1Chapter 15 Audit Sampling for Tests of Controls and Substantive Tests of Transactions
Review Questions
A representative representative sample sample is one in which which the character characteristics istics of interest interest for 15-1 the sample are approximately approximately the same as for the population (that is, the sample accurately represents the total population). If the population contains significant misstatements, misstatements, but the sample is practically practically free of misstatements, misstatements, the sample is nonrepresentative, which is likely to result in an improper audit decision. he auditor can never know for sure whether he or she has a representative sample because the entire population is ordinarily not tested, but certain things, such as the use of random selection, can increase the likelihood of a representative sample. !tatistical !tatistical sampling is the use of mathematical measurement measurement techni"ues 15-2 to calculate formal statistical results. he auditor therefore "uantifies sampling risk when statistical sampling is used. In nonstatistical nonstatistical sampling, the auditor does not "uantify sampling risk. Instead, conclusions are reached about populations on a more #udgmental basis. $or both statistical and nonstatistical methods, the three main parts are% 1. '. .
&lan the sample !ele !elect ct the the sam sampl ple e and and perf perfor orm m the the test tests s valuate th the re results
In replacement sampling, an element in the population can be included 15- in the sample more than once if the random number corresponding to that element is selected more than once. In nonreplacement sampling, an element can be included only once. If the random number corresponding corresponding to an element is selected more than once, it is simply treated as a discard the second time. Although both selection approaches approaches are consistent consistent with sound statistical theory, auditors rarely use replacement sampling* it seems more intuitively satisfying to auditors to include an item only once. A simple random sample is one in which every possible combination combination of 15-! elements in the population has an e"ual chance of selection. wo methods of simple random selection are use of a random number table, and use of the computer to generate random numbers. Auditors Auditors most often use the computer to generate random random numbers because it saves time, reduces the likelihood of error, and provides automatic documentation of the sample selected.
1+1
In systematic sampling, the auditor calculates an interval and then 15-5 methodically selects the items for the sample based on the si-e of the interval. he interval is set by dividing the population si-e by the number of sample items desired. o select + numbers from a population of 1,+/, the auditor divides + into 1,+/ and gets an interval of +/. 0e or she then selects a random number between / and 2. Assume the auditor chooses 1. he first item is the number 1. he next is 3, then 11, 13, and so on. he advantage of systematic sampling is its ease of use. In most populations a systematic sample can be drawn "uickly, the approach automatically puts the numbers in se"uential order and documentation is easy. A ma#or problem with the use of systematic systemat ic sampling samplin g is i s the th e possibili p ossibility ty of bias. 4ecause of the way systematic samples are selected, once the first item in the sample is selected, other items are chosen automatically. his causes no problems if the characteristics of interest, such as control deviations, are distributed randomly throughout throughout the population* population* however, in many cases they are not. If all items of a certain type are processed processed at certain times of the month or with the use of certain document numbers, a systematically drawn sample has a higher likelihood of failing to obtain a representative sample. his shortcoming is sufficiently serious that some 5&A firms prohibit the use of systematic sampling. he purpose of using nonstatistical sampling for tests of controls and 15-" substantive tests of transactions is to estimate the proportion of items in a population containing a characteristic or attribute of interest. he auditor is ordinarily interested in determining internal control deviations or monetary misstatements for tests of controls and substantive tests of transactions. A block sample is the selection of several items in se"uence. se"uence. 6nce the 15-# first first item item in the the bloc block k is sele select cted ed,, the the rema remain inde derr of the the bloc block k is chos chosen en automatically. hus, to select + blocks of '/ sales invoices, one would select one invoice and the block would be that invoice plus the next 12 entries. his procedure would be repeated other times.
1+'
15-$
he terms below are defined as follows% T%R&
'%()*)T)+*
a. Acce Accept ptab able le risk risk of assessing control risk too low (A7A57)
he risk the auditor is willing to take of accepting a control as effective or a rate of monetary misstatements as tolerable, when the true population exception rate is greater than the tolerable exception rate.
b. 5omp 5omput uted ed upp upper er exception rate (587)
he highest estimated exception rate in the population at a given A7A57.
c. sti stima mate ted d popu popula lati tion on exception rate (&7)
he exception rate the auditor expects to find in the population before testing begins. It is necessary to plan the appropriate sample si-e.
d. !ampl !ample e excep exceptio tion n rate rate (!7)
he actual rate of exception discovered in the sample. It is calculated by dividing the actual number of exceptions in the sample by the sample si-e.
e. olera olerable ble excep exceptio tion n rate rate (7)
he exception rate the auditor will permit in the population and still be willing to use the assessed control risk and9or the amount of monetary misstatements in the transactions established during planning.
he sampling unit is the population item from which the auditor selects 15-, sample items. he ma#or consideration in defining the sampling unit is making it consistent with the ob#ectives of the audit tests. hus, the definition of the population and the planned audit procedures usually dictate the appropriate sampling unit. he sampling unit for verifying the occurrence of recorded sales would be the entries in the sales #ournal since this is the document the auditor wishes to validate. he sampling unit for testing the possibility of omitted sales is the shipping document from which sales are recorded because the failure to bill a shipment is the exception condition of interest to the auditor. 15-1 he tolerable exception rate (7) represents the exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and9or the amount of monetary misstatements in the transactions established during planning. 7 is determined by choice of the auditor on the basis of his or her professional #udgment. he computed upper exception rate (587) is the highest estimated exception rate in the population, at a given A7A57. $or nonstatistical sampling, 587 is determined by adding an estimate of sampling error to the !7 (sample exception rate). $or statistical sampling, 587 is determined by using a statistical sampling table after the auditor has completed the audit testing and therefore knows the number of exceptions in the sample.
1+
15-11 !ampling error is an inherent part of sampling that results from testing less than the entire population. !ampling error simply means that the sample is not perfectly representative of the entire population. :onsampling error occurs when audit tests do not uncover errors that exist in the sample. :onsampling error can result from%
1. '.
he he aud audito itor;s r;s failu failure re to recog recognini-e e exce excepti ption ons, s, or or Inapp Inappro ropri priat ate e or or ine ineff ffect ective ive audit audit proce procedu dures res..
here are two ways to reduce sampling risk% 1. '.
Increase sa sample si si-e. 8se 8se an appro appropr pria iate te meth method od of sele select ctin ing g sampl sample e items items from from the the population.
5areful design of audit procedures and proper supervision and review are ways to reduce nonsampling risk. attribute is the definition definition of the characteristic characteristic being tested and the 15-12 An attribute exception conditions whenever audit sampling is used. he attributes of interest are determined directly from the audit program. characteristic being tested for in a population. population. An 15-1 An attribute is the characteristic exception exception occurs when the attribute attribute being tested for is absent. he exception for the audit procedure, the duplicate sales invoice has been initialed indicating the performance of internal verification, is the lack of initials on duplicate sales invoices. 15-1! olerable exception rate (7) is the result of an auditor;s #udgment. he suitable 7 is a "uestion of materiality and is therefore affected by both the definition and the importance of the attribute in the audit plan. It represents the exception rate that the auditor will permit in the population and still be willing to conclude that the control is operating effectively and9or the amount of monetary misstatements in the transactions established during planning is acceptable. he sample si-e for a 7 of 3< would be smaller than that for a 7 of <, all other factors being e"ual. 15-15 he appropriate A7A57 is a decision the auditor must make using professional #udgment. he degree to which the auditor wishes to reduce assessed control risk below the maximum is the ma#or factor determining the auditor;s A7A57. he auditor will choose a smaller sample si-e for an A7A57 of 1/< than would be used if the risk were +<, all other factors being e"ual.
1+
15-1" he relationship between sample si-e and the four factors determining sample si-e are as follows%
a. b. c. d.
As the the A7A A7A57 57 incr increa eases ses,, the the re"ui re"uire red d sampl sample e si-e si-e decr decrea eases ses.. As the the popu populat lation ion si-e si-e incre increase ases, s, the the re"u re"uire ired d sampl sample e si-e si-e is is norma normally lly unchanged, or may increase slightly. As the the 7 7 incre increas ases es,, the the sampl sample e sisi-e e decr decreas eases. es. As the the & &7 7 increa increase ses, s, the the re"u re"uire ired d sampl sample e si-e si-e incre increase ases. s.
15-1# In this situation, the sample exception rate (!7) is <, the sample si-e is 1// and the A7A57 is +<. $rom the +< A7A57 table (able 1+2) then, the 587 is .3<. his means that the auditor can state with a +< risk of being wrong that the true population exception rate does not exceed .3<.
exceptions is the investigation investigation of individual individual exceptions exceptions to 15-1$ Analysis of exceptions determine the cause of the breakdown in internal control. !uch analysis is important because because by discove discovering ring the nature nature and causes causes of individ individual ual excepti exceptions ons,, the auditor can more effectively evaluate the effectiveness of internal control. he analysis attempts to tell the =why= and =how= of the exceptions after the auditor already knows how many and what types of exceptions have occurred. 15-1, >hen the 587 exceeds the 7, the auditor may do one or more of the following%
1.
'.
.
.
7evis 7evise e the the 7 7 or the the A7A A7A57 57.. his his alte altern rnati ative ve sho should uld be be follo followe wed d only when the auditor has concluded that the original specifications specifications were too conservative, and when he or she is willing to accept the risk associated with the higher specifications. xpan xpand d the samp sample le si-e si-e.. his his alter alternat native ive shou should ld be foll follow owed ed whe when n the auditor expects the additional benefits to exceed the additional costs. hat is, the auditor believes that the sample tested was not representative of the population and that exceptions are not expected in the expanded sample. 7evise 7evise ass assess essed ed contr control ol risk risk upw upward ard.. his his is like likely ly to incr increas ease e substantive procedures. 7evising assessed control risk may be done if 1 or ' is not practical and additional substantive procedures procedures are possible. >rit >rite e a lett letter er to mana manageme gement nt.. his his acti action on shou should ld be done done in con#unction con#unction with each of the three alternatives alternatives above. ?anagement should should always always be inform informed ed when when its intern internal al contro controls ls are not not operating operating effectively. If a deficiency in internal control is considered to be a significant deficiency in the design or operation of internal control, professional standards re"uire the auditor to communicate the significant deficiency to the audit committee or its e"uivalent in writing. If the client is a publicly traded company, the auditor must evaluate the deficiency to determine the impact on the auditor@s
1++
15-1, .continued/
report on internal control over financial reporting. If the deficiency deficiency is deemed to be a material weakness, the auditor@s report on internal control would contain an adverse opinion. 15-2 7andom (probabilistic) selection is a part of statistical sampling, but it is not, by itself, statistical measurement. o have statistical measurement, it is necessary to mathematically generali-e from the sample to the population. &robabilistic selection must be used if the sample is to be evaluated statistically, although it is also acceptable to use probabilistic selection with a nonstatistical evaluation. If nonprobabilistic selection is used, nonstatistical evaluation must be used. 15-21
he decisions the auditor must make in using attributes sampling are% >hat are the ob#ectives of the audit test Boes audit sampling apply >hat attributes are to be tested and what exception conditions are identified >hat is the population >hat is the sampling unit >hat should the 7 be >hat should the A7A57 be >hat is the &7 >hat generali-ations can be made from the sample to the population >hat are the causes of the individual exceptions Is the population acceptable In making the above decisions, the following should be considered%
he individual situation. ime and budget constraints. he availability of additional substantive procedures. he professional #udgment of the auditor.
&ultiple Choice Questions (rom C0A %aminations
15-22
a.
(1)
b.
()
c.
(')
d.
()
15-2
a.
(1)
b.
()
c.
()
d.
()
15-2!
a.
()
b.
()
c.
(')
1+3
'iscussion Questions and 0roblems
15-25
a.
SA&0)*3 4*)T
*4&%R)*3 S6ST%& (+R T7% 0+04AT)+*
%8C% S%%CT)+* (+R&4A
1. !ales in invoice
All in invoices numbered ///1 to 3'11
C7A:B4>:(1,3'11)
'. 4ill of lading
All bills of lading numbered '12'3 through 'D+11 (if a random number table is used, the leftmost digit E'F can be dropped)
C7A:B4>:('12'3, 'D+11)
. 5ustomer
A pair of random numbers, where the first random number is the page number (11/), and the second random number is the line number on the page (13/)
C7A:B4>:(1,1/)
A pair of random numbers, where the first random number is the page number (11D+), and the second random number is the invoice as counted down from the top of the page (1+)
C7A:B4>:(1,1D+)
. Gine Gine numbe numbers rs on the sales #ournal that that have a sales invoice recorded on them
1+
and C7A:B4>:(1,3/)
and C7A:B4>:(1,+)
15-25 .continued/
An example random sampling plan prepared prepared in xcel (&1+'+.xls) is available on the 5ompanion >ebsite. >ebsite. he command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu (math H trig) functions. It may be necessary to add the analysis tool pack to access the 7A:B4>: function. 6nce the formula is entered, it can be copied copied down down to selec selectt addit addition ional al rando random m numbe numbers. rs. >hen >hen a pair pair of rando random m numbers is re"uired, the formula for the first random number can be entered in the first column, and the formula for the second random number can be entered in the second column. b.
$irst $irst five five num numbe bers rs using using syste systema matic tic selec selectio tion% n%
SA&0)*3 4*)T
)*T%R9A
1. !ales invoice
1' (3'119+/)
'. 4ill of lading
1' ('D+11'12'3) C 3+D+9+/J
. 5ustomer
11 (+3 lines9+/)
RA*'+& START)*3 0+)*T
()RST 5 SA&0% )T%&S
3
''/11
&age 1, line KD
3 121 1+ 2 +3 ''/11 ''1 '''+ ''/ ''+2 0age 1 1 1 1 1
ine D 12 / 1 +'
8sing systematic selection, selection, the definition definition of the sampling unit for determining determining the selection interval for population is the total number of lines in the population. he he lengt length h of the the interv interval al is roun rounde ded d down down to ensure ensure that all line numb numbers ers selected are within the defined population.
1+D
15-2"
a.
o test test whet whethe herr shipm shipmen ents ts have have been been bille billed, d, a sampl sample e of ware wareho hous use e removal slips should be selected and examined to see if they have the proper sales invoice attached. he sampling unit will therefore be the warehouse removal slip.
b.
Attribut Attributes es sampling sampling method % Assuming the auditor is willing to accept a 7 of < at a 1/< A7A57, expecting no exceptions in the sample, the appropriate appropriate sample si-e would be 3, determined determined from able 1+D. Nonstatistical sampling method % here is no one right answer to this "uestion because the sample si-e is determined using professional #udgment. Bue to the relatively small 7 (<), the sample si-e should not be small. It will most likely be similar in si-e to the sample chosen by the statistical method.
c.
!yst !ystem emat atic ic samp sample le sele select ctio ion% n%
''D2
C
3
C
//
C
1D'+
C
&opu opulati latio on sisi-e e of of wa wareho rehous use e re remova movall sli slips ps (+'113D'). !ample si si-e us using st statistical sa sampling (s (students@ answers will vary if nonstatistical nonstatistical sampling was used in part b. Interval (' (''D293) ifif st statistical sa sampling is is us used (students@ answers will vary if nonstatistical sampling was used in part b). 7andom st starting po point.
!elect warehouse removal slip 1D'+ and every //th warehouse removal slip after (1+1'+, 1+'+, etc.) 5omputer generation of random numbers using xcel (&1+'3.xls)% C7A:B4>:(13D',+'1) he command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu menu (math (math H trig) trig) funct function ions. s. It may be neces necessa sary ry to add add the the analysis tool pack to access the 7A:B4>: function. 6nce the formula is entered, it can be copied down to select additional random numbers. d.
6the 6therr audit audit proce procedur dures es that that could could be perf perform ormed ed are% are% 1. est extension ions on attached sales invoice ices for clerical accuracy. (Accuracy) '. est est tim time e dela delay y bet betwe ween en war wareh ehou ouse se rem remov oval al sli slip p date date and and billing date for timeliness of billing. (iming) . rac race e entr entrie ies s into into per perp petua etuall inven invento tory ry rec recor ords ds to to dete determ rmin ine e that inventory is properly properly relieved for shipments. shipments. (&osting and summari-ation)
1+2
15-2" .continued/
15-2#
e.
he he test test perf perform ormed ed in in part part c can cannot not be be used used to to test test for for occu occurre rrenc nce e of sales sales because because the auditor auditor already already knows that inventor inventory y was shipped for these sales. o test for occurrence of sales, the sales invoice entry in the sales #ournal is the sampling unit. !ince the sales invoice numbers are not identical to the warehouse removal slips it would be improper to use the same sample.
a.
It would would be appr approp opri riat ate e to use use attr attrib ibut utes es sampl samplin ing g for for all all aud audit procedures except audit procedure 1. &rocedure 1 is an analytical procedure for which the auditor is doing a 1//< review of the entire cash receipts #ournal.
b.
he he appro appropr priat iate e sampl samplin ing g unit unit for audi auditt proce procedu dure res s '+ is a line line item, item, or the date the prelisting of cash receipts is prepared. he primary emphasis in the test is the completeness ob#ective and audit procedure ' indicates there is a prelisting of cash receipts. All other procedures can be performed efficiently and effectively by using the prelisting.
c.
he he att attri ribu bute tes s for for test testin ing g are are as foll follow ows% s% A4')T 0R+C%'4R%
d.
ATTR)4T%
'
5ash receipts in the prelisting are recorded in the cash receipts #ournal.
5ustomer name, date, and amount are e"ual on the prelisting and cash receipts #ournal.
5ash discounts were approved on the related remittance advice.
+
5ash included in the prelisting has been included on the deposit slip.
he he samp sample le si-es si-es for for each each attrib attribut ute e are are as follow follows% s%
A4')T 0R+C%'4R%
T%ST +( C+*TR+ +R S4STA*T)9% T%ST +( TRA*SACT)+*S
'
SA&0% S):% ARACR
T%R
%0%R
SA&0% S):%
! of
+<
3<
1<
D
! of
+<
3<
1<
D
of 5
+<
D<
'<
+
! of
+<
3<
1<
D
1+1/
15-2$
a.
b.
4ecaus ause the sam sample si-e i-es under nonsta statisti istic cal sampli mplin ng are are determined using auditor #udgment, students@ answers to this "uestion will vary. hey will most likely be similar to the sample si-es chosen using attributes sampling in part b. he important point to remember is that the sample si-es chosen should reflect the changes in the four factors (A7A57, 7, &7, and population si-e). he sample si-es si-es shou should ld have have fairly fairly predic predicta table ble relati relations onship hips, s, given given the changes in the four factors. he following reflects some of the relationships that should exist in student@s sample si-e decisions%
1. '. . .
SA&0% S):% 2/ M 5olumn 1 M 5olumn ' M 5olumn 1
+. 3. .
N 5olumn 1 N 5olumn + M 5olumns H
%80A*AT)+* Liven Becrease in A7A57 Becrease in 7 Becrease in A7A57 (column is the same as column ', with a smaller population si-e) Increase in 7&7 Becrease in &7 Becrease in 7&7
8sin 8sing g the the attr attrib ibut utes es sam sampl plin ing g tab table le in in Table 15-$, the sample si-es for columns 1 are% 1. DD '. 1' . 1D1 . 1' +. '+ 3. 1D . 12
c. C7A*3% )* (ACT+RS
%((%CT +* SA&0% S):%
)4STRAT)+* )* 0ART a or b
1. Increase Increase in A7A57. A7A57.
Becrease
5ompare columns and 1
'. Increa Increase se in in 7. 7.
Becrease
5ompare columns and ' (population si-es are not consistent, but this has little effect on sample si-e)
. Increa Increase se in & &7. 7.
Increase
5ompare columns 3 and +
. Increase Increase in popu populati lation on si-e.
:o effect or slight increase
5ompare columns and '
1+11
15-2$ .continued/
15-2,
d.
he he diffe differe renc nce e in the the sampl sample e si-e si-e for col colum umns ns and and 3 resu result lt from from the larger A7A57 and larger 7 in column 3. he extremely large 7 is the ma#or factor causing the difference.
e.
The greatest effect effect on the sample size is the difference between between TER and EPER . $or columns and , the differences between the 7 and &7 were < and '< respectively. respectively. hose two also had the highest sample si-e. >here the difference between 7 and &7 was great, such as columns + and 3, the re"uired sample si-e was extremely small. Population size had a relatively small effect on sample size . he difference in population si-e in columns ' and was 22,/// items, but the increase in sample si-e for the larger population was margin marginal al (actua (actually lly the the sample sample si-e si-es s were were the same same using using the the attributes sampling table).
f.
he he sampl sample e si-e si-e is ref refer erre red d to as the the initi initial al sam sampl ple e si-e si-e becau because se it is based on an estimate of the !7. he actual sample must be evalua evaluated ted befor before e it is possi possible ble to know know wheth whether er the sample sample is sufficiently large to achieve the ob#ectives of the test.
a.
P
A+;A*C% (+R SA&0)*3 %RR+R S4(()C)%*T<
S%R
T%R-S%R
1.
'<
<
Oes
'.
'<
<
&robablyP
.
'<
<
:o (due to small sampling si-e)
.
'<
<
&robablyP
+.
'<
<
:o (due to smaller sample si-e)P
3.
1/<
:A
:o (!7 exceeds 7)
.
/<
+<
Oes
D.
/<
+<
:o due to small sample si-e
!tudent !tudents@ s@ answer answers s as to to whethe whetherr the allowan allowance ce for for samplin sampling g error error risk risk is sufficient will vary, depending on their #udgment. 0owever, they should recogni-e the effect that lower sample si-es have on the allowance for sampling risk in situations , + and D.
1+1'
15-2, .continued/
b.
8sing 8sing the attribut attributes es sampl sampling ing table table in in abl able e 1+2, 1+2, the 587s 587s for columns 1D are% 1. '. . . +. 3. . D.
./< .3< 2.'< .3< 3.'< 13.< ./< 11.<
c. C7A*3% )* (ACT+RS
%((%CT +* C4%R
)4STRAT)+*S )4STRAT)+*S )* 0ART a or b
1
Becrease in A7A57
Increase
5ompare columns 1 and '
'
Becrease in population si-e
:o effect or minor decrease
5ompare columns and '
Becrease in sample si-e
Increase
5ompare columns ' and (both sample exception rates are '<)
Becrease in the number of exceptions in the sample
Becrease
5ompare columns 3 and
d.
he he factor factor tha thatt appea appears rs to hav have e the gre greate atest st effec effectt is the the number number of of excep exceptio tions ns foun found d in the the sample sample compa compare red d to sample sample si-e. si-e. $or $or example, in columns + and 3, the increase from '< to 1/< !7 dramatically increased the 587. &opulation si-e appears to have the least effect. $or example, in columns ' and , the 587 was the same same using using the attri attribu bute tes s sampli sampling ng table table even even thou though gh the the population in column was 1/ times larger.
e.
he he 587 587 repre represen sents ts the the result results s of the the actual actual samp sample le wher whereas eas the the 7 represents what the auditor will allow. hey must be compared to determine whether or not the population is acceptable.
1+1
15-
a. and b.
he sample sample si-es si-es and and 587 587s s are are shown shown in the the follo followin wing g table table%%
ACT4A SA&0% S):%
)*)T)A SA&0% S):% (R+& TA% 15-$
1
1//
1'
'
1//
S%R
C4%R (R+& TA% 15-,
T%R
'./<
3.'<
3./<
22
/./
./
./
3/
3+
1.
3.
D./
1//
2
./
2./
+./
+
'/
1D
+./
1D.1
'/./
3
3/
3/
1.
M'/./
1+./
a.
he he audit auditor or sele select cted ed a samp sample le si-e si-e small smaller er than than that that dete determ rmin ined ed from the tables in populations 1 and . he effect of selecting a smaller sample si-e than the initial sample si-e re"uired from the table is the increased likelihood of having the 587 exceed the 7. If a larger sample si-e is selected, the result may be a sample si-e larger than needed to satisfy 7. hat results in excess audit cost. cost. 8ltima 8ltimatel tely, y, howeve however, r, the compa comparis rison on of 587 587 to 7 determines whether the sample si-e was too large or too small.
b.
he he !7 !7 and and 587 587 are are sho shown wn in in colu column mns s and and + in the the pre prece cedi ding ng table.
c.
he he popula populatio tion n result results s are una unacc ccept eptab able le for for popul populat ation ions s 1, , and and 3. In each of those cases, the 587 exceeds 7. he auditor;s options are to change 7 or A7A57, increase the sample si-e, or perform other substantive tests to determine whether there are actually material misstatements in the population. An increase in sample si-e may be worthwhile worthwhil e in population populati on 1 because the 587 exceeds 7 by only a small amount. Increasing sample si-e would not likely result in improved results for either population or 3 because the 587 exceeds 7 by a large amount.
d.
Anal Analys ysis is of excep excepti tion ons s is nece necess ssar ary y even even when when the popul populat atio ion n is acceptable because the auditor wants to determine the nature and cause of all exceptions. If, for example, the auditor determines that a misstatement was intentional, additional additional action would be re"uired even if the 587 were less than 7.
1+1
15- .continued/
e. T%R&
15-1
a.
*AT4R% +( T%R&
1. stima stimated ted popu populat latio ion n excep exceptio tion n rate
:onstatistical estimate made by auditor.
'. oler olerab able le excep exceptio tion n rat rate e
Audit decision. decision.
. Accep Acceptab table le risk risk of of asse assessi ssing ng control risk too low
Audit decision. decision.
. Actu Actual al samp sample le si-e si-e
Audit decision decision (determined (determined by other audit decisions).
+. Actua Actuall numbe numberr of exce excepti ption ons s in the sample
!ample result.
3. !amp !ample le exc excep epti tion on rat rate e
!ample result.
. 5ompu 5omputed ted upp upper er excep exceptio tion n rate rate
!tatistical conclusion about the population.
he actual actual allo allowa wance nce for for samp samplin ling g risk risk is show shown n in the the follo followin wing g table% table%
S%R
C4%R 1/.<
ACT4A A+;A*C% (+R SA&0)*3 R)S= .C4%R-S%R/
1
./<
3.<
'
./
.2
.2
./
1'.1
D.1
./
.3
.3
b.
he he 587 587 is highe higherr for attr attrib ibut ute e 1 than than attr attrib ibut ute e ' beca becaus use e the sample si-e is smaller for attribute 1, resulting in a larger allowance for sampling risk.
c.
he 587 587 is is highe higherr for for attrib attribute ute than than attr attribu ibute te 1 becaus because e the the audit auditor or selected a lower A7A57. his resulted in a larger allowance for sampling samplin g risk to achieve the lower lower A7A57.
d.
If the the audi auditor tor incre increas ases es the the samp sample le si-e si-e for for attrib attribute ute by +/ +/ items items and finds no additional exceptions, exceptions, the 587 is +.1< (sample si-e of 1+/ and three exceptions). If the auditor finds one exception in
1+1+
the additional items, the 587 is 3./< (sample si-e of 1+/, four
1+13
15-1 .continued/
exceptions). >ith a 7 of 3<, the sample results will be acceptable if one or no exceptions are found in the additional +/ items. his would re"uire a lower !7 in the additional sample than the !7 in the original sample of ./ percent. >hether a lower rate of exception is likely in the additional sample depends on the rate of exception the auditor expected in designing the sample, and whether the auditor believe the original sample to be representative. 15-2
a.
b.
he he foll follow owin ing g sho shows ws which which are except exceptio ions ns and why% why% )*9+)C% *4&%R
%8C%0T)+*<
+/'D
:o
rror was detected and corrected by client.
321
:o
!ales invoice was voided.
3D1/
Oes
&roof of shipment not presented.
3
:o
5redit collection problem* should be noted for review of allowance for doubtful accounts.
3'+
Oes
Buplicate sales invoice not properly filed.
D1
Oes
Invoices not recorded by proper date* represents potential cutoff problem.
D+'D
Oes
5ustomer orders not included in invoice package to verify compliance with the order.
D+33
Oes
rror in pricing. :o internal verification.
DD/
Oes
Buplicate sales invoice not properly filed.
2132
Oes
5redit not authori-ed.
22
Oes
Internal verification of price extensions and postings of sales invoices was not included.
T60% +( %8C%0T)+*
It is is inapp inappropr ropriate iate to set set a single single acce acceptab ptable le tole tolerabl rable e except exception ion rate and estimated population exception rate for the combined exceptions because each attribute has a different significance to the auditor and should be considered separately separately in analy-ing the results of the test.
1+1
15-2 .continued/
c.
he he 587 587 ass assumi uming ng a +< A7A A7A57 57 for for each each attrib attribute ute and and a samp sample le si-e of 1+/ is as follows%
)*9+)C% *4& *4&%R %R
'%SCR)0T )0T)+* )+* +( +( AT ATTR) TR)4T 4T% %
*4&%R +( %8C%0T)+*S
S%R
3D1/
!hipping document not located
1
.3<
3'+ DD/ D+'D
Buplicate sales invoice9customer order not located
'.//<
D1
Invoice date improper
1
.3<
D+33
&rice extensions po postings incorrect
1
.3<
D+33 22
&rice extensions and postings not internally verified
'
1.<
2132
5redit not authori-ed
1
.3<
d. )*9+)C% *4&%R
T%R-S%R
SA&0)*3 %RR+R S4(()C)%*T<
3D1/
+.<
Oes
3'+ DD/ D+'D
./<
&robablyP
D1
+.<
Oes
D+33
+.<
Oes
D+33 22
.3<
&robablyP
2132
+.<
Oes
P !tudents !tudents@@ answers answers will will most likely likely vary for for this attribu attribute. te.
1+1D
15-2 .continued/
e.
$or $or each each excep exceptio tion, n, the the audit auditor or shou should ld check check wit with h the con contro trolle llerr to determine an explanation explanation for the cause. In addition, the appropriate appropriate analysis for each type of exception is as follows%
)*9+)C% *4&%R
15-
%8C%0T)+* A*A6S)S
3D1/
5onfirm firm the the accou count balan lances ces to the the cus custome tomers rs** exami xamin ne the the reduction in the perpetual inventory records.
3'+
race race the amou mount to to the sale sales s #o #ourna rnal an and acco ccounts rec receiva ivable master file* examine the shipping document and recompute the sale amount.
D1
Beter termin mine who reco record rde ed the invo invoiice and che check sev several ral othe thers prepared by him or her to determine if the problem consistently occurs.
D+'D
xamin mine th the ac accou counts receiv ceiva able master ter fil file e fo for su subse"uent ca cash receipt* examine sales invoices for other invoices to the same customer to determine if customer orders were attached.
D+33
5heck th the price rice on othe ther in invoice ices to to the the same custo stomer. 5he 5heck the price on other invoices that have the same product.
DD/
!ee 3'+
2132
5heck cre cred dit histo story of cu custome tomerr an and eva evalu lua ate co collect lectib ibil ilit ity y of of th the customer;s account.
22
7echeck actu ctual pri pric ce, ex exten tensio sions an and posti stings* determin rmine e wh who the clerk was and check several other invoices for proper indication of performance.
a.
Attributes sampling approach: he test of control attribute had a 3< !7 and a 587 of 1'.2<. he substantive test of transactions attribute has !7 of /< and a 587 of .3<. in the the attri attribut butes es sampl sampling ing Nonstatistical Nonstatistical sampling approach: As in approach, the !7s for the test of control and the substantive test of transactions are 3< and /<, respectively. !tudents@ estimates of the 587s for the two tests will vary, but will probably be similar to the 587s calculated under the attributes sampling approach.
b.
Attributes sampling approach: approac h: 7 is +<. 587s are 1'.2< and .3<. herefore, only the substantive test of transactions results are satisfactory. Nonstatistical sampling approach: 4ecause the !7 for the test of control is greater than the 7 of +<, the results are clearly not acceptable. !tudents@ estimates for 587 for the test of control
1+12
15- .continued/
should be greater than the !7 of 3<. $or the substantive test of transactions, the !7 is /<. It is unlikely that students will estimate 587 for this test greater than +<, so the results are acceptable for the substantive test of transactions. c.
If the the 58 587 7 exce exceed eds s the the 7 7,, the the audi audito torr may% may% 1. '. . .
7evi 7evise se the the 7 7 if he or she she thi think nks s the the orig origin inal al spec specif ific icat atio ions ns were too conservative. xpan pand th the sa sample ple sisi-e e ifif cost ost pe permit mits. Alte Alterr the the subs substa tant ntiv ive e pro proce cedu dure res s ifif pos poss sible ible.. >rit >rite e a lett letter er to mana manage geme ment nt in con# con#un unct ctio ion n wit with h eac each h of of the the above to inform management of a deficiency in their internal controls. If the client is a publicly traded company, the auditor must evaluate the deficiency to determine the impact on the auditor@s report on internal control over financial reporting. If the deficiency is deemed to be a material weakness, the auditor@s report on internal control would contain an adverse opinion.
In this case, the auditor has evidence that the test of control proce procedu dures res are not not effec effectiv tive, e, but but no excep exceptio tions ns in the the sample resulted because of the breakdown. An expansion of the attributes test does not seem advisable and therefore, the auditor should probably probably expand confirmati confirmation on of accounts accounts receivable receivable tests. tests. In addition, he or she should write a letter to management to inform them of the control breakdown. d.
Alth Althou ough gh misst misstat atem emen ents ts are are more more likel likely y when when contr control ols s are not not effective, control deviations do not necessarily result in actual misstatements. hese control deviations involved a lack of indication of intern internal al verif verifica icatio tion n of pricin pricing, g, extens extension ions s and footi footings ngs of invoices. he deviations will not result in actual errors if pricing, extensions and footings were initially correctly calculated, or if the individual responsible for internal verification performed the procedure but did not document that it was performed.
e.
In this this case case,, we want want to fin find d out why why some some invo invoic ices es are are not int inter erna nalllly y verified. &ossible reasons are incompetence, carelessness, regular clerk on vacation, etc. It is desirable to isolate the exceptions to certain clerks, time periods or types of invoices.
1+'/
Case
15-!
a.
Audit Audit samp samplin ling g could could be be conv conveni enient ently ly used used for for proce procedur dures es and and since each is to be performed on a sample of the population.
b.
he he most most appr appropr opriat iate e samp samplin ling g unit unit for cond conduc uctin ting g most of of the audit sampling tests is the shipping document because most of the tests are related to procedure . $ollowing the instructions of the audit program, however, the auditor would use sales #ournal entries as the sampling sampling unit for step and shipping shipping document document numbers for step . 8sing shipping document numbers, rather than the documents themselves, allows the auditor to test the numerical control over shipping documents, as well as to test for unrecorded sales. he sele select ctio ion n of numb number ers s will will lead lead to a samp sample le of actu actual al ship shippi ping ng documents upon which tests will be performed.
c.
Note: The sampling sampling data sheet that follows assumes an attributes difference between the sampling data sampling approach. he only difference sheet for attributes sampling and for nonstatistical sampling is the actual determination of sample si-e. $or nonstatistical sampling, students@ answers will vary, but will most likely be comparable to the sample si-es determined under attributes sampling.
'%SCR)0T)+* +( ATTR)4T%S
%0%R
T%R
ARACR
)*)T)A SA&0% S):%>
1./
+./
1/
!hipping document agrees with related duplicate sales invoice.
/./
./
1/
+
he duplicate sales invoice has attached a copy of the shipping document, shipping order, and customer order.
1./
+./
1/
he shipping order has proper credit approval.
1./
+./
1/
he duplicate sales invoice has internal verification of computations.
1./
+./
1/
he duplicate sales invoice has the same price and "uantity as approved price list and shipping document.
/./
./
1/
+
5ustomer name, amount and date agrees between duplicate sales invoice and sales #ournal and subsidiary ledger.
/./
./
1/
+
A duplicate duplicate sales invoice invoice exists for the shipping document selected.
P
assume assumes s the ship shippin ping g docu documen mentt is the the sampl sampling ing unit unit..
1+'1
Q )ntegrated Case Application 15-5
a. and d. 0)**AC% &A*4(ACT4R)*3?0ART 9
Client@ &innacle ?anufacturing
estt of ransactionsRAc"uisitions. ransactionsRAc"uisitions. Audit Area@ ests of 5ontrols and !ubstantive es vendors; invoices, invoices, receiving reports, purchase purchase 'efine the +bective.s/ +bective.s/% xamine vendors; orders, and other related documents to determine whether the system has functioned as intended and as described in the audit program. 'efine the population preciselB .including stratification if anB/ % Souchers from 1919'//2 to 1/919'//2. $irst voucher number T 31. Gast voucher number T 131'. 'efine the sampling unit organiDation of population items and random selection procedures% Soucher number, recorded se"uentially in the ac"uisitions #ourna #ournal* l* random random number number functi function on in electro electronic nic spread spreadshe sheet. et. 0lanned Audit
Actual Results
S%R
Calculated Sampling %rror .T%R-S%R/
1
.<
'.<
/
/
/
+<
+/
+/
/
/
+<
1/<
+/
+/
/
/
+<
+<
1/<
+/
+/
1
'<
<
3<
1/<
/
/
/
/<
3<
'escription of Attributes
%0%R
T%R
ARACR
)nitial Sample SiDe
1. vidence vidence of internal internal verificat verification ion of voucher package including propriety of purchase, dates, unit costs, prices, extensions, footings, account classification, recording in #ournal, and posting and summari-ation. (3a, b)
/
3<
1/<
/
/
'. &rices &rices on vendors; vendors; invoice invoices s conform to approved price limits established by management. (3c)
/
+<
1/<
/
. &rice times times "uantity "uantity and other other calculations on the vendor;s invoice are correct. (3d)
1<
+<
1/<
. vidence vidence of proper proper accoun accountt classification on vendors; invoices. (3e)
1<
+<
+. Bates on on entries entries in purchase purchases s #ournal agree with dates dates on receiving reports. (3f)
1<
/
3. vidence vidence of internal internal verificat verification ion of each purchase voucher. (3g) Results@
*otes@
*umber Sample of SiDe %ce pt ptions
4ased on the results of the tests, all controls appear effective except for evidence of internal verification. !ince !ince there there was also an error on timing timing and an error in comparing the vendor;s vendor;s invoice invoice amount to the ac"uisitions #ournal that is not included as an attribute, a larger than normal sample in yearend testing of accounts payable is appropriate. 1. he planned planned audit variabl variables es are #udgmental #udgmental.. he results results of the prior prior year from part III were were used to decide &7. Initial sample si-e and 587 are #udgments. '. here here was an error error discovered discovered where where there was no attribute attribute.. his happens happens in practic practice e too. he auditor auditor should not ignore the exception even though it is an unplanned discovery.
1+''
15-5 .continued/
b. Client@ &innacle ?anufacturing
!ubstantive est of ransactionsR5ash ransactionsR5ash Audit Area@ ests of 5ontrols and !ubstantive Bisbursements 'efine the +bective.s/@ +bective.s/@ xamine cancelled checks and other related documents to determine whether the system has functioned functioned as intended and as described in the audit program. 'efine the population preciselB .including stratification if anB/@ 5ancelled checks checks from 1919'/ 1919'//2 /2 to 1/919 1/919'// '//2. 2. $irst $irst check check number number T D'3. D'3. Gast Gast check check number T '3D. 'efine the sampling unit organiDation of population items and random selection procedures@ 5heck number, recorded se"uentially in the cash disbursements #ournal* random number function in electronic spreadsheet. 0lanned Audit
Actual Results
'escription of Attributes
%0%R
T%R
ARACR
)nitial Sample SiDe
1. &ayee, &ayee, name, name, amount, amount, and date date on cancelled check agrees with related purchases #ournal and cash disbursements entry. (2a)
/
+<
1/<
/
'. vidence vidence of signatu signature, re, proper proper endorsement and cancellation of each check. (2b)
/
+<
1/<
/
. Bate on cancelle cancelled d check agrees agrees with bank cancellation date. (2c)
/
+<
1/<
/
. 5ash discounts are correct. (2d)
/
+<
1/<
/
1+'
*umber Sample of SiDe %cept ceptiions ons
S%R
Calculated Sampling %rror .T%R-S%R/
15-5 .continued/
c.
&opu &opula lati tion on C vouc vouche herr numb number ers s 31 31 to 131 131' ' !ample si-e C +/ 7andom !election% If rando random m selec selectio tion n is perfo performe rmed d using using xcel xcel,, the the comma command nd to select numbers randomly from the population is% C7A:B4>:(31, 131') he command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu (math H trig) functions under the EinsertF menu. It may be nec necess essary ary to add the the analy nalys sis tool tool pack ack to acc access ess the 7A:B4>: function. 6nce the formula is entered, it can be copied down to select additional random numbers. he random numbers will vary for each student, so they are not listed in this solution.
)nternet 0roblem Solution@ ApplBing Statistical Sampling Sampling
Auditors perform both statistical statistical and nonstatistical nonstatistical sampling. A recent 15-1 article in The CPA ournal titled titled E!tatistical !ampling 7evisitedF 7evisitedF by :eal 4. 0it-ig highlights highlights some of the advantages advantages of using statistical sampling techni"ues. techni"ues. 7ead the article (http%99www.nyss (http%99www.nysscpa.org9 cpa.org9cpa#our cpa#ournal9'// nal9'//9+/9ess 9+/9essentials9p entials9p/.htm) /.htm) as background before answering these "uestions%
1.
>hat is the primary primary differen difference ce between between nonsta nonstatist tistical ical sampling sampling and statistical sampling Answer@ he primary difference between nonstatistical and statistical sampling is that statistical sampling allows the auditor to "uantitatively measure sampling risk using the laws of probability. In nonstatistical sampling, the auditor is only able to "ualitatively assess sampling risk using auditor #udgment.
1+'
)nternet 0roblem 15-1 .continued/
'.
>hat >hat reas reason ons s are ofte often n given given to supp suppor ortt the deci decisi sion on to use use non non statistical sampling versus statistical sampling Answer@ Audito Auditors rs fre"u fre"uent ently ly #usti #ustify fy the the use use of of nonst nonstati atisti stical cal samp samplin ling g by noti noting ng the additional costs associated with the use of statistical sampling. hey argue that statistical sampling is more costly due to the cost of training auditors on the use of statistical sampling, costs of selecting the sample using random selection, and the cost of sampling evaluation that re"uires the "uantification of sampling risks using formulas based on probability theory. he article highlights, however, that the ready availability of computers and offtheshelf software with statistical sampling applications built in have virtually mitigated most of these concerns.
.
>hat >hat is is the the main main advan advantag tage e of of stat statist istica icall samp samplin ling g Answer@ he primary advantage of statistical sampling is the ability to "uantitatively measure sampling risk within a specific confidence interva interval. l. he ability ability to "uantit "uantitativ atively ely measure measure samplin sampling g risk distinguishes statistical sampling from nonstatistical sampling, where the auditor is left to #udgment as to the extent of sampling risk present
.
Bescr Bescribe ibe what what is mea meant nt by by Epro Eprobab babili ility ty sampl sampling ingF. F. Answer@ In probability sampling, every item in the population under audit has a known chance of selection. he decision as to which items in the population to select is left to the laws of chance, not to auditor #udgment.
+.
>hat >hat is the the Eupp Eupper er conf confide idenc nce e limitF limitF as as referr referred ed to in in the the artic article le Answer@ he upper confidence limit is the pro#ected misstatement plus the allowance allowance for sampling risk. he auditor uses the upper confidence confidence limit to evaluate whether the sample result is acceptable or not. If the the uppe upperr conf confid iden ence ce limi limitt exce exceed eds s the the maxi maximu mum m tole tolera rabl ble e misstatement amount, the auditor decides that the misstatement in the the popu popula lati tion on may may exce exceed ed the tolera tolerable ble amount amount.. If the upper upper confidence limit is less than the maximum tolerable misstatement, the auditor decides that the potential misstatement in the population is acceptable (tolerable).
(*ote% *ote% Internet problems address current issues using Internet sources. 4ecause Internet sites are sub#ect to change, Internet problems and solutions may change. 5urrent information on Internet problems is available at www.pearsonhighered.com9aren www.pearsonhighered.com9arens.) s.)
1+'+
