1. Nicole Sung wishes to test the valuation of inventory in the audit of Jody Wong Enterprise of Park City. The client has $10,000,000 in total recorded inventory, composed of 2,000 accounts. The auditors have determined the following:
Tolerable misstatement $500,000
Risk of incorrect acceptance 5%
Risk of Incorrect rejection 10%
Expected misstatement $50,000
Nicole Sung has decided to use probability-proportional-to-size sampling.
a. For planning the sample, calculate:
(1) Required sample size.
(2) Sampling interval.
b. Assume that Nicole Sung has tested the sample and discovered five misstatements:
Book Value Audited Value Difference Taint
$ 15,000 $ 14,700
18,000 17,400
25,000 24,500
66,000 55,000
78,500 75,100
Calculate:
(1) Projected misstatement.
(2) Basic precision.
(3) Incremental allowance.
(4) Upper limit on misstatement.
c. Explain how Nicole Sung would consider the results calculated in b.
 
2. Nicholas Wunsch using mean per unit sampling to evaluate the reasonableness of the book value of accounts receivable of Enlin Xiao, Inc. Enlin Xiao, Inc. has 650,000 receivable accounts with a total book value of $65,000,000. Nicholas Wunsch estimates the population’s standard deviation as being equal to $15. After examining the overall audit plan, Nicholas Wunsch believes that the account's tolerable misstatement is $800,000, and that a risk of incorrect rejection of .10 (risk coefficient = 1.64) and a risk of incorrect acceptance of .15 (risk coefficient = 1.04) should be used.
a. Calculate the required sample size.
The formula for determining sample size in mean-per-unit sampling is:

the formula in the attached photoNow ignore your sample size calculation in part "a," and assume that your answer was a sample size, of 1600 (the square root of 1600 is 40) and that you obtained the following results:Average audited; value of items in sample $96
Average book value of items in sample $98
Standard Deviation in the sample (audited values) $14
Standard Deviation in the sample (book values) $15
b. Using mean-per-unit sampling, calculate the projected misstatement for the population.
c. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to form a statistical conclusion concerning the book value of the population ($65,000,000). That is, calculate an interval and either "accept" or "reject" the client's book value.

 

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