Equation (4) gives TDC(tJ for a given audit interval. Assuming the firm to be a going concern for an indefltiite period, the objective is to find the audit interval t^, which minimizes the sum of TDC(O over a long planning horizon, which allows for a large number of audit intervals.
For an infinite planning horizon (and therefore an infinite number of audit intervals), we follow the procedure in Boritz and Broca (p. 11) to derive the optimal /„ by differentiating eq. (4) with respect to /„. The result is the following equation, which differs from that in Boritz and Broca (1986) due to our extension in specifying the audit cost as a function of the audit interval; see eq. (2).