UTILIZATION OF CASE-BASED REASONING IN AUDITING
Determining the Audit Fee
Robert Zenzerović
Faculty of Economics and Tourism “Mijo Mirković, PhD” Pula,Universit of Rijeka, Preradovićeva 1/1, Pula, Croatia
Keywords: Audit fee, case-based reasoning, decision making.
Abstract: Case-based reasoning represents a method for solving problems and decision making support which is based
on the previous business experience. It uses cases from the past to solve new problems. Case can be defined
as conceptualized piece of knowledge representing the experience that teaches a lesson fundamental to
achieving the goals of the decision maker and it usually incorporate input (situation part of the case) and
output features (solution part of the case). Many studies tried to explain types and impact of different factors
that determine audit fees. Mostly all authors concentrate their research on the impact of following
determinants: auditee size, auditee complexity, auditee profitability, ownership control, timing variables,
auditor location and auditor size. In paper all mentioned factors are described except auditor size and
location since these factors are not significant in Croatian audit service market. All significant audit fee
determinants will be appropriately quantified in order to build a case-based reasoning model for determining
audit fee for smaller and mid sized auditing firms in Croatia but also for the same firms in the other,
particularly transition, countries too.
1 INTRODUCTION
The transitional period in Croatia started at the
beginning of nineties. In that time social ownership
left its place to private owned companies what
meant that the financial statement auditing will
become obliged very soon. Couple of years later,
precisely in 1993., The Accounting and Auditing
Acts were brought. According to The Accounting
Act all big companies, and medium companies
1
if
they are organized as joint stock companies, have to
audit their financial statements once a year. Once in
a tree years small companies, if they are organized
as a joint stock companies, have to make the review
of financial statements. Other companies don’t have
a legal obligation to audit financial statements but
they sometimes do that because of creditors
requesting. Considering the fact that Croatia is still
transitional economy, Croatian companies are
looking on auditing mainly as a legal obligation
which has to be fulfilled. According to mentioned
they are looking for auditing firms which will offer
1
Company size is measured by their assets, revenues
and number of employees according to the
Accounting Act.
the lowest price for performing financial statement
audit.
Today, in Croatian audit market operate about
200 audit firms. During the past 11 years the
competition on audit service market was strong
mainly because many of small auditing firms were
founded. Like in other countries most of banks and
biggest companies are audited by “Big four”
2
auditing firms. Other companies are audited by
smaller auditing firms and the competition is
particularly strong in this segment of audit market.
This “non big four” auditing firms are faced with
problem of determining the audit fee when
competing for new client. During informal
interviews with audit partners in smaller and
medium size auditing firms it was found that
problem of determining the audit fee when bidding
for new clients often occurs. The motivation of this
article is to develop a model based on case-base
reasoning which can be useful for smaller and
medium size auditing firms when biding for a new
client. Article is structured in the following way: at
the start the characteristics of case-based reasoning
are explained after what determinants of audit fee
are described. Application of case-base reasoning
2
Deloitte & Touche, Ernst & Young, KPMG and
PriceWaterhouseCoopers
182
Zenzerovi
´
c R. (2006).
UTILIZATION OF CASE-BASED REASONING IN AUDITING - Determining the Audit Fee.
In Proceedings of the Eighth International Conference on Enterprise Information Systems - AIDSS, pages 182-188
DOI: 10.5220/0002439301820188
Copyright
c
 SciTePress

model in auditing when determining the audit fee is
explained at the end.
2 CASE-BASED REASONING
During the last decade different methods of
transforming data into business intelligence have
emerged. Information systems like OLAP systems,
rule based systems, case-based reasoning, neural
networks, fuzzy logic has found different
applications in management, auditing, finance and
many other areas as a very helpful management
tools. Case-based reasoning represents a method for
solving problems and decision making support
which is based on the previous business experience.
It uses cases from the past to solve new problems.
These types of decision making systems are based
on the fact that in many cases a new problem is
partly known to decision maker because it often
reflects situations experienced in the past. Therefore,
if problem was successfully solved in the past the
same experience can be used to solve the current
problem. Otherwise, if solution of an old problem
was inappropriate than that kind of solution should
be avoided in the current problem. As the main
advantages of case-based reasoning systems
following could be pointed out:
1. it solves problem quickly by retrieving
similar cases, rather than generate solutions
from the scratch,
2. it can solve problems in domains that are
not understood completely
3. it can remember past mistakes and warn
users not to repeat these mistakes
4. it can use past cases to determine which
parts of a problem to focus on
5. it can create justification for proposed
solution by comparing and contrasting new
problem with the old problem (Morris,
2002., p. 1).
First step in case-based reasoning process is
introduction of a new problem which has to be
solved. The problem is represented as a target case
which consists of features that describes the situation
decision maker is interested in matching. When
solving a new problem case-based reasoning system
firstly finds similar case from the past. After that
system adjust old solution and for any difference
between old and new case, and provide solution for
the new problem. At the end system stores the new
case and its solution into data base, from which it
can be retrieved and used in solving the future
problems.
Central point in the system represents cases.
Case is conceptualized piece of knowledge
representing the experience that teaches a lesson
fundamental to achieving the goals of the decision
maker. Cases have to be represented in a way which
enables effective usage by the reasoner. They
usually incorporate input feature and output feature.
Input feature represent important attributes of cases
that effect decision making. Some authors point out
that input features form so called situation part of the
case (Dhar, Stein, 1997., p. 151). Before entering
cases into case base it is important that input features
names and values are defined. Input features value
can take different forms, like numeric value, yes or
no value, text value, etc. On the other hand output
features describe solution part of the problem.
Once, when target case is inputted in the system
with its input features, case-based reasoning system
has to retrieve the most similar cases from the case
base. Retrieving case from the case base represents a
very important step in the case-based reasoning
working cycle. Retrieval of relevant cases depends
on indexing of cases. The easiest way to do indexing
is to a priori set important features for the problem
solution. That set of selected features represents a
probe that is sent in the case base in order to find
similar cases, cases which have selected features.
In order to do match and retrieval of the similar
cases from the case base there must be used some
similarity assessment method because decision
maker should not expect perfect match (in most
situation values of the selected features for old and
new case will not be the same). Therefore, it is
necessary to define some similarity metrics. An
example of such metrics is nearest neighbor method
which works well in situations where features have
numerical value. After the most similar case is
retrieved from the case base it can be used for
finding interesting information and after that
reasoner can adjust and send a new probe with
different features for retrieving of new case. On the
other hand case-based reasoning system can be
designed to make automatic adjustments in solution
part of the case on the base of differences in
situation part of the cases, providing the solution for
the new case.
Case-based reasoning process is illustrated in
Figure 1 where case-based reasoning steps are
shown (Hwang, Shin, Han, 2004., p. 25.).
UTILIZATION OF CASE-BASED REASONING IN AUDITING - Determining the Audit Fee
183

Figure 1: Case-based reasoning process.
Case-based reasoning systems have different
areas of business applications. According to some
authors until 1997 there was developed more than
100 CBR systems (Lopez de Mantaras, Plaza, 1997.,
p. 21). As an example of using case-based reasoning
in auditing, system called SCAN is developed in
order to provide audit recommendations (Morris,
2002., p. 10 - 11).
3 DETERMINANTS OF AUDIT
FEES
Many authors tried to explain types and impact of
different factors that determine audit fees. They
found that the same factors have different impact
depending on the size of audit service market and
the impact of some of them is not precisely known.
But mostly all of them concentrate on researching
the impact of following audit fee determinants:
auditee size, auditee complexity, auditee
profitability, ownership control, timing variables,
auditor location and auditor size. Each determinant
is explained except auditor size considering the fact
that the article is focused on developing the case-
based reasoning model for determining audit fee for
non big four firms so the size of auditor is not
important. Auditor location is not considered too
according to fact that it is the determinant which
depends on characteristics of each audit services
market. For example, in United Kingdom auditor
location is important variable because audit staff
costs are higher in Southeast than in other region
while in Croatia, and in most transitional countries,
there is no significant difference between regions.
This determinant can be used in other countries
depending on the characteristics of their audit
services market.
3.1 Auditee Size
Researches have found that auditee size is the most
significant explanatory variable in determining audit
fee. Auditee size can be measured by total assets and
by total revenues. Most of researches used total
assets as measure of auditee size and it is suitable
particularly when audit approach is balance sheet
based. Factors like the age profile of assets and
chosen accounting policy can make the total assets
measure different between similar companies.
Auditee size measured by total revenues is better
approach when auditor has a transaction based
approach to the audit. For building the model total
revenues will be used as the measure of auditee size.
When considering the relationship between auditee
size and auditor fee it must be noticed that it is not
linear. The studies have shown that proportionate
increase in audit fee is decreasing function of
auditee size what can be explained by presumption
that the bigger the auditee is the strongest internal
control procedures it will have. This relationship is
represented in the Figure 2.
Figure 2: Relationship between audit fee and auditee size.
3.2 Auditee Complexity
When auditing complex companies auditors are
faced with much more work to be done. Complex
companies are considered those with many
subsidiaries, dislocated business units, companies
with big numbers of unusual transactions, and
different internal controls, companies with particular
balance sheet composition and companies that have
subsidiaries which are operating in different
branches. They deserve much more attention and
request much more time when auditing what usually
result in higher audit fee. When auditing companies
with many subsidiaries auditor has to charge higher
fee because he or she has to audit separate financial
statements and if the subsidiaries are situated in
foreign country costs became even higher. Auditor
has to pay attention on intra-group transactions,
Audit fee
Auditee size
Feature Indexing
Feature
weighting
Adaptation Rule
New Problem
Indexing Cases
Case Retrieval
Case Adaptation
Solution
Knowledge Base
Case
Indexes
Case
Base
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taxation and pricing policies. If the subsidiaries are
operating in different branches (the business is
diversified) auditor has to get specific knowledge
about business and the costs became higher again.
Diversification can be measured by Herfindahl index
∑
=
=
n
i
i
SH
1
2
(1)
where S
i
represent turnover of the i-th segment as a
proportion of total revenue of the auditee. Dislocated
business units have influence on price too. Auditor
has to visit all those locations what usually make
audit more expensive. Big numbers of unusual
transactions and complex system of internal controls
takes more time for testing and put the pressure on
costs too. Companies with particular balance sheet
composition include companies which have big
proportion of inventory and debtors in total assets.
Mentioned items are more difficult to audit then for
example cash or fixed assets and it can result in
higher fee. For building model the complexity will
be represented by scale from 0 to 10 where 0 means
low complexity of auditee and 10 very complex
companies. Auditor usually makes estimation on
complexity considering the factors like: number of
subsidiaries, location of subsidiaries and business
units, Herfindahl index which measure
diversification, number of different branches in
which company is operating, and two ratios:
inventory/total assets and debtors/total assets.
3.3 Auditee Profitability
The impact of auditee profitability on audit fee is
more important when auditee is facing financial
problems than when it is generating profit. Auditee
profitability may cause changes in audit fee in two
ways. When auditee has financial problems it is
trying to control all overhead costs which might
result in lower fee. But on the other hand, financial
distresses put in front of auditor need to focus more
directly on valuation of assets, the status of a auditee
as a going concern, possible breaches of loan
covenants etc. what may rise the audit fee. In
building the model return on equity (ROE) will be
used as a ratio which represents auditee profitability.
3.4 Ownership Control
Development of financial statements audit is the
result of divorcement between ownership and
control (management) of the company. Diverse
ownership structure requires more extensive and
higher quality audit than in the case of auditee
owned by only couple of shareholders with
relatively high shareholdings so it is logical to
expect that the extent of audit services demanded
will be a function of ownership control which will
be measured by the number of shareholders.
3.5 Timing Variables
Auditing is a quite seasonable activity with busy
season which start at January and lasts till June.
Auditors often charge a premium for performing
audit in this period of year what can be a result of
shifting the audit emphasis to pre year end testing
with higher audit costs or auditor has to engage new
human resources. Another timing variable is auditee
request for audit report i.e. time which past from the
end of accounting year to the date of audit report.
Shorter the period is the audit fee is expected to be
higher as it is possible that auditor has to engage
new work force to audit financial statements. For
building a model it will be used the period from the
end of accounting year to the issuance date of audit
report measured by number of weeks.
4 DESIGNING THE CBR MODEL
FOR DETERMINING THE
AUDIT FEE
In order to design case-based reasoning model it is
necessary to define feature names and values at the
start. In order to keep model simple and easy for
understanding six features shown in Table 1 are
used. It should be pointed out that first five features
represent input features or situation part of the case
and the last feature (audit fee) represents output
feature or solution part of the case. On the basis of
the previous experience and business data it is
necessary to build data base that will contain cases
from the past. The easiest way to build such data
base is to find records on all the clients from the
past. After that for each client feature values must be
determined and inputted into the data base (case
base). On the basis of such approach in building data
base it will be assumed that the data shown in Table
2 is included into data base of auditing firm.
UTILIZATION OF CASE-BASED REASONING IN AUDITING - Determining the Audit Fee
185

Table 1: Features and their characteristics.
Feature Type Measurement unit Feature value span
Auditee size - Revenue Numerical Money units (MU) 0 - 100.000.000
Auditee complexity Numerical Number 0 - 10
Auditee profitability - ROE Numerical Number -0,5 - 0,5
Number of owners Numerical Number 1 - 500
Timing variable - Weeks Numerical Number 5 - 25
Audit fee Numerical Money units (MU) 10.000 - 100.000
Table 2: Model of case-based reasoning data base.
Case Size (MU) Complexity Profitability Ownership Time Fee (MU)
A 18.000.000 2 0,47 8 23 2.890
B 28.000.000 3 0,21 2 14 4.475
C 31.500.000 3 0,19 9 25 6.000
D 37.900.000 2 0,31 5 8 18.700
E 56.700.000 4 -0,02 35 7 19.870
F 69.900.000 7 -0,05 78 17 53.290
Table 3: Probe input features for the clients X, Y and Z.
Features Probe case -new
client Size (MU) Complexity Profitability Owners Time
x 21.900.000 3 0,17 3 7
y 42.970.000 5 0,21 13 18
z 62.700.000 7 0,35 29 9
In the situation when a new client is analyzed in
order to determine auditing fee, case-based
reasoning model requires setting up a probe that is
send to data base. It should contain values of
relevant input features in order to find the most
similar case in the data base. It can be assumed that
potentially new clients have the features presented in
Table 3.
On the basis of the send probe into the data base
the case-based reasoning system will find the most
similar case using similarity metrics. For the
simplicity of the model nearest neighbor method is
used. It calculates the geometric distance between
probe and the all cases from the base. Geometric
distance (GD) for each feature can be defined by the
following formula:
()
2
2
probecaseoldGD −= (2)
After geometrical distance is calculated for each
feature j case-based reasoning system must calculate
total geometrical distance (TGD) for each old case i
and each feature j. Total geometrical distance can be
calculated, by using the following formula (Babić,
1997., p. 42):
() []
2
n
1j
2
iji
probecaseoldwTGD
∑
=
−= (3)
Where j represents feature (j= 1…n) and i old case
(i=1...m).
For the simplicity of this paper it will be assumed
that all features have the same importance and
weights (w) of features can be excluded from the
calculations. But if reasoner is not valuing all
features by the same importance than a priori
features weights have to be defined. Research of
importance of each audit fee determinant is opened
and some results can be potentially useful in
improving this model. Since calculation of total
geometrical distance requires adding geometrical
distances of each feature arises the problem of
different measurement scales of features. In order to
deal with that problem all values in data base must
be normalized. Among different approaches of
normalization so called vector normalization will be
used. Vector normalization procedure requires that
each feature value must be divided by the feature
norm. Normalized values r
ij
are calculated from
original values x
ij
by using the following formula
(Babić, 1997., p. 24):
2
2
ij
ij
ij
X
x
r
∑
= (4)
Normalized data calculated on the basis of the
previous formula and original data from the Table 2.
are presented in the Table 4.
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186

Table 4: Model of normalized case-based reasoning data base.
Case Size Complexity Profitability Ownership Time
A 0,170370 0,179605 0,504183 0,162255 0,564003
B 0,265020 0,269408 0,225273 0,040564 0,343306
C 0,298147 0,269408 0,203819 0,182537 0,613047
D 0,358723 0,179605 0,332546 0,101409 0,196175
E 0,536665 0,359211 -0,021455 0,709865 0,171653
F 0,661603 0,628619 -0,053636 1,581984 0,416872
x 0,207283 0,269408 0,182364 0,060846 0,171653
y 0,406711 0,449013 0,225273 0,263664 0,441394
z 0,593455 0,628619 0,375455 0,588174 0,220697
In the case of clients X, Y and Z case-based
reasoning system would calculate the total
geometrical distance scores for each old case which
are presented in Table 5.
Table 5: Total geometrical distance scores.
Case TGD for x TGD for y TGD for z
A 0,526514 0,481191 0,834537
B 0,187219 0,334259 0,757870
C 0,467284 0,283815 0,751118
D 0,236220 0,415752 0,704340
E 0,761134 0,598065 0,500557
F 1,662868 1,383325 1,102228
On the basis of all previous calculations and
usage of nearest neighbor method based on the
geometrical distances case-based reasoning system
would finish matching procedure finding that the
most similar case in comparison to client X is old
case B. Namely, old case B has the smallest total
geometrical distance score (0,187219). On the basis
of such finding reasoner would check data base and
find that auditing fee for old client B is 4.475 MU.
Therefore, amount of 4.475 MU represents starting
point in establishing the final fee for the new client
X. In the same way one can notice that the most
similar cases to clients Y and Z are cases C and E.
According to audit fee charged for cases C and E
reasoner is able to conclude that the starting point
for making decision on audit fee for client Y is 6.000
MU, and for client Z 19.870 MU. In the more
advanced mode of working, case-based reasoning
system for determining audit fee might take into
consideration
differences among cases B and X input features in
order to make adjustments to the solution part of the
problem, i.e. audit fee amount, or the auditor can
adjust audit fee according to his previous
experience.
5 CONCLUDING REMARKS
Case base reasoning, as a method for solving
problems and decision making support based on the
previous business experience, can be useful
instrument in making decision about audit fee. New
problems often are not completely new but consist
of situations which are partly known to decision
makers and in that sense case-based reasoning can
be very helpful tool. The advantages of case-based
reasoning, like velocity in solving problems by
retrieving similar cases, simplicity, solving problems
in domains that are not understood completely and
remembering past mistakes and warning users not to
repeat these mistakes, resulted in use of case base
reasoning systems in different area of business
applications like bank lending, employee tax status,
audit recommendations etc. In order to be accurate
and flexible this method, which transform data into
business intelligence, depends on the number and
diversity of cases stored in the case base. The
probability that the new problem will be
appropriately solved would be higher if the case-
based reasoning model has more cases.
In this paper case base reasoning model was built
using the most important audit fee determinants -
auditee size, auditee complexity, auditee
profitability, ownership control and timing variable.
All these determinants (input features) combined
with appropriate audit fee which has been charged in
the past (output feature) represent a case stored in a
case base. Problem of determining audit fee to the
potentially new client case-based reasoning model is
able to solve by finding a similar case with similar
input features and suggesting the audit fee that can
be charged. In order to find adequate case in case
base, model use similarity assessment method called
nearest neighbor method. Considering the fact that
all input features have the same weights the future
work can be focused on estimating the weights for
each feature and finding new features i.e. audit fee
UTILIZATION OF CASE-BASED REASONING IN AUDITING - Determining the Audit Fee
187

determinants. Perfect matching of old cases and new
problem usually does not occur so there can be used
different methods for making adjustments to audit
fee considering the differences among input features
of old and new case what can be used for improving
the model in the future work. On the other hand, the
auditor can decide to make adjustments to audit fee
according to his previous experience. The key
accuracy factor of this model is appropriate case
base. More cases it has, more accurate the solution
i.e. audit fee will be. This model can be useful for
small and medium size auditing firms in competing
for new clients as a guideline for making decision on
audit fee. Its implementation and theoretical
development will probably result in different
improvements which will be helpful for auditors in
making more precise decisions.
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