A STUDY OF FACTORS WHICH AFFECT
AUDIT EIIIDENCE ACCUMULATIBN

Dissertation tor the Degree of PM).

MICHIGAN STATE UNIVERSITY
JOHN NEAL KISSINSEH

1974

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STUDY OF FACTORS WHICH AFFECT I;

AUDIT EVIDENCE ACCUMULATION

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A STUDY OF FACTORS WHICH AFFECT
AUDIT EVIDENCE ACCUMULATION

By

John Neal Kissinger

   
  
  
  
  
   
  
   
   
  

The purpose of this dissertation is to examine the auditor's
decision process with regard to questions of evidence accmnulation.
Effectively, the study consists of three sections:

1. development of a normative framework for audit evidence
accumulation decisions,
2. detailed discussion of certain individual factors indicated
by that framework as relevant to such decisions, and
3. empirical evaluation of the relative influence of a mnnber of
these factors in actual audit situations.
bevel meat of a Normative Framework for
Audit Evidence Accumulation Decisions
The first section of the dissertation actually presents two such
frameworks, The first framework suggests that ideally, with regard to
the client's financial statements as a whole, the auditor's objective
should be to select that collection of evidential matter which maxi-
Mus his net expected utility (a function of the audit fee, the costs
“Pbtaining evidence, and the risk of sanctions for failing to detect
79.39.1181 error existing in the client's reports) within the bounds of

Mdentinl support requirements and available time and staff.

 

 

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John Neal Kissinger

The putPMe Of this initial framework is to facilitate the identifica-
tion and classification of factors which logically should affect audit
evidence accumulation.

If it is to serve as a practical guide to audit program develop-
ment, however, the framework must be modified to overcome the inherent
difficulties associated with the measurement of utility and to take
into account the fact that financial statements are actually a complex
set of individual assertions which the auditor must verify. The "sec-
ond best" normative framework which results from such modification sug-
gests that the auditor should determine the nature, extent, and timing
of his audit tests in such a manner as to minimize the cost of obtain-
ing evidence within the bounds of minimum evidential Support require-
nents (for each material assertion in the client's financial state—
ments), available time and staff, and within the bounds of some maxi-

nnm acceptable risk of sanctions.

Detailed Discussion of Certain Individual Factors
Indicated by the Framework as Relevant to Such Decisions

The second section of the dissertation deals with three specific
categories of factors which affect audit evidence accumulation decisions:
1. factors which define the evidential support function for a
given type of audit evidence obtained at a given time,
factors which determine the minimum evidential support neces-
sary to justify a professional opinion on a given financial
statement assertion, and
factors which influence the probability that the auditor will
incur sanctions for failing to detect a material error given

that such error exists in his client's records.

 

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mprimry focus Of disCV-lssion in this section is each factor's
expected effect 0“ the three parameters of the auditor's evidential
collection:
1. the type-(8) of evidence included,
2. the time(s) Of collection of each type, and
3. the number of units of each type collected at a given time.
mirical Evaluation of the Relative Influence of a
Ember of these Factors in Actual Audit Situations
The final section of the dissertation reports an empirical study
of the relative influence of a number of factors on evidence accumula-
tion decisions in the areas of sales and accounts receivable. Tenta-
tive conclusions of this study (which was based on data extracted from
the work papers for fifty-three clients of seven public accounting
firms) are as follows:
1. Multiple discriminant analysis indicated that, for the clients
observed, Generally Accepted Auditing Standards and individual
firm policy were the primary determinants of procedure selec-
£322 in the area of sales. Furthermore, with the possible
exception of client internal check and internal control, no
other independent variable seems to have had any significant
effect on the sample auditors' decisions in this area. With
respect to accounts receivable, the primary determinant of
test selection appears to have been Generally Accepted Audit-
ing Standards. Additionally, however, the evidence suggests
that four factors largely influenced whether a given receiv-
able would be confirmed positively, negatively, or not at all.

These factors were the size of the receivable relative to

 

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«1..-; in the trial balance, the age of the receivable, the
3gqta1 number of receivables in the trial balance, and the

1 firm performing the audit.

(*‘~an hypothesis test indicated that a general model utilizing

'. the quality of the client's internal control and the date of

'gNTVtho client's year-end as its only independent variables pre-

1 “listed the sample auditors' timing decisions (for both sales
lead accounts receivable tests) significantly better than
, chance.

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;J‘ thtiple linear regression indicated that, for the clients
observed, the firm performing the audit, the client's size,
the quality of the client's internal control and the distri-
ibution of the client's ownership had the greatest association
:3;:' filth.the auditor's sample size decisions in both the areas of

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'"' «~eeted’that the mean receivable dollar balance affected the

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A STUDY OF FACTORS WHICH AFFECT
AUDIT EVIDENCE ACCUMULATION

By

John Neal Kissinger

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Accounting and Financial Administration

1974

 

 

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‘ ; incur know how much their encouragement
moral support has meant to me throughout
. f ten; of this dissertation, and to
If“, Warren Higgins, my first, and most

' ' ' laaccounting teacher.

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ACKNOVLEDGMENTS

I owe a debt of gratitude to a great many people for contributions
of one sort or another to this dissertation.

First, I would like to thank my dissertation committee. Profes-
sor Alvin A. Arena, chairman of the committee, provided the initial
idea for my topic and contributed excellent guidance and moral support
throughout. Professor George C. Mead made innumerable useful sugges-
tions and editorial comments. Professor James H. Stapleton found ...
no, made time in an already overcrowded schedule to serve as the com-
mittee's statistician.

I would also like to thank Janet Eyster, the statistical consul-
tant at Michigan State University, for her superb technical assistance
during the statistical design phase of my empirical study.

I am, of course, particularly grateful to those who provided finan-
Cisl support during my tenure at Michigan State. The university,
through its Alumni Distinguished Graduate Fellowship Program, provided
such support during the initial classwork stage of my program. The
Department of Accounting and Financial Administration provided both
fellowship and assistantship support during this same period. Coopers
and Lybrand, as they have for so many other Michigan State doctoral
students, provided me with a generous dissertation grant. Finally,

A hoth the Department of Accounting and Financial Administration at

iii

 

 

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pggreet deal from and was much impressed by those certified
[25
--{tants who were willing to take time to visit with me dur-

co;rse of my data gathering. Without their assistance and the

‘ it; provided, I could obviously never have performed this study.
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TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . .

LIST OF FIGUMS I C I C O I O I I I I I O O I O O 0

Chapter

I.

 

INTRODUCTION . . . . . . . . . . . . .

Audit Evidence And Evidential Collections . . .
A Decision Theory Approach to Audit Evidence
Accumulation Decisions . . . . . . . . . . .
Constraints of the Audit . . . . . . . . .
The Objective Function . . . . . .
Factors which Determine the Degree of Support
a Given Evidential Collection Will Provide
Factors which Determine the Minimum Evidential
Support Necessary to Justify a Professional
Opinion on a Given Set of Financial
Statements . . . . . . . . . . . . . . . .
Factors which Determine the Time Required to
Obtain a Given Collection of Audit Evidence
and Factors which Determine the Maximum Time
Available to the Auditor for the Collection
of Evidence . . . . . .
Factors which Determine the Staff Required to
Obtain a Given Evidential Collection and
Factors which Determine the Staff Available
for a Given Audit Engagement . . . . . . . .
Factors which Determine the Audit Fee
Associated with Each Evidential Collection .
Factors which Affect the Cost of Obtaining a
Given Evidential Collection . . . . .
Factors which Affect the Auditor' 3 Evaluation
of the Expected Disutility of Sanctions
Associated with a Given Evidential Collection
Summnmy . . . . . . . . . . . . . . . . . . . . .

 

10
12

14

16

20

21

22

23

23
29

 

 

II. A OONSTRUCT OF AUDITOR BEHAVIOR . . . . .

A Propositions Approach Construct for Audit
Evidence Accumulation . . . . . . . . .

An Approximation of the Ideal . . . . . . . . . . .

Estimating p(F|Ma(\ E' ) . . . . .

A Modified Propositions Approach Construct for
Audit Evidence Accumulation . . . . . . .
Identify All the Material Propositions

Contained in the Set of Financial

Statements under Examination . . . . . .
For Each Proposition: a. Determine the

Degree of Evidential Support Required for

Evaluation of that Proposition, b. Select

the Kind(s) and Estimate the Quantity(ies)

of Evidential Matter Necessary to Provide

the Required Degree of Evidential Support,

c. Design the Audit Procedure(s) Necessary

to Yield the Desired Kind(s) and

Quantity(ies) of Evidence, d. Apply the

Procedure(s) and Amass a Collection of

Evidential Matter, and e. Evaluate the

Collection of Evidence (If the Evidence

Provides Sufficient Justification, Render

an Opinion on the Proposition. If Not,

Either Gather More Evidence or Disclaim an

Opinion on that Proposition.) . . . . . . .
Based upon the Results of the Individual

Proposition Evaluations, Render (or Disclaim)

an Opinion on the Financial Statements Taken

as a Whole . . . . . . . . . . . . . . . . . .

Summary . . . . . . . . . . . . . . . . . . . . . .

 

      

III. EACTORS WHICH DEFINE THE EVIDENTIAL SUPPORT FUNCTION
FOR A GIVEN TYPE OF AUDIT EVIDENCE OBTAINED AT A
Gm Tm I I I I I C I I I I I O I C I I I I I I I

The Relevance of the Specific Type of Evidential
Matter to the Audit Engagement . . . . . . . . .
Expected Influence on Audit Program . . . . . . .

The Reliability of the Specific Type of
Evidential Matter . . . . . . . . . . . . . . .
Expected Influence on Audit Program . . . . . . .

The Timeliness of the Evidential Matter . . . . . .
Expected Influence on Audit Program . . . . . . .

The Statistical Parameters of the Population
Underlying the Assertion the Auditor Wishes
to Evaluate . . . . . . . . . . . . . . . . . . .
Expected Influence an Audit Program . . . . . . .

The Existence of Corroborative Evidence . . . . . .
Expected Influence on Audit Program . . . . . . .

Summary . . . . . . . . . . . . . . . . . . . . . .

vi

35

38
53

57

59

61

71
72

78

96
100
101
102
104

 

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IV. FACTORS WHICH DETERMINE THE MINIMUM EVIDENTIAL
SUPPORT NECESSARY TO JUSTIFY A PROFESSIONAL
OPINION ON A GIVEN FINANCIAL STATEMENT

   
  
  
   
   
  
  
  

 

ASSERTION . . . . . . . . . . . . . . . . . 107
Generally Accepted Auditing Standards and Other
Authoritative Pronouncements of the AICPA . . . . . . 108
Expected Influence on Audit Program . . . . . . . . . 110
Authoritative Pronouncements of the SEC . . . . . . . . 110
Regulatory Commission Requirements . . . . . . . . . . 111
Policies of Individual Firms . . . . . . . . . . . . 111
Expected Influence on Audit Program . . . . . . . . 112
Specific Terms of the Auditor's Contract with
His Client . . . . . . . . . . . . . . . . 113
Expected Influence on Audit Program . . . . . . . . . llS
Materiality Considerations . . . . . . . . . . . . . 116
Expected Influence on Audit Program . . . . . . . . . 124

The Auditor' 8 Evaluation of the Probability
that a Given Financial Statement Assertion

is Materially Misstated . . . . . . . . 127
The Auditor' 3 Evaluation of the Quality of
His Client's Relevant Internal Controls . . . . . . 128
The Auditor' 5 Assessment of the General
"Riskiness" of His Client . . . . . . . . . . . . . 142
Summary . . . . . . . . . . . . . . . . . . . . . . . 144

V. FACTORS WHICH INFLUENCE THE PROBABILITY THAT THE
AUDITOR WILL INCUR SANCTIONS FOR FAILING TO DETECT
A MATERIAL ERROR GIVEN THAT SUCH ERROR EXISTS IN

HIS CLIENT'S RECORDS . . . . . . . . . . . . . . . . . . 147
The Nature of the Specific Error Involved . . . . . . . 149
Expected Influence on Audit Program . . . . . . . 150
The Degree of Exposure the Client's Statements
Receive . . . . . . . . . . . . . . . . . . . . . . 151
The Client's Size . . . . . . . . . . . . . . . 152
The Nature of the Client's Operations . . . . . . . . 152
The Distribution of the Client's Ownership . . . . . 154
Loan Covenants which Require the Client to
Maintain Specified Account Balances or
Ratios . . . . . . . . . . . . . . . . 156
Expected Influence on Audit Program . . . . . . . . . 157
The Probability that the Client Will File
Bankruptcy Subsequent to the Audit . . . . . . . . . 158

Factors which Affect or Indicate the Degree

and Types of Financial Crisis the Client

Can Withstand. . . . . . . . . . . . . . 159
Factors which Indicate the Probability that the

Client Will Face a Financial Crisis which

Exceeds Those Capabilities . . . . . . . . . . . 161
Expected Influence on Audit Program . . . . . . . . . 163
Sm” I I O I I I I I O I I I . 0 I O l O O I 0 t I U I 164

vii,

VI. AN EMPIRICAL STUDY OF THE RELATIVE INFLUENCE OF
FACTORS WHICH AFFECT AUDIT EVIDENCE ACCUMULATION

The Scope of the Study . . . . . . . . . . . .

The Sample . . . . . . . . . . . . . .
The Public Accounting Firms . . . . . . . . .
The Clients . . . . . . . . . .

The Method of Obtaining Data . . . . . . .
A Caveat . . . . .
The Dependent Variables and the Basic Approach
The Independent Variables . . . . . .
A Study of Factors which Affect the Selection
of Audit Procedures in the Areas of Sales
and Accounts Receivable . . . .
The Audit Area of Sales . . . .

in the Area of Sales . . . . . . . .
The Audit Area of Accounts Receivable . . . .

 

in the Area of Accounts Receivable . . .

>

Study of Factors which Affect the Timing of

Audit Evidence Accumulation in the Areas of

Sales and Accounts Receivable . . . . . .

The Audit Area of Sales . . . . . . .

The Audit Area of Accounts Receivable . . .

Summary and Conclusions: Timing of Evidence
Accumulation in the Areas of Sales and
Accounts Receivable . . .

The Audit Area of Accounts Receivable . . . .

Summary and Conclusions: Sample Size of Audit
Tests in the Areas of Sales and Accounts
Receivable . . . . . . . . .

 
    
   
  

the Relative Influence of Factors which Affect
Audit Evidence Accumulation . . . . . . . .

VII. SUMMARY, CONCLUSIONS AND SUGGESTIONS FOR FURTHER
RESEARCH I l I I I I I I I I I I O I I O I

A Programming Framework for Audit Evidence

Accumulation Decisions . . . . . . .
Some Factors Relevant to Audit Evidence
Accumulation Decisions . . . . . . . . .

Factors which Define the Evidential Support
Function for a Given Type of Audit Evidence
Obtained at a Given Time . . . . . . . .

viii

Summary and Conclusions: Procedure Selection

Summary and Conclusions: Procedure Selection

Summary and Conclusions: Procedure Selection
in the Areas of Sales and Accounts Receivable .

A Study of Factors which Affect the Sample Size
of Audit Tests in the Areas of Sales and
Accounts Receivable . . . . . . . . .
Basic Methodology . . . . . . . . . . . . . .
The Audit Area of Sales . . . . . .

Summary and Conclusions: An Empirical Study of

167

168
169
169
169
173
174
175
176

195

195

239
247

249

250

251
253
255

258
258
261
264

277

291

295

295

300

301

 

 

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Factors which Determine the Minimum Evidential
Support Necessary to Justify a Professional
Opinion on a Given Financial Statement
Assertion . . . . . . . 303
Factors which Influence the Probability that
the Auditor W111 Incur Sanctions for Failing
to Detect a Material Error Given that Such
Error Exists in His Client's Records . . . . . . . 305
An Empirical Study of the Relative Influence of
Factors which Affect Audit Evidence Accumulation . . 308
Factors which Affected the Selection of Audit
Procedures ; . . . . . . . 309
Factors which Affected the Timing of Audit
Tests . . . . . . . . . . . 312
Factors which Affected the Sample Size of
Audit Tests . . . . . . . . . . . . . . . . . . . 313
Conclusions . . . . . . . . . . . . . . . 313
Suggestions for Further Research . . . . . . . . . . . 316
LIST 0? REFERENCES . . . . . . . . . . . . . . . . . . . . . . 320
ix

 

 

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A 5m“? of the independent variables included in
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LIST OF TABLES

Expected influence of factors which define the

evidential support function for a given type

of audit evidence gathered at a given time on

the three parameters of the auditor's evidential
collection: (1) the type of evidence included,
(2) the time of collection of each type, and (3)
the nuflaer of units of each type collected at a
giventime.................

Ellpected influence of factors which determine the

minimum evidential support necessary to justify
a professional opinion on a given financial
statement assertion on the three parameters of
the auditor's evidential collection: (1) the

types of evidence included, the times of collection
0f each type, and (3) the number of units of each

type collected at a given time . . . . .

EmuPlea of financial crises and indicators of a

client's ability to withstand them . . . .

Exputed influence of factors which influence the
PI‘Obability that the auditor will incur sanctions
for failing to detect a material error given that

“Ch error exists in his client's records on the
three Parameters of the auditor's evidential
collection: (1) the types of evidence included,
(2) the times of collection of each type, and (3)
the nunber of units of each type collected at a
given time . . . , _

on. colla- on.

1"Mimi's which affect audit evidence accumulation

Md their operationalization for empirical study

the stud

sharized results of the study of factors which

Effect the selection of audit procedures in the
ireaofsales“).........-----'

Page

105

145

160

166

178

194

241

 

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8. Stnmaarized results of the study of factors which

affect the selection of audit procedures in the
area of sales (B) . . . . . . . . . . . . . . . . . . . 244

9. Summarized results (A) of the study of factors
which affect the sample size of audit tests in
the areas of sales and accounts receivable . . . . . . 278

10. Summarized results (B) of the study of factors
which affect the sample size of audit tests in
the areas of sales and accounts receivable.
(X indicates that the factor appears_in the
regression function which maximized R2 for the
dependent variables in question.) . . . . . . . . . 281

 

 

xi

 

I

LIST OF FIGURES

Figure Page

1. Graphic representation of the relationship
between the financial statement user's
evaluation of the significance of a given
item in the statements relative to all
other statement items, and the relative
influence of that item on his decision
modeloutput...............

 

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CHAPTER I
INTRODUCTION

The third standard of auditing field work, as set forth by the
Committee on Auditing Procedure of the American Institute of Certified

Public Accountants, requires that:

Sufficient competent evidential matter is to be
obtained through inspection, observation, inquiries
and confirmations to afford a reasonable basis for an
opinion regarding the financial statements under exam-
ination.1

The Committee has noted that:

The amount and kinds of evidential matter required
to support an informed opinion are matters for the au-
ditor to determine in the exercise of his professional
judgment after a careful study of the circumstances in
the particular case. In making such decisions, he
should consider the nature of the item under examina-
tion; the materiality of possible errors and irregu-
larities; the degree of risk involved, which is depend-
ent on the adequacy of the internal control and the
susceptibility of the given item to conversion, manipula-
tion, or misstatement; and the kinds and competence of
evidential matter available.

Until recently, auditing literature has reflected little effort

toward further elaboration of specific relationships between

 

100mmittee on Auditing Procedure, American Institute of Certi-
fied Public Accountants, Statement on Auditing Standards No. 1,
III York: American Institute of Certified Public Accountants, 1973,
p. 5.

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"circmstances" of the audit and audit evidence accumulation. The
publix: accounting profession has apparently been content to live with
a'Walack.box" approach (similar to that represented below) with "pro-

fessional judgment" the "black box."

   
 
   
  
  
  
  
  
  
  
  

 

Materiality Considerations

Internal Control Evaluations::\y

Available Evidential Audit
-———__)
Alternatives Professional ———+

~_’/fn) Judgment Program
Professional Guidelines

In an effort to improve this situation, at least two research efforts,

 

 

 

 

one by Arena and the other by Anderson, Giese, and Booker, have fo-
cused specifically on factors relevant to audit evidence accumulation
decisions, and each has contributed insight into audit program devel-
opment.
In his doctoral dissertation, Arens identified the following as
"variables of the audit":
1. risk:
a. probability of material error existing in the client's
financial statements,
b. probability that the auditor will incur sanctions if
he fails to discover such error, and
c. probability that the auditor will fail to discover and
properly interpret such error,
materiality,
internal controls,

cost of accumulating evidential matter,

 

 

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t-‘rgliability of various types of evidential matter,
$33,. relevance of various types of evidential matter to the
h - - . assertion to be proved,
' R 5'3 fiiuliness of evidential matter,
u #5, size, of population underlying a given assertion,

' .

I 9. variance of the population underlying a given assertion,

13:5.
‘5',L_'1p, expected rate of error in the population underlying a given
' {113‘ I
‘ ‘ assertion, and

existence of corroborative evidential matter.3

-- rd... -- _:custom and authoritative pronouncements,

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,4 {'43 ghe'relative risk in the engagement,
A ' 53. client's size,

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is. client 8 trading on the equity, '

client' a acquisition of other companies through the , M":

‘,~' «SH.

, ‘ .3! .1..-

uiseuance of junior equities, yif;,..; 53

I~'l~ 1

,. . '57.; , 2 ' b ‘ . tfi‘lgégglj‘
M3,: ‘ "The, Adequacy of Audit Evidence Acctmulation in 1'3"

- *1 'octoral thesis, School of Business Administration, £7}: - ;

, 1970) warm};

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4
g. longevity of engagement,
h. auditor independence, and
1. general economic conditions,
5. the auditing team, and

6. fee restraints. 4

The efforts of both Arena and Anderson, Giese, and Booker have
greatly expanded the number of identified black box inputs. However,
the attuel relationship between these inputs and the resulting black
box output, the audit program, remains, for the most part, undefined.

The objective of the following dissertation is to explore the
131le box further -- to probe the auditor's decision process with re-
and to questions of evidence accumulation. Essentially, the study
consists of three parts:

1. development of a conceptual framework for audit evidence

accumulation decisions ,

2. discussion of certain factors indicated by this framework as
relevant to such decisions, including analysis of their po-
tential effect on an audit program, and

3. e1111)11':l.<:al evaluation of the relative influence of a number

Of these factors in actual audit situations.

‘5 these three general topics suggest, the research is intended to
like 1”“ normative and descriptive contributions to the field of
”mun:-

\

45' H. Anderson, J. w. Giese, and Jon Booker, "Some Propositions

”m Amining," The Accounting Review 45 (July 1970>= 524'31-

  

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5

The normative contributions lie in the conceptual framework and
discussion of relevant variables. While a number of authors have dis-
cussed factors which influence or should influence the auditor's ac-
cumulation of evidence, no one has yet attempted to relate these
"variables of the audit" to audit programs in some sort of functional
manner. This study is a first step in that direction —— but only a
first step. The functions developed are of a general, abstract nature,
intended to identify and place in perspective those factors which
should affect the auditor's work. While the functions are not suffi-
ciently specific to operate as audit program "generators," they do
suggest a logical framework for the auditor's decision process in
questions of evidence accumulation.

The descriptive contribution, on the other hand, lies in the em-
pirical study which identifies a number of relevant factors to which
the auditor's program appears relatively insensitive and thus suggests
areas Where the auditor might improve his approach to evidence accumu-
lation.

The first part of the study, which includes the remainder of
Chapter I and Chapter II, suggests the appropriateness of a decision
theory or programming framework for audit evidence accumulation deci-
sions and derives two such frameworks. The first (Chapter I) is based
upon two fundamental assumptions: (1) for any given engagement, the
auditor has before him a number of complete alternative audit programs
from which he must select one as a basis for an opinion on the client's
fiinancial statements taken as a whole, and (2) the auditor wishes to

slits his selection in such a manner as to maximize his net egpected
1.x

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6
utiligz. The second framework (Chapter II) then relaxes these assump—
tions one-at-a—time, modifying the model in order: (1) to reflect the
notion that an auditor's responsibility for an opinion on his client's
financial statements taken as a whole implies a responsibility for the
validity of each individual material assertion contained in those
statements, and (2) to replace the highly abstract objective of util-
ity maximization with the more practical one of cost minimization.

The frameworks developed in these first two chapters suggest a
number of basic categories into which factors relevant to audit evi-
dence accumulation decisions fall. The second part of the disserta—
tion, therefore, considers, in some depth, three of these categories,
specifically:

1. factors which define the evidential support function for a

given type of audit evidence obtained at a given time
(Chapter III),

2. factors which determine the minimum evidential support nec-
essary to justify a professional opinion on a given finan-
cial statement assertion (Chapter IV), and

3. factors which influence the probability that the auditor
will incur sanctions for failing to detect a material error
given that such error exists in his client's records
(Chapter V).

The primary focus of discussion in these chapters is the expected
effect of each factor on the three parameters of the auditor's eviden-

; 'j'collection:
J“ .

 

    

the type(s) of evidence included,

N

. the time(s) of collection of each type, and

w

. the number of units of each type collected at a given time.

In the dissertation's final section, Chapter VI, attempts to
evaluate empirically the relative influence of a number of factors on
actual audit practice in the areas of sales and accounts receivable.
A summary (Chapter VII) of the results, conclusions, and limitations
of the research, as well as suggestions for its extension, closes the
dissertation.

Let us now turn to the decision theory framework for audit evi-

dence accumulation which comprises the remainder of this chapter.

Audit Evidence and Evidential Collections

Let us define a unit of audit evidence as any factual item
"available to an auditor from which he may know or infer the relative
truth or falsity of the assertions in financial statements,"5 and let
' us define a "collection" or "accumulation" of audit evidence as any
set whose elements are units of evidential matter. In general, such a
set will have three parameters:6

1. the type of evidential matter included (confirmations, test

counts, etc.),
2. the times of collection of each type, and

3. the number of units of each type collected at a given time.

 

5R. K. Hautz, "The Nature and Reliability of Audit Evidence,"

- f.The Journal of Accountancy 105 (May 1958): 46.

  

serene, pp. 83-84.

 

 

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.1._',' 1! t3.
? ‘*,How, for any given set of financial statements, a wide variety

‘ : factors:

dtgree of evidential support provided,
':,3. cost of accumulation,

3;. time required for accumulation, and

staff required for accumulation.

firdiiénsbie to assume that for any audit engagement (i.e., any
{£93.9audit circumstances") and for any well-defined set of

moldhed'to the above factors, one particular collection of

E t - {qij' i-l, 2,'..., m; 1-1, 2, ..., n}

 

 
 
 

 

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”1:fd2 " ah is the relative weight assigned to the hth variable,

vh is the value assigned to the hth variable,

. b" , Bopt is the "optimal" evidential collection for the

particular engagement and given set of criteria,

and

T,:.—: qij is defined as above.

.“"were able to identify and measure precisely all possible
' ‘ pon' releVant variables (audit "circumstances" -- see su ra,

pp- 2-4) .

,Iug. assigned the same relative importance to each variable,

.ef;

1.‘,,accepted the same set of evidential accumulation criteria, 7

’5146??9~

performed in a reasonably consistent manner.
lone.

Manhunt, that individual auditors differ in the vari-

Similarly, to the extent that individual auditors

unpredisely measuring such variables as they have iden-

eéeatent that they behave inconsistently from engage-

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10
at the present. 0n the other hand, identification of a framework
which indicates the relevant place of each audit variable (or even
each type of audit variable) in the evidential accumulation process

does seem both feasible and worthwhile.

A Decision Theory Approach to Audit Evidence
Accumulation Decisions

\

Toward that end, let us consider the audit as an exercise in
decision theory -— i.e., let us suppose that, for any given engagement,
the auditor has available to him a number of alternative evidential
collections from which he must select one as a basis for his opinion,

and consider how he might make that selection.

Constraints of the Audit

36fore discussing the auditor's decision rule for selecting an
evidential collection, let us note that certain factors may restrict
that selection. We have previously observed that associated with each
c011¢action of audit evidence and a function of its composition are a
maker of factors, including the degree of evidential support the col-
lection provides, the time required to gather the collection, and the
staff l"Nil-tired to gather the collection. Each of these factors may be

6‘“fleet to constraint.

The Degree of Evidential Support
_the Collection Provides
The third standard of auditing field work states that the au—

dit” NM: obtain "sufficient competent evidential matter . . . to af-

ford ‘ I‘edsonable basis for an opinion regarding the financial

 

11
statements under examination."7 This standard requires (as will be
demonstrated later) that the auditor accumulate at least a minimum
level of evidential support before he may render a professional opin-
ion. Clearly, then, the auditor must reject all evidential alterna—

tives which do not provide this minimum level of evidential support,

i.e., he must select an evidential collection, Ek’ such that:

B(Ek) a Bmin (C-l)

where: B(Ek) is the degree of evidential support provided by
the collection, and
Bmin is the minimum evidential support necessary to
justify a professional opinion on a given set of
financial statements.

The Time Reguired to Gather
the Collection

 

Let us denote the total time necessary for an auditor to obtain
a given evidential collection as T(Ek)' This requirement will be a
function of the collection's composition and the manner in which the
auditor obtains it. Clearly, however, the auditor is constrained in
the total amount of time available to him —- the maximum, Tmax’ being
the difference between the date he accepts the engagement and the date
at which his client requires a report. Thus, the auditor must select

a collection, Ek, such that:

'1'(Ek) s Tm (C-Z)

 

-v :2.7culllittee on Auditing Procedure, p. 5.

 

   

12

The Staff Required to
Gather the Collection

A third function of the composition of any given evidential col-
lection will be the size and expertise of the staff required to obtain
it. Obviously, the auditor must eliminate from consideration all col-
lections which are beyond the capabilities of his staff, i.e., he must

select a collection such that:

SR(Ek) 5 SRmax (C-3)

 

where: SR(Ek) denotes the staff requirements of the collection,

  
  
  
  
  
  
  
  
  
  
 
   
  
 

SRmax denotes the limits on size and expertise of the

auditor's staff.

The Objective Function
Having rejected any evidential collections which violate one or
more of the above constraints, the auditor will, hopefully, still have
a number remaining from which to make his final selection. (Otherwise,
presumably, he must require a redefinition of one or more constraints,
or refuse the audit engagement.) The rational choice from these re-
, maining collections would seem to be the one which affords the auditor
a maximum net egpected utility with respect to the following:
1. fee revenues,
2. costs of evidence accumulation, and

3. expected disutilities of sanctions (penalties).

* ; In.eymbolic form, the objective function which represents this

' selection rule is:

t
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13

Maximize U+(R(Ek)) + u'<c<sk)) + E[U~(S(Ek))]

where: U+(R(Ek)) is the utility of the fee revenue associ—

ated with evidential collection Ek’

U—(C(Ek)) is the disutility of the cost of gathering
collection Ek’ and

E[U’(S(Ek))] is the expected disutility of sanctions

associated with collection Ek.

Combining this objective function with the constraints gives the
following normative model for auditor behavior:
Given a number of alternative evidential col-
lections relevant to a particular audit, choose the

collection, Ek’ which maximizes:

u+(n<nk)) + u‘<C(Ek)> + EIU'(S(Ek))]
subject to the constraints:

B(Ek) z B .

T(Ek) s T , and

SR(Ek) 5 SR D
where all factors are defined as above.

The framework of this general model would seem to suggest that
the factors which influence audit evidence accumulation may, in fact,

fall into nine basic categories:

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14

1. factors which determine B(Ek)’ the degree of support a given
evidential collection will provide,

2. factors which determine Bmin’ the minimum evidential support
necessary to justify a professional opinion on a given set
of financial statements,

3. factors which determine T(Ek)’ the time required to obtain a
given collection of audit evidence,

4. factors which determine Tmax’ the maximum time available to
the auditor for the collection of evidence,

5. factors which determine SR(Ek), the staff required to obtain
a given evidential collection,

6. factors which determine SRmax’ the staff available for a
given audit engagement,

7. factors which determine R(Ek), the audit fee associated with
any given evidential collection,

8. factors which affect C(Ek)’ the cost of obtaining a given
evidential collection, and

9. factors which affect E[U-(S(Ek))], the auditor's evaluation
of the expected disutility of sanctions associated with a

given evidential collection.

Let us now look at these categories individually, identifying
the factors relevant to each.
Factors which Determine the Degree of Support a
Given Evidential Collection Will Provide
Iflae degree of support a given evidential collection will provide

downside ISPOR:

 

 

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15
l. the composition of the collection, i.e.,
a. the types of evidence included,
b. the times of collection of each type, and
c. the number of units of each type collected at a given
time, and
2. the evidential support function for a given type of evidence

obtained at a given time.

The slope of this function, which we may denote as b(qij)’ and
which defines the degree of evidential support provided by q units of
type i evidence obtained at time, tj’ depends primarily upon:

1. the relevance of the specific type of evidential matter to

the audit engagement,

2. the reliability of the specific type of evidential matter,

itself a function of:
a. the conclusiveness of the given type of evidence, and
b. the possibility of misinterpreting evidence of this
nature,
3. the timeliness of the evidential matter, itself a function
of:
a. the time at which the evidence is obtained, and
b. the quality and comprehensiveness of the client's in-
ternal controls,
4. the statistical parameters of the population underlying the

assertion the auditor wishes to evaluate:

 

   

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16

a. size,
b. variance,
c. rate of error, and

5. the existence of corroborative evidence.

Chapter III analyzes these factors which influence an auditor's
evaluation of the support provided by a unit of any given type of ev-

idence gathered at a given time, and considers their effect on his

audit program.

Factors which Determine the Minimum Evidential Support
Necessary to Justify a Professional Opinion on
a Given Set of Financial Statements
Before identifying the variables in this category, let us con-
sider, in more detail, the concept of "minimum evidential support."
We have previously noted that for any given set of financial

statements, a wide variety of evidential accumulations may be avail—

able to the auditor. Because of the likelihood of substantial vari-

ation in their composition, these collections will undoubtedly exhibit

differing degrees of evidential support. Were the auditor able to

identify all the possible collections of evidential matter relevant to

a particular audit engagement, then conceivably he could rank them ac—
cording to the relative degree of support provided. Now, even though
the auditor is not likely to be able to identify every available col-
lection, the notion that such an ordering is (at least conceptually)
possible has important implications.

one of these implications is that associated with each possible

glk‘Etion of evidence. E10 15 8 sped-fie level °f evidential support,

 

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17

B(Ek)’ which is a real-valued function of the collection's composition,
and which permits us to denote the hypothetical ordering of collections

as follows:

E1, 32, ..., En, 3 B(E1)_<_ B(Ez) g 5 B(En) g

where the index refers to the collection's location in the overall

ranking and where, for all Ei # Ej such that B(Ei) = B(E ), order

:1
makes no difference.
At this point, let us consider two collectively exhaustive and
mutually exclusive categories for audit evidence accumulations:8
1. E°, accumulations which provide insufficient evidential sup—
port for an opinion on the financial statements in
question, and
2. E+, accumulations which provide sufficient evidential sup-

port for an opinion on the financial statements in

question.

Furthermore, in connection with these two categories, let us make the
following additional assumption:
If the auditor considers a collection of evidence,
3*, sufficient in support to allow an opinion on a set of
financial statements, then he will also consider all col-
lections providing equal or greater evidential support

sufficient for an opinion on those statements, i.e.,

 

8The equivalent statement in set notation is:
r, 3" 3'? UE+ - E, E'° OE" - o, where E’° and 15"" are defined as
sbove,=lf is the set of all possible collections of evidence and ¢
represents the null set.

 

   

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18

   
  
  
  
 
 
  
 
  
  
  
  
  
  
  
   
   

;"!‘.’"E’+ +V E c E 3 303*) < B(E ) E 5 E+
k ‘ k ' k '

te result of this assumption is that the evidential support

fed with any evidential collection of type E“ will always be

cE+ +B(Eik)<B(E),VE andE.

‘14“! sE‘ andE j J

l. t I
':

flop/{31) Z B(F‘j)’ then E

.1
1 must also be sufficient to support an opin-

qand hence 21 s E+. This is impossible, however, since E1 5 E'°

Since we have assumed that for all possible collections of audit
fee, Bk t 5', Bali) is a real value, the set

(B(E :81 s 13°C E} is a real-valued set, hence any number, b,

“iletatements, the auditor places an upper bound on the degree
"ital support considered insufficient for any opinion on those

:,n|is upper bound is, of course, any B(E ) 3E1: E+

:l

7i~§+ implies that 3031) < 3033) for all E1 6 E'°. A defining

the real number system, however, is that "Every set S of

Eif- E V. .
e; .. . that has an upper bound has a least upper bound,"10

» bpumd, b', which is less than or equal to all the other '.':
ti. .slohnson and Fred L. Kiokemeister,c alcusu_1 ,Boston: g'fi
Q es, 1959, p. 128. “9%

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a,_
‘
a. ,L-
'.‘”
N‘-
7“
\
e. :.,.
‘
.
I
1
s. V._
st:
‘
I
o .m.
u
l '4
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.
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19
upper bounds of S. Therefore, H° must have a least upper bound which

we may denote B , such that for all E1 9 E with B(Ei) < Bmin’ then

min
+
0
£1 a E , and such that for all Ej e E with B(Ej) z Bmin’ then Ej e E .
This least upper bound, Bmin’ is the minimum level of evidential sup—

port which the auditor will accept as sufficient to allow an opinion
on the financial statements under examination. The collection(s) of

evidence, E s E+, which minimize B(E ) - B 3 0 will be the
n min min

mi
"minimum collection(s)" for this particular set of statements and the

audit program which yields the collection(s), Emin’ will be the "mini—
mum audit program(s)."11

If one examines the above lists of variables identified by Arens
amlby Anderson, Giese, and Booker, he should note that certain of
fines factors are directly related to this minimum evidential support
remflrement. These factors, which will be discussed in detail in
Chapter IV include:

1. Generally Accepted Auditing Standards and authoritative

pronouncements of the AICPA,

2. authoritative pronouncements of the SEC,

3. regulatory commission requirements,

4. policies of individual public accounting firms,

5. specific terms of the auditor's contract with his client,

6. materiality considerations, and

 

11The notion of a "minimum audit program" is, of course, not
mu. Cf. R. K. Mautz and Donald L. Mini, "Internal Control Evaluation
an Audit Program Modification," The Accounting Review 41 (April
1966): 283-291. These authors define a 'minimum audit program" as
?tbe nature and extent of audit work which would be necessary under
“cbmditions of excellent control." (p. 284)

 

1- 3.,

 

p
O
5

i

9.

  
    
 
  

20
7. the auditor's evaluation of the probability that his
client's financial records contain material error,

the auditor's findings during his review of the

a.
client's internal control system,

b. the auditor's findings in actual tests of the
client's records,

c. the auditor's assessment of the general "riskiness"

of the client, based on the client's financial health,
operating and reporting policies, prior auditor—

client relations, etc.

 

Factors which Determine the Time Required to
Obtain a Given Collection of Audit Evidence
and
Factors which Determine the Maximum Time Available
to the Auditor for the Collection of Evidence

   
  

The time required to obtain a given collection of audit evidence

Hull depend upon:
1. the composition of the collection,

2. the nature and quality of the client's accounting system,

and

3. the efficiency of the staff used to obtain the collection.
Ihr purposes of this dissertation, however, let us consider the last
two of these factors as given and constant, and therefore treat T(Ek)
is a function solely of the composition of the evidential collection
95 interest.

Also for purposes of this dissertation, let us define Tmax as
‘ given and constant, and merely the difference between the date at

0

i.?ihich the auditor accepts the engagement, to, and the date at which

   

 

_-:oP V;-
nuow. .-‘-.

A
u

. u .. .
a: .9 a R u - u Hr. II
.0. as a A u e
...u 3. .ps . a '6 .c
I n A 0 0‘ u .D . o It A v a a
I." C u D b O u . I A I
Av . VI - i .3
.v» I wt - u in.
I I n I - I I. ‘ O' ‘ C M
o . c I a Q s a I
re . .. .3... m u
of... _u‘ 1 \ t \

 

 

21

the client requires a report, tr (i.e. = t — t , where all

, T
max r 0
factors are defined as above), and refrain from further analysis of
either of these classes of factors.
Factors which Determine the Staff Required to

Obtain a Given Evidential Collection
nd

a
Factors which Determine the Staff Available
for .3 Given Audit Engagement

The staff required to obtain a given evidential collection will
depend upon:
1. the composition of the collection, and

2. the nature and quality of the client's accounting system.

A881“. for purposes of this dissertation, let us assume that the
latter factor is given and constant, and therefore treat SR(Ek) as a
flIIICtion solely of the composition of the evidential collection of in-
terest.
The staff available for a given audit engagement, on the other
hand, will depend upon:
1. the size and capabilities of the auditor's firm, and
2. staff requirements of concurrent engagements (in part, a
function of the time of year at which the audit is per-
formed).
17°: Purposes of this dissertation, however, let us assume that for any
siven audit, Slim, is constant and given and refrain from further

“evasion of the factors relevant to this constraint.

 

 

>..

Ia-yA
I D I
aubuso
a.

-¢' ...1
‘ "

1....
a- .‘,
" he

 

 

..
.-
.

\ ‘
‘ Io,.

‘ I‘

 

 

 

.

‘.

'.'».
55.:

fr'

Ira

‘s

.-
I
‘«

 

 

22

Factors which Determine the Audit Fee Associated
with Each Evidential Collection

Anderson, Giese, and Booker have noted that:

The audit fee is generally determined by multi-
plying a standard billing rate for each rank (in the
audit staff hierarchy) by the number of hours worked
by that rank. The standard billing rate is currently

between two and three times the direct salary for
each rank.12

Atleast up to a limit, then, audit fees (and their related utility)
vary directly with audit costs. The limit, of course, is the maximum
feethe client will accept before terminating the engagement and find-
ing another auditor. If we denote this maximum fee as Rmax’ we may

define R(Ek) as follows:
R(C(E )). R(C(E )) R
R(Ek) - k k max

Rmax. R<C<Ek>>

IA

R .
max

IV

where: R(C(Ek)) defines the audit fee associated with eviden-

tial collection, E , as an increasing function

k
of the cost of obtaining that collection, and

13
RCE ) and R are defined as above.
k max

Since more detailed analysis of the behavior of R(Ek) 18 “11"
necessary for purposes of this dissertation, let us also refrain from

fuI'ther consideration of this factor.

‘.-

12
Anderson, Giese, and Booker, p. 530.

3
Apparently, in many audit engagements, the fee is a matter of
negoflation prior to the auditor's work. In such cases, our defini-

tion of R(Ek) becomes:
R E -
where R(E ) and R are defined as above.
k max

UndOUbtedIY. however, budgeted costs enter into the bargaining.

 

v
I,
I“

V
v .

e
?
f“

C
ch

1
a...

nu...

0-.
in.‘

I u. _ ,
-. '-; ~.
.,.‘ "
.
. .
- -‘ : - .-
‘- . .“
t
“ I
< V ...l
“t... -s
.04.
I
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A. -
h“: P.
\ . ..
'5 g be,”
"ml
‘.'
, .
'1.

P
.H
t _
c“
9;.
L”:
i
; ;._ .
' \
"V

 

o W-
V«
I‘.‘_
e ‘ .
\‘t‘ -
Vt
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x": I;
‘
.fi 0
h
“l. 5"
‘G
‘.
a
I?
I I
"F'A
M's

 

23
Factors which Affect the Cost of Obtaining
a Given Evidential Collection
The cost of obtaining a given evidential collection will depend
mmn:
1. the composition of the collection,
2. the nature and quality of the client's accounting system,
3. the efficiency of the staff used to obtain the collection,
and

4. the wage rate of the audit staff.

ABEUM however, for purposes of this dissertation, let us consider the
lastthree of these factors as given and constant, and therefore treat
CCfiJ as a function solely of the composition of the evidential col—
lection of interest. (In any case, this factor should be the dominant
mm.)

While the topic of audit evidence cost is an interesting one,
and one worthy of research, further analysis of this factor is beyond
the Scope of this dissertation.

Factors which Affect the Auditor's Evaluation of
the Expected Disutility of Sanctions Associated
with a Given Evidential Collection

Arena has noted that:

-- . one of the factors that an auditor should con-

Sider in deciding upon the adequacy of audit evidence

18 the sanctions which can be expected if the finan-

cial statements are not fairly presented.l
\

14
Arens, pp. 35-36.

 

 

 

4:...”

V- o. .

.

'w-r.L .
1

'-~ u -
‘ I

 

 

 

 

 

 

 

 

24

These sanctions, or penalties, may take a number of forms depending
upon who imposes them (the client, the Securities and Exchange Com-
mission, the accounting profession, or society as a whole), and de-
pending upon the cause, type and degree of error in the client's fi—
nancial statements. The most common forms, in order of apparent in-
creasing severity are:

l. adverse publicity,

2. admonition from the SEC15 or AICPA,

3. loss of client,

4. lawsuit,

5. loss of right to practice before the SEC,

6. expulsion from the AICPA and/or loss of license to prac-

tice, and

7. conviction in criminal action.

Such sanctions are a potential source of disutility to the au-

ditor in terms of lost reputation, lost self-esteem and reduced

*1

”The greater exposure generally afforded an SEC client's finan-
cial statements actually affects the auditor's risk of sanctions in at
least three ways:

1- it introduces the SEC as a potential source of sanctions,

2. it increases the probability of legal action should the an:
ditor fail to detect material error existing in the client a
statements, and

3- it increases the probability of adverse effect on the au-
ditor's public image.

The implications are obvious -- ceteris paribus, the auditor should
logically recluire a greater degree of evidential support for an SEC
client than for a non-SEC client. (See infra, pp. 154-156). Compare
this com11‘1810n, however, to the fiction frequently espoused by prac-
utioners (and perhaps the official position of the AICPA) that an
mm“ 13 an audit" regardless of the client's status.

e . ' ,I.
...u o.. .
‘7;

'.‘
.
--...,
V
v 6..-.
u.
4'o.,
0.5..
I I
‘H..-
.U .-
'. ‘~-...
“«vo
evo.‘
.
i“
no
' .u. I
" ...t‘
.1
"- "--.-
‘Iu.
, 1.}:N ‘
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s.
..~V~‘
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9c
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25
pnfiits. Pbr example, the disutilities associated with a lawsuit in-
clude:
l. adverse publicity (which invariably occurs whether the au-
ditor wins the case, loses the case or settles out of court),
2. defense costs, e.g., fees for lawyers and expert witnesses,
court costs, staff time necessary to prepare the defense,
and

3. the cost of any settlement the court might impose.

For any given audit, the expected disutility associated with a par-
timflar sanction is actually the product of four factors and, for any

Siwmlcollection of evidential matter, B we may define the expected

k9
dimudlity of the ith particular sanction, EIU-(Si(Ek))]y as:

E[U_(Si(Ek))] = p(M) p(F|M n Ek) p(SilF n M n Bk) EIU'(Si|Sin Bk”:

Where: p(M) is the probability that the client's

records contain material error,
p(FIMiW Bk) is the probability that the auditor
fails to detect such error given that
it exists in the client's records and
he selects evidential collection, Ek’
PCSilFn MIW Ek) is the probability that the auditor

will incur sanction 81’ given that,
having selected evidential collection

Ek’ he fails to detect a material error
\

16 h fessional
The auditor can generally shift this cost throug pro

:Lflulity insurance. Lost lawsuits, however, are likely to increase
e c°3t8 0f such insurance.

26
which exists in his client's records,
and
E[U—(SiISi n Ek)] is the eXpected disutility of sanction
Si’ given that, having obtained eviden—
tial collection Ek’ the auditor incurs

that sanction.l7

Let us look at each of these factors in somewhat more detail.

The Probability that the Client's Records
Contain Material Error, p(M)

This probability will be, primarily, a function of the quality
and comprehensiveness of the client's internal controls. We have al—
ready noted that p(M) is also an important factor in determining the
minimum evidential support necessary to justify a professional opinion,
and that it will be discussed in detail in Chapter IV. We need not,

therefore, analyze it further at this time.

 

17Here we assume that the auditor will not incur a sanction un-

less material error exists and he fails to discover it. Therefore,
$1, the occurrence of the iEH—sanction, is equivalent to Silfi Fifi M,
the intersection of the occurrences of the ith sanction, the existence
of material error, and the auditor's failure to discover the material

error, and E[U (Silsifl E k)] is equivalent to

am“ (silsin an no Ek)].

27
The Probability that the Auditor Fails to
Detect Material Error Given that It Exists
in the Client's Records and He Selects
Evidential Collection E,, p(FIM4fi E,)

This probability is a decreasing function of the evidential sup-
port provided by the auditor's collection,18 and is hence a function
of:

1. the composition of that collection, and

2. the evidential support function for a given type of evidence

obtained at a given time.

We have already identified the factors which affect this function and
indicated that Chapter III will be devoted to their analysis.
th

The Probability that the i Sanction
Will Be Imposed Given that, Having Se-
lected Evidential Collection E,, the
Auditor Fails to Detect a Matefial Error
which Exists in His Client's Records,
p(S.IF n M n E.)

This probability depends primarily upon:

1. the composition of Ek’
2. the nature of the specific error involved,
3. the degree of exposure the client's statements receive, in—

dicated by:

a. the client's size,

b. the nature of the client's operations,

 

18More specifically, let us assume a one-to-one relationship in

both directions between B(Ek) and p(FIM n Ek)’ i.e.,
p(FIM n Ek) =- f(B(Ek)) and B(Ek) =- g(p(FlM n Ek)),
such that for all B(Ei) < B(Ej), p(FIM n E1) > p(FIM n E1), and

for all 3031) - B(E ), p(FIM n E1) = p(FIM n Ej)’ and conversely.

J

28
c. the distribution of the client's ownership, and
d. loan covenants which require the client to maintain
specified account balances or ratios,
4. the probability that the client will file bankruptcy sub-
sequent to the audit, indicated by:
a. factors which affect or indicate the degree and types
of financial crisis the client can withstand, e.g.:
(1) factors which indicate the client's financial
position,
(2) economic conditions related to the availability
of external capital,
(3) the client's rate and method of growth, and
b. factors'which affect or indicate the probability that
the client will face a financial crisis which exceeds
its capabilities, e.g.:
(l) the nature of the client's operations,
(2) economic conditions relevant to the client's
marketplace,

(3) the client's method of financing operations.

A more detailed discussion of these variables and their expected

influence on the auditor's program forms the basis of Chapter V.

The Expected Disutility of the ith Sanction
Given that, Having Obtained Evidential Col-
lection EL,_the Auditor Incurs that

Sanction,“ELU'(sii§1n El ll

The value which the auditor attaches to this factor will, of

course, depend upon the specific sanction. For some sanctions such as

29

admonition, loss of right to practice before the SEC, expulsion from
the AICPA and/or loss of license to practice, and imprisonment, the
expected disutility is apt to be a constant, dependent upon charac-
teristics of the auditor, himself, and independent of the specific
client involved or the degree of audit evidence which the auditor has
accumulated. On the other hand, the expected disutility of losing a
given client should be a direct function of that client's size. Like-
wise, the expected disutility of adverse publicity or lawsuit should
depend upon the size of the client, the size and nature of the error,
and the degree of support provided by the auditor's evidential collec-
tion. A detailed analysis of each of the individual sanctions and the
type of disutility it may cause the auditor, however, is beyond the

scope of this dissertation.

Summary

While, in general, auditing literature indicates little attempt
on the part of the public accounting profession to define the rela-
tionship between "circumstances of the audit" and the auditor's pro-
gram, the efforts of Arena and of Anderson, Giese, and Booker have at
least specifically identified many of the factors which appear to bear
a logical relationship to audit evidence accumulation. This chapter
has outlined a decision theory framework for studying the relationship
of such audit variables to the nature, timing, and extent of audit

testing.

30
This framework, in summary, assumes that:
Given a number of alternative evidential collections
relevant to a particular audit, the auditor should select

that collection Ek, which maximizes:

U+<R(Ek>> + u’<c<Ek>> + E[u‘(s<Ek>)1 (0-1)

subject to the constraints:

B(Ek) 2 3min (C—l)
T<Ek) s '1‘max (0-2)
snack) _<_ SRmax (c-3)

where:
U+(R(Ek)) is the utility of the audit fee associated

with evidential collection Ek’

U—(C(Ek)) is the disutility of the cost of obtaining

evidential collection Ek’

E[U-(8(Ek))] is the expected disutility of sanctions

associated with evidential collection Ek’

B(Ek) is the degree of support provided by evi-

dential collection Ek’

Bmin is the minimum evidential support necessary
to justify a professional opinion on a
given set of financial statements,

T(Ek) is the time required to accumulate eviden-

tial collection Ek’

31
Tmax is the maximum time available to the au-
ditor for gathering evidence on a given
audit engagement,
SR(Ek) denotes the audit staff required to accu—
mulate evidential collection Ek’ and

SRmax denotes the staff available for a given

audit engagement.

Analysis of each of the parameters of the above framework has
indicated three of the categories of factors which influence audit
evidence accumulation particularly worthy of further study. These
categories are:

1. factors which define the evidential support function for a

given type of evidence obtained at a given time:
a. the relevance of the specific type of evidential
matter,
b. the reliability of the specific type of evidential
matter, itself a function of:
(l) the conclusiveness of the given type of evi-
dence,
(2) the possibility of misinterpreting evidence of
this nature,
c. the timeliness of the evidential matter, itself a
function of:
(l) the time at which the evidence is obtained, and
(2) the quality and comprehensiveness of the

client's internal controls,

32
d. the characteristics of the population underlying the
assertion the auditor wishes to evaluate:
(1) size,
(2) variance,
(3) rate of error, and
e. the existence of corroborative evidence,

2. factors which determine the minimum evidential support nec-
essary to justify a professional opinion on a given set of
financial statements:

a. Generally Accepted Auditing Standards and other author-
itative pronouncements of the AICPA,
b. authoritative pronouncements of the SEC,
c. regulatory commission requirements,
d. policies of individual public accounting firms,
e. specific terms of the auditor's contract with his
client,
f. materiality considerations, and
g. the auditor's evaluation of the probability that his
client's records contain material error, based on:
(1) the auditor's findings during his review of the
client's internal control system, and
(2) the auditor's findings in actual tests of the
client's records, and

3. factors which influence the probability that the auditor will

incur sanctions for failing to find a material error given

that such error exists in his client's records:

33
a. the composition of his evidential collection,
b. the nature of the specific error involved,
c._ the degree of exposure the client's statements re-
ceive, indicated by:
(l) the client's size,
(2) the nature of the client's operations,
(3) the distribution of the client's ownership, and
(4) loan covenants which require the client to
maintain specified account balances or ratios,
and
d. the probability that the client will file bankruptcy
subsequent to the audit, indicated by:
(1) factors which affect or indicate the degree and
types of financial crisis the client can with-
stand, e.g.:
(a) factors which indicate the client's fi—
nancial position,
(b) economic conditions related to the avail-
ability of external capital,
(c) the client's rate and method of growth,
and
(2) factors which affect or indicate the probabil-
ity that the client will face a financial

crisis which exceeds its capabilities, e.g.:

34
(a) the nature of the client's Operations,
(b) economic conditions relevant to the
client's marketplace, and
(c) the client's method of financing opera-

tions.

While the above framework is useful for studying factors rele—
vant to audit evidence accumulation decisions it is virtually useless
for any other applications. Therefore before we look in depth at the
factors and attempt to determine their specific effects on the au-
ditor's evidential collection, let us consider further the framework,
itself, and its underlying assumptions in an attempt to develop a
modified construct which provides more useful guidelines for actual

auditing situations.

 

8.
e.

I"

 

 

CHAPTER II

A CONSTRUCT OF AUDITOR BEHAVIOR

The decision theory model of the audit presented in Chapter I
assumed that the auditor had before him a number of different possible
evidential collections from which he must select one to support his
overall opinion on the financial statements under examination. While

this assumption reflects conceptually what happens in an audit, and

 

while it leads to a useful framework for the identification and con-
sideration of factors which influence audit evidence accumulation, it
does not, nor does it intend to, describe the physical process in-
volved in the development of an audit program. In actual practice,
the auditor obviously does not, at one fell swoop, attempt to define a
collection of evidence sufficient to support an overall opinion on the
financial statements under examination. The amount and variety of
evidence necessary to support an overall opinion precludes such an
approach. Instead, the auditor typically divides his work into a num-
ber of distinct audit areas (e.g., cash, sales and accounts receivable,
fixed assets, etc.), performs tests on the fairness of presentation
within each area, and, based on the results of these area tests, ren-

ders an opinion on the financial statements taken as a whole.

35

rm- '1 a»

 

 

36

Now, evaluation of any given audit area is, in itself, likely to
be a complex matter since, as Mautz has noted, each area consists of a
number of individual assertions or propositions concerning the cli—
ent's activities or records.1 Presumably, falsity or material error
in even one of these propositions may lead to material error in the
financial statements taken as a whole. Therefore, before he can ac-
cept an audit area as fairly presented, the auditor must attempt to
identify and evaluate all the material assertions relevant to that
area. As Mautz puts it:

. . . an audit report is a composite and a complex

opinion . . . based upon and made up of a host of

subsidiary opinions or judgments. The financial

statements which the independent auditor examines

and about which he expresses an Opinion are them-

selves composed of a large number of individual

prepositions on which he must make judgments and

form opinions.2
Therefore:

The procedure of judgment formation in audit-

ing must of necessity commence with the individual

propositions which in the aggregate make up the fi-

nancial statements. Only after these have been re-

viewed and judged is an auditor in position to make

his important, over-all judgment.

Apparently, then, "theoretical" as well as practical consider-
ations require the auditor to approach an audit examination from the

standpoint of the individual assertions contained in his client's fi-

nancial statements. Therefore, the purpose of this chapter will be to

 

1R. K. Mautz, "Evidence, Judgment, and the Auditor's Opinion,"
The Journal of Accountancy 107 (April 1959): 40.

21bid.

3Ibid., p. 42.

 

4-.

1.

..-

or.

w
e...»

 

 

37
expand and revise our model of audit evidence accumulation so that it

' "propositions" approach. As we shall see, the re-

incorporates Mautz
sulting construct, while more closely aligned to the physical process
of audit evidence accumulation, will still be normative in nature --
and, unfortunately, will be virtually impossible of any practical ap-
plication. Because of the model's lack of applicability, the chapter
will conclude with suggestions as to how an auditor might at least ap-
proximate the ideal which the normative construct represents.

The basic framework for the revised model consists of the fol-

lowing steps:4

 

4This framework is essentially a combination of Mautz and

Sharaf's outline of "auditing methodology for dealing with problems or
issues of fact:
1. Recognition (acceptance) of the composite problem (the audit
assignment).
2. Observation of facts relevant to the problem.
3. Subdivision of the composite problem into individual prob—
lens.
4. Determination of available evidence pertinent to each indi-
vidual problem.
5. Selection of applicable audit techniques and development of
appropriate procedures.
6. Performance of procedures to obtain evidence.
7. Evaluation of evidence
a. With respect to pertinence and validity.
b. For indications of any additional problems.
c. With respect to adequacy for judgment formation.
8. Formulation of judgment
a. On individual propositions.
b. On the composite problem." (p. 27)

and their outline of "the procedure of judgment formation:
1. Recognition of the proposition to be proved.
'2. Evaluation of the proposition as one requiring evidence of a
high or moderate degree of probability.
3. Collection of evidence within the given limits of time and
cost.
4. Evaluation of the evidence obtained as valid or not valid.

‘iiE!

 

Was-tip at I." .

38

1. identify all the material propositions contained in the set
of financial statements under examination,

2. for each proposition:

a. determine the degree of evidential support required to
justify an opinion on the proposition,

b. select the kind(s) and estimate the quantity(ies) of
evidential matter necessary to provide the required
degree of evidential support,

c. design the audit procedure(s) necessary to yield the
desired kind(s) and quantity(ies) of evidence,

d. apply the procedure(s) and amass a collection of evi-
dential matter, and

e. evaluate the collection of evidence (If the evidence
provides sufficient justification, render an opinion
on the proposition. If not, either gather more evi-
dence or disclaim an opinion on that proposition.),

3. based upon the results of the individual proposition evalu-
ations, render (or disclaim) an opinion on the financial
statements as a whole.

A Propositions Approach Construct for
Audit Evidence Accumulation

Before looking at the above framework in depth, let us consider

how the requirement that the auditor evaluate each individual proposi—

tion in a set of financial statements would alter our Chapter I model.

 

5. Formulation of judgment as to the proposition at issue."
(p. 103)

R. K. Mautz and Hussein A. Sharaf, The Philosophy of Auditing, Menasha,
Wisconsin, George Banta Company, Inc., 1964, pp. 27, 103.

 

we».

 
 
 

 

39
Clearly, regardless of whether the auditor defines his eviden-
tial requirements "at one fell swoop" or proposition by proposition,
the overall time and staff requirements for obtaining any resulting
collection may not exceed the time and staff available for the engage—
ment. Therefore, as in the case of the original model, the following

constraints hold:5

T(Ek) g Tmax’ and (C-2)
SR(Ek) S SRmax. (C-3)

Likewise, since it seems reasonable to assume that, regardless
of how he determines his evidential requirements, the auditor's goal
is to maximize his net expected utility from the audit, our model's

objective function remains unchanged, i.e.:
Maximize U+(R(Ek)) + U-(C(Ek)) + E[U-(50319)]. (0-1)

In fact, the only difference between our original model and one
which requires the auditor to identify and evaluate each material

proposition is that, in the first case, the evidential collection must

 

5At this point, let us note that the time and staff constraints,
as set forth above, are symbolic, representing the notion that time
and staff requirements may not, in any way, exceed the time and staff
available for the audit. In this respect, each of the constraints
actually represents a number of sub-constraints. Enumeration of these
sub-constraints, however, is unnecessary for the purposes of the pres-
ent discussion.

We might also note that, in general, the time and staff avail-
able for an engagement can affect all three parameters of the auditor's
evidential collection. With one exception, however (the effect of
staff availability on audit timing), actual testing of the relative
influence of these constraints on audit evidence accumulation is be-
yond the scope of this dissertation.

 

 

 

 

<..

 

4O

satisfy an overall support constraint while, in the second case, it
must satisfy a support constraint for each assertion to be tested --
the presumption being that if the auditor has identified all the ma—
terial propositions in the financial statements and if he has accumu—
lated sufficient evidential matter to support or refute each proposi-
tion, then he has also met the evidential requirements for an opinion
on the financial statements taken as a whole. In this case, then, we

must replace the single constraint:

302,) 2 3mm. <c—1)

with the set of r constraints:

ba(Ek) z bamin’ (a = 1, 2, ..., r) (C-la)

where: ba(Ek) is the degree of support provided by evidential

collection E for the auditor's opinion on the

k

ath assertion of his client's financial state-

ments,

bamin is the minimum evidential support necessary for a

professional opinion on that ath assertion, and,

both b (E ) and b are determined by the same fac-
a k am

in
tors that determine, respectively, B(Ek) and Bmin in

the original model.6

 

6Note that a factor which affects bamin for any given assertion
is thus that assertion's relative materiality. Furthermore, a factor
which contributes to ba(Ek) is the existence of corroborative evidence.
In a piecemeal opinion, the financial statement item of interest is
logically of greater relative materiality than it would be as part of
a complete set of financial statements. Also, in a piecemeal opinion,
the auditor does not have the degree of corroborative evidence nor-
mally available in an overall audit. For both of these reasons, then,

 

 

41
At this point, let us recall that, in Chapter I, we assumed that
the probability that an auditor will fail to detect material error
which exists in his client's financial records given that he has se-
lected evidential collection, Bk, and the evidential support provided
by that collection bear a one—to-one inverse relationship to one an-

other, i.e.:

p(FlM n Ek) = Hawk» and B(Ek) = g(p(F|M n Ek))

such that for all B(Ei) < B(E ), p(FlMlW Ei) > p(FIMlfi Ej)’ and for

3

all B(Ei) = B(E ), p(FIM,F|Ei) = p(FIM n Ej)’ and conversely. (Supra,

J
footnote 18, p. 27.)

The analogous case for our current model is:
n B =
p(FIMa Ek) f(ba(Ek)) , and ba(Ek) g(p(rlnal n 13k»,

such that for all ba(Ei) < ba(E ),

J

p(FIMan E1) > p(FlMafi E), and

:1

for all ba(Ei) = ba(E ), p(FlMan E1) = p(FIMan E),

j j

and conversely,

where: p(FIMan Ek) is the probability that the auditor will
fail to discover material error which exists in the ath
assertion of the client's records, given that he selects

evidential collection Ek.

It follows from this assumption that a set of constraints equiv-

alent to:

ba(Ek) 2 bamin (a = l, 2, ..., r) (C-la)

 

the auditor must normally test an item more extensively for a piece-
meal opinion than for an overall opinion on the financial statements
of which that item is a part.

 

42

would be:

p(FIMat1 2k) 5 pamax (a = 1, 2, ..., r) (C-lb)

where: pamax is the maximum allowable probability that the au-
ditor will fail to detect material error which
exists in the ath assertion of his client's state—
ments (obtained, at least conceptually, by substi-

tuting bam n for ba(Ek) in the function,

i
7
mask»).

and we may write our revised model as:

Maximize: U+(R(Ek)) + u‘(c<ak)) + E[U-(8(Ek))] (0-1)
subject to: T(Ek) s Tmax (C—2)
SR(Ek) s SRMx (C—3)
ba(Ek) z bamin (a = 1, 2, ..., r) (C-la)

or
p(FIMal1 ER) 5 pamax (a = 1, 2, ..., r) (C-lb)

 

7Given statistical sampling techniques, this alternative set of
constraints would appear, in most cases, to be more easily quantifi-
able than "degree of evidential support."

 

 

 

 

u

v,
p.

 

 

 

 

 

 

43

Unfortunately, neither formulation of the above model is of much
Practical use to the auditor (except insofar as it identifies or
places in proper perspective variables relevant to his evidential ac-
cumulation problem). Even though the various parts of the model are
conceptually quantifiable, in practice their quantification would be
difficult and, in many cases, arbitrary (e.g., quantification of the
expected disutility of sanctions as a function of the evidential col-
lection selected). Therefore, until the accounting profession per-
forms considerably more extensive research on the relationships be-
amen evidential matter and evidential support, and until auditors
agree on quantifiable operational definitions of the factors relevant
to evidence accumulation, simultaneous solution of the massive system
of equations proposed above seems beyond reach.

The obvious question which arises, then is whether it is pos-
sible to construct an approximation to the ideal represented by the
above model -- either a system of equations which auditors could solve
or estimate the solution of, or at least a set of guidelines they
udght follow to relate relevant factors to the audit evidence accumu-
lation process.

The following is an attempt to modify the "propositions approach"
nmdel to arrive at such an approximation. One should keep in mdnd
that even though this approximation may relax some of the conditions
ct the original model, it must remain normative in nature since it
suggests an approach auditors mighg follow in determining evidential
requirements rather than attempting to describe the process they ac-

tually g9 follow.

 

..
'H
...t ,.
a
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v
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Run.
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bl.
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0

he.

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5,;v‘.
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L
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K o u
‘:. ‘3
at
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\

vi.
rl‘
’ 1

(I)

I

 

 

44

An Approximation of the Ideal

 

The primary hindrance to applying the "propositions approach"
Emmel as it now stands would seem to be the objective function. Au-
ditors appear reasonably able to identify and work within time and
staff constraints, and, while their estimates of such requirements may
be crude, they also seem able to satisfy evidential support con—

straints (even if only through considerable "overauditing"). The ob-

jective function, however, poses two barriers to practical application:

1. measurement of the expected disutility of sanctions as a
function of audit evidence obtained, and

2. assumption that net utility is the factor to be maximized
and the difficulties inherent in any attempt to measure

utility.

Overcoming the second barrier is, of course, a simple matter.
¢3ne need merely adopt "revenue" and "cost" as surrogates for "utility"

and "disutility," and thus change the objective function to:

Maximize R(Ek) - C(Ek) - E[C(S(Ek))] (O-la)

where: R(Ek) is the audit fee associated with evidential
collection Ek’
C(Ek) is the cost of obtaining evidential collec-
tion Ek’ and
E[C(S(Ek))] is the expected cost of sanctions associated

with collection Ek.

 

ld‘

I D
‘a

...:
IDEA:

n

2.:
to
' I
on

"‘

€21

 

.. on. o
‘ 5b..L

’.f

.

'.‘ . .
‘I "‘ '."y
"'Cwo- u-

1

r“ a u'
w x

'3 rd.

“ A. .
. i‘ I
hung“ ‘

1' I
'9... .A R .

“"i H: .‘C

"‘ ,1“...
‘§. “‘.':

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§.\..~‘ 'C‘
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'.' '.'v- ‘
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2;”
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5“ r131
\-
‘3 l"

 

45

Certainly R(Ek) and C(Ek) are more objectively measurable than
their respective utilities. For E[C(S(Ek))], however, the case is not
so clear. Some sanctions are difficult indeed to assign a dollar
cost -- conceptually, let alone practically. For example, one may
question whether it even makes sense to view admonition, loss of li-
cense, expulsion from the AICPA, or imprisonment in terms of dollars
and cents. Thus, even relaxing the assumption that net utility is the
factor to be maximized does not render the objective function applica-
ble to actual audit situations.

Suppose, however, that we eliminate for the moment the expected
cost (or disutility) of sanctions from consideration. The objective

function would then become:

Maximize R(Ek) - C(Ek)' (0-2)

Profit maximization, however, seems somehow inappropriate as an objec-
tive for a service professional such as the public accountant. Cer-
tainly where the auditor's charges are a function of his direct ex-
penses, professional ethics should prevent his performing tests for
the sole purpose of increasing his fee. Furthermore, for many engage-
ments, the auditor's fee is a fixed amount -- the result of negotia-
tions prior to any actual field work. Therefore, if we omit the ex-
pected cost of sanctions from the objective function, let us assume
ggst minimization as the auditor's objective rather than profit maxi-

mization. We may then write the objective function as simply:

Minimize C(Ek)° (0-3)

“‘1!

 

a
'v «it

"'~'\" 0..

r
“a. .

,_. ‘.‘!
M 8-»‘13:

. 'o.
. , ‘.D‘
‘ e
.
'.‘”7‘1
gs
'"ui'.
-
n.
.a 9‘
IA‘
‘1

46
Now, even though reasons of practicality may require the auditor
tocmdt the expected disutility of sanctions from his objective func—
tion, he cannot completely ignore this relatively important factor and
still hope to approximate any "ideal" model. Therefore, since he can—
not include the expected disutility of sanctions in his objective

function, he must introduce it as a constraint of the form:

E[U <s<ak>>1 s Umax(s) (c—4)

where: E[U-(8(Ek))] is the expected disutility of sanctions
associated with evidential collection Ek’
and
Umax(s) is the maximum expected disutility of sanc-
tions the auditor is willing to accept and
is strictly a function of firm policy and

individual auditor preference.

The expected disutility of sanctions proves to be much easier to
handle in this form. In the first place, the auditor need not measure
it with the precision he would require were it part of his objective
function. Instead, he may simply offset any lack of precision in the
factor's measurement by obtaining sufficient evidence to insure slack
in the constraint —- i.e., a margin of safety -- at least equal to his
lack of precision.8 Of even greater importance, however, is the fact

that treating the expected disutility of sanctions as a constraint

_—

8The general effect of this constraint (discussed more fully on
pp. 61-63) is to increase the auditor's evidential support requirement
beyond the "minimum necessary for a professional opinion" on any given
assertion.

 

 

47

removes the restriction that it be combinative with revenues and costs
and, as we shall see, enables the auditor to replace it with an equiv-
alent set of constraints even easier to handle from a practical stand-
point.

The first step toward this proposed simplification is to replace
the overall disutility constraint with a set of similar constraints --
one corresponding to each material assertion in the client's financial
statements. Recall that in our "propositions approach" construct, we
have assumed that the auditor's responsibility for an opinion on any
set of financial statements extends to a responsibility for evaluating
eadh individual material proposition or assertion contained in those
statements. Because of this responsibility, an auditor faces the risk
of incurring sanctions for failure to detect material error in each
proposition he evaluates. We may denote the expected disutility of
sanctions associated with any particular assertion, a, as

E[U-(8(Ek,a))]. and note that, in general:

E[U'(S(Ek,a))] = p(Ma) p(FIMa n Ek) E[Msila n Man Ek)
E[U_(SiISi n F n Man Ek)]],

where: p(Ma) is the probability that the
ath assertion is materially
misstated,
p(FIMal‘ Ek) is the probability that the
auditor fails to detect

such error given that it

 

nil

 

48
exists and he selects evi-
dential collection Ek’
P(Si|F 0 Ma,“ Ek) is the probability that the
auditor will incur sanction,
81’ given that, having se—
lected evidential collec—

tion E he fails to detect

k’
a material misstatement
which exists in the 3th
assertion, and

E[U-'(SiIS:L n F n Ma 0 Ek)] is the expected disutility
of sanction 81’ given that,
having obtained evidential
collection Ek’ the auditor
incurs the sanction for
failing to detect a mate-

rial error which exists in

the ath assertion.

Now, presumably, the expected disutility of sanctions for fail-
ure to detect material error in the financial statements as a whole is
merely the sum over all propositions of the expected disutility of
sanctions for failure to detect material error in each proposition.

Therefore, we may rewrite our constraint:

 

E... 4,-

IL’
'o.

~L

 

49

E[U (8(Ek))] §E[U (8(Ek.a>)]

Emma) p(FIMan Ek) Elwin? n “a n Bk)

E[U-(Silsi n F n Man Ek)]]]

Umax(S) (i = l, 2, ..., s; a = l, 2, ..., r)

IA

One way of assuring that the auditor will satisfy constraint,

(C-4), is to require that for each assertion, a:

p(Ma) p(FlMan Ek) E[p(Si|F n Man ER)

Umax(s)

r (C-éa)

E[U (silsin an Man Ek)]] _<_

where: r is the number of assertions contained in the financial

statements.

Therefore, a set of constraints, one for each material assertion in
the financial statements can replace the original overall disutility
constraint.

Evaluation of the right side of each of these constraint in-
equalities is relatively simple once the auditor has determined
U;ax(S) (which we previously noted will be a function of firm policy
and individual auditor preference). Evaluation of the left side, how-

ever, is complicated because of the number of factors the auditor must

take into account:

to
ha .
kknot

‘ I

J- p18.
a.
A
5|

(7‘

SO
1. p(Ma), a function of the quality and comprehensiveness of
the client's relevant internal controls,
2. p(FIMalfi Ek)’ a function of the composition of evidential
collection, Ek’
3. p(SiIF n Ma 0 Ek)’ a function of:
a. the composition of evidential collection Ek’
b. the nature of the specific error involved,
c. the degree of exposure the client's statements will
receive, indicated by the client's: (1) size, (2)
nature of operations, (3) ownership distribution, (4)
issuance of covenanted securities, and
d. the client's general health, indicated by the client's:
(1) general financial condition, (2) rate and method
of growth, (3) method of financing operations, and (4)
general economic environment, and
4. E[U-(Silsin F n Man Ek)], a function of:
a. the specific sanction, and the auditor's utility
function,
b. (in some cases) the composition of evidential collec-
tion Ek’ and
c. (in some cases) the size and nature of the misstate-

ment 0

Clearly, it would be far more convenient if the left side of the
inequality were a function solely of the composition of Ek’ and the
right side incorporated all the other relevant factors. Then the au-

ditor would only have to consider these factors once, rather than once

:L 8'5

.I-

‘v‘ .0 u..-
:~~D~~ Dish

!a;..,_"_.

’
“ ~15...
"rm ‘ . .
.n.'.’ ‘CG

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st}
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51
for each evidential collection evaluated. Fortunately, we can con—
struct such a set of constraints.
Toward that end, let us note first of all, that since p(Ma) is
independent of Ek’ we may divide both sides of the inequality by this

factor, leaving:

p(FIMa n Ek) §[p(SilF n Ma n Bk)

(3)

max

E[U (Silsin F 0 Man ER“ 3 m.

(C-4b)

We have previously assumed that p(FIMaifi Ek) is a decreasing
function of ba(Ek)’ the evidential support provided by collection Ek
for the auditor's evaluation of the ath assertion in the client's fi-
nancial statements. Since no a priori reason exists for us to believe
that the auditor's probability of incurring sanctions or his expected
cost for sanctions incurred should increase as his evidential support
increases, let us also assume that, for each sanction, Si’
p(SilF n Ma n Ek) and E[U (Silsi n F n Ma 0 Ek)] are decreasing or

constant functions of ba(Ek)' Then it must follow that:

p(FIMan Ek) E[p(SilF n Man Ek) E[U (silsin F n Man Ek)]]

is not only also a decreasing function of ba(Ek)’ but is an increasing

function of p(FlMan Ek), i.e., for p(FlMan Eh) _<, p(FlMa n E ),

J

p(FIMafi Eh) E[p(SilF 0 Man Eh) E[U-(silsin F n Man Eh)“

)E[U-(Si|Sin F 01430 E )1],

3

s p(FIMan EJ) E[p(SilF n Man Ej

I.’
-3

I"

9.. ‘

a.
'1 . ‘I
in“...

.
a

‘t
‘vu

0A
U

52

with equality holding in this statement if and only if:
n = .
p(‘r‘lMa Eh) p(FlManEj>
Now, suppose that the auditor could identify the collection, E',
for which:

p(FIM n El) E[p(SilF n Ma n Ek)
- n
E[U (Si'Si FnMan Ek)]] gr

takes its maximum value. Then clearly, any other collection, E he

k9
might wish to evaluate would satisfy constraints, C-4b, if and only if:

p(FIMan Ek) E[p(SiIF n Man Ek) E[U (silsin Fn Man Ek)]]

s, p(FIMan a') Z[p(Si|F n Man 13') E[u‘(silsin F n Man E')]],
1

Since, however, p(FIMan Ek) E[p(SilF n Man Bk)

E -
[U (SilS1 n F n Ma n Ek)]] is an increasing function of p(FIMa fl Ek)’
the auditor need only insure that his collection satisfies:

p(FIMan Bk) _<_ p(FIMan E') to satisfy this condition. Therefore, the

set of constraints:

p(FlMan '31.) s p(FlMan E‘) (a .. 1, 2, r) (C-4c)

is equivalent to the set of constraints:
0
p(FlMa Bk) E[fisilF n Man Ek)

u’ (S)
- _w— _
E[U (silsin F A Man Ek)]] 5 IIPWaH (c 4b)

Tzea

- -
“" OQQ'A'
a , 4

". b.5bhh

'2.-

‘uis F

'4 I
.- ~ A
t

5

.4:

53
Estimating p(FIMa n E')

The advantage of the set of constraints, C-4c, is that the left
side factor is a function solely of the evidential collection under
consideration, while the other factors relevant to these constraints
(23255, p. 50) now exert their influence on the right side. A concep-
tual problem arises, however, with respect to the calculation of

p(FIMan E'). If the value of Z[p(SiIF n Ma 0 E')
i

E[U-(Si'Si n F n Ma n E')]] were independent of the value of
p(FlMa n E'), then solving the inequality for this latter factor would
be a simple matter of dividing both sides of the constraint by the

summation. Since, however, Z[p(SilF n Ma n E')
i

E[U-(Silsi n F n Man E')]] may be a function of p(FIMan E'), the
auditor cannot use this approach. In fact, in order to calculate the
value of p(FIMa n E'), he must first know the actual composition of
E' -- but it is most unlikely that he will ever have this information
in an actual audit situation. If, however, he could approximate

ZIP(SilF n M n E') E[U-(S ls n F n M n E')]] with an appropriate
1 a i i a

constant, he might still be able to obtain a useful estimate of
p(FIMan E') which does not require specific knowledge of the compo-
sition of E'.

In fact, a useful approximation of Z[p(SilF n Ma n E')
i

E[U-(SilSin F n Ma n E')]] does exist. Recall that the auditor's
evidential collection must already satisfy another set of constraints

with respect to p(F’IMa n Ek)’ specifically:

{Mu
eral‘

S“:

1‘”

'.'-ere o

54

p(FIMan Bk) 5 p (a = 1, 2, ..., r) (C-3a)

where:

P

8.1118)!

amax

is determined by: (1) generally accepted auditing
standards and authoritative pronouncements of the
AICPA, (2) authoritative pronouncements of the
SEC, (3) commission requirements (for regulated
industries), (4) policies of individual public
accounting firms, (5) specific terms of the
auditor-client contract, (6) materiality consider-
ations, and (7) the auditor's evaluation of the
probability that the ath assertion of his client's

financial records contains material error.

Now presumably, if the auditor's evidential collection satisfies

this requirement, then for each sanction, Si’ p(SiIFtfi Math Ek) will
be quite low (in most cases - O), and hence not extremely sensitive to
further decreases in p(FIMaiO Ek)' Furthermore, for most sanctions
(the main exception being lawsuits), E[U-(Silsi n F n Ma n Ek)] is apt
to be generally insensitive to changes in P(F|Ma" Ek)° Therefore,
E[fisilr n Ma n Ek) E[U-(Silsi n F n Ma n Ek)]] should not vary dras-

tically with changes in p(FIMalfi Bk) 5 pamax' For this reason,

E'MSiIF“ Ma n (Ek : p(Fn Man Ek) - pmx»

E[U-(Silsin F n Ma n (Ek : p(FlMan Ek) = pamax))]]

where: 13(51'1' n Ma n (Ek : p(FlMan Ek) = pamax” is the prob-

ability that the auditor will incur sanction, 81’

given that, having obtained the minimum evidential

55
support necessary for a professional judgment on
the ath assertion in his client's financial
statements, he fails to discover a material mis—
statement existing in that assertion, and
E[U"(sils1 n F n Ma n (Ek : p(FIMa n Bk) = pamax)) is
the expected disutility of sanction, 81’ given
that, having obtained the minimum evidential sup-
port necessary for a professional judgment on the
ath assertion in his client's financial state—
ments, the auditor fails to discover a material
misstatement existing in that assertion and

therefore incurs the sanction,

suggests itself as an approximation of Z[p(SilF n Ma n E')
i
_ (\ ' .
E[U (silsin to M8 E )1]
Adopting this approximation permits at least a conceptual esti-
mate of p(FIMa n E') (without requiring actual knowledge of the com-

position of E') as follows:

U (S)
p(FlMan E') a max

r[p(Ma)] E[p(SilF n Ma n (1:k : p(FIMa n Ek) a pamaxn

E[U-(SiISin Fn Ma n (Ek : p(FlMan Ek) - pamax))]]

To the auditor, p(FIMal1 E') represents the maximum acceptable
probability (based upon his evaluation of the expected disutility of
sanctions) that he will fail to detect a material error existing in

the ath assertion of his client's financial statements. Therefore,

56

let us denote our estimate of this probability as pamaxrisk' If the

auditor is to be able to replace the set of constraints:

p(FIMa n Ek) 5 p(FIMa n E') (a = 1, 2, ..., r) (C-4c)
with a similar set:
p(FIMa n Bk) 5 pamaxrisk (a a: l, 2, r) (C—4d)

he must first be sure that p s a conservative estimate, i.e.,

amaxrisk i

'
p kf_p(F|ManE).

amaxris

If, and only if, this condition holds, any evidential collection which
satisfies the C-4d constraints will also satisfy the C-4c constraints,

since, in this case, p , will obviously be the tighter con-

amaxrisk
straint.
To see whether this condition indeed holds, we must consider two

v n V
possible cases, (1) p(FIMan E ) s pamax’ and (2) p(FIMa E ) > pamax'

We have previously asstnned Z[p(SiIF n Ma n Bk)
1

E[U-(Silsin F n Man Ek)]] to be a decreasing or constant function of
p(FIMatfi Ek)° Therefore, if p(FIMalfi E') s pamax’ obviously:
v ' v
E[fisilF n Man E) E[U (silsin F n Man E )1]
n : =
s, §[p(si[F n Ma (Ek p(FIMan Ek) p ))

amax

E[U-(Silsi n F n Ma n (Ek : p(FlMaO Ek) = pamax))]]’

U (S)
in which case, since division of-;T§%E-7T by the latter factor must
a

3 .14

..
I
l “n!
F
V. I.
on, a

.h

""‘N we

‘ I

Q
h ...‘1 h
4
~-
7‘.
I
O
‘-.
a
w.‘ \. .“I

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Jo'"

57

yield a smaller probability than division by the former factor:

!
pamaxrisk S p(FlMa" E )’

If, however, p(FlMadfl E') > pamax’ the senses of the above in-

equalities are all reversed and:

'
pamaxrisk > p(F'Man E )'

Therefore, p is a conservative estimate of p(FIMatfi E') if,

amaxrisk

and only if,

V
p(FIMa n E > 5 pm.
This situation is actually sufficient, however, since where

' '
p(FLMaofl E ) > p , the pamax constraint will govern the auditor s

behavior, and the fact that p > p(FIMain E') will not matter

amaxrisk
since the C-4c (or C-4d) constraint will be superfluous anyway.

Now, admittedly, substitution of the somewhat tighter C-4d con-
straints for the C-4c constraints may result in overauditing. If,
however, p(SilF n Ma n ER) and E[U (sills1 n F n Ma n Ek)] are, in
fact, relatively insensitive to changes in p(FIMacfl Ek) < pamax (as we
have assumed), the overauditing due to this substitution will not be
extensive.

A Modified Propositions Approach Construct for
Audit Evidence Accumulation

 

substitution of the objective function:
Minimize C(Ek) , (0-3)

and the set of constraints:

p(FIMaO Ek) s p (a = 1, 2, r) (C-4d)

amaxrisk

'0‘ D. R
.-

.u on.

(J
I].

 

m. ,‘h
..

'I‘I‘ ‘
" " bn‘
‘ Q
1.. I
-
‘vu.i

w...-

u... .

a" ‘-
0“. ‘H

0..

""5

‘1 :‘O'_ o
I

\4
o U‘:I
|
.i
«:O '.‘
" ~
'- r.
J '-

58

for the objective function:

Maximize U+(R(Ek)) + U'(C(Ek)) + E[U-(8(Ek))] (0-1)

leaves the following modified (normative) "propositions approach"

model:

Minimize C(Ek)

subject to the constraints:

T<Ek) S Tmax

SR(Ek) S SRmax

p(FIMan Ek) .<. pamax’ or ba(Ek) 2, bamin (a=l, 2, ..., r)
p(F'Man Ek) E pamaxrisk’ or ba(Ek) Z baminrisk9 (a=1, 2’ °°" r)

To show how this modified "propositions approach" model relates
to actual audit situations, the remainder of this chapter explores the
model's implications for the following steps in audit judgment forma-

tion (originally introduced supra, p. 38):

 

9Since we have assumed ba(Ek) a decreasing function of
P(FIMa n Ek), the set of constraints:

ba(Ek) g baminrisk (a = 1, 2, ..., r) (C-4e)
is equivalent to the set of constraints:
p(FIMan ER) 5 pamaxrisk (a - 1, 2, ..., r) (C-4d)

where baminrisk signifies to the auditor the minimum evidential sup-
port necessary for an opinion on the ath assertion of his client's
financial statements given the client's "health" and the exposure his
statements will receive. The value of baminris is obtained, at least
conceptually, by substituting Pamaxrisk for p(F Ma nsEk) in the func-
tion, ba(Ek) - g(p(FIMain Ek)), or as a direct function of the factors

which determine pamaxrisk (supra, p. 50).

a.

 

 

 

59

1. identify all the material propositions contained in the set
of financial statements under examination (pp. 59-60),

2. for each proposition:

determine the degree of evidential support required to
justify an opinion on the proposition (pp. 61-63),
select the kind(s) and estimate the quantity(ies) of
evidential matter necessary to provide the required
degree of evidential support (pp. 64-68),

design the audit procedure(s) necessary to yield the
desired kind(s) and quantity(ies) of evidence (p. 68),
apply the procedure(s) and amass a collection of evi—
dential matter (p. 68),

evaluate the collection of evidence (If the evidence
provides sufficient justification, render an opinion on
the proposition. If not, either gather more evidence

or disclaim an opinion on that proposition.),

3. based upon the results of the individual proposition evalu-
ations, render (or disclaim) an opinion on the financial

statements as a whole (pp. 71-72).

1 Identify All the Material Propositions Contained

in the Set of Financial Statements
under Examination

Identifying all of the important propositions comprising a given
financial statement item will usually require great care on the an?

(fitor's part since such propositions are often subtle. For example,

consider the following:

r

6O

Marketable Securities . . . . . . . . . . $20,000.

Amxmding to Mautz, this typical balance sheet item contains "at least
fmnrpropositions requiring competent evidential matter for their dis-
position:

1. That the company owns the investments.

2. That the amount shown is reasonable and determined in ac—

cordance with generally accepted principles of accounting.
3. That the investments are actually marketable.
4. That they are classified appropriately in the financial

statements."10

Important as the task of proposition identification is, however,
fluther discussion of this phase of the auditor's work is beyond the
scope of this dissertation, which is primarily concerned with the au-

cfltor's approach to verifying such propositions as he is able to iden-

tify.

10R. K. Mautz, "The Nature and Reliability of Audit Evidence,"
Eh; Journal of Accountancy_105 (May 1958): 44.

61

For Each Proposition:
3. Determine the Degree of Evidential Support Required
for Evaluation of that Proposition,

b. Select the Kind(s) and Estimate the Quantity(ies) of
Evidential Matter Necessary to Provide the
Required Degree of Evidential Support,

c. Design the Audit Procedure(s) Necessary to Yield the
Desired Kind(s) and Quantity(ies) of Evidence,

d. Apply the Procedure(s) and Amass a Collection of
Evidential Matter, and
e. Evaluate the Collection of Evidence (If the Evidence
Provides Sufficient Justification, Render an
Opinion on the Proposition. If Not, Either
Gather More Evidence or Disclaim an
Opinion on that Proposition)

flatermine the Degree of Evidential
Mort Reflired

 

 

The relationship between this step in the performance of an au-
cfit engagement and the modified "propositions approach" model should
be Obvious. This is the point at which the auditor determines bamin

and}: (or, equivalently, pamax and p ). We have a1-

aminrisk amaxrisk

ready identified the factors which determine these constraints (gpppg,
rm. 19-20, 50), and will discuss them further in Chapters IV and V,
respectively.

Ideally, of course, the auditor would obtain quantitative mea-
muements for each of these factors, substitute their values in appro-
priate mathematical functions, and thereby derive quantitative con—
Straints. In actual practice, however, virtually none of the relevant
factors lend themselves to meaningful quantification. Furthermore,
the appropriate functions for relating these factors to b

amin’

, and p are not apt to be well defined. These

baminrisk’ pamax amaxrisk

constraints, therefore, must, at least for the present, remain subjec-
tive in nature. Even if the auditor is unable to place quantitative

measures on the degree of evidential support necessary for him to

 

 

62

judge the validity of a particular financial statement assertion, how—
ever, he can define what, in terms of evidential matter, he needs to
support an opinion on the assertion's truth or falsity, and even if he
is unable to define precisely the maximum acceptable probability that
he will fail to find a material error which exists in a particular as-
sertion of his client's financial statements, he should be able to ar-
rive at a rough estimate of that probability.

At any rate, regardless of the form these constraints take, the
basic approach to their determination is the same. Ideally, the au-
ditor should first define his minimum evidential requirements based
upon:

1. Generally Accepted Auditing Standards and other authorita-

tive pronouncements of the AICPA,

2. authoritative pronouncements of the SEC,

3. commission requirements for regulated industries,

4. policies of his accounting firm,

5. specific terms of his contract with his client,

6. materiality considerations, and

7. his evaluation of the probability that his client's records

contain material error, based on:
a. his findings during his review of the client's in-
ternal control system,
b. his findings in actual tests of the client's records,
c. his evaluation of the "general" riskiness of the cli—
ent.
When he has established these minimum requirements, he should then

evaluate their adequacy in the light of such risk factors as:

63
l. the degree of exposure the client's statements will receive,
indicated by:
a. the client's size,
b. the nature of the client's operations,
c. the distribution of the client's ownership, and
d. loan covenants which require the client to maintain
specified account balances or ratios,
2. the probability that the client will file bankruptcy subse—
quent to the audit, indicated by:
a. factors which affect or indicate the degree and types
of financial crisis the client can withstand, e.g.:
(1) factors which indicate the client's financial
position,
(2) economic conditions related to the availability
of external capital,
(3) the client's rate and method of growth, and
b. factors which affect or indicate the probability that
the client will face a financial crisis which exceeds
its capabilities, e.g.:
(l) the nature of the client's operations,
(2) economic conditions relevant to the client's
marketplace,

(3) the client's method of financing operations.

 

u ,
.acr4

|‘¢I ‘

. __
:v p.

‘.‘..g g ‘

.. .
.T;'. .-
" “r L.

; .~-...

n" ¥~nl
I. .

3‘ .

-'

.

z

' ...,

'4. ‘~~e

 

o
.: ‘.‘. v
Z') '.'. ‘.a.
a,,:
\‘II
a
‘ i a
‘ '~ d

 

.U
I
‘1":‘1 "r
[it
.I: .
' L" a.
1 “e
V
t f:
.t

~ I
I. ‘.'l
'. :I
"a K
I?”
\V-.i

64

Select the Kind(s) and Estimate the
Quantity(ies) of Evidential Matter
Necessary to Provide the Required
.Qggree of Evidential Support

Having determined the evidential support requirements for a par—

 

ticular financial statement assertion, the auditor's next step is to
convert these requirements into specific evidential requirements,

i.e., convert from bam and b (or p and p ) to

in aminrisk amax amaxrisk
qij' At this point, let us note that, in general, any unit of eviden-
tial matter displays one of the following mutually exclusive charac-
teristics:
1. it tends to support the proposition in question ("positive”),
2. it tends to refute the proposition in question ("negative"),

3. it neither supports nor refutes the proposition in question

("neutral").

The evidential support provided by a given evidential collection, Ek’

will be a function of the number of positive and negative units of
each type of evidence included in the collection and the degree of
support provided for an opinion on that assertion by a unit of posi-

tive or negative evidence of a given type,11 i.e.:

ba(Ek) - : i = l, 2, ..., m; j = l, 2, ..., n})

(a = 1, 2, ..., r)

11Thus we assume that "neutral" units or types of evidential
matter contribute evidential support a O.

65

where: denotes the number of units of type i evidence

qija

gathered at time, t , which are "positive" with re-

3
spect to the ath assertion in the client's finan—
cial records, and

qija denotes the number of units of type i evidence

gathered at time, t , which are "negative' with re-

3

spect to the ath assertion in the client's finan-

cial records.

Now, if each individual proposition in a set of financial state-
ments were entirely independent of all other propositions in those
statements, and if each proposition required entirely different types
of evidential support for its verification, the auditor's attempts at
minimizing audit costs would consist of minimizing the cost of gather-
ing sufficient evidence to verify each assertion individually. To be
sure, he would have to consider a number of factors, including:

1. requirements of Generally Accepted Auditing Standards and
other authoritative pronouncements of the AICPA, SEC, and
other relevant regulatory commissions,

2. staff constraints,

3. time constraints,

4. the evidential support function for each available type of
evidence obtained at each possible time of collection, a
function including the following variables in addition to

the number of units involved:

e.

66
the relevance of the specific type of evidential
matter to each proposition,
the reliability of the specific type of evidential
matter, itself a function of:
(l) the conclusiveness of the given type of evi-
dence, and
(2) the possibility of misinterpreting evidence of
this nature,
the timeliness of the evidential matter, itself a
function of:
(l) the time at which the evidence is obtained, and
(2) the quality and comprehensiveness of the cli-
ent's internal controls,
the statistical parameters of the population under-
lying the assertion he wishes to evaluate:
(1) size,
(2) variance,
(3) rate of error, and

the existence of corroborative evidence,

5. the cost function of each type of evidential matter.

Nevertheless, for each assertion, the auditor would probably not

be concerned with more than a few relevant types of evidence, and he

would not have to handle the decision complications posed by situa-

tions in which certain types of evidence provided support for more

than one assertion.

67
This pure state, however, does not exist since, as Leight has

noted:

. . an audit is like the piecing together of a jig-
saw puzzle, one piece gives us the outline for the
next piece. When we audit one account, we get some
information about another account, and when we are
finished auditing all the accounts they will fit to—
gether and form a picture . 12

Therefore, if the auditor tests each assertion separately without
reference to any other assertions, he will undoubtedly be guilty of
grossly "overauditing." On the other hand, because of the large numr
ber of assertions, available types of evidence, and extent and timing
alternatives, finding the specific collection which absolutely mini-
mizes audit costs (except purely by accident) is undoubtedly beyond
the auditor's capacity. Nevertheless, the norm suggests some basic
guidelines which might aid him to reduce the extent of overauditing.
First of all, as the auditor attempts to identify types of evi-
dence relevant to a given assertion, he should keep in mind three po-
tential sources of evidential support for his opinion:
1. evidential matter specifically selected for evaluation of
the assertion in question,
2. evidential matter specifically selected for evaluation of
some other assertion, and

3. the actual status of other assertions.

Secondly, because "an audit is like the piecing together of a

jigsaw puzzle,‘ when determining the type, extent, and timing of

 

12Lester A. Leight, "Recommended Opinions and Disclaimers,"
The New York Certified Public Accountant 33 (June 1963): 412.

 

rid

 

 

 

 

 

 

 

 

68

specific tests he will perform on any particular proposition, the au-
ditor should remain aware of the possibility that, by the time he
comes to judge that proposition, he may already have a fair amount of
evidential support on which to base his judgment -- support obtained
during the evaluation of other propositions. Furthermore, when se-
lecting the type, extent and timing of tests he wishes to perform (in
addition to considering Generally Accepted Auditing Standards and time
and staff constraints, and in addition to evaluating each potential
test with respect to its cost and the degree of evidential support it
should provide for his opinion on the assertion of interest), the au-
ditor should also evaluate each potential test on the basis of eviden—
tial support it may provide for his opinion on other assertions in the
client's financial statements.
Design the Audit Procedures Necessary
to Yield the Desired Kind(s) and
Qpanti§y(ies) of Evidence

This step merely involves translating evidential requirements
into specific tests and procedures capable of yielding the desired
kinds and quantities of evidential matter and further discussion of it
is unnecessary for the purposes of this dissertation.
:Apply the Procedures and Amass a
Collection of Evidential Matter

This step is self-explanatory.

.41.-

 

 

a.

\1
"

 

 

o,
r
\

 

 

 

69

Evaluate the Collection of Evidence.
(If the Evidence Provides Sufficient
Justification,*Render an Opinion on
the Proposition. If Not, Either
Gather More Evidence or Disclaim an
Opinion on that Proposition.)

 

 

 

 

 

 

In this step, the auditor essentially looks at his collection,
+ -
identifies the set, {qija’ qija .

and solves the function introduced in the previous section to deter-

b . , b . 2 b .
amin amln aminrlsk
mine ba(Ek)° If ba(Ek) z , then pre—

baminrisk’ baminrisk Z bamin

sumably the auditor will accept assertion a. Likewise, if

bamin’ bamin Z baminrisk
I-ba(Ek)l z , then presumably he will

aminrisk’ baminrisk 3 bamin
reject the assertion. If, however, Iba(Ek)| < bamin’ or

'ba(Ek)' < b hen he must either obtain more evidential sup-

aminrisk’ t
port or disclaim any opinion on that assertion.

That this third (inconclusive) situation is possible points up
an important fact which we shall return to in Chapter IV, i.e., in
steps (b) and (c), the auditor only estimates the evidential collec-
tion which should satisfy his evidential requirement, ba(Ek)° Until
he actually gathers and evaluates that collection, however, he cannot

know whether his estimate actually does satisfy his requirement.

Clearly, when an auditor eventually evaluates his collection, if:

bamin’ bamin baminrisk
Ib(E)I> .
a k

>
aminrisk' baminrisk ’ bamin

he will have overaudited, and, if the cost of collecting and

i = l, 2, ..., m; j = l, 2, ..., n},

Juli

 

't

 

 

.‘z\

 

\L‘

7O
evaluating a unit of the audit evidence selected is greater than zero,
he will have incurred excess costs. Of course, he can avoid over-
auditing by collecting and evaluating one unit of evidence at a time
until he achieves his desired degree of evidential support. As a
matter of fact, in the absence of effective constraints on time and
staff, if the marginal cost of collecting and evaluating a particular
type of audit evidence is constant, this approach is the optimal one
from a cost standpoint. In most cases, however, the marginal cost of
collecting and evaluating a particular type of audit evidence will
probably pp£_be constant, but rather will be a decreasing function
(over the relevant range) of the number of units collected and evalu-
ated in a "batch." Therefore, if the auditor obtains his collection
one unit at a time, or, more generally, if he obtains a collection

such that:

'ba(Ek)' < bamin’ or 'bawk)l < baminrisk’

he stands to incur excess costs due to "underauditing." At any rate,
cost may not be the only relevant factor since constraints on time
and/or available staff may exist, e.g., time constraints would un-
doubtedly preclude an auditor's collecting receivable confirmations
one-at-a-time (though evaluation of receivable confirmations could be
a sequential type process). Therefore, the auditor must weigh the
costs and risks of overauditing against the costs and risks of under—
auditing when he initially determines his plan for collecting and
evaluating evidence. A certain degree of "programmed" overauditing

‘may be quite rational on the auditor's part, if, as seems likely, the

71
per unit costs of underauditing a particular proposition exceed those

of overauditing that proposition.13

Based upon the Results of the Individual Proposition
Evaluations, Render (or Disclaim) an Opinion on
the Financial Statements Taken as a Whole
Mautz has summarized the process by which the auditor moves from

his individual evaluations of each assertion contained in a given set

 

13At this point, some comments concerning overauditing seem in

order. So far, we have identified four causes of or reasons for an
auditor's obtaining greater evidential support for a given proposition
than is strictly necessary in the circumstances:

1. failure or inability to consider all possible sources of
evidential support for a given proposition,

2. to justify higher audit fees,

3. to offset the lack of precision inherent in current methods
of determining bamin or baminrisk: i.e., to offset the risk
that he will underestimate his evidential support require-
ment for a particular proposition due to his inability to
measure that requirement precisely, and

4. to offset the risk of underauditing, i.e., to offset the
risk that his initial estimate of an evidential collection
sufficient to yield his evidential support requirements will
prove to be inadequate, thus leading to excess costs.

For the sake of completeness, let us add a fifth reason occasionally
found in practice:

5. because the client requests, and is willing to pay for, the
auditor's performing certain tests or procedures deemed un-
necessary by the auditor for an Opinion on the client's
statements.

Of these five reasons for overauditing, the first is to some de-
gree beyond the auditor's control and hence leads to unintentional exr
cesses and the second is clearly unacceptable in the light of profes-
sional ethics. At least within limits, however, the third and fourth
seem justifiable for the reasons enumerated above. The limits, of
course, are where the auditor relies on overauditing to compensate for
completely ignoring relevant audit variables. (The fifth reason
listed, of course, requires no justification.)

72
of financial statements to an opinion on that set of statements taken
as a whole. He states:

In forming a composite or over-all opinion as to
the fairness of presentation of the financial statements,
the auditor is concerned not with evidence, but with
the relative weight to be accorded his various judgments
on the many subsidiary propositions on which he has ac—
quired evidence and formed opinions. At this point he
reviews each of these many propositions and his judgment
on them, evaluates their importance, balances them
against any contrary judgments, and sums them all up.

It is like an algebraic summation with both positive and
negative elements, some of which are far more important
than others. In those cases in which the "untrue" propo-
sitions outweigh the "true," the auditor must refrain
from giving a standard opinion. If only a few important
propositions are unacceptable and a majority are satis-
factory, a qualified opinion may be forthcoming. Even a
"clean" opinion, however, does not mean that all propo-
sitions were proved true; it means only that no material
propositions were found to be unsatisfactory. On balance,
and taken in the aggregate, they constitute a fair pre-
sentation of events and results as the auditor under-
stands them.14

 

Summagy
Chapter I introduced the following as a normative model for

audit evidence accumulation:

Maximize U+(R(Ek)) + U-(C(Ek)) + E[U"(S(Ek))] (0-1)
subject to: B(Ek) a 13min (c-1)
T(Ek) _<_ Tmax (c-2)
Sunk) 5 Slim. (0-3)

 

1l'Mauts, "Evidence, Judgment, and the Auditor's Opinion," p. 44.

73

While this construct provided a useful framework for identifying and

studying factors which influence audit evidence accumulation, it is of

little other practical use.

This chapter, therefore, has considered ways of modifying and,

where necessary, approximating the ideal in such a manner as to arrive

at a normative construct compatible with the following general frame—

work of audit judgment formation and capable of practical application

within this framework:

1. identify all the material propositions contained in the set

of financial statements under examination,

2. for each proposition:

a.

determine the degree of evidential support required to
justify an opinion on the proposition,

select the kind(s) and estimate the quantity(ies) of
evidential matter necessary to provide the required
degree of evidential support,

design the audit step(s) necessary to yield the de-
sired kind(s) and quantity(ies) of evidence,

apply the steps and amass a collection of evidential
matter, and

evaluate the collection of evidence (If the evidence
provides sufficient justification, render an opinion
on the proposition. If not, either gather more evi-

dence or disclaim an opinion on that proposition.),

 

74
3. based upon the results of the individual prOposition evalu—
ations, render (or disclaim) an opinion on the financial

statements as a whole.

Essentially, two modifications of the original model are neces-
sary to achieve this goal:

1. replacement of the original constraint:

B(Ek) 2 Bmin’ (C-l)
with the set of constraints:

ba(Ek) Z bamin’ (a = l, 2, ..., r) (C-la)
or their equivalent:

p(FlMan ER) 2 pamax’ (a - 1, 2, ..., r) (C-lb)

where: ba(Ek) is the degree of support provided by

evidential collection Ek for the au-
ditor's opinion on the ath assertion
of his client's financial statements,
bamin is the minimum evidential support

necessary for a professional opinion
on that ath assertion,

p(FlMa n ER) is the probability that the auditor
will fail to detect material error
which exists in the ath assertion of

his client's records given that he

selects evidential collection Ek’

75
p is the maximum allowable probability
amax

that the auditor will fail to dis-
cover material error which exists in
the ath assertion of the client's
statements,

ba(Ek) and p(FIMa n Ek) are determined by the
same factors which determine B(Ek) in
the original model, and

b and p are determined by the same fac-
amax

amin

tors which determine B in the
min

original model,

2. replacement of the original objective function:

Maximize U+(R(Ek)) + u'(c<ak)) + E[u'csmkm (0-1)

with the objective function:

Minimize C(Ek) (0-3)

and the set of constraints:

p(FIMa n Bk) 5. pammisk (a = 1, 2, r) (c-ad)
.gp their equivalent:

where: p(FlMa n Ek) and ba(Ek) are defined as above,

p represents to the auditor, the maximum

amaxrisk

acceptable probability (based upon his

evaluation of the expected disutility of

baminrisk

76

sanctions) that he will fail to detect a
material error existing in the ath asser-
tion of his client's financial statements,
and

represents, to the auditor, the minimum
evidential support necessary for an opin-
ion on the ath assertion of his client's
financial statements (based upon his

evaluation of the expected disutility of

sanctions).

These modifications result in the following normative construct

of auditor behavior with respect to evidence accumulation:

Minimize C(Ek)

IV

subject to: ba(Ek)

or

p(FIMa n

IA

T(Ek)

IA

SR(Ek)

hawk) a

or

p(FlMan ER) 5 p

(0-3)
bamin (a = l, 2, ..., r) (C-la)
Bk) 5 pamax (a = l, 2, ..., r) (C-lb)
Tmax (C-2)
SRmax (C—3)
baminrisk (a - l, 2, ..., r) (C-4e)

(a = 1, 2, ..., r) (C-4d)

amaxrisk

One of the primary problems with constructs of human behavior is

that one can seldom test them directly.

Unfortunately, the above

77

normative models of auditor behavior are no exception. The best one
can usually do with such constructs is to measure the behavioral vari—
ables which they suggest, observe behavior under conditions repre-
sented by these variables, and attempt to determine whether the ob-
served behavior has been consistent with the construct's predictions.

Each of the next three chapters considers factors which the
above constructs of auditor behavior have identified as relevant to
audit evidence accumulation. Their objectives will be to justify in-
clusion of each factor in its particular class of audit variables, and
to indicate how each factor should influence audit evidence accumula-
tion. Chapter VI will then compare a number of these predictions with
observations taken from actual audit situations to determine whether
auditor behavior is, in fact, sensitive to the selected factors.

Let us, therefore, now look in more depth at the "factors which
define the evidential support function for a given type of audit evi-

dence obtained at a given time."

 

CHAPTER III

FACTORS WHICH DEFINE THE EVIDENTIAL SUPPORT
FUNCTION FOR A GIVEN TYPE OF AUDIT
EVIDENCE OBTAINED AT A GIVEN TIME

Chapter I identified the following as factors which define the

evidential support function for a given type of audit evidence ob-

tained at a given time:

1.

the relevance of the specific type of evidential matter to
the audit engagement,
the reliability of the specific type of evidential matter,
itself a function of:
a. the conclusiveness of the given type of evidence, and
b. the possibility of misinterpreting evidence of this
nature,
the timeliness of the evidential matter, itself a function
of:
a. the time at which the evidence is obtained, and
b. the quality and comprehensiveness of the client's in-
ternal controls,

the statistical parameters of the population underlying the

assertion which the auditor wishes to evaluate:

78

79
a. size,
b. variance,
c. rate of error, and

5. the existence of corroborative evidence.

This chapter will examine these factors in some depth and iden-
tify each factor's logical effect on the three parameters of the au-
ditor's evidential collection:

1. the type(s) of evidence included,

2. the time(s) of collection of each type, and

3. the number of units of each type collected at a given time.

The Relevance of the Specific Type of Evidential
Matter to the Audit Engaggment

 

 

For the purposes of this discussion, let us define a type of
audit evidence as relevant (or pertinent) to an audit engagement if
that type is a valid basis for inference concerning:

1. the truth or falsity of one or more financial statement

assertions (direct relevance), and/or

2. the degree of evidential support provided for one or more

financial statement assertions by a unit of some other type

of evidential matter (indirect relevance).

Mautz emphasizes the importance of the auditor's exercising
great care in evaluating evidential matter with respect to this prop-
II

erty since, . . . there is often a considerable risk of unconscious

inference that may lead one to accept evidence that is not at all

a-pb

Iv. h

..‘u.

I.
_p..

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gut.

 

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80

pertinent."1 He attributes this risk, at least in part, to "the dif-
ficulty of separating the several propositions to be proved with re-
spect to a given item in the financial statements and questioning each
of these prOpositions separately,"2 and therefore concludes that "the
auditor must be wary in his use of evidential material. Unless it is
pertinent to the precise point at issue, it cannot be considered com-
patent for his purposes."3

Mautz makes an important point in this last statement. If a
given type of audit evidence is not relevant to a particular financial
statement proposition, then regardless of its reliability, timeliness,
and degree of corroboration, it can provide pp support whatsoever for
an opinion on that proposition. Therefore, in his attempt to estimate
the degree of evidential support provided for a particular financial
statement assertion by a given number of units of a given type of
audit evidence, the first factor the auditor must ascertain is whether
or not the type is relevant to, and hence at all capable of providing
evidential support for, an opinion on that assertion. Only then does
it make sense for him to consider such evidence in terms of reliabil-
ity, timeliness, population characteristics, and the extent to which

corroborative evidence exists.

 

1R. K. Mautz, "The Nature and Reliability of Audit Evidence,"
The Journal of Accountanpy 105 (May 1958): 44.

2Ibid.

81
Expected Influence on Audit Program

Relevance, as defined above, reflects Arens' notion that this
property is an absolute rather than a relative, i.e., "that evidence
is either relevant to the assertion or not relevant."4 We have de-
fined this factor as exclusively a "measure" of whether or not a unit
of a given type of audit evidence is capable of providing anz degree
of support at all for an opinion on a particular financial statement
item. As such a measure, it takes on only two values: zero (0) if
the particular type of evidence is not relevant to the assertion in
question, and one (1) if it is. The value it will assume depends en-
tirely upon the type of evidence involved and neither changes in
timing nor in the number of units obtained will affect that value.
Therefore, the only parameter of the auditor's evidential collection
which this factor may influence is the png of evidence included.

The Reliability of the Specific Type
of Evidential Matter

 

For purposes of this discussion, let us adopt a modified version
of Arens' definition of reliability as it pertains to audit evidence --
"the extent or degree to which a type of evidence can be considered an
accurate representation of reality"5 at the time that evidence is ob-
tained. In connection with his definition, Arens further notes that:

In auditing the measure of reliability can be
considered a continuum ranging from almost complete

 

4A1vin A. Arens, "The Adequacy of Audit Evidence Accumulation in
Public Accounting" (Doctoral Thesis, School of Business Administra-
tion, University of Minnesota, 1970), p. 123.

5Ibid., p. 106.

82
undependability, as in the case of rumor, to near

certainty6 as in the case of some kinds of physical
evidence.

Of all the factors which influence the degree of evidential sup-
port provided by a unit of a given type of audit evidence, "reliabil-
ity" has undoubtedly received the greatest attention in the profes-
sional literature. Therefore, before considering the effect of eviden-
tial reliability on the auditor's program, let us briefly review a
number of studies pertinent to this factor -- Specifically those of
Stettler,7 Mautz,8 Windal,9 and Arena.10

The earliest of these studies was that of Stettler. He sug-
gested, as the major classes of evidence, in order of generallz de-
creasing reliability: "physical evidence, documentary evidence orig—
inating outside the client's organization, evidence originating within
the client's organization, the client's books of record, and ratios
and comparisons."11 He concluded, however, that while "some indication
of the reliability of an item of evidence is apparent from the classi-

fication into which it falls, . . . there is great variation

 

7Howard F. Stettler, "Auditing Standards and Competence of
Evidential Matter," The Accountinijeview 29 (January 1954): 121-26.

 

8Mautz, pp. 40-47.

9Floyd W. Windal, "Standards of Reliability for Audit Evidence,"
The New York Certified Public Accountant 31 (June 1961): 394-400.

 

10Arens, pp. 106—122.

11Stettler, p. 126.

in the reliability of items within any given classification . . .,

83
"12

and, as factors influencing this variation, he identified:

l.‘ the independence of the evidence from the client's control,

2. the susceptibility of the evidence to suppression, manipula-

tion, alteration, or counterfeiting by members of the cli-
ent's organization,

3. the degree of judgment required for evaluation of the evi-
dence,

4. the qualifications of the person evaluating the evidence,
and

S. the quality of the client's internal control.13

In a similar study, Mautz adopted a somewhat more abstract set

of evidential categories:

that:

. . . "real evidence," for examination of the thing
itself; "testimonial evidence," for assertions of
human being8° and "indirect evidence," for all other
facts . . .14

Relating these classifications to audit techniques, he suggested

Real evidence is provided by:
Physical examination and count
Recomputation
Retracing bookkeeping procedures

Testimonial evidence is provided by:
Confirmation
Inquiry

 

12Ibid.

13Ibid., pp. 123—26.

14Mautz, p. 43.

84

Indirect evidence is provided by:
Examination of authoritative documents
Scanning
Examination of subsidiary records
Correlation with related information.

Then with respect to his three-way classification, he argued:

Real evidence is material which convinces one
of the truth of the proposition to be proved without
the necessity of an inference . . .

Testimonial evidence is obtained through state-
ments from others and requires an inference by the
auditor . . .

Indirect evidence is the "all other" category,
composed of a great variety of information all of
which requires an inference by the auditor.16

Like Stettler, Mautz maintained that, ”Audit evidence varies

considerably in reliability among the major classes of evidence and

also within each class,"17 and, in addition to the pertinence of the

particular type of evidence to the proposition to be proved, and the
timeliness of the evidence (both of which we are considering sepa—
rately), he identified the following factors as influencing the rel-
ability of a particular type of evidential matter:18

1. the possibility of the auditor's misinterpreting
the evidence,

2. the conclusiveness of the evidence,

3. the knowledge of the ones providing testimonial
evidence, 19

4. the "responsibility and integrity"
providing testimonial evidence,

of the ones

 

15Ibid.

16Ibid.

17Ibid., p. 47.

18Ibid., pp. 44-46.

191bid., p. 44.

85

the "extent of bias or self interest on the part
of"20 the ones providing testimonial evidence,
"the ossibility of manipulation or falsifica-
tion" 1 of the type of evidence,

the qualifications of the person obtaining the
evidence,

the quality of the client's internal control.

Windal's approach to the evaluation of audit evidence reliabil-

ity differed somewhat from that of Stettler and Mautz. This author

set forth three general "standards of reliability for audit evi-

dence":22

1.

Evidence which is obtained from a source independ-
ent of the enterprise being audited tends to be
more reliable than evidence obtained from a source
within that enterprise.

Evidence which is objective in nature tends to be
more reliable than evidence which reflects personal
judgment or bias.

Evidence obtained by the auditor himself or by his
representative tends to be more reliable than evi—
dence supplied by another, except where the au-
ditor is not qualified to obtain that evidence.23

He then evaluated each of Mautz' nine audit techniques (supra,

pp. 83-84) with respect to these standards. He summarized his find—

ings in the following table:

 

20

Ibid.

21

Ibid.

22windal, p. 394.

23

Ibid., p. 395.

86

APPLICATION OF GENERAL STANDARDS

General General General
Standard No. 1 Standard No. 2 Standard No. 3
Independent Objective First Hand

Physical examination

and/or count . . . A A A
Confirmation . . . . A A C
Examination of orig—

inal documents and

comparison with

the record . . . . B A A
Recomputation . . . . B A A
Retracing bookkeep-

ing procedures . . C A A
Correlation with

related informa-

tion . . . . . . . B B A
Examination of sub-

sidiary records . . C B A
Scanning . . . . . . C C A
Inquiry C B C

Legend: A - independent, objective, or first hand
B - partly independent, objective, or first hand
C - not independent, objective, or first hand.24

 

Like the previously mentioned authors, Windal concluded that re-
liability could vary substantially between the specific techniques in
any given class and suggested that one could explain this variance, at
least in part, through the following "special" standards:

1. Evidence based on internal data which have been
derived from an accounting system containing ade-
quate internal control tends to be more reliable
than evidence based upon data derived from a
system without such control.

2. Evidence obtained from outside sources which
maintain formal accounting records and/or have a
sense of public or personal responsibility tends
to be more reliable than evidence obtained from

 

24Ibid., p. 400.

87

an outside source with inadequate records and/or
little or no sense of public or personal respon-
sibility.

3. The examination of items which are relatively
more susceptible to fraud tends to give less re-
liable evidence than the examination of items
less susceptible to fraud.

4. In those special situations where the auditor is
not qualified to apply a particular technique,
the evidence obtained from such application is
relatively unreliable.

5. Confirmations which can be handled without effort
by the party confirming tend to be less reliable
than confirmations which require effort.25

The final study of evidential reliability which we shall review
is from Arens' doctoral dissertation. This author evaluated the fol—
lowing modified version of Mautz' classification system:

1. Real evidence.
a. Physical examination.
b. Recomputation.
2. Testimonial evidence.
a. Statements by independent third parties.
b. Statements by officers and employees.
3. Documentary evidence.
a. Authoritative documents originating outside
the client's organization.
b. Authoritative documents originating within
the client's organization.
4. Other.
a. Calculations or correlations.

b. Subsidiary or detailed records,26

with respect to three general standards adapted from Windal's "general"
and "special" standards (supra, pp. 85—87):

1. Independence. Evidence which is obtained from a
source outside the organization being audited is
more reliable than evidence obtained from within
the organization.

 

25Ibid., p. 395.

26Arens, p. 108.

 

88

2. Qualification. Evidence obtained from a person
who is qualified to give the correct information
is more reliable than the information obtained
from an unqualified person.

3. Judgment. Evidence obtained which requires con-
siderable judgment to determine the correctness
of the information is less reliable than evidence
which requires little judgment.27

Arens summarized his conclusions in the following table (also

adapted from Windal):28

*
Types of Evidence
Independence Qualifications Judgment
Real evidence

Physical examination A A A-B
Recomputation A A A

 

Testimonial evidence
Statements by third

parties B A-C A-C
Statements by officers
and employees D A-C A-C

 

Documentary evidence
Originating outside the

 

 

organization C A—B A-B
Originating within the

organization D A-B A—B

Others

Calculation and correla-

tion A A C
Subsidiary or detailed

record D A-B A—B

*

A - Obtained by the auditor.

B - Obtained directly from a third party by the auditor.

C - Obtained from the client but originally prepared by

a third party.
Obtained from the client and prepared by the client.

U
I

 

27Ibid., p. 109.

28Ibid., p. 121.

89

Taken together, the four above mentioned studies appear to iden—
tify the factors most relevant to the evaluation of evidential reli-
ability. At this point, therefore, it seems appropriate to combine
and summarize these studies' findings. Toward that end, let us first
note that two factors identified by Mautz: (1) the possibility of the
auditor's misinterpreting the evidence, and (2) the conclusiveness of
the evidence, are actually at a higher level of abstraction than the

others. In fact, these two may serve as defining classes into which

 

all the others fall -- the first concerned with the auditor's ability
to reason correctly from evidence at hand to the "reality" represented
by that evidence, and the second concerned with the extent to which a
particular type of evidence compels the auditor's mind to a decision
on a given proposition's validity, if he assumes his interpretation of
that evidence to be correct.

Adopting these two defining classes, we may summarize the fac-
tors which should influence the auditor's evaluation of evidential re-
liability as follows:

1. factors which affect the auditor's possibility of misinter-

preting a particular type of evidence:
a. the degree of judgment required for interpretation of
the evidence, and
b. the qualifications of the one interpreting the evi-
dence,
2. factors which affect the auditor's evaluation of the conclu-

siveness of a particular type of evidence:

90

a. the degree of inference required to establish a rela—

tionship between the evidence and the proposition in

question,

b. the possibility that the evidence may be intentionally

misleading, itself a function of:

(1)

(2)

(3)

(4)

independence of the evidence from the client's
control,
general susceptibility of the particular type
of evidence to suppression, manipulation, al-
teration, or counterfeiting,
aspects of the client's internal controls which
may affect the susceptibility of the particular
type of evidence to suppression, manipulation,
alteration or counterfeiting, or which might
affect the likelihood of motivation for such
tampering with the particular type of evidence,
quality of the evidential source with respect
to:

(a) responsibility and integrity, and

(b) extent of bias or self-interest, and

c. the possibility that the evidence may be unintention-

ally misleading, itself a function of:

(1)

(2)

qualifications of the evidential source (knowl-
edge), and
qualifications of the one gathering the evi-

dence.

91

Unfortunately, no one has yet devised a method for combining the
individual measures of these "sub-factors" into an overall measure of
evidential reliability. However, of primary interest to this disser-
tation are the implications of evidential reliability (however mea-
sured) for audit evidence accumulation, rather than specific methods
of evaluating this factor. Therefore, and because of the enormity of
the problem, development of any such measure is beyond the scope of
this dissertation. For this reason, let us assume that the auditor is
capable of evaluating evidential reliability and consider which of the
parameters of his evidential collection such evaluations may logically

affect.

Expected Influence on Audit Program

We have defined evidential reliability as "the extent or degree
to which a type of evidence can be considered an accurate representa-
tion of reality at the time that evidence is obtained." (Spppp,

p. 81). This factor may, to some extent, affect all three parameters
of the auditor's evidential collection; however, its greatest effect
should be on the pypgg of evidence included.

Ideally, in order to determine the lowest-cost means of satisfy-
ing his evidential support requirements the auditor would consider
both the marginal cost and marginal support functions for each avail-
able evidential alternative. Clearly, however, ceteris paribus, the
marginal support provided by the nth unit of a given type of audit
evidence will be greater the more reliable is that type. Therefore,
subject to time and staff limitations and cost considerations, the

auditor should, as Ray puts it, "examine the most reliable evidence

92
first in order that he may get to the point of audit satisfaction in

the quickest and easiest manner."29

Thus "reliability" does logically
affect the pngg of evidence included in the auditor's collection.

Likewise, this factor may affect the extent parameter of that
collection. Clearly, the less reliable is a particular type of evi-
dential matter, the more units of that type the auditor will require
to reach a given level of assurance. Even if he examines every exist-
ing unit of a particular type of evidence, however, to the extent that
the type is less than one hundred per cent reliable, the auditor can-
not be certain he has an accurate representation of the underlying
reality. In other words, inherent reliability sets an upper bound on
the.£p£gl evidential support which a given type of evidential matter
can provide. For this reason, for most financial statement asser-
tions, no single type of evidence is likely to be sufficient of itself
to satisfy the auditor's support requirements. Presumably, however,
the proportion in which the auditor obtains different types of eviden-
tial matter will depend upon the relative marginal reliability and
cost of each type. Thus, again, reliability may logically affect the
extent parameter of his evidential collection.

The effect of inherent evidential reliability on the third
parameter of the auditor's collection, timing, is less straightforward
and perhaps even more limited. Note that the auditor's opinion is

concerned with the "fairness" of his client's financial statements at

a particular point in time —- the opinion date. To the extent that

 

 

29J. C. Ray, "Classification of Audit Evidence," The Journal of
Accountangy 117 (March 1964): 45.

 

 

93
the auditor obtains any evidence prior to this date, he must project
its support forward. For this reason, the evidential support provided
by interim tests depends not only upon the inherent reliability (as
defined above) of evidence resulting from such tests, but also upon
the extent to which "reality" at the interim test date reflects "re-
ality" at the later opinion date (the timeliness of the evidence).

If the status of a particular financial record assertion (i.e.,
the quality of the financial record population of entries or aggrega-
tions of entries as a surrogate for some real world population of
events or physical items) were constant over time, the degree of sup-
port provided by the nth unit of a particular type of relevant audit
evidence would be solely a function of the reliability of that type of
evidence and would be independent of the point in time at which the
auditor obtained such evidence. In this case, reliability could have
no effect on the auditor's timing decision. If, at the other extreme,
the assertion in question were such that its status at any one point
in time would provide no indication whatsoever of its status at any
other point in time, then this fact would dominate the auditor's tim-
ing decision, he would test the assertion at the year's end regardless
of the type of evidence available, and hence evidential reliability
would again have no effect on his timing decision.

Both of these extremes are unlikely, however, and between them
lies the majority of situations faced by the auditor -- the probability
of change over time in the status of the given assertion being positive
and of a magnitude dependent upon the quality and comprehensiveness of

the client's internal controls. (See the discussion in Chapter IV of

94
the expected influence of the auditor's evaluation of the probability
that his client's financial records contain material error on the tim-
ing of evidential accumulation, ipfigg, pp. 136-139.) It is concep-
tually possible that over a given time interval, the possibility of
change in a particular financial record assertion's status will be
sufficiently small that this factor does not dominate the auditor's
timing decisions, yet sufficiently large that the support provided by
any given type and quantity of evidence obtained within that interval
varies with the actual collection time. In this case, since the in-
herent reliability of a particular type of evidence is important in
defining that type's marginal evidential support function at a given
point in time, this factor can affect the timing parameter of the au-

ditor's evidential collection.

The Timeliness of the Evidential Matter

 

In the previous section, we have defined "timeliness" as the ex-
tent to which "reality" at the time an auditor obtains evidential mat-
ter reflects "reality" at the auditor's opinion date. The importance
of this factor is obvious. To the extent that the status of any given
financial statement assertion is subject to drastic change over time,
evidence gathered at an interim date may prove invalid as support for
the auditor's evaluation of that assertion as of his opinion date.

As we shall see in Chapter IV, evidential "timeliness" is
closely related to the quality and comprehensiveness of the client's
internal controls. Therefore, with the exception of looking at its
influence on the auditor's program, let us defer further discussion of

this factor until Chapter IV.

95
Expected Influence on Audit Program

To some extent, "timeliness," as defined above, may affect all
three parameters of the auditor's evidential collection. This partic-
ular factor's most pronounced influence, however, should be on timing
decisions. We have already indicated this effect above. Let us con-
sider it here, however, in somewhat different terms. As Mautz and
Mini have noted, accounting systems are probabilistic rather than de-
terministic in nature.30 Therefore, however small it may be, the
probability of change over time in the status of a particular finan-
cial record assertion is mathematically positive and the auditor must
assume that a given type and quantity of evidence gathered at an in-
terim date will never provide a pppg accurate reflection of that as-
sertion's opinion date "reality" than the same type and quantity of
evidence actually obtained at some later date. In other words, the
auditor must assume that evidential support is a decreasing function
of the length of the time interval between the date at which he ob-
tains evidence and his opinion date.31 The slope of this function is
determined by the quality and comprehensiveness of the client's inter-

nal controls.

 

30R. K. Mautz and Donald L. Mini, "Internal Control Evaluation
and Audit Program.Modification," The Accounting Review 41 (April
1966): 284.

 

31More specifically, for all h and k such that
- - <
(th top) > (tk top)’ then ba(qih) ' ba(qik)
where: th and t are two alternative dates for the accumulation

k of audit evidence,
top is the opinion date, and

ba(qih) and ba(qik) are the degrees of support provided

for the a assertion by q units of type i
evidence gathered at times, th and tk’ respec-
tively.

96

The effect of "timeliness" as defined above, on the auditor's
timing decisions is that this factor interacts with the inherent "re—
liability" of available evidential alternatives to determine the ear-
liest date at which the auditor may obtain evidence adequate to satis—
fy opinion date support requirements. In the extreme case, where the
"reality" of a financial record assertion is subject to drastic change
over time, this factor will actually dominate the auditor's selection
of a date for testing that assertion - compelling him to obtain his
evidence at year end.

With respect to the influence of "timeliness" on the type and
extent parameters of the auditor's evidential collection, the analysis
is similar. If one accepts the assumption that, for any particular
financial record assertion, the support provided by a given type and
quantity of evidential matter is a decreasing function of the time in-
terval between the date at which the auditor obtains such evidence and
his opinion date, then one must conclude that the earlier an auditor
tests that assertion, the greater precision he must require in his
test. Furthermore, the degree to which the auditor's precision re-
quirements will vary over time depends upon the slope of the function
relating "timeliness" to the length of the interval between test date
and opinion date.

The Statistical Parameters of the ngulation
UnderlyingLEhe Assertion the Auditor
Wishes to Evaluate

In the strictest sense, every financial statement assertion is

an inference drawn from some underlying population whose elements are

entries or aggregations of entries (existing at a given point in time)

. .
'n 9'
In U‘

1: t1

...,.
. 1
rs-UI

:v"

VOA-l

‘n . a
o ‘P‘
vhh

u...
U
"A .C

Q
In. ,

'.‘ v u.
I I

l
'-
“'791
.‘96.

9—4

97
in the client's financial records. Such underlying populations are,
in turn, surrogates for "real-world" populations whose elements are
occurrences or physical items. For example, financial statement as-
sertions concerning (perpetual) "Merchandise Inventory" are infer-
ences drawn from a population whose elements, specific aggregations of
certain client acquisitions, and dispositions, are surrogates for the
population of merchandise actually available for sale. Likewise, as-
sertions concerning "Accounts Receivable" are inferences drawn from a
population whose elements, the records of amounts due the client for
goods or services rendered, are surrogates for the client's right to
receive such amounts.

To the extent that inferences are properly drawn ppd financial
record populations are "good" surrogates for their "real-world" coun-
terparts, financial statement assertions will accurately reflect "re-
ality." Therefore, the auditor has two primary responsibilities in
evaluating any particular financial statement assertion:

1. he must determine whether the assertion is a valid inference

from its underlying financial record population, and

2. he must determine whether or not that financial record popu-

lation is a "good" surrogate for its "realdworld" counter-

part.

The first of these determinations is primarily a matter of
evaluating the client's logic and/or his clerical accuracy. Therefore,
we need not consider it in further detail. The second determination

is, however, of interest here.

98

Essentially an auditor has two approaches to determining whether
or not a financial record population is a "good" surrogate for a
"real-world" population. The "direct" approach (applicable, e.g., in
the case of inventories) is to actually observe the "real-world" popu-
lation and compare it with the surrogate, either on an item-by-item
basis or in some form of aggregation. Where the "real-world" popula-
tion's elements have no concrete physical existence, however (e.g.,
accounts receivable or transactions which have occurred in the past),
the auditor obviously cannot adopt this approach. In such cases, the
best he can do is attempt to establish indirectly the extent to which
each element in a financial record population represents its "real-
world" counterpart by examining documentary, testimonial, and/or what-
ever other types of relevant evidential matter may be available.

Fortunately for the auditor, statistical theory teaches that one
need not observe ggggz_element in a population to arrive at fairly ac-
curate conclusions about that population. For this reason, the audi-
tor need not evaluate every entry or aggregation of entries underlying
a particular assertion to evaluate the extent to which that assertion
reflects "reality." The precise number of elements he must observe
varies, not only with the precision and level of confidence he desires,
but also with the following statistical parameters of the assertion's
underlying population:

1. size,

2. variance, and

3. rate of error.

32I

5b New

99
For an indication of how these factors interact to determine the
number of elements one must evaluate to draw conclusions about a spe-
cific population, one need only consider the statistical formulae for
"attributes" and "variables" sample size determination. These formu-

lae are, respectively:

n- PUT) ,[O<p<l,t>O,N>O],and

 

 

where: n - sample size,
SE - desired sample precision,
N - population size,
p - per cent of occurrence (error) in population,
t - confidence level factor,

SE; - sampling error of average,
32
o a variance of population,

and, from them, it follows that for a given precision and confidence
level, the required sample size, n:
1. varies directly (but not proportionately) with the popula-
tion size, N, for both "attributes" and "variables" samples,

32Herbert Arkin, Handbook of Samplipgjfor Auditing and Account-
ipgj‘New York, McGraw-Hill Book Company, Inc., 1963, pp. 96, 604-05.

 

 

 

mg

f‘d .'

‘1'

100
2. varies:
a. directly with p g .5, and inversely with p > .5 for
"attributes" samples, and
b. directly with the variance of the population for

"variables" samples .

Expected Influence on Audit Program

The size and variance, or rate of error of populations underly-
ing financial statement assertions can obviously affect the extent
parameter of the auditor's evidential collection. Presumably, the
more elements of a population the auditor must evaluate to form an
opinion on inferences drawn from that population, the more units of
any type of evidence relevant to those elements he must observe. This
means that, even though the support which a given type of evidential
matter provides for evaluation of a particular population's elements
may be constant, the degree of support which that unit provides for
evaluation of the population as a whole (and hence any inferences
drawn from.that population) will vary with the number of elements the
auditor must evaluate, and hence with such population characteristics
as size, variance, and rate of error.

While these statistical parameters may directly affect the num-
ber of elements an auditor must evaluate before forming any opinion on
a particular population as a whole, they only require that he evaluate
the appropriate number. They do not dictate pp! he must evaluate
those elements. Therefore, and since an auditor typically attempts to
obtain evidence independent of the population he desires to evaluate,

characteristics of the population under examination have no logical

 

 

l1

101
direct relationship to the £1pg_of evidence he obtains. Likewise,
since the auditor bases timing decisions upon his evaluations of the
tendency of "real-world" populations to change over time and the abil-
ity of his client's accounting system to adequately reflect such
changes, the size and variance (or rate of error) of any financial
record population at a fixed point in time have no logical direct re-
lationship to the timing parameter of his evidential collection.
(Through their effect on the extent parameter of his evidential col-
lection, however, population characteristics may indirectlz influence
the other two parameters of that collection if the auditor faces re-

strictive time or staff constraints.)

The Existence of Corroborative Evidence

 

When the auditor's evidential collection contains more than one
type of evidence relevant to a particular financial statement asser-
tion, the support which all these types provide, in combination, for
an opinion on that assertion may differ significantly from the sum of
the support which each type would provide individually. This possi-
bility exists because, in addition to directly supporting an opinion
on the assertion in question, each individual type of evidence may
also affect the reliability of one or more of the other types, i.e.,
types which corroborate one another will tend to increase each other's
reliability while types which conflict with one another will tend to
decrease each other's reliability. (Thus, while the existence of
satisfactory controls in the area of accounts receivable is, to some
extent, evidence in support of the proposition that the items in the

client's accounts receivable trial balance reflect valid claims, it

 

Ina
5'?

«J o'-

ht;

(
‘ M
b.

102
also increases the reliability of confirmations returned in agreement
with the client's records and decreases the reliability of confirma-
tions returned in disagreement with those records, and conversely.)
Mautz and Sharaf have recognized the interactive effect of dif-
ferent types of evidential matter relevant to the same assertion.
They conclude:
. . . Although evidence is seldom conclusive, the
more kinds of evidence we find in support of a given
proposition, the more likely that proposition is to
be true. . . . _
If some . . . types of audit evidence . . .
pertinent to this particular proposition . . . can-
not be obtained, we lose by just so much the oppor-
tunity of becoming convinced. An attack launched
, from three directions is not so strong as one from
nine directions.33
Expected Influence on Audit Program
The degree to which the various types of evidence relevant to a
particular financial statement assertion corroborate or conflict with
one another may affect all three parameters of the auditor's eviden-
tial collection. However, this factor is apt to have its greatest in-
fluence on the tzpes of evidence and the number of units of each type
he obtains.
When the auditor decides to obtain more than one type of eviden-
tial matter to support his opinion on a given financial statement as-

sertion, it seems reasonable that he will expect the various types he

selects to corroborate. (If they are all relevant and reasonably re-

liable, he may assume they will all essentially reflect the same basic

 

33R. K. Mautz and Hussein A. Sharaf, The Philosophy of Auditin ,
Menasha, Wisconsin, George Banta Company, Inc., 1964, p. 98.

II,
has

E:

H.-
J...

I;’

Q
:1.

t,"

It

 

 

 

103
"reality.") In some cases, however, evidence which provides support
for an inference concerning the truth or falsity of a financial state-
ment assertion may also increase (or decrease) the reliability of some
other type of relevant evidence to the extent that the auditor decides
to include (exclude) such evidence from his collection. In this man-
ner, corroborative evidence may influence the Ezpp_parameter of his
evidential collection. For example, whether credits to customer ac-
counts in the subsidiary ledger will be a reasonably reliable or
highly unreliable source of information concerning the validity of re-
ceivables depends largely upon whether or not the client's internal
controls in this area include an appropriate separation of duties.
For this reason, whether the auditor will rely solely on such entries
as a follow-up for non-responses to receivable confirmations or
whether he will require additional evidence, e.g., remittance advices,
may hinge on evidence obtained during his evaluation of the client's
relevant internal controls.

Likewise, since the auditor expects that various types of evi-
dence relevant to a particular financial statement assertion will
basically corroborate one another, he should expect that the types he
collects will each contribute a certain degree of support toward his
overall requirement for an opinion on that assertion. Clearly, then,
the more different types of evidence the auditor obtains, the fewer
units of any given type he should require. Thus, corroborative evi-
dence can influence the extent parameter of his collection. (Note,
however, that if, in fact, two or more of the types he collects con-

flict with one another, these types will, to some extent, cancel each

104
other's evidential support, and thus require the auditor to obtain
either more units of the same types, or some other relevant type, in
order to resolve the conflict. In this manner, conflicting evidence
can affect both the extent and 51p; parameters of the auditor's evi-
dential collection.)

The existence of corroborative or conflicting types of evidence
relevant to a given financial statement assertion should normally
exert far less influence on the timing parameter of the auditor's evi-
dential collection than on that collection's other two parameters. We
have previously suggested that, where the status of a particular area
of a client's financial records as a "realdworld" surrogate is not
likely to vary greatly over time, the reliability with which the au—
ditor can evaluate that status may, to a limited degree, affect his
timing decisions. (figpxa, pp. 92-94.) To the extent, therefore, that
corroboration or conflict among different types of evidence can affect
the overall reliability of the auditor's collection relevant to a
given financial statement assertion, such corroboration or conflict

may influence the timing parameter of that collection.

Summagz
As its title indicates, this chapter is a discussion of factors
which define the evidential support function for a given type of audit
evidence gathered at a given time. An important part of this discus-
sion has centered around how such factors might logically affect the

three parameters of the auditor's program:

105
l. the type of evidence included,
2. the time of collection of each type, and

3. the number of units of each type collected at a given time.

The following table (of a type which will also appear in the summaries
of Chapters IV and V) summarizes the conclusions of this aspect of the

chapter.

Table l.--Expected influence of factors which define the evidential

support function for a given type of audit evidence gathered at a

given time on the three parameters of the auditor's evidential col-

lection: (l) the type of evidence included, (2) the time of collec-

tion of each type, and (3) the number of units of each type collected
at a given time

Variable Type Timing Extent
Relevance 0 O 0
Reliability 0 O 0
"Timeliness" 0 O 0
Statistical Parameters O O O
Corroborative Evidence 0 O 0

Key:

0 direct influence on this parameter of the auditor's
program

0 indirect or limited influence on this parameter of the
auditor's program

0 no influence on this parameter of the auditor's program

Of the factors discussed in this chapter, then, relevance, re-
liability, and the existence of corroborative evidence are the primary

determinants of the txpegs) of evidence the auditor will require to

106

achieve a given degree of evidential support, statistical parameters
(size and variance or rate of error), reliability, and the existence
of corroborative evidence are the primary determinants of the number
of units of each type he will require to achieve that level, and
"timeliness" (the extent to which "reality" at the time the auditor
obtains evidential matter reflects "reality" at his opinion date) is
the primary determinant of the pigs at which he will obtain his evi-
dence.

This chapter has tacitly assumed that the auditor's overall evi-
dential support requirement for an opinion on any particular financial
statement assertion is fixed and given. Actually, however, this re-
quirement will vary from engagement to engagement for a given asser-
tion, and from assertion to assertion for a given engagement. An im-
portant group of factors which affect evidential support requirements
are those "factors which determine the minimum evidential support
necessary to justify a professional opinion on a given financial
statement assertion." Let us, therefore, now turn our attention to

the factors in this category.

CHAPTER IV

FACTORS WHICH DETERMINE THE MINIMUM EVIDENTIAL
SUPPORT NECESSARY TO JUSTIFY A PROFESSIONAL
OPINION ON A GIVEN FINANCIAL
STATEMENT ASSERTION

Having identified a material assertion in his client's financial

statements, the auditor must determine the degree of evidential sup-
port necessary to establich its validity or invalidity, before he can
design any specific audit steps to test that assertion. In the pre-
vious chapter, we assumed the auditor's evidential support requirements
were fixed and given. Actually, however, such requirements are a func-
tion of two basic types of factors:

1. factors which determine the minimum evidential support
necessary to justify a professional opinion on a given
financial statement assertion, and

2. factors which influence the probability that the auditor

will incur sanctions for failing to detect a material

error given that such error exists in his client's records.

In this chapter and Chapter V, we shall adopt an approach simi-
lar to that of Chapter III, examining reapectively the factors in each
of these categories and suggesting how one might logically expect each
individual factor to affect an auditor's program. The following fac-

tors, identified in Chapter I as determinants of the minimum evidential

107

108
support necessary to justify a professional Opinion on a given finan-
cial statement assertion, form the basis for the remainder of discus-
sion in this chapter:
1. Generally Accepted Auditing Standards and other authorita-
tive pronouncements of the AICPA,
2. authoritative pronouncements of the SEC,
3. regulatory commission requirements (for regulated indus-
tries),
4. policies of individual public accounting firms,
5. specific terms of the auditor's contract with his client,
6. materiality considerations, and
7. the auditor's evaluation of the probability that a given
financial statement assertion is materially misstated, based
upon:
a. the auditor's findings during his review of the
client's internal control system,
b. the auditor's findings in actual tests of the client's
records, and
c. the auditor's assessment of the general "riskiness"
of the client, based on the client's financial
health, operating and reporting policies, prior
auditor-client relations, etc.

Generally Accepted AuditingTStandards and Other
Authoritative Pronouncements of the AICPA

 

The standard form scope paragraph of the auditor's report reads

as follows:

109

We have examined the balance sheet of X Company as
of December 31, 19 . . ., and the related statements of
income and retained earnings and changes in financial posi-
tion for the year then ended. Our examination was made
in accordance with generally accepted auditing standards
[italics mine], and accordingly included such tests of the
accounting records and such other auditing procedures as
we considered necessary in the circumstances.

Clearly, this specific reference to generally accepted auditing stand-
ards indicates the auditor's obligation to abide by such standards and
guidelines as the profession has adopted.

In recognition of this obligation, Grinaker has written:

The specific reference to generally accepted audit-
ing standards in the scope paragraph . . . indicates that
these standards represent the official position of the
profession as to the means of establishing reasonable
gpgunds for belief concerning the fair presentation of
the financial statements. Generally accepted audit stand-
ards, promulgated by the American Institute of CPA's come
mittee on auditing procedure, express the underlying prin-
ciples which control the nature and extent of the evidence
to be obtained by means of auditing procedures.2

Hill and Jennings have also acknowledged the auditor's respon-
sibility for certain tests because they are prescribed by the profes-
sion, stating:

It is the inescapable responsibility of each accountant

to determine the scope of examination which he should

make before giving his opinion on financial statements
under review. In reaching this determination, the ex-
amining accountant must necessarily give the most serious
weight to the fact that the profession has adopted audit-
ing standards which require the application of the extended
procedures specified in Auditing Statement No. 1

 

1Committee on Auditing Procedure, American Institute of Certi-
fied Public Accountants, Statement on Auditing Standards No. 1, New
York: American Institute of Certified Public Accountants, 1973, p. 81.

2Robert L. Grinaker, "The Accountant's Responsibility in Expres-
sing an Opinion," The Journal of Accountancy 110 (November 1960): 66.

110
[confirmation of receivables and observation of inven-
tories] whenever they are both practicable and reason—
able of application. If, notwithstanding, the examin-
ing accountant concludes that he may omit such pro-
cedures from his examination and satisfy himself by
other means, he must assume the burden of justifying

his failure to conduct his examination in accordance
with generally accepted standards.3

Although Hill and Jennings only refer to two Specific procedures
above, their observation applies equally well to all facets of an
audit. Wherever the profession has adopted standards or guidelines
for procedure, the individual accountant must comply, or must bear the
burden of justifying his departure from those standards and guide-

lines.

Expected Influence on Audit Program
In general, the standards, guidelines, etc., adopted by the

AICPA and set forth in such pronouncements as the Statements on Audit-

 

ing Procedure and Industry Audit Guides, are broad in nature and in-

 

 

tended to apply to a wide variety of situations. Therefore, while

they may require the auditor to collect specific types of evidential
matter on any given engagement (e.g., inventory observations), they
are not sufficiently specific to affeCt the extent or timing param-

eters of his evidential collection.

Authoritative Pronouncements of the SEC

 

If his client's securities are traded publicly, the auditor must

consider requirements of the Securities Exchange Commission when

 

3Gordon M. Hill and Alvin R. Jennings, "Extensions of Auditing
Procedure," The New York Certified Public Accountant 23 (May 1953):
340.

 

111
developing his audit program. To the extent that the SEC requires in-
formation not normally included in a privately held company's state-
ments, the auditor may have to extend his testing. Furthermore, while
the commission normally expects the auditor to follow generally ac-
cepted auditing standards, it may, in the future, choose to issue
audit guidelines of its own. Such guidelines will, as was the case
with generally accepted auditing standards, undoubtedly tend to be
broad in nature; therefore, the only parameter of the auditor's evi-
dential collection which they are likely to affect is the Eng of evi-

dence included.

Regglatory Commission Requirements
Like requirements of the SEC, regulatory commission requirements
may call for additional information in the client's statements or
oblige the auditor to collect specific £1222 of evidence. Furthermore,
however, in some cases, such requirements may also affect the extent
parameter of the auditor's evidential collection. For example, audits
of brokers require one hundred per cent confirmation of receivables,

short and long positions, and securities held for customers.

Policies of Individual Firms
During their discussion of factors which the auditor considers
when gathering evidence, Anderson, Giese, and Booker note in passing

that "authoritative pronouncements from the home office . . . have

112
influenced audit programs."4 In the case of some firms, this may be
somewhat of an understatement. Obviously, whenever his firm has
adapted specific approaches to the audit, the individual public ac-
countant may be expected to incorporate them into his program. Firm
policies may take the form of broad guidelines (e.g., calling for the
use of statistically determined sample sizes wherever possible), or
they may take the form of specific required procedures (e.g., standard
audit programs which are to be used as a starting point for each audit

area).

Expected Influence on Audit Program

Firm policies may obviously dictate that certain £1pg§_of evi-
dence be included in any given audit program. In addition, there is
indication that they may, to some degree, influence the extent to
which an auditor gathers a given type of evidence. For example, one
large national firm which has recently placed emphasis on statistical
sampling requires confidence levels of at least 90% and ranges of re-
liability not in excess of 10%.

One might also argue that firm policy can affect the timing of a
given procedure. At least one large national firm does have separate
standard programs for interim and year-end work in each audit area.
The function of the distinction in this case, however, appears to be
merely to indicate which procedures ppp be performed at an interim

date rather than which procedures should be, since in some cases both

 

4H. M. Anderson, J. W. Giese, and Jon Booker, "Some Propositions

about Auditing," The AccountinggReview 45 (July 1970): 528.

113

programs are applied at year end. Furthermore, the items contained in
the "year end" program appear to be of the nature that they either can-
not be performed at an interim date (e.g., cutoff work) or are used to
update interim results (e.g., audit step: "Reconcile the 'Accounts
Receivable' trial balance for the period from the confirmation date to
year end. Note any unusual or large transactions during this period,
and consider confirming new accounts with significant balances.").

Apparently, then, while firm policies may influence the extent
and timing parameters of an evidential collection, their impact will
be far more pronounced on the pypg_of evidence included.

Specific Terms of the Auditor's
Contract with His Client

 

 

Strictly speaking, this factor does not affect the minimum evi-
dential support necessary to justify a professional opinion on a given
set of financial statements (i.e., the requirements of an "ordinary"
audit). Nevertheless, if the auditor's contract with his client con-
tains terms which redefine and extend his responsibilities beyond
those of an "ordinary" audit, or which restrict the SCOpe of certain
types of testing, then such terms may affect his audit program.

When the auditor accepts responsibilities beyond those of an
"ordinary" audit, he increases the evidential support necessary to
satisfy the requirements of his engagement, even though the require-
ments for an opinion on the client's statements remain unchanged.

For example, a contract calling for the auditor to evaluate and
recommend improvements in his client's internal control system may

well require testing beyond the level anticipated by the Committee on

114
Auditing Procedure of the American Institute of Certified Public Ac-
countants when they observed:
The study and evaluation [of internal control] con—
templated by generally accepted auditing standards should
be performed for each audit to the extent the auditor con-
siders necessary . . . to establish a basis for reliance
thereon in determining the nature, extent, and timing of

audit tests to be applied in his examination of the finan-
cial statements.5

Likewise, a contract calling for the auditor to express an opinion on
a specific financial statement item in addition to his opinion on the
statements as a whole will likely require him to test that item more
extensively than usual. In this case, the additional testing becomes
necessary because of the increased importance accorded the specific
item. Evidential requirements for an opinion on the statements as a,
whole, however, are unaffected.

The auditor-client contract may also contain provisions which
limit the scope of the auditor's examination,requiring that he omit
certain types of evidential matter from his collection entirely, or
that he restrict, in some manner, the extent or timing of specific
tests. Even where such restrictions on the "auditor's freedom to se-
lect procedures and examine evidence"6 do not prevent him from gather-
ing sufficient, competent evidence to allow an opinion on his client's
statements, they may incline him to raise the minimum level of support.
Certainly the restrictions must influence his means of achieving that

level.

 

5Committee on Auditing Procedure, p. 14.

6Ibid., p. 85.

115
Expected Influence on Audit Program

Specific terms in the auditor-client contract which extend the
auditor's responsibilities or restrict the scope of his testing may
influence any or all of the three parameters of his evidential collec-
tion: types of evidence included, times of collection of eadh type,
and the number of units of each type collected at a given time.

Whenever the auditor accepts extended responsibility, one would
logically expect him to obtain a greater amount of evidential support
than he would in an "ordinary" audit of the same client. If the ex-
tended responsibility is for an area other than the areas of an or-
dinary audit, it may require him to obtain additional types of audit
evidence. If, on the other hand, the additional responsibility is for
an "ordinary" audit area, the auditor may be able to satisfy his ad-
ditional evidential requirements by increasing the sample size of a
test he would ordinarily perform, or by shifting that test's timing
(e.g., from an interim date to year end) if such a shift increases
significantly the degree of evidential support provided by each unit
of evidence collected.

We have already noted that the client can contractually re—
strict, to some extent, any of the parameters of the auditor's evi-
dential collection. Such restrictions are apt to affect the auditor's
evidential collection in areas other than those directly involved in
the original limitations since, as Leight has noted:

. . . an audit is like the piecing together of a jigsaw

puzzle, one piece gives us the outline for the next

piece. When we audit one account, we get some informa-

tion about another account, and when we are finished.

auditing all the accounts, they will fit together and
form a picture. . . . But when a limited audit is

116

made, we do not . . . see the whole picture, but only
parts of the picture. Therefore the extent of the
auditing tests must be greater to obtain the same level
of assurance. ,

Whenever the client limits the auditor's scope, and the auditor is

,
still able to generate the evidential support necessary for an opinion
on the client's statements, then the auditor must have adopted pro-
cedures alternative to those the client restricted or he must have ex-

tended his tests or altered his timing in other unrestricted areas, or

performed some combination of the three.

Materiality,Considerations
The American Accounting Association's Committee on Concepts and
Standards Underlying Corporate Financial Statements has given the con-
cept "materiality" its most widely accepted definition:

Materiality, as used in accounting, may be described as
a state of relative importance. The materiality of an
item may depend on its size, its nature, or a combina-
tion of both. An item should be regarded as material

if there is reason to believe that knowledge of it would
influence the decisions of an informed investor.

According to the Committee on Auditing Procedure:

The concept of materiality is inherent in the work
of the independent auditor. There should be stronger
grounds to sustain the independent auditor's opinion
with respect to those items which are relatively more
important and with respect to those in which the possibilities

 

7Lester A. Leight, "Recommended Opinions and Disclaimers," The
New York Certified Public Accountant 33 (June 1963): 412.

8Committee on Concepts and Standards Underlying Corporate Finan-
cial Statements, American Accounting Association, Accounting and Re-
pprtipg Standards for Corporate Financial Statements and Precediug

Statements and Supplements, Evanston: American Accounting Associa-
tion, 1957, p. 8.

 

117

of material error are greater than with respect to those
of lesser importance or those in which the possibility
is remote.9

Because of the importance attached to this factor by the Committee,
materiality considerations clearly belong among variables which deter-
mine the minimum evidential support necessary to justify a profes-
sional opinion on a given set of financial statements.

Behind the Committee's pronouncement on the importance of mate-
riality as an audit variable are two primary considerations: the cost
of audit evidence accumulation and the degree of sophistication of the
typical financial statement user's decision model.

Arens has recognized the economic importance of the materiality
concept, stating:

The importance of materiality, as it relates to the
auditor's determination of whether or not errors or omis-
sions exist in a client's records, results from the fact
that there is an economic cost to auditing. The number
of hours the auditor spends in accumulating audit evidence
is generally directly related to the client's audit fee.
If the auditor spends substantial time in verifying infor-
mation which is not relevant to the statement user's in-
formation needs, an unnecessary audit cost results. A CPA
performs the audit function most efficiently when the in-
formation which is most relevant to the user's needs is em-
phasized in the audit and the least relevant information
is given less attention.10

In a similar vein, Mautz and Sharaf have noted:

Materiality is always of interest in auditing. Be-
cause cost and time are so important in the performance
of an engagement, transactions, events, and even irregu-
larities of little or no materiality cannot be given the

 

9Committee on Auditing Procedure, p. 6.

10Arens, P. 50.

118

attention which must be reserved for material transac—
tions, events and irregularities.11

Undoubtedly, financial statement users would prefer to know that
the accounting records underlying any given set of financial records
were free of all error. Such users, however, would not likely be wil-
ling to incur the cost of this ideal situation, even if it were attain-
able. What is more important, though, is that the typical statement
user is not likely to require absolutely error-free financial state-
ments. Rare indeed is the decision model sufficiently SOphisticated
to include as variables every assertion comprising a set of financial
statements, or so sensitive that minor misstatements would alter ad-
versely investment decisions based thereon.

Rather, the typical statement user must screen out numerous
assertions as insignificant, if he is to reduce the factors he con-
siders in his final decision to a manageable number. During this
screening process (whether done consciously or not), he evaluates each
individual item's significance relative to the other items in the fi-
nancial statements.

If we make the seemingly reasonable assumption that the typical
statement user makes such evaluations with reference to his decision
model, we are left with two conclusions. First of all, the influence
of any item on the output of his decision model will vary directly
with his evaluation of that item's significance relative to the other

statement items. Secondly, there will be some level of relative

 

11R. K. Mautz and Hussein I. Sharaf, The Philosophy of Auditing,
Menasha,'Wisconsin: George Banta Co., Inc., 1964, p. 118.

119
significance which separates factors to be included in the decision
from factors to be ignored.

We may represent these results graphically, as follows:

 

 

 

Y
“a“oz': E
U313 I
m s u a |
3 “.u I
m 5 o a
s u o I
Hind-DH
muons I
s m and '
F as:
o'; o'o I
>~H I
'3 u a m B '
«355:.
seam '
“Hog , I x
O A D

User's evaluation of the significance
of a given financial statement item
relative to all financial statement
items.

Figure 1. Graphic representation of the relationship
between the financial statement user's evaluation of
the significance of a given item in the statements
relative to all other statement items, and the rela-
tive influence of that item on his decision model
output.

The function represented by the graph in Figure 1 is simply:

r

O, x < OA

y - (f(x), OA 5 x < OD (4.1)

 

 

L OE, x 2 OD

120
where: x is the user's evaluation of the significance of a
given financial statement item relative to all statement

items,12

y is the relative influence of a financial statement
item on the output of the statement user's decision

model, hence:

y = 0 indicates the item has no effect on the
user's decision model output, i.e., the item
is not material,

y = f(x) indicates the item's relative influence

on the user's decision model output, its
relative materiality, is a function of its

significance relative to all statement

items,13

y = OE indicates the item completely determines

the output of the decision model.14

 

12The x-value assigned to a given financial statement item is,

itself, undoubtedly a complicated function of a number of variables,
the most important of which are probably:

1. the balance attached to the item,

2. the basic nature of the item, and

3. the importance of the item in combination with other items.
This function is apt to vary from user to user, and when we also con-
sider that the decision model function of Figure l is apt to vary from
user to user with respect to the values of OA, OD, and the form of
f(x), it is easy to see why the auditor, who may not even know the
statement users let alone their relevant functions, occasionally finds
the determination of an item's materiality a thorny problem.
13The form taken by f(x) is restricted only in that it should be
monotonically increasing. While it might appear as in Figure 1, un-
doubtedly a step-function would be more appropriate.

14In this case, of course, all the other financial statement
items must have relative significance less than OA.

121
Even though, presumably, an assumption of the above function is
that each item included as a variable in the statement user's decision
model is "correct" as it appears in the statements, "correctness" need
not imply absolute precision. Instead, the typical user of financial
statements should be satisfied if: (1) those statements are suffi-
ciently accurate to allow him to correctly identify significant items

(i.e., he should have confidence that no appprently immaterial item is

 

so grossly misstated that discovery of the misstatement would render
the item material), and (2) the items he selects as variables for his
decision model are sufficiently accurate that any subsequently dis-
covered errors will not affect the model's output.

The foregoing discussion of materiality and the audit client's
financial records contains reference both to "material items in the

' and to "material errors or misstatements of

financial statements,‘
items in the financial statements." At this point, let us distinguish
between the two somewhat different uses of the concept and discuss the
implications of each for the auditor's reSponsibility in audit evidence
accumulation. A material item in the financial statements is any item
included as a variable in the typical statement user's decision model.
A material error or misstatement of an item in the financial state-
pgppg, on the other hand, is one whose subsequent discovery would
alter the output of the user's decision model.

Grinaker has written, "for the auditor to render an unqualified

‘pgofessional opinion that . . . financial statements present fairly,

 

he must believe and have reasonable_grounds for his belief that the

 

122

15
statements are free from material misstatement . . ."

Now, if a
financial statement user considers an item to be immaterial (i.e.,
ignores it for decision-making purposes), the subsequent discovery of
an error in that item should have no effect on the output of his de-
cision model, unless the item has been so grossly misstated that its
subsequent correction discloses it to have been sufficiently signifi-
cant for consideration as a decision variable in the first place.
Thus, for apparently immaterial financial statement assertions, the
range of allowable error, i.e., error which does not affect the output
of the typical statement user's decision model, may be rather large.

The range of allowable error for material financial statement
items, i.e., items included as variables in the typical statement
user's decision model, on the other hand, should vary directly with
these items' relative influence on the decision model output. Thus,
even though an item is material, its range of allowable error may be
moderately large if its actual influence in the decision process is
relatively small. If an item dominates the decision process, however,
even a slight error may affect the decision model's output and hence
be material.

For the above reasons, we may conclude that the auditor's basic
responsibilities differ between immaterial and material items. Spe—
cifically, if an item appears immaterial, the auditor's responsibility
is to gather sufficient evidential support to satisfy himself that the

item is, in fact, immaterial. For a material item, however, he

 

15Grinaker, p. 64.

123
requires sufficient evidential support to assure himself that it is
accurately stated within the limits of error allowed by the statement
user's decision model. This latter requirement is apt to be far more
restrictive than the former.

Regrettably, even though materiality is such an important fac-
tor, it is extremely difficult to measure. Arens notes the primary
reason, stating:

One of the difficulties in establishing objec—

tive measurements of materiality and relating it to

evidence accumulation requirements is the lack of

knowledge by auditors of the misstatements or omis-

sions which affect the decisions of particular user

groups. This results primarily from the large number

of diverse user groups which rely upon financial

statements, as well as the inability or unwillingness

of most specific user groups to specify their maximum
materiality error or omission tolerances.l6

Thus, while, in most cases, the auditor, using past experience as a
guide, may believe himself able to distinguish between immaterial and
material items in a given set of financial statements, his attempts at
measuring (i.e., determining precisely) a particular item's relative
materiality can be, at best, crude and highly arbitrary. He simply
has too few guidelines to follow, let alone an operational definition

of the concept.17

 

16Arens, p. 51.

17For a detailed discussion of the problems involved in develop-
ing materiality guidelines as well as suggested approaches to these
problems, see Arens, pp. 47-74. Specifically, he considers the fol-
lowing factors relevant to useful materiality guidelines: "the indi-
vidual account," "combination of accounts," "combination of misstate-
ments and omissions," "types of errors or misstatements existing in
the accounts," "correct vs. incorrect account balances," "the differ-
ences between unknown errors in immaterial accounts and known errors
in material accounts," "the nature of the item."

The Financial Accounting Standards Board has also included this
tapic on its agenda.

124

In 1964, the editorial board of the Journal of Accountancy sum-

 

marized perhaps the primary reason for this situation. Recognizing
the diverse variety of factors which influence materiality decisions,

they concluded:

Materiality cannot be decided solely on the basis of a
percentage of net income or a percentage of some other
basic figure. Whether an item is material or not may
depend on much more than a financial measurement. It
may also depend upon the nature of the item being mea-
sured. In some cases, the nature of the item is the
principle basis for the decision.18

Despite the lack of relevant guidelines, public accountants must
make materiality decisions with respect to their clients' financial
reports -- decisions which can influence their accumulation of audit
evidence. The problem of how they make, or should make, such deci-
sions is easily a research project in itself, and is thus beyond the
scope of this dissertation. Therefore, we must bypass that problem
and concentrate, instead, on the implications of materiality deci—

sions, however made, for audit evidence accumulation.

Expected Influence on Audit Program

According to Mautz and Sharaf:

In most cases it is relatively easy to determine
if a financial statement assertion is material or not,
If it is not, the auditor need obtain only sufficient
evidence to persuade (as contrasted with assure) him
that the assertion involved is or is not valid. Borrow-
ing the terminology of law he should reqpire apprepon-
derance of evidence. If the assertion is one that is
material, however, he should require considerably
stronger evidence. Here he should attempt to eliminate
any reasonable doubt . . . This means that for material
assertions, the evidence must be compelling -- and this

 

 

18"Materiality," Journal of Accountancy_ll7 (April 1964): 35‘36~

 

125
is possible only for existence of present physical
things and for mathematical assertions -- or a combi-

nation of types of evidence must be obtained.19
[Italics mine.]

In general, the auditor can alter his evidential support by altering
any or all of the three parameters of his evidential collection:

types of evidence included, times of collection of each type, and numr
ber of units of each type collected at a given time. As we shall see,
materiality considerations may influence all of these parameters.

Expected Influence on Types
of Evidence Included

 

Arens suggests the importance of materiality considerations for
this parameter of the auditor's evidential collection when he writes:

Audit procedures are classified as required pro-
cedures and optional procedures. A required procedure
must be performed for every audit where the assertion
or account being considered is material. Optional
procedures are determined by the following variables
of auditing: (1) internal control, (2) materialipy,
(3) reliability, (4) cost, (5) risk of sanctions.20
[Italics mine.]

 

 

 

Clearly, the implication is that Arens believes certain pro-

cedures "required" when an item is material need not be performed when

 

the item appears immaterial. Note, however, that Arens does not imply
that the auditor may completely ignore items in the financial records
which appear immaterial. Rather, he argues that, even for these
items, the auditor requires a certain degree of evidential support,

noting:

 

19Mautz and Sharaf, p. 105.

20Arens, p. 128.

126

. . . the true or corrected balance is unknown by the
auditor before the work is completed. . . . If an
item is immaterial as stated on the books, the auditor
may not perform any work to verify the account balance.
If, however, the correct balance is material, the au-
ditor will have passed up a material item on the basis
of immateriality. This results in a paradox that the
correct balance is the basis for determining what is a
material misstatement, yet the correct balance is un—
known. There is no simple solution to the problem.

The ultimate answer, however, is that there will be
some procedures used in every_audit which will aid the
auditor in the discovery of this type of misstatement.21
[Italics mine.]

 

 

 

We have previously suggested that the auditor's responsibility
concerning apparently immaterial items in the financial records dif—
fers significantly from his responsibility concerning material items
in those records. If an item is immaterial, and hence the auditor
need only ascertain that it is not grossly misstated, then he may con-
clude with the Canadian Institute of Chartered Accountants, that the
following general tests are sufficient for his needs:

1. learn what the item represents;

2. decide that it appears reasonable;

3. check the amount to the general ledger and scrutinize the

relevant account;

4. decide that in comparison to similar items from the previous

years it is reasonable;

5. decide that there are no special circumstances that would

render material this otherwise immaterial item.22

 

21Arens, pp. 55-56.

22Study Group on Audit Techniques, Canadian Institute of
Chartered Accountants, Materiality in Auditing, Toronto: Canadian
Institute of Chartered Accountants, 1965, pp. 8-9.

 

127

If, on the other hand, an item is material and hence the auditor must
determine its accuracy within even moderately close tolerances, his
testing will most likely have to include more, and considerably more
specific, procedures than those listed above.
Expected Influence on the Time of
Collection of Each Type of Evidence

In general, the more recent a unit of audit evidence, the more
support it is likely to provide. Therefore, and because the auditor
requires significantly greater evidential support for material items
than for immaterial items, materiality considerations may, in part,
determine whether he performs certain tests at an interim date or at
year end. As we shall see, however, the better the client's internal
control system, the less evidential support he will lose by shifting
his testing from year-end to an interim date. Therefore, by them-
selves, materiality considerations are likely to have relatively
little effect on the timing parameter of the auditor's evidential col-
lection.

The Auditor's Evaluation of the Probability that

a Given Financial Statement Assertion
Is Materially Misstated

 

The Committee on Auditing Procedure of the AICPA has stated
that:

. . . it should be understood that the ultimate risk
against which the auditor and those who rely on his
opinion require reasonable protection is a combina-
tion of two separate risks. The first of these is
that material errors will occur in the accounting
process by which the financial statements are

128
developed. The second is that any material errors

that occur will not be detected in the auditor's ex-
amination.

The obvious implication of this statement is that the prudent auditor
must require more evidential support for any given financial statement
assertion, the greater is the probability of material error in that
assertion. At least two factors are likely to affect an auditor's
evaluation of this probability:
1. his evaluation of the quality (comprehensiveness and effec-
tiveness) of his client's relevant internal controls, and
2. his assessment of the general "riskiness" of his client,
based on the client's financial health, operating and re- '

porting policies, prior auditor-client relations, etc.

The remainder of this chapter is devoted to a study of these

factors and their effect on audit evidence accumulation.
The Auditor's Evaluation of the Quality of His
Client's Relevant Internal Controls

The Committee on Auditing Procedure suggests the following gen-

eral definition for internal control:
Internal control comprises the plan of organiza-

tion and all of the co-ordinate methods and measures

adopted within a business to safeguard its assets,

check the accuracy and reliability of its accounting

data, promote Operational efficiency and encourage ad—
herence to prescribed managerial policies.24

As evidence of the importance accorded this factor by the Committee

and the AICPA, the second standard of auditing fieldwork requires that:

 

23Committee on Auditing Procedure, p. 39.

24Ibid., p. 15.

129
There is to be a proper study and evaluation of
the existing internal control as a basis for reliance
thereon and for the determination of the resultant

extent of the tests to which auditing procedures are
to be restricted.25

Perhaps no other variable of the audit has received such exten-
sive exposure in the professional literature -- most of the discussion
centering around: (1) the extent of the auditor's responsibility for
evaluating his client's internal control system, and (2) the effect of
such evaluation on subsequent evidence accumulation. While a detailed
analysis of the auditor's responsibility for evaluating his client's
internal control system is beyond the scope Of this dissertation, a
summary of the AICPA's current position on the subject should serve as
a useful prelude to the discussion of the effect such evaluation may
logically have on the auditor's program.

The Auditor's Responsibility for Evaluating
His Client's Internal Controls

 

In Statement on Auditinngtandards No. l, the Committee on Audit-

 

.ing Procedure discusses both the nature and the scope Of the auditor's

responsibility under the second fieldwork standard.

The Nature of the Responsibility
According to the Committee on Auditing Procedure:

The study to be made as the basis for the evalua-
tion of internal control includes two phases: (a)
knowledge and understanding of the procedures and
methods prescribed and (b) a reasonable degree of as-
surance that they are in use and are Operating as

 

25Ibid., p. 5.

130

planned. These two phases are referred to as the re-
view of the system and tests of compliance, respec-
tively.26

Concerning the first phase of the study, the Committee notes:

The review of the system is primarily a process
of obtaining information about the organization and
the procedures prescribed and is intended to serve as
the basis for tests of compliance and for evaluation
of the system. The information required for this pur—
pose ordinarily is obtained through discussion with
appropriate client personnel and reference to documen-
tation such as procedure manuals job descriptions,
flowcharts, and decision tables.2

Presumably, the auditor must always perform this first phase of the

With regard to tests of compliance, however, such is not the

case, since the auditor only needs to know that internal control pro-

cedures are operating as prescribed if he intends to rely on such pro-

cedures as evidence of financial statement assertion validity. In the

words of the Committee on Auditing Procedure:

The purpose of tests of compliance is to provide
reasonable assurance that the accounting control pro-
cedures are being applied as prescribed. Such tests
are necessary if the prescribed procedures are to be
relied upon in determining the nature, timing, or exp
tent of substantive tests of particular classes of
transactions or balances, . . . but are not necessary
if the procedures are not to be relied upon for that
puppose. [Italics mine.] The auditor may decide not
to rely upon the prescribed procedures because he con-
cludes either (a) that the procedures are not satis-
factory for that purpose or (b) that the audit effort
required to test compliance with the procedures to
justify reliance on them in making substantive tests

 

 

26Ibid., p. 27.

27Ibid., pp. 27-28.

131

would exceed the reduction in effort that could be

achieved by such reliance.28
The Scope of the Responsibility

In defining the gpppg_of the auditor's responsibility under the
second fieldwork standard, the Committee on Auditing Procedure subdi-
vides internal control into two categories -- administrative control
and accounting control. According to the Committee:

Administrative control includes, but is not limited
to the plan Of organization and the procedures and

records that are concerned with the decision processes
leading to management's authorization of transactions. . . .

 

29

while:

Accounting control comprises the plan of organi-
zation and the procedures and records that are con-
cerned with the safeguarding of assets and the reli-
ability Of financial records and consequently are de-
signed to provide reasonable assurance that:

 

a. Transactions are executed in accordance
with management's general or specific
authorization.

b. Transactions are recorded as necessary
(1) to permit preparation Of financial
statements in conformity with generally
accepted accounting principles or any
other criteria applicable to such state-
ments and (2) to maintain accountability
for assets.

c. Access to assets is permitted only in
accordance with management's authoriza-
tion.

d. The recorded accountability for assets
is compared with the existing assets at

 

231bid., p. 28.

29Ibid., p. 20.

132
reasonable intervals and appropriate

action is taken with respect to any dif-
ferences.30

Having made this distinction, the Committee concludes that:
. . . accounting control is within the sc0pe of the
study and evaluation of internal control contemplated
by generally accepted auditigg standards, while ad-
ministrative control is not.
Expected Influence on Audit Program

The auditor's evaluation Of the comprehensiveness and effective-
ness of his client's internal controls is unique among the factors
which determine minimum evidential support requirements. This param-
eter is the pp;y_one which is, itself, based on actual audit evidence
-- the review of the client's internal control system and tests Of
compliance. Therefore, as one might expect, the factor has a funda-
mentally different effect on audit program development. The following
normative approach to evaluating a given financial statement assertion
indicates this difference. Essentially, the approach consists of four
steps:

1. Determine the minimum evidential support required for an
Opinion by professional standards, regulatory agency re-
quirements, firm policies, auditor—client contract terms,
and materiality considerations.

2. Determine the extent to which the risk of sanctions neces-

sitates an increase in this minimum.

 

3oIbid.

31Ibid., p. 27.

133
3. Determine the degree of evidential support provided by the
internal control evaluation and any other existing corrob-
orative evidence.
4. Determine the nature, extent, and timing of substantive
tests necessary to provide adequate support to establish (or

refute) the assertion at the required level of assurance.

As this approach suggests, the auditor's evaluation of his
client's internal control does not actually affect his overall require-
ment for evidential support. Rather, the evaluation is a potential
source of evidential support and therefore, in part, determines the
degree to which additional (i.e., substantive) testing is necessary.

The Committee on Auditing Procedure has written:

The purpose Of the auditor's study and evalua-
tion of internal control . . . is to establish a basis
for reliance thereon in determining the nature, extent,

and timing of audit tests to be applied in his examina-
tion of the financial statements. [Italics mine.]32

 

Clearly, then, the Committee feels that such "study and evalua-
tion" may affect all three parameters of the auditor's evidential col—

lection. Let us consider the reasoning behind this position.

Effect on the Type of Evidence Obtained
Mautz and Mini argue that:

Program planning . . . is essentially a problem
of allocating audit resources as effectively and eco-
nomically as possible in an effort to achieve the audit
objective. As a basis upon which to allocate these
audit resources, the auditor must concern himself with
the relative probabilities that an array Of possible
irregularities, or deviations from fact, will be present

 

32Ibid., p. 14.

134
in the financial data under review; that is, the ex-
tent and nature Of his audit procedures must be di-

rected primarily at those irregularities that are most
probable in his particular client's organization.33

For any given financial statement assertion, the presence of an
adequate, functioning set of relevant internal controls generally in-
sures a low probability of misstatement. The absence of such con-
trols, on the other hand, while it need not always result in material
misstatement, does increase the probability Of, or at least the pro-
pensity for, errors and irregularities. Therefore, wherever the au-
ditor's evaluation of his client's internal control indicates an in-
herent inadequacy or chronic lack of compliance, he must perform such
substantive tests as are necessary to assure him that no material mis-
statement has occurred. Since, however, the specific weakness in-
volved determines which tests he must perform, the auditor's evalua-
tion of his client's internal control system will affect the type
parameter of his evidential collection. In the words of Mautz and
Mini:

. . . the judgment process by which internal control

is related to the audit program . . . takes the form

of a line of reasoning illustrated by the following

questions:

1. What features of internal control are mis-
sing?

2. What irregularities are thereby permitted?

3. What modifications in our minimum audit pro-

gram will be of most help in testing for the
occurrence of such irregularities?3

 

33R. K. Mautz and Donald L. Mini, "Internal Control Evaluation
and Audit Program Modification," The Accountinngeview 41 (April
1966): 287.

3"I‘bid., p. 290.

135

One should not infer, however, that the auditor need only per-

form substantive tests where his internal control evaluation has iden-

tified an inadequacy. As the Committee on Auditing Procedure
out:

There are inherent weaknesses that should be
recognized in considering the potential effectiveness
of any system of accounting control. In the perform-
ance of most control procedures, there are possibili-
ties of errors arising from such causes as misunder-
standing Of instructions, mistakes in judgment and per-
sonal carelessness, distraction or fatigue. Further-
more, procedures whose effectiveness depends On segre-
gation of duties Obviously can be circumvented by col-
lusion. Similarly, procedures designed to assure the
execution and recording of transactions in accordance
with management's authorizations may be ineffective
against either errors or irregularities perpetrated by
managers with reapect to transactions or to the esti-
mates and judgments reguired in the preparation Of
financial statements.3

Because of such limitations on the effectiveness of internal
the Committee concludes:

The second standard [of fieldwork] does not con-
template that the auditor will place complete reliance
On internal control to the exclusion of other auditing
procedures with respect to material amounts in the fi-
nancial statements. 6

points

control,

The obvious implication is, as Mautz and Mini37 and Arens38 have both

earlier suggested, that there exists a minimum program or minimum set

of procedures required for all engagements, even under ideal internal

 

35Committee on Auditing Procedure, p. 22.

36Ibid., p. 34.

37Mautz and Mini, pp. 283-289.

38Arens, p. 85.

.1

C.

..‘e

136
control conditions. Furthermore, it follows that departures from

ideal controls require apprOpriate modification of that minimum.

Effect on the Timing of Evidence Accumulation
Arens has written:

It is appropriate tO perform balance sheet veri-
fication tests at a time other than year end only when
the auditor believes that the transactions which take
place between verification time and the period end
will be correctly recorded. Since . . . the internal
control in existence does affect the probability of
error, it follows that it should also affect the au—
ditor's confidence about the validity of transactions
between verification time and year-end time. It is
true that if internal controls are weak in the area
under consideration, the auditor is not justified in

performing the balance verification at a time other
than year end.

The auditor attests to the content of a set of financial reports
at a particular date. If he has obtained evidential matter on or
after the statement date, presumably, any support provided by that
evidence relates directly to information contained in those statements.
If, however, he has Obtained the evidence prior to the actual state-
ment date, he must project its support forward. In general, while
evidence that a financial statement item is free from material error
on June 30'p§y_support the opinion that the same item is free of
material error on December 31, it need not. The degree of reliability
with which the auditor may project interim evidential support depends
upon: (1) the degree to which the recording of transactions and safe-

guarding Of assets occurs within a well-defined deterministic

 

39Ibid.

‘N’i
Syn-a

'4’-
H

“A

137
framework, i.e., a perfectly predictable system, and (2) the degree to
which this system remains constant over the period of the projection.

Unfortunately for the auditor, as Mautz and Mini note, internal
control systems, however well-defined, comprehensive, and normally
effective, are p25 deterministic. Because they contain human elements,
such systems are subject to breakdowns and are hence probabilistic."0
In other words, every activity which takes place within a given
client's control system has a probability, however small, of resulting
in an error in that client's records. Furthermore, as Mautz and Mini
also note, no system is so comprehensive as to govern every possible
business activity which may occur -- and, in general, activities be—
yond systematic control are particularly subject to inconsistent and
erroneous treatment.41 Thus, if an auditor obtains interim-date evi-
dence in support of a given financial statement item, he must accept
the possibility that a material error or abstraction will occur with
respect to that item between the time of evidence accumulation and the
date of his opinion. For this reason, the reliability of interim evi-
dential support must always be somewhat less than perfect.

Clearly, the smaller the probability of "post—testing" error or
irregularity, the greater is the reliability with which the auditor
can project interim test results forward. For any given financial
statement item, however, this probability is, in turn, a function of

the following:

 

40Mautz and Mini, pp. 284-85.

41Ibid., p. 286.

138

l. the probability that activity relevant to the item, but be-
yond the client's system of internal control will occur,

2. the probability that activity relevant to the item but be-
yond the client's system of internal control will be im-
properly handled, given that such activity occurs,

3. the probability that activity relevant tO the item and with-
in the client's system of internal control will be im-
properly handled,

4. the distribution of errors which can occur,

5. the volume of activity (relevant to the given item) between
the test date and the statement date (in general, likely to
be a function of the length of the period), and

6. the auditor's definition of material error.

Now, if we assume that, with respect to any given statement
item, the auditor's definition of material error is a constant, the
only variable of the above six over which he has any direct control is
the volume of activity which takes place between the testing date and
the statement date. Thus, if the auditor is to hold the probability
Of "post-testing" material error to an acceptable level, he must first
evaluate (or, at least, estimate) the other relevant variables and
then adjust his timing accordingly.

Of the variables which the auditor must evaluate, two (the prob-
ability that activity beyond the client's control system will occur,
anti the probability that activity within the system will be handled
erroneously) are direct functions of the comprehensiveness and effec-

t1V's—ness Of the client's internal control system. Thus, the auditor's

‘1
(LL

"'1 4
1

p.4-

but:

Opes.

bow

-\~

[It

hit

 

139
evaluation of the internal controls should influence his evaluation of
these variables, and hence affect the timing parameter of his eviden-

tial collection.

Effect on the Extent of Evidence Accumulation

Material error in a client's financial statements may result
from either:

1. a few unacceptably large errors in the client's records, or

2. an unacceptably large number of small errors.

As Arens points out:

If a single transaction or subsidiary account balance
is so large that its misstatement would render the
overall financial statements incorrect, the auditor
can verify the transaction or subsidiary account re-
gardless of the quality of the internal control in
effect. A careful auditor is expected to stratify
populations and perform 100 per cent verification pro-
cedures on any strata which have a small number of
large transactions.42

For this reason, we may conclude (with Arens) that:
. . . internal control evaluation can have no effect

on the extent of procedures performed when the auditor
is concerned about a small number Of large errors.

Where the auditor is concerned about a large number of small errors,
however, such is not the case and reference to statistical sampling
most clearly illustrates the effect.

In general, use of statistical sampling requires the auditor to

sPecify two parameters: sample precision, "the range or limits within

 

 

42Arens, pp. 89-90.

'3ibid., p. 90.

140
"1'4 o s s
which the sample result is expected to be accurate, and reliability
(confidence level), "the mathematical probability of achieving that

degree of accuracy."45 While recognizing that sample precision and

reliability "are statistically inseparable, the Committee on Auditing

Procedure suggests that:

. . . one of the ways in which these measures can be
usefully adapted to the auditor's purpose is by relat-
ing precision to materiality and reliability to the
reasonableness for the basis Of his opinion.46

We have already noted that:

. . . the ultimate risk against which the auditor and
those who rely on his Opinion require reasonable pro-
tection is a combination of two separate risks. The
first of these is that material errors will occur in
the accounting process by which the financial state-
ments are developed. The second is that any material
errors that occur will not be detected in the auditor's
examination.47

Clearly, for any given financial statement assertion, the first
risk will vary inversely with the quality and comprehensiveness of the
client's relevant internal controls while the second risk will vary
inversely with the extent of the auditor's testing. Therefore, since:

The combined risk of both these adverse events

occurring jointly is the product of the respective
individual risks . . 48

 

44Committee on Auditing Procedure, p. 45.

45Ibid.

461bid., p. 38.

47Ibid., p. 39.

48lbid., p. 51.

141
it follows that if the auditor desires to hold the combined risk to
some given acceptable level, the greater is the probability of mate-
rial error in the client's records, the more extensively he must test
for such error.

One may also arrive at the same conclusion in a somewhat more
roundabout manner. Note that if the auditor's combined risk of mate-
rial error in a given financial statement item is, e.g., .05, then his
overall degree of assurance that such error does pp£_exist is .95, the
complement of the combined risk. One should not, however, confuse nor

equate the overall deggee of assurance which the auditor will require

 

to establish a financial statement item's validity with the reliability

 

.leyei at which he must perform any given substantive test on that
item. The auditor's overall assurance requirement should be a func-
tion of the following factors: (1) professional standards, (2) regu-
latory agency requirements, (3) firm policies, (4) auditor-client
contract terms, (5) materiality considerations, and (6) risk factors.
This requirement should not, however, vary with the types of evidence
which the auditor collects in his attempt to achieve it. Therefore,.
since the auditor's evaluation of his client's internal control system
is essentially evidence, this factor should not affect his overall

assurance requirement. On the other hand, the confidence level at

 

which the auditor performs a particular substantive test should depend

not only upon his overall assurance requirement, but also uppn the

 

extent to which collateral evidence contributes to that requirement.
In other words, the auditor's overall degree of assurance is the re-

sult of:

142

. . . combining the reliability from one or more
statistical samples that serve a particular purpose
with the "subjective reliance assigned to . . . any
other auditing procedures" that serve the same pur—
pose.

Therefore, we may conclude with the Committee on Auditing Procedure

that:

The auditor's judgment concerning the reliance
to be assigned to internal accounting control and
other relevant factors should determine the reliabil—
ity level to be used for substantive tests. Such re-
liability should be set so that the combination of it
and the subjective reliance on internal accounting
control and other relevant factors will provide a
combined reliability level conceptually equal to that
which would be used . . . if the auditor's evaluation
indicate[d] that little if any reliance should be
assigned to internal accounting control for the pur-
pose Of particular substantive tests.50

The Auditor's Assessment of the General
"Riskiness" of His Client
In general, the auditor's assessment of the general "riskiness"
of his client, based on the client's financial health, operating and
reporting policies, prior auditor-client relations, etc., may affect
his audit program in two ways. First of all, to the extent it affects

his evaluation of the expected risk of sanctions, this factor may

 

49Ibid., pp. 51-52.

SQEQLQL, p. 52. The Committee suggests that:

The concept . . . can be applied by use of the
following formula:

- “£11151
3 1 (1-0)

where:

Reliability level for substantive tests
Combined reliability level desired . . .
Reliance assigned to internal accounting
control and other relevant factors. (p. 53.)

GNU)
IIIIII

143
influence the auditor's overall evidential support requirements. This
effect receives detailed consideration in Chapter V.

The factor may also affect the auditor's evidential collection
to the extent that it corroborates or conflicts with other evidential
matter. For example, suppose a client's internal control system ap-
pears adequate and effective. The auditor will likely place more re-
liance on that system in restricting his substantive tests if the
client is in sound financial health and has well-established operating
and reporting policies than if the client faces insolvency or has
questionable Operating and reporting policies.

In the former case, the evaluation of internal control and the
assessment of the client's "riskiness" tend to corroborate one another
in predicting a low probability of material error in the client's fi-
nancial statements. In the latter case, however, since the two types
of evidence conflict, the auditor has little choice but to place
greater reliance on substantive tests to settle the issue. (For a
more detailed discussion of the effect of corroborative evidence on

audit evidence accumulation, see supra, pp. 101-104.)

Expected Influence on Audit Proggam

 

In the present context, the auditor's assessment of client

"riskiness" primarily affects his audit program indirectly through its

 

tendency to augment or reduce the reliability of evidential support
provided by his evaluation of client internal controls. Since, how-
ever, the auditor's evaluation of his client's internal controls can
affect all three parameters of his evidential collection, client

"riskiness" can also affect all three parameters.

144
Summagy
This chapter has dealt with factors which, in part, determine
the auditor's support requirements for an opinion on a given financial
statement assertion -- Specifically, the "factors which determine the

minimum evidential support necessary to justify a professional opinion"

 

on such an assertion as an element of the overall financial statements.
As in the previous chapter, an important part of this discussion has
centered around whether and how the individual factors considered
might logically affect the types of evidence the auditor obtains, the
times at which he obtains a given type, and the number of units of a
given type he obtains at a given time. Also as in the previous chap-
ter, the following table summarizes the conclusions of this aspect of

the discussion.

145

Table 2.--Expected influence of factors which determine the minimum
evidential support necessary to justify a professional opinion on a
given financial statement assertion on the three parameters of the
auditor's evidential collection: (1) the types of evidence included,
(2) the times of collection of each type, and (3) the number of units
of each type collected at a given time.

Variable Type Timing Extent

Generally Accepted Auditing
Standards 0 O 0

SEC Pronouncements O 0 0

Commission Requirements (for

Regulated Industries) 0 O O
Policies of Individual Public

Accounting Firms 0 O 0
Terms of the Auditor-Client

Contract 0 O O
Materiality Considerations 0 O I

Auditor's Evaluation of the
Probability that a Given
Financial Statement Assertion
Is Materially Misstated O O 0
Key:

0 direct influence on this parameter of the auditor's
program

0 indirect or limited influence on this parameter of the
auditor's program

0 no influence on this parameter of the auditor's program.

Of the factors discussed in this chapter, then, while all ex-
cept "terms of the auditor-client contract" may exert considerable in-
fluence on the type parameter of the auditor's evidential collection,
materiality considerations and the auditor's evaluation of the prob-

ability that a given financial statement assertion is materially

146
misstated are likely to have the greatest influence on the timing and
extent parameters of that collection.

For some engagements, the auditor may consider the expected cost
of sanctions for failure to detect material error sufficient to re-
quire that he obtain evidential support beyond the minimum necessary
for a professional Opinion. Factors which affect this expected dis-
utility may thus also influence the auditor's program. Let us there-

fore turn our attention to factors of this nature.

CHAPTER V

FACTORS WHICH INFLUENCE THE PROBABILITY THAT THE
AUDITOR WILL INCUR SANCTIONS FOR FAILING TO
DETECT A MATERIAL ERROR GIVEN THAT SUCH
ERROR EXISTS IN HIS CLIENT'S RECORDS

The auditor never achieves perfect knowledge of the degree to
which a given set of financial records reflects "reality." Even if
examination of every entry in those records, every asset allegedly
owned by the client, every available supporting document, etc., could
yield this degree of knowledge, such examination would undoubtedly be
infeasible, both from the standpoint of cost, and of available time
and staff. For this reason, however small it may be, the possibility
always exists that an auditor will fail to detect material error in a
given assertion of his client's financial statements. If subsequently
discovered, however, such failure may lead to any or all of the fol-
lowing sanctions:

1. adverse publicity,

2. admonition from the SEC or AICPA,

3. loss of client,

4. lawsuit,

5. loss of right to practice before the SEC,

6. expulsion from the AICPA and/or loss of license to practice,

and

7. conviction in criminal action.

147

148
Since these sanctions are a source of potentially great disutility,
whenever conditions indicate a greater than usual probability of their
occurrence, the prudent auditor may elect to extend his testing beyond
that necessary to satisfy "minimum" professional requirements.

In addition to the composition of the auditor's evidential col-
lection, Chapter I identified the following as factors which may in-
fluence the probability that an auditor will incur sanctions for fail-
ing to detect a material error existing in his client's records:

1. the nature of the specific error involved,

2. the degree of exposure the client's statements receive,

indicated by:
a. the client's size,
b. the nature of the client's operations,
c. the distribution of the client's ownership,
d. loan covenants which require the client to maintain
specified account balances or ratios,
3. the probability that the client will file bankruptcy subse-
quent to the audit, indicated by:
a. ,factors which affect or indicate the degree and types
of financial crisis the client can withstand, e.g.:

(1) factors which indicate the client's financial'
position ("Retained Earnings" balance, liquidity
situation, etc.),

(2) economic conditions related to the availability
of external capital,

(3) the client's rate and method of growth,

149

b. factors which affect or indicate the probability that
the client will face a financial crisis which exceeds
its capabilities, e.g.:
(l) the nature of the client's operations,
(2) economic conditions relevant to the client's
marketplace,

(3) the client's method of financing Operations.

These factors form the basis of discussion for the remainder of this

chapter.

The Nature of the Specific Error Involved
Whether or not sanctions are likely to result from an auditor's
failure to detect material error in his client's financial statements
may depend, to some extent, upon the actual nature of the error. For
example, Arens has suggested:

The management of the client is more likely to
impose sanctions against the auditor for failure to
find errors which reflect permanent losses of assets
than for those which result from assigning costs and
revenues to the wrong period . . . [i.e.,] management
is likely to be more unhappy with the auditor if he
fails to discover a defalcation than with an equal
dollar amount of sales cut-off error.

Other users are likely to complain more when
errors are found to overstate net income rather than
understate it. The only users who are significantly
hurt by understatements are potential stockholders
and creditors who failed to invest because of the un-
derstatement, or former investors who sold their in-
vestments because of the understatement. Historically,
neither of these users have had a serious effect upon
lawsuits or other serious sanctions.

 

1Alvin A. Arens, "The Adequacy of Audit Evidence Accumulation in
Public Accounting" (Doctoral thesis, School of Business Administration,
University of Minnesota, 1970), pp. 40-41.

150
Expected Influence on Audit Program

Obviously, an auditor does not know, before the fact, specif-
ically which type(s) of material error his examination will fail to
uncover. Nevertheless, the relationship between nature of error and
risk of sanctions may directly affect his audit program. Presumably,
associated with each financial statement assertion are a number of
(identifiable) potential types Of material error, each of which, in
turn, is more or less likely to result in sanctions should the auditor
fail to detect it. Chapter IV suggested that the auditor's goal in
reviewing his client's system of internal control should be to deter-
mine which types of error have a high propensity to occur within that
system. The auditor should, however, be aware 0f.§ll the errors char-
acteristic of a given type of financial statement assertion, whether
they have a high propensity to occur within the client's internal con-
trol system or not. Furthermore, whenever he considers the risk of
sanctions unusually high for a particular type of error, he is justi-
fied in specifically testing for that error even though his review of
the client's internal control system indicates such an error is un-
likely. In this manner, the relationship between nature of error and
risk of sanctions may directly affect the £122 parameter_of the au—

ditor's evidential collection.

 

This relationship may also indirectly affect the extent and
timing parameters of that collection. Chapter 11 suggested that the
probability an auditor will incur sanctions for failing to detect
material error in his client's statements and the probability that he

will fail to detect such error in the first place, are both decreasing

 

151

functions of the degree of evidential support he obtains. The audi-
tor, however, has three potential approaches to increasing evidential
support: (1) introduce new types of (relevant) evidence into his col—
lection, (2) increase the number of units obtained of some type(s) of
evidence already included in that collection, and (3) reduce the
length of the period of time between the date at which he obtains evi-
dence and the date of his opinion on the financial statements under
examination. For this reason, whenever an auditor considers the risk
of sanctions associated with a particular type of error sufficiently
great to warrant evidential support in excess of the "minimum" re-
quirements of a professional opinion and other factors in the audit
(such as those discussed in Chapter IV) already require him to perform
tests relevant to the detection Of this type error, the risk consider-
ations may cause him to increase his sample size and/or wait until
year end to perform his tests. Since the factor does not specifically
indicate which course of action the auditor should take, however, its
effect on extent and timing is indirect rather than direct.

The Deggee of Exposure the Client's
Statements Receive

 

Given that an auditor has failed to detect a materially mis-
stated assertion in his client's statements, then, presumably, the
greater the number, financial sophistication, and sensitivity to error
of the users of those statements, and the greater the number of people
actually made aware of the error, the greater is the probability the
auditor will suffer sanctions of one form or another. At least four
factors can affect and/or indicate to the auditor the degree and na-

ture of exposure his client's statements will receive and hence may

152

influence the composition of his evidential collection. Specifically,
these factors are:

l. the client's size,

2. the nature of the client's Operations,

3. the distribution of the client's ownership, and

4. loan covenants which require the client to maintain speci-

fied account balances or ratios.

At this point, let us consider each of these factors in somewhat more

detail.

The Client's Size

Generally speaking, the larger a client's operations, the more
likely information concerning those operations will receive exposure
in the various news media. At least roughly, then, a given client's
size (as measured, for example, by total asset book value) should in-
dicate to the auditor the probable extent of adverse publicity (a
sanction whose primary disutility lies in resulting losses of current
and potential engagements and their attendant revenues) he may expect
should he fail to detect material error in that client's financial

statements .

The Nature of the Client's Operations
Arens suggests that not only are the activities of larger cli-
ents most apt to receive news media attention, certain types of cli-
ent are also more likely than others to be in the public eye. Thus,

for example, he contends that, "Material errors in audited financial

153
statements of charitable organizations . . . almost always create ad-

verse publicity for the CPA."2

The nature of a given client's operations may also influence the
type of exposure his financial reports will receive. This effect be-
comes important whenever a certain class of statement user is partic-
ularly inclined to impose sanctions (and to impose more severe sanc-
tions) should the auditor pass a material misstatement. Thus Arens

states that, for example:

. . . misstatements in governmental financial state-

ments often result in sanctions that are more extreme

than would exist for a privately owned company with

similar misstatements.

In addition to influencing the extent and type of exposure a
given client's financial statements will receive, the nature of his
operations may affect the auditor's risk of sanctions in a somewhat
more direct manner. According to Arens, evidence indicates that:

. . . If the client is forced to file bankruptcy subse-

quent to the audit, the probability of the accountant's

being required to defend his audit work is significantly
higher than if the client is under no financial strain.4

For this reason, Anderson, Giese, and Booker argue that to the

extent the basic nature of a client's operations affect the financial

and economic risks he must take, this basic nature also affects the

auditor's risk of sanctions.

 

ZIbidO, p. 41.

3Ibid.

41bid., pp. 38—39.

5H. M. Anderson, J. W. Giese, and Jon Booker, "Some Propositions
About Auditing," The Accounting:Review 45 (July 1970): 529.

154

For the sake of completeness, let us also note in passing that
the nature of a given client's operations may have a far more basic
influence on the auditor's evidential accumulation process than
through its effect on his expected cost of sanctions. To the extent
that different types of clients have different accounting systems
(e.g., compare a construction company using completed contract in-
come accounting with a municipality engaged in fund accounting), eval-
uation of their financial reports may require the auditor to obtain
evidence in support of fundamentally different types of assertions.
Since, however, the study of such differences would be a major re-

search project in itself, it is beyond the scope of this dissertation.

The Distribution of the Client's Ownership

This factor influences both the extent and type of exposure fi-
nancial statements receive. The distribution of partnership or
closely-held corporation financial statements is normally limited to a
relatively few owners (disregarding creditors for the time being) who
are frequently managers as well. For a publicly-held corporation,
however, financial statement exposure is likely to be considerably
more extensive. Not only will the number of owners receiving c0pies
of the statements be considerably larger in most cases, whole new
classes of interested parties -- the SEC, financial analysts, employ-
ees, the general public -- also enter the picture.

This greater exposure afforded a publicly-held client's state-
ments affects the auditor's risk of sanctions in at least three ways:

1. it introduces the SEC as a potential source of sanctions

such as:

155

admonition - which, because of the SEC's weight may
have serious adverse effect on the auditor's reputa-
tion,

temporary delisting (revocation of permission to prac-
tice before the SEC) - essentially a stronger admoni-
tion which adds the loss of revenue during the delist-
ment period to adverse effect on the auditor's reputa-
tion, and

permanent delisting - which is, of course, effectively
the loss of all clients who must report to the SEC

(generally an auditor's largest clients),

2. it increases the probability of legal action should the au-

ditor fail to detect material error existing in the client's

statements since:

8.

not only are the client (through its management), or
any of its usually numerous owners potential plain-
tiffs, so too are any number of "third parties" whose
identity may well be unknown to the auditor at the
time he expresses his Opinion,

as Arens suggests, the probability that any individual
potential plaintiff will press suit is undoubtedly
greater because such parties do not bear as "personal"
and "sympathetic" a relationship to the auditor as do
the ownerdmanagers of partnerships and closely-held

corporations,6 and

 

6Arens, p. 40.

156
3. it increases the probability of adverse effect on the audi-
tor's public image since, the greater the number of people
potentially affected by material error in a given client's
financial statements, the greater is the probability that
discovery of such error will be publicly disclosed.
Loan Covenants which Require the Client to Maintain
Specified Account Balances or Ratios

Frequently, in its loan agreements, a financial institution will
place constraints on the balance(s) of specified accounts (e.g., long-
term debt), account aggregates (e.g., current assets), and/or account
ratios (e.g., acid-test, working capital, debt-equity) in the bor-
rower's financial statements. The purpose of such restrictions is, of
course, to provide some assurance that the borrower will be able to
meet his repayment schedule. To insure that the borrower is, in fact,
satisfying the constraints, the lender may require audited financial
reports.

The effect of this type of statement exposure on the auditor's
risk of sanctions is obvious. If an auditor attests that his client
is operating within covenant constraints and subsequently the client
defaults on his debt, eventual disclosure that an account or accounts
relevant to the covenant were materially misstated is almost certain
to result in litigation. Therefore, one might reasonably expect that,
in situations where the client seems in a weak financial position
and/or he does not substantially exceed loan covenant agreements, the

prudent auditor will extend his testing (at least in areas relevant to

157

the covenants) beyond the "minimum" requirements for a professional

opinion.

Expected Influence on Audit Program

We have suggested that, through its effect on the auditor's
evaluation of the probability that he will incur sanctions should he
fail to detect a material error in his client's financial statements,
the extent and type of exposure those statements receive may influence
him to obtain evidential support in excess of the "minimum" required
for a professional opinion. In general, however, while this factor
may indicate to the auditor a need for extended evidential support, it
is not likely to indicate specifically what parameter(s) of his evi-
dential collection he must alter to obtain such support. This deci-
sion must depend upon the factors (previously discussed in Chapter
III) peculiar to each individual engagement which define the eviden-
tial support function for a given type of audit evidence obtained at a
given time, upon marginal evidential cost functions, and, of course,
upon the auditor's constraints. In other words, statement exposure
may affect any or all of the parameters of the auditor's evidential
collection (type(s) of evidence included, time(s) of collection of
each type, and the number of units of each type collected at a given

time) indirectly. However, it will not affect any of them directly.

158

The Probability that the Client Will File
Bankruptcy Subsequent to the Audit

Arens considers this factor "the most important" of the "condi-

tions which affect the probability of sanctions for failure to dis-

7
cover misstatements . . ." He writes:

. . . If the client is forced to file bankruptcy
subsequent to the audit, the probability of the ac—
countant's being required to defend his audit work
is significantly higher than if the client is under
no financial strain. Even a large unexpected de-
crease in net income or other financial statement
item*will tend to make the users suspect that the
correct financial condition was not reported. This
is a natural reaction for financial statement users,
especially outside investors and creditors. It can
result from the honest belief that the auditor neg-
ligently failed to discover an existing error or
from the users' desire to recover part of the loss
they incurred regardless of the adequacy of the audit
work performed. The importance of financial condi-
tion on the probability of serious sanctions result-
ing is evident from the numerous recent lawsuits
arising after bankruptcy or near-bankruptcy has oc-
curred for several large companies.

To accurately appraise the probability that a client may face
bankruptcy subsequent to an audit, the auditor must weigh two differ-
ent types of factors:

1. factors which affect or indicate the degree and types of

financial crisis the client can withstand, e.g.:
a. factors which indicate the client's financial position,
b. economic conditions related to the availability of ex-
ternal capital,

c. the client's rate and method of growth, and

 

7Ibid., p. 38.

81b1do, pp. 38-390

159
2. factors which affect or indicate the probability that the
client will face a financial crisis which exceeds its capa-
bilities, e.g.:
a. the nature of the client's operations,
b. economic conditions relevant to the client's market-
place,
c. the client's method of financing operations.
Factors which Affect or Indicate the Degree and Types
of Financial Crisis the Client Can Withstand
Let us define a financial crisis as any event which has the po-
tential to precipitate bankruptcy. Identification and discussion of
all such crises is a major study in itself and hence is beyond the
scope of this dissertation. The important point, however, is that the
auditor, based upon his association with his client and his (supposed-
ly) intimate knowledge of his client's operations, should be able to
identify which types of crisis can pose a threat to the continuation
of those operations. Furthermore, because of the effect client bank-
ruptcy subsequent to the audit may have on his risk of sanctions (more
Specifically, lawsuits), he should evaluate the adequacy of a "minimum"
evidential collection with respect to such weaknesses as he identifies.
At least three factors effect, or can indicate to the auditor, the de-

gree and types of financial crisis a given client can withstand.

Factors which indicate the Client's Financial Position
Clearly, such factors are a source of information concerning
that client's ability to withstand financial crisis. The following

table, while by no means comprehensive, suggests a few of the more

160

obvious crises a client may face along with financial condition indi-

cators an auditor might use to determine the client's ability to with-

stand them.

Table 3.--Examp1es of financial crises and indicators of a client's
ability to withstand them

Indicator of a Client's

Crisis Ability to Withstand
Operating loss "Retained Earnings" balance
Debt repayment requirements Liquidity situation
Loss of a major customer Degree of concentration of business

with one or a few customers

Casualty loss Casualty insurance, "Retained Earn-
ings" balance

Economic Conditions related to the
Availability of External Capital

 

 

The client's financial condition primarily indicates his inter-
nal capacity to meet financial crisis. In evaluating his overall ca-
pacity to meet such crisis, however, the auditor must, in most cases,
also take into account the client's ability to draw upon external
sources of capital in an emergency situation, i.e., his line of credit
and his potential for generating external investment. Of course, one
important factor relevant to this ability is the client's existing
capital structure, particularly his outstanding debt. Other relevant
factors the auditor might consider, however, include the status of the
money market (13 money generally available or is it "tight"?) and the
general attitude of the investing public (Is the stock market "bullish"

or "bearish"?).

161

The Client's Rate and Method of Growth

 

As Anderson, Giese, and Booker note, "rapid growth through mer-

gers and acquisitions,"

especially if such growth is effected by the
issuance of "junior stock equities," may increase a client's danger of
bankruptcy substantially since "this method of expansion . . . depends
heavily on an ever increasing stock-price, which in turn means [a re-
quirement for steadily] increased earnings."9 In other words, ceteris
paribus, one would expect that a client committed to a long-term pro-
gram of merger expansion through the issuance of junior equities would
have far less ability to absorb an operating loss, or even reduced
profits, than might otherwise be the case, since such loss or reduc-
tion could terminate the expansion program at a fatally premature
state.
Factors which Indicate the Probability that the
Client Will Face a Financial Crisis which
Exceeds Those Capabilities

Even though a client may have little capability to withstand
certain types of financial crisis, the probability of bankruptcy due
to such crises may still be small if they have a low probability of
occurring. For this reason, the auditor should consider the probabil-
ity that the client will actually face a financial crisis which ex-

ceeds his withstanding capabilities. At least three factors may af-

fect, or indicate this probability to the auditor.

 

9Anderson, Giese, and Booker, p. 529.

162

The Nature of the Client'sggperations

We have already discussed in some detail the effect of this fac-
tor on the auditor's risk Of sanctions and therefore need not explore
it further here except to reiterate that clearly, certain types Of
Operations are inherently riskier than others. Thus, for example,
Anderson, Giese, and Booker note that "other things equal," a commod-
ity trader will bear greater "financial and economic risk" than will a

foundry.10

Economic Conditions relevant
to the Client's Marketplace

 

Although its measurement is admittedly difficult, the effect Of

such conditions is undeniable. For example, ceteris paribus, the cli-

 

ent's chances of sustaining operating losses in times Of recession,
stiff competition, or declining demand for the client's product are
clearly greater than they would be in times Of market expansion, little
or ineffectual competition, or expanding demand for the client's prod-
uct. I
The Client's Method of
Financing7Qperations

Ceteris paribus, a client's danger of financial crisis should be
greater, the more he relies upon debt as a source of financing.
"Trading-on-the—equity" is a double-edged sword -- it will amplify a
loss in the same way that it amplifies gains. Hence it increases the

possibility that the client will incur an Operating loss greater than

it can absorb. Furthermore, the greater the amount Of debt

 

loIbid.

163
outstanding, the greater is the danger that eventual repayment re-
quirements may force the client to liquidate assets essential to the

operation Of his business.

Expected Influence on Audit Program

The auditor's evaluation of the probability that his client will
file bankruptcy subsequent to the audit should affect his evidence ac-
cumulation in essentially the same manner as his evaluation of the ex~
tent and type of exposure his client's statements will receive, i.e.,
while the potential effect Of client bankruptcy on the auditor's risk
of sanctions may influence him to Obtain evidential support in excess
Of the "minimum" required for a professional opinion, those factors
which indicate the probability of client bankruptcy are not likely to
indicate to the auditor specifically which parameters of his evidential
collection he must alter to Obtain such support. Again, this decision
must depend upon the factors (previously discussed in Chapter III) pe-
culiar to each individual engagement which define the evidential sup-
port function for a given type of audit evidence Obtained at a given
time, upon marginal evidential cost functions, and, Of course, upon
the auditor's constraints. Thus, as in the case of statement exposure,
while potential client bankruptcy may affect any or all of the param-
eters Of the auditor's evidential collection (type(s) of evidence in-
cluded, time(s) of collection of each type, and the number of units of
each type collected at a given time) indirectly, this factor will not
affect any of them directly. Since, however, the auditor is likely to

identify in advance the type(s) of crisis which may precipitate a

164
particular client's bankruptcy, he may only require extended eviden-

tial support in areas relevant to such crises.

Summary

The auditor's failure to detect material error existing in his
client's financial statements may lead to any or all Of the following
sanctions:

l. adverse publicity,

2. admonition from the SEC or AICPA,

3. loss of client,

4. lawsuit,

5. loss of right to practice before the SEC,

6. expulsion from the AICPA and/or loss of license to practice,

and '

7. conviction in criminal action.

Since such sanctions are a source of potentially great disutil-
ity to the auditor, whenever conditions indicate a greater than usual
probability of their occurrence, the prudent auditor may elect to ex-
tend his testing beyond that necessary to satisfy "minimum” evidential
requirements. Therefore, this chapter has dealt with the following
factors, each of which affects, or at least may indicate to the audi-
tor the probability that he will incur sanctions should he fail to de-
tect material error existing in his client's financial statements:

1. the nature of the specific error involved, .

2. the degree of exposure the client's statements receive, in-

dicated by:

165
a. the client's size,
b. the nature of the client's operations,
c. the distribution of the client's ownership,
d. loan covenants which require the client to maintain
specified account balances or ratios,
3. the probability that the client will file bankruptcy subse-
quent to the audit, indicated by:
a. factors which affect or indicate the degree and types
Of financial crisis the client can withstand, e.g.:
(1) factors which indicate the client's financial
position ("Retained Earnings" balance, liquid-
ity situation, etc.),
(2) economic conditions related to the availability
of external capital,
(3) the client's rate and method of growth,
b. factors which affect or indicate the probability that
the client will face a financial crisis which exceeds
its capabilities, e.g.:
(1) the nature of the client's Operations,
(2) economic conditions relevant to the client's
marketplace,

(3) the client's method of financing operations.

As in the previous two chapters, the following table summarizes

the effect such factors might logically have on the auditor's program.

166

Table 4.--Expected influence of factors which influence the probabil-
ity that the auditor will incur sanctions for failing to detect a
material error given that such error exists in his client's records on
the three parameters Of the auditor's evidential collection: (1) the
types of evidence included, (2) the times of collection Of each type,
and (3) the number Of units of each type collected at a given time.

Variable Type Timing Extent

Nature of the Specific Error In-
volved O 0 0

Degree Of Exposure the Client's
Statements Receive 0 O 0

Probability that the Client Will
File Bankruptcy Subsequent to
the Audit 0 O 0
Key:

0 direct influence on this parameter of the auditor's
program

0 indirect or limited influence on this parameter Of the
auditor's program

0 no influence on this parameter Of the auditor's program.

Chapters I-V have identified and discussed in varying detail a
number of factors which seem logically capable of influencing audit
evidence accumulation. Whether or not such factors do, in fact, af-
fect the auditor's work, however, is a matter for empirical investiga-
tion rather than theoretical speculation. Therefore, let us turn to
such a study, examining actual audit working papers, in an attempt to
' evaluate the relative influence Of a number of "audit variables" on

evidence accumulation in the areas Of sales and accounts receivable.

CHAPTER VI

AN EMPIRICAL STUDY OF THE RELATIVE INFLUENCE
OF FACTORS WHICH AFFECT AUDIT
EVIDENCE ACCUMULATION

Chapters I-V of this dissertation have proposed a normative
framework for audit evidence accumulation decisions and discussed fac-
tors which that framework suggested as relevant to such decisions.
Unfortunately, as seems to be the case with most constructs of human
behavior, a valid method of testing the model directly (i.e., through.
the observation or interrogation of auditors) is not apparent. Simi-
larly, indirect testing (i.e., through the observation of audit work—
papers) of the degree to which auditor behavior corresponds to the
model per se is extremely difficult, if not impossible, because of the
general complexity of an audit engagement, the interactive (corrobora-
tive) effect of various types of evidence, and the difficulty Of at—
taching combinative quantitative measurements tO many of the variables
involved. However, by making restrictive assumptions with respect to
certain of these variables and controlling others, the study reported
in this chapter attempts to provide at least some insight into the
auditor's decision process.

The complexity Of the normative framework presented in Chapters
I-V and the limited resources available for this research precluded

any comprehensive test of that framework. Instead, the following

167

168

study is intended as a descriptive examination Of auditor behavior.
More specifically, the study's Objective is to determine whether or
not a sample of audit work-papers reflects any relationship between the
composition of the auditors' evidential collections (the dependent
variable) and those factors identified in Chapters I-V (the independ-
ent variables) which:

1. define evidential support functions,

2. determine minimum evidential support requirements,

3. affect the auditor's risk of sanctions, or

4. constrain the auditor's choice of evidential collection.

The Scope Of the Study

Because it is virtually impossible to Observe any human decision
process directly and because it is extremely difficult to construct
reliable "self-report" instruments, an audit work-paper.review was
selected as the source of data for this study. Time and cost consid-
erations required, however, that such a review be restricted to a
limited number of audit areas. Eventually, "sales" and "accounts
receivable" were chosen for the following reasons:

I. both are typically material financial statement items,

2. while the tests performed for their verification are fre-
quently interrelated, these tests are largely independent of
the tests performed in other financial statement areas --
thus minimizing the likelihood of unobserved interactive
effects,

3. while "sales," as an income statement item, requires ing}:

rect verification through "tests Of transactions" (system

169

tests), "accounts receivable,"

as a balance sheet item, per—
mits direct verification through confirmation (a balance
test) -- thus both major auditing approaches are included,
and

4. detailed documentation could be expected in these areas with

respect to population characteristics as well as tests per-

formed.

The Sample

 

The data for this study, Obtained during the period of November,
. 197l-April, 1972, extracts from the audit work-papers for fifty—three
clients of seven public accounting firms. Although the confidential
nature of the information provided by these firms dictates that they,
as well as their clients must remain anonymous, the following should

give some indication of the sample's general composition.

The Public Accounting Firms
The public accounting firms here represented are by no means a
random sample from some well-defined population. Rather, they are
seven firms who had clients of the type desired and who were willing
to participate. Except to assure the reader that these firms are rep-
resentatives of "good" current practice, however, the author will not
disclose any demographic information relating to them since such dis-

closure might endanger their anonymity.

The Clients
As was the case with the participating firms, the clients repre-

sented in this study are not a random sample. Rather, each cooperating

170
public accounting firm selected from among its own clients using the
following criteria:

1. in all cases, sales and accounts receivable should be mate—
rial items,

2. in all cases, the clients should have received unqualified
opinions,

3. the selected clients should be free of "unusual auditing
problems" (as defined by the selecting firm) in the areas of
sales and accounts receivable,

4. manufacturing and merchandising concerns would be prefer-
able; however, some service organizations might be accept-
able (subject to the researcher's approval); in all cases,
municipalities, financial institutions, fiscal agents, etc.,
would be unacceptable,

5. the work-papers should not pose the reviewer any serious
problem with respect to time consumption or ability to lo—
cate all relevant information contained therein. (For this
requirement, the firms received the following additional
guidelines:1

a. current assets should be less than $10,000,000,
b. sales should be less than $20,000,000,
c. the client should have no more than a few independent
divisions and/or subsidiaries.
The firms received instructions, however, that they might

waive any or all of these supplementary guidelines if, in

 

1Perhaps a better guideline would have been: total weight Of
one year's work-papers should not exceed five pounds.

171
their opinion, the client's work-papers would not pose the

reviewer serious problems.

The actual breakdown of the sample by participating firm is:2

 

§1£m_ Number of Clients Reviewed
A 10
B 10
C 5
D 5
E 10
F 3
G 10

Firms A through F provided data from each client's three most
recent audits except in the cases of one client from Firm B and two
from Firm E, each Of which had retained the auditor for less than
three years. Firm G, on the other hand, provided informatiOn only for
the most recent year's audit, stating that the storage location of
prior years' work-papers made retrieval impractical.

0f the fifty-three clients whose work-papers provide the data
for this study:

1. forty-two are manufacturers, nine are merchandising con-

cerns, and two are service organizations,

 

2To safeguard the anonymity of participants in this study, iden-
tifying firm letters were randomly assigned and bear no relationship
to, e.g., size or alphabetical order.

172
2. thirty-seven are partnerships or closely-held corporations,
and of the remaining sixteen which are publicly owned, seven
are listed on the New York Stock Exchange and one is listed
on the American Stock Exchange,
3. six acquired one or more subsidiaries within the three pre-
vious years, and Of the nine total acquisitions:
a. seven were effected by an exchange Of cash,
b. two were effected by an exchange of stock,
c. eight were accounted for as purchases,
d. one was accounted for by the equity method,
4. sixteen had loan covenants, of which:
a. five pertained to retained earnings only,
b. one pertained to working capital only,
c. ten pertained to both retained earnings and working
capital, and
5. thirty-five reported on a calendar-year basis, while eight-
een had a fiscal year ending on a date other than

December 31.

Furthermore, among these fifty-three clients, in the most recent year
audited (at the time of the data collection):
1. sales and accounts receivable internal controls ranged from
poor to excellent,

2. the dollar value of accounts receivable ranged from $2600 to

 

$10,641,000; the number Of accounts receivable ranged from

two accounts to fifteen thousand,

173
3. the book value of total assets ranged from $121,000 to
$26,917,000,
4. sales ranged from $269,000 to $69,824,000,
5. net income before taxes ranged from —$2,857,000 to
$5,570,000,
6. stockholders' equity ranged from $75,000 to $20,912,000, and

7. outstanding long-term debt ranged from none to $8,043,000.

In summary, the sample consists Of medium sized, profit-oriented
clients which had no significant auditing problems in the areas of
sales and accounts receivable and which received a clean opinion. In
these respects, the sample is relatively homogeneous and one would
therefore expect a certain degree of similarity in the sample audit
programs. Even within the bounds set by the sample selection criteria,
however, client variations in size, nature Of operations, distribution
of ownership, rate and method of growth, methOd Of financing Opera-
tions, quality of internal control, and composition Of accounts re-
ceivable appear sufficient to have caused variation in the nature, ex-
tent, and timing of audit procedures if the auditor considered such

factors when developing his program.

The Method of Obtaining Data
Initially, the researcher hoped to personally review each co-
operating firm's work-papers in order to Obtain the data for this

study. Firms A, B, D, and E (thirty-five clients) did, in fact,

174
permit such an approach.3 However, as it affected firm selection, the
confidentiality of the auditor-client relationship also required mod-
ification of the method of Obtaining data from firms C, F, and G
(eighteen clients). These firms stated as a precondition to their
participation in the study that their own people must perform the
work-paper review and denied the researcher first hand access to such

records. This situation, unfortunately, introduced the possibility Of

 

variance in the reliability of data obtained -- both because Of the
potential for biased reporting, and because of the difference in the
reviewers' experience with their respective firms (reviewers ranged
from a partner (Firm F) to juniors (Firm C)). Nevertheless, this re-
searcher feels that the actual risk Of biased and/or inaccurate report-
ing was sufficiently small to be far outweighed by the value Of having

firms C, F, and G participate in the study.

A Caveat
Obviously, for the reasons enumerated above, this sample of
firms and clients is far removed from any statistical ideal in terms
of size and composition. Unfortunately, the Obstacles of data confi-
dentiality, firm conservatism, and the Obviously limited resources of
a one-man study necessitated the researcher's approach. Therefore,

the reader should keep in mind that the data at hand can strictly pur-

 

port to describe the "state Of the art" Of auditing in the participat-

ing firms only. Any attempts to draw inferences about the public

 

3In all cases where the author reviewed client work-papers, the

public accounting firm involved provided extensive assistance and
supervision to insure that the review would be a thorough one.

175
accounting profession in general from this data run the risk of re-

sulting in invalid conclusions.

The Dependent Variables and the Basic Approach

 

As previously noted, the objective of this study is to determine
whether or not the participating firms' work-papers reflect any rela-
tionship between the composition Of the auditors' evidential collec-
tions (the dependent variables) and those factors identified in Chap-
ters I—V (the independent variables) which:

1. define evidential support functions,

2. determine minimum evidential support requirements,

3. affect the auditor's risk of sanctions, or

4. constrain the auditor's choice of evidential collection.

One problem which immediately arises is that in defining the
composition of any evidential collection, one must consider three
separate parameters:

1. the types of evidence included,

2. the times of collection of each type, and

3. the number Of units Of each type collected at a given time.

Since these parameters interact to determine the degree of evidential
support the collection will provide, an auditor's decisions concerning
them must be, to some extent, interdependent. Ideally, then, this
study would consider all three parameters simultaneously as dependent
variables. Unfortunately, the diverse nature of the parameters and
the lack of any explicit, well-defined function which might relate

them to some one-dimensional variable (e.g., "degree Of evidential

176
support provided") precludes such an approach. Rather, each param-
eter must be analyzed as a separate dependent variable with the other
parameters admitted into the analysis as independent variables wherev-
er interaction seems an important consideration. Thus the empirical
study which follows is subdivided into three parts:
I. a study of factors which affect the selection of audit
procedures (i.e., types Of evidence) in the areas Of sales
and accounts receivable (pp. 195-251),
II. a study of factors which affect the timing of audit tests
in the area of sales and accounts receivable (PP- 251-53).
III. a study of factors which affect the sample size of audit

tests in the areas of sales and accounts receivable

(PP 0 258-91) .

Although the specific techniques of analysis will differ for
each part, the basic approach will be the same.
1. enumerate the independent factors (identified in Chapters
I-V) relevant to auditor decisions concerning the parameter
in question, and
2. determine which of these factors, if any, seem to explain
the auditor's decisions (as reflected in actual work-papers)

with respect to that parameter.

The Independent Variables
Chapters I-V suggested a number of factors which should influ-
ence the auditor's selection of an evidential collection. The follow-

ing table (Table 5) summarizes these factors and indicates their

177
treatment in the empirical study. Table 7 then lists the independent

variables actually included in that study.

178

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179

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180

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181

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182

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183

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184

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185

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186

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187

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188

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189

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190

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191

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192

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194

Table 6.--A summary Of the independent variables included in the study

 

 

Variable Desigpation Variable
x1 Timeliness Of evidential matter
x2 Dollar balance Of the client's gross accounts
receivable
x3 Total number of accounts receivable in the

client's trial balance

x“ Mean accounts receivable dollar balance

x5 Client's net sales

x6_11 Policies of individual public accounting firms

x12 Accounts Receivable/Sales

x13 Accounts Receivable/Total Assets

x1“ Accounts Receivable/Net Income

x15 Sales/Total Assets

x16 Sales/Net Income

x17, x21 Auditor evaluation of client internal control
- sales

x18, x22 Auditor evaluation Of client internal check --
sales

x19, x23 Auditor evaluation of client internal con-
trol -- accounts receivable

x20, x21+ Auditor evaluation of client internal check
-- accounts receivable

x25 Client's total assets

x26 Client's total stockholders' equity

x27_28 Nature of the client's Operations

x29_31 Distribution of the client's ownership

x32_33 Nature and existence of restrictive loan
covenants

x31+ Client's "Retained Earnings" balance

x35 Client's net income before taxes and extraor—
dinary items

x36 Client's debt/equity ratio

x37_38 Client's rate and method Of growth

x39 Date of client's fiscal year-end

195

A Study Of Factors which Affect the Selection of

 

Audit Procedures in the Areas of Sales

 

and Accounts Receivable

 

The Audit Area of Sales

Arens identifies the following auditing procedures as relevant

4
to one or more financial statement assertions regarding "sales":

1.
2

r R
r R

H
50
LA.)

GNO‘LD#
O

10.
11.

12.
R l3.

14.

15.
16.
17.
18.
19.

20.
21.
22.
23.
R 24.

Foot and crossfoot the sales journal.

Summarize the detail and trace the totals to the gen-
eral ledger.

Reconcile the list Of accounts receivable to the ac-
counts receivable control account.

Foot individual subsidiary accounts.

Confirm accounts receivable.

Compare actual inventory to perpetual inventory.
Perform cut-Off procedures.

Trace entries from the sales journal to the subsidi-
ary ledger.

Trace entries from the subsidiary ledger to the sales
journal.

Trace from sales journal entries to sales invoices.
Trace from sales invoices to sales journal entries.
Compare customer, invoice number and amount.

Trace from sales invoices to shipping documents.
Trace from shipping documents to sales invoices.
Compare customer name and quantity shipped.

Trace from shipping documents to perpetual inventory
records. Compare descriptions and quantities.

Trace from shipping documents to sales orders.
Account for a sequence of sales invoices.

Account for a sequence of shipping documents.

Review the sales journal for duplicate sales invoices.
Review sales invoices for shipping document numbers
appearing on more than one invoice.

Compare sales prices with approved price lists.
Recompute extensions and footings.

Compare discounts allowed with authorized sales terms.
Compare freight charged with authorized charges.
Compare sales classifications to supporting documents.

 

4

Alvin A. Arena, "The Adequacy of Audit Evidence Accumulation in

Public Accounting" (Doctoral Thesis, School of Business Administration,
University of Minnesota, 1970), pp. 145-149.

196
The capital "R" appearing before a number of the above proce-
dures identifies those which Arens considers required.5 A lower case
"r," on the other hand, precedes those procedures which each of the
sample firms performed in at least ninety per cent of their reported
audits (eighty per cent for firms which reported only five clients).
Apparently, then, not all of the sample public accounting firms

agree with Arens regarding the status of:

13. Trace from shipping documents to sales invoices, Compare
customer name and quantity shipped.

24. Compare sales classification with supporting documents.
While Firms C, D, F, and G did, in fact, apparently consider the for-
mer procedure "required" (according to the above Operational defini-
tion), none of the remaining firms recorded performing it in more than
thirty per cent of their reported audits. Similarly, although Firms
C, D, and G appeared to regard the latter procedure as "required," and
Firms F and A documented its performance in two Of three and eight of
ten reported audits, respectively, Firm B reported its performance in
only two of ten audits and Firm E never showed evidence of having per-
formed it.

Two different conclusions are consistent with the above facts,
either:

1. not all public accounting firms regard the procedures as

"required," or

 

5Ibid.

197
2. while all the sample firms do consider performance Of the

procedures required, some do not always document such per-

formance in their work-papers.

While recognizing the latter possibility, the researcher considers the
former more likely and therefore treats the two procedures, as well as
the others not preceded by a lower case "r," as "Optional" for the re—

mainder of the study.

Basic Methodology

Initially, the following general model, derived from the analy-
sis in Chapters III-V, was hypothesized for each of the specific as-

sertions comprising the audit area Of sales:
E1 ' f(xl’ xs’ xe.-Io.’ "17’ "18’ x21, x22, "25’ “26’ "27-28’

x29—31’ x32-33’ xau’ x35’ xae’ x37-38’ x39’ XHO’ x51)

where: E1 is the set of tests selected by the auditor from the
set of all Optional tests relevant to the ith sales
assertion,
f is a linear function,
x0 is the percentage of "Accounts Receivable" dollar

value confirmed by any means (positive confirma-

tions, negative confirmations, and alternative pro-

cedures),

198
x“1 is the percentage Of the total number of "Accounts
Receivable" confirmed by any means (positive confir-
mations, negative confirmations, and alternative
procedures), and
6

all other x1 are defined as in Table 5.

Ideally, this study would have treated the audit area of sales
as a whole, taking as its dependent variable the set of all optional
sales tests performed by the auditor. Unfortunately, because Of the
small sample size relative to the number Of optional procedures, this
approach was impracticable. Essentially, feasibility required a re-
duction in the "range" Of the dependent variable, i.e., a reduction in

the number of possible combinations Of procedures available to the au-

 

ditor. Analyzing the area of sales into its component assertions and
treating each assertion as an independent problem accomplished this
reduction. Thus, this section actually consists Of thirteen separate
studies, each taking as its dependent variable the auditor's selection
from optional tests relevant to a specific sales assertion.7 Justifi-
cation for this approach derives primarily from the auditor's respon—
sibility for all material assertions contained in his client's finan-
cial statements whether he consciously attempts to verify each one

individually or not.

 

6Since Firm G effectively performed all of the optional proce-
dures on all Of its engagements here represented, its ten clients are
omitted from this part of the study.

7The specific set of assertions adopted are those identified by
Arens, pp. 145-157. Arens also indicates the procedures relevant for
testing each of the assertions.

199

In addition to requiring a reduction in the gapgg of the depend-
gp£_variable, the study's relatively small sample size also limited
the number of independent variables which could be considered simul-
taneously before random correlation would confound the analysis. For
this reason, rather than evaluating the above general model's ability
to predict the auditor's choice of Optional procedures, each of the
following analyses had to be content with the somewhat more restricted
problem of identifying factors which seemed to exert the greatest in-
fluence in that choice.

The approach adopted to achieve this end was the same for all
assertions considered -- essentially a two-step process involving dis-
criminant analysis.8

The objective of the first step was to eliminate independent
variables which exhibited no ability to predict the auditor's selec-
tion of optional procedures. Toward this Objective, the sample obser-
vations were grouped according to Optional procedures performed and

subjected to a stepwise discriminant analysis.9 As each additional

 

8Discriminant analysis is a form Of regression analysis appli-
cable in situations where one desires to classify Observations into
two or more groups based upon certain characteristics of the Observa-
tions.

For discussions Of this technique, see: T. W. Anderson, Ag
Introduction to Multivariate Statistical Analysis (New York: John
Wiley and Sons, Inc., 1958), H. C. Fryer, Concepts and Methods of Exr
perimental Statistics (Boston, Allyn and Bacon, Inc., 1966), or C. R.
Rao, Advanced Statistical Methods in Biometric Research (New York:
John Wiley and Sons, Inc., 1952).

9The specific analytical tool employed was the U.C.L.A. Bio-
medical program, "BMDO7M -- Stepwise Discriminant Analysis" as de-
scribed in: W. J. Dixon, ed., BMD Biomedical Computer Programs (Uni-
versity of California Press, 1970), pp. 587-605, and available through
the program library of the University of Kansas Computation Center.

This particular program has the attractive feature of admitting

200
independent variable entered the analysis, the resulting discriminant
function was evaluated empirically by an approach which Lachenbruch
and Mickey refer to as the "resubstitution" method.10 Effectively,
when the inclusion of additional independent variables could no longer
improve the frequency of accurate classification (or materially im-
prove the significance level Of the existing classification), the dis-
criminant analysis terminated. At this point, variables not included
in the final discriminant function were eliminated from further con-
sideration.

Unfortunately, as Lachenbruch and Mickey have noted, for small
samples, the resubstitution approach to evaluating a discriminant
function tends to favorably bias the estimated frequency of correct
classification.11 This tendency is unfortunate for two reasons.

First of all, such biased estimates may have resulted in the
erroneous elimination Of one or more "useful" variables (i.e., vari-
ables with some ability to discriminate) —- a regrettable though un-

avoidable contingency since the "resubstitution" method was the only

approach economically feasible considering the sample size and number

 

independent variables into the discriminant function one-by-One, in
decreasing order of ability to discriminate, forming a new function
as each variable enters.

10P. A. Lachenbruch and M. R. Mickey, "Estimation of Error Rates
in Discriminant Analysis," Technometrics 10 (February 1968): 3.

The "resubstitution" method consists Of using the discriminant
function to reclassify the Observations which originally determined
that function. The resulting predicted, or ex post, classifications
are then compared to the actual, or ex ante, classifications to esti-
mate the function's predictive accuracy.

llIbid.

 

201
of independent variables involved. Actually, however, this problem
was probably not severe. Since the Specific stepwise analysis used
admits variables in decreasing order Of ability to discriminate, one
may reasonably expect that any which were erroneously omitted were
probably not highly significant, especially since an extremely low
significance level (<.50) for elimination was purposely set in recog—
nition of the problem.

Clearly the more important consequence Of the resubstitution
method's tendency to bias the frequency of correct classifications is
that, while one may reasonably assume that the variables eliminated in
step one had little or no ability to predict the auditor's selection
of optional procedures, one cannot draw any useful valid conclusions
about the variables remaining in the analysis after that step.

For this reason, a second step was necessary. The primary ob-
jectives Of this second step were:

1. determine the "best" (in the sense of ability to predict 22g
of parsimony) combination of variables remaining after step
one, and

2. determine whether a model based on that combination could,
in fact, predict significantly better than chance the au-

ditor's selection of optional procedures.

Accomplishing the first Objective required a method of evaluat-
ing discriminant functions which would yield an unbiased estimate of

the frequency of correct classifications. Fortunately, such a method

202
(essentially a Special type of "holdout" approach)12 became feasible
with the greatly reduced number Of independent variables. Lachenbruch
and Mickey describe the method as follows:
. . . take all possible splits Of size one in one
group and the remainder in the other. This has the

effect of successively omitting one Observation from
the computation of the discriminant function.13

In other words, given n observations, one calculates n discrimi-
nant functions, holding out a different observation each time as the
verification sample. The resulting discriminant functions are then
each used to reclassify their reapective hold-out Observation, and the
proportion of accurate groupings thus obtained yields an unbiased es-
timate of the probability of accurate classification.14

An added attraction of this approach is that it does not depend
upon an assumption of normality and therefore is useful where "nor-
mality is questionable (e.g., when a large number of dichotomies are
used as variables) and the sample size is small relative to the number

Of variables."15

 

12The basic idea of the "holdout" methods is to divide the sam-
ple observations into two groups. The first group (classification
group) is then used tO define a discriminant function which, in turn,
is used to classify the Observations in the second (holdout or veri-
fication) group. The predicted classifications are then compared to
the actual classifications to estimate the function's predictive ac-
curacy. For discussion and evaluation of the approach see Lachenbruch
and Mickey .

13Lachenbruch and Mickey, p. 4.

14Ibid.

15lbid., p. 10.

203

Given this method for evaluating discriminant functions, the se-
lection of a "best" combination of independent variables in each given
case was simply a matter of determining which combination maximized
the frequency of correct classifications. In those cases where more
than one combination satisfied this criterion, the one with the fewest
variables was considered "best."

After selection of the "best" combination of independent vari-
ables, all that remained was to determine whether that combination
could predict the auditor's selection of optional procedures better
than chance. The tests chosen for this part of the analysis were
tests of significance for sample prOportions described by Clark and
17

Schkade16 (for two-group classifications) and Mosteller and Bush

(for multi-group classifications).

 

16Charles T. Clark and Lawrence L. Schkade, Statistical Methods

for Business Decisions (Cincinnati: South-Western Publishing Co.,
1969). pp. 417-418.

The formula for calculating z is:
r - 1/2 - E(g) a r - 1/2 - nw
o

 

 

 

z:
r Vnw(l-n)
where: r is the number of correct classifications,

E(r) is the number of correct classifications ex-
pected by chance,
or is the standard deviation of r,

n is the number Of Observations, and
n is the probability of Obtaining a correct
classification by chance.
To insure a conservative (with respect to the significance test)
estimate of E(r), n was defined as follows:

2 2 2 2
t t +
t1 2 1 t2 t1°1 t2°2
n n n n ‘ 2
n
1" I

2 2
tlc1 + t2c2 tlc1 + t2c2 (t1) (t2)
, > ——- + __.
2 2 n n
n n

 

 

 

204
In all, the above two-step analysis was performed on thirteen
separate assertions of the audit area Of sales. Let us now turn to
the results of the analysis. (In addition to the thirteen assertions
specifically analyzed, Arens also identified four for which all rel—
evant procedures were "required" procedures. These four are included

in the following report for the sake of completeness.)

 

where: ti is the number of Observations which actually be-
long to the ith group, and
c is the number of observations classified in the
1th group by the discriminant function.

17Frederick Mosteller and Robert R. Bush, "Selected Quantitative
Techniques," in Handbook of Social Psychology, ed. by Gardner Lindzey
(Reading, Massachusetts: Addison Wesley Publishing Co., Inc., 1954)
pp. 310-311.

The formula for calculating z is:

 

z a r - 1/2 - m

 

O
r
m =-————-
n
2 _ 1 2 _ 2
o - 2 [(2 tici) n X tici(ti+ci) + n Ztici]
n (n-l)

where: r is the number of correct classifications,

m is the expected number of correct classifications,
or is the standard deviation Of r,

n is the number of Observations,

t is the number of Observations which actually be-
long to the 1th group, and

c1 is the number of observations classified in the
ith group by the discriminant function.

205
Assertion I: "The records of transactions Obtained from the client

are mechanically accurate and balance with the general

ledger."18

Relevant,procedures:

 

r 1. Foot and crossfoot the sales journal.
r 2. Summarize the detail and trace the totals to the

general ledger.19
Since all of the sample firms apparently considered both of

these procedures "required," further analysis was unnecessary.

Assertion II: "The same sales transaction information was recorded in

both the sales jpurnal and the subsidiagy ledger."20

Relevantyprocedures:

 

r l. Reconcile the list of accounts receivable to the
accounts receivable control account.
2. Foot individual subsidiary accounts.
3. Trace entries from the sales journal to the sub-
sidiary ledger.
4. Trace entries from the subsidiary ledger to the

sales journal.21

 

18Arens, p. 145.

19Ibid.

201bid., p. 146.

21Ibid.

206
Of these procedures, the sample firms considered the last three
"optional." Thus, based on possible combinations of Optional proce—
dures, there were eight groups into which a given Observation might

fall. The actual groupings were as follows:

 

 

Number Of Optional Procedures Performed (X)

9222p. Observations $32. $32. .131

I 5

II 2 X

III 18 X

IV 2 X

V 4 X X

VI 2 X X

VII 5 X X

VIII 3 X X X

Groups 11, IV, and VI lacked the sufficient number of Observa-
tions (3) for discriminant analysis and were therefore omitted from
further study.

Utilizing the remaining groupings to eliminate variables with no
apparent ability to predict the auditor's selection of Optional proce—
dures relevant to this assertion, step one Of the analysis reduced the

initial hypothesized model to the following:

Ell ' f(xl, x ).

6-10’ x18’ x21’ x27-2a’ x29-31’ x39

Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction Of

the model to:

207

E = f(x1

II )'

X
8’ 29-31

Classification functions, derived with x18 (internal check (1))
and x29_31 (indicator variables for the distribution of the client's
ownership) as the independent variables and evaluated by means of the
modified holdout method described above, yielded the following confu-

sion matrix:22

 

 

 

Actual Group Predicted Group Membership
Membership 1_ III 2_ VII VIII Total
I 5 O 0 0 O 5
*
III u 9 1 2 1 17
V 2 O 2 0 0 1+
VII 3 2 0 0 0 5
VIII 0 0 2 0 2 4
Total 14 11 5 2 3 35

a
The discriminant functions were unable to classify one of
Group III's Observations.

As the above matrix indicates, the classification functions pre-

dicted group membership correctly for eighteen observations (51.4 per

 

22The "Total" column designates the number of Observations_§gf
tually belonging to a given group. The "Total" ng_designates the
number of observations which the discriminant functions classified
into a given group. Each individual cell, c1 indicates the number
of observations belonging to the ith group which the discriminant
functions classified into the jt group. Thus, for example, the
above matrix indicates that while a total Of five Observations ac-
tually belonged to Group I, the discriminant function classified a
total of fourteen observations (including the five which actually be-
longed) into that group. Furthermore, since correct classifications
appear on the left-to-right diagonal, the matrix reveals that the dis-
criminant functions predicted group membership correctly for eighteen
(5 + 9 + 2 + 0 + 2) Observations.

 

208
cent of all observations classified). The number of correct classifi-
cations one would expect by chance (supra, p. 203, footnote 16) is
only 8.5 (24.3 per cent). Thus the classification functions did per-
form significantly better than chance (o < .000048).

Another set of classification functions which performed almost
as well also deserves mention here because of the Specific variables
involved. These functions are derived from the model:

EI

" f(x ),

I 6-10

(i.e., indicator variables for the firm which performed the audit are
the only independent variables) and, when evaluated by the modified

holdout approach, yielded the following confusion matrix:

 

 

 

 

Actual Group Predicted Gropp Membership
Membership 1 I_I_I_ !_ ill VIII Total
I 3 2 0 0 o 5
III 5 7 0 S 0 18
v 1 o 0 1 2 1+
VII 2 0 0 3 0 5
VIII 0 0 1 0 3 4
Total 12 9 1 9 5 36

In this case, the classification functions accurately predicted
the group membership of sixteen observations (44.4 per cent). The
number of correct predictions one would expect by chance is 8.2 (22.8
per cent). Thus these classification functions also performed signif-

icantly better than chance (a < .000968).

209

The importance of this result is that, for assertion II, based
solely on the knowledge of which firm performed the audit, one can
predict significantly better than chance which combination of proce—
dures were selected for a given Observation. If this result Should
hold true over the majority of the assertions studied, it may tend to
indicate that different public accounting firms do, in fact, adopt
different basic approaches to the audit Of sales. For this reason,

the model:

E a
i f(xe-lo)

will be Specifically tested for all remaining assertions.

Assertion III:23 "Every actual shipment of merchandise was recorded

24

 

 

as shipped."

 

Relevant procedures:

 

r 1. Confirm accounts receivable.

r 2. Compare actual inventory to perpetual inven-

tory.25

Since all of the sample firms apparently considered both of

these procedures "required," further analysis was unnecessary.

 

23Arens lists this assertion, along with the next two under the

more general assertion: "Every actual current period merchandise
shipment was reflected in current period sales." Arens, p. 146.

24Arens, p. 146.

25Ibid.

210

Assertion IV: "Every recorded shipment was billed."26

Relevantgprocedures:

r 1. Confirm accounts receivable.
2. Account for a sequence of shipping documents.
3. Trace from shipping documents to sales in-

voices.

Of these procedures, the sample firms considered the last two
"Optional." Thus, based on possible combinations of optional proce-
dures, there were four groups into which a given observation might

fall. The actual groupings were as follows:

 

 

Number Of Optional Procedures Performed (X)
Group Observations $2) (3)
I 22
II 9 X
III 1 X
IV 8 X X

Group III lacked the sufficient number of observations for dis-
criminant analysis and was therefore eliminated from further study.
Utilizing the remaining groups, however, and eliminating vari-

ables with no apparent ability to predict the auditor's selection of

 

27Ibid.

211
optional procedures relevant to this assertion, Step one of the analy—

sis reduced the initial hypothesized model to the following:

E = f(xs, ).

IV "6-10’ "18’ "22’ "25’ "26’ "36

Selecting the "best" combination of these remaining variables,
step two of the analysis resulted in a further reduction of the model

to:

E = f(xs, x

IV 18’ "22’ "25’ "26’ "36)°

Classification functions, derived with x5 (total sales), x18
(internal check (1)), x22 (internal check (2)), x25 (total assets),
x26 (stockholders' equity), and x36 (debt/equity ratio) as the inde-
pendent variables and evaluated by means of the modified holdout meth-

od, yielded the following confusion matrix:

 

 

Actual Group Predicted Group Membership,
Membership _I _I_I_ fl lot-E

I 15 4 3 22

II 1 8 0 9

IV 1 4 3 8

Total 17 16 6 39

As the above matrix shows, the classification functions pre-
dicted group membership correctly for twenty-six Observations (66.7
per cent). The number of Observations one would expect by chance in
this case is 14.5 (37.2 per cent). Thus, the classification functions

performed significantly better than chance (a < .0000481).

212
Another set of classification functions which performed almost
as well also deserves mention because of the fact that the functions

were far more parsimonious. These functions were based on the model:

E = f(x , x
18

IV 5)

2

Classification functions, derived with x18 (internal check (1)),
and x26 (stockholders' equity) as the independent variables and evalu-
ated by the modified holdout method yielded the following confusion

matrix:

 

 

 

Actual Group Predicted Group Membership
Memb e rsh i) _I_ E 11 Igt_a_l_

I 18 0 4 22

II 9 4 1 9

IV 4 1 3 8

Total 26 5 8 39

These classification functions predicted group membership cor-
rectly for twenty-five observations (64.1 per cent). The number of
correct classifications one would expect by chance is 17.5 (44.9 per
cent). Thus these functions also performed significantly better than
chance (a < .00256).

Finally, classification functions based on the assumption that:

EIV = f(x6_10)

yielded the following confusion matrix:

213

 

 

 

Actual Group Predicted Group Membership
Membership __1 _II .1! .EEEEL
I 15 1 6 22
II 2 3 4 9
Iv 1 3 4 8
Total 18 7 14 39

In this case, the classification functions accurately predicted
the group membership of twenty-two observations (56.4 per cent). The
number of correct predictions one would expect by chance is 14.6 (37.4
per cent). Thus these classification functions also performed somewhat

better than chance (a < .00621).

Assertion V: "Every sales billing was recorded in the sales
28
I!

 

ournal.

Relevantgprocedures:
r 1. Confirm accounts receivable.
2. Trace from sales invoices to sales journal en-
tries.

3. Account for a sequence of sales invoices.2

Of these procedures, the sample firms considered the last two
"optional." Thus based on possible combinations of Optional proce-
dures, there were four groups into which a given Observation might

fall. The actual groupings were as follows:

 

28Ibid.

291bid.

214

 

 

Number of Optional Procedures Performed (X)
EEQEE Observations £22_ .(3)
I 6
II 5 X
III 12 X
IV 19 X X

Utilizing the above groupings to eliminate variables with no
apparent ability to predict the auditor's selection of Optional pro-
cedures relevant to this assertion, step one of the analysis reduced

the initial hypothesized model to the following:

E - f(xl,

V , x ).

’ x 37-38

"17’ "26’ "32-33’ "34’ "35 36

Selecting the "best" combination of these remaining independent
variables, step two Of the analysis resulted in further reduction Of

the model to:

- f(x , x , x , x36).

Ev 17’ x26 34 35
Classification functions, derived with x17 (internal control

(1)), x26 (stockholders' equity), x3k ("Retained Earnings" balance),

x35 (net income), and x36 (debt/equity ratio) as the independent vari-

ables and evaluated by means of the modified holdout method, yielded

the following confusion matrix:

215

 

 

 

Actual Group Predicted Group Membership
Membership_, i_ ii_ iii_ 1!. igigi
I 0 5 0 1 6
II 3 l 0 1 S
III 2 3 4 3 12
IV 1 4 2 12 19
Total 6 13 6 17 42

In this case, the classification functions predicted group mem-
bership correctly for seventeen Observations (40.5 per cent). The
number of correct classifications one would expect by chance is 11.8
(28.1 per cent). Therefore, while the classification functions per—
formed better than chance, the difference was not as significant as in
the previous analyses (a < .0392).

On the other hand, classification functions derived from the

model:

Ev I f("e-10)

generated the following confusion matrix:

 

 

Actual Group ‘ Predicted Gropp Membership
Membership i i_I_ iii if; _'l_‘_o_t_ai
I 0 2 4 0 ' 6
II 2 0 2 1 S
III 4 1 S 2 12
IV 4 8 7 0 19

 

Total 10 11 18 3 42

216
Here the classification functions only predicted the group mem-
bership of five Observations (11.9 per cent) correctly. The number Of
accurate predictions one would expect by chance is 9.2 (21.9 per cent).
Thus, in this case, the classification functions actually predicted
group membership somewhat worse than chance although the difference is

probably not significant (u < .0643).

Assertion VI:30 "Each recorded shipment was stated the same as the

actual shipment."31

 

Relevant4procedures:

 

r 1. Confirm accounts receivable.
r 2. Compare actual inventory to perpetual inven-
tory.

3. Trace from shipping documents to perpetual
inventory records. Compare descriptions and
quantities.

4. Trace from shipping documents to sales

orders.32

Of these procedures, the sample firms considered the last two

"optional." Thus, based on possible combinations Of Optional

 

30Arens lists this assertion, along with the next three under
the more general assertion: "Each recorded merchandise Shipment was
correctly recorded (customer, description, quantity, price, mechanical
accuracy, and terms of shipment)." Arens, p. 147.

31Arens, p. 147.

32Ibid.

217
procedures relevant to this assertion, step one of the analysis re—

duced the initial hypothesized model to the following:

EVI a f("5’ "6-10’ "16’ "21’ "26’ "35’ "36)“

Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

EVI - f(x6_10).

Classification functions derived with x6_10 (indicator variables
for the firm which performed the audit) as the independent variables
and evaluated by means of the modified holdout method, yielded the

following confusion matrix:

 

 

 

Actual Group Predicted Group Membership_
Membership _I_I_ ii _I_V M

I 19 0 0 19

II 7 2 4 13

IV 0 0 5 5

Total 26 2 9 3 7

In this case, the classification functions accurately predicted
the group membership for twenty-six observations (70.3 per cent). The
number of correct predictions one would expect by chance is 15.3 (41.4
per cent). Thus these classification functions performed considerably

better than chance (a < .00000130).

218

Assertion VII:33 "Each recorded billing was stated the same as the

 

 

recorded shipment jwith respect to customer and

quantity shipped]."34

 

Relevantgprocedures:
r 1. Confirm accounts receivable.
2. Trace from shipping documents to sales in-
voices. Compare customer name and quantity

shipped.35

Although Arens regards both of these procedures as required, the
frequency with which a number of the sample firms omitted the second
one indicates that at least some public accountants consider it "op-

tional." Thus, there were two groups into which a given Observation

might fall. The actual groupings were as follows:

 

 

Number of
Group Observations Optional Procedures Performed (X)
I 21 0
II 22 X

Utilizing the above groupings to eliminate variables with no

apparent ability to predict whether or not the auditor would perform

 

33Arens does not distinguish between this assertion and Asser-
tion VIII, but rather combines the two as simply: "Each recorded
billing was stated as the recorded shipment." Arens, p. 147.

34Arens, p. 147.

35Ibid.

219
this optional procedure, step one of the analysis reduced the intial

hypothesized model to the following:
EVII a f("e-10’ x17, "18’ x21’ x22’ x39)-

Selecting the "best" combination of these remaining variables,

step two resulted in further reduction of the model to:

Classification functions, derived with x6_ 0 (indicator variables

1

for the firm which performed the audit), x (internal control (1)),

17

and x22 (internal check (2)), as the independent variables and evalu-

ated by means Of the modified holdout method yielded the following

confusion matrix:

 

 

 

Actual Group Predicted Group Membership_
Membership, __i .11 Total
I 18 3 21
II 5 17 22
Total 23 20 43

The above matrix reveals that the classification functions pre-
dicted group membership correctly for thirty-five Observations (81.4
per cent). The number of correct classifications one would expect by
chance (supra, p. 203, footnote 16) 13 21,5 (50 per cent). Thus the
classification functions did perform significantly better than chance

(a < .0000481) in this case.

220
Another set of classification functions which deserves mention

here because of its parsimony is the set derived from:

Ev11 = f("17’ "22)“

These functions, evaluated by the modified holdout approach yielded

the following confusion matrix:

 

 

 

Actual Group Predicted Grppp Membership
Membership __i .ii Total
I 18 3 21
II 9 13 22
Total 27 16 43

In this case the classification functions accurately predicted
the group membership of thirty-one observations (72.1 per cent). IThe
number of correct predictions one would expect by chance is 21.5 (50
per cent). Thus these functions also performed significantly better
than chance (a < .00307).

Finally, classification functions derived from:

EVII ' "("6-10)

and evaluated by the modified holdout approach generated the following

confusion matrix:

 

 

Actual Group Predicted Group Membership
Membership __i ii. Total
I 14 7 21
II 6 16 22

 

Total 20 23 43

221
Here the classification functions correctly predicted group mem-
bership for thirty observations (69.8 per cent). The number of cor-
rect predictions one would expect by chance is again 21.5 (50 per

cent). Thus, these functions also performed better than chance

(a < .00776).

AssertiOn VIII: "Each recorded billing was stated the same as the

recorded shipment jwith respect to price, mechanical

accuragy and terms of Shipment]."36

Relevant4procedures:

r 1. Confirm accounts receivable.
2. Compare sales prices with approved price lists.
3. Recompute extensions and footings.
4. Compare cash terms used with authorized terms.

5. Compare actual freight charged with correct

freight charges.37

Of these procedures, the sample firms considered the last four
"optional." Thus, based on possible combinations Of optional proce-
dures, there were sixteen groups into which a given observation might

fall. The actual groupings were as follows:

 

36Ibid.

37Ibid.

222

 

 

Number of Optional Procedures Performed ,(X)

inpp Observations .iii .121 .131 .LOL

I 8

II 0 X

III 0 X

IV 5 X

V l X

VI 0 X X

VII 0 X X

VIII 0 X X

IX 0 X X

X 0 X X

XI 17 X X

XII 0 X X X

XIII 0 X X X

XIV 2 X X X

XV O X X X

XVI 5 X X X X

The only groups containing a sufficient number of observations
for discriminant analysis were I, IV, XI and XVI, therefore, these
were the only groups considered in forming the classification func-
tions.

Utilizing the four groups, step one of the analysis reduced the

initial hypothesized model to the following:

E . ,
VIII f(xe-IO’ x17, "40)

223
Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in further reduction of

the model to:

f(x ).

EVIII 7 6-10

Classification functions, derived with x6_ (indicator vari-

10
ables for the firm which performed the audit) as the independent vari-
ables and evaluated by means of the modified holdout method, yielded

the following confusion matrix:

 

 

 

Actual Group Predicted Group Membership
Membership i H Xi E; M
I 8 o o 0 8
IV 4 0 0 1 5
XI 5 0 12 0 17
XVI 2 0 2 l 5
Total 19 0 14 2 35

In this case, the classification functions accurately predicted
the group membership of twenty-one observations (60 per cent). The
number of correct classifications one would expect by chance is 11.4
(32.6 per cent). Thus the functions performed significantly better

than chance (a < .000108).

224
Assertion IX: "Each sale recorded in the saie§_journa1 was stated the

same as the billing."38

Relevantgprocedures:
r 1. Confirm accounts receivable.
2. Trace from sales invoices to sales journal en-

tries. Compare customer, invoice number and
39

amount.

Most of the sample public accounting firms appear to consider
the latter of these procedures as optional. Thus, there were two pos-
sible groups into which a given sample Observation might fall. The

actual groupings were as follows:

 

 

Number of
Group Observations Optional Procedure Performed (X)
I 13 0
II 30 X

Utilizing the above groupings to eliminate variables with no
apparent ability to predict whether or not the auditor would perform

this procedure, step one reduced the initial hypothesized model to the

following:

E 8 f(

Ix "6-10’ "17’ "21’ "22’ "25’ "37-38)'

 

381bid., p. 148.

391618.

225
Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction Of

the model to:

E = f(

1x "6-1o)°

Classification functions derived with x6_10 (indicator variables
for the firm which performed the audit) as the independent variables
and evaluated by means of the modified holdout method generated the

following confusion matrix:

 

 

 

Actual Group Predicted Gropp Membership
Membership -i _ii Total
I 8 5 13
II 2 28 30
Total 10 33 43

In this case, the classification functions accurately predicted
the group membership of thirty-six Observations (83.7 per cent). The
number of correct predictions one would expect by chance is twenty-six
(60.5 per cent). Thus, the classification functions performed signif-

icantly better than chance (a < .00159).

226

Assertion X: "Each sale recorded in the sales journal was correctly
40

 

classified."

 

Relevantgprocedure:

 

1. Compare sales classifications to supporting doc-

ments . 41

At least some of the sample public accounting firms apparently
considered this procedure Optional. Therefore, there were two pos-
sible groups into which a sample observation might fall. The actual

groupings were as follows:

 

 

Number of
Group Observations Optional Procedure Performed (X)
I 20 0
II 15 X

Utilizing these groupings to eliminate variables with no ap-
parent ability to predict whether or not the auditor would perform
this procedure, step one reduced the initial hypothesized model to

the following:

E - f x x x x x x x x x x x .
X ( 1’ 6-10’ 18’ 25’ 26’ 29-31’ 34’ 35’ 36’ 40’ 41)

 

401618.

41Ibid.

227
Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

E = f(x6__1 ).

X 0

Classification functions, derived with x (indicator variables

6-10
for the firm which performed the audit) as the independent variables
and evaluated by means Of the modified holdout method, yielded the fol-

lowing confusion matrix:

 

 

 

Actual Group Predicted Gropp Membership
Membership _i_ _ii Total
I 16 4 20
II 3 12 15
Total 19 16 35

In this case, then, the classification functions predicted group
membership correctly for twenty-eight observations (80 per cent). The
number of correct classifications one would expect by chance is 17.9
(51.1 per cent). Thus, the classification functions did perform Sig-
nificantly better than chance (a < .000687).

A classification function which also deserves mention here be-

cause Of its parsimony is the function derived from:
Ex - f(x35)'
This function (with net income its only independent variable) generated

the following confusion matrix:

228

 

 

 

Actual Group Predicted Group Membership
Membership_, -_i _ii Total
I 17 3 20
II 8 7 15
Total 25 10 35

Thus the classification function accurately predicted group mem—
bership for twenty-four observations (68.6 per cent). The number of
correct predictions one would expect by chance is 18.6 (53.1 per
cent). In this case, the classification functions performed somewhat

better than chance (a < .0495).

Assertion XI:42 "No actual merchandise shipment was recorded as a

 

shipment more than once."43

Relevant piecedures:
r 1. Confirm accounts receivable.

r 2. Compare actual inventory to perpetual inven-

tory.“

Since all of the sample firms apparently considered both of

these procedures "required," further analysis was unnecessary.

 

42Arens lists this assertion, along with the next two under the
more general assertion: "NO merchandise shipment was recorded more
than once." Arens, p. 148.

43Arens, p. 148.

44Ibid.

229

Assertion XII: "NO recorded merchandise shipment was billed more than

 

 

once."

Relevant procedures:

 

r 1. Confirm accounts receivable.
2. Review sales invoices for shipping document

numbers appearing on more than one invoice.46

The sample public accounting firms considered the latter of
these procedures Optional. Therefore, based on possible combinations
of Optional procedures, there were two groups into which a given ob—

servation might fall. The actual groupings were as follows:

 

 

Number of
Group Observations Optional Procedure Performed (Xi
I 32 0
II 4 X

Utilizing these groupings to eliminate variables with no ap-
parent ability tO predict whether or not the auditor would perform
this procedure, step one reduced the initial hypothesized model to the

following:

E I x x x x x
XII f("1’ x6-10’ 17’ 18’ 21’ 22’ x29-31’ x37-38’ 39’

"40’ "41"

 

45161-1.

46Ibid.

230
Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

EXII = f("e-10"

Classification functions, derived with x (indicator vari-

6—10
ables for the firm which performed the audit) as the independent vari-
ables and evaluated by means of the modified holdout method, generated

the following confusion matrix:

 

 

 

Actual Group Predicted Group Membership
Membership _ii “ii Total
I 30 2 32
II 2 2 4
Total 32 4 36

Even though, as the above matrix indicates, these classification
functions accurately predicted group membership for thirty-two obser-
vations (88.9 per cent), since the number of correct predictions one
would expect by chance is 28.9 (80.3 per cent), the functions did not

perform significantly better than chance (a < .1401).

231
Assertion XIII: "No billiug_of sales was recorded in the sales

_jpurnal more than once."47

Relevant procedures:
r 1. Confirm accounts receivable.

2. Review the sales journal for duplicate sales

invoices."8

The sample public accounting firms considered the latter Of
these procedures Optional. Therefore, based on possible combinations
of optional procedures, there were two groups into which a given ob-

servation might fall. The actual groupings were as follows:

 

 

Number of
Group Observations Optional Procedure Performed (X)
I 33 0
II 10 X

Utilizing these groupings to eliminate variables with no ap-
parent ability to predict whether or not the auditor would perform

this procedure, step one reduced the initial hypothesized model to the

following:

E - f(xl, x

XIII 6-10’ "22’ "27-28’ "29-31’ "39"

 

47Ibid.

balbid.

232
Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

E = f(xl,

XIII "6-10’ "22’ "39"

Classification functions, derived with x1 (indicator of eviden-
tial "timeliness"), x6_10 (indicator variables for the firm which per-
formed the audit), x22 (internal check (2)), and x39 (indicator of
client's year end) as the independent variables and evaluated by means
of the modified holdout method, generated the following confusion

matrix:

 

 

 

Actual Group Predicted Group Membership
Membership ._i _ii Total
I 29 4 33
II 3 7 10
Total 32 11 43

As the above matrix indicates, these classification functions
accurately predicted group membership for thirty-six Observations
(83.7 per cent). The number of correct classifications one would ex-
pect by chance is 27.7 (64.4 per cent). Thus, the functions performed
significantly better than chance (a < .00554).

As an alternative, classification functions, derived with x6_10

as the independent variables and evaluated by means of the modified

holdout method yielded the following confusion matrix:

233

 

 

 

Actual Group Predicted Group Membership(
Membership, _i; ii_ Total
I 25 8 33
II 4 6 10
Total 29 14 43

In this case, the classification functions predicted group mem-
bership correctly for thirty-one Observations (72.1 per cent). The
number of correct predictions one would expect by chance is 27.7 (64.4
per cent). Thus, these classification functions did not perform sig-

nificantly better than chance (a < .1841).

Assertion XIV:49 "Each recorded Shipment was for an actual ship-

50

 

ment."

Relevant procedures:

 

r 1. Confirm accounts receivable.
r 2. Compare actual inventory to perpetual inven-
tory.
3. Trace from shipping documents to perpetual
inventory records.
4. Trace from shipping documents to sales

orders.51

 

9Arens lists this assertion, along with the next two under the
more general assertion: "Each recorded sale was valid." Arens,
pp. 148-149.

50Arens, p. 149.

51I618.

234
Of these procedures, the sample firms considered the last two
"optional." Thus, based on possible combinations of Optional proce-
dures, there were four groups into which a given observation might

fall. The actual groupings were as follows:

 

 

Number of Optional Procedures Performed (XL
inpp. Observations _(il Sél_
I 19
II 7 X
III 6 X
IV 5 X X

Utilizing these groupings to eliminate variables with no appar-
ent ability to predict the auditor's selection of Optional procedures
relevant to this assertion, step one of the analysis reduced the ini-

tial hypothesized model to the following:

EXIV ' f("5’ "6-10’ "18’ "25’ "35’ "36"

Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

E = f(

XIV "6-10) °

Classification functions, derived with x (indicator vari-

6-10
ables for the firm‘which performed the audit) as the independent vari-
ables and evaluated by means of the modified holdout method, generated

the following confusion matrix:

235

 

 

 

Actual Group Predicted Group Membership
Membership __I_ _I_I_ _I_i_l_ _I_V 1933i
I 19 0 0 0 19
II 3 2 O 2 7
III 4 0 O 2 6
IV 0 O O 5 5
Total 2 6 2 0 9 3 7

As the above matrix indicates, the classification functions ac-
curately predicted group membership for twenty-six Observations (70.3
per cent). Since the number of correct classifications one would ex-
pect by chance is only 14.9 (40.3 per cent), the functions obviously

performed significantly better than chance (a < .000000287).

Assertion XV: "Each recorded billingwas for a recorded shipment."52

 

Relevant_procedures:
r 1. Confirm accounts receivable.
2. Trace from sales invoices to Shipping docu-

ments . 53

The sample public accounting firms considered the latter of
these procedures optional. Therefore, based on possible combinations
of optional procedures, there were two groups into which a given Ob—

servation.mdght fall. The actual groupings were as follows:

 

521618.

531618.

236

 

 

Number of
Group Observations Optional Procedure Performed (X)
I 18 0
II 20 X

Utilizing these groupings to eliminate variables with no appar-
ent ability to predict whether or not the auditor would perform this
procedure, step one reduced the initial hypothesized model to the fol-

lowing:

E - f(

xv x6-10’ "17’ "21’ "26’ "41"

Selecting the "best" combination of these remaining independent
variables, step two of the analysis resulted in a further reduction of

the model to:

Exv ' f("s-10"

Classification functions, derived with x6_10 (indicator vari-
ables for the firm which performed the audit) as the independent vari-
ables and evaluated by means of the modified holdout method, generated

the following confusion matrix:

 

 

 

Actual Group Predicted Group Membership
Membership_ __i ii. Total
I 14 4 18
II 8 12 20
Total 22 16 38

As the above matrix indicates, these classification functions

accurately predicted group membership for twenty-six observations

237
(68.4 per cent). The number of correct classifications one would ex-
pect by chance is 19.0 (50.1 per cent). Thus, in this case, the clas-
sification functions performed significantly better than chance

(a < .0183).

Assertion XVI: "Each sale recorded in the sales journal was for a
54

 

recorded billiug."

Relevant procedures:
r 1. Confirm accounts receivable.
2. Trace from sales journal entries to sales in-

55

voices.

The sample public accounting firms considered the latter of
these procedures optional. Therefore, based on possible combinations
of optional procedures, there were two groups into which a given ob-

servation mdght fall. The actual groupingswere as follows:

 

 

Number of
Group Observations Optional Procedure Performed (X)
I 30 0
II 9 X

Utilizing these groupings to eliminate variables with no appar-

ent ability to predict whether or not the auditor would perform this

 

541618.

551618.

238
procedure, step one reduced the initial hypothesized model to the fol-

lowing:

EXVI = f(xl’ x53 "6—10’ ‘25, "27-28’ "37-38’ x40)'

Selecting the "best" combination of these remaining independent

variables, step two of the analysis resulted in a further reduction of

 

the model to:

E = f(

XVI "6—10"

 

Classification functions, derived with x (indicator vari- - I

6-10
ables for the firm which performed the audit) as the independent vari-
ables and evaluated by means of the modified holdout method, generated

the following confusion matrix:

 

 

 

Actual Group Predicted Group Membership
Membership, _i_ ii_ Total
I 28 2 30
II 5 4 9
Total 33 6 39

As the above matrix indicates, these classification functions
predicted group membership correctly for thirty-two Observations (82.1
per cent). The number of correct predictions one would expect by
chance is 26.8 (68.7 per cent). Thus, in this case, although the
classifications performed somewhat better than chance, the difference

is probably not highly significant (o < .0526).

239

Assertion XVII: "All recorded sales were a result of current period

 

 

transactions and [no] recorded sales were a result of

 

subseqpent or prioriperiod shipments."56

 

Relevant procedures:

 

r 1. Confirm accounts receivable.

r 2. Perform cut-off procedures.57

Since all of the sample public accounting firms apparently con-
sidered both of these procedures "required," further analysis was un-
necessary.

Summary and Conclusions: Procedure Selection
in the Area of Sales

Tables 7 and 8 (infra, pp. 241-45 ) summarize the results of the
foregoing analysis. The first table indicates that, for eleven of the
thirteen assertions examined, some combination of independent vari-
ables predicted better than chance (a < .05) which tests the auditor
would select. However, for at least two reasons, one should view
these results with a certain degree of skepticism.

The first of these reasons concerns the Specific manner in which
the audit area of sales was analyzed into component assertions. Un-
doubtedly, because of the amount and variety of evidence necessary to
support an overall Opinion on any given set of financial Statements,
the public accountant must subdivide each audit into smaller, rela-

tively independent areas of investigation. Chapter II argued

 

56Ibid.

57Ibid.

 

240
(pp. 36-38) that the individual financial statement assertion is the
most appropriate level Of disaggregation for the auditor's evidence
selection decisions. Unfortunately, the work-papers examined in the
course of this study provided little indication of the actual manner
in which the practicing public accountant subdivides an audit (beyond
the level of general audit "areas" such as sales, accounts receivable,
cash, inventories, etc.). Furthermore, even if the sample auditors
did select their evidential matter with Specific assertions in mind,
their work-papers did not indicate what assertions they considered or
whether those assertions corresponded with Arens' set. Therefore, (1)
to the extent that assumed and actual levels of disaggregation dif-
fered, and (2) to the extent that assumed and actual assertions dif-
fered, the results of the foregoing analysis may be invalid.

The second reason for skepticism concerning the results of the
above analysis is the exploratory approach it adapted. Instead of
testing specific hypotheses about any one particular combination of
independent variables (the traditional approach), this analysis sought
to identify those combinations with the greatest predictive ability
for each assertion. Unfortunately, because of the relatively large
number of potential independent variables (providing literally thour
sands of combinations to choose from) and the relatively small number
of sample Observations, it is possible that the apparent predictive
ability of some resulting independent variable combinations may be
nothing more than random correlation.

Because of these two problems (questionable validity of the man-

ner in which "sales" was analyzed into component assertions and danger

 

241

 

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246
of random correlation), the greatest value of the above analysis un-
doubtedly lies in the methodology it introduces (the actual limita-
tions of the analysis arise from the small sample size, not from the
methodology employed) and the questions it raises (particularly con-
cerning the auditor's approach to disaggregating evidence accumulation

decisions) rather than in its Specific results. Nevertheless, at Q}
least two of these results are sufficiently important to warrant fur- _flg

ther discussion here. I

 

First of all, variables x6_10, by themselves, predicted the au— ,1»
ditor's test selection better than chance (a < .05) for nine of the 1 i
thirteen assertions examined. These indicator variables for the firm
which performed the audit were the most accurate predictors of proce-
dure selection for eight assertions and combined with other variables
to form the most accurate set of predictors for two more. The fact
that they turn up so often as, or among, the "best" combinations of
independent variables indicates that x6_10 probably had predictive
ability beyond mere random correlation. Apparently then, each of the
sample firms had its own (to some extent unique) basic approach to the
audit of sales for clients of the size and nature included in this
study -- an approach that was relatively insensitive to variations (of
the magnitude encountered here) in the other factors considered.

The other result worthy of mention is the frequency with which
one of both of the internal check factors (x18 and x22) and one or
both of the internal control factors (x17 and x21) survived step one

(nine and eight times out of thirteen, respectively). These results

prObably indicate that the sample auditor's programs were, in fact,

 

247
to some extent sensitive to the quality of their client's internal
check and internal control, although the evidence here is not nearly

so compelling as that regarding x6_10.

The Audit Area of Accounts Receivable
Arens identifies the following auditing procedures as relevant
to one or more financial Statement assertions regarding "accounts re— 1} 4
’ “Tr

ceivable":58

 

l. Aged trial balance procedures.

 

r R a. Foot the list Obtained from the client.

r R b. Reconcile the total with the general ledger.

r R c. Compare the detail list to the subsidiary
ledger.

r R d. Review the listing for non-customer accounts and

consignments.
2. Confirmation of Accounts Receivable.

a. Positive Confirmations.

r R (1) Send positive confirmations.
r R (2) Send second requests to non-respondents.
r R (3) Reconcile apparent differences disclosed

by positive confirmations.

 

58Arens, pp. 145-155. Note that these procedures are primarily
applicable to determining the validity of accounts receivable. Proce-
dures applicable to determining the collectibility of such accounts
are defined as beyond the scope of the study.

 

248
b. Negative Confirmations.
(1) Send negative confirmations.
r R (2) Reconcile apparent differences disclosed
by negative confirmations.
r R c. Alternative Procedure -- Trace collections re-

59

ceived on Open account.

The capital "R" and lower case "R" appearing before all of the
above procedures except:

2. b. (1). Send negative confirmations.
identify, respectively, those procedures which Arens considers re-
quired and those procedures which all of the sample firms performed in
at least ninety per cent of their reported audits (eighty per cent for
firms which reported only five clients).

Because it provides essentially the same information as positive
confirmation, though usually with considerably less reliability, nega-
tive confirmation is not really an "Optional" procedure in the sense
of the "optional" sales tests described above. Rather, it is an 3i:
ternative means of satisfying the basic requirement of Generally Ac-
cepted Auditing Standards that accounts receivable be confirmed. Only
if the auditor cannot achieve adequate and economically feasible
coverage of his client's accounts receivable through positive confir-
mation alone does negative confirmation become a valid (and, in fact,

a required) procedure.

 

59Arens identifies this procedure as a required follow-up for

"non-reSponses" to positive confirmations. In fact, all of the sample
firms performed this procedure as a required follow-up for both types
of confirmation and for "responses" as well as "non-responses."

249

Summary and Conclusions: Procedure Selection in
the Area of Accounts Receivable

The absence of "optional" procedures in the area of accounts re-
ceivable precluded tests of the nature performed in the area of sales.
Nevertheless, while the number of Observations is insufficient to per-
mit more than tentative generalizations, the work-papers reviewed sug-
gest some tendencies worthy of mention here.

Essentially, four factors appear to have influenced most greatly
the selection of accounts for a particular type of confirmation.

These factors were: the size Of a receivable relative to others in
the trial balance, the age of the account, the total number of receiv-
ables in the trial balance, and individual firm policies.

Clearly the most important factor in the selection of an account
for positive confirmation was its size relative to other receivables
in the trial balance. For all of the sample firms except G (which se-
lected accounts randomly and without regard to dollar balance), the
predominant approach was to select receivables in excess of some mini-
mum dollar balance -- the particular minimum in any given case gen-
erally being dependent upon and in considerable excess of the trial
balance average. This method of selection was, in fact, the only one
recorded in the sample work—papers from firms, C. D, and E. Firms A,
B, and F, however, also occasionally added ninety-day-old receivables
(in some cases again setting a minimum dollar balance) to their posi-
tive confirmations.

Besides the size and age of individual accounts, another factor
which seems to have affected the auditor's confirmation approach was

the total number of receivables in the trial balance. Generally, as

250
long as this number did not exceed some maximum (which varied from
firm to firm) the sample auditors tended to perform all confirmation
positively. Otherwise, they tended to use a mixture Of positive and
negative confirmation.

The predominant method of specifying accounts for negative con-
firmation was simply random or pseudo-random selection from all re-
ceivables (or all receivables in excess of some minimum dollar balance)
not already designated for positive confirmation. The actual extent
of negative confirmative coverage varied from firm to firm. However,
in general, Firms A and E seemed to confirm a larger percentage of ac-
counts negatively than did Firms B, C and D. (Firms F and G did not
utilize negative confirmation sufficiently often to permit generaliza-
tions about their approach.

Summary and Conclusions: Procedure Selection in
the Areas of Sales and Accounts Receivable

The foregoing analysis has concerned itself with factors which
affect the section of audit procedures in the areas of sales and ac-
counts receivable. Although a regrettably, but unavoidably, small
sample limited the Study somewhat, the following tentative conclusions
seem reasonable.

First of all, the results suggest that, at least for the cli-
ents observed, Generally Accepted Auditing Standards and individual
firm policy were the primary determinants of test selection in the
area of sales. Additionally, the results suggest that client internal

check and internal control may have had some influence in this area.

251

With respect to accounts receivable, on the other hand, the pri-
mary determinant of test selection appears to have been Generally Ac-
cepted Auditing Standards. Additionally, however, the size, age, and
number of receivables in the client's trial balance, and specific firm
policies probably influenced whether a given receivable would be con-
firmed positively, negatively, or not at all.

After he has determined which procedures he will perform, the
auditor must decide when and to what extent he will perform them. The
remainder of this chapter is concerned with factors which influence
these latter two decisions. Let us, therefore, turn to a study of
factors which affect the timing of audit procedures in the areas Of
sales and accounts receivable.

A Study_of Factors which Affect the Timingiof
Audit Evidence Accumulation in the_Areas
of Sales and Accounts Receivable

Chapters III-V identify a number of factors seemingly capable of
having an indirect or limited effect on the auditor's timing decisions
(e.g., see supra, pp. 105, 145, and 166). The only factor identified
in these discussions as capable of directly affecting such decisions,
however, is the quality and comprehensiveness Of the client's internal
control. With regard to this factor's expected effect, Chapter IV'S
argument (supra, pp. 136-139) suggests that the absence Of adequate
internal control in a given audit area will generally necessitate
year-end testing. The presence of adequate control, however, although
an essential precondition, is not, in itself, sufficient reason for

the auditor to obtain his evidence at an interim date. Year-end tests

252
provide inherently more reliable evidence than interim tests, regard-
less of the status of the client's internal control.

Reduced reliability notwithstanding, however, two factors not
specifically discussed in Chapters III-V, time constraints and staff
constraints, may cause the auditor to schedule some tests at an in-
terim date. Time constraints are most likely to occur in the audits
of larger, publicly-held clients, since such clients frequently desire
to issue their financial statements within a fairly Short time (e.g.,
a month) after the close of their fiscal year. Staff constraints, on
the other hand, are most likely to become an important consideration
whenever an auditing firm has a large number of engagements in progress
simultaneously.

All of the sample clients in this Study were relatively small,
most were closely-held, and none imposed any kind of restrictive dead-
line on the auditor's Opinion. Therefore, time constraints were con-
trolled out of the analysis. A number of the sample clients did, how-
ever, have a fiscal year which coincided with the calendar year.
Therefore, Since the public accountant's peak season traditionally be-
gins toward the end of December, the following general model was hy—
pothesized for timing decisions with regard to sales tests of trans-
actions and accounts receivable confirmation:

1. If the client's internal control is inadequate, either due
to a lack of separation of cash-handling and record-keeping
functions or for some other reason, schedule the appropriate
test(s) at or after the client's year-end regardless of when

that year-end occurs.

253
2. If the client's internal control is adequate:

a. if the client's fiscal year does not and during the
busy season (operationally defined as December-
February), schedule the appropriate test(s) at or
after the client's year end,

b. if the client's fiscal year ends during the busy sea-
son, schedule the appropriate test(s) at an interim

date.

The following analysis evaluates this model's predictive ability

when applied to the sample observations.

The Audit Area of Sales
In mathematical form, the above model, as hypothesized with re-

gard to sales tests of transactions,60 appears as follows:

0; x21 I 0, 2E x39 = 0

t8 I f(x21, x39) I

1; x21 I 1, and x39 I l

 

60Another factor which undoubtedly affects when the auditor will

perform a particular test is the nature of the test, itself. Thus,
for example, sales tests actually fall into two basic categories:
tests of transactions and cut-Off tests. Because Of the nature and
objective of cut—Off procedures, however, and the fact that they are
seldom particularly time consuming, such procedures are almost always
deferred until the client's year-end regardless of the "circumstances
of the audit." Since, in forty-seven of the fifty-one sample Observa-
tions for which the auditor reported performing cut-Off tests, he per-
formed those tests at year end, no further analysis was considered
necessary. (Note, however, that in all of the four cases where the
auditor performed his cut-off tests at an interim date, the client had
"good" internal control and a fiscal year which ended December 31.

254
where: t8 indicates the model's prediction as to when the
auditor performed his sales tests of transactions;
it assumes a value of zero if the model predicts the
auditor performed such tests at or after the cli-
ent's year end and a value of one if it predicts he

performed such tests at an interim date;

x21 indicates the quality and comprehensiveness of the
client's internal control over sales; it is assigned
a value of zero if the auditor evaluated such con-
trol as inadequate or if no separation of record-

keeping and cash-recording functions existed and a

value of one, otherwise, and

x39 indicates the client's fiscal year end; it assumes a
value of one if that year end occurs in December,
January, or February and a value of zero if it oc-

curs at any other time.

The method adopted to evaluate this model was essentially the
same as that adopted to evaluate the classification functions of the
previous section. First, the model predicted timing decisions for
each sample observation. Then, these predictions were compared with
the auditor's actual timing decisions. The following confusion matrix

summarizes the results of the comparisons:

255

Actual Timing Decision - Predicted Timing Decision -
_iests of Transactions Tests of Transactions

 

Interim Year-End Total

 

 

Interim l6 8 2“
Year-End 3 26 29
Total 19 34 53

As the above matrix indicates, the hypothesized model accurately
predicted the auditor's timing decision forty-two times (79.2 per
cent). The number of correct predictions one would expect by chance61
is 27.2 (51.3 per cent). Therefore, in this case, the model performed

significantly better than chance (a < .0000481).

The Audit Area of Accounts Receivable
In mathematical form, the general timing model as hypothesized

with regard to accounts receivable confirmation,62 appears as follows:

 

1The estimate of the number of correct predictions one would
expect by chance as well as the test of significance used in this
analysis is again that found in Clark and Schkade, pp. 417-18, and
described in the preceding section of this chapter (supra, pp. 203-204).

62Accounts receivable tests, like sales tests, actually fall
into two categories: confirmation procedures and trial-balance proce-
dures. As in the case of sales cut-off tests, trial balance tests ap-
pear to belong to the class of procedures usually deferred until the
client's year-end regardless of the "circumstances of the audit."
Thus, since in forty-seven of the fifty-three sample engagements, the
auditor performed his accounts receivable trial balance procedures at
the client's year end, no further analysis was performed. (Again
note, however, that in all six cases where the auditor performed his
trial balance procedures at an interim date, the client had at least
"adequate" internal control over accounts receivable and a fiscal year
which ended December 31.)

256

0; x = 0, pp x = 0

23 39

t ' f("23’ "39) 3

a/r

1; x = 1, and x = l

23 39

where: ta/r indicates the model's prediction as to when
the auditor confirmed accounts receivable; it
assumes a value of zero if the model predicts
the auditor performed confirmation at or
after the client's year end and a value of
one if the model predicts he performed this

test at an interim date;

x23 indicates the quality and comprehensiveness
of the client's internal control over ac-
counts receivable; it is assigned a value of
zero if the auditor evaluated such control as
inadequate or if no separation of record-
keeping and cash-handling functions existed

and a value of one otherwise; and
x39 is defined as above.

Comparing this model's predicted timing decision with the aur
ditor's actual timing decision for each sample observation yielded the

following confusion matrix:

257

Actual Timing Decision - Predicted Timing Decision -
Confirmation of Receivables Confirmation of Receivables

 

 

Interim Year—End Total

 

Interim 13 6 19
Year-End 6 28 34
Total 19 34 53

As the above matrix indicates, in this case, the hypothesized
model predicted the auditor's timing decision correctly forty-one
times (77.4 per cent). The number of correct predictions one would
expect by chance is 28.6 (54.0 per cent). Here, again, the model per-
formed significantly better than chance (o < .000687).

Summary and Conclusions: Timing of Evidence
Accumulation in the Areas of Sales
and Accounts Receivable

For both sales tests of transactions and the confirmation of ac-
counts receivable, a model employing the quality of client internal
control and date of client year-end as independent variables predicted
the sampled timing decisions significantly better than chance. While
this model performed better than one based on either of the above
variables alone (Specifically with respect to clients which had "ade-
quate" internal control and a fiscal year-end outside the auditors'
normal busy season), the introduction of additional independent vari-
ables, such as the firm which performed the audit, distribution of the
client's ownerahip and the existence of loan covenants, did not im-

prove its performance. Therefore, a reasonable conclusion would seem

258
to be that the hypothesized model reflects the sample auditors' normal
timing decision rule for clients of the size and nature included in
this Study.

To this point in the chapter, we have attempted to draw some em-
pirical conclusions concerning factors which affect the type and £127
ipg'parameters of the auditor's evidential collection. To complete
the analysis, let us turn to an empirical study of factors which af-
fect the extent parameter of that collection.

A Study_Of Factors which Affect the Sample Size

of Audit Tests in the Areas of Sales
and Accounts Receivable

 

Chapters III-V identify numerous factors logically capable Of
affecting the extent parameter of the auditor's evidential collection.
Unfortunately, because the number of potential independent variables
was relatively large compared to the number of sample observations,
determination and evaluation of a general model of the auditor's sam-
ple size decision process was infeasible. For this reason the Study
is restricted to the more limited objective of identifying factors

which seemed to exert the greatest influence in that process.

Basic Methodology
Toward this objective, each of the following analyses employed
multiple linear regression63 to identify the combination of independ-

11.
ent variables which explained, most fully, observed variations in the

 

63For discussion of this technique, see T. W. Anderson, An In-

troduction to Multivariate Statistical Analysis (New York: John Wiley
and Sons, Inc., 1958), or almost any introductory mathematical statis-
tics text.

259

auditor's sample selection decision. The basic approach involved
initially forming a least squares equation which included, as inde-
pendent variables, all factors identified in Chapters III-V as rele-
vant to that decision (the dependent variable). From this equation,
independent variables were then deleted, one-at-a-time, in increasing
order of their ability to account for variation in the dependent vari-
able.64 As each independent variable dropped out of the analysis, a
new multiple linear regression function was formed and evaluated with
respect to its ability to explain such variation.

Although the usual measure of this ability is the coefficient of
multiple determination (R2),65 that measure proved inadequate here.
AS Ruble, Kiel and Rafter note, R2 is always an increasing function of
the number of independent variables involved in an analysis (i.e., the
introduction of an additional independent variable into a least squares
function, even though that variable has little or no actual relation-

ship to the dependent variable, will never decrease R2 and may increase

it somewhat due to spurious correlation).66 Since the effects of

 

64The Specific analytical tools employed were two of the Michigan
State University Agricultural Experiment Station's STAT series computer
routines, "LS-Least Squares," as described in William L. Ruble, Donald
Kiel, and.Mary E. Rafter, STAT Series Description No. 7, LS-Calculation
of Least Squares (Regpessiou) Problems on the LS Routine (East Lansing:
Michigan State University Agricultural Experiment Station, 1969), and
"LSDEL-Stepwise Deletion of Variables from a Least Squares Equation,"
as described in Mary E. Rafter and William L. Ruble, STAT Series De-
scription No. 8, LSDEL-Stepwise Deletion of Variables from a Least
Oguares Equation (East Lansing: Michigan State University Agricul-
tural Experiment Station, 1966). Both routines are available through
the program library of the Michigan State University Computation
Center.

65Ruble, Kiel, and Rafter, pp. 5—6, 34.

66Ibid., p. 34.

 

260
Spurious correlation tend to increase as the number of independent
variables increases, and since the number of sample Observations was
relatively small, this study required a measure of explained variation
which would take potential random correlation into account -- a re-
quirement which R2 obviously does not fulfill.

A measure which does fulfill this condition, however, is E2, the
coefficient of multiple determination adjusted for degrees of freedom
in the analysis.67 Unlike its unadjusted counterpart, R2 will ipf
crease as independent variables are deleted from a regression function
so long as the resulting loss in explained variation is not suffi-
ciently significant to offset the increase in the degrees of freedom
adjustment factor.

For this reason, independent variables were deleted from the re-
gression function until R2 attained its maximum value. Since, how-
ever, even the use of 22 may not have entirely eliminated the possi-
bility of random correlation, the results reported for each of the
following analyses include:

1. the combination of independent variables which maximized R2,

in decreasing order of importance,

2. any variables whose deletion from this combination would re-

duce the optimum E2 by no more than .05 per variable, and

 

67 -2 N-l

2
Ibid. R I 1 I'fi:E:I'(1-R )

where: N is the number of observations,
K is the number of independent variables, and

R2 is the coefficient of multiple determina-
tion.

261
3. R2 for the five or six most important factors in the optimum

function.

Let us now turn to the results of the analysis.

The Audit Area of Sales
Initially, the following general model was hypothesized to ex-
plain the auditor's sample size decisions with regard to sales tests

of transactions:68

X

q I f(xl, x3, x“, x

s 5’ 6-8’ "14’ "15’ "21’ "22’ "25’ "26’

1’ "

"27-28’ "29-3 32-33’ "34’ "35’ "36’ "37-38’ "39’ "40’

"41’ "42’ "44)
where: qs is the number of observations in the auditor's sales
tests of transactions sample,

f is a linear function,

x1+0 is the percentage of "Accounts Receivable" dollar
balance confirmed by any means (positive confirma-
tions, negative confirmations, and alternative pro-

cedures),

 

68With regard to the other basic category of sales tests, cut—
off procedures, sample Size data was insufficient to permit similar
analysis. In fact, even for sales tests of transactions, specific
sample-size data was relatively scarce -- appearing in only twenty-
nine of the fifty-three sets of work-papers reviewed. Thus, one must
be particularly aware of the potential effects of Spurious correla-
tions.

262
x”1 is the percentage of the total number of accounts
receivable confirmed by any means (positive confir-

mations, negative confirmations, and alternative

procedures),

x“2 indicates the quality and comprehensiveness of the
client's internal control over sales and assumes a
value of zero if the auditor evaluated such control
as inadequate or if no separation of record-keeping

and cash-handling function existed and a value of

one, otherwise, and

"44 is an indicator variable for the time at which the
tests of transactions were performed, and assumes a
value of one if the tests were performed during the

auditor's busy season (January-March) and a value of

zero, otherwise, and

all other x1 are defined as in Table 5.

Of these variables, the combination which maximized R2 (.6711)

was, in order of decreasing importance:

 

 

Variable(s) Factor Rgpresented
x6_8 the firm which performed the audit,69
x27_28 the nature of the client's operations,

 

69Only Firms A, B, C, and E are represented here. The other

three provided insufficient information with regard to tests of trans-
actions to permit inclusion.

Variable(sl

 

"32-33

22

42

"29-31

41

34

21

26

The last three factors,

263

Factor Represented

 

the existence and nature of loan covenants be-
tween the client and one or more creditors,

the auditor's evaluation of his client's in-
ternal check over sales,

the quality of the client's internal control
over sales (auditor's evaluation adjusted
for any lack of separation of record-keeping
and cash handling functions),

the distribution of the client's ownership,

the percentage of the total number of accounts
receivable confirmed by any means,

the client's "Retained Earnings" balance,

the auditor's evaluation of his client's inter-
nal control over sales, and

the client's total stockholders' equity.

and x , each made a marginal

"26’ "21 34

contribution to E2 of less than .0240. Furthermore, deletion of all

70

three from the analysis reduces R2 only slightly to .6289. There-

fore, one may reasonably question whether these variables' apparent

relationship to tests of transactions sample size was, in fact, more

than random correlation.

 

70

The further deletion of the next least important factor, x
reduces R2 to .5626, a loss in explained variation of .0663.

41’

264
On the other hand, the five most significant factors71 in the
regression function have the following effect on 82 when admitted to

that function in order of decreasing importance:

 

 

Factor Admitted ResultingE2
"6-8 .0000
x27_28 .3071
x32_33 .4295
x22 .4851
sz .5163

These results would seem to indicate that, at the least, the first
four factors do bear more than a random relationship to auditor tests

of transactions sample size decisions.

The Audit Area of Accounts Receivable
A problem‘which arose with respect to this analysis was how to
measure extent of accounts receivable confirmation. Should the basis

be the number of receivables confirmed or the dollar value of those

 

receivables? Should only positive coverage be considered or Should
coverage by negative confirmation and alternative procedures, such as
tests of Subsequent collection, be included as well? Because the sam-
ple auditors' actual approach to selecting accounts for confirmation
almost invariably referred, in some manner or other, to the dollar

balance of such accounts, and because, presumably, no rational auditor

 

71Since, in the case of some indicators (i.e., "6—8’ x27-2

9
x32_ 3) more than one independent variable was required to describe a
particular factor, the five factors here referred to actually repre-
sent ten independent variables in the regression function.

 

265

acting in his client's interest would perform a particular verifica-
tion technique on a given receivable unless: (l) he considered veri-
fication of that receivable necessary for his Opinion on the client's
financial statements, and (2) he was willing to accept the result of
his selected technique as evidence of the account's status, this re-
searcher believes that the percentage of "Accounts Receivable" dollar
balance confirmed by any means is the most meaningful measure avail-
able.72 So that the reader may draw his own conclusions, however, re—
sults appear below for analyses adopting each of the following mea-

sures of extent as their dependent variable:

1. the percentage of the total number of accounts receivable

 

confirmed positively,
2. the percentage of the total number of accounts receivable
confirmed by any means,

3. the percentage of "Accounts Receivable" dollar balance con-

 

firmed positively,

4. the percentage of "Accounts Receivable" dollar balance con-

 

firmed by any means.

Furthermore, since the auditor's usual approach to selecting receiv-

ables for confirmation did not refer to any percentage of total

 

72Another possible method of measuring extent of receivables

confirmation might have been to look at the reliability and confidence
level (holding one constant and treating the other as the dependent
variable) with which the auditor could estimate his client's "Accounts
Receivable" dollar balance based upon the confirmation sample. Since,
however, the sample auditors did not, themselves, adopt statistical
parameters to define the extent of their receivables coverage, analyz-
ing their decision model in terms of such parameters did not seem suf-
ficiently meaningful to warrant the practical problems involved in
converting the reported confirmation data into statistical terms.

266
coverage, per se, but rather called for positive confirmation of "all
accounts with a balance in excess of $xxx," and negative confirmation
of :1 random or pseudo-random "representative sample of all accounts
not: receiving a positive confirmation," the results reported below
alsc: include those of analyses which adopted as their dependent vari-
ables:

5. the smallest dollar balance receivable (less than ninety
days old) considered for positive confirmation in a given
audit, and

6. the smallest dollar balance receivable (less than ninety
days old) considered for confirmation by any means in a

given audit.

In all cases, the following general model was hypothesized to

exPlain the auditor's sample selection decision:

,X,X,X ,X ,X

3 4 5 6—11 ’ x

, X

‘1 ' f(x1: x2: x 193 3209

12 13 14

a/r
"23’ "24’ "25’ "26’ "27’ "28’ "29-31’ "32-33’ "34’ "35’
"36’ "37-38’ "39’ "43’ "45)

where: qa/r is the "extent" of accounts receivable confirmation

as defined in each specific analysis,

x1+3 indicates the quality and comprehensiveness of the
client's internal control over accounts receivable
and assumes a value of zero if the auditor evaluated
such control as inadequate or if no separation of

record-keeping and cash-handling functions existed

and a value of one otherwise,

 

267
x1+5 is an indicator variable for the time at which con-
firmation was performed and assumes a value of one
if it was performed during the auditor's busy sea-
son (January-March) and a value of zero otherwise,
and

all other x1 are defined as in Table 5.

The Percentage of the Total
Number of Accounts Receivable
Confirmed Positiveiy,

 

 

The combination of independent variables which maximized R2

(.6584) was, in order of decreasing importance:

 

 

 

Variable(e) Factor Represented

"6-11 the firm which performed the audit,73

x29_31 the distribution of the client's ownership,

x26 the client's total stockholders' equity,

x” the client's mean accounts receivable dollar
balance,

x13 the ratio of the client's "Accounts Receiv-

’ able" to total assets,

x1.3 the quality of the client's internal control
over accounts receivable (auditor's evalu-
ation adjusted for any lack of separation
of record-keeping and cash-handling func-
tions),

73

All seven public accounting firms are represented here.

268

Variable(s) Factor Represented

 

x32_33 the existence and nature of loan covenants be-

tween the client and one or more creditors,

x36 the client's debt/equity ratio,
"27-28 the nature of the client's Operations,
x2 the dollar balance of the client's gross ac-

counts receivable,

"24 the auditor's evaluation of the client's in-
ternal check over accounts receivable,

x39 an indicator variable for the date of the cli-

ent's fiscal year end.

The last six of these factors, x39, x22, x2, "27-28’ x36 and
x32_33, each made a marginal contribution to R2 of less than .0295.
Furthermore, deletion of all six factors (nine independent variables)
from the analysis reduces R2 only slightly to .5508. Therefore, one
cannot rule out the possibility that these variables' apparent rela-
tionship to the percentage of the total number of receivables con-
firmed positively is, in fact, merely spurious correlation.

On the other hand, the six most significant factors (thirteen
independent variables) in the regression function have the following
effect on R? when admitted to that function in order of decreasing

importance:

269

 

 

Factor Admitted Resultiug,R2
___ 74

x6-11

x29_31 .0899
x26 .2938
x1+ .4501
x13 .5022
"43 .5508

These results would seem to indicate that, in combination, at
least the first four factors do bear more than a random relationship
to the percentage of the total number of accounts receivable confirmed
positively.

The Percentage of the Total

Number of Accounts Receivable
Confirmed by Any Means

 

 

AS the close relationship between this and the previously ex-
amined dependent variable might lead one to expect, the combination of
factors which maximized R2 (.6458) in both cases is almost identical,
not only in the factors included, but also in the relative Significance

'of those factors:

 

 

 

Variable(e) Factor Represented
x6_11 the firm‘which performed the audit,75
x29__31 the distribution of the client's ownership,
x25 the client's total assets,
7""-—-" indicates that the program did not calculate R2 at that

step of the analysis.

75All seven public accounting firms are represented here.

270

 

Variab1e(s) Factor Represented
x“ the client's mean accounts receivable dollar
balance,
x13 the ratio of the client's "Accounts Receivable"

to total assets,

"43 the quality of the client's internal control
over accounts receivable (auditor's evalu-
ation adjusted for any lack of separation of
record-keeping and cash-handling functions),

x the dollar balance of the client's gross ac-
counts receivable,

x39 an indicator variable for the date of the cli-
ent's fiscal year end,

x2“ the auditor's evaluation of the client's inter-
nal check over accounts receivable,

x32_33 the existence and nature of loan covenants be-

tween the client and one or more creditors,

26 the client's total stockholders' equity,

3“ the client's "Retained Earnings" balance.

The last three of these factors, and x32_33, each made

"34’ "26
a marginal contribution to R2 of less than .0190. Furthermore, dele-
tion of the three factors (four independent variables) from the anal-
ysis reduces R2 only slightly to .6182. Therefore, one may seriously
question whether these variables' apparent relationship to the per-

centage of the total number of receivables confirmed by any means is,

in fact, more than Spurious correlation.

271
On the other hand, the six most significant factors (thirteen
independent variables) in the regression function have the following

effect on R2 when admitted to that function in order of decreasing

 

 

importance:
Factor Admitted ResultingR2
"6—11 ”"
x29_31 .0964
x25 .2251
x“ .2616
x13 .3291
x1+2 .4295

These results would seem to indicate that the factors do bear
more than a random relationship to the percentage of the total number
of accounts receivable confirmed by any means.

The Percentage of "Accounts

Receivable" Dollar Balance
Confirmed.Positiveiy

The combination of independent variables which maximized R2

(.8166) in this case was, in order of decreasing importance:

 

 

 

Variable(e) Factor Represented
"6-10 the firmnwhich performed the audit,76
x29_31 the distribution of the client's ownership,
76

All firms except Firm G are represented here.

Variable(s)

"4

12

25

43

"32-33

"37-38

34

35

13

36

39

23

272

Factor Represented

 

the client's mean accounts receivable dollar
balance,
the ratio of the client's "Accounts Receivable"
to net sales,
the client's total assets,
the "timeliness" of accounts receivable confir-
mation,
the quality of the client's internal control
over accounts receivable (auditor's evalua-
tion adjusted for any lack of separation of
record-keeping and cash-handling functions),
the existence and nature of loan covenants be-
tween the client and one or more creditors,
the existence and nature of any subsidiary ac—
quisitions effected by the client,
the client's "Retained Earnings" balance,
the client's net ordinary income before taxes,
the ratio of the client's "Accounts Receivable"
to total assets,
the client's debt/equity ratio,
an indicator variable for the date of the cli-
ent's fiscal year end,
the auditor's evaluation of the client's inter-

nal control over accounts receivable.

273

Deletion of x2 reduces R2 by only .0033. On the other hand,

3
the next two factors in the list, x39 and "36’ each made seemingly
substantial contributions to E2 -- .0485 and .0545, respectively.

Despite this fact, however, deletion of x23, x39, "36’ x13, x35, x3“,

x37_38, x32_33, x“3 and x1 (twelve independent variables) only reduces
R2 to .5827. Therefore, one may not rule out the possibility that any
apparent relationship between these factors and the percentage of
"Accounts Receivable" dollar balance confirmed positively is merely
Spurious correlation.

On the other hand, the six most Significant factors (twelve in-

dependent variables) in the regression function have the following

effect on Ez when admitted to that function in order Of decreasing

 

 

importance:

Factor Admitted Resulting R2
x6-10 "’
x29-31 "'

x“ .1370
x12 .3433
x25 .5827
x .5928

These results would seem to indicate that at least the first
five factors do hear more than a random relationship to the percentage

of "Accounts Receivable" dollar balance confirmed positively.

274

The Percentage of "Accounts
Receivable" Dollar Balance
Confirmed by Any Means

 

The combination of independent variables which maximized R2

(.3906) for this dependent variable was, in order of decreasing ime

 

 

 

portance:
Variable(s) Factor Represented
x27_28 the nature of the client's operations,
x29_31 the distribution of the client's ownership,
x26 the client's total stockholders' equity,
x12 the ratio of the client's "Accounts Receivable"
to net sales,
x3“ the client's "Retained Earnings" balance,
x6_lo the firm which performed the audit,77
x2“ the auditor's evaluation of the client's inter-
nal check over accounts receivable,
x3S the client's net ordinary income before taxes,
x25 the client's total assets,
x13 the ratio of the client's "Accounts Receivable"
to total assets,
"37-38 the existence and nature of any subsidiary ac-
quisitions effected by the client,
x32_33 the existence and nature of loan covenants be-
tween the client and one or more creditors.
——7 77

As in the previous case, all firms except Firm G are repre-
sented here.

275
Deletion of the last eight of these factors (fourteen independ-
ent variables) reduces R2 only Slightly to .3642. Therefore, one can-
not rule out the possibility that any apparent relationship between
these factors and the percentage of "Accounts Receivable" dollar bal-
ance confirmed by any means is merely spurious correlation.

On the other hand, the remaining four factors (seven independent

.fl

variables) have the following effect on R2 when admitted to the re-

gression function in order of decreasing importance:

 

 

 

Factor Admitted ResultingR2 Z
x2 7-2 8 "" L
x29_31 .0874
x26 .2530
x12 .3642

These results would seem to indicate that the factors do bear
more than a random relationship to the percentage of "Accounts Receiv-
able" dollar balance confirmed by any means.

The Smallest Dollar Balance
Receivable (Less than NinetnyayS

Old) Considered for Positive
Confirmation in a Given Audit

 

 

 

In this case, regression analysis failed to identify any combi-
nation of more than one independent variable which was sufficiently
associated with the dependent variable to yield an R2 greater than
zero. A single independent variable, x25 (the client's total assets)
maximized the adjusted coefficient of determination at only .0204.

These results would seem to indicate that none of the factors

276

considered in this study bear any Significant linear relationship to

the smallest dollar balance receivable considered for positive confir-

mation in a given audit.

The Smallest Dollar Balance

 

Receivable (Less than Ninety Days

 

Old) Considered for Confirmation

 

by Any Means in a Given Audit

 

The combination of independent variables which maximized R2

(.3727) for this dependent variable was, in order of decreasing im-

portance:

Variable(e)

 

26

12

The last two of

Factor Represented

 

the client's net sales,

the time at which confirmation was performed,

the quality of the client's internal control
over accounts receivable (auditor's evalua-
tion adjusted for any lack of separation of
record-keeping and cash-handling functions),

the client's mean accounts receivable dollar
balance,

the dollar balance of the client's gross ac-
counts receivable,

the client's total stockholders' equity,

the ratio of the client's "Accounts Receivable"

to net sales.

these factors, x and x each made a marginal

12 26

contribution to R2 of less than .0205. Furthermore, deletion of these

277

factors (two independent variables) only reduces R2 to .3467. There-
fore, one may reasonably question whether the variables' apparent re-
lationship to the smallest dollar balance receivable considered for
confirmation by any means in a given audit is, in fact, more than
spurious correlation.

On the other hand, the five most significant factors (five inde-
pendent variables) in the regression function have the following ef-

fect on R2 when admitted to that function in order of decreasing im-

 

 

portance:
Factor Admitted ResultingR2
x5 .0681
"45 .0927
x,+3 .1587
x“ .2329
x2 .3467

These results would seem to indicate that the five above factors
bear more than a random relationship to the percentage of the total
number of accounts receivable confirmed by any means.

Summary and Conclusions: Sample Size of Audit
Tests in the Areas of Sales
and Accounts Receivable

Tables 9 and 10 summarize the results of the foregoing analysis.
These tables both indicate that, in every case but one (the smallest
dollar balance receivable considered for positive confirmation), some

combination of independent variables appeared to bear more than a

random relationship to the relevant Operational definition of the

278

 

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281

Table lO.--Summarized results (B) of the study of factors which affect
the sample Size of audit tests in the areas of sales and accounts
receivable. (X indicates_that the factor appears in the regression
function which maximized R2 for the dependent variable in question.)

 

 

 

 

 

Sales Tests of Percentage of the Total Number of
Transactions Accounts Receivable Confirmed:
Factors Sample Size Positively By Any Means
"1
x2 X X
"3
X" X"
"4
"5
X" X" X"
"6-11
"12
e *
x X X
13
x
14
"15
"19
"20
x21 or x23 X
X" X X
"22 °" "24
X"
"25
*
x26 X X X
*
X X

"27—28

 

I"

282

Table 10--Continued

 

 

 

 

 

Sales Tests of Percentage Of the Total Number of
Transactions Accounts Receivable Confirmed:
Factors Sample Size Positively By Any Means
*
x29_31 X X X
* X X
"32-33 "
X
x31+ X
"35
x36 X
"37-38
x39 X X
"40
x!+1 X
* *
x or x X X X
42 43
"44 °" "45

 

*
apparently significant factor

Factors

 

X orx

X orx

x
27-28

x29-31

23

24

283

Table lO--Continued

 

 

 

 

 

 

Percentage of "Accounts Smallest Dollar Balance
Receivable" Dollar Receivable Considered
Balance Confirmed: for Confirmation:

Positivelyf Oy Any Means Positiveiy_ Oy Any Means
X
*
X
k *
X X
*
X
*
X X
* *
X X X
X X
X
X
*
X X X
*
X
*
X
* *
X X

 

284

Table 10--Continued

 

 

 

 

 

 

 

Percentage of "Accounts Smallest Dollar Balance
Receivable" Dollar Receivable Considered
Balance Confirmed: for Confirmation:
Factors Positively Oy Any Means Positively By Any Means
"32-33 " "
x3“ X X
35 X X
36 X
"37-38 " "
39 X
40
41
X"
42 °" "43 "
*
x or x X

44 45

285
auditor's sample selection decision. One must, however, regard these
results as only tentative for two reasons.

First of all, evidence indicates that the sample auditors did
not all use the same decision rule to select receivables for confirma-
tion. The two primary approaches taken were:

1. select all accounts in excess of some minimum dollar balance FT~

(in which case the dependent variable was the minimum dollar
balance), and

2. select sufficient accounts to assure confirmation of a Spec-

 

ified percentage of the "Accounts Receivable" dollar balance
(in which case the dependent variable was the specified per-

centage).78

Because of the limited number of work—papers available for this
Study, grouping Observations according to the auditor's sample selec-
tion rule and performing individual analysis on each of the resulting
groups was impossible. Instead, all the Observations had to be com-
bined in a Single analysis.

The necessary assumption for such an approach is, of course,
that the two sample selection rules are essentially equivalent.
Since, however, it seems likely that most auditors do have some level
of overall coverage in mind when they impose a minimum dollar balance

requirement on receivables to be confirmed, this assumption appears

 

78A third potential approach, not adopted in any of the sample

audits is, "Select a 'Statistical sample' which assures specified
levels of confidence and reliability." In this case, of course, the
Specified Statistical parameters would have been the dependent vari-
ables. '

286

reasonable. Nevertheless, to the extent that the two approaches are
not equivalent, the reliability of the foregoing analysis is impaired.

The second reason one must regard the results of the above anal-
ysis as merely tentative is the fact that, as was the case in the
Study of factors which affect the selection of audit procedures, the
number of potential independent variables was relatively large com— ”a:
pared to the number of sample observations -- a situation which in-
variably amplifies the possibility that Spurious correlation may have
confounded the analysis.

With these limitations in mind, let us attempt some generaliza-

 

uq _-

tions about the results of the analysis. Based upon frequency of oc-
currence in the final regression functions (i.e., the regression func-
tions which maximized R2 for the various dependent variables con-
sidered), four factors appear to have had the greatest overall associ-
ation with the extent of audit testing in both the areas of sales and
accounts receivable:

l. the firm'which performed the audit,

2. the client's size,

.3. the quality and comprehensiveness of the client's internal

control, and

4. the distribution of the client's ownership.

Although the number of observations precludes more than tenta-
tive conclusions, a closer look at the effects of these factors would

seem worthwhile .

287

The Firm which Performed the Audit

 

As Table 10 reveals, , the variables which represented this

"6-11
factor, appeared in the final regression function for five of the seven
analyses performed, and among the most Significant factors four times.
With respect to the behavior of specific firms, the sample data indi-
cates the following:
1. with regard to sales tests of transactions, Firms B, C and E
tended to draw larger samples (thirty or more observations
in Sixteen of twenty-one audits for which data was avail-
able) than did Firms A and D (fifteen or fewer observations
in ten of eleven observations for which data was avail-
able), 79
2. with regard to accounts receivable, Firms A, B, C and E all
tended to confirm more extensively than Firm D. Of the
firms with the greatest coverage, however, while all per-
formed substantial positive confirmation, Firms A and E re-
lied somewhat more heavily on negative confirmation than did
B and C. On the other hand, Firm D's coverage although not

as extensive as that of the other four firms was primarily

positive.

The Client's Size

 

Two measures of this factor which correlated highly with one
another (r I .906) were included among the study's independent vari—

ables -- the client's total assets, and x the client's total

"25’ 26’

 

79Insufficient information was available to permit any generali-
zation about Firms F and G.

288
stockholders' equity. As Table 10 indicates, at least one of these
factors appeared in the final regression function for each of the
seven analyses performed. Furthermore, one or the other appeared
among the most Significant variables four times.

In general, correlation coefficients associating these factors

with the several independent variables examined indicate that:

l. the size of the auditor's test of transaction samples tended
to vary directly with the client's size,

2. the total number of receivable confirmations sent also
tended to vary directly with the client's size, however, the
percentage of receivable coverage, both positive and overall
tended to decline as the Size of the client increased.

The_Ouality and Comprehensiveness
of the Client's Internal Control

Two indicators of this factor were included among the study's

independent variables, x22 ("24” the auditor's evaluation of his cli-
ent's internal control system with regard to sales (accounts receiv-

able) and x ), this evaluation adjusted for the degree of separa-

42 ("43
tion of cash-handling and record-keeping functions within that system.
In both the case of sales and of accounts receivable, the two indica-
tors correlated moderately (r I .484 and .511, respectively).

As Table 10 indicates, at least one of these indicators appeared
in the final regression function for six of the seven analyses per-
formed, and at least one appeared among the most significant factors

four times. Correlation coefficients associating these factors with

the several independent variables examined indicate that both the size

 

289
of the auditor's test of transactions sample and the extent of ac-
counts receivable confirmation coverage ( positive and overall) tended
to vary inversely with the quality and comprehensiveness of the cli-
ent's internal control.

The Distribution of the
Client's Ownership

 

 

As Table 10 discloses, x29_31, the variables which represented
this factor, appeared in the final regression function for five of the
seven analyses performed, and among the most significant factors four
times. A priori, one would expect the extent of the auditor's testing
to increase as his client's ownership becomes more widespread. The
actual effect of this factor in the sample audits, however, is not en-
tirely clear. Nevertheless, evidence seems to indicate that:

l. with regard to sales tests of transactions, the sample au-

ditors tended to increase the number of observations if the
client was listed on the New York Stock Exchange, but did
not apparently test publicly-held clients whose shares were
traded over-the-counter any more extensively than privately-
held clients,80

2. with regard to the confirmation of accounts receivable, the

sample auditors tended to increase both their total and

positive coverage if the client was publicly rather than

privately held.

 

80Datawas insufficient to permit any generalizations concerning

clients whose Shares were traded on the American Stock Exdhange.

290
In addition to the four above factors, two more which had an
observable association with the extent of testing in the area of ac-
counts receivable were:
1. the mean accounts receivable dollar balance, and

2. the relative materiality of "Accounts Receivable."

The Mean Accounts Receivable
Dollar Balance

 

 

As Table 10 reveals, x the independent variable which repre-

1+9

sented this factor, appeared in the final regression function for four

of the six analyses related to the extent of accounts receivable con-

 

firmation. Furthermore, in each case, this variable was among the
most significant.

In general, the sample evidence seems to indicate that the
smallest dollar balance receivable considered for confirmation (both
positive and by any means) and the percentage of receivable coverage
(both positive and total) all tended to vary directly with the mean
receivable dollar balance.

The Relative Materiality of
"Accounts Receivable"

 

Two measures of this factor which correlated highly with one
another (r I .804) were included among the study's independent vari-
ables -- x12, the ratio of the client's "Accounts Receivable" to net
sales, and x13, the ratio of the client's "Accounts Receivable" to
total assets. As Table 10 indicates, at least one of these factors

appeared in the final regression function for five of the six analyses

291
related to the extent of accounts receivable confirmation. Further-
more, one or the other appeared among the most significant factors
four times.

In general, the sample evidence tends to indicate that, as the
relative materiality of "Accounts Receivable" increased, the percent-
age confirmed, both positive and total, tended to decrease. While
this result may indicate that the sample auditors had a different
measure of the factor than the ones adOpted in this study, it probably
merely indicates that absolute rather than relative materiality was
the important consideration in their conscious decision process, and

that the decision process inadvertently led to less extensive confir-

 

mation.

Summary and Conclusions: An Empirical Otudy of
the Relative Influence of Factors which
Affect Audit Evidence Accumulation

 

This chapter has concerned itself with an empirical study of the
relative influence of a number of factors logically capable of affect-
ing audit evidence accumulation. The study, based on sample data ex-
tracted from the work-papers for fifty-three clients of seven public
accounting firms, consisted of three sections:

1. a Study of factors which affected the selection of audit

procedures in the areas of sales and accounts receivable,

2. a Study of factors which affected the timing of audit tests

in the areas of sales and accounts receivable, and

3. a study of factors which affected the sample size of audit

tests in the areas of sales and accounts receivable.

 

292

Although the specific techniques of analysis differed for each
part, the basic approach was the same:

1. enumerate the factors (identified in Chapters I-V) relevant
to auditor decisions concerning the parameter in question,
and

2. determine which of these factors, if any, seemed to explain
the sample auditors' decisions with respect to that param-
eter.

Factors which Affected the Selection
of Audit Procedures

Results of this study indicate that, for the clients observed,
Generally Accepted Auditing Standards and individual firm policy were
the primary determinants of test selection in the area of sales.
Additionally, the results suggested that client internal check and
internal control may have had some influence in this case.

With respect to accounts receivable, on the other hand, the pri-
mary determinant of test selection appears to have been Generally
Accepted Auditing Standards. Additionally, evidence suggests that
four factors largely influenced whether a given receivable would be
confirmed positively, negatively, or not at all. These factors were
the size of the receivable relative to others in the trial balance,
the age of the receivable, the total number of receivables in the

trial balance and the firm performing the audit.

 

293

Factors which Affected the
Timing of Audit Tests

 

 

Results of this Study indicate that, for the clients observed,
quality of client internal control and date of client year-end were
the primary determinants of the timing of audit tests in both the ar-
eas of sales and accounts receivable.

Factors which Affected the
Sample Size of Audit Tests

 

 

Results of this study suggest that, for the clients observed, the
firm performing the audit, the client's size, the quality and compre-
hensiveness of the client's internal control and the distribution of
the client's ownership had the greatest association with the auditors'
sample size decisions in both the areas of sales and accounts receiv-
able. Additionally, evidence indicates that the mean receivable dol-
lar balance affected the auditors' decision with respect to the small-
est dollar balance receivable considered for confirmation (both posi-
tive and by any means) and the percentage of receivable coverage (both
positive and total).

The foregoing study has been intended as a descriptive examina-
tion of auditor behavior. More specifically, the study's objective
has been to determine whether or not audit work-papers representative
of "good" current practice appear to reflect any relationship between
the composition of the auditor's evidential collection (the dependent
variable) and those factors identified in Chapters I—V (the independ-

ent variables) which:

 

294

1. define evidential support functions,

2. determine minimum evidential support requirements,

3. affect the auditor's risk of sanctions, or

4. constrain the auditor's choice of evidential collection.
Certainly, one can point to procedural weaknesses in the Study. The
sample data was random neither with respect to the participating firms
nor the clients selected. The number of independent variables was
relatively large compared to the number of sample observations. The
method of operationalizing certain of the variables, both independent
and dependent, iS open to question. The method of reducing the Study
of factors which affected procedure selection to manageable propor-
tions is likewise Open to question. For these reasons, one should not
regard the results reported above as more than tentative. Neverthe-
less, if only because of some methodology suggested, some questions
raised, and, perhaps most importantly, the knowledge that public ac-
counting firms were, in fact, willing to provide data for such a

study, this researcher considers the inquiry to have been worthwhile.

 

CHAPTER VII

SUMMARY, CONCLUSIONS, AND SUGGESTIONS

FOR FURTHER RESEARCH

The purpose of this dissertation has been to study the auditor's
decision process with regard to questions of evidence accumulation.
Effectively, the Study consisted of three sections. First, Chapters I
and II suggested a programming framework for audit evidence accumula-
tion decisions. Then, Chapters III-V discussed, in detail, certain
individual factors indicated by the framework as relevant to such de-
cisions. Finally, Chapter VI attempted to evaluate empirically the
relative influence of a number of those factors in actual audit situa-

tions.

A Programming Framework for Audit Evidence
Accumulation Decisions

Chapter I outlined the following programming framework for audit
evidence accumulation decisions:
Given a number of alternative evidential collections rel-
evant to a particular audit, the auditor should select that col-

lection, E which maximizes:

k,

U+<R<Ek>> + u’(c<Ek>> + E[U-(8(Ek))]

295

 

296

subject to the constraints:

IV
on

B(Ek) min

T

T(Ek) max

IA

SR(Ek) 5 SRmx

where:
U+(R(Ek)) is the utility of the audit fee associated with

evidential collection Ek’

U-(C(Ek)) is the disutility of the cost of obtaining

 

evidential collection Ek’

E[U-(8(Ek))] is the expected disutility of sanctions

associated with evidential collection Ek’

B(Ek) is the degree of support provided by evidential

collection Ek’

Bmin is the minimum evidential support necessary to

justify a professional Opinion on a given set

of financial Statements,

T(Ek) is the time required to accumulate evidential

collection Ek’

Tmax is the maximum time available to the auditor

for gathering evidence on a given audit en-

gagement,

SR(Ek) denotes the audit staff required to accumulate

evidential collection Ek’ and

297
SRmax denotes the staff available for a given audit

engagement.

This framework is a useful context in which to identify and study
factors relevant to audit evidence accumulation decisions Since, cor-
responding to each of the nine parameters which comprise it, is a cat-
egory of factors relevant to such decisions. Unfortunately, the con-
struct is of little further use. For this reason, Chapter 11 modified
it in such a manner as to make it compatible with, and capable of prac-
tical application in, the following framework for audit judgment forma-
tion:

1. identify all the material propositions contained in the set

of financial statements under examination,

2. for each proposition:

a. determine the degree of evidential support required to
justify an opinion on the proposition,

b. select the kind(s) and estimate the quantity(ies) of
evidential matter necessary to provide the required
degree of evidential support,

c. design the audit step(s) necessary to yield the desired
kind(s) and quantity(ies) of evidence,

d. apply the step(s) and amass a collection of evidential
matter, and

e. evaluate the collection of evidence (If the evidence
provides sufficient justification, render an opinion on
the proposition. If not, either gather more evidence

or disclaim an opinion on that proposition), and

 

3.

298
based upon the results of the individual proposition evalua-
tions, render (or disclaim) an Opinion on the financial

statements as a whole.

Essentially, two modifications of the original model were neces-

sary to achieve this goal:

1.

replacement of the overall evidential support constraint:

B(Ek) 3- 8min

with the set of constraints:

ba(Ek) 3 b (a = 1, 2, ..., r)

amin’
or their equivalent:

p(FIMa(1 Bk) 5 pamax’ (a = l, 2, ..., r)

where: ba(Ek) is the degree of support provided by eviden-
tial collection Ek for the auditor's opinion on the

at assertion of his client's financial statements,

bamin is the minimum evidential support necessary for

a professional Opinion on that ath assertion,

p(FIMaI\ Ek) is the probability that the auditor will

fail to detect material error which exists in the ath
assertion of his client's records given that he se-

lects evidential collection Ek’

f.

299
pamax is the maximum allowable probability that the
auditor will fail to discover material error which

th
exists in the a assertion of the client's state-

ments,

ba(Ek) and p(FIMaIW Ek) are determined by the same
factors which determine B(Ek) in the original model,

and

b and p are determined by the same factors

which determine Bm in the original model,

in

replacement of the original Objective function:

Maximize Hawk» + U‘(C(Ek)) + E[U'(S(Ek))1

with the objective function:

Minimize C(Ek)

and the set of constraints:

p(FIMan ER) 3. P (a = 13 2: °°’9 r)

amaxrisk

.35 their equivalent:

where:

ba(Ek) " baminrisk

p(FIMarfi Ek) and ba(Ek) are defined as above,

p represents, to the auditor, the maximum

amaxrisk

acceptable probability (based upon his evaluation of

the expected disutility of sanctions) that he will

 

 

300
fail to detect a material error existing in the ath

assertion of his client's financial statements, and

baminrisk represents, to the aud1tor, the minimum
evidential support necessary for an opinion on the
8th assertion of his client's financial statements

(based upon his evaluation of the expected disutility as.

of sanctions).

These modifications resulted in the following general framework

for audit evidence accumulation decisions:

 

1.

Develop the audit program in such a manner as to:

Minimize C(Ek)

subject to: ba(Ek) 2 bamin (a = l, 2, ..., r)

or

p(FIMaIW Bk) 5 pamax (a = 1, 2, ..., r)

T(Ek) 5 Tmax

SR(Ek) 5 SR.max

ba(Ek) 2 baminrisk (a = l, 2, ..., r)
or

p(FIMalW Ek) g "amaxrisk (a = l, 2, ..., r).

Some Factors Relevant to Audit Evidence
Accumulation Decisions

 

 

Analysis of each of the parameters comprising the framework pre-

sented above indicated three categories of audit variables particularly

301

worthy of further study. Accordingly, the second section of this dis-

sertation was devoted to a discussion of:

1.

factors which define the evidential support function for a
given type of audit evidence obtained at a given time
(Chapter III),

factors which determine the minimum evidential support neces-
sary to justify a professional opinion on a given financial
Statement assertion (Chapter IV), and

factors which influence the probability that the auditor will
incur sanctions for failing to detect a material error given

that such error exists in his client's records (Chapter V).

The primary focus of the discussion was on the factors' expected ef-

fects on the three parameters of the auditor's evidential collection:

1.

2.

3.

the type(s) of evidence included,

the time(s) of collection of each type, and

the number of units of each type collected at a given time.
Factors which Define the Evidential Support

Function for a Given Type of Audit
Evidence Obtained at a Given Time

Chapter III identified the following factors as belonging to this

category:

1.

the relevance of the specific type of evidential matter to
the audit engagement,
the reliability of the specific type Of evidential matter,

itself a function of:

 

 

302
a. the conclusiveness of the given type of evidence, and
b. the possibility of misinterpreting evidence of this

nature,

3. the "timeliness" of the evidential matter, itself a function

 

of:
a. the time at which the evidence is Obtained, and
b. the quality and comprehensiveness of the client's in-
ternal controls,

4. the statistical parameters of the population underlying the

 

assertion which the auditor wishes to evaluate, e.g.:
a. size,
b. variance,
c. rate of error, and

5. the existence of corroborative evidence.

 

In summary, Chapter III concluded the following with regard to
the expected influence of these factors on the auditor's evidential
collection:

1. factors capable of affecting the type parameter:

a. directly:
(1) relevance of evidential matter,
(2) reliability of evidential matter,
(3) existence of corroborative evidence,
b. indirectly, or in a limited manner:

(1) "timeliness" of evidential matter,

(2) statistical parameters of the underlying popula-

tion.

 

 

 

303
2. factors capable of affecting the timing parameter:
a. directly: "timeliness" of evidential matter,
b. indirectly; or in a limited manner:
(1) reliability of evidential matter,
(2) statistical parameters Of the underlying pOpula-
tion,
(3) existence of corroborative evidence.
3. factors capable of affecting the extent (sample size) param-
eter:
8. directly:
(1) statistical parameters of the underlying popula-
tion,
(2) existence of corroborative evidence,
b. indirectly, or in a limited manner:
(1) reliability of evidential matter,
(2) "timeliness" of evidential matter.
Factors which Determine the Minimum Evidential
Support Necessary to Justify a Professional
Opinion of a Given Financial
Statement Assertion
Chapter IV identified the following factors as belonging to this
category:
1. Generally Accepted Auditing Standards and other authoritative
pronouncements of the AICPA,
2. authoritative pronouncements of the SEC,
3. commission requirements for regulated industries,

4. policies of individual public accounting firms,

 

 

304

5. specific terms of the auditor's contract with his client,

6. materiality considerations,

7. the auditor's evaluation of the probability that a given

financial statement assertion is materially misstated, based

upon:
a. the auditor's findings
ent's internal control
b. the auditor's findings

records.

In summary, Chapter IV concluded
expected influence of these factors on
tion:

1. factors capable of affecting

a. directly:

during his review of the cli-
System, and

in actual tests of the client's

the following with regard to the

the auditor's evidential collec-

the type parameter:

(1) Generally Accepted Auditing Standards,

(2) SEC pronouncements,

(3) regulatory commission requirements,

(4) individual CPA firm policies,

(5) materiality considerations,

(6) auditor evaluation of the probability that a

given financial Statement assertion is mate-

rially misstated.

b. indirectly, or in a limited manner: auditor-client

contract terms,

2. factors capable of affecting the timing parameter:

 

 

305
a. directly: auditor evaluation of the probability that a
given financial statement assertion is materially mis-
Stated,
b. indirectly, or in a limited manner:

(1) individual CPA firm policies,

(2) auditor-client contract terms,

(3) materiality considerations,

3. factors capable of affecting the extent parameter:
a. directly:

(1) materiality considerations,

(2) auditor evaluation of the probability that a
given financial statement assertion is mate-
rially misstated,

b. indirectly, or in a limited manner:
(1) individual CPA firm policies,
(2) auditor—client contract terms.
Factors which Influence the Probability that the
Auditor Will Incur Sanctions for Failing to
Detect a Material Error Given that Such
Error Exists in His Client's Records
Chapter V identified the following factors as belonging to this
category:
1. nature of the specific errors involved,
2. the degree of exposure the client's statements receive, in-
dicated by:
a. the client's Size,

b. the nature of the client's operations,

 

 

 

306
c. the distribution of the client's ownership, and
d. loan covenants which require the client to maintain
specified account balances or ratios,
3. the probability that the client will file bankruptcy subse-
quent to the audit, indicated by:
a. factors which affect or indicate the degree and types
of financial crisis the client can withstand, e.g.:
(1) factors which indicate the client's financial
position ("Retained Earnings" balance, liquidity

situation, etc.), ,

 

(2) economic conditions related to the availability
of external capital,
(3) the client's rate and method of growth, and
b. factors which affect or indicate the probability that
the client will face a financial crisis which exceeds
its capabilities, e.g.:
(1) the nature of the client's operations,
(2) economic conditions relevant to the client's
marketplace,

(3) the client's method of financing operations.

In summary, Chapter V concluded the following with regard to the
expected influence of these factors on the auditor's evidential collec-
tion:

1. factors capable of affecting the iype_parameter:

a. directly: nature of the specific error involved,

b. indirectly, or in a limited manner:

 

307
(1) degree of exposure the client's statements re-
ceive,
(2) probability that the client will file bankruptcy
subsequent to the audit,
2. factors capable of affecting the timing parameter:
a. directly: none,
b. indirectly, or in a limited manner: E1:”
(1) nature of the specific error involved, ‘
(2) degree of exposure the client's statements re-

ceive,

 

(3) probability that the client will file bankruptcy .2?
subsequent to the audit,
3. factors capable of affecting the extent parameter:
a. directly: none,
b. indirectly, or in a limited manner:
(1) nature of the specific error involved,
(2) degree of exposure the client's statements re-
ceive,
(3) probability that the client will file bankruptcy

subsequent to the audit.

While a number of authors have discussed factors which influence
or Should influence the auditor's accumulation of evidence, no one has
previously attempted to relate these "variables of the audit" to audit
programs in some sort of functional manner. This part of the disserta-
tion has been a first step in that direction -— but only a first step.

The models developed are of a general, abstract nature, clearly not

308
sufficiently Specific to operate as audit program "generators." The
value of the models lies in the fact that they have identified and
placed in perSpective numerous factors which Should affect the au—
ditor's work and have suggested a logical framework for his decision
process in questions of evidence accumulation.
An Empirical Study of the Relative Influence

of Factors which Affect Audit
Evidence Accumulation

 

 

 

The final section of this dissertation reports an empirical study
of the relative influence of factors identified in the previous section
on actual audit evidence accumulation decisions. This research ef-
fort's objective was to determine whether or not a sample of audit
work-papers would reflect any relationship between the composition of
the auditor's evidential collection (the dependent variable) and those
factors identified in Chapters I-V (the independent variables) which:

1. define evidential support functions,

2. determine minimum evidential Support requirements,

3. affect the auditor's risk of sanctions, or

4. constrain the auditor's choice of evidential collection.

To accomplish this objective, the study, based on sample data extracted
from the work-papers for fifty-three clients of seven public accounting
firms, consisted of three sections:

1. a study of factors which affected the selection of audit pro-

cedures in the areas of sales and accounts receivable,

2. a study of factors which affected the timing of audit tests

in the areas of sales and accounts receivable, and

 

 

 

309
3. a Study of factors which affected the sample Size of audit

tests in the areas of sales and accounts receivable.

Because the study faced such obstacles as data confidentiality,
firm conservatism, and the limited resources of a one-man inquiry, cer-
tain procedural weaknesses were inadvertent. Thus, the sample data was
random neither with respect to the participating firms nor the clients
selected and the number of independent variables was relatively large
compared to the number of sample observations. Furthermore, the
methods of Operationalizing certain of the variables (dependent epe_in-
dependent), and of reducing to manageable proportions the study of fac-
tors which affected procedure selection are both open to question. For
these reasons, one must regard the results reported below as merely
tentative and should exercise great caution and Skepticism in attempt-
ing to draw any conclusions from them about the general state of the
art in public accounting.

Factors which Affected the Selection
of Audit Procedures

In this study, multiple discriminant analysis indicated that, for
the clients observed, Generally Accepted Auditing Standards and individ-
ual firm policy were the primary determinants of test selection in the
area of sales. Furthermore, with the possible exception of client in-
ternal check and internal control, none of the other independent vari-
ables selected for this particular study seemed to have any significant
effect on the sample auditors' decisions.

With respect to accounts receivable, on the other hand, the pri-

mary determinant of test selection appeared to be Generally Accepted

 

 

Auditin

this 81

factor

firmeI

size

of th

and I

find
audi

tha

310
Auditing Standards (evidenced by the lack of "optional" procedures in
this area). Additionally, however, the evidence suggested that four
factors largely influenced whether a given receivable would be con-
firmed positively, negatively, or not at all. These factors were the
size of the receivable relative to others in the trial balance, the age
of the receivable, the total number of receivables in the trial balance
and the firm performing the audit.

In a number of respects, the above results corroborate Arens'
findings in an earlier study based on the work-papers for "twenty-eight
audit clients of five different CPA firms."1 Reporting the results of
that study, Arens wrote:

It was clear from a review Of the working papers that

there was a concept of a minimum program for every audit in

the Study. This was demonstrated by the fact that some pro-

cedures were performed for every audit reviewed. . . . In

addition, there were other procedures for each audit area
which were performed for a large portion of the clients.2

He further noted, however, that:

. . . there were substantial differences in the procedures
used by different CPA firms . . . an indication that the
different CPA firms have different concepts about which pro-
cedures are required for an audit . . . [and] that each of
the CPA firms in the Study has some notion of what a minimum
audit program should be . . .3

Finally, although he found that, "in a small number of cases the

internal control system appeared to influence the selection of audit

 

1Alvin A. Arens. "The Adequacy of Audit Evidence Accumulation in
Public Accounting" (Doctoral Thesis, School of Business Administration,
The University of Minnesota, 1970), p. 260.

2Ibid., p. 261.

3Ibid., p. 262.

 

311

procedures,"4 and "materiality had an occasional influence,"5 he con-
cluded that, in general, the "variables of the audit" did not "have a
significant effect on the audit procedures selected for the audit cli-
ents in this study."6

Although all of the above findings agree with the present study,
some disagreement exists with regard to the type of accounts receivable
confirmation selected and the follow-up on non-returned positive con—
firmations. According to Arens, in his Study:

The results indicated that the type of confirmation

and the follow-up on non-returned positive confirmations

by second requests and alternative procedures was dependent

more upon the CPA firms than upon any of the variables of

the audit, but the composition of the population did have
some effect on the type of confirmation used.

In the present Study, on the other hand, evidence indicated that,
although firm policy and population composition continued as the two
primary factors determining the nature of receivable confirmation,
population characteristics appeared somewhat more important. The ev-
idence further indicated that all the firms in the present study per—
formed extensive follow-up procedures on returned as well as unreturned

positive confirmations.

 

"Ibid., p. 263.

5Ibid., p. 264.

6Ibid., p. 263.

7Ibid.

8The fact that Arens' study was performed prior to the issuance
of SAP No. 43 (which made follow—up procedures mandatory whenever the
auditor has unreturned receivables confirmations), while this study is
based on audits subsequent to that pronouncement probably explains this
latter difference in findings.

 

 

312
Factors which Affected the Timing of Audit Tests
Three factors appeared, a priori, likely to have the greatest in-
fluence on auditor decisions concerning the timing parameter of his
evidential accumulation:
1. the quality and comprehensiveness of the client's internal
control,

2. time constraints, and

 

3. Staff constraints.

Since time constraints, generally only occurring in the audits of

 

large publicly—held clients, were effectively controlled out of the Hi"
analysis, the study hypothesized the following general model to explain
the sample auditor's timing decisions with regard to sales tests of
transactions and accounts receivable confirmation:
1. If the client's internal control is inadequate, either due to
a lack of separation of cash-handling and record-keeping
functions, or for some other reason, schedule the appropriate
test(s) at or after the client's year-end regardless of when
that year-end occurs.
2. If the client's internal control is adequate:
a. if the client's fiscal year does not end during the
busy season (operationally defined as December-
February), schedule the appropriate tests at or after
the client's year—end,
b. if the client's fiscal year ends during the busy sea-
son, schedule the appropriate test(s) at an interim

date.

 

313

In both cases, this hypothesized model predicted the sample au-

ditors' timing decision significantly better than chance.

Factors which Affected the Sample
Size of Audit Tests

In this study, multiple linear regression indicated that, for the

clients observed, the firm performing the audit, the client's Size, the

quality of the client's internal control and the distribution of the
client's ownership had the greatest association with the auditor's

sample size decisions in both the areas of sales and accounts receiv-

able.

balance affected the auditor's decision with respect to the smallest

Additionally, evidence indicated that the mean receivable dollar

 

dollar balance receivable considered for confirmation (both positive

and by any means) and the percentage of receivable coverage (both posi-

tive and total).

sions

To some extent, these results corroborate the following conclu-
of Arens' earlier study:

. . . the extent of the sample in accounts receivable de-
pended primarily upon the population size and the CPA per-
forming the audit although the composition of accounts
receivable did have some effect. The other variables of
auditing had no perceptible effect upon the sample size in
confirmation.9

The present results, however, do indicate the influence of several fac-

tors apparently not manifested in Arens' data.

Conclusions

 

The normative framework for audit evidence accumulation decisions

developed in the first two chapters of this dissertation and summarized

 

9Ibid., pp. 263-264.

 

314
above is mathematical in format -- implying that the ideal approach to
such decisions would be quantitative. Unfortunately, few factors rel-
evant to audit evidence accumulation lend themselves to meaningful
quantification. Furthermore, the functions relating such factors to
appropriate parameters in the decision framework are not apt to be well

defined. These practical limitations, however, do not negate the

 

validity of the framework, itself. That the auditor may not be able to IF":
quantify: (1) professional requirements, (2) the risk of sanctions,

(3) evidential support functions, or (4) time, staff and cost consider-

ations does not imply that he ought to ignore them. fig

Whether or not the auditor does, by and large, ignore such con-
siderations is an empirical question. For purposes of discussing this
study's findings on the matter, it is useful to classify factors rel-
evant to audit evidence accumulation decisions into two categories:

(1) constants of the audit (factors which do not vary from client to
client, e.g., Generally Accepted Auditing Standards, firm policies,
and, perhaps available Staff), and (2) variables of the audit (condi-
tions which depend to some extent on the particular client involved,
e.g., the relative materiality of various statement items, quality and
comprehensiveness of the client's internal controls, factors which af-
fect or indicate the auditor's risk of sanctions, etc.).

Both the present study and Arens' earlier work identify certain
procedures performed during all or almost all of the observed audits.10

These findings tend to support a hypothesis that the factors classified

as constants of the audit do affect evidence accumulation decisions to

 

10Supra, pp, 195, 247-48.

 

315

the extent that they define a minimum set of procedures for all engage—
ments. On the other hand, in both studies, individual firm policy ap-
pears to have been a significantly greater cause of differences in
procedure selection and Sample size determination than any of the other
factors considered. This finding suggests, as Arens has noted,11 that
CPA firms do not entirely agree as to which procedures belong in their
minimum set, and further implies that audit evidence accumulation de- “um?
cisions are relatively insensitive to most factors which fall into the

category of variables of the audit.

 

At least two explanations are consistent with both this latter I "ng
conclusion and the normative decision framework discussed above. The ‘
first is Simply that, in general, the practicing public accountant per-
ceives costs of evaluating and incorporating variables of the audit
into his evidence accumulation decisions greater than costs of over- or
underauditing which may result from ignoring such variables in favor of
a Standard audit program.'

Perhaps a more satisfying explanation, however, is that the aur
ditor does consider at least some of the variables, such as materiality,
quality of internal control, client liquidity, leverage, etc., but

treats them as dichotomies rather than continuous variables. In other

 

 

words, he evaluates a statement item as either material or immaterial,
client internal control as either adequate or inadequate, client 1i-
quidity and leverage as either tolerable or intolerable, etc., but
makes little or no attempt to measure relative differences beyond these

dichotomies.

 

11Arens, pp. 262, 263.

316

If public accountants treat variables of the audit as dichoto-
mies, they are apt to perceive less difference among clients (espe-
cially of similar size and nature of Operations) and, as a result,
their audit programs are apt to exhibit less variation than if they
evaluated such factors along a continuum. In this case the relatively
small and perhaps homogeneous12 samples, as well as the somewhat unso-
phisticated analytical techniques employed, may have denied both the
present study and that of Arens sufficient sensitivity to detect such
relationships between audit variables and evidence accumulation deci-

sions as may have actually existed.

Suggestions for Further Research

 

AS is generally the case where human behavior is involved, two
avenues exist along which one might conduct research in the area of
audit evidence accumulation-descriptive study and normative Study.

The purpose of descriptive research is simply to explain or de-
scribe actual behavior. In the area of audit evidence accumulation,
appropriate objectives for this type of study would appear to include:

1. identifying the manner in which public accountants subdivide

an audit (into audit areas, Specific financial statement
assertions, etc.) for the purpose of determining evidence re-
quirements, and identifying the Specific set of financial

statement assertions they attempt to evaluate,

 

2Homogeneous in the sense that the sample auditors may not have
perceived the differences in variables of the audit as significant from
observation to observation.

 

 

317
identifying the factors which public accountants consider
when constructing an audit program (i.e., the independent
variables in their evidence accumulation decision model), and
identifying these factors' relative influence and Specific
effects on audit program development (i.e., the functions in

the auditor's evidence accumulation model).

In contrast to the purpose of descriptive research, the function

of normative research is to identify or define an ideal. Appropriate

objectives for this type of study in the area of audit evidence accumu-

lation would appear to include:

1.

identifying the optimal manner (from a cost-benefit stand—
point) of subdividing an audit (into audit areas, financial
statement assertions, etc.) for the purpose of determining
evidence requirements,

identifying all the assertions generally contained in a set
of financial statements,

identifying all factors relevant to audit evidence accumula-
tion decisions,

identifying the relative influence and specific effects such
factors should have on audit evidence accumulation, which, in
turn, requires:

a. development of methods for measuring such factors as
well as guidelines for relating them to evidence ac-
cumulation decisions,

b. ~determination of the costs and benefits of measuring

such factors with varying degrees of precision and of

 

 

318
incorporating them into audit evidence accumulation
decisions, and
c. a study of the sanctions an auditor may receive for
failing to detect material error which exists in his
client's statements, factors which may indicate the
auditor's risk of incurring such sanctions, and the
cost of sanctions if incurred,
5. defining more precisely the relationship between evidential
matter and evidential support, and
6. defining a "minimum" set of audit procedures to be performed
for all engagements where the relevant financial statement
assertion is material -- regardless of the Status of other

audit variables.

Generally speaking, research in the area of audit evidence ac-
cumulation has been scarce. On the descriptive side, both the present
study and that of Arens have attempted to identify factors which public
accountants consider when constructing an audit program, as well as the
relative influence and specific effect of such factors. On the norma-
tive side, these same two studies have also attempted to identify the
factors relevant to audit evidence accumulation decisions and the rela-
tive influence and specific effect such factors should have. Anderson,
Giese and Booker have also identified a number of factors relevant to
evidence accumulation decisions.13 Along somewhat different lines, for

selected audit areas, Arens has provided a comprehensive list of

 

13H. M. Anderson, J. W. Giese, and Jan Booker, "Some Propositions

about Auditing," The Accounting Review 45 (July 1970): 524-31.

 

 

 

319
financial statement assertions (as well as the audit procedures rel-
evant to their evaluation), and, for some areas, has even gone SO far
as to suggest "minimum" procedures. Finally, a number of authors have
discoursed on the relationship between evidential matter and evidential
support.1"

Undoubtedly, there have been other studies in the area of audit
evidence accumulation. NO research effort, however, appears to have
been of sufficient scope and depth to rank as definitive. Thus, for
someone interested in this area, considerable opportunity would appear

to exist for both original and worthwhile research into any or all of

the topics mentioned above.

 

14Cf. Arens, pp. 106-22; R. K. Mautz, "The Nature and Reliability

of Audit Evidence," The Journal of Accountaney 105 (May 1958): 40-47;
Howard F. Stettler, "Auditing Standards and Competence of Evidential
Matter," The Accountingzgeview 29 (January 1954): 121-26; Floyd W.
Windal, "Standards of Reliability for Audit Evidence," The New York
Certified Public Accountant 31 (June 1961): 394-400.

 

 

 

 

 

 

 

LIST OF REFERENCES

LIST OF REFERENCES

Anderson, H. M.; Giese, J. W.; and Booker, Jon. "Some Propositions
about Auditing." The Accounting Review, 45 (July, 1970), 524-31.

 

Anderson, T. W. An Introduction to Multivariate Statistical Analysis.
New York: John Wiley and Sons, Inc., 1958.

 

Arens, Alvin A. "The Adequacy of Audit Evidence Accumulation in Public
Accounting." Doctoral Thesis, School of Business Administration,
University of Minnesota, 1970.

Arkin, Herbert. Handbook of Sampling_ior Auditing and Accounting.
New York: McGraw-Hill Book Company, Inc., 1963.

 

Clark, Charles T., and Schkade, Lawrence L. Statistical Methods for
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Committee on Auditing Procedure, American Institute of Certified Public
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Committee on Concepts and Standards Underlying Corporate Financial
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Dixon, W. J., ed. BMD Biomedical Computer Programs. University of
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Fryer, H. C. Concepts and Methods of Experimental Statistics. Boston:
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Grinaker, Robert L. "The Accountant's Responsibility in Expressing an
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Hill, Gordon M., and Jennings, Alvin R. "Extensions of Auditing Pro-
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1953), 337-41.

320

 

321

Johnson, Richard E., and Kiokemeister, Fred L. Calculus. Boston:
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Lachenbruch, P. A., and Mickey, M. R. "Estimation of Error Rates in
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Leight, Lester A. "Recommended Opinions and Disclaimers." The New
York Certified Public Accountant, 33 (June, 1963), 408-12.

 

"Materiality." The Journal of Accountaney, 117 (April, 1964), 35-36.

Mautz, R. K. "Evidence, Judgment, and the Auditor's Opinion." The
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. "The Nature and Reliability of Audit Evidence." The Journal
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, and Mini, Donald L. "Internal Control Evaluation and Audit
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, and Sharaf, Hussein A. The Philosophy Of Auditipg. Menasha,
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Mosteller, Frederick, and Bush, Robert R. "Selected Quantitative
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Rafter, Mary E., and Ruble, William L. Stat Series Description No. 81
LSDEL -- Stepwise Deletion of Variables from a Least Squares

Equation. East Lansing: Michigan State University Agricultural
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Rao, C. R. Advanced Statistical Methods in Biometric Research. New
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Ray, J. C. "Classification of Audit Evidence." The Journal of Account-
ancy, 117 (March, 1964), 42-47.

 

Ruble, William L.; Keil, Donald; and Rafter, Mary E. STAT Series De-
scription No. 7, LS -- Calculation of Least Squares (Regression)
Problems on the LS Routine. East Lansing: Michigan State Uni-
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Stettler, Howard F. "Auditing Standards and Competence of Evidential
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322

Study Group on Audit Techniques, Canadian Institute of Chartered
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stitute of Chartered Accountants, 1965.

 

Windal, Floyd W. "Standards of Reliability for Audit Evidence." The
New York Certified Public Accountant, 31 (June, 1961), 394-400.

 

'_ _! III "Pq-‘ng

 

 

      

  

   

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