# Monetary Unit Sampling

Last Updated :

21 Aug, 2024

Blog Author :

N/A

Edited by :

Alfina L.

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## What Is Monetary Unit Sampling?

Monetary Unit Sampling is a statistical method in auditing used to figure out the monetary discrepancies in the accounts of a population by selecting selected samples. The main purpose of this sampling method is to determine if there are any misstatements in the amounts of financial statements.

The monetary unit sampling method is an effective tool for auditors. It uses the probability test to detect these misstatements. As a result, they can easily detect errors in the audit report. Also, it acts as a vital tool in substantive tests. However, the auditors might be biased toward large samples, thus ignoring the smaller ones.

##### Table of contents

- Monetary unit sampling (MUS) is a popular statistical plus sampling method that allows auditors to select some samples and find and tally the total monetary value of the population.
- It is also known as dollar unit sampling or probability proportional to size sampling. This tool has a major application in the auditing process.
- To conduct MUS, selecting sample size, sample method, tolerable tainting, and probability of misstatements is important.
- The statements are proper if the upper and lower Misstatement bounds are less than tolerable misstatements. However, if they exceed the limit, then there are large errors.

### How Does Monetary Unit Sampling Work?

The monetary unit sampling method (MUS), also known as dollar unit sampling, is a statistical tool that selects some random samples and based on it, determines the total value of the population. Here, every dollar in the transaction acts as a separate sampling unit. This method works appropriately with financial data. Therefore, auditors can use monetary unit sampling in auditing to detect errors or misstatements within the accounting books.

The characteristics of monetary unit sampling makes it a probability proportional to size sampling. However, before the computerized systems, the monetary unit sampling in auditing was done manually. In the later stage, spreadsheets were used to conduct this sampling. Here, auditors define monetary value or dollars as a sampling unit. Each dollar transaction has an equal chance of being included as a sample. Thus, they would analyze and analyze some samples from each accounting transaction. After the analysis, the auditor would estimate the total financial value of the population (data set) based on the results of the samples.

The selection of monetary value can be difficult for the auditor. However, the concerned person tries to select a larger sample and ignore the smaller ones. Since large items have a high risk, MUS is useful during low error rates. As a result, it can be difficult to determine the hidden errors.

Soon after, the auditor compares the printed amount with the estimated misstatement. If there is any difference, it depicts the probability or chance of errors in that data set (financial records). For example, auditors might estimate a 10% probability that cash balance misstatements will not exceed $50,000. However, if they do exceed, there are high chances of errors and audit risks.

### Calculation Steps

Let us look at the steps for the monetary unit sampling formula for a better understanding:

#### #1 - Determining And Calculating The Sample Size

When the auditor implements this sampling, they use a random starting point and average sampling interval (ASI). However, it is vital to select the right sample size during the process. The sample size depends on four factors: confidence, materiality, population, and expected errors. So, a large sample size will cover most of the factors. However, a smaller sample might only adhere to materiality. Moreover, the sample size should not be a guessing game. Rather, it must be based on professional knowledge and judgment.

#### #2 - Selecting The Sample Method

There are various methods to calculate the monetary unit sampling. It includes fixed interval, random, cell, top stratum cutoff, subsampling, and sampling without repeats.

- The fixed interval method selects samples after every fixed gap. For example, every 20th transaction or 55th monetary unit.
- The random method gives the ultimate freedom to select any item in any order.
- In cell format, items are arranged in cells or groups. Later, one sample is selected from it.
- The top Stratum Cutoff allows auditors to set an upper and lower limit on samples. Any record item beyond this limit will not be included in the sample.
- The subsampling method allows the selection of only one item from a sample field with several separate transactions.
- As the name suggests, sampling without repeats neglects the chance of including any repeated item in the sample.

#### #3 - Calculating The Probability Of Samples

The next step involves calculating the misstatement of the sample items. Once the auditor performs the previous steps, they can arrange the samples per overstatement and understatement. Likewise, calculate the probability of each sample and set the upper precision limit and misstatement bound.

The monetary unit sampling formula for misstatement bounds and others are as follows:

*Misstatement Bound = Estimated Misstatement * Incremental Factor*

*Sampling Interval = Population Value / Sample Size*

*Upper Bound = Total overstatement bound – Projected understatement.*

*Lower Bound = Total understatement bound – Projected overstatement.*

In the later stage, Maximum Tolerable Taintings (%) is determined by dividing the misstatement (over or understatement) by the book value of the sample item. For example, if the book value of sample #21 is 1000, and the overstatement is 25, then tainting is 40%.

#### #4 - Evaluating The Sample Results

After selecting the appropriate sample method and size, the evaluation process becomes crucial. The following are the criteria for finding the errors:

- If the Upper Misstatement Bound (UMB) and Lower Misstatement Bound (LMB) are less than tolerable taintings, then the sample items are not misstated. In short, they are fairly stated and have no errors.
- But, if UMB and LMB are more than tolerable tainting, there are high chances of errors.

However, there are different assumptions if the misstatement is more or less than the sampling interval.

### Examples

Let us look at the examples of monetary units to comprehend the concept better:

#### Example #1

Suppose Sheldon is an auditor in a reputed firm. He has been auditing a large automobile company for the past few days. However, he finds it difficult to monitor each item in the books. Therefore, Sheldon adopts the MUS. As per the characteristics of monetary unit sampling, he considers a few items from the large group. Later, using software, select samples and start analyzing them. In this process, Sheldon finds misstatements in the samples.

For instance, sample #245 is a cash item, and the probability states that there is an 80% chance that misstatements will not exceed $25,000. So, if this is true, it indicates that the financial statements are true.

Considering the above example, if Sheldon notices overstatements, the scenario changes. If a 90% probability depicts misstatements to exceed this bound, then there are high chances of errors. As a result, the threat of audit risk also rises. Therefore, it is a diverting factor influencing business operations.

#### Example #2

Let us imagine that James owns a reputed company that operates a conglomerate business. And every once a year, the firm conducts the auditing procedures. However, when the actual audit started, it was not possible for the auditor (Carel) to check the financial statements of ten subsidiaries. As a result, she decided to include monetary unit sampling. Thus, from 10,000 transactions, Carel selected just a few that would determine the authenticity of the statements.

However, within the process, the auditor found several upper-bound misstatements. For instance, the sample #425 is an accounts payable item with a value of $3,750. However, it is overstated as $5,000 for declining the income earned. As a result, it leads to misrepresentation of financial statements.

### Advantages And Disadvantages

Let us look at the advantages and disadvantages of monetary unit sampling that play a vital role in the analysis:

Advantages | Disadvantages |
---|---|

It is easier to implement than classical variables sampling. | Despite sampling, it assumes that the audited value cannot exceed the recorded value. |

Here, the characteristics of the population do not matter during sample size selection. | It does not select smaller samples but rather ignores them. |

No hassle of subdividing the population | MUS fails to recognize that large misstatements could project false reports. |

If there are no misstatements, the sample size is perfect. | There is no space or special treatment for negative balances. |

Every monetary unit (or item) has an equal chance to be assigned as a sample. | High chance that auditors will reject the recorded amounts. |

### Frequently Asked Questions (FAQs)

**1. What is monetary unit sampling materiality?**

In MUS, materiality refers to the importance of a misstatement or any omission made in the financial statements. Selecting sample size acts as an important factor. Therefore, materiality decreases sample size, whereas other factors like confidence increase the size.

**2. Is monetary unit sampling random?**

The auditors have the choice to either choose a random sampling method. Or else a fixed interval or non-repetitive sampling method. However, the first item has a random selection. Later on, other methods can be followed since every sample has an equal chance of selection.

**3. What is the difference between monetary unit sampling and attribute sampling?**

Although monetary unit and attribute sampling are statistical methods, they have distinct features. The former is a type of variable sampling that selects a few samples and finds the total population value. In contrast, the latter calculates the proportion of items in a population with similar characteristics.

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