Scott Duffney, CPA, has randomly selected and audited a sample of 100 of Will-Mart’s accounts receivable. Will-Mart has 3,000 accounts receivable accounts with a total book value of $3,000,000. Duffney has determined that the account’s tolerable misstatement is $250,000.

His sample results are as follows:
Average audited value $990
Average book value 998
Calculate the accounts receivable estimated audited value and projected misstatement using the:
(a) Mean-per-unit method.
(b) Ratio method.
(c) Difference method.

The answer is:

(a) Mean-per-unit method:

Estimated audited value: $990 * 3,000 = $2,970,000

Projected misstatement: $3,000,000 - $2,970,000 = $30,000

(b) Ratio method:

Sample net misstatement: 100 * ($990 - $998) = -$800

Projected misstatement: $800 / ($998 * 100) * $3,000,000= $24,048

Estimated audited value: $3,000,000 - $24,048 = $2,975,952

(c) Difference method:

Projected misstatement: $800 / 100 * 3,000 = $24,000

Estimated audited value: $3,000,000 -  $24,000 = $2,976,000

Explanation:

(a) Mean-per-unit method: The mean-per-unit method estimates the total value of the population by using the  sample audited mean as an estimate of the true population mean, and extending this  estimated population mean by the number of items in the population.

(b) Ratio method:

The projected misstatement using the ratio method is calculated as:

 Absolute value of Sample net misstatement  / Book value of sample  * Population book value

Estimated audited value: Book value - Projected misstatement

(c) Difference method:

The projected misstatement using difference estimation would be calculated as:

 Absolute value of Sample net misstatement  / Sample items  * Population items

Estimated audited value: Book value - Projected misstatement

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