Solutions to Inventory
Inventory Solution-1
Problem 17-18, p. 552
The table below shows sales, cost of sales, and inventory data for Aladdin Products Supply Inc., a
wholesale distributor of cleaning supplies. All amounts are in the thousands.
2012
Sales
2011
2010
2009
$23.2
$21.7
$19.6
$17.4
17.1
16.8
15.2
13.5
Beginning inventory
2.3
2.1
1.9
1.5
Ending inventory
2.9
2.3
2.1
1.9
Cost of Sales
REQUIRED:
a. Calculate the following ratios:
1)
Gross margin as a percentage of sales
2)
Inventory turnover
b. List several logical causes of the changes in the two ratios.
c. Assume that $500,000 is considered material for audit planning purposes for 2012. Could any of the
fluctuations in the computed ratios indicate a possible material misstatement? Demonstrate this by
performing a sensitivity analysis.
d. What should the auditor do to determine the actual cause of the changes?
Inventory Solution-2
Solution Problem 19-20
Gross margin %
Inventory turnover
a.
•
•
•
•
•
b.
•
•
•
2012
26.3%
6.6
2011
22.6%
7.6
2010
22.4%
7.6
2009
22.4%
7.9
Logical causes of the changes in the gross margin as a percent of sales include:
Selling prices were raised without a corresponding increase in cost of sales.
The method of accounting for inventory was changed, causing a higher ending inventory (more
expenses absorbed into inventory) and lower cost of sales.
Inventory cutoff was improper, causing sales to be recorded without the corresponding entry to cost
of sales.
The product mix of the company changed. More high markup items were sold than in previous
years.
An improper journal entry was recorded that adjusted the gross margin upwards.
Logical causes of the changes in the inventory turnover include:
The increased selling prices that caused the gross margin percent to increase, reduced demand for
the product, and decreased the inventory turnover.
The company is building its inventory supply in anticipation of increased sales in the future.
The company’s inventory contains obsolete or unsalable merchandise that is affecting the turnover
rate.
Inventory Solution-3
c.
26.3%  22.6% = 3.7% increase of gross margin %
3.7% X sales of $23.2 million = $858,000 potential misstatement of sales
$17.1 million (2010 COGS)/(7.6 (2011) inventory turnover = $2.25 million
$ 2.9 million  2.25 million = $650,000 potential misstatement of inventory
Both calculations indicate a potential misstatement exceeding $500,000.
d. The auditor should discuss the two changes with the client and obtain a reasonable
explanation for them. He or she should then perform appropriate procedures to verify the
validity of the explanation. Ultimately, the auditor must be confident the change does not
result in a misstatement in the financial statements.
Inventory Solution-4
Problem 17-16, p. 551
Items 1 through 8 are selected questions typically found in questionnaires used by auditors to obtain an
understanding of internal controls in the inventory and distribution cycle. In using the questionnaires for a particular client,
a ‘yes’ response to a question indicates a possible internal control, whereas a ‘no’ response indicates a potential
weakness.
1. Does the receiving department prepare prenumbered receiving reports and account for the numbers periodically for
all inventory received, showing the description and quantity of materials?
2. Is all inventory stored under the control of a custodian in areas where access is limited?
3. Are all shipments to customers authorized by prenumbered shipping documents?
4. Is a detailed perpetual inventory master file maintained for raw materials inventory?
5. Are physical inventory counts made by someone other than storekeepers and those responsible for maintaining the
perpetual inventory master file?
6. Are standard cost records used for raw materials, direct labour, and manufacturing overhead?
7. Is there a stated policy with specific criteria for writing off obsolete or slow moving inventory?
8. Is the clerical accuracy of the final inventory compilation checked by a person independent of those responsible for
preparing it?
a.
b.
c.
d.
REQUIRED:
For each of the preceding questions, state the purpose of the internal control.
For each internal control, list a test of controls to test its effectiveness.
For each of the preceding questions, identify the nature of the potential financial misstatement(s) if the control is
not in effect.
For each of the potential misstatements in part (c), list a substantive audit procedure to determine whether a
material misstatement exists.
Inventory Solution-5
Solution to 17-16
b. Test of Control to Test
Effectiveness
Verify numerical sequence of
receiving reports and observe
matching invoices received from
vendors.
c. Potential Financial Misstatement d. Substantive Audit Procedure
Understatement of inventory or
payment for goods received.
Trace quantity and description on
vendor’s invoice to receiving report.
2. To minimize theft or unrecorded
disbursement of inventory.
(Occurrence)
Discussion with client and
observation.
Overstatement of inventory.
Compare physical count to perpetual
records.
3. To ensure inventory shipments
are recorded as sales.
(completeness)
Verify numerical sequence of
shipping orders.
Understatement of sales.
Overstatement of inventory.
Trace quantity and description on
bills of lading to attached shipping
orders.
4. For accuracy and current record
of inventory. (Accuracy)
Examine receiving and requisition
documents, and observe
maintenance of perpetual records.
Misstatement of inventory.
Compare physical count to perpetual
inventory record.
5. To ensure physical inventory
counts are accurate. (Accuracy,
existence, and completeness)
Observation and discussion with
client.
Misstatement of inventory.
Compare physical count to perpetual
inventory record.
6. To assure reasonable costs are
used for inventory and cost of
goods sold. (Accuracy)
Review procedures for determining
standard costs.
Misstatement of income and/or
inventory.
Trace costs from supporting
documents to development of
standards.
7. To ensure obsolete goods are
classified as such. (Accuracy)
Discussion with client.
Overstatement of inventory.
Analytical tests of inventory.
8. To make sure inventory
compilation is accurate. (Accuracy)
Observation and discussion with
client.
Misstatement of inventory.
Reperform clerical tests of inventory
compilation.
a. Purpose of Internal Control
1. To ensure inventory is recorded
when received and that payments
made are for goods received, and
quantities and descriptions are
accurate. (Completeness, accuracy,
and occurrence)
Inventory Solution-6
Problem 19-22, p. 664, Canadian 11th. Edition
You are testing the summarization and cost of raw materials and purchased part
inventories as part of the audit of Rubber Products and Supply Corp. There are 2,000
inventory items with a total recorded value of $648,500.
Your audit will compare recorded descriptions and counts with the final inventory
listing, compare unit costs with vendors’ invoices, and extend unit costs times quantity. A
misstatement in any of those is defined as a difference. You plan to use monetary unit
sampling.
You make the following decisions about the audit of inventory:
Tolerable misstatement (same as for upper as for lower)
Average percent of error assumption - overstatements
Average percent of error assumption - understatements
$24,000
For items not selected
in the sample
50%
100%
Acceptable risk of incorrect acceptance
5%
Estimated error rate in the population (EPER used to calculate sample size)
0.5
Inventory Solution-7
REQUIRED:
a. What are the advantages of using monetary unit sampling in this situation?
b. What is the sample size necessary to achieve your audit objectives using monetary unit sampling?
c. Disregarding your answer to part (b), assume that a sample of 125 items is selected and that the
following differences between book and audited values are identified (understatements are in
parentheses). The book or recorded amounts are also shown.
d.
Item No.
Difference
Book Amount
1
$19
$700
2
11
136
3
(19)
820
4
40
250
5
90
300
6
38
210
7
(90)
8
70
300
9
(85)
950
Total
$74
2,150
For each of the other 116 items in the sample, there was no difference between book and audited
values.
Based on this sample, calculate the adjusted overstatement and understatement error bounds.
Are the book values misstated?
Inventory Solution-8
Solution Problem 19-22 page 664
a. There are two potential advantages to using monetary unit sampling in this situation:
•
If few errors are found, MUS provides a statistically reliable result.
•
Dollar impact of errors can be quantified statistically.
b.
Calculating the Allowable percent misstatement bound or TER
A simple calculation as follows:
NOTE: TER = (Materiality/Average percent of misstatement assumption)/Population value
Note that a lower average percent of misstatement gives a higher TER. This makes sense since the amount
of misstatement is lower. This will thus require a smaller sample size.
Thus for Upper Bound:
(24,000/0.5)/648,500 = 0.074
For Lower Bound:
(24,000/1.00)/648,500 = 0.037
Allowable percent misstatement bound (TER)
Required sample size from the attributes table—5 percent risk
of incorrect from table on Slide 14
7.4%
62
3.7%
140
Note that 62 and 140 sample sizes have to be interpolated from the
table on slide 14
Inventory Solution-9
c. Misstatements
Item Recorded Accounts
Misstatement Misstatement Divided
Receivable Amount
by Recorded Amount
1.
$700
$19
0.027
2.
136
11
0.081
3.
820
(19)
(0.023)
4.
250
40
0.16
5.
300
90
0.3
6.
210
38
0.181
7.
2,150
(90)
(0.042)
8.
300
70
0.233
9.
950
(85)
(0.089)
Percentage Misstatement Bounds
Read along the row of 125 sample size on the first table (5% ARACR)
Number of
Upper Precision
Misstatements Limit from Table
13-8
0
0.024
1
0.037
2
0.049
3
0.061
4
0.072
5
0.082
6
0.093
Increase in Precision Limit
Resulting from Each
Layer (Layers)
0.024
0.013
0.012
0.012
0.011
0.010
0.011
Inventory Solution-10
* Note the descending order
of the actual misstatements
Determination of Initial Upper and Lower Misstatement Bounds
Overstatements
Number of Misstatements
Upper
Precision
Limit Portion
0
1
2
From table on slide 16
3
4
5
6
Upper precision limit
Initial misstatement bound
Understatements
Number of Misstatements
0.024
0.013
0.012
0.012
0.011
0.010
0.011
0.093
$648,500
648,500
648,500
648,500
648,500
648,500
648,500
Unit
Misstatement
Assumption
*
0.500
0.300
0.233
0.181
0.160
0.081
0.027
Misstatement
Bound Portion
(Columns
2 X 3 X 4)
$7,783
2,529
1,813
1,409
1,141
525
193
$15,392
Upper
Precision
Limit Portion
0
1
From table on slide 16
2
3
Lower precision limit
Initial misstatement bound
Recorded
Value
0.024
0.013
0.012
0.012
0.061
Recorded
Value
648,500
648,500
648,500
648,500
Unit
Misstatement
Assumption
*
1.000
0.089
0.042
0.023
Misstatement
Bound Portion
(Columns
2 X 3 X 4)
$15,564
750
327
179
$16,820
Inventory Solution-11
Determination of Adjusted Misstatement Bounds
Number of
Misstatements
Initial overstatement
bound
Understatement
misstatements
1
2
3
Sum
Adjusted overstatement
bound
Unit
Misstatement
Assumption
0.154 * (648,500/125) = 799
Sample
Size
Recorded
Population
Point
Estimate
Bounds
$15,392
0.089
0.042
0.023
0.154
125
$648,500
$799
(799)
$14,593
0.982 * (648,500/125) = 5095
Number of
Misstatements
Initial understatement
bound
Overstatement
misstatements
1
2
3
4
5
6
Sum
Adjusted understatement
bound
Unit
Misstatement
Assumption
Sample
Size
Recorded
Population
Point
Estimate
Bounds
$16,820
0.300
0.233
0.181
0.160
0.081
0.027
0.982
125
$648,500
$5,095
(5,095)
$11,725
Inventory Solution-12
d. Both the adjusted overstatement misstatement bound ($14,593) and the adjusted understatement misstatement bound ($11,725)
are less than the tolerable misstatement ($24,000) so you would conclude that the book value is not misstated.
Inventory Solution-13
Estimated Population
Exception Rate ( percent
misstatement assumption)
Tolerable Exception Rate (TER)
(in percentage)
2
3
4
5
6
7
8
9
10
15
20
29
46
46
46
46
46
46
46
46
61
61
61
61
61
76
76
89
116
179
19
30
30
30
30
30
30
30
30
30
30
30
30
30
40
40
40
40
50
68
14
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
30
30
37
5-Percent ARACR
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
5.00
6.00
7.00
149
236
.
.
.
.
.
.
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99
157
157
208
.
.
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.
74
117
117
117
156
156
192
227
.
.
.
.
.
.
.
.
.
.
.
.
59
93
93
93
93
124
124
153
181
208
.
.
.
.
.
.
.
.
.
.
49
78
78
78
78
78
103
103
127
127
150
173
195
.
.
.
.
.
.
.
42
66
66
66
66
66
66
88
88
88
109
109
129
148
167
185
.
.
.
.
36
58
58
58
58
58
58
77
77
77
77
95
95
112
112
129
146
.
.
.
32
51
51
51
51
51
51
51
68
68
68
68
84
84
84
100
100
158
.
.
.
Inventory Solution-14
TER
EPER
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.50
5.00
5.50
6.00
7.00
7.50
8.00
8.50
2
3
4
5
6
7
8
9
10
15
20
10–Percent ARACR
114
194
194
265
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76
129
129
129
176
221
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57
96
96
96
96
132
132
166
198
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.
45
77
77
77
77
77
105
105
132
132
158
209
.
.
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.
38
64
64
64
64
64
64
88
88
88
110
132
132
153
194
.
.
.
.
.
.
.
.
.
.
32
55
55
55
55
55
55
55
75
75
75
94
94
113
113
131
149
218
.
.
.
.
.
.
.
28
48
48
48
48
48
48
48
48
65
65
65
65
82
82
98
98
130
160
.
.
.
.
.
.
25
42
42
42
42
42
42
42
42
42
58
58
58
58
73
73
73
87
115
142
182
.
.
.
.
22
38
38
38
38
38
38
38
38
38
38
52
52
52
52
52
65
65
78
103
116
199
15
11
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
25
18
34
18
34
18
34
18
45
25
52
25
.
52
25
.
60
25
. Inventory
68 Solution-15
32
ACTUAL NUMBER OF DEVIATIONS FOUND
SAMPLE SIZE
0
25
30
35
40
45
50
55
60
65
70
75
80
90
100
125
150
200
11.3
9.5
8.2
7.2
6.4
5.8
5.3
4.9
4.5
4.2
3.9
3.7
3.3
3.0
2.4
2.0
1.5
1
17.6
14.9
12.9
11.3
10.1
9.1
8.3
7.7
7.1
6.6
6.2
5.8
5.2
4.7
3.7
3.1
2.3
2
3
4
5
6
7
8
9
5 PERCENT RISK OF OVER RELIANCE
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19.5
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16.9
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14.9 18.3
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13.3 16.3 19.2
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12.1 14.8 17.4 19.9
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11.0 13.5 15.9 18.1
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10.1 12.4 14.6 16.7 18.8
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.
9.4 11.5 13.5 15.5 17.4 19.3
.
8.7 10.7 12.6 14.4 16.2 18.0 19.7
8.2
7.7
6.8
6.2
4.9
4.1
3.1
10.0
9.4
8.4
7.6
6.1
5.1
3.8
11.8
11.1
9.9
8.9
7.2
6.0
4.5
13.5
12.7
11.3
10.2
8.2
6.9
5.2
15.2
14.3
12.7
11.5
9.3
7.7
5.8
16.9
15.8
14.1
12.7
10.3
8.6
6.5
18.4
17.3
15.5
14.0
11.3
9.4
7.1
20.0
18.8
16.8
15.2
12.2
10.2
7.7
10
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18.1
16.4
13.2
11.0
8.3
Inventory Solution-16
Sample size
ACTUAL NUMBER OF DEVIATIONS FOUND
0
1
2
3
4
5
6
7
8
9
10
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17.9
15.7
14.0
12.7
10.6
8.0
6.4
19.5
17.2
15.3
13.8
11.6
8.7
7.0
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10 PERCENT RISK OF OVER RELIANCE
20
25
30
35
40
45
50
55
60
70
80
90
100
120
160
200
10.9
8.8
7.4
6.4
5.6
5.0
4.5
4.1
3.8
3.2
2.8
2.5
2.3
1.9
1.4
1.1
18.1
14.7
12.4
10.7
9.4
8.4
7.6
6.9
6.3
5.4
4.8
4.3
3.8
3.2
2.4
1.9
.
19.9
16.8
14.5
12.8
11.4
10.3
9.4
8.6
7.4
6.5
5.8
5.2
4.4
3.3
2.6
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18.1
15.9
14.2
12.9
11.7
10.8
9.3
8.3
7.3
6.6
5.5
4.1
3.3
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19.0
17.0
15.4
14.0
12.9
11.1
9.7
8.7
7.8
6.6
4.9
4.0
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19.6
17.8
16.2
14.9
12.8
11.3
10.1
9.1
7.6
5.7
4.6
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18.4
16.9
14.6
12.8
11.4
10.3
8.6
6.5
5.2
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18.8
16.2
14.3
12.7
11.5
9.6
7.2
5.8
18.6
16.6
15.0
12.5
9.5
7.6
Inventory Solution-17