Fairview Publishing Company, incorporated in 1974, is a small, closely held publisher of high school textbooks. A local accounting firm has reviewed the preparation of the financial statements, performed certain audit procedures, and prepared the tax returns for many years. The accountants' report has always contained a disclaimer of opinion, because the stockholders would not permit confirmation of receivables or observation of inventories.

The company plans to "go public" in about three years. In anticipation of this, they engaged you in May to perform an audit for the year ended June 30 The company's first fiscal quarter is usually the most profitable; the last quarter is usually a break-even situation.

The company has a job order cost system for determining its unit cost prices for each textbook. If a book has not been ordered by any customer for twelve months, it is "no valued," scrapped, and discontinued. Only a minimal quantity is maintained of each title until a firm order is received. The compans expects that it has no more than \(\$ 3,000\) inventory of any one title.

You have completed your yearend inventory work and found the client's perpetual records were remarkably accurate with respect to quantities, unit prices, and extensions. No errors "ere located and it was concluded that the perpetual records can be relied on for beginning inventory quantities.

However, as to the beginning inventory amount, the client is not able to produce a listing with detail sufficient to provide at: audit trail. They can find only an adding machine tape we support the recorded amount. \(\$ 1,405,105\). The tape is in no particular order.

At june 30 of the prior year, the company had exactly 1.000 different titles in inventory. This agrees with the number of entries on the tape and with the number of perpetual records having a quantity at the beginning of the current year.

In this case, \(\$ 150.000\) is considered a material amount. Internal controls have been determined to be 80 percent effective in preventing material errors from occurring. Supplemental audit procedures regarding the beginning inventor balance are quite extensive and are estimated to be 40 percent effective in detecting material misstatement The desired combined reliability kevel is 95 percent. Some pricing errors are expected of an alpha risk of 95 percent is considered reasonable. Based on this years inventory the standard deviation should approximate \(\$ 635\) and you have decided to use one stratum.

Required:

a. What is the nature and objective of the test?

b. Compute beta risk

c. What desired precision should be used in determining sample size? (Round down to the nearest \(\$ 10,000\).)

d. Calculate sample size (without replacement) using the estimated standard deviation of \(\$ 635\) and the desired precision determined in c above.

e. Assuming the sample produces an audited value of sample items of \(\$ 123,954\) and a standard deviation of \(\$ 662\), calculate (1) the estimated total population value and (2) the achieved precision interval.

f. Compute adjusted achieved precision.
g. Interpret the results of the sample.