Monetary Unit Sampling(MUS) & Probability Proportional to Size(PPS) | CPA Exam

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Summary

In this session led by Professor Farhad, the focus is on introducing Monetary Unit Sampling (MUS) and its specific method called Probability Proportional to Size (PPS). This statistical sampling approach is detailed, contrasting it with non-statistical methods discussed in prior sessions. The primary goal of MUS is to test account balance details, and each dollar holds a unit as opposed to each account. The session explains the workings of PPS through account selection based on dollar amounts, stressing on Excel usage for practical demonstration. Professor Farhad further explores the advantages of MUS, especially in targeting larger monetary figures, while briefly discussing its limitations and assumptions. This serves as an introductory part, leading to a more detailed exploration in future sessions.

Highlights

Introduction to Monetary Unit Sampling (MUS) and Probability Proportional to Size (PPS)! 🎓
MUS focuses on dollar amounts as the sampling unit, giving insight into possible account balance misstatements! 💡
Professor Farhad illustrates the selection process using PPS, emphasizing account probabilities based on their dollar totals! 📈
The session explores the advantages of MUS, particularly its efficiency and applications in auditing! 🔍
Highlighting potential limitations of MUS, especially when dealing with negative or zero dollar balances! 🚫

Key Takeaways

Monetary Unit Sampling (MUS) uses statistical methods focusing on dollar amounts instead of account numbers! 💰
Probability Proportional to Size (PPS) ensures larger balances have a higher chance of selection! 📊
MUS is efficient with its interval selection, often reducing audit costs! 🕵️‍♂️
MUS is particularly useful when looking for overstatements in account balances! 💼
While beneficial, MUS can be limiting with negative or zero balances and often requires computer assistance! 🖥️

Overview

Professor Farhad opens the session explaining Monetary Unit Sampling (MUS) and how it leverages Probability Proportional to Size (PPS) to focus on sampling the monetary value within accounts instead of the number of accounts. This approach ensures larger balances have an increased chance of selection, enabling auditors to focus on more significant figures within financial statements.

The video includes a practical demonstration using Excel, illustrating the approach to selecting samples based on monetary units. Through various examples, Professor Farhad encourages understanding this probabilistic method by comparing it to the non-statistical sampling methods discussed previously, emphasizing its efficiency for auditing.

Moreover, while MUS’s advantages like reduced auditing costs and targeting overstatements are highlighted, potential constraints such as handling of zero or negative balances and reliance on electronic data within audits are also addressed. This serves as a precursor to a more in-depth exploration planned for future sessions.

Chapters

00:00 - 00:30: Introduction to Monetary Unit Sampling and Probability Proportional to Size This chapter, presented by Professor Farhad, serves as an introduction to the topics of monetary unit sampling and probability proportional to size (PPS). The focus is on understanding how to select a sample using PPS. The session aims to lay the groundwork, with the promise of more detailed examples and further reinforcement in subsequent sessions.
00:30 - 01:00: Statistical vs Non-statistical Sampling The chapter focuses on statistical sampling, contrasting it with non-statistical sampling discussed in a previous session. It directs readers who are unfamiliar with the concept to refer to an auditing playlist that includes a complete course on auditing. The speaker underscores that understanding statistical sampling requires knowledge of prior concepts such as non-statistical sampling, suggesting an educational progression in the topic covered in the course.
01:00 - 05:30: Monetary Unit Sampling: Concepts and Examples The chapter titled 'Monetary Unit Sampling: Concepts and Examples' explores the statistical method of monetary unit sampling (MUS) used in auditing, particularly for tests of detailed balances. It emphasizes the importance of understanding non-statistical sampling methods, which were discussed in the two prior recordings, before delving into statistical approaches like MUS. The chapter serves as an introduction to this common statistical sampling method, setting the stage for deeper exploration in subsequent sections.
05:30 - 15:30: Sample Selection Using Probability Proportional to Size (PPS) The chapter titled 'Sample Selection Using Probability Proportional to Size (PPS)' discusses variable sampling, which is useful for detecting misstatements in account balances. This method is crucial for substantive work aimed at collecting evidence related to account balances. The technique combines the statistical simplicity of attribute sampling with the ability to deliver results expressed in dollar amounts, making it a powerful tool for accountants and auditors. The chapter also touches upon the concept of monetary unit sampling (MUS), hinting at differences or comparisons with PPS.
15:30 - 21:00: Alternative Methods for Sample Selection In the chapter on 'Alternative Methods for Sample Selection', the focus is on understanding the difference between statistical and non-statistical sampling. The key distinction is in the definition of the sampling unit. In monetary unit sampling, each dollar is used as a unit rather than each account, emphasizing the individual value rather than grouping by account. This method highlights the importance of considering each dollar independently in sampling processes.
21:00 - 25:30: Advantages of Monetary Unit Sampling Monetary Unit Sampling (MUS) focuses on sampling dollar amounts instead of the number of accounts. This means that higher dollar amounts have a higher probability of being selected in the sample. Therefore, the population size considered in MUS is the dollar amount rather than the number of accounts. Understanding this distinction is crucial in MUS. Additionally, the sample size in MUS is determined using a specific formula, and the process of sample selection is also carried out accordingly.
25:30 - 37:00: Disadvantages and Limitations of MUS In this chapter, the focus is on explaining the disadvantages and limitations of using Monetary Unit Sampling (MUS). Using a methodology called PPS or Probability Proportional to Size, accounts are selected for sampling. The chapter aims to elucidate how this process emphasizes larger amounts, providing a quick walkthrough using hypothetical account balances of $3,000, $2,000, $1,000, and others totaling $6,500 and $2,500, respectively. The chapter serves to illustrate potential issues and constraints when applying MUS in practical scenarios.
37:00 - 40:30: Suitability of MUS and Conclusion This chapter discusses the suitability of Monetary Unit Sampling (MUS) in auditing financial figures. The speaker presents various numerical figures and illustrates how to work with them, revealing different totals. The primary objective is to demonstrate the application and mechanics of MUS in an audit context. The exact totals are secondary to understanding the process shown herein.

Monetary Unit Sampling(MUS) & Probability Proportional to Size(PPS) | CPA Exam Transcription

00:00 - 00:30 hello and welcome to the session this is Professor Farhad and this session we're going to look at an introduction to monetary unit sampling and specifically we're going to be looking at how to select the sample which is we're going to be looking at probability proportional to size or PPS now before we proceed this is basically an introduction so basically I'm gonna introduce the topic then in the next session or more more specific example to see how it works then I'll work another example to reinforce the point so keep
00:30 - 01:00 that in mind also before we before you start now this this form of sampling is a statistical sampling so we're looking at statistical sampling because in the prior session we looked at non statistical sampling so if you did not look at the prior session or you just happen to stumble upon this recording and you're not sure what the sampling is in order thing you can go to my auditing playlist the complete auditing course and I have one two three four five six
01:00 - 01:30 seven recording about auditing prior to this one but specifically in the in the prior two I looked at non statistical sampling which is very helpful if you view non statistical sampling before you use statistical sampling so let's go ahead and get started monetary unit sampling or M us okay it's the most common statistical method so this is a statistical method of sampling for tests of detail balances tests of detailed balances another word for it
01:30 - 02:00 it's a variable sampling variable sampling means we're looking for a misstatement in the account balance we use this method when we are collecting substantive when we are doing substantive work to collect evidence about the account okay because it has the statistical simplicity of attribute sampling yet provides a statistical result Express and dollar amount so it's a very powerful tool that we're going to be using so what is the difference between monetary unit sampling mus and
02:00 - 02:30 the prior session when we use non statistical sampling what's the difference between the two the first thing is the definition of the sampling unit in an individual is an individual dollar so when we are the with monetary unit sampling if you think about the word monetary monetary is money monetary is dollar what are we going to do we are going to be using each dollar as a unit rather than using each account as a unit that's going to
02:30 - 03:00 be each dollar so think about it the launcher is your dollar amount the higher is your probability of being selected that's why it's a monetary unit sampling okay that's the first difference it's not per account it's per dollar amount the population size is recorded dollar population not account and I am repeating myself here but it's very to understand this the sample size is determined using the formula which we'll see later sample selection is done
03:00 - 03:30 using PPS probability proportional to size this is how we select accounts let me show you real quick how does this work why is it how does it emphasize the other amount let's assume you are dealing with a population of I'm just going to throw some numbers and account for $3,000 and account for 2,000 and account for a thousand that's six five hundred twenty five hundred that's in
03:30 - 04:00 the 1250 and 250 and a thousand I think I have ten thousand here to three thousand five six sixty five hundred seven nine ten okay let's just work with these figures okay then add a thousand here okay let's add those accountant but it doesn't matter what the total is I just want to show you how this works so let's go ahead and
04:00 - 04:30 add the balances so this is Alyssa's account receivable three thousand plus two thousand plus one thousand plus 500 plus 2500 plus a thousand actually it is ten thousand so ten thousand is the total here's what's gonna happen those are 10 different accounts so this is account number one account number two account number three four five six and
04:30 - 05:00 seven so we have seven different accounts here well if we look at account number one account number one has one seven percent chance being selected as an account one seven chance so if we are using random sampling will take one divided by seven and that's gonna give account number one not a bad 14% chance of being selected that's that's a four using non statistical sampling basically we're using the account number now if
05:00 - 05:30 we're using the dollar amount account number one has three thousand out of 10,000 chance it has a 30% chance so notice when we're using the dollar amount as a unit larger amount larger dollar amount will have a larger chance a larger chance of being selected okay and this is the idea behind the concept of what probability proportional to size
05:30 - 06:00 so the larger your dollar amount size the higher power probability you're going to be selected what's the assumption here the assumption is larger amount are more important which is it makes sense because if they have errors the errors will be larger it's an assumption but that's a fair assumption to make okay so so this is what we mean by the population size is recorded by a dollar amount so we're going to look at an example on how to select okay sample selection is done using probability proportional to size we're going to look
06:00 - 06:30 at an account receivable as an example the auditor generalized from the sample to the population used in monetary unit sampling we'll see this later when we get to the decision decision stage how do we journalize about the population how do we generalize about the population so let's take a look at this population and this is an account receivable population we have 12 accounts we have 12 account and here's the dollar amount for account number one 357 the dollar amount for account number
06:30 - 07:00 two the dollar amount for account number three so this these are the column then we have the cumulative for example account number one 357 what's the cumulative dollar amount and unit we compute the punitive 357 account number two is twelve eighty one what's the cumulative dollar amount of the population it's 1281 plus 350 plus 357 then account number three is $60 what's the cumulative of the population will add $60 to the prior balance and will
07:00 - 07:30 give us 16 98 now what I did is I created Exedy annex in excel sheet and I believe it's it will be more beneficial for you to see this from an excel sheet perspective so this is the same data except that I created this excel sheet and basically again what's the cumulative 357 how do we come up with 16 16 38 it's the recorded amount plus the previous balance recorded amount plus the previous balance recorded amount plus the previous balance they went even
07:30 - 08:00 a step further and what I did because this is gonna be helpful when you're doing PP PBS sampling what you can do is you could compute the range for example for item number one it falls between zero balance and 357 because it's 357 dollars item two population item two item two it falls from what you do as you again once you run the cumulative 16 16 38 item number two falls in between
08:00 - 08:30 358 which is the prior so this is the range let me just do this independent so this is the first range from 0 to 357 then the second range it's going to be starting from 358 to 1638 how do they come up a third 1638 it's the cumulative okay up to that point range 3 is from
08:30 - 09:00 1639 basically add 1 all the way to 1698 then the range for item for the 1644 to 2271 so on and so forth and let me show you the formula just in case you want to do this in Excel so basically what I did is it's the prior ending range plus one then the the end of the range is the cumulative up to that point so this is how I computed it so those are branches you're gonna see that they're gonna become a little bit helpful or they may help you
09:00 - 09:30 understand PPS a little bit better okay so this is how it works now we're gonna go ahead and we decided let's assume just for the sake of simplicity we decided to select four items four items four items so there's our sample equal to four now don't worry how we came up with the sample we're gonna learn later how to come up with a sample I just want to show you practically how does it work because when I talk about the sampling and I want you to be wasting your time figuring out how to select the four
09:30 - 10:00 items so we're gonna be selecting four items so here's what we do the total population is seven thousand three hundred and thirty six dollars you guys see this this is the total population seven thousand three hundred and thirty six okay so the population so we're dealing with seven thousand three hundred and seventy-six dollars what we do first we want to select four sample equal to four so once we know the sample
10:00 - 10:30 equal to four and once again don't worry about this we need to calculate something called the interval what is the interval it's the dollar amount of the population divided by the sample this is we called the interval the interval is 1844 once we have the interval once we have the interval which is right here now we have more than one way to proceed so we're gonna work two examples what we can do is this we can select a number randomly we can say randomly select number between 1 0 a1
10:30 - 11:00 and 1844 so let's assume the number selected number selected equal to 822 so we selected the number as a starting point as a starting point between 1 and 1844 okay it happens to be a 22 now what what do we need to do so this is item number one item number one is we need to select the the dollar amount that falls within that range 18:22 then how do we how do we proceed
11:00 - 11:30 further for item two we're gonna take 1822 and add to it 1844 so the item number two that we select it has to be falls within this range okay item number three it's gonna be the prior and plus I'm gonna add to it I'm sorry I made a mistake here it's a 22 which is this number here a 22 plus plus 1844 so item
11:30 - 12:00 number why it's not adding 1844 give me one moment please so the number selected I gotta put this in a different cell the number selected equal to threaten the random start is a 22 let me just do something real quick so the random start equal to 822 so item one would be 822 the item 1 will be a 22 and how do I select item number 2 what I
12:00 - 12:30 do is I take item 1 and I add to it the interval 1844 add to it the interval so item number 2 will fall within this range then I'm gonna take the prior number then after with 1844 so item number 3 I item 3 Falls item 3 falls
12:30 - 13:00 within this range in item 4 I'm gonna take the amount add to what the interval an item for false where then should fall within this range this is item 4 falls within this range falls within this range so now I need to select my sample how do I select my sample let's go up here and item 1 is in the range of 822 so this is item 1 because this was the
13:00 - 13:30 starting point so notice I did this randomly so item 1 is a 22 not in item 1 notice item 2 so 822 8:22 falls within this range fall within 358 to notice a 22 fall within this range therefore I select papadum number 2 so item number 2 is selected for this is 1
13:30 - 14:00 so I'm done with this now I need to look forward 2666 2666 it's this it falls within this range I select item number 5 then 45 1045 4510 falls within this range so I select item 7 we can select item 7 and let's see I'm 7
14:00 - 14:30 + 63 50 54 63 50 force falls within this range I select item pin okay I can tell is selected so those are the 10 the 10 items now if you don't do the range
14:30 - 15:00 basically hopefully you know that a 22 if you don't do the range hopefully you know that a 22 falls below those two figures hopefully you know hopefully you know that 266 falls within this range here therefore I select item 2 I select item 5 hopefully you know that 45 10 falls within this range therefore I select 7 I just like to show you the range because if this is the first time you're looking at this you may not you know I just want to make sure you're comfortable with it so this is what we did we selected those four items is this
15:00 - 15:30 the only way we can do this absolutely not absolutely not this is one way of selecting those four items okay now how else can we select items we can basically if we want 4 numbers I just I'm gonna tell Excel I could just tell Excel random random between 1 and 73 76 so what I'm
15:30 - 16:00 gonna tell excel is to choose a random number between 1 and 73 76 this is the number and I can do this I'm gonna this is gonna change what's gonna change random so I'm gonna tell the excel sheet to select four numbers for me and hopefully it will illustrate what I need to illustrate so those are the four numbers so what I do now those are the four random numbers 36 36 so what I do I'm gonna come up here and see where let's forget about all of this now just this isn't this is other method so let
16:00 - 16:30 me just remove all those highlight no fill okay so another way to do it is to select those four Figg 36 36 what does 36 36 fall's 36 36 falls within this range so what do I say I say select item number seven so this is 36 36 so item
16:30 - 17:00 number seven is selected item number seven is selected the second drum random number was 2287 2287 2287 falls within this range therefore I select item five wow it's a coincident that they're the same one this is a strictly coincident 963 963 falls within this range item
17:00 - 17:30 number two again this is unbelievable the the coincident and the third item is 1916 excellent 1916 falls within this range item four so those are my starting point let's assume one of my numbers let's assume that one of my random numbers happen to be happened to be 3500 why did I chose 3,500 3,500 for
17:30 - 18:00 within this range so I would have number seven selected two times I will not have number seven selected two times but basically I would only have three and hold have three items of my selection so pts could reduce your could you could produce your could reduce your the number of item you select for sampling okay assuming that I happen to trend my select that the 3,500 happened to be selected okay so hopefully you know your
18:00 - 18:30 onder's you know mechanically how to select the items now we're gonna have more work to do with this but now we know how to select the items use in PPS okay and we assume that you know the interval we assume the sample is 4 so we make certain assumptions we're going to clarify later okay so let's just talk about real quick on what are the advantages or when monetary unit sampling is is is preferable okay so monetary unit sampling appeals to
18:30 - 19:00 auditor at least for for at least for four reasons and the method automatically increased the likelihood of selecting higher higher dollar amount in the population remember the higher your dollar amount the higher the probability you're gonna select this amount because this amounted again if you're dealing with a million dollar balance and you have an account balance that's two hundred thousand this balance has a 20% chance being selected okay because you're using the dollar amount that's assumed you're using 1 million
19:00 - 19:30 the other balance that you're using account numbers as as as as a selection so if you have let's assume you have 100 accounts you have 100 accounts so the $20,000 represent only one account so the chance of the 20 $200,000 being selected is 1 over 100 or 1% because we have 100 accounts if you're using accounts if you if you're using the dollar amount if you use in the dollar amount there's a 20% chance this account
19:30 - 20:00 be in select so notice it emphasizes the the higher the dollar amount the more important they have the probability you will select this amount and hopefully it makes sense it makes sense it's similar to stratification and stratification you cannot do the same thing you remember we did in the prior session certain accounts above it above a dollar amount you always ordered them separately we order the 100% as well monitor unit sampling often reduces the cost of the audit because several items are tested at once again we saw that for
20:00 - 20:30 example if you selected to the same you may you may select the same interval more than once so you select the same item to test both intervals so your sample size is lower and we'll see that later as well in another example it's easy to apply monitor unit sampling why because samples can be evaluated by the application of simple tables again we'll see this later so it's easy when we get to the evaluation phase how to make it a decision it's a statistical decision
20:30 - 21:00 we're gonna be using tables again monitor unit sampling provide the statistical conclusion rather than a non statistical one okay what does that do it proof it gives us a more defensible decision down the road in case we were sued the other thing you want to be aware of is when you're when you're using monetary unit sampling you are testing for overstatement so you're not testing for understatement you're testing if the account is over reported so that's that's if that's what you want to do what are some disadvantages to the
21:00 - 21:30 to the monetary unit sampling first we have to understand the term which we'll talk about later is misstatement bound misstatement down is the estimate of the likely maximum overstatement given an acceptable rate of incorrect acceptance what happened is this at some point we're gonna have to say what number we could live with what number maximum number we could live with now remember we're gonna choose a table own statement we're gonna have a tolerable in the statement but also above the tolerable misstatement we're gonna have a
21:30 - 22:00 misstatement down so something above this because we can tolerate this but you're gonna be misstatement bound is above this so of the if the dollar bonus statement is a 100000 the misstatement bound could be 150 okay so what is the likely miss because remember we are sampling when we sample we always have to project more than what we found because we're sampling so this is the misstatement bound how far can we go what is the likely maximum statement and the population usually is
22:00 - 22:30 software computers okay so what is the disadvantage when you use in magnitude unit sampling the Miss statement bound when Miss statement are found may be too high to be useful by the auditor and we'll see we'll see this later so sometime what's gonna happen when we do the projection then the statement bound they could be too high okay so to overcome this problem we'll select the larger size and we'll see we'll see this later just know that that that could be the case also it may be cube or some to select EPS sampling from large
22:30 - 23:00 population without computer assistance that's not really a problem most auditors use software also what's what's not good about mus or it doesn't work if you have negative balances if you have small and zero balances you just simply don't select them they have a look for example zero balances they have zero chance of being selected because what's the chance of selecting a zero out of a million zero percent chance you just doesn't appear on your radar if it's a small balance if the balance is $500 and you have a million dollar balance it's a
23:00 - 23:30 very small amount and also if you have credit balances for customers negative balances which is for account receivable credit balances those are not selected as well and then you can turn them into positive then you know run the run run your numbers okay but that may not be the case so for all these reasons auditor commonly use em us when zero or few miss statements are expected so you would use em u.s. monetary unit sampling when there's expected zero or few miss statement okay also the data has to be
23:30 - 24:00 accessible in electronic format because it's you want to run the numbers and you may be you might be dealing with large large numbers okay this is basically an introduction for M us in the next session we would look at a more specific example would look at an example and we go through the steps to see how we make a decision using M us now again the most important thing here is study is to know how to select the sample you remember
24:00 - 24:30 when we selected the samples and you know when we selected the sample how did we do it so make sure you know this because in the next session when I go there I'm just going to assume you know it we'll work with other steps if you have any questions any comments by all means email me or see me in class and if you're studying for your CPA exam make sure you study hard it's worth it