There is a distinction between the audit report interval and the interval between auditor/client interaction.- The interval between an audit report remains limited by regulatory requirements. However, the trend to more frequent reporting and less stringent regulatory requirements for auditing' has created opportunity for greater flexibility in the choice of audit report interval. There is also increasing variation
in the interval between auditor/client interaction. We observe anecdotal evidence of more frequent interaction between auditor and client (i.e., informal reporting, special projects, additional assurance services). This is perhaps the early manifestation of the predicted trend toward shifting the attest function from a focus on financial statements to the procedures and processes used to present data for access by end users (see, for example, Wallman [1997]; Elliott [19941). More frequent interaction with the client has led to the development of standards and techniques for continuous auditing. The CICA (1999) state that embedded modules, digital agents, and integrated tools could be designed to operate with varying degrees of frequency; and that such automated procedures would be supplemented from time to time with procedures requiring the personal presence of the auditor. It is legitimate to ask how often such client/auditor interaction ought to take place in the same way as it is becoming legitimate to ask how often the audit report ought to take place. The focus in this study is on the audit report interval but we suggest there is potential for wider application of the optimizing approach to scheduling auditor/client interaction in provision of the growing range of assurance services. Our approach is to apply a model of optimal internal audit scheduling to the timing of external audit intervals for private, family-controlled companies. The internal audit planning problem has been examined using two different approaches (see Anderson and Young [1988] for a review). One approach is to determine the optimal allocation of a fixed audit budget among multiple audit units. This problem is how much to spend on an auditable unit at fixed intervals of time rather than how often to audit the unit. See Patton, Evans, and Lewis (1983) and Anderson and Young (1988) for examples of this formulation of the audit planning problem. The alternative approach, applied in this paper to an external audit setting, is to determine how often to audit a unit based on costs and benefits which change over time. Wilson and Ranson (1971) were the first to model this approach formally.
They were followed by Hughes (1977), Boritz and Broca (1986), and Knechel and Benson (1991). The method is to adapt the machine replacement problem by dividing an organization into a number of auditable units. Each unit is assigned a relative risk score that indicates the rate at which losses are expected to accrue in the absence of an audit. Given an invariant cost of an audit for each unit the optimal audit interval is that which minimizes the discounted sum of all relevant costs, which consist of the audit cost and the losses that accrue in the ahsence of an audit. The planning horizon is long enough to allow many audit cycles and may be infinite. In Hughes (1977). the optimal interval hetween audits is randomly determined by a Bayesian rule, given the assumption that an auditable unit is either incompliance or out-of-compliance. Boritz and Broca (1986), however, follow the method in Wilson and Ranson (197!) in assuming that the auditable unit becomes progressively out-of-compliance as the interval between audits increases. The pattern of losses that accrue in the absence of an audit is determined by a loss function. The Boritz and Broca paper shows how the Wilson and Ranson model can be applied by developing a method of calibrating the model and solving it using numerical methods. This approach is extended by Knechel and Benson (1991) to include a budget constraint for overall audit resources. Hence their model is constrained version of the unconstrained optimization problem in Bodtz and Broca (1986).
There is a distinction between the audit report interval and the interval between auditor/client interaction.- The interval between an audit report remains limited by regulatory requirements. However, the trend to more frequent reporting and less stringent regulatory requirements for auditing' has created opportunity for greater flexibility in the choice of audit report interval. There is also increasing variation
in the interval between auditor/client interaction. We observe anecdotal evidence of more frequent interaction between auditor and client (i.e., informal reporting, special projects, additional assurance services). This is perhaps the early manifestation of the predicted trend toward shifting the attest function from a focus on financial statements to the procedures and processes used to present data for access by end users (see, for example, Wallman [1997]; Elliott [19941). More frequent interaction with the client has led to the development of standards and techniques for continuous auditing. The CICA (1999) state that embedded modules, digital agents, and integrated tools could be designed to operate with varying degrees of frequency; and that such automated procedures would be supplemented from time to time with procedures requiring the personal presence of the auditor. It is legitimate to ask how often such client/auditor interaction ought to take place in the same way as it is becoming legitimate to ask how often the audit report ought to take place. The focus in this study is on the audit report interval but we suggest there is potential for wider application of the optimizing approach to scheduling auditor/client interaction in provision of the growing range of assurance services. Our approach is to apply a model of optimal internal audit scheduling to the timing of external audit intervals for private, family-controlled companies. The internal audit planning problem has been examined using two different approaches (see Anderson and Young [1988] for a review). One approach is to determine the optimal allocation of a fixed audit budget among multiple audit units. This problem is how much to spend on an auditable unit at fixed intervals of time rather than how often to audit the unit. See Patton, Evans, and Lewis (1983) and Anderson and Young (1988) for examples of this formulation of the audit planning problem. The alternative approach, applied in this paper to an external audit setting, is to determine how often to audit a unit based on costs and benefits which change over time. Wilson and Ranson (1971) were the first to model this approach formally.
They were followed by Hughes (1977), Boritz and Broca (1986), and Knechel and Benson (1991). The method is to adapt the machine replacement problem by dividing an organization into a number of auditable units. Each unit is assigned a relative risk score that indicates the rate at which losses are expected to accrue in the absence of an audit. Given an invariant cost of an audit for each unit the optimal audit interval is that which minimizes the discounted sum of all relevant costs, which consist of the audit cost and the losses that accrue in the ahsence of an audit. The planning horizon is long enough to allow many audit cycles and may be infinite. In Hughes (1977). the optimal interval hetween audits is randomly determined by a Bayesian rule, given the assumption that an auditable unit is either incompliance or out-of-compliance. Boritz and Broca (1986), however, follow the method in Wilson and Ranson (197!) in assuming that the auditable unit becomes progressively out-of-compliance as the interval between audits increases. The pattern of losses that accrue in the absence of an audit is determined by a loss function. The Boritz and Broca paper shows how the Wilson and Ranson model can be applied by developing a method of calibrating the model and solving it using numerical methods. This approach is extended by Knechel and Benson (1991) to include a budget constraint for overall audit resources. Hence their model is constrained version of the unconstrained optimization problem in Bodtz and Broca (1986).
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