Question

(1) Give some examples of the MUS (Monetary Unit Sampling) or probability proportionate to size (PPS) process and calculations that are conservative and explain why they are conservative.

(2) Describe some non-statistical alternatives to MUS and discuss why the auditor might use them.

(3) In your own words, mention the major advantages and disadvantages of MUS over classical variables sampling.

Answer 1

Q.1

Monetary Unit Sampling, also called probability-proportional-to-size or dollar-unit sampling, to determine the accuracy of financial accounts. With monetary unit sampling, each dollar in a transaction is a separate sampling unit. A transaction for $40, for example, contains 40 sampling units. Auditors usually use monetary unit sampling to sample and test accounts receivable, loans receivable, and inventory.

Here’s an example of how monetary unit sampling works. The audit client’s accounts receivable book value is $300,000, and the sample size is set at 96 records.

1. Figure the sampling interval by dividing book value by sample size (300,000/96).

2. Arrange the client’s accounts receivable in an ordered list using some sort of ordering sequence.

   For example, you can arrange them alphabetically by customer name or numerically by customer number.

3. Pick a random number between 1 and 3,125.

   For this method to work correctly, the random number has to be less than the sampling interval and greater than the smallest sampling unit. Auditors usually use a random-number-generator computer program to pick the random number. The sampling unit and sampling interval limits are programmed into the software before the task is run. In this case, say the software selects the random number 556.

The following table shows an calculated example.

Customer Balance $435 $785 $1,510 $5,000 Cumulative Balance $435 $1,220 $2,730 $7,730 Sampling Item Customer Name ABC Electric Best Friend Cat Care Brandy's Grill Buddy's Gas Station (1) $556 (2) $3,681

Take the alphabetically ordered list shown in the Customer Name column, which lists every customer balance by dollar amount, and count each dollar until you get to $556 (remember that the random number generator gives you the number 556 in Step 3 in the previous numbered list). The cumulative dollar amount for ABC Electric is under $556.

That tells you that the first sampling item is Best Friend Cat Care, which at a cumulative total of $1,220 is the first customer in the list with a cumulative balance over $556. The client gives you the Best Friend Cat Care file. You go through these ordered invoices (usually the invoices are ordered by date) to find the invoice with the 556th dollar. That invoice is your item to sample.

To select your next invoice to sample, add the sampling interval of $3,125 to your random number of $556. This equal $3,681, which is your next sampled item dollar amount. Brandy’s Grill at $2,730 cumulatively is under $3,681, so skip past Brandy’s to Buddy’s. Follow the same procedure you use for Best Friends to find the Buddy invoice with the 3,681st dollar.

Although the table only goes as far as Buddy’s, your client has many more customers. To pick the next sampling item, add the sampling interval of $3,125 to your prior sampling item of $3,681, which equals $6,806, and so on until you reach the last name in the customer list.

When you’re sampling, you’re looking for misstatements. If an invoice should have been entered for $986, for example, and it was entered as $896, the misstatement is 9 percent of the transaction (the inverse of 896/986). If the total misstatements exceed your assessed tolerance level, you have to decide whether to perform other procedures.

Q.2

Non-statistical sampling is the selection of a test group that is based on the examiner's judgment, rather than a formal statistical method. For example, an examiner could use his own judgment to determine one or more of the following: The sample size. The items selected for the test group.

1. For non-statistical sampling, auditing standards permit the auditor to use any of the selection methods.

2. MUS uses PPS sampling that allows the physical inclusion of an item more than once in the sample.

3. Auditor must consider that the true population misstatement may be larger due to sampling error.

4. With nonstatistical population the auditor uses judgment to decide if the potential misstatement in the population is greater than tolerable misstatement.

5. MUS computes misstatement bounds that provide an objective evaluation.

Q.3

Advantages of MUS

The important advantages of MUS are:

1. It normally produces smaller sample sizes than other substantive sampling plans.

2. There is no difficulty in expressing a conclusion in monetary terms.

3. The application of rupee unit sampling is not contingent on knowledge of the population size. This permits sample selection to be started before the total value of the final population is known. As will be explained later in the session, the average sampling interval can be worked out without details of population size.

4. No rupee stratification is necessary, as this will be accomplished automatically, thus avoiding problems of determining optimum strata boundaries and allocation of sample size among strata.

5. It is relatively easy to apply compared to other sampling plans.

6. The problem of detecting the large but infrequent errors is solved, since all items greater than the sampling interval will be selected.

Disadvantages of MUS

The main disadvantages of MUS are the following:

1. Accounts/items with nil balances will have no chance of selection.

2. The more an item is understated; the less likely the item has a chance of selection. Hence, MUS is less useful for finding understatements.

3. A large percentage error in a small transaction can significantly increase the computed error limit.

4. It is very difficult to use MUS in a non-computerized environment as totaling the sample items in the population for the purpose of finding out the particular item in which the dollar falls.

5. MUS is more time consuming than other sampling plans, as the number of sampling units (rupee) is higher than in attribute sampling (physical unit like voucher, cheque).