church and zhang - 2006 - a model of mandatory auditor rotation

We show that auditor independence is improved with mandatory rotation, but that the net benefit is sensitive to the rotation period, startup cost, the cost associated with biased reports

A Model of Mandatory Auditor Rotation

Bryan K Church College of Management Georgia Tech Atlanta, GA 30332-0520 404.894.3907

bryan.church@mgt.gatech.edu

Ping Zhang Rotman School of Management University of Toronto Toronto, ON M5S 3E6 416.946.5655

pzhang@mgmt.utoronto.ca

January 2006

We gratefully acknowledge the helpful comments of Shawn Davis

A Model of Mandatory Auditor Rotation

Abstract

We develop a theoretical model to compare the relative merits of a system that requires auditor rotation to one that does not We show that auditor independence is improved with mandatory rotation, but that the net benefit is sensitive to the rotation period, startup cost, the cost associated with biased reports, auditors’ learning, and the time span of managers’ incentives Mandatory auditor rotation is preferable if the rotation period is long, startup costs are high, the cost of biased reports is high, auditor learning is dramatic in terms of improving audit efficiencies over time, and the manager

is myopic (focused on short-term payoffs)

A Model of Mandatory Auditor Rotation

I Introduction

The need for mandatory auditor rotation has long been debated A primary

concern is that if the incumbent is retained over time, the auditor may become

complacent and objectivity may be impaired (e.g., Mautz and Sharaf, 1961) Regulators have periodically called for mandatory rotation in order to preserve auditor independence,

including the Metcalf Report (United States Senate, 1976), the Securities and Exchange Commission’s Staff Report on Auditor Independence (SEC, 1994), and Congressional

testimony (see e.g., Zeff, 2003)

In the United States, the accounting profession has staunchly opposed mandatory rotation, arguing that such a requirement would increase the cost and risk of conducting

an audit (e.g., American Institute of Certified Public Accountants, 1978; General

Accounting Office, 1996) The profession contends that problems are more likely to occur in the initial years of the auditor-firm relationship because the auditor has less knowledge of the firm In support of the argument, the American Institute of Certified Public Accountants (1992) documents that cases of alleged audit failure (between 1979 and 1991) occur three times more frequently in the first two years of the auditor-firm relationship (see also Palmrose, 1986; 1991) Carcello and Nagy (2004) show that

fraudulent financial reporting, as evinced by the SEC’s Accounting and Auditing

Enforcement Releases between 1990 and 2001, is more likely to occur in the first three years of the auditor-firm relationship

Yet the issue of mandatory rotation continues to be discussed and has resurfaced

as a fall out of the accounting scandals that occurred at the beginning of the 21st century Section 207 of the Sarbanes-Oxley Act of 2002 requires the U.S Comptroller General to study the potential effects of mandatory auditor rotation The inherent difficulty of such

a study, though, is that the auditor-firm relationship can only be observed under the current system Hence, it is problematic to assess the relative merits of a system that mandates auditor rotation compared to one that does not require rotation.1

To shed insight into the auditor rotation issue, archival research has examined the relationship between auditor tenure and proxies for audit quality and/or the credibility of financial data Geiger and Raghunandan (2002) find a negative association between auditor tenure and auditor-reporting failure.2 Mansi, Maxwell, and Miller (2004) report a negative association between auditor tenure and the cost of debt financing Others document a positive association between auditor tenure and earnings quality – real and perceived (Johnson, Khurana, and Reynolds, 2002; Myers, Myers, and Omer, 2003; Ghosh and Moon, 2005) Accordingly, archival findings suggest that benefits arise as auditor tenure is extended

But as mentioned earlier, archival studies are unable to determine the effect of mandatory auditor rotation because data are available only under the current system (i.e., one that does not require rotation) Dopuch, King, and Schwartz (2001) conduct a

controlled, laboratory study, which allows them to assess behavior with and without

1 Some countries mandate auditor rotation, including Austria (every six years) and Italy (every nine years) Greece requires rotation every six years for public sector companies, and banks incorporated in Singapore must rotate every five years Spain previously required rotation (every nine years), but repealed the law one year before it would have had a practical effect

2 According to Geiger and Raghunandan (2002), auditor-reporting failure occurs when the auditor issues a clean audit report to a firm that files for bankruptcy in the following year

auditor rotation Their findings indicate that mandatory rotation can improve auditor independence, but that welfare may be higher (for the auditor and the firm) in the absence

of rotation While the findings are intriguing, the experimental design does not provide for a comparison of the total costs and benefits of the alternative systems Such a

comparison is necessary, however, to determine whether mandatory auditor rotation is optimal

Because prior research does not provide a basis to perform a complete analysis of the relative merits of mandatory rotation, we develop a theoretical model to formally consider the issue We find that auditor independence is improved with mandatory rotation, but that the net benefit is sensitive to the rotation period, startup cost, the cost associated with biased reports, auditors’ learning, and the time span of managers’

incentives Mandatory auditor rotation is preferable if the rotation period is long, startup costs are high, the cost of biased reports is high, auditor learning is dramatic in terms of improving audit efficiencies over time, and the manager is myopic (focused on short-term payoffs)

The remainder of the paper is organized as follows Section II presents the basic model, and Section III introduces the firm’s incentive to report biased accounting values Sections IV and V examine the effect of auditor experience and managerial payoffs, respectively, on the results Section VI provides concluding remarks

II The Model

We start with a model similar to that of DeAngelo (1981) and Magee and Tseng (1990) Each operating period a firm hires an auditor to verify the reported accounting

value (financial data) The engagement is for one period and contingent fees are not allowed At the beginning of the period, auditors submit bids to provide services A firm hires the auditor whose bid provides the lowest cost If the incumbent auditor submits the lowest cost bid, the incumbent is retained Otherwise, a new auditor is hired.3 When a new auditor is hired, startup costs (i.e., one-time fixed costs) are incurred by each party, denoted M for the firm and A for the auditor

We assume that the audit market is competitive and all auditors possess the same audit technology.4 To compete for an engagement, auditors submit bids that cover their minimized costs The auditor’s cost per period includes two components: the cost of conducting the audit and the expected cost of liability from audit failures Let ε be audit effort, C be the examination cost, u be misstatement in the reported accounting value, and

L be the expected liability Then C is an increasing function of ε, and L is an increasing function of the absolute value of u If there is no known bias in the reported accounting

value, the size of misstatement equals the size of audit error The audit error, denoted x,

is a random number with an expected value of zero and its absolute value is a decreasing function of ε Let Lx≡L(u=x), the auditor’s expected liability from audit errors alone

Auditor effort is chosen to minimize the cost C+Lx each period.5 We first consider the auditor’s pricing strategy when the firm’s manager does not have an incentive to report any specific (biased) accounting value, referred to as the benchmark case

We start by introducing three parameter variables The first variable is the

discount factor, denoted γ The second is the expected auditor turnover rate per period,

3 If more than one new auditor submits the lowest cost bid, the firm randomly chooses a new auditor

4 These assumptions are not essential for the conclusions obtained in the study, but allow us to streamline the analysis and presentation

5 The bias incorporated in the accounting value is negotiated between the auditor and manager and is not directly affected by the auditor’s effort

denoted δ The value of δ reflects the possibility that (1) the firm ceases operations at period end and (2) the auditor severs the relationship with the firm due to cost and/or specialization considerations Thus, δ reflects a normal turnover rate before considering disagreements.6 At period end, the incumbent knows whether the firm requires services

in the next period and whether the incumbent will be available to submit a bid to provide such services The third parameter variable is the maximum number of consecutive periods that the incumbent can be retained by a specific firm, denoted N

The incumbent is retained (prior to period N+1) as long as the incumbent’s bid equals the lowest bid from competing new auditors plus M (the startup cost incurred by the firm to engage a new auditor) If P is the lowest price that a new auditor bids, then in the first period all auditors bid P and one is hired In all subsequent periods the

incumbent bids P+M and is retained At time 1, the incumbent is available to bid with a probability of δ in the second period, a probability of δi-1 for the ith period, and a

probability of δN-1 for the final period of service At the beginning of the first period, the auditor prices the audit such that the expected discounted total cost equals the expected discounted total revenue: that is, economic profit is zero in a competitive audit market

The quasi rent generated by the auditor in period i, denoted qi, is revenue minus cost for the period and the total quasi rents after period i are the expected present value of all future quasi rents, which has a value of Qi+1= qi+1+ qi+2δγ+qi+3 (δγ)2+…+ qN-i (δγ)N-i-1

6 Turnover also may arise due to disagreements over the accounting value, which can result in the auditor resigning or being fired In the benchmark case, the firm does not have an incentive to report a biased

Lemma 1: When the maximum number of consecutive periods that the auditor can be

retained is N, the expected present value of all future quasi rents after period i, Qi+1, is (M+A)(1-(δγ)N-i)/(1-(δγ)N), which is a decreasing function of i If N is infinitely large, the future quasi rent after period i is a constant of (M+A)

Proof: See Appendix

III Auditor Independence in a Non-Cooperative Game

We introduce the assumption that the firm’s manager has an incentive to report a specific accounting value in some periods The incentive arises with a probability of α (≤1) at the end of each period Let d be the difference between the reported accounting value and the auditor’s unbiased estimate of value.7 The size of misstatement (u) is the

sum of the deviation (d) and the audit error (x), where the deviation (d) equals the

difference between the manager’s desired reporting value and the auditor’s unbiased estimate.8 The auditor’s expected liability is L(u) The auditor chooses effort, ε, to

minimize the cost C(ε)+Lx, where Lx≡L(u=x) is the auditor’s expected liability from audit

errors alone Let D be the auditor’s expected incremental liability of endorsing the firm’s desired accounting value, then D=L(u)-Lx for a given audit effort The value of D is an increasing function of d and D>Qi if d>di*)

When the firm’s manager has an incentive to report a specific, desired accounting value, the manager presents the value to the auditor for endorsement If the auditor

7 In this paper we assume that the manager knows the auditor’s unbiased estimate of the firm value This assumption simplifies the analysis, but does not alter the paper’s main results Interested readers are referred to Zhang (1999) in which the auditor’s unbiased estimate is private information and the manager is unable to observe it

8 The manager’s desired reporting value arises for various reasons, including the market’s expectation of the reported accounting value and the effect of the reported value on the manager’s compensation

endorses the desired value, the manager receives a benefit of B and the auditor incurs an incremental liability with expected value of D If the auditor does not endorse the desired accounting value, the manager does not receive the benefit and the auditor does not incur the incremental liability However, the auditor may not be retained in future periods (i.e., the auditor may not be permitted to submit a bid for the next period’s audit service)

Proposition 1: The auditor does not endorse the manager’s desired accounting value in

Proof: See Appendix

Proposition 1 implies that the auditor compromises independence as long as each

of the following conditions is satisfied: (1) the auditor derives benefits from repeat

engagements with the firm, (2) the expected future benefits exceed the incremental expected liability that arises from endorsing the firm’s desired accounting value, and (3) the auditor may be retained indefinitely

The benefit from endorsing the desired accounting value is zero if the auditor is not available to provide audit services in the next period (B=0) In this situation, the auditor does not endorse a biased report because such behavior increases the auditor’s expected liability without a consequent gain (D>0) If the auditor is available to provide audit services in the next period, endorsing the desired accounting value produces

expected benefits from potential future engagements However, the auditor does not endorse a biased report if the expected benefit is less than the incremental expected liability that accompanies such behavior (B<D) Hence, the auditor does not endorse a biased report that exceeds an upper limit

If the maximum number of consecutive periods that the auditor can be retained is definite (i.e., auditor rotation is mandated), the auditor does not endorse a biased report even if the expected benefit from potential future engagements exceeds the incremental expected liability When the number of consecutive engagements with a specific auditor

is fixed, backward induction leads to equilibrium in which the auditor does not endorse biased reports By comparison, if the number of consecutive engagements is indefinite (i.e., auditor rotation is not required), backward reduction cannot be used to derive

equilibrium behavior In this case, the forward reductions and trembling hand refinement lead to equilibrium in which auditors endorse a biased report if gains from future

engagements exceed the incremental expected liability (B>D)

Magee and Tseng (1990) find that the auditor does not compromise independence unless specific conditions are satisfied In their model, the firm has a definite life As a result, the maximum number of consecutive engagements cannot exceed the life of the firm (N periods) When the firm’s life is not definite and auditor rotation is not required,

the auditor can potentially be retained in perpetuity Zhang (1999) concludes that, in such a situation, the auditor may endorse a desired (biased) accounting value in exchange for future quasi rents Our conclusion that mandatory rotation improves auditor

independence is consistent in spirit with Magee and Tseng (1990) and Zhang (1999), though the prior research does not explicitly consider auditor rotation

Is mandatory auditor rotation beneficial?

Based on the earlier discussion, auditor independence is preserved with a system

of mandatory auditor rotation (i.e., N is definite) But the benefits of such a system relative to one in which rotation is not required are not entirely one sided The benefits of mandatory rotation as compared to no rotation are a function of the rotation requirements

or, more specifically, the size of N

Proposition 2: Mandatory rotation can be beneficial if N is sufficiently large

Proof: See Appendix

To determine the benefits of mandatory rotation relative to non-rotation, we need

to measure and compare the total costs associated with audits under each system during a firm’s life The total cost consists of the cost of conducting the audit (C) and the

expected cost of liability from audit failure (L) The cost of conducting the audit includes startup and testing costs The expected liability includes costs that arise from audit errors and biases in financial statements The auditor’s liability serves as a measure of the cost

of audit failure

Startup costs are higher under a system of mandatory rotation because such costs must be incurred periodically.9 The expected cost of liability, on the other hand, is higher under a system of no rotation because the auditor may endorse a biased report The net effect, as to which system is beneficial, depends critically on the rotation period (N) If N

is small, the total cost under a system of mandatory rotation could be greater than that with no rotation because startup costs are high But if N is sufficiently large, the total cost under a system of mandatory rotation is lower than that with no rotation In other words, mandatory auditor rotation is beneficial if rotation is not required too frequently

Corollary 1: The threshold number of consecutive engagements that produces

indifference between a system of mandatory rotation and one of no rotation is an

increasing function of startup costs and a decreasing function of the size and frequency of the required reporting deviation

Proof: See Appendix

If the firm’s manager demands specific reports more frequently and/or the size of the requested reporting deviation is large, mandatory auditor rotation can result in

benefits even if the rotation period is not large (i.e., rotation is required more frequently) The benefits are decreasing, however, as startup costs increase Opponents of mandatory rotation contend that startup costs are high and argue that the benefits of rotation do not cover the cost of auditor switching Such arguments are consistent with the above

9 Subsequently, we consider the effect of auditor rotation on the cost of conducting the audit That is, auditor learning and cost efficiencies may be associated with auditor tenure

analysis Thus far, however, we treat startup costs independent of the cost of the required reporting deviation (i.e., the manager’s desired reporting bias)

From Proposition 1, the maximum size of the required reporting deviation is a function of future quasi-rents Because the expected reporting bias should be a function

of the maximum reporting bias, the expected reporting bias is then a function of the future quasi rent Under a system of no rotation, the auditor endorses reporting bias as long as the incremental expected liability is less than the present value of future quasi rents (M+A) Thus, the auditor’s expected incremental liability, D, of endorsing the desired accounting value and, in turn, the cost of audit failure is a direct function of M+A

Proposition 3: When the cost of the required reporting deviation is a direct and linear

function of startup costs, the threshold maximum number of consecutive engagements with a specific firm is not affected by the cost, but by the relative size of the deviation cost to startup costs If the maximum number of consecutive engagements is greater than the threshold value, higher startup costs lead to greater benefit of mandatory auditor rotation

Proof: See Appendix

Proposition 3 suggests that using high startup costs as an argument to oppose mandatory auditor rotation is one sided and inappropriate If the rotation period is small, high startup costs can result in greater costs under a system of mandatory rotation than no rotation However, if the rotation period is sufficiently large, high startup costs can result

in greater benefit from mandatory rotation In the absence of auditor rotation, high startup costs lead to higher quasi rents, which lead to higher reporting bias and, in turn, a higher cost of audit failure (i.e., higher expected cost of auditor liability) Mandatory auditor rotation can reduce the high cost of audit failure Furthermore, the benefit of a system of mandatory rotation, over one of no rotation, increases as startup costs increase given that the rotation period exceeds the threshold number of periods

IV Auditor Experience with the Firm

Opponents of mandatory auditor rotation contend that ongoing relations between the firm and the auditor result in the auditor obtaining unique knowledge of the firm’s operations If auditor rotation is required, the benefits of such knowledge are lost Therefore, we introduce auditor experience into the model

We use the prior number of engagements with a specific firm, n, to represent auditor experience (i.e., auditor tenure) Now assume that audit error is a function of

audit effort and auditor experience, x(ε, n) Further we assume that∂∂ ≤0

n

Lemma 2: Assume that an auditor endorses a desired accounting value in period 1 as

long as the bias is within the acceptable range Then if the present value of the auditor’s future quasi rents increases in later periods, the auditor does not increase the maximum bias endorsed in those periods

Proof: See Appendix

When the expected total future quasi-rents increase in later periods, the auditor has more discretion for endorsing a larger reporting bias in later periods However, the incumbent does not do so because the firm’s manager cannot find a more compromising auditor in the market The incumbent does not needlessly incur an increase in expected liability by endorsing a larger bias Rather the incumbent auditor endorses the same reporting bias as a new auditor would endorse

Lemma 3: The auditor’s expected liability and the total audit cost are decreasing

functions of auditor experience

Proof: See Appendix

Lemma 3 suggests that the audit is conducted more proficiently as the auditor gains experience Firm-specific experience enables the auditor to conduct tests more effectively and to plan the audit more efficiently As a consequence, auditor experience leads to fewer audit errors and reduces total audit cost

Proposition 4: The auditor’s experience does not affect the results presented in

Proposition 1 However, the quality of the reported accounting value increases as the auditor’s experience increases

Proof: See Appendix

Financial reporting quality can be measured by the auditor’s total expected

liability because auditor liability is a monotonic increasing function of misstatements in

the reported accounting value Lower financial reporting quality implies greater

misstatement in the reported accounting value, which implies higher expected liability Under a system of mandatory rotation, the auditor does not endorse biased reports and the auditor’s expected liability is a decreasing function of auditor experience Thus the quality of the reported accounting value increases as the auditor’s experience increases

Under a system of no rotation, the auditor endorses biased reports As shown earlier (Lemma 2), the expected reporting bias is the same across periods, regardless of the auditor’s experience But audit errors are reduced as the auditor gains experience and, in turn, the auditor’s expected liability is lowered Therefore, under a system of no rotation, financial reporting quality also is an increasing function of auditor experience

Recent studies conclude that auditor rotation is not desirable because empirical

evidence suggests that financial reporting quality increases as auditor tenure (experience) increases From Proposition 4, financial reporting quality increases with auditor

experience under both systems (rotation and no rotation) Because the empirical tests are conducted only under the current system (i.e., one that does not require auditor rotation), the practical implications for rotation are not clear That is, the findings do not provide insight into the relative merits of mandatory auditor rotation

Corollary 2: If significant learning occurs in early periods of the auditor-firm

relationship, the benefit derived from mandatory rotation could be higher

Proof: See Appendix