The auditors wish to test the valuation of accounts receivable in the audit of Kaplan Corporation. The client has of total recorded receivables, composed of 2,000 accounts. The auditors have decided to use structured non-statistical sampling and have determined the following:

Tolerable misstatement $50,000
Assessment of inherent and control risk Moderate
Risk related to other substantive procedures Moderate

a. Calculate the required sample size.
b. Assume that the auditors have tested the sample and discovered three misstatements:

Book value Audited value
$100 $90
512 600
900 520

The remainder of the sample had an average value (book and audited) of S501.OO. Use the ratio estimation method to calculate the projected misstatement of the population.

c. Use the results obtained in (b) to come to a conclusion about whether to "accept" or "reject" the population.

a. The required sample size  = 32

b.  Projected misstatement  = $18,826

c. The population will be accepted

Explanation:

a. The required sample size can be calculated as below:

Sample size = (population book value * reliability factor)/Tolerable misstatement

                     =($1000,000*1.6)/$50,000

 Sample size  = 32

b. For all the three accounts, the book value is $(100 +512 + 900) = $1,512

For all the three accounts, the audited value is $(900 + 600+ 520) = $1,210

Since the remainder of the sample has an average book  and audited value of  $501, then the total misstated accounts = $510 * 29 =$14529.

The total values (book and audited) are below:

                                                           Audited value ($)          Book value ($)

3 accounts with misstatement              1,210                               1,512

Other 29 accounts                                 14,529                            14,529

Total                                                        15,739                             16,041

In the given sample, the misstatement is  $(16,041 - 15, 739) =$ 302

The projected misstatement is calculated below :

Projected misstatement = (Sample net misstatement/Book value of sample) * Book value of population

Projected misstatement = ($302 */$16,041) * $1000,000

   Projected misstatement  = $18,826

c. Since the projected misstatement does not approach $50,000, it follows that the population will be accepted