Chapter F, Problem 70EP

a)

To determine

Compute the sample rate of deviation and ULRD by using the Person J’s sample.

Explanation of Solution

Sample rate of deviation: It is a rate of deviations found in the audit sample. It is determined by dividing the deviations found in the sample with the sample size.

$\text{Samples rate of deviation = }\frac{\text{Sample deviations }}{\text{Sample size}}$

Compute the sample rate of deviation:

$\begin{array}{c}\text{Samples rate of deviation = }\frac{\text{Sample deviations }}{\text{Sample size}}\\ =\frac{0\text{deviations}}{93}\\ =0\end{array}$

Therefore, sample rate of deviation is 0%.

Upper Limit Rate of Deviation (ULRD): it is a statistical measure used by the audit team to adjust the sample rate of deviation for the acceptable level of sampling risk. The rate of deviation has a probability of totaling or over and above the true population rate of deviation.

Compute the ULRD for the given situation:

• The acceptable risk of overreliance is 5%. Therefore, sample evaluation table for 5% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 0.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 3.3.

b)

To determine

Discuss the difference between the ULRD and the sample rate of deviation computed in the requirement (a). Explain the manner this difference associated to the use of statistical sampling.

Explanation of Solution

Allowance for sampling risk: It is the difference between the ULRD and sample rate of deviation. It adjusts the sample rate of deviation to permit the audit team to control the exposure to the risk of overreliance.

$\text{Allowance for sampling risk = ULRD}-\text{Sample rate of deviation}$

The difference between the ULRD and the sample rate of deviation is referred as allowance for sampling risk. It is the risk of overreliance to adequate levels and replicates the chance that Person J has chosen a non-representative sample.

c)

To determine

Identify Person J’s conclusions regarding the operating effectiveness of Company T’s internal control.

Explanation of Solution

As the ULRD is below the tolerable rate of deviation, Person J should conclude that the internal controls are functioning properly. Therefore, Person J can depend on internal control as scheduled, and keep the control risk at scheduled levels.

d)

To determine

Calculate the sample rate of deviation and ULRD if there is three deviations found by Person J and identify Person J’s conclusions regarding the operating effectiveness of Company T’s internal control.

Explanation of Solution

Compute the sample rate of deviation:

$\begin{array}{c}\text{Samples rate of deviation = }\frac{\text{Sample deviations }}{\text{Sample size}}\\ =\frac{3\text{deviations}}{93}\\ =0.0322\text{or 3}\text{.22\%}\end{array}$

Therefore, sample rate of deviation is 3.22%.

Compute the ULRD for the given situation:

• The acceptable risk of overreliance is 5%. Therefore, sample evaluation table for 5% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 3.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 8.4.

As the ULRD is beyond the tolerable rate of deviation, Person J should conclude that the internal controls are not functioning properly. Therefore, Person J should decrease the scheduled level of reliance on internal control and it leads to increase control risk.

e)

To determine

Compute the maximum number of deviations that Person J can identify without reducing the reliance on Company T’s internal control.

Explanation of Solution

Compute the ULRD for the zero deviations:

• The acceptable risk of overreliance is 5%. Therefore, sample evaluation table for 5% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 0.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 3.3.

Compute the ULRD for one deviation:

• The acceptable risk of overreliance is 5%. Therefore, sample evaluation table for 5% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 1.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 5.2.

Therefore, the maximum number of deviations that Person J can identify without reducing the reliance on Company T’s internal control is zero as the ULRD at 1 deviation is exceeding the tolerable rate of deviation.

f)

To determine

Compute the maximum number of deviations that person J can identify at 10% risk of overreliance. Explain the differences between the number computed in this requirement and number computed in the requirement (e).

Explanation of Solution

Compute the ULRD for the zero deviations:

• The acceptable risk of overreliance is 10%. Therefore, sample evaluation table for 10% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 0.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 2.6.

Compute the ULRD for one deviation:

• The acceptable risk of overreliance is 10%. Therefore, sample evaluation table for 10% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 1.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 4.3.

Compute the ULRD for two deviations:

• The acceptable risk of overreliance is 10%. Therefore, sample evaluation table for 10% risk of overreliance is used to determine the ULRD.
• Sample size is 90.
• The number of deviations realized by the audit team is 2.
• The ULRD is the value set up at the crossing of the row in the second point and the column in the third point.

Therefore, the ULRD is 5.9.

Therefore, the maximum number of deviations that Person J can identify without reducing the reliance on Company T’s internal control is two as the ULRD at 2 deviations is exceeding the tolerable rate of deviation.

ULRD computed in this requirement is lower than the ULRD computed in the requirement (e). It is because of the accepting the higher level of sampling risk which decreases the allowance for sampling risk. In other words, lower the overreliance risk higher the ULRD.