Question

Green, CPA, performed Classical Variables Sampling to examine the inventory balances of ABC Company. Green audited 120 items from a sample and found an audited value of $34,600. The sample had a recorded balance of $36,000. If the entire inventory contained 2,400 items and the total recorded balance of the inventory was $570,000.

a. Give the estimated account balance under each of the following methods (SHOW YOUR WORK):

i. Ratio estimate

ii. Mean-per-unit

iii. Difference estimation

b. Using the difference estimate, what is the projected misstatement in inventory?

Answer 1

Based on the above question, the data can be simplifed as follows :-

No. of items audited = 120

Audited value = $34,600

Recorded Value = $36,000

1.) Ratio estimate compares the sample estimate of the variable with the population total. This is used as a classical method of Variables sampling. The ratio estimation is a ratio of proportion of error in sample applied to the population value to estimate the total error.

As in our case :-

Sample Recorded Balance = $36,000

Sample Audited Balance = $34,600

Difference = $1,400

The Ratio estimate is 3.89% ($1,400/$36,000)

2.) Mean per unit sampling estimates the total value of the population by using the sample audited mean as the estimate of the true population mean and extending the dervied sample audited mean to the number of items in the population.

Based on the above data , we can calculate mean per unit as follows :-

No.of audited items = 120

Audited Value = $34,600

Mean per unit = $34,600/120 = 288.33

This mean per unit can be multiplied by 2,400 (total items) to project to population = 288.33 * 2400 = $6,92,000

Mean per unit sampling Variance = $692,000 - $570,000 = $122,000

3.) Difference Estimation estimates and projects the difference found in the audited balance to the total inventory balance by :-

Audited items = 120

Total items = 2400

Difference noted = $1,600

Difference estimation now uses a ratio to find out the projected value of misstatement based on the audit procedures performed in the audit sample selected.

= ($2,400 * $1,600)/120

= $32,000

$32,000 would be the projected misstatement in inventory by using the Difference Estimate method of sampling.