Chapter 17
Audit Sampling for
Tests of Details of Balances
Accounts Receivable
1
Aaron
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
Kelly Mc
Substantive Tests of Balances
What do Substantive Tests measure
calculate the dollar misstatements in
account balances
4
Sampling Methods
Non statistical sampling
Statistical sampling
monetary unit sampling
variables sampling
difference estimation
ratio estimation
Mean-per-Unit
5
Work Paper 2
College Business Computer
Sales Collection cycle
Sales
performed by:
date:
Tad
1/27/2009
nature of test Substantive tests of transactions
objective
The objective of this procedure is to determine if the sales account is overstated.
assertion(s)
Occurrence and Accuracy
1
1
1
1
1
1
1
1
1
1
6523
6526
6532
6537
6542
6545
6552
6560
6562
6565
4973
4975
4981
4985
4990
10153
10155
10161
10165
10170
4998
5006
5008
5011
10178
10186
10188
10191
0.00
0.00
0.00
0.00
0.00
(3,432.00)
0.00
(874.00)
0.00
(16,576.00)
Trusco Tank
9,182.00
San Luis Ready Mix
22,546.00
Copeland's Sports Superstoresds
4,188.00
Standard Motor Co.
4,538.00
Airport Auto Center
12,664.00
Flora Design Studio
3,432.00
F. McLintocks
18,908.00
Foothill Cyclery
12,446.00
Sinsheimer, Schiebelhut & Baggett -PC
11,982.00
Hind Inc.
16,576.00
sample average
projected value
9,558.00
430,110.00
Book Value
projected error
489,029.00
-58,919.00
-2,088.20
-93,969.00
6
Page 413
Test of Details - sampling
Objective ---derived from management assertions
Define a misstatement
“
population
“
sampling unit
Specify tolerable misstatement ---- a dollar amount
risk of incorrect acceptance βeta risk
Determine sample size
Select the sample
Perform the procedure
Project the sample results to the population
7
Test of Details – sampling
inventory handout
Objective
all recorded inventory exist as of 12/31
physical quantities on hand agree INV records
costs used to value INV are correct
Define misstatement
population
sampling unit
incorrect cost or quantity
items in parts inventory
SKU or part number
Specify tolerable misstatement
risk of incorrect acceptance
Determine sample size
$200,000
5%
387
Select the sample
Perform the procedure
Project the sample results to the population
8
Grace
what is the audit risk model ?
9
Audit Risk Model
AAR IR CRPDR
PDR  f (CR) 
c
CR
AR RoMM PDR
rearrange PDR 
AAR
RoMM
if PDR  high  limited Substantiv e Tests
if PDR  low  extensive Substantiv e Tests
10
Ishrak
pretend GAAS requires AAR ≤ .05
Controls are effective, we assess CR as 0.03
Which audit approach will we take ?
11
Mackenzie
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 Planned Detection Risk ?
12
Sami
pretend GAAS requires AAR ≤ .05
Controls are ineffective, we assess CR as MAX
Which audit approach are we going to take ?
13
Catherine
pretend GAAS requires AAR ≤ .05
Controls are ineffective, we assess CR as MAX (1.00)
We are taking the Primarily Substantive Approach
What is the Planned Detection Risk ?
14
Melissa
pretend GAAS requires AAR ≤ .05
Controls are effective, not great but
Somewhat effective and
we assess CR as 0.25
What is the Planned Detection Risk ?
15
Anne
pretend GAAS requires AAR ≤ .05
Controls are effective, not great but
somewhat effective and
we assess CR as 0.25
Which audit approach will we take?
16
Tori
is Detection Risk
risk of incorrect rejection
Type I or  risk
risk of incorrect acceptance Type II or  risk
17
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
18


type II
type I
19
20
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
21
projected error + allowance for sampling risk
must be less than
tolerable error
22
Accept
cv
23
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.
24
$1,110.32
C V
Accept
allowance for
sampling risk
tolerable error
$200,000 or
$117.44
BV
25
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?
26
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.
27
n=
Book value
Sample total
441,567.00
overstatement
Allowance for
sampling risk
387
Mean
N=
Projection
1,154.18
1703
1,965,560.03
1,141.00
1703
1,943,123.00
13.18
22,437.03
Zβ for 0.05
1.645
error plus allowance
73.59
86.77
1703
125,323.77
147,760.80
28
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.
29
$1,110.32
C V
Accept
allowance for
sampling risk
tolerable error
$200,000 or
$117.44
BV
30
n=
Book value
Sample total
441,567.00
overstatement
Allowance for
sampling risk
387
Mean
N=
Projection
1,154.18
1703
1,965,560.03
1,094.09
1703
1,863,235.27
60.09
102,324.76
Zβ for 0.05
1.645
error plus allowance
73.59
133.68
1703
125,323.77
227,648.53
31
Chris
Which assertions relate to Inventory and
Accounts Receivable?
32
33
Valuation & allocation
34
Valuation & allocation
35
V&T what we did
College Business Computer
Sales Collection cycle
Sales
performed by:
date:
Tad
2/28/2006
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
1
1
1
1
1
1
1
1
1
1
6523
6526
6532
6537
6542
6545
6552
6560
6562
6565
4973
4975
4981
4985
4990
10153
10155
10161
10165
10170
4998
5006
5008
5011
10178
10186
10188
10191
0.00
0.00
0.00
0.00
0.00
(3,432.00)
0.00
(874.00)
0.00
(16,576.00)
Trusco Tank
9,182.00
San Luis Ready Mix
22,546.00
Copeland's Sports Superstoresds
4,188.00
Standard Motor Co.
4,538.00
Airport Auto Center
12,664.00
Flora Design Studio
3,432.00
F. McLintocks
18,908.00
Foothill Cyclery
12,446.00
Sinsheimer, Schiebelhut & Baggett -PC
11,982.00
Hind Inc.
16,576.00
sample average
projected value
9,558.00
430,110.00
36
Page 436-437
Difference
Estimation
Sales Collection cycle
Sales
date:
2/28/2011
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
invoice
1
1
1
1
1
1
1
1
1
1
6523
6526
6532
6537
6542
6545
6552
6560
6562
6565
4973
4975
4981
4985
4990
10153
10155
10161
10165
10170
4998
5006
5008
5011
10178
10186
10188
10191
a mount
Trusco Tank
9,182.00
San Luis Ready Mix
22,546.00
Copeland's Sports Superstoresds
4,188.00
Standard Motor Co.
4,538.00
Airport Auto Center
12,664.00
Flora Design Studio
3,432.00
F. McLintocks
18,908.00
Foothill Cyclery
12,446.00
Sinsheimer, Schiebelhut & Baggett -PC
11,982.00
Hind Inc.
16,576.00
sample average
projected value
sample std deviation
a udite d
a mount
diffe re nce
0.00
0.00
0.00
0.00
0.00
(3,432.00)
0.00
(874.00)
0.00
(16,576.00)
-2,088.20
-93,969.00
5,203.64
37
customer
name
invoice
6521 Hind Inc.
sales
to date
12,376.00
12,376.00
14,314.00
26,690.00
9,182.00
1,344.00
10,020.00
22,546.00
35,872.00
37,216.00
47,236.00
69,782.00
6527 Copeland's Sports Superstoresds32,807.00
102,589.00
6522 Foster's Freeze
6523
6524
6525
6526
T rusco T ank
Foothill Cyclery
Performing Arts Center
San Luis Ready Mix
6528 Madonna Inn
6529 T rusco T ank
7,688.00
8,076.00
110,277.00
118,353.00
6,482.00
124,835.00
Apple Farm Inn
11,020.00
Copeland's Sports Superstoresds
4,188.00
Barbich, Longcrier, Hooper & King Accountancy
10,426.00
Flora Design Studio
4,476.00
First Presbyterian Church
1,344.00
Kimball Motor Co.
4,188.00
Standard Motor Co.
4,538.00
Performing Arts Center
4,834.00
135,855.00
140,043.00
150,469.00
154,945.00
156,289.00
160,477.00
165,015.00
169,849.00
6530 Foster's Freeze
6531
6532
6533
6534
6535
6536
6537
6538
6539 Pacific Conservatory of the Performing
2,594.00
Arts172,443.00
6540
6541
6542
6543
6544
6545
6546
Barbich, Longcrier, Hooper & King Accountancy
1,344.00
Hind Inc.
4,188.00
Airport Auto Center
12,664.00
Foster's Freeze
9,182.00
Madonna Inn
15,976.00
Flora Design Studio
3,432.00
Copeland's Sports Superstoresds
1,344.00
6552 F. McLintocks
336,289.00
8,376.00
18,102.00
344,665.00
362,767.00
5,832.00
368,599.00
1,990.00
28,628.00
3,432.00
370,589.00
399,217.00
402,649.00
19,970.00
422,619.00
6560 Foothill Cyclery
12,446.00
6561 Barbich, Longcrier, Hooper & King Accountancy
1,344.00
6562 Sinsheimer, Schiebelhut & Baggett -PC
11,982.00
435,065.00
436,409.00
448,391.00
6555 Standard Motor Co.
6556 Sinsheimer, Schiebelhut & Baggett -PC
6557 Airport Auto Center
6558 T rusco T ank
6559 San Luis Ready Mix
6563 San Luis Medical Center
6564 Kimball Motor Co.
6565 Hind Inc.
sample size = 10
+ 48,902.90
122,805.80
+ 48,902.90
171,708.70
+ 48,902.90
73,902.90
122,805.80
19,370.00
467,761.00
4,692.00
16,576.00
472,453.00
489,029.00
48,902.90
Page
420-29
MUS
171,708.70
220,611.60
269,514.50
+ 48,902.90
+ 48,902.90
318,417.40
+ 48,902.90
367,320.30
+ 48,902.90
292,197.00
297,411.00
317,381.00
18,908.00
6553 San Luis Ready Mix
6554 Apple Farm Inn
25,000.00
73,902.90
173,787.00
177,975.00
190,639.00
199,821.00
215,797.00
219,229.00
220,573.00
6547 Apple Farm Inn
39,340.00 259,913.00
6548 Barbich, Longcrier, Hooper & King
12,314.00
Accountancy
272,227.00
6549 Performing Arts Center
19,970.00
6550 Barbich, Longcrier, Hooper & King Accountancy
5,214.00
6551 Neal-T ruesdale Insurance
19,970.00
25,000.00
269,514.50
318,417.40
367,320.30
416,223.20
+ 48,902.90
465,126.10
+ 48,902.90
416,223.20
38
39
40
41
42
43