Simulations can indicate the relative importance of P and C/M in explaining the dispersion of audit intervals across the sample of firms. A measure of the relative dispersion of optimal r., across the sample is given by the coefficient of variation, V, of optimal /„.''' In the first set of simulations, the value of C/M was set at the same level of 6.5 for all firms {6.5 is the mean value of C/M for the sample). Given this value for C/M, simulations are conducted for alternative values of the beta scaling factor. The value of V for each simulation is then compared with the value in the baseline case, which is equal to 0.62. Table I gives the results. The effect of setting C/M equal to 6.5 for all firms is to reduce the value of V substantially from 0.62 to between 0.06 and 0.15. depending on the value of the beta scaling factor. This shows that variation in C/M between firms accounts for a large amount of the dispersion of optimal /„ across firms. Table I also shows the results of a second set of simulations in which the value of P is set at 0.59 for all firms (0.59 is the mean value across the sample) and the baseline beta scaling factor of 0,01 is applied. In this simulation. the values of C/M for all firms are then scaled by various factors. This indicates the effect of the different values of C/M across firms on the variation in audit intervals; and the use of scaling factors for C/M determines this effect for different levels of C/M. A comparison of the Ys from these simulations with the baseline case indicates that variation in P across firms has little impact on the relative dispersion of optimal /„. These results suggest that, for our data and given the rate of interest of 6 percent, relative audit costs are more important than relative riskiness in explaining the dispersion of optimal audit intervals across firms. The Appendix gives a mathematical analysis of the effect of changes in audit costs, riskiness and the interest rate on the optimal audit interval based on the solution to eq. (5), which applies to the infinite horizon.
Simulations can indicate the relative importance of P and C/M in explaining the dispersion of audit intervals across the sample of firms. A measure of the relative dispersion of optimal r., across the sample is given by the coefficient of variation, V, of optimal /„.''' In the first set of simulations, the value of C/M was set at the same level of 6.5 for all firms {6.5 is the mean value of C/M for the sample). Given this value for C/M, simulations are conducted for alternative values of the beta scaling factor. The value of V for each simulation is then compared with the value in the baseline case, which is equal to 0.62. Table I gives the results. The effect of setting C/M equal to 6.5 for all firms is to reduce the value of V substantially from 0.62 to between 0.06 and 0.15. depending on the value of the beta scaling factor. This shows that variation in C/M between firms accounts for a large amount of the dispersion of optimal /„ across firms. Table I also shows the results of a second set of simulations in which the value of P is set at 0.59 for all firms (0.59 is the mean value across the sample) and the baseline beta scaling factor of 0,01 is applied. In this simulation. the values of C/M for all firms are then scaled by various factors. This indicates the effect of the different values of C/M across firms on the variation in audit intervals; and the use of scaling factors for C/M determines this effect for different levels of C/M. A comparison of the Ys from these simulations with the baseline case indicates that variation in P across firms has little impact on the relative dispersion of optimal /„. These results suggest that, for our data and given the rate of interest of 6 percent, relative audit costs are more important than relative riskiness in explaining the dispersion of optimal audit intervals across firms. The Appendix gives a mathematical analysis of the effect of changes in audit costs, riskiness and the interest rate on the optimal audit interval based on the solution to eq. (5), which applies to the infinite horizon.
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