Chapter G, Problem 57EP

a)

To determine

Compute the upper limit on misstatements for 5 percent level of incorrect acceptance and identify the relationship noticed between the risk of incorrect acceptance and the upper limit on misstatements.

Explanation of Solution

Tainting percentage: Tainting percentage is the amount that indicates the proportion by which a “logical unit is misstated” and it is ascertained by dividing the difference among the “recorded balance and the audited value by the recorded balance”.

Formula for calculating tainting percentage is as below:

$\text{Tainting}\text{percentage}\text{=}\frac{\left(\text{Recorded}\text{balance}-\text{Audited}\text{value}\right)}{\text{Recorded}\text{balance}}$

Upper limit on misstatements: An upper limit misstatement (ULM) is the figure of three components namely, “the projected misstatement, the incremental allowance for sampling risk and the basic allowance for sampling risk “or it is the amount having $\left(\text{1}-\text{Risk}\text{of}\text{incorrect}\text{acceptance}\right)$ the possibility of equaling or exceeding the “ true amount” of misstatement in the population.

The steps involved with calculating the upper limit on misstatements are as follows:

• Initially for calculating the “upper limit on misstatements”, projected misstatements must be calculated by finding out the difference between the “audited value” of an item and recorded balance an item.
• Second, “basic allowance for sampling risk” must be computed by multiplying the sampling interval and confidence factor.
• Finally, “incremental allowance for sampling risk” is computed by multiplying the “projected misstatement” and “incremental confidence factor”.

All of the misstatements must be considered in the upper limit on misstatements computation.

Calculate the upper limit on misstatements.

Step 1: Calculate the tainting percentage.

Account	Recorded Amount (a)		Audited value (b)	Misstatement $\text{c=}\left(\text{a}-\text{b}\right)$		Tainting Percentage $\left[\text{d}\text{=}\frac{\text{c}}{\text{a}}\right]$
X-21	$3,000		$1,200	$1,800		0.60
Z-24	$550		$440	$110		0.20
AA-02	$6,000		$1,500	$4,500		0.75

Table (1)

Step 2: Calculate the projected misstatement.

Account	Tainting Percentage		Sampling interval		Projected misstatement
X-21	0.60	×	$10,000	=	$6,000
Z-24	0.20	×	$10,000	=	$2,000
AA-02	0.75	×	$10,000	=	$7,500
					$15,500

Table (2)

Step 3: Calculate the incremental allowance.

Account	Projected Misstatement		Incremental factor minus 1 (Refer to table 4)		Incremental Allowance
X-21	$7,500	×	$\left(\text{4}\text{.75}\text{–3}\text{.00 – 1}\right)$	=	$5,625
Z-24	$6,000	×	$\left(\text{6}\text{.30}\text{–}\text{4}\text{.75 – 1}\right)$	=	$3,300
AA-02	$2,000	×	$\left(\text{7}\text{.76 –}\text{6}\text{.30 – 1}\right)$	=	$920
					$9,845

Table (3)

Note: “For every projected misstatement, whose recorded balance is smaller than the sampling interval, rank the projected misstatements in descending order depending upon the dollar amount”.

Step 4: Calculate the basic allowance for sampling risk.

$\begin{array}{c}\begin{array}{l}\text{Allowance}\text{for}\\ \text{sampling}\text{risk}\end{array}\}\text{=}\text{Sampling}\text{interval}\text{×}\text{Confidence}\text{factor}\\ \text{=}\text{\$10,000}\text{×}\text{3}\text{.0}\\ \text{=}\text{\$30,000}\end{array}$

Note: Confidence factor (3.00) is selected for 0 overstatement misstatements as these sampling intervals do not contain an overstatement error.

Working note (1): Identify the Confidence Factors for Sample Evaluation:

Number of overstatement misstatements	Risk of incorrect acceptance  is 5%
0	3.00
1	4.75
2	6.30
3	7.76

Table (4)

Note: Refer to exhibit GA.2.

Step 5: Calculate the upper limit on misstatements.

Particulars	Amount
Projected misstatement	$15,500
Incremental allowance for sampling risk	$9,845
Basic allowance for sampling risk	$30,000
Upper limit on misstatements	$55,345

 Table (5)

Therefore, upper limit on misstatements is $55,345.

b)

To determine

Compute the upper limit on misstatements for 10 percent level of incorrect acceptance and identify the relationship noticed between the risk of incorrect acceptance and the upper limit on misstatements.

Explanation of Solution

Calculate the upper limit on misstatements.

Step 1: Calculate the incremental allowance.

Account	Projected Misstatement		Incremental factor minus 1 (Refer to table 7)		Incremental Allowance
X-21	$7,500	×	$\left(\text{3}\text{.89}\text{–}2.\text{31 – 1}\right)$	=	$4,350
Z-24	$6,000	×	$\left(\text{5}\text{.33}\text{–}3.89\text{– 1}\right)$	=	$2,640
AA-02	$2,000	×	$\left(\text{6}\text{.69}\text{–}5.\text{33 – 1}\right)$	=	$720
					$7,710

Table (6)

Note: “For every projected misstatement, whose recorded balance is smaller than the sampling interval, rank the projected misstatements in descending order depending upon the dollar amount”.

Step 2: Calculate the basic allowance for sampling risk.

$\begin{array}{c}\begin{array}{l}\text{Allowance}\text{for}\\ \text{sampling}\text{risk}\end{array}\}\text{=}\text{Sampling}\text{interval}\text{×}\text{Confidence}\text{factor}\\ \text{=}\text{\$10,000}\text{×}2.31\\ \text{=}\text{\$23,100}\end{array}$

Note: Confidence factor (2.31) is selected for 0 overstatement misstatements as these sampling intervals do not contain an overstatement error.

Working note (2): Identify the Confidence Factors for Sample Evaluation:

Number of overstatement misstatements	Risk of incorrect acceptance  is 10%
0	2.31
1	3.89
2	5.33
3	6.69

Table (7)

Note: Refer to exhibit GA.2.

Step 3: Calculate the upper limit on misstatements.

Particulars	Amount
Projected misstatement	$15,500
Incremental allowance for sampling risk	$7,710
Basic allowance for sampling risk	$23,100
Upper limit on misstatements	$46,310

 Table (8)

Therefore, upper limit on misstatements is $46,310.