Question

Question 1: Ratio estimation and difference estimation are two widely used variables sampling plans. Required: a. Under what conditions are ratio estimation or difference estimation appropriate sampling plans for estimating the total dollar value of a population? b. What relationship determines which of these two plans will be most efficient in a particular situation?

Question 2: Bill Jones wishes to use nonstatistical sampling to select a sample of his client's 3,000 accounts receivable, which total $330,000. He believes that $30,000 represents a reasonable tolerable misstatement. He also has assessed both the combination of inherent and control risk at the maximum level and the risk that other substantive procedures will fail to detect a material misstatement at the maximum. He wishes to use a structured approach. Use the formula presented in the text to calculate the required sample size.

Question 3: 1. 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 Required: Calculate the accounts receivable estimated audited value and projected misstatement using the:

a. Mean-per-unit method. b. Ratio method. c. Difference method.

Answer 1

Question 1 :

1. Ratio and difference estimation techniques are appropriate when all of the following conditions are met :

• every item in the population has a known book value.
• an audited or corrected value maybe ascertined for every item included in the sample.
• differences between audited and book values are relatively frequent.

2. The relationship of the differences in audited and book value to book values determines whether ratio or difference estimation will be more effective. Ratio estimation is more effective when the differences are nearly proportional to book values. Thus, the ratios of audited to book values will be relatively constant. This occurs more frequently than might be apparent because of the tendency for transactions and errors to be nearly proportional to account balances. When misstatements are not nearly proportional to account balances, the variability of the ratios of audited to book values increases. This may cause difference estimation to become the more efficient technique.

Question 2 :

The required sample size is calculated as :

Sample size = population value * reliability factor / tolerable misstatement

                     = $330000 * 3.00 / $30000 = 33

Question 3 :

(a.) The mean per unit method estimates the total value of the population by (1) using the sample audited mean as an estimate of the true population mean, and (2) extending this estimated population mean by the number of items in the population as follows :

$990 * 3000 accounts = $2970000 estimated audited value.

The projected misstatement is equal to the client's book value minus the estimated audited value :

$3000000 - $2970000 = $30000 projected misstatement (overstatement)

(b.) The projected misstatement using the ratio method is calculated as follows :

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

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

Book value of the sample = 100 * $998 = $99800

Projected misstatement = - $800 / $99800 * $3000000 = $24048 overstatement

The estimated audited value would be calculated as follows :

Estimated audited value = Book value - projected overstatement = $3000000 - 24048 = $2975952

(c.) The projected misstatement using difference estimation would be calculated as follows :

Projected misstatement = Sample net misstatement / Sample items * Population items = - $800 / 100 * 3000 = $24000 overstatement

The estimated audited value would be calculated as follows :

Estimated misstatement = Book value - Projected misstatement = $3000000 - 24000 = $2976000.