Monetary Unit Sampling and Estimation Methods, Widely Used in Auditing

Description

Sampling and evaluation methods to apply Monetary Unit Sampling (or in older literature Dollar Unit Sampling) during an audit of financial statements.

Details

Monetary Unit Sampling (MUS), also known as Dollar Unit Sampling (DUS) or Probability-Proportional-to-Size Sampling (PPS), is a sampling approach that is widely used in auditing.

This package was written mainly for a research project. However, it should be possible to use the methods for practical auditing, too. Furthermore, the package comes with ABSOLUTELY NO WARRANTY. Use it at your own risk!

You have to walk through four steps: 1. Plan a sample and determine the sample size, use function: MUS.planning 2. Extract the sample, use function: MUS.extract 3. Audit the extracted sample (e.g. by asking for debtor confirmations). 4. Evaluate the audited sample, use function: MUS.evaluation

Author(s)

Henning Prömpers, André Guimarães Maintainer: Henning Prömpers <henning@proempers.net>

See Also

MUS.planning for planning a sample, MUS.extraction for extraction of the planned sample and MUS.evaluation for evaluation of the extracted and audited sample.

Examples

## Simple Example
library(MUS)
# Assume 500 invoices, each between 1 and 1000 monetary units
example.data.1 <- data.frame(book.value=round(runif(n=500, min=1,
max=1000)))
# Plan a sample and cache it
plan.results.simple <- MUS.planning(data=example.data.1,
tolerable.error=100000, expected.error=20000)
# Extract a sample and cache it (no high values exist in this example)
extract.results.simple <- MUS.extraction(plan.results.simple)
# Copy book values into a new column audit values
audited.sample.simple <- extract.results.simple$sample
audited.sample.simple <- cbind(audited.sample.simple,
audit.value=audited.sample.simple$book.value)
# Edit manually (if any audit difference occur)
#audited.sample.simple <- edit(audited.sample.simple)
# Evaluate the sample, cache and print it
evaluation.results.simple <- MUS.evaluation(extract.results.simple,
audited.sample.simple)
print(evaluation.results.simple)

Calculate a binomial bound for a Monetary Unit Sampling evaluation.

Description

Calculates a binomial bound for a Monetary Unit Sampling evaluation.

Please treat as experimental.

Usage

    MUS.binomial.bound(x, scope, as.pct, include.high.values, confidence.level)

Arguments

Value

Upper Error Limit calculed using the binomial bound.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

See Also

MUS.evaluation for evaluation of the audited sample.

Examples

# Assume 500 invoices, each between 1 and 1000 monetary units
data <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
# Plan a sample and cache it
plan <- MUS.planning(data=data, tolerable.error=10000, expected.error=2000)
# Extract a sample and cache it (no high values exist in this example)
extract <- MUS.extraction(plan)
# Copy book value into a new column audit values, and inject some error
audited <- extract$sample$book.value*(1-rbinom(nrow(extract$sample), 1, 0.05))
audited <- cbind(extract$sample, audit.value=audited)
# Evaluate the sample, cache and print it
evaluation <- MUS.evaluation(extract, audited)
MUS.binomial.bound(evaluation)

Calculate a conservative sample size.

Description

Calculate a conservative sample size (AICPA, 2012). Based on Technical Notes on the AICPA Audit Guide Audit Sampling, Trevor Stewart, AICPA, 2012.

Usage

  MUS.calc.n.conservative(confidence.level, tolerable.error, expected.error, book.value)

Arguments

Value

Returns the (conservative) sample size.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

Examples

MUS.calc.n.conservative(0.95, 100000, 50000, 10000000)

Combine MUS objects (joining strata into a full set).

Description

Combine a list of MUS objects into a single object. Typical use case is to group multiple strata into a single object. Works with MUS.planning.result, MUS.extraction.result and MUS.evaluation.result objects.

Usage

  MUS.combine(object.list)

Arguments

Value

An object of the same type of the first item in the list is returned containing an aggregation of the objects in the list.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

Examples

## Simple Example
# Assume 500 invoices, each between 1 and 1000 monetary units
stratum.1 <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
plan.1 <- MUS.planning(data=stratum.1, tolerable.error=100000, expected.error=20000)

stratum.2 <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
plan.2 <- MUS.planning(data=stratum.2, tolerable.error=100000, expected.error=20000)

plan.combined <- MUS.combine(list(plan.1, plan.2))

print(plan.combined)

Calculate a high error rate bound for a combined Monetary Unit Sampling evaluation.

Description

Calculate a high error rate bound for a combined Monetary Unit Sampling evaluation.

Please treat as experimental.

Usage

    MUS.combined.high.error.rate(evaluation, interval.type)

Arguments

Value

Upper Error Limit calculed using high error rate evaluation for a combined sample.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

See Also

MUS.evaluation for evaluation of the audited sample. MUS.combine for combining multiple evaluations.

Examples

# Assume 500 invoices, each between 1 and 1000 monetary units
data1 <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
# Plan a sample and cache it
plan1 <- MUS.planning(data=data1, tolerable.error=10000, expected.error=2000)
# Extract a sample and cache it (no high values exist in this example)
extract1 <- MUS.extraction(plan1)
# Copy book value into a new column audit values, and inject some error
audited1 <- extract1$sample$book.value*(1-rbinom(nrow(extract1$sample), 1, 0.05))
audited1 <- cbind(extract1$sample, audit.value=audited1)
# Evaluate the sample, cache and print it
evaluation1 <- MUS.evaluation(extract1, audited1)

# Assume 500 invoices, each between 1 and 1000 monetary units
data2 <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
# Plan a sample and cache it
plan2 <- MUS.planning(data=data2, tolerable.error=10000, expected.error=2000)
# Extract a sample and cache it (no high values exist in this example)
extract2 <- MUS.extraction(plan2)
# Copy book value into a new column audit values, and inject some error
audited2 <- extract2$sample$book.value*(1-rbinom(nrow(extract2$sample), 1, 0.05))
audited2 <- cbind(extract2$sample, audit.value=audited2)
# Evaluate the sample, cache and print it
evaluation2 <- MUS.evaluation(extract2, audited2)

combined <- MUS.combine(list(evaluation1, evaluation2))
MUS.combined.high.error.rate(combined)

Evaluate a sample using Monetary Unit Sampling.

Description

Evaluate a sample using Monetary Unit Sampling. At the end of the evaluation step, you get to know the audit conclusion for the population. To conduct the evaluation step it is required that you audited the sample and high values before. You can use print() for a comprehensive output.

Usage

MUS.evaluation(extract, filled.sample, filled.high.values,
col.name.audit.values, col.name.riskweights,
interval.type, print.advice, tainting.order,
experimental, combined)

Arguments

Value

An object MUS.evaluation.result is returned which is a list containing the following elements:

Author(s)

Henning Prömpers <henning@proempers.net>

Examples

## Simple Example
# Assume 500 invoices, each between 1 and 1000 monetary units
example.data.1 <- data.frame(book.value=round(runif(n=500, min=1,
max=1000)))
# Plan a sample and cache it
plan.results.simple <- MUS.planning(data=example.data.1,
tolerable.error=100000, expected.error=20000)
# Extract a sample and cache it (no high values exist in this example)
extract.results.simple <- MUS.extraction(plan.results.simple)
# Copy book value into a new column audit values
audited.sample.simple <- extract.results.simple$sample
audited.sample.simple <- cbind(audited.sample.simple,
audit.value=audited.sample.simple$book.value)
# Edit manually (if any audit difference occur)
#audited.sample.simple <- edit(audited.sample.simple)
# Evaluate the sample, cache and print it
evaluation.results.simple <- MUS.evaluation(extract.results.simple,
audited.sample.simple)
print(evaluation.results.simple)

## Advanced Example
example.data.2 <- data.frame(own.name.of.book.values=round(runif(n=500,
min=1, max=1000)))
plan.results.advanced <- MUS.planning(data=example.data.2,
col.name.book.values="own.name.of.book.values", confidence.level=.70,
tolerable.error=100000, expected.error=20000, n.min=3)
extract.results.advanced <- MUS.extraction(plan.results.advanced,
start.point=5, seed=1, obey.n.as.min=TRUE)
extract.results.advanced <- MUS.extraction(plan.results.advanced)
audited.sample.advanced <- extract.results.advanced$sample
audited.sample.advanced <- cbind(audited.sample.advanced,
own.name.of.audit.values=audited.sample.advanced$own.name.of.book.values)
#audited.sample.advanced <- edit(audited.sample.advanced)
evaluation.results.advanced <- MUS.evaluation(extract.results.advanced,
audited.sample.advanced,
col.name.audit.values="own.name.of.audit.values")
print(evaluation.results.advanced)

Extend a MUS sample.

Description

Extends a sample that requires further evidence. Works with MUS.extraction.result.

Please treat as experimental.

Usage

  MUS.extend(extract, new_plan=NULL, additional.n=NULL)

Arguments

Value

Returns an extended MUS.extraction.result object.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

Examples

## Simple Example
# Assume 500 invoices
mydata <- data.frame(book.value=
  round(c(runif(n=480, min=10,max=20000),
  runif(n=20, min=15000,max=50000)))
)

# Plan a sample and cache it
plan <- MUS.planning(data=mydata,
tolerable.error=50000, expected.error=3000)

# Extract a sample and cache it
extract <- MUS.extraction(plan, obey.n.as.min=TRUE)

# Create a new plan
new_plan <- MUS.planning(data=mydata,
tolerable.error=50000, expected.error=5000)

# extends the sample using the new plan
extended <- MUS.extend(extract, new_plan)

# extends the sample by 20 itens using the original plan
extended20 <- MUS.extend(extract, additional.n=20)

Extract a sample using Monetary Unit Sampling.

Description

Extract a sample using Monetary Unit Sampling. At the end of the extraction step, you get to know the items that you have to audit.

Usage

MUS.extraction(plan, start.point, seed, obey.n.as.min, combined)

Arguments

Value

An object MUS.extraction.result is returned which is a list containing the following elements:

Author(s)

Henning Prömpers <henning@proempers.net>

See Also

MUS.planning for planning a sample and MUS.evaluation for evaluation of the extracted and audited sample.

Examples

## Simple Example
# Assume 500 invoices, each between 1 and 1000 monetary units
example.data.1 <- data.frame(book.value=round(runif(n=500, min=1,
max=1000)))
# Plan a sample and cache it
plan.results.simple <- MUS.planning(data=example.data.1,
tolerable.error=100000, expected.error=20000)
# Extract a sample and cache it
extract.results.simple <- MUS.extraction(plan.results.simple)

## Advanced Example
example.data.2 <- data.frame(own.name.of.book.values=round(runif(n=500,
min=1, max=1000)))
plan.results.advanced <- MUS.planning(data=example.data.2,
col.name.book.values="own.name.of.book.values", confidence.level=.70,
tolerable.error=100000, expected.error=20000, n.min=3)
extract.results.advanced <- MUS.extraction(plan.results.advanced,
start.point=5, seed=0, obey.n.as.min=TRUE)

Calculate MUS Factor.

Description

Calculate MUS Factor (AICPA, 2012). Based on Technical Notes on the AICPA Audit Guide Audit Sampling, Trevor Stewart, AICPA, 2012.

Usage

  MUS.factor(confidence.level, pct.ratio)

Arguments

Value

Returns the MUS factor.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

Examples

MUS.factor(0.95, 0.5)

Calculate the moment bound for a Monetary Unit Sampling evaluation.

Description

Calculates the moment bound (Dworkin & Grimlund, 1984) for a Monetary Unit Sampling evaluation.

Please treat as experimental.

Usage

    MUS.moment.bound(x, confidence.level, as.pct, include.high.values)

Arguments

Value

Upper Error Limit calculed using the moment bound.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

See Also

MUS.evaluation for evaluation of the audited sample.

Examples

sample = c(rep(0, 96), -.16, .04, .18, .47)
MUS.moment.bound(sample)

# Assume 500 invoices, each between 1 and 1000 monetary units
data <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
# Plan a sample and cache it
plan <- MUS.planning(data=data, tolerable.error=10000, expected.error=2000)
# Extract a sample and cache it (no high values exist in this example)
extract <- MUS.extraction(plan)
# Copy book value into a new column audit values, and inject some error
audited <- extract$sample$book.value*(1-rbinom(nrow(extract$sample), 1, 0.05))
audited <- cbind(extract$sample, audit.value=audited)
# Evaluate the sample, cache and print it
evaluation <- MUS.evaluation(extract, audited)
MUS.moment.bound(evaluation)

Calculate a multinomial bound for a Monetary Unit Sampling evaluation.

Description

Calculates a multinomial bound for a Monetary Unit Sampling evaluation.

Please treat as experimental.

Usage

    MUS.multinomial.bound(x, as.pct, include.high.values)

Arguments

Value

Upper Error Limit calculed using the multinomial bound.

Author(s)

Andre Guimaraes <alsguimaraes@gmail.com>

See Also

MUS.evaluation for evaluation of the audited sample.

Examples

# Assume 500 invoices, each between 1 and 1000 monetary units
data <- data.frame(book.value=round(runif(n=500, min=1, max=1000)))
# Plan a sample and cache it
plan <- MUS.planning(data=data, tolerable.error=10000, expected.error=2000)
# Extract a sample and cache it (no high values exist in this example)
extract <- MUS.extraction(plan)
# Copy book value into a new column audit values, and inject some error
audited <- extract$sample$book.value*(1-rbinom(nrow(extract$sample), 1, 0.05))
audited <- cbind(extract$sample, audit.value=audited)
# Evaluate the sample, cache and print it
evaluation <- MUS.evaluation(extract, audited)
MUS.multinomial.bound(evaluation)

Plan a sample using Monetary Unit Sampling.

Description

Plan a sample for Monetary Unit Sampling. At the end of this planning step, you get to know the sample size.

Be aware that this MUS routines cannot calculate with decimals. Furthermore, you must provide book values etc. as Euro-Cent so that no decimals occur.

Usage

MUS.planning(data, col.name.book.values, confidence.level,
tolerable.error, expected.error, n.min, errors.as.pct, conservative, combined)

Arguments

Value

An object MUS.planning.result is returned which is a list containing the following elements:

Author(s)

Henning Prömpers <henning@proempers.net>

See Also

MUS.extraction for extraction of the planned sample and MUS.evaluation for evaluation of the extracted and audited sample.

Examples

## Simple Example
# Assume 500 invoices, each between 1 and 1000 monetary units
example.data.1 <- data.frame(book.value=round(runif(n=500, min=1,
max=1000)))
# Plan a sample and cache it
plan.results.simple <- MUS.planning(data=example.data.1,
tolerable.error=100000, expected.error=20000)

## Advanced Example
example.data.2 <- data.frame(own.name.of.book.values=round(runif(n=500,
min=1, max=1000)))
plan.results.advanced <- MUS.planning(data=example.data.2,
col.name.book.values="own.name.of.book.values", confidence.level=.70,
tolerable.error=100000, expected.error=20000, n.min=3)

Pretty and comprehensive printing of MUS evaluation results

Description

Pretty and comprehensive printing of MUS evaluation results that can be used for working papers.

Usage

## S3 method for class 'MUS.evaluation.result'
print(x, error.rate, print.misstatements,
  print.planning, print.extraction, print.error.as.pct, print.advice,
	style, use.pander, ...)

Arguments

Author(s)

Henning Prömpers <henning@proempers.net>

See Also

MUS.evaluation for evaluation of the extracted and audited sample.

Pretty and comprehensive printing of MUS extraction results

Description

Pretty and comprehensive printing of MUS extraction results that can be used for working papers.

Usage

## S3 method for class 'MUS.extraction.result'
print(x, print.title,
  print.planning, style, use.pander, ...)

Arguments

Author(s)

Henning Prömpers <henning@proempers.net>

See Also

MUS.extraction for extraction of the audit sample.

Pretty and comprehensive printing of MUS planning results

Description

Pretty and comprehensive printing of MUS planning results that can be used for working papers.

Usage

## S3 method for class 'MUS.planning.result'
print(x, print.title,
  style, use.pander, ...)

Arguments

Author(s)

Henning Prömpers <henning@proempers.net>

See Also

MUS.planning for planning of the audit sample.