17–31 (continued)
b. Determination of ARIA – Note that there are many ways to
estimate ARIA. One method is as follows:
ARIA = AAR / (IR x CR x APR)
Expected misstatement as a percent of tolerable misstatement:
Tolerable misstatement as a percent:
= TM / Population
Confidence factor
(15% ARIA, 0.30 expected misstatement 3.41
c. The same ARIA must be used for the entire combined test. It would
Expected misstatement as a percent of tolerable misstatement:
Tolerable misstatement as a percent:
= TM / Population
Confidence factor
(10% ARIA , 0.30 expected misstatement 4.33
Tolerable misstatement
as percentage of population ÷ .02
= Sample size 217
17–20
17–31 (continued)
It may seem counterintuitive that the sample for the combined test
is larger than the sum of the sample sizes for the individual tests.
which would decrease the sample size.
d. The generation of random numbers using Excel (P1731.xls)
to obtain the sample of 38 accounts receivable for confirmation
would be obtained as follows:
entered directly onto the spreadsheet, or can be selected from the
formula tab (math & trig functions). It may be necessary to add the
analysis tool pack to access the RANDBETWEEN function.
a. This nonstatistical (i.e., nonprobabilistic or judgmental) sample is
considered to be an unstratified sample since all 23 items over
$10,000 were examined 100%. The remaining 7,297 items were
tested with a sample of 77 items. Although this was not a probabilistic
follows:
Items over $10,000:
Projected Misstatement = Audited value – Recorded value
= 432,000 – 465,000
= (33,000) overstatement
17–32 (continued)
Items under $10,000 – average misstatement amount method:
Projected Misstatement = Average sample misstatement
x population size
Items under $10,000 – proportional amount method:
Projected Misstatement = Sample misstatement ratio
x population book value
Where sample misstatements are:
ITEM
AUDITED
VALUE
RECORDED
VALUE
MISSTATEMENT
12
19
33
35
51
59
74
Totals
4,820
385
250
3,875
1,825
3,780
0
14,935
5,120
485
1,250
3,975
1,850
4,200
2,405
19,285
(300)
(100)
(1,000)
(100)
(25)
(420)
(2,405)
(4,350)
Total misstatement is either:
(33,000) + (412,207) = (445,207) overstatement
or
(33,000) + (121,635) = (154,635) overstatement
17–22
17–32 (continued)
course of action would be to ask the client to make a study of their
records for all population items to identify more accurately the
misstatements that exist and correct them.
evaluated as follows:
Misstatement taintings:
ITEM
AUDITED
VALUE
MISSTATEMENT
PERCENT
12
19
33
35
51
59
74
4,820
385
250
3,875
1,825
3,780
0
(300)
(100)
(1,000)
(100)
(25)
(420)
(2,405)
(.058)
(.206)
(.800)
(.025)
(.014)
(.100)
(1.000)
$29,805 ([$2,760,000 – 465,000)]/77).
17–32 (continued)
(a)
TAINTING
(b)
SAMPLING
INTERVAL
( c = a x b)
PROJECTED
MISSTATE–
MENT
(d)
INCREMENTAL
CHANGE IN
CONFIDENCE
FACTOR
(e = c x d)
PROJECTED
MISSTATEMENT
PLUS
INCREMENTAL
ALLOWANCE FOR
SAMPLING RISK
1.00
.800
.206
.100
.058
.025
.014
29,805
29,805
29,805
29,805
29,805
29,805
29,805
29,805
23,844
6,140
2,981
1,729
745
417
1.75
1.55
1.46
1.40
1.36
1.33
1.30
52,159
36,958
8,964
‘4,713
2,351
991
542
Totals
65,661
106,678
Add basic precisions
29,805 x 3.00
89,415
Upper misstatement bound
196,093
Upper misstatement bound from sample 196,093
Misstatement of 100% items 33,000
Total overstatement bound 229,093
differences being due to rounding.
17–33 ACL Problem
a. The total amount of the outstanding invoices is $893,619.03.
sampling interval is $19,935.06.
b. If materiality is increased to $60,000 and expected errors are
decreased to $1,000, the revised sample size is 35 and the revised
sampling interval is $25,290.04.
and invoice amount are included.
17–24
17–33 ACL Problem (continued)
invoice number
customer
number
invoice
date
invoice
amount
173640036989
0260797
2/11/2014
25011.4
173640037011
0242798
2/10/2014
13753.12
173640037536
0244434
4/22/2014
3429.66
173640037593
0252175
4/30/2014
17004.23
173640037693
0236320
5/3/2014
11115.81
173640038411
0243854
6/15/2014
27173.13
173640038744
0237175
7/1/2014
6052.44
173640038911
0249158
7/12/2014
28821.31
173640039362
0259570
8/10/2014
13519.56
173640039521
0235160
8/24/2014
9587.28
173640039647
0253578
8/26/2014
15741.48
173640040049
0253788
9/17/2014
3036.8
173640040153
0252448
10/13/2014
10972.27
173640040293
0248604
10/12/2014
14133.79
173640040377
0264539
10/12/2014
18666.34
173640040415
0247433
10/18/2014
20320.17
173640040503
0251970
10/21/2014
5750.41
173640040573
0236508
11/5/2014
3980.42
173640040605
0257213
10/28/2014
17143.72
173640040631
0248346
10/29/2014
6294.89
173640040664
0261976
11/9/2014
20569.66
173640040680
0252465
11/9/2014
2431.97
173640040720
0240055
11/17/2014
6661.59
173640040731
0259568
11/19/2014
15432.77
173640040772
0258661
12/3/2014
15356.38
173640040782
0234884
12/2/2014
15545.3
173640040797
0238961
12/3/2014
24142.46
173640040802
0257582
12/16/2014
6724.86
173640040816
0243802
12/3/2014
15574.82
173640040817
0258807
12/1/2014
14932.8
173640040821
0245569
12/7/2014
28542.97
173640040822
0250585
12/15/2014
27191.46
173640040832
0244664
12/13/2014
21167.14
173640040838
0262871
12/6/2014
6107.62
173640040852
0234230
12/7/2014
4635.68
173640040864
0242115
12/14/2014
15486.06
173640040875
0236705
12/24/2014
24763.72
173640040877
0251255
12/23/2014
6163.95
173640040901
0263666
12/31/2014
8396.13
173640040911
0250021
12/24/2014
25454.3
173640040912
0260018
12/29/2014
16846.11
173640040920
0251367
12/27/2014
19521.23
17–25
17–33 ACL Problem (continued)
than the sampling interval.
e. The largest invoice selected for testing is $28,821.31. There are
11 invoices in the sample that are larger than the sampling interval
of $19,935.06. There are also 11 invoices larger than the sampling
the sample.