 Hello and welcome to the session. This is Professor Farhad in which we would look at the monetary unit sampling specifically the tolerable and the upper statement bound. This topic is covered on the CPA auditing exam and I'm going to show this in a form of a simulation and an auditing course, whether it's a graduate or undergraduate courses. This topic is challenging for many students because they don't like statistics and when you combine statistics with accounting, it turns people off and often students don't learn this in college. And when they get to the CPA exam, they struggle on this topic. So hopefully through this example, I can make it easier for you. But if you want to learn more about this topic, visit my auditing course, auditing and attestation course where you would learn the basics because this is an exercise where you would learn the basics, the explanation of what I will be doing today. 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So in the prior session, what we did is, and I'm going to put the prior session in the description because it's very important, we were asked to calculate the sample size for a company that had, there was auditing inventory with a population of 3,140 inventory items. The dollar value was 19,325. The tolerable misstatement was 575,000. The acceptable risk of incorrect acceptance was 10% and no misstatement was expected. So in the prior session, we computed the sample size happens to be 77. Also in the prior session, they said, assume your starting point is 123,608, compute the cumulative dollar amount associated with the first five sample items. And that's what we did in the prior session. How will the auditor determine the physical inventory item associated with each dollar amount? So it's very important that you look at the prior session or you don't have to look at the prior session. As long as you know how to compute the sample size, as long as you know how to know how to select the five items, you're good to go. But if you feel you want more confidence, please look at the prior session. Also, what's important is the 10% acceptance of an incorrect acceptance and no misstatement was expected in the population, as well as the tolerable misstatement because we're going to be using this information now, which is now, is what? Now is assumed that a sample of 100 units was obtained and assume that the following three misstatements were found. So we selected rather than 77, we selected 100, it doesn't matter. So we selected more than what the sample suggested, but the point is we found three misstatements and those are the three misstatements. We had an inventory recorded value of $897.16. When we audited, we find out when we selected this item, we find out the value is 609.16. We had $47 and two pennies of some inventory, but when we find out it doesn't exist, the audited value is zero or the value of it is zero. It might exist, but it really has no value because it's obsolescence. We had another item for 1621.68 and the true value is 1521.68, the audited value. So now what they want us to do is calculate the overstatement bound and draw the conclusion whether the population is acceptable. Basically, we need to know is the population is acceptable as stated. So we need to figure out what's called the upper misstatement bound because we know the tolerable misstatement. We can tolerate 575 and we're going to add to this something called allowance risk. And if that allowance risk, that risk, that additional risk because we're sampling is above a certain number, if above the 575, then we're just, we're not going to go ahead. We're going to say that the population is not fairly stated. So to work this example, it's best to work it in an Excel sheet because we're going to be doing quite a few of computation. So let's go ahead and look at the Excel sheet. Let's take a look at this Excel sheet. And basically we are starting with the information that we have, which is the misstatement as well as the recorded value, those misstatements right here, the recorded value. So the first thing is you want to find the difference between each item and dollar amount as well as percentage. Let's take a look at misstatement number one, the item number one. So let's take a look at it. The first misstatement, we had the recorded value of 897. The orated value was 609. The factual misstatement, the difference was 288. Therefore we overstated the value by 288. Now we find the percentage. The percentage is 0.32, which is we overstated this amount by 32%. Then we have misstatement two, which was $47. The orated value was zero. Simply put, we overstated by 47 and the error is 100% or one. And we have the third misstatement. You guys get the point. So first we find the dollar difference, which is the factual misstatement. Then we express this in a percentage. So this is the tainting percentage. Now what's going to happen is we're going to take those tainting percentage and we have to project them. Because remember, what we did is sampling. Sampling means we did not look at everything. We did not look at everything. Now, before we even start the sampling process, we know that the confidence factor. Now if you don't know what the confidence factor is, please look at the prior session. The confidence factor for this exercise is 2.31. Now how did we come up with this confidence factor? I'm going to tell you how we came up with it. We assumed 10% the risk of incorrect acceptance and we assumed to expect zero misstatement. So this is how we came up with 2.31. Let me show you here. So we said the risk of incorrect acceptance is 10% and we expected no misstatement. Therefore, the confidence factor was 2.31. So this was computed in the prior session. Therefore, what we say is even if we don't find any misstatement, we expect to have issues with projected misstatement of 446,407. So even if we did not find any misstatement, we take the sampling interval, which we computed earlier, 193,250. This was called the sampling interval and we multiply this by 2.31. So let's assume we did not find any of this. Let's assume this did not exist. We would still say we could be wrong up to 446,407 because we sampled, but that's not true. We found 3 errors, 1, 2, 3. Now we're going to take those errors and project them and add a sampling factor, then add the 446,407. So how do we compute this tainting misstatement? Here's what's going to happen. The first thing is we're going to take those 3 tainting misstatement and we're going to organize them from the highest to the lowest. Simply put, from the highest to the lowest would look something like this. Basically what we do is we say 1, 2, 3. The first, the largest one obviously is number 2. Now it becomes number 1. The second one is 32%. The third one is 0.06. Now we already computed the sampling interval. We put the sampling interval in 133,250. Now we have to project. Project means take the sampling interval and project this tainting percentage because we find a problem and the problem is 100%. So simply put here's what's going to happen. We're going to take the sampling interval times 1 to project it to the population 100. The projected error is 193,250 and we'll do the same thing for the other 2 errors. We have to project it. Simply put, taken the sampling interval multiplied by a tainting percentage. But we don't stop there. If we added those 3, it means we have 267 and $63.25. But when we started our problem and the problem we said that we expect to find zero misstatement and the original problem says we expect to find zero misstatement. We find 1, 2, 3 because when we started our confidence interval, we expect zero misstatement right here. But that's not true. We have 1, 2, 3 misstatement. Now here's what's going to happen. We're going to take our errors, our projected misstatement and even add an incremental change in the confidence factor because our confidence factor simply was incorrect. We thought it's 2.31 when initially we thought 2.31 because we assumed zero misstatement. We were pretty confident that their inventory is good. Now we find out 3 mistakes. We have to change our computation. And for each error, we have to find the incremental change. Incremental changes. What's the difference between 2.31 and the next level of finding one mistake 3.89? So let's look at this. Let me pull a calculator. It's better if I pull a calculator so you can see the computation. Now I'm going to take 3.89 minus 2.31 and the increase 1.58. Now I'll do the same thing between the first and the second error because remember I found 3 errors. Therefore I have to keep on going. Now I find the difference between 2 and 1 which is 5.33 confidence factor minus 3.89. I have to increase, I have to multiply my projection by 1.44. And I'll do the same thing for the third error 6.69 minus 5.33. So simply put overall my confidence is 6.6 should have been 6.69. So I needed to increase my sample but I am adjusted for that. So I'm adjusting for that 6.69 minus 5.33 and that's 1.36. So I'm going to take those incremental increases in my confidence factor and multiply them by my projected misstatement. So there we go. So you know where these numbers are coming from now. 1.58, 1.44, 1.36. Those are the incremental, the increases because I found more than one mistake. Now what I do is I project, I compute my projected misstatement plus the allowance that I'm sampling. There's a risk. If you're sampling, there's a risk. If you found one mistake, it doesn't mean that's the only mistake. It's an indication that you might have more mistakes. So you have to find the incremental allowance risk. Therefore I'm going to take my projected misstatement times the incremental factor and that's going to be 3.05, 3.35 and I'll do the same thing for the other two mistakes. I take the projected misstatement, which is I take the projected misstatement times the incremental factor. Now I can add them all up. Then I have to add to them, I have to add to them my precision, which was my original estimation is, even if I don't find anything, I'm going to assume I have 446,407 because I'm sampling, but now I find out there's a problem. I have to add my projected misstatement plus the incremental. Therefore I add those two and when I add those two, I come up with 857,000. This is the upper misstatement bound. So this is the upper misstatement bound. Based on the upper misstatement bound, I can make a decision. What is my decision? Remember in my original problem, I said I can tolerate up to 575,000 of misstatement. Well what I find out is this. After I did all my computation, my upper misstatement bound is something in the 857,000, which is above 575. What do I do? I reject. I don't accept that the balance is fairly stated. Simply put, based on this calculation, the population is not acceptable. Why? Because the upper misstatement bound exceed the tolerable misstatement. So 857,118 is greater than 575, which is my tolerable misstatement. I don't accept this population. I need to do more work. I don't accept their balance. Otherwise I could have lived if this amount was lower than 575. So this is basically how this works. You could see this in a form of a simulation. You could see this in a form of multiple choice or many form of multiple choice. You just, I mean, if I'm testing you about this, I can ask you 15 to 20 different multiple choice questions on the data like this, or I can, this is an actual simulation, or this could be an actual simulation where you have to select things and input things in an Excel sheet. If you have any questions, by all means, let me know. As always, I would like to invite you to visit my website where I do what? I teach you the material. I don't, I don't review it with you. My job, when I teach, I teach to, to college students and college students, they need to learn the material. So I suggest you check out my website, farhatlectures.com, and for one law subscription, you can subscribe to all my courses, whether it's accounting, finance, or CPA supplementary material. Study hard. CPA is a long-term investment in your career. Good luck and stay safe, especially if you are still living through this coronavirus. Good luck.