Question

Please help with problem 8-56 and 8-57. Thank you!!!

8-56 106 Assume you are planning the confirmation of accounts receivable. There are 2,000 customer accounts with a total book! value of $5,643,200. Tolerable misstatement is set at $200,000, and expected misstatement is $40,000. The risk of incorrect accep- tance is 30%. The ratio of expected to tolerable misstatement is 20%, and the ratio of tolerable misstatement to the population is 3.5% (round down to 3% for use in Exhibit 8.7) a. What is the sample size? b. What is the sampling interval? c. What is the largest value you can use for a random start? d. Using the following list of the first fifteen items in your popula- tion, a random start of $25,000, and a rounded sample interval of $100,000, identify the items to be included in your sample. Cumulative Cumulative Book Plus Included in BookR andom Start Sample? Book Value Selection Amount (S) Item Random Start Ocvw 3,900 26,000 5,000 130,000 2,000 260,000 100 25,000 19,000 10,000 9,000 2.500 65,000 110,000 6,992 12 14 15

Answer 1

The sample size is 54 a Total population size Sample size Sampling interval 5643200 54 104504 =5643200/54 The largest item that can be used for the sample item is the sampling interval i.e., 104504. Though, the best practice is to round off the sampling interval to either 104000 or 105000 if selected manually. By way of following the first 15 item in our population with a random start of 25000 and a rounded sample interval of 100000, the items to be included in the sample are Cumulative amount Book value Sample item Item Random start 25000 28900 3900 54900 26000 5000 59900 4 130000 189900 YES 2000 191900 260000 6. 451900 YES 100 452000 25000 477000 8. 496000 19000 10 10000 506000 YES 11 9000 515000 517500 12 2500 13 65000 582500 14 110000 692500 YES 6992 15 699492 The first sample item is the one that first causes the cumulative total to equal or exceed the sampling interval i.e., $100,000. Successive sample items are those first causing the cumulative total to equal or exceed multiples of the intervals. i.e., for item 4, the cumulative total first exceeded $100,000 or multiple of $100,000 and hence item 4 is considered for sample. Similarly, for item 6, the cumulative total first exceeded $200,000 or multiple of $100,000. Likewise, we need to select the item after adding which the total crosses $100,000 or multiples of $100,000. The probability of selecting any particulars item is proportional to the number of dollars in it Probability of selection 3900 Book value Item 4% 26000 26% 2 100% 130000 100% 360000 4 Book value 3900% Sampling interval Probability of selecting the item 3.9% or 4% 100000% All items with a book value equal to or greater than the interval will be selected for auditor evaluation. These items are referred to as top- stratum items. For customer 6, the book value is 260,000. If we add this total to cumulative total till item 5, we will get 451,900. The selection points are $200,000, $300,000 and $ 400,000 using sampling interval. Hence, the book value for customer 6 has 3 selection points but it will be examined only once. Thus, the number of logical units (customer balances) will be less than the sample size of dollar units.