3.3 Case II: No Fraud is Detected in Period One
3.4.4 Efficiency and Cost Effectiveness o f Rotation / Retention Rules 150
In the current setup, a mandatory rotation regime will force clients to switch auditors after the first period. Given that the auditor-client match is ex-ante unobservable, clients will have to chose a second period auditor at random from the pool of successors, ju st as occurs in period one. Note that the outcome o f the first period audit will condition the beliefs that the pool of successor auditors have regarding the client’s first and second period type and that these beliefs will condition the second
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period fees as was determined in Propositions 3.1 and 3.4. It is easy to show that the fee after a no fraud report will be lower than the fee after a fraud report due to the increased probability that the client be fraudulent in the second period. The first period report, however, will have no effect on the expected second period fraud detection probability.
A successor auditor will be a high type with probability o) and a low type with probability (1-fD), and therefore the expected second period fraud detection technology will be given by O s .
Under a mandatory retention regime, clients are forced to retain the incumbent auditor, and incumbents cannot resign the engagement. Under this regime, auditors will have to make a bid for both periods at the beginning of period one. From a fraud detection point o f view, retention is equivalent to scenario 1 in the deregulated market where incumbents are always retained. Therefore, the expected second period fraud detection probability (as determined at the beginning of period one), will also be equal to d>s , as was determined in Proposition 3.11.
The above shows that there is no difference between rotation and retention rules as far as the expected fraud detection probability is concerned: In both regimes, the expected second period fraud detection probability will be given by <I>S. We have seen, however, that the second period fee under a rotation regime will depend on the outcome of the first period audit, and that under a retention regime, auditors will have to price out all uncertainties over the entire two periods, including the possibility of being a low type
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for the entire duration of the audit. 82 Therefore, is seems plausible that these rules may induce a different price for the entire two period audit. Lemma 3.8 states, however, that the expected cost for the audit of both periods is equal for both rotation and retention rules.
L em m a 3.8: The sum o f the first and expected second period audit fees under a m andatory rotation regime is equal to the total fe e fo r the entire two period audit under a mandatory retention regime, and is given by:
2 - X + L - ằ - ( l - đ J) - e - ( y l + y 2) (3.27)
Lemma 3.8 does not imply that the actual cost for a given auditor-client engagement under both regimes will be the same, but rather, that the expected cost when determined before period one under both regimes will be equal. While the actual total fee under a retention regime will always be as given in (3.27), the actual fees paid under a rotation regime will fluctuate depending on the outcome of the first period audit.
Note, however, that the actual cost under a rotation regime must average out across the
82 One could argue that under a mandatory rotation regime some o f the second period uncertainty for the successor auditor could be resolved by communicating with the predecessor as stipulated under SAS No.
7, Communications Between Predecessor and Successor Auditors, and that this resolved uncertainty would lower the second period fee. This assumes, however, that fluid communication w ill exist between the two auditors, that the predecessor will be willing to reveal her type, and that this communication occurs before the bid is submitted to the client. This, however, contradicts with Glezen and Elser [1996], who find, in a survey setting, that 77% o f successor auditors communicate with the predecessor auditor only if the proposal is accepted.
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population o f auditor-client engagements, and will equal the average cost under a retention regime.
Lemma 3.8 also implies that if any form o f switching costs existed, then retention rules would be better than rotation rules.
In order to fully characterize and compare the rotation and retention regimes with the deregulated audit market, we must first determine the total expected audit fees for the two periods in the deregulated audit market. This issue is addressed next.
The expected first period cost is equal for all auditors in both the deregulated audit market and in any of the rotation/retention regimes. This expected first period cost is given by:
K+Lq(l-<t>s)-0ri (3 -2 8 )
The expected second period cost in the deregulated market will depend on the auditor’s type and the beliefs she has that the client be fraudulent in the second period.
We have already seen that for given parameter values, a low type incumbent will be better off resigning the second period engagement because her second period cost is greater than the successor’s bid. If, on the other hand, an incumbent is a high type, her second period cost will always be lower than the bid made by the pool of potential successor auditors and will, therefore, earn quasi-rents in the second period if retained by the client.
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Note, however, that the audit market is perfectly competitive and that this implies that auditors will make, in expectation, zero profits. Therefore, all auditors must determine the likelihood o f receiving quasi-rents in period two and discount these expected quasi-rents from their first period audit fee. Any auditor who would not do so, would stand no chance o f being engaged in period one because o f a higher bid for the first period audit. That is, lowballing must occur in the deregulated market.
Lemma 3.9 confirms this intuition and states that the first period audit fee in the deregulated market will be below the auditor’s first period cost as given in (3.28), i.e., lowballing occurs, but that the magnitude of the discount will be different depending on which o f the four second period scenarios holds.
L em m a 3.9: The fir s t p erio d audit fe e w ill always be below the a u d ito r’s firs t p erio d cost in the deregulated market. The magnitude o f the lowball w ill depend on which o f the fo u r second period scenarios is expected. That is, the firs t p erio d audit fee is given by:
K + L q - ( \ - < S > s ) - 6 y x - LB(Sc, y2), fo r Sc e {Scl, Sc2, Sc3, ScA} (3.29)
where LB( Sc, y2) > 0, denotes the lowball in each o f the fo u r possible scenarios, which w ill be a function o f y 2.S3
83 Due to the length o f the expressions that represent the lowball amount in each o f the four scenarios, they are not reproduced here. See proof o f Lemma 3.9 for these expressions.
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It is interesting to note that the lowballing will exist in the deregulated audit market despite the fact that no switching or learning costs exist. Lowballing in the current setup is a competitive response to the expectation o f future quasi-rents to incumbent auditors caused by a technological advantage in the fraud detection technology. This differs from DeAngelo [1981], where switching and learning costs are needed to justify the existence o f lowballing.
The actual second period audit fee in the deregulated market will depend on the first period report and on how y 2 compares with Y 2 should fraud be detected, or with
y 2 should no fraud be reported in the first period. Note, however, that at the beginning o f period one, all auditors can compute the expected second period fee, which as anticipated, will be scenario dependent. This expected second period audit fee is given by:84
Pr(fV .i) ' F s\^f.\ , Y2 ■*" Pr( ^ w .i) ' P's > Y i (3.30)
where Fs [Z)^ , , y2 denotes the corresponding second period audit fee when fraud has been detected in period one as given in either (3.10) or (3.11) o f Lemma 3.5 depending on how Y i compares to / 2, and Fs\d nfx,y2 , the second period audit fee when no fraud has been detected in period one as given in Lemma 3.7, depending on how y2
84 A formal derivation o f the expected second period audit fee for all four second period scenarios is presented in the proof o f Proposition 3.12.
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compares to y2. For example, if scenario 1 holds (i.e., y 2 < y^ and y 2 < y2), then the expected second period audit fee will be given by:
Having characterized the expected fraud detection technologies, the expected costs and fees for each scenario in the deregulated market and for the rotation / retention regimes, we can now compare the efficiency and cost effectiveness of rotation / retention rules against the expected outcome in the deregulated market.
Note that under any rotation or retention regime only one scenario exists, as opposed to the four possible scenarios in the deregulated market, unless the rotation / retention rule can be made contingent on the first period audit outcome. Proposition 3.12 states how unconditional rotation / retention rules compare with the deregulated audit market.
Proposition 3.12: In terms o f efficiency and cost effectiveness, the deregulated audit m arket compares with mandatory rotation and retention rules as follow s:
i) The deregulated audit market is more efficient and more cost effective than m andatory rotation or retention regimes when in the deregulated audit market auditor switches occur only after a no-fraud report, that is, i f scenario 2 holds.
®s-o-y\ 6-<t>L ■Q y l
2 ' l - Q L - 0 - y l
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ii) The deregulated audit market is as efficient and cost effective as a mandatory rotation or a mandatory retention regime when in the deregulated audit m arket auditor switches can occur both after a fra u d or no-fraud report (i.e., scenario 4), or when auditor switches never occur (i.e., scenario I).
iii) The deregulated audit market is less efficient and less cost effective than a mandatory rotation or mandatory retention regime only in the case where in the deregulated audit market auditor switches occur only after a fra u d report, that is, i f scenario 3 holds.
Proposition 3.12 implies that no unconditional (not scenario dependent) rotation or retention rules exists that is either efficient and/or cost effective when compared to the deregulated market. That is, when the entire range o f possible market conditions is considered, the deregulated market is more efficient than a market where auditor engagements are mandated by a regulatory body, despite the existence o f successful client opinion shopping in the deregulated market under some circumstances.
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