1. Problem DC 10-1, Page 547 (Original Problem)
When Marge Simpson, PA, audited the Candle Company inventory, a random sample of inventory types was chosen for physical observation and price testing. The sample size was 80 different types of candles and candle-making inventory. The entire inventory contained 1,740 types, and the amount in the inventory control account was $166,000. Simpson had already decided that a misstatement of as much as $6,000 in the account would not be material. The audit work revealed the following eight errors in the sample of 80.
Book Value
(a)
Audit value
Error Amount
(b)
% Misstatement
b/a
$600.00
$622.00
$(22.00)
(0.037)
15.50
14.50
1.00
0.065
65.25
31.50
33.75
0.517
83.44
53.45
29.99
0.359
16.78
15.63
1.15
0.069
78.33
12.50
65.83
0.840
13.33
14.22
(0.89)
(0.067)
93.87
39.87
54.00
0.575
$966.50
$803.67
$162.83
Percent misstatement for the whole sample:
162.83/ = 17%. Could use 20% for Slide 51

2. Assume the sample was chosen using Monetary Unit Sampling, and the sampling risk is 10%. Simpson also assumes that the Misstatement Assumption for zero misstatements is 50% for both over and under misstatements. Is the inventory materially misstated?
Total Population =
166,000.00
Sample Size = 80
ARACR =
10.00%
Upper Misstatement Unit Error Assumption
50.00%
Lower Misstatement Unit Error Assumption
Materiality
6,000
This part of the population is not in the sample. Thus zero misstatements have been found here because these items have not been examined.
Sample
The misstatements of the sample, as percentages, are known . See previous slide 29.
The misstatements of the remaining part of the population are not known. Thus a misstatement assumption has to be made. E.g. they are 50% misstated. See next slide.

3. Could use 20% based on actual deviations. But still would be material
Overstatements
Number of Misstatements
(1)
Upper Precision Limit Portion
(2)
Recorded
Value
(3)
Misstatement Unit Error Assumption (4)
Bound Portion
2x3x4
Overstatements
0.029
166,000
0.500
$2,407 1
0.019
0.840
2649 2
0.018
0.575
1718 3
0.016
0.517
1373 4
0.359
954 5
0.015
0.069
172 6
0.065
162
Upper Precision Limit
0.128
Initial Misstatement Bound
$9,435

4. ACTUAL NUMBER OF DEVIATIONS FOUND
Sample size
ACTUAL NUMBER OF DEVIATIONS FOUND 1 2 3 4 5 6 7 8 9 10
10 PERCENT RISK OF OVER RELIANCE (RIA or Beta Risk) 20
10.9
18.1
24.5
30.5
36.1
41.5
46.8
51.9
56.8
61.6
66.2 25
8.8
14.7
20.0
24.9
29.5
34.0
38.4
42.6
50.8
54.8 30
7.4
12.4
16.8
21.0
28.8
32.5
36.2
39.7
43.2
46.7 35
6.4
10.7
14.5
18.2
21.6
28.2
31.4
34.5
37.6
40.6 40
5.6
9.4
12.8
16.0
19.0
22.0
27.7
33.2
35.9 45
5.0
8.4
11.4
14.3
17.0
19.7
22.3
24.8
27.3
29.8
32.2 50
4.6
7.6
10.3
12.9
15.4
17.8
20.2
22.5
24.7
27.0
29.2 55
4.2
6.9
11.8
14.1
16.3
18.4
20.5
22.6
24.6
26.7 60
3.8
8.7
10.8
15.0
16.9
18.9
20.8
22.7 65
3.5
5.9
8.0
10.0
12.0
13.9
15.7
17.5
19.3
22.8 70
3.3
5.5
7.5
9.3
11.1
14.6
18.0
19.6
21.2 75
3.1
5.1
7.0
10.4
12.1
13.7
15.2
18.3
19.8 80
2.9
4.8
6.6
8.2
9.8
11.3
15.8
17.2
18.7 90
2.6
4.3
7.3
10.1
11.5
16.7
100
2.3
3.9
5.3
7.9
9.1
12.7
125
1.9
6.3
8.3
10.2
11.2
150
1.6
3.6
4.4
6.1
7.8
8.6
200
1.2
2.0
2.7
3.4
4.0
6.5
7.1
300
0.8
1.3
1.8
4.7
400
0.6
1.0
1.4
1.7
2.4
3.0
500
0.5
1.1
2.1
1.9
1.8
1.6
1.6
1.5
1.9
The Upper and Lower Bounds must be determined. What do these mean?
Obtain the Precision Limits from this table – 10% RIA

5. Understatements Number of Misstatements (1)
Upper Precision Limit Portion
(2)
Recorded
Value
(3)
Misstatement Unit Error Assumption (4)
Bound Portion
2x3x4
Understatements
0.029
166,000
0.500
$2,407 1
0.019
0.067
211 2
0.018
0.037
111
Upper Precision Limit
0.066
Initial Misstatement Bound
$2,729

6. Offsetting Adjustments
Number of Misstatements
Misstatement Unit Error Assumption
(a)
Sample Size
(b)
Recorded Population
(c)
Point Estimate
a(c/b)
Bounds
Initial Overstatement Bound
$9,435
Understatement Misstatements 1
0.067 80
166,000
139
(139) 2
0.037 77
(77)
Total
0.104
216
(216)
Adjusted Overstatement Bound
9,219
Initial Understatement Bound
2,729
Overstatement Misstatements
0.840
1743
(1743)
0.575
1193
(1193) 3
0.517
1073
(1073) 4
0.359
745
(745) 5
0.069
143
(143) 6
0.065
135
(135)
2.425
5032
(5032)
Adjusted Understatement Bound
-2303
As the Upper Bound is greater than the materiality of $6,000, there may be a material misstatement

7. Tolerable misstatement
The Decision Rule
Reject
Tolerable misstatement
($6,000)
$6,000
$2,303
LMB
$9,219
UMB
Problem
Since materiality is $6,000, there may be material misstatement.

8. Problem EP 10-5, Page 546 – Point Estimate
Assume the results shown below were obtained from a stratified sample. Required : Apply the ratio calculation method (Point Estimate) to each stratum to calculate the projected likely misstatement (PLM). What is the PLM for the entire sample?
SAMPLE RESULTS
Stratum
Population Size
Recorded Amount
Sample
Misstatement Amount
PLM 1 6
$100,000
$(600)
(600) 2 80
75,068 23
21,700
(274)
(948) 3
168
75,008 22
9,476
(66)
(522) 4
342
75,412
4,692
(88)
(1,414) 5
910
74,512
1,973
869
Total
1,506
$400,000 96
$137,841
$(1,005)
(2,615)
1: (600)/100,000 x 100,000 = (600)
2: (274)/21,700 x 75,068 = (948)
3: (66)/9,476 x 75,008 = (522)
4: (88)/4,692 x 75,412 = (1,414)
5: 23/1,973 x 74,512 = 869
Cannot do this:
(1,005)/137,841 x 400,000 = (2916)
NOT CORRECT!

9. Problem DC 10-1, Page 547 – The Difference Method
Sample size is 80
Population consists of 1,740 types
Book Value
(a)
Audit value
Error Amount
(b)
% Misstatement
b/a
$600.00
$622.00
$(22.00)
(0.037)
15.50
14.50
1.00
0.065
65.25
31.50
33.75
0.517
83.44
53.45
29.99
0.359
16.78
15.63
1.15
0.069
78.33
12.50
65.83
0.840
13.33
14.22
(0.89)
(0.067)
93.87
39.87
54.00
0.575
$966.50
$803.67
$162.83
Projected likely misstatement = ((162.83)/80)X 1740 = ( ).
Remember that TM = $6,000
This is a little over half of what is considered material (tolerable) and would likely be acceptable