,088.20
projected value                                                -93,969.00
sample std deviation                                             5,203.64

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Page 420-29 MUS
Miller Motor Co.
year-end physical inventory
worksheet

retail                extended
line qty   SKU                            price      cost         cost
1   5 4470312 Tail lamp bulb               4.42       2.65          13.26            0        13.26
2 40 1118019 Oil filter                    7.30       4.38         175.20        13.26       188.46
3 240 1851974 Spark plug                   9.76       5.86       1,405.44       188.46     1,593.90
4 43 3873086 Air intake filter            44.28      26.57       1,142.42     1,593.90     2,736.32
5 …     …                …                                      …
…     …                …                                      …
…     …                …                                      …
984 21 6202037 Shock                       112.30      67.38       1,414.98 900,356.90 901,771.88
985   2 3680387 Fuel pump diesel           131.98      79.19         158.38 901,771.88 901,930.26
986 11 6730291 Wheel steel                 221.53     132.92       1,462.10 901,930.26 903,392.35
987 19 6037192 Brake pads                  224.24     134.54       2,556.34 903,392.35 905,948.69
988   3 5119378 Water pump                 293.98     176.39         529.16 905,948.69 906,477.85
989   4 4030026 Alternator                 335.04     201.02         804.10 906,477.85 907,281.95
990 …     …                …                                      …
…     …                …                                      …
…     …                …                                      …
1701   2 2780189 Transmission 4l60e m30   1,857.31   1,578.71       3,157.43 1,955,805.42 1,958,962.84
1702   1 1616045 Engine - 4.3L            2,886.86   2,453.83       2,453.83 1,958,962.84 1,961,416.67
1703   1 1478027 Engine - 6.0L            4,874.53   4,143.35       4,143.35 1,961,416.67 1,965,560.03
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