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OR Spectrum (2011) 33:265–285
DOI 10.1007/s00291-010-0221-4
REGULAR ARTICLE
An overlooked effect of mandatory audit–firm rotation
on investigation strategies
Wuchun Chi
Published online: 1 July 2010
© Springer-Verlag 2010
Abstract Section 207 of the Sarbanes–Oxley Act of 2002 (hereafter, the SOX Act)
passed by the US Congress requires a study of mandatory auditor rotation of regis-
tered public accounting firms. In the debate over the costs and benefits of mandatory
audit–firm rotation, one cost has been overlooked: that of more aggressive monitor-
ing. Because few countries have put such mandatory rotation into practice, there is
little empirical evidence available for analysis of its costs and benefits. My research,
therefore, uses an analytical approach to demonstrate that, in a firm that has a well-
functioning independent board, as required by section 301 of the SOX Act, the board
will adopt a more aggressive strategy in investigating the collusion between the man-
ager and the auditor and pay a higher audit fee than it would have done in an envi-
ronment with no audit–firm rotation requirement. The results of this research alter the
balance between the costs and benefits of a mandatory audit–firm rotation requirement
and should not be ignored by regulators considering implementing such a requirement.
Keywords Sarbanes–Oxley Act · Audit–firm rotation · Audit fees ·
Investigation strategy
1 Introduction
Recent scandals involving accounting irregularities have damaged the credibility of
accounting audits. In an attempt to help restore this lost credibility, the US Congress
passed the Sarbanes–Oxley Act of 2002 (hereafter the SOX Act). Section 203 of this
act mandates audit–partner rotation, and section 207 requires a study of mandatory
W. Chi (
B
)


National Chengchi University, 64, Zhi-nan Road, Section 2,
Wenshan, 11623 Taipei, Taiwan, Republic of China
e-mail:
123
266 W. Chi
rotation of registered public accounting firms.
1
This research aims to contribute to
such study by uncovering and examining an overlooked cost of mandatory audit–firm
rotation.
Such an examination, if properly conducted, cannot focus solely on section 207 of
the act. It must also consider other requirements imposed by this legislation, including
higher standards for the makeup and role of the independent audit committee (section
301). Such joint requirements complicate the analysis of any effects of mandatory
rotation, for they mandate additional changes to which those effects might also be
attributed. Of particular note when considering section 301 is the possibility that man-
datory rotation actually hamstrings the board by preventing it from rewarding good
audits by retaining a well-performing auditing firm.
2
Another complication of this study is the lack of relevant data. Because few coun-
tries have put such mandatory rotation into practice, there is little empirical evidence
available for analysis of its costs and benefits. My research, therefore, uses an analyt-
ical approach to examine the economic costs of mandatory rotation in a setting that
also includes an independent audit board or committee.
The traditional view of auditor rotation involves a tradeoff between the benefits and
drawbacks of familiarity. This paper does not enter this debate, but rather provides an
analysis of certain drawbacks that have gone unnoticed but should be considered in
future debates on auditor rotation. One side of the traditional view of rotation holds that
familiarity with clients is crucial to produce greater understanding and an improved
ability to identify and evaluate risks for clients and that rotation limits an auditor’s

ability to develop such an understanding and ability. On the other hand, some auditing
professionals also recognize that over-familiarity may be a significant threat to audi-
tor independence. The potential impairment of auditor independence constitutes the
basic reason for requiring audit–partner and/or audit–firm rotation. In addition, new
auditors, an inevitable consequence of auditor rotation, may provide a fresh, unjaded
view of the firm during the audit process.
The SOX Act reflects these traditional views. Specifically, section 203 of the SOX
Act treats audit services as unlawful if the lead or the coordinating audit partner
provides services for five consecutive years to a certain client. In addition, section
207 of the SOX Act requires the Comptroller General to conduct a study to exam-
ine the potential effects of the mandatory rotation requirement on registered public
accounting firms within one year of the passage of the SOX Act. One can say that
section 207 suggests that mandatory audit–firm rotation may be an effective means
of restoring the credibility of the audit function. This paper examines this suggestion
1
In general, there are two types of auditor rotation: audit–partner rotation and audit–firm r otation. Since
the SOX Act has already enforced audit–partner rotation in section 203 but merely calls for the study of
audit–firm rotation, this paper focuses on audit–firm rotation. For simplicity, in this article, “mandatory rota-
tion” refers to audit–firm rotation rather than to audit–partner rotation. Following the requirements of SOX
207, the Government Accountability Office (formerly the Government Accounting Office) is responsible
for studying the effectiveness and implications of audit firm rotation.
2
The idea of mandatory auditor rotation existed prior to recent reforms. In fact, the Report of the
Commission on Auditors’ Responsibilities (The Cohen Commission) (1978) recommended mandatory
rotation. The Cohen Report reasons that “[s]ince the tenure of the independent auditor would be limited,
the auditor’s incentive for resisting pressure from management would be increased” (p. 108).
123
An overlooked effect of mandatory audit–firm rotation 267
by focusing on the economic costs of mandatory audit–firm rotation while taking into
account the enhanced role of an independent board (or an independent audit com-

mittee), which is required by section 301 of the SOX Act, which addresses board
effectiveness.
Stressing the idea that the audit committee plays an active role in corporate gov-
ernance and acknowledging that there exists a potential for side payments to audi-
tors from managers (Lee and Gu 1998),
3
I analytically examine the effectiveness of
implementing mandatory audit–firm r otation. Although conventional wisdom sug-
gests that requiring mandatory rotation will enhance auditor independence, this study
suggests that the mandatory audit–firm rotation requirement is likely to make the
audit committee adopt a more aggressive investigation strategy to examine the possi-
bility of collusion between the manager and the auditor as well as pay a higher audit
fee. Therefore, the mandatory audit–firm rotation requirement creates a cost burden
to the firm, namely an extra audit fee payment and a higher monitoring cost due
to a more aggressive anti-collusion strategy. The conclusion of this study runs con-
trary to the conventional perspective that treats the mandatory rotation requirement
as a means to enhance audit effectiveness and, in turn, improve the quality of finan-
cial reporting. This conventional perspective ignores the existence of an independent
audit committee that is mandated by section 301. Such an independent audit com-
mittee represents the interests of shareholders and helps ensure the objectivity of the
audit process by decreasing the possibility of collusion between management and
auditor—the very possibility that auditor rotation is supposed to guard against. Such a
functional redundancy would not necessarily be a drawback of auditor rotation, but in
fact this rotation does have a cost: the elimination of an incentive to the auditor. The
board can no longer reward good performance—which would include the avoidance
of collusion with management—by continuing to hire the auditor, so the incentive for
such collusion is actually increased. By failing to consider the role of the board (or
audit committee) in providing incentive and reducing collusion, prior literature has
assumed that auditor rotation can only increase auditor independence, not decrease it.
When we consider the possibility of such a drop in auditor independence, however,

3
Although manager–auditor side payments were generally prohibited even before the SOX Act, Lee and
Gu (1998) indicate that side payments could take several forms, some of which were prima facie legal (e.g.,
the auditor might be appointed by the manager on behalf of the shareholders and the manager could use
the appointment itself as a side payment to sway the auditor) and some of which might be legally justified
(e.g., granting the auditor with consulting contracts). Generally, preventing or detecting side payments can
be legally difficult and expensive. See Footnote 5 (p. 536) of Lee and Gu (1998) for a detailed discussion
of potential side payments between the manager and the auditor. The SOX Act of 2002 has added more
restrictions on such side payments, prohibiting, for example, most types of consulting and the hiring of
former auditors by the audited firms within a year of the audit(United States Code 2002). A public account-
ing firm can, however, still perform non-auditing services, such as tax services. Some recent studies provide
circumstantial evidence that tax services can be a channel for side payments. Dhaliwa et al. (2004), for
example, find that changes in effective tax rates (ETR) between the third and fourth quarters are related
to efforts toward earnings management. Omer et al. (2006) further find that one-year-ahead marginal tax
rate and ETR reductions are associated with higher tax-service fees paid to the audit firms. Although this
evidence is not definitive, it suggests that, despite the provisions of the SOX Act, there may exist channels
for managers to deliver side payments to auditors.
123
268 W. Chi
the costs of auditor rotation in the context of an independent audit committee become
clear.
The remainder of the paper is organized as follows. Section 2 reviews the debate
on auditor independence, tenure, and mandatory rotation. Section 3 describes the audit
pricing model and the investigation strategy of the audit committee in
non-rotation-required and rotation-required environments. Section 4 discusses the
solution and explains the economic consequences of mandatory rotation. I present
concluding remarks in Sect. 5.
2 The debate
Since independence is the cornerstone of the auditing function, both legislators and
financial statement users are highly concerned with this issue. To reduce the potential

threat to auditor independence, proponents of mandatory rotation express the belief
that poor quality of financial statements is associated with extended auditor tenure. For
example, in July 2003, the International Federation of Accountants (IFAC) issued a
report, Rebuilding Public Confidence in Financial Reporting, in which it treats exces-
sive familiarity as potentially resulting in auditors’ complacency or hesitancy to chal-
lenge appropriately, thereby reducing the level of skepticism necessary for an effective
audit (International Federation of Accountants (IFAC) 2003). Louwers (1998) found
that the length of the auditor–client relationship affects auditors’ propensity to issue
a going-concern disclosure to a distressed client. Hence, proponents of rotation sug-
gest that it could significantly improve the overall quality of an audit and enhance the
quality of the financial reporting process (e.g., Imhoff 2003; Dopuch et al. 2001).
However, the existence of a well-functioning independent board (or an indepen-
dent audit committee), such as required by section 301 of the SOX Act, may render
those arguments invalid. The independent board or audit committee represents the
interests of shareholders, particularly by ensuring the objectivity of the audit process.
International Federation of Accountants (IFAC) (2003) also believes that the audit
committee needs to interact directly and, at times, forcefully with both management
and auditors in areas that in the past have been largely handled outside the commit-
tee.
4
In prior literature, discussions on the function of audit committees (e.g., Booth
et al. 2002; Klein 2002) and the effectiveness of mandatory rotation (e.g., Arrunada
and Paz-Ares 1997; Catanach and Walker 1999; Dopuch et al. 2001) have generally
been treated as independent issues. However, the effectiveness of mandatory rotation
in improving the quality of financial statements is directly influenced by the func-
tion of the audit committee, since this committee is closely involved in the process
of preparing these financial statements. Therefore, it is important to include the role
4
The report recommends that each member of an audit committee should be financially literate, and at
least one (and preferably a majority) of the committee’s members should have substantial financial expe-

rience. The report also recommends that everyone on the audit committee (members and non-members of
management alike) should receive training both with respect to their general responsibilities and regarding
the operations, business issues, financial reporting, control systems, and risk management processes of the
company itself.
123
An overlooked effect of mandatory audit–firm rotation 269
of an effective audit committee in discussing the merits of the mandatory rotation
requirement.
5
In a situation where section 301 of the SOX Act is actually enforced, I assume that
the possibility that management might threaten the audit firm is eliminated. That is,
this paper analyzes the r esult of a theoretical effectiveness of section 301 of the SOX
Act and assumes that the concerns over enforcement expressed in the past literature,
such as those over managers’ improper influence on auditors due to auditors’ fear
of losing clients due to disagreement with managers’ financial reporting preferences
(e.g., Farmer et al. 1987).
6
Cautious optimism about the effective enforcement of Sec-
tion 301 is justified by recently issued auditing standards that require communication
between auditors and audit committees about unrecorded misstatements (SAS No.
89, American Institute of Certified Public Accountants (AICPA) 1999a) and the audi-
tor’s judgment about the quality, not just the acceptability, of accounting principles
and underlying estimates in the financial statements (SAS No. 90, American Institute
of Certified Public Accountants (AICPA) 1999b). Those requirements enhance the
importance of the audit committee, giving it a critical role that dominates the role
of managers in affecting the outcome of accounting negotiations with the client. In
summary, auditor rotation becomes less pivotal in a situation where there exists a well
functioning independent board (or independent audit committee) as required by the
SOX Act than in a pre-SOX Act environment where auditors can never be completely
independent.

7
Opponents of mandatory rotation assert that auditors have to gain experience and
build client-specific assets from the ongoing relationship in order to develop a greater
ability to detect accounting irregularities (Arrunada and Paz-Ares 1997). Geiger and
Raghunandan (2002) have also demonstrated that there are significantly more audit
failures in the earlier years of the auditor–client relationship. Some recent empirical
studies have investigated the relationship between auditor tenure and discretionary
accruals and found that short audit tenure leads to lower audit quality (e.g., Johnson
et al. 2002; Myers et al. 2003; Ghosh and Moon 2005; Chen et al. 2008).
8
The evi-
dence shows that the mandatory rotation requirement decreases audit effectiveness
5
Members of the board that are independent of management are likely to be more effective in overseeing
management than those that are not. This study assumes that there exists a well-functioning independent
board or audit committee in the firm.
6
See Bazerman et al. (1997) for a general discussion of the challenges faced by auditors when they know
that the client “ may hire and fire auditors at will” (p. 91).
7
This idea is echoed in the following paragraph from the General Accounting Office required study on the
potential effects of mandatory audit firm rotation on public accounting firms (US Government Accounting
Office 2003): “We also believe that if audit committees regularly evaluated whether audit firm rotation would
be beneficial, given the facts and circumstances of their companies’ situation, and are actively involved in
helping to ensure auditor independence and audit quality, many of the benefits of audit firm rotation could
be realized at the initiative of the audit committees rather than through a mandatory rotation requirement”
(p. 9).
8
This approach treats audit quality as a function of earnings quality, which is measured by discretionary
accruals. Other proxies for earnings quality include restatements (Stanley and DeZoort 2007, and fraudulent

financial reporting ( Carcello and Nagy 2004). In addition, studies investigating the relation between audit
firm tenure and perceptions of earnings quality include Mansietal.(2004), who use the cost of debt financ-
ing to proxy for creditor perceptions, and Ghosh and Moon (2005), who use earnings response coefficients
123
270 W. Chi
and thus lowers the quality of financial reporting. In addition, the National Com-
mission on Fraudulent Financial Reporting (The Treadway Commission) (1987) has
recommended that the peer review program of the AICPA’s SEC Practice Section pay
closer attention to the first-year audits of public clients. This recommendation was
made partly because the Commission’s review of fraud-related cases revealed that
a significant number of those cases involved companies that had recently changed
auditors (p. 54). Further, the Quality Control Inquiry Committee of the AICPA’s SEC
Practice Section found that audit failure occurs almost three times as often on first- or
second-year audits (American Institute of Certified Public Accountants(AICPA) 1992).
In summary, these investigations suggest that mandatory rotation could diminish audit
effectiveness and thus lower the quality of financial reporting.
In spite of the existing empirical evidence, there are at least two reasons to examine
the issue via the analytical approach. First, the results of the empirical studies (e.g.
Johnson et al. 2002; Myers et al. 2003; Ghosh and Moon 2005; Chen et al. 2008)were
found in a legal environment that did not require audit firm rotation. An analytical
analysis can provide supplemental arguments and another perspective to complement
prior empirical evidence. Second, audit quality is determined by separate factors: the
auditor’s ability to discover errors or breaches, and the degree of independence required
to report the errors truthfully (DeAngelo 1981). All existing empirical evidence, how-
ever, is based on a joint test of auditors’ independence and ability. To address how
mandatory rotation affects auditor independence and audit pricing, I assume that audit
effort is unchanged either in a rotation-required or non-rotation-required environment.
In the next section, I simplify the model of Lee and Gu (1998) to examine the costs
associated with mandatory auditor rotation, particularly monitoring costs and audit
fee payments. The focus of the Lee and Gu (1998) study is to examine the relationship

between low-balling and auditor independence. They analyze the interaction among
the firm owner, the manager, and the auditor, and conclude that low-balling consti-
tutes an efficient dynamic contracting mechanism for hierarchal agency. Specifically,
they find that low-balling creates a disincentive for unscrupulous audit behavior when
the right to hire and fire the auditor lies with the owner. The present paper uses the
same framework to analyze the difference in the optimal investigation strategies under
rotation-required and non-rotation-required environments where the right to hire and
fire the auditor lies in an independent board (or an independent audit committee).
3 The investigation strategies
To examine how mandatory rotation affects audit pricing and auditor independence,
I analyze the audit fee payments and optimal investigation strategies of the audit
committee in non-rotation-required and rotation-required environments, respectively.
Because of its focus on the role of the auditor, this paper does not examine alternative
footnote 8 continued
to proxy for investor perceptions. Regarding the effect of mandatory rotation on audit quality, Chietal.
(2009), using evidence from Taiwan, find no evidence that mandatory audit–partner rotation has positive
effects on audit quality. Likewise, Ruiz-Barbadillo et al. (2009), using evidence from Spain, come to similar
conclusions regarding mandatory audit–firm rotation.
123
An overlooked effect of mandatory audit–firm rotation 271
strategies to induce truthful reporting, such as a contract between the audit committee
and the manager, for such a strategy eliminates consideration of the auditor.
3.1 The optimal investigation strategy in a non-rotation-required environment
I assume that the audit market is price competitive and that the client’s switching costs
and auditor’s start-up costs are non-zero. Following the model from DeAngelo (1981),
I calculate the audit fee in a non-rotation-required environment (denoted by NR). Let
F
1;NR
represent the audit pricing in the initial engagement, and F
n;NR

= F
NR
(for
n ≥ 2), the audit fee for subsequent periods. Further, there is a constant component
to audit cost in each period, A
n
= A (for n ≥ 2), and a start-up cost, K , in the initial
period so that A
1
= A + K represents the initial audit. A client who switches his or
her auditor incurs a transaction cost, denoted by S. Finally, r is the discount rate that
applies to the auditor’s future profits.
Fact 1: In a non-rotation environment:
1. The audit fee on the initial engagement is F

1;NR
= A + K −
K+S
1+r
,
2. The audit fee on all subsequent audits F

NR
= A +
r
1+r
(K + S), and
3. F

NR

− F

1;NR
= S > 0.
Proof See DeAngelo (1981) or the brief outline in Appendix 1.
Assuming that a firm has a well-functioning audit committee that has the respon-
sibility to hire and fire the auditor, I employ the following monitoring and incentive
structure, similar to the one used in the Lee and Gu (1998). Particularly, the board
employs a manager to handle production and an auditor to verify the reported infor-
mation. However, the auditor might accept a side payment B to report with bias in
favor of the manager.
9
Because a pure strategy of constantly monitoring an expert and,
therefore, relatively efficient auditor removes the advantage of hiring such an auditor,
it is too costly for the board to adopt such a pure strategy to always investigate whether
there exists collusion between the auditor and the manager. For the same reason, a
pure strategy never to investigate is not beneficial for the board either.
Accordingly, I assume the board chooses a mixed strategy to scrutinize the collu-
sion, with probability π
1;NR
in the first period of auditing, and π
NR
in each subsequent
period. Furthermore, if the board investigates and the two agents (i.e., the manager and
the auditor) have colluded, the board will discover the misconduct with probability p
(where 0 < p < 1). When the two agents behave loyally, there is no evidence that
can suggest an allegation of malpractice by the two agents, whether the boards inves-
tigates or not. Finally, when the collusion is revealed at a certain time, the auditor pays
a one-time legal punishment D and his future income is normalized to zero.
10

In other
words, the entire calculation of profit from collusion includes three parts: the periods
before collusion is detected, during each of which some profit should be expected; the
9
To focus on the issue of mandatory rotation, I treat the side payment B exogenously for tractability.
10
To examine how mandatory rotation affects the auditor’s independence, I omit the penalty on the
manager.
123
272 W. Chi
period when collusion is detected, which will result in a penalty; and the periods after
collusion has been detected, during which the profit from collusion will be zero.
I will start by describing the auditor’s strategy—a pure strategy either of indepen-
dence or collusion—in the non-initial period. If the auditor does not collude with the
manager, the present value of his total profits is:
(F
NR
− A)(1 + r)
r
. (1)
However, when he colludes with the manager, the auditor receives a payoff B +
F
NR
− A with probability (1 − π
NR
) + π
NR
(1 − p), since the board could either not
investigate (with probability 1 − π
NR

) or investigate (with probability π
NR
) but not
discover the misconduct (with probability 1 − p). When the board discovers the collu-
sion of the two agents, the auditor pays the fixed court-determined penalty D.
11
Since
the auditor has the same optimization problem in each non-initial period, if an auditor’s
best choice is to collude in a given period, it is implied that collusion will constitute the
best strategy in each subsequent period as well. Consequently, the expected present
value of the auditor’s profits from the collusion strategy in a non-initial auditing period
is:
[
(1 − π
NR
· p)(B + F
NR
− A) − π
NR
· p · D
]
×

1 +
1 − π
NR
· p
1 + r
+


1 − π
NR
· p
1 + r

2
+···

=
[
(1 − π
NR
· p)(B + F
NR
− A) − π
NR
· p · D
]
·
1 + r
r + π
NR
· p
. (2)
The probability factor must be included for each period, because it is only by surviv-
ing previous periods (each of which involves its own probability) that an auditor will
be able to participate in any following period (each of which, again, involves its own
probability). In other words, a particular payoff depends upon an auditor surviving
previous periods as well as the current one. Recall that the expected present value of
profits for an auditor who chooses an independent strategy is given by Eq. (1). Letting

11
For simplicity, this paper follows Lee and Gu (1998), which treats the court-determined damages as
fixed. That is, I omit the potential effect of audit liability regimes (Hillegeist 1999), materiality uncertainty
(Patterson and Smith 2003), and inconclusive evidence of fraud (Patterson and Wright 2003). This paper
assumes that the auditor cannot receive the net profit, including side payments, of the engagement auditor
(B + F
NR
− A) if he colludes and is discovered. This assumption can simplify the proof, although the
major conclusion of this study will be unchanged if D excludes the incurred A, regardless of collusion or its
detection. In addition, one may argue that it should include the “fresh view effect” of the successor auditor
into the model. In fact, to assess how audit–firm tenure affects audit quality, Myers et al. (2003) examined
the relationship between abnormal accruals and audit–firm tenure. They found no evidence that a lengthy
audit–firm tenure has a negative effect on audit quality. In fact, their results show that audit–firm tenure
enhances, rather than decreases, audit quality, which implies that short audit tenure leads to lower earnings
quality because auditing expertise, accumulated by tenure, is important for auditors to detect accounting
irregularities. Thus, this paper does not assume any “positive” or “negative” role of the new successor
auditor, who might have less client-specific expertise than the predecessor auditor.
123
An overlooked effect of mandatory audit–firm rotation 273
Y denote the result of Eq. (2) subtracted from Eq. (1), we have:
Y =

(F
NR
− A)(1 + r)
r



[(1 − π

NR
· p)(B + F
NR
− A) − π
NR
· p · D]·
1 + r
r + π
NR
· p

. (3)
A positive result for Eq. (3) means that an independent strategy—one free from
collusion—is the best course of action for the auditor in a non-initial period. On the
other hand, to collude with the manager is the auditor’s rational behavior for a negative
Y . Taking the partial derivative of Eq. (3) with respect to F
NR
− A and B yields:
∂Y
∂(F
NR
− A)
=
(1 + r)
2
π
NR
· p
r(r + π
NR

· p)
> 0, and (4)
∂Y
∂ B
=−
(1 − π
NR
· p)(1 + r)
r + π
NR
· p
< 0. (5)
The results show that Y is increasing with the normal audit profit (F
NR
− A), and
decreasing with the level of the side payment. Therefore, either a lower normal engage-
ment profit earned by the auditor or a higher side payment afforded by the manager, will
induce collusion and threaten auditor independence. Because investigation is costly,
the board will choose the lowest π
R
for which Y is equal to zero.
12
After a simple
arrangement, π

NR
satisfies the following condition:
π

NR

=
1
p
·
B
B +
1+r
r
(F
NR
− A) + D
. (6)
Substituting F

NR
from Fact 1 into Eq. (6) yields:
π

NR
=
1
p
·
B
B + K + S + D
. (7)
Equations (6) and (7) readily show that the higher the probability p or the audit profit
during the non-initial periods, F
NR
− A, the lower the probability that the board will

investigate. In addition, the board should adopt a more aggressive investigation strategy
(i.e., π

NR
increases) when the affordable side payment from the manager increases.
Next, I calculate the board’s optimal investigation strategy in the initial period. For
a competitive audit market, the profit of an auditor with independence is zero. How-
ever, if the auditor compromises his independence then he earns an extra B in period
1 (with probability 1 − π
1;NR
· p) or pays punishment D if collusion is detected by
the board (with probability π
1;NR
· p). Using Eq. (7), which assumes zero profit in
12
In other words, I assume that an auditor who is indifferent between independence and collusion will
choose to remain independent.
123
274 W. Chi
audit markets, and the backward induction approach, I arrive at the net expected value
of profits from the collusion strategy (1 − π
1;NR
· p)B − π
1;NR
· ( pD).
13
Further, the
optimal randomized investigation of the board in the initial period, π

1;NR

,is:
π

1;NR
=
B
p · (B + D)
. (8)
Equation (7) subtracted from Eq. (8) yields:
π

1;NR
− π

NR
=
1
p
·

B · (K + S)
(B + D) · (B + K + S + D)

> 0. (9)
Equation (9) s hows that the board’s investigation effort is highest in the initial period.
Along with Fact 1, which shows that the audit fee increases after the initial period,
this equation offers a simplified version of the findings in Lee and Gu (1998).
14
Iuse
the results from this section as a benchmark to compare with an environment with

mandatory auditor rotation.
Proposition 1 For an environment without mandatory rotation:
π

1;NR
=
1
p
·
B
B + D
, (8)
π

NR
=
1
p
·
B
B + K + S + D
, (7)
π

1;NR
− π

NR
> 0. (10)
Proposition1 expresses the investigation strategies of the independent audit com-

mittee in a non-rotation environment in each period in terms of side payments (B),
penalties to the auditor for collusion with the manager (D), and the probability of
discovery of misconduct (p); for periods after the initial one, the auditor’s set-up costs
(K) and the client’s switching costs (S) are added.
3.2 The optimal investigation strategy in a rotation-required environment
To analyze how mandatory rotation affects the board’s investigation strategy in each
period, I use π
n;R
(N) to represent the mixed strategy in period n (1 ≤ n ≤ N), where
13
Ideally, this formula should be expressed as (1 − p·π
1;NR
)· (B+ Present Value of an Audit Engagement
in an Initial Year) −π
1;NR
· (pD). However, assuming a zero-profit audit market, the term Present Value
of an Audit Engagement in an Initial Year, reduces to zero.
14
The fact that the fee in the initial period is lower than in subsequent periods is what is commonly referred
to as “low-balling” or “low introductory pricing.” As compared to legal enforcement and investigation strat-
egy , Lee and Gu (1998) explain that low-balling itself is an economical mechanism to self-fulfilled auditor
independence. In Sect. 3.2, I will show that mandatory rotation interferes with this mechanism.
123
An overlooked effect of mandatory audit–firm rotation 275
1 is the initial period and N is the imposed limit on the maximum length of a given
auditor–client relationship in a rotation-required environment (denoted by R). Let
F
n;R
(N) be the audit fee in period n and 
n;R

(N) represent the present value of the
auditor’s total future profit (including period n), under the presumption that the auditor
does not collude with the manager in period n. I use the following conditions to cal-
culate π

n;R
(N), the optimal investigation strategy of the board in a rotation-required
environment:
Terminal value condition:

N;R
(N) = F
N;R
(N) − A. (11)
Present value condition:For2≤ n ≤ N − 1,

n;R
(N) =[F
n;R
(N) − A]+

n+1;R
(N)
1 + r
. (12)
Competition condition:

1;R
(N) = 0 (13)
The terminal value condition describes the auditor’s profit in the last period; the

present value condition shows that the present value of the auditor’s profit in period
n equals his audit profit in the current period plus the present value of the profit in
period n + 1 discounted to period n;thecompetition condition reflects the assumption
of a highly competitive audit market.
15
By the method of backward induction, the board adopts an optimal mixed strategy
π

N;R
(N) that makes the auditor indifferent to the choice between independence and
collusion at the terminal audit period N. That is:

N;R
(N) =[1 − p · π

N;R
(N)]·[B + 
N;R
(N)]− p · D · π

N;R
(N). (14)
The left hand side of the equation shown above is the expected utility of the auditor
who adopts an independent strategy, and the right hand side is his expected utility
under a collusion strategy. Rearranging the terms gives the result
π

N;R
(N) =
1

p
·
B
B + 
N;R
(N) + D
. (15)
15
Regarding the technical descriptions of terminal value condition, present value condition, and competi-
tion condition, refer to Magee and Tseng (1990) (hereafter, MT).The variables N and n in this study differ
from those of the same name in Magee and Tseng (1990). For MT, N is the number of periods in the life of
the client (after which the firm closes), while in this study N is the maximum number of periods of a given
auditor–client relationship (after which the auditor must be rotated). In MT, subscript n is the number of
periods left in the client firm’s life, while I use it simply to denote the number of the period. Finally, the
value of incumbency at time zero (the last period) in MT is 0, because the company has closed, but in the
present study N represents the condition at the beginning of the period, rather than at the end, when it too
would equal 0.
123
276 W. Chi
Assuming that the board adopts π

N;R
(N) in period N , the board chooses the follow-
ing π

N−1;R
(N) to equalize the auditor’s expected utility from the i ndependent and
collusion strategies in period N − 1:

N−1;R

(N) =[1 − p · π

N−1;R
(N)]
·[B + 
N−1;R
(N)]− p · D · π

N−1;R
(N), (16)
and
π

N−1;R
(N) =
1
p
·
B
B + 
N−1;R
(N) + D
. (17)
Using the same procedure, to prevent collusion, the board’s optimal mixed strategy of
π

n;R
(N) satisfies the condition:
π


n;R
(N) =
1
p
·
B
B + 
n;R
(N) + D
. (18)
However, in order to find the exact solution, it is necessary to examine the audit fee
in each period F
n;R
(N) under a rotation-required environment.
IuseP to denote the audit price offered by a potential bidder. Since the audit market
is assumed to be competitive and every new bidder who appears each time is in his
initial engagement period, the bidder’s offering price P satisfies the condition:
(P − A − K) +
P + S − A
1 + r
+
P + S − A
(1 + r)
2
+···+
P + S − A
(1 + r)
N−1
= 0. (19)
The first part of the summation represents the current audit profit of the bidder

(P − A − K ). The subsequent parts show that when the bidder becomes an incumbent
auditor, he has a pricing advantage S and a cost advantage K as compared to all his
rivals. The terms sum to zero due to the constraint of the competition condition in the
audit market. After rearranging, the bidder’s offering price is given by:
P = (A − S) +
(S + K ) · r · (1 + r)
N−1
(1 + r)
N
− 1
. (20)
Given the incumbent auditor’s pricing advantage, S, the audit fee during the non-initial
auditing period is P + S. In particular,
F

2;R
(N) = F

3;R
(N) =···= F

N;R
(N) = F

R
(N) = P + S, (21)
which can be written as
F

R

(N) = P + S = A +
(S + K ) · r · (1 + r)
N−1
(1 + r)
N
− 1
. (22)
123
An overlooked effect of mandatory audit–firm rotation 277
The audit fee in the initial period F

1;R
(N) is:
F

1;R
(N) = P = ( A − S) +
(S + K ) · r · (1 + r)
N−1
(1 + r)
N
− 1
. (23)
Consistent with Fact 1, Equations (22) and (23) show that the amount of fee cutting,
given by F

R
(N)− F

1;R

(N) = S, is the same in both rotation-required and non-rotation
required environments.
Proposition 2 For an environment with mandatory rotation:
π

1;R
(N) =
1
p
·
B
B + D
, and (24)
π

n;R
(N) =
1
p
·



B
B + D + (S + K ) ·
(1+r)
N
−(1+r)
n−1
(1+r)

N
−1



. (25)
Proof See Appendix 2.
These two equations portray the audit committee’s investigation strategies for the
first period and for each subsequent period, respectively. The difference between the
two equations lies in t he denominator of the second factor; besides the subscript to
identify the period (n), the second equation includes three additional parameters: the
auditor’s set-up costs (K), the client’s switching costs (S), and the maximum length
of the rotation period (N).
4 Comparison between the two regimes
This section examines the economic consequences of mandatory rotation from the
point of view of optimal investigation strategy and audit pricing. Table 1 summarizes
the board’s optimal investigation strategies in Propositions 1 and 2 via two dimen-
sions—“rotation-required versus non-rotation required” and “initial period versus non-
initial period.”
The following proposition summarizes the relative impact of the board’s optimal
investigation strategies under the different regimes.
Proposition 3 For 2 ≤ n ≤ N:
Table 1 Summary of the board’s investigation strategy

Initial period Non-initial period
Rotation-required
1
p
·
B

B+D
1
p



B
B+D+(S+K )·
(1+r)
N
−(1+r)
n+1
(1+r)
N
−1



Non-rotation
1
p
·
B
B+D
1
p
·
B
B+K +S+D
N is the maximum length of the auditor–client relationship and n (2 ≤ n ≤ N) is a given auditing period

123
278 W. Chi
Fig. 1 Comparison of rotation-required and non-rotation-required investigation strategies, with different
rotation periods
1. The board’s investigation strategy is more aggressive in the initial auditing period
in both rotation-required and non-rotation required environments. Specifically,
π

1;R
(N)>π

n;R
(N) and π
1;NR


n;NR
.
2. In a rotation-required environment where N is fixed, the board’s optimalinvestiga-
tion strategy is a strictly convex function of n. Specifically, π

n+1;R
(N) − π

n;R
(N)
and [π
R
n+2
(N) − π

R
n+1
(N)]−[π
R
n+1
(N) − π
R
n
(N)] > 0.
3. Whether rotation is required or not, the board’s optimal investigation strategy is
the same in the initial auditing period. However, in all subsequent periods, the
board should adopt a more aggressive investigation strategy in a rotation-required
environment. Specifically, π

1;R
(N) − π

1;NR
= 0 and π

n;R
(N) − π

NR
> 0.
4. In a rotation-required environment where N is variable, the investigation level
in a fixed period n is a decreasing function of N. Specifically, π

n;R
(N + 1) −

π

n;R
(N)<0.
Proof See Appendix 3.
I use Fig. 1 to illustrate Proposition 3. The horizontal axis measures the auditing
period n, and the vertical axis measures the corresponding optimal investigation strat-
egy of the board. The bold lines reveal the investigation strategy in a rotation-required
environment over shorter and longer periods of rotation, while the thin line shows the
investigation strategy in a non-rotation-required environment. Proposition3 states that
the board chooses the most aggressive investigation level in the initial audit period,
irrespective of whether auditor rotation i s required or not.
16
Please note that the con-
tinuous lines in Figures 1 and 2 link results for discrete cases. Also, the descending
bold line in both figures represents the initial periods for both the rotation-required
and non-rotation-required regimes. Further, in a rotation-required environment, the
lowest investigation level occurs in the period immediately following the initial one
(i.e., n = 2). As n increases, the investigation level increases at a higher and higher
rate. Therefore, except for the initial audit period where π

1;NR
equals π

1;R
(N),the
board has to pay additional investigation costs in a mandatory rotation environment.
16
Please note that the continuous lines in figures 1 and 2 link results for discrete cases. Also, the descending
bold line in both figures represents the initial periods for both the rotation-required and non-rotation-required

regimes.
123
An overlooked effect of mandatory audit–firm rotation 279
Table 2 Summary of the auditing pricing

Initial period Non-initial period
Rotation-required (A − S) +
(S+K )·r·(1+r)
N−1
(1+r)
N
−1
A +
(S+K )·r·(1+r)
N−1
(1+r)
N
−1
Non-rotation A + K −
K+S
1+r
A +
r·(K +S)
1+r
N is the maximum length of the auditor-client relationship
In fact, the reason why investigation strategies π
NR
and π
R
are different at n ≥ 2,

but become the same at n = 1 is very intuitional. It is the level of auditor’s future
quasi-rents that determines the aggressiveness of the investigation strategy adopted by
the board. For comparison, the discounted future quasi-rents in non-rotation-required
and rotation-required environments are different in all periods except the initial one.
A comparison of the two optimal investigation strategies in the non-initial period in the
last column of Table1 shows that the difference of these two strategies will converge
to zero when N goes to infinity.
17
Figure 1 also compares two scenarios, one of an investigation strategy with a shorter
period of rotation, and another with a longer. For a given shorter mandatory rota-
tion period N1, and a longer period N2, Propositions 3–4 states that for all periods
2 ≤ n ≤ N1, π

n;R
(N1)>π

n;R
(N2). In other words, the board should choose a
more aggressive investigation strategy in a rotation-required environment with more
frequent rotations. Using Fact 1 and equations (22) and (23), Table 2 shows how man-
datory rotation affects the audit fee in each period. Proposition 4 reports the details.
The following proposition shows the audit fees under the different regimes.
Proposition 4 1. As compared with a non-rotation-required environment, a rota-
tion-required environment shows a higher audit fee, both in the initial and the non-
initial auditing periods. In other words, F

1;R
(N)>F

1;NR

and F

n;R
(N)>F

N
R.
2. In a rotation-required environment, both the initial audit fee F

1;R
(N) and the
non-initial audit fee F

n;R
(N) are decreasing functions of N.
Proof See Appendix 4.
I use Fig. 2 to illustrate the intuition of Proposition 4. The horizontal axis measures
the auditing period n, and the vertical axis measures the corresponding audit fee. The
bold lines reveal the audit fee in rotation-required environments with a shorter and a
longer period of rotation, and the thin line portrays the fee in a non-rotation-required
environment. Although the cost advantage of the incumbent auditors allows for a lower
initial period fee in both the two rotation-required environments and the non-rotation
required environment, the auditing price is higher in an environment with mandatory
auditor rotation. Briefly stated, in terms of audit fee payment, the mandatory rotation
requirement represents a cost burden to the firm.
17
In fact, the conclusion is not subject to the discounted zero-profit assumption, as long as the present
value of the initial engagement in a non-rotation-required regime is constant. That is, if we compare the
rotation-required to the non-rotation-required environment, the auditor’s profit in each non-initial period is
different; however, if the present values of an initial engagement in the two environments are the same, the

results of this paper are unchanged.
123
280 W. Chi
Fig. 2 The audit fee payment in different rotation periods
For a given shorter mandatory rotation period N1, and a longer period N2, Propo-
sitions 4, 2 states that F

n;R
(N1)>F

n;R
(N2) for all periods 2 ≤ n ≤ N1. That is, the
cost burden of a higher audit fee payment increases when mandatory rotation is more
frequent.
5 Conclusion
The study of mandatory audit–firm rotation is called for by section 207 of the SOX
Act. A particular feature of the current paper is that its discussion of the effectiveness
of mandatory audit–firm rotation explicitly includes the assumption that section 301
of the SOX Act, which requires an independent board to manage the auditing process,
will be effectively implemented in firms. The strengthened role of such an audit com-
mittee can significantly alleviate potential concerns that auditor–client over-familiarity
will compromise auditor independence and, therefore, the quality of financial reports.
Using a setting where the auditor relationship with the firm is with the board (or
the audit committee), as mandated by section 301 of the SOX Act, instead of with
the manager, I examine the effectiveness of mandatory audit–firm rotation in terms of
the more costly monitoring strategies of the board and the higher audit fee paid by the
firm in such an environment.
This paper demonstrates that, if a firm has a well-functioning audit committee, the
monitoring cost of the audit committee and the firm’s audit fee payment will be higher
due to the mandatory audit–firm rotation requirement than they would have been with-

out required rotation. These findings have some general methodological ramifications.
Specifically, it is not realistic to examine the role of the auditor in isolation from the
board or auditing committee, for, under section 301 of the SOX Act, the quality of
financial reporting is not the responsibility of the auditor alone, but is shared by the
board. Therefore, the debate over the effectiveness of mandatory audit–firm rotation
should include consideration of the role of the board. Since familiarity with the client
is vital to an effective audit process, the mandatory audit–firm rotation requirement—
which was instituted to address concerns about excess familiarity—may in fact reduce
the quality of financial reporting by making it impossible for an auditor to accumulate
valuable familiarity. In cases where the effective implementation of SOX 301 results
in higher audit fee payment and causes the board to adopt a more aggressive strategy
123
An overlooked effect of mandatory audit–firm rotation 281
to prevent collusion between manager and auditor, legislation that is aimed at pro-
tecting the public interest may indeed harm it by imposing economic costs that can
be avoided in the presence of well-functioning audit committees. I t is important to
remember that the conclusions of this study are based on the critical assumption that
firms have qualified audit committees ready to take responsibility for the auditing
process. Accordingly, a policy implication of this paper is that it is more worthwhile
to enhance the real function of audit committees rather than to focus on audit–firm
rotation.
Several cautions should be emphasized. The conclusion of this study is based on
the premise that SOX 301 is effectively enforced, but the paper does not attempt to
argue that this is in fact the case. In addition, the potential agency costs that exist
between the audit committee and investors may leave a role for mandatory auditor
rotation even in a post-SOX environment. Finally, the analysis of this paper does not
include the costs of enhancing the functioning of audit committees.
Acknowledgments I wish to thank the National Science Council for its generous financial assistance.
Appendix 1: A simple description of DeAngelo’s Model (1981)
Under a non-rotation environment, , the present value of the auditor’s profit in the

initial engagement for a given client is:
 = (F
1;NR
− A
1
) +
F
NR
− A
r
. (A1-1)
If the client does not switch his auditor, the present value of the audit fee payment is
F
NR
+
F
NR
r
. When the client decides to switch to another auditor, however, the present
value of the audit fee payment becomes ( A + K ) +
A
r
. Because of the switching cost
S, the upper bound of the audit fee in the non-initial engagement period proposed by
the incumbent auditor is:
F
NR
+
F
NR

r
≤ ( A + K) +
A
r
+ S. (A1-2)
In particular, K and S determine the incumbent value of the auditors. For a profit-
maximizing auditor who extracts all the quasi-rent, Eq. (A1-2) can be rewritten thus:
F

NR
= A +
r · (K + S)
1 + r
.
Finally, competition in the audit market implies that:
(F

1;NR
− A
1
) +
F

n;NR
− A
r
= 0 ⇒ F

1;NR
= A + K −

K + S
1 + r
.
123
282 W. Chi
Appendix 2: Proof of Proposition2
I calculate 
n;R
(N) in the denominator of Eq. (9) to prove the proposition. Given the
competition condition (i.e., 
1;R
(N) = 0 ), the optimal investigation strategy in the
initial period of an engagement is π

1;R
(N) =
1
p
·
B
B+D
. For the other periods, t he
denominator becomes:

n
= F

R
(N) − A +
F


R
(N) − A
(1 + r)
+
F

R
(N) − A
(1 + r)
2
+···+
F

R
(N) − A
(1 + r)
N−n
=
F

R
(N) − A
(1 + r)
N−n
·

1 + (1 + r) + (1 + r)
2
+···+(1 + r)

N−n

=
F

R
(N) − A
(1 + r)
N−n
·
(1 + r)
N−n+1
− 1
r
.
Substituting Eq. (10) into the above 
n
, I find that:

n
=



(S+K )·r·(1+r)
N−1
(1+r)
N
−1
(1 + r

N−n
)



·
(1 + r)
N−n+1
− 1
r
=
S + K
(1 + r)
N
− 1
·

(1 + r)
N
− (1 + r)
n−1

.
Substituting the above 
n
into Eq. (9), I get that:
π

n;R
(N) =

1
p
·
B
B + D + (S + K ) ·
(1+r)
N
−(1+r)
n−1
(1+r)
N
−1
.
Appendix 3: Proof of Proposition3
Proof of Proposition 3-1: Let γ =
(1+r)
N
−(1+r)
n−1
(1+r)N −1
. Since 0 <γ <1, π

n;R
(N) =
1
p
·
B
B+D+(S+K)·γ
. Further, that π


1;R
(N)>π

n;R
(N) is obvious.
Proof of Proposition 3-2: From Proposition 2:
π
n;R(N)
=
B
p
B + D +
S+K
(1+r)
N
−1
·[(1 + r)
N
− (1 + r)
n−1
]
=
k
1
k
2
+ k
3
· f (n)

where k
1
=
B
p
> 0, k
2
= B + D > 0, k
3
=
S+K
(1+r)
N
−1
, and f (n) = (1 + r)
N

(1 + r)
n−1
. I summarize the following six mathematical facts:
1. f (n)>0 (since 1 ≤ n ≤ N).
2. f (n + 1) − f (n) =−(1 + r)
n
+ (1 + r)
n−1
=−r · (1 + r)
n−1
< 0.
3. [ f (n + 2) − f (n + 1)]−[f (n + 1) − f (n)]= f (n + 2) − 2 f (n + 1) + f (n) =
−r

2
· (1 + r)
n−1
< 0.
123
An overlooked effect of mandatory audit–firm rotation 283
4. f (n) ·[f (n + 1) − f (n + 2)]+ f (n + 2) ·[f (n + 1) − f (n)] > 0.
proof :
First, multiply fact (3) by − f (n + 2), to get the result
f (n + 2) ·[f (n + 1) − f (n + 2)]+ f (n + 2) ·[f (n + 1) − f (n)] > 0.
Next, use the fact that f (n)> f
(n + 2)>0 (from fact 2) and [ f (n + 1) − f (n +
2)] > 0 to find
f (n) ·[f (n + 1) − f (n + 2)]+ f (n + 2) ·[f (n + 1) − f (n)] > 0.
5. π
n+1;R
(N) − π
n;R
(N) =
−k
1
k
3
[ f (n+1)− f (n)]
[k
2
+k
3
f (n+1)]·[k
2

+k
3
f (n)]
> 0.
6. [π
n+2;R
(N)−π
n+1;R
(N)]−[π
n+1;R
(N)−π
n;R
(N)]=π
n+2;R
(N)−2π
n+1;R
(N)
+ π
n;R
(N)>0.
proof Using fact (5), we get:
k
1

−k
2
k
3
[ f (n+2)−2 f (n+1)+ f (n)]+k
2

3
{ f (n)[ f (n+1)− f (n+2 )]+ f (n+2)[ f (n+1)− f (n)]}

[k
2
+k
3
f (n+2)]·[k
2
+k
3
f (n+1)]·[k
2
+k
3
f (n)]
> 0.
Proof of Proposition 3-3 The first part is obvious. In addition,
π

n;R
− pi

n;NR
=
1
p
·
B(S + K )(1 − γ)
[B + D + (S + K) · γ ]·[B + K + S + D]

> 0.
Proof of Proposition 3-4: Let γ =
(1+r)
N
−(1+r)
n−1
(1+r)
N
−1
, hence π

n;R
(N) =
1
p
·
B
B+D+(S+K)·γ
. Since (1 + r)
N
>(1 + r)
n−1
> 1, 0 <γ <1. Since γ is a decreasing
function of N, π

n;R
(N) is also a decreasing function of N.
Appendix 4: Proof of Proposition4
Proof of Proposition 4-1: From Table 2, the relative magnitudes of F


n;R
(N) and F

NR
depend on the relative sizes of
(1+r)
N−1
(1+r)
N
−1
and
1
1+r
. Because
(1 + r)
N−1
(1 + r)
N
− 1

1
1 + r
=
1
(1 + r) −
1
(1+r)
N−1

1

1 + r
> 0,
F

n;R
(N) − F

NR
> 0 is proved. In addition, using the fact that F

n;R
(N) − F

1;R
=
F

NR
− F

1;NR
= S and F

n;R
(N) − F

NR
> 0, we see that F

1;R

(N)>F

1;NR
.
Proof of Proposition 4-2: From the formulas of F

1;R
(N) and F

n;R
(N),itiseasyto
see that they relate to Nviathe factor:
(1 + r)
N−1
(1 + r)
N
− 1
=
1
(1 + r) −
1
(1+r)
N−1
.
123
284 W. Chi
Hence, it is straightforward to get the result that either F

1;R
(N) or F


n;R
(N) is a
decreasing function of N.
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