 Hello, and welcome to this session. This is Professor Farhad in which we would look at economic order quantity known as EOQ. This topic is covered in a corporate finance, cost and managerial accounting courses, as well as the CPA exam, BEC section, and the CMA exam. As always, I would like to remind you to connect with me on LinkedIn. If you haven't done so, YouTube is where you would need to subscribe. I have 1,700 plus accounting, auditing, tax, and finance lectures, as well as Excel tutorial. If you like my lectures, please like them, share them. If they benefit you, simply put, they might benefit other people. Share the wealth connect with me on Instagram. On my website, farhadlectures.com, you will find additional resources, whether you're taking finance course, cost accounting, whether you're studying for your CPA, CMA, you name it. I have accounting supplemental material that's going to help you improve your performance and help you pass your professional certification, especially the CPA exam. So to illustrate the economic order quantity or EOQ, I'm going to assume we're going to be working with a burger stand, where we're going to be selling burgers. And what do we need to sell burgers? We need burger patties. And here's the problem. We can order a lot of patties up front, or we could not order a lot. So what's the problem if we have too many burgers on hand or not enough burgers? Let's start with if we have too little burger. We're going to run out of sales. And that's a problem. If somebody comes to you, if this customer comes and you tell them, look, I would love to sell you the burger, but I don't have a burger. Would you like a hot dog? Not really. They came for a burger and you don't have the burger. So that's a problem. The other problem is, is having too much inventory. Too much inventory means you have too many of these patties on hand. And that may not be good as well. One, you may not have enough space to store them. So you could have a storage issue. You don't have enough space. You might, because you have too many, and remember food could spoil, you could have spoilage, you could have lost some of them. So it's not in your best interest to have too many. And for some inventory, they become up, they have obsolescence. They become obsolete, although they may be, they may be still in good condition. For example, if you have Windows 95 software CDs, they're useless. Even if you have thumbnails, nobody buys thumbnails anymore because everything is in the cloud. So simply put your inventory, if you have too much of it, it could become obsolescence. So it's very important to be aware of our inventory because inventory is a cost. Because if I tie up money, if I invest in patties, I'm taken away from other things. I'm taken away money from my investments, from my bank account, from other things. And I want to have too much money. So what is the cost of our inventory? The cost of our inventory consists of our inventory cost, which is the purchase cost, plus what we called order cost because you need to order to restart the inventory. There is a cost, for example, delivery cost. And there's a carrying cost. Maybe you might have to pay insurance. You might have to have someone every once in a while going and count the inventory. So that's a carrying cost. So I can to minimize my order costs. To have this order cost minimize, which is delivery cost, I can order once a year. That's it. I can order all my burgers once a year. So do you see any problem with this? Sure I do. I don't have enough space. And if I order a lot, they may go bad if I don't sell them. So I cannot order once a year. So I don't have enough space to store it. And it might go bad. It might spoil. Another thing is I can order on demand. Every time I need a burger, I can order that parry for the burger. That's not feasible. Well, it is feasible if the person that I'm buying the burger from is just next door. So I can run, get two or three burgers and cook them and serve them. But that's not feasible. Oftentimes, that's not feasible. And if I order on demand, which is the opposite of order once a year, I have a high delivery cost or high ordering cost. So the problem is I need to balance between the two. And this is where the EOQ formula would help us minimize those two costs, those two. So for example, suppose Wimpy's Old Star Burger start out with 3,600 burger parries. This is what we have in our inventory to start with. This is what we have. Annual sales, we estimate that annual sales is 46,800 burgers, which is based. How do we know the annual sales based on prior years? So on average, we sell 900 burgers per week. If we take this amount divided by 3,600, we sell approximately 900 burgers a year. All the available inventory will be sold after four weeks. So if we have 3,600 on hand, if we divide this by 900, this equal to four. So every four weeks, what's going to happen, our inventory will go down to zero. So we'll start with 3,600 burgers and we'll start to sell them at some point after four weeks. So every week, we'll reduce them by 900. By week four, we'll have zero. Then we'll have to reorder again 3,600, which is this is the quantity, and start the process again. Now remember, since we have the burgers, since we have 3,600 burgers, we have what's called the carrying cost. So the carrying costs are normally assumed to be directly proportional to inventory levels. And this makes sense. The more inventory you have, the more cost you have. If you don't have a lot of inventory, you should have less cost, not generally speaking. So here's what's going to happen. Suppose Q is the quantity of burgers that won't be ordered each time. So let's assume we ordered 3,600. We call this the restocking quantity, 3,600. Here's what's going to happen. Our average inventory is 1,800 burgers every four weeks. Why? Because we start at 3,600, then we go down, and at some point we're going to be low 1,800, and at some point we're going to be zero. If we compute the average, well, we'll take the highest point, the lowest point, the average is 1,800. So the average inventory is the quantity, which is the quantity of burgers that we order divided by two. Why? Because at some point we're going to be carrying more than 1,800 and the first two weeks we will have more than 1,800. The following two weeks we'll have less than 1,800, on average we'll have 1,800. So that's the average inventory. So we're going to call, average inventory will just be the quantity divided by two. So we're going to let CC be the carrying cost per inventory. So this is CC is the carrying cost. So what is our cost in inventory? Well, if we want to compute our carrying cost, we'll look at average inventory, which in our situation 1,800 times the carrying cost, average inventory is 3,600 divided by two. So simply put, this is what it looks like. 3,600 divided by two, this is my average inventory. And we're going to assume for every burger it's going to cost us 75 pennies to maintain. Maybe it's the electric bill, maybe we need someone to go in and count it, count the inventory to take an inventory count. Maybe someone needs to cut it. So on average cost us 75 cents. So simply put our total carrying cost for 1,800 burger on average, 75 pennies equal to 1,350 per year. So this is our carrying cost. This is the carrying cost. Okay, now let's take a look at what we call now restocking or ordering cost. Ordering cost, we're going to, they assume to be fixed ordering cost means you have to pay for someone to place the order and they will deliver it to you, they charge you a fee. Maybe also have to pay the fee to order and to deliver. Simply put, there is a cost to order or restocking fee. So for WIMP, we're going to assume their annual sales is 46,800 and the order size, they're going to order 3,600 at a time. So simply put, they're going to have 13 orders per year which is 46,800 divided by 3,600. So we're going to assume that the fixed cost per order is F. It means they're going to have to pay a fee for ordering. Every time they order, they have to pay a fee. Let's just make it simple delivery fee. So we're going to take that fixed cost times the number of orders. Now, how do we find the number of orders? It is T which is the sales divided by the Q which is 13. Okay, the total sales per year divided by the quantity per order, 3,600 will give us 13 order. And now we're going to assume our fixed cost, the fixed cost for our purposes, it's going to be $50. So if we take $50 times 13, we'll find our cost, okay? Well, 13 assuming these numbers, 46,800 divided by 3,600. So this is what's going to be our restocking cost. So it's a fixed number, $50 times the T divided by Q which is the total sales divided by the quantity order, okay? So for WIMP, we had a carrying cost, remember, of 75 pennies per year, fixed cost of $50 per order and T, the sales is 46,800. Now, what we can do just to kind of look at this, let's use some different quantities. Let's assume we order, we order 3,000, our restocking quantity, 3,500. So if this is our restocking quantity, our carrying cost, let's focus on the carrying cost here, we're going to take 3,500 divided by two times 75 pennies and that's going to give us $1,312. Now, restocking fee, restocking fee is, we're going to take $50, $50 which is the fixed fee times the 46,500 divided by Q and here we're assuming Q is 3,500, okay? Now, if we take, if we multiply the ordering or the restocking cost, the restocking cost is $668.60. Now, we can try these figures, these computation on different quantity. If we go from 3,500 to 3,000 to 2,500, 2,000, 1,500, 1,500. So notice, if we order only, if the ordering quantity, if we reorder every 500 burgers, our total cost is 4,867. Why? Because we are reordering often because we're only ordering 500, our restocking fee is very high. You notice that our restocking fee, our order, our order is very high, but we're not carrying a lot. Notice our carrying cost is 187. If we order on the other extreme, the highest number that we have on this graph, 3,500, notice our restocking or ordering is very low because every time we order, we order a lot. Therefore, our ordering cost is very low, but notice what's gonna happen to our carrying cost. Our carrying cost is very high. So notice, I'm showing you the two extreme. So what's the optimal point? The optimal point is, if you notice, if you're looking at the numbers, we go from 1,881, $1,905, $1,873, then it goes, then the cost goes up again. So notice at some point, the cost is minimal. And when is the cost minimal? The cost is minimal when those two equal to each other, when we minimize them and they practically equal to each other. So what's the optimal quantity to order? 2,500. So based on this information, based on this information, what does that mean? It means the EOQ, okay? It's when this formula, I'm showing you where it's coming from, when this formula equal to this formula. So this is what we're saying. When it's when the carrying cost equal to the restocking cost. So when the quantity divided by two times CC equal to the fixed cost, T divided by Q, okay? Now we can just kind of, if those two are equal to each other, we can just solve. And now we have Q square equal to two T times F over CC. Now, if we solve for Q, what we have is the square root of two T times F divided by the carrying cost. And this is the EOQ. Simply put, the EOQ is when we have, when we take the number two, okay? Now you know where the number two is, where we have the averages, times the total sales. The total sales is how much year for the year? The total sales is 46,800. So if you take two times, 46,800 times the fixed cost is 50 divided by the carrying cost for this example is 20. I'm sorry, the carrying cost is, sorry, 75 pennies. 75 pennies. You square root all of those and it's going to give you something close to 2,500. It's going to be around 2,490 or something like this. So let's look at another example to illustrate this EOQ concept. Let's assume we start each period with 100 pairs of hiking boots. That's what we're selling hiking boots. The carrying cost per pair is $3. Think of insurance cost, think of boxing those shoes. The carrying is $3. So what is the total carrying cost? Well, how many on average, how many shoes do I need on average? If I have 100 at the beginning of the period, zero at the end, I have 50 on average times $3. So the carrying cost is 150. Now, suppose I sell 600 pairs per year. That's my estimate. How many times will I have to restock? Well, if I sell 600 per year and I need 600 to start with for every period, so I need to order six times. Six times 100, they sell, I buy another 100. So six times, six times. Now, assume the ordering cost or the restocking cost is $20 per order. So I have to pay 20 for every restocking order. Well, that means my total restocking cost equal to 120. So notice I ask you specifically, what's the carrying cost? What's the restocking or the ordering cost? It's 120 and 150 based on these figures. Now, I need to find out what's my optimal order size because I said here, I'm gonna order, simply put, I'm gonna have six order, each one is 100, that might not be the optimal. Maybe I can reduce this. Maybe I can reduce this. Maybe this is, in other words, notice the 120 and the 150. Remember, 150 is not equal to 120. I want to, one day equal to each other. This is my optimal point. So I'm not paying too much carrying cost. I'm not paying too little of one and too much of the other. I wanna make sure what's my optimal point. Well, to compute my optimal point, I have to use the formula that we just learned, the EOQ. So what's the EOQ? It's the square root of two times sales, the estimated sales per year, times the ordering cost divided by the carrying cost, which is the carrying cost for us is $3. The ordering cost is 20 and this is T equal to 600. Let's take a look at the formula here. So the square root of two times 600 times 20 divided by three will give us the optimal order. Quantity is 89.44. Now 89, you can make it 90, you can make it 89. It doesn't really matter here, but the point it's around 89. Now, how many times would I need to order if I'm ordering 89 for every time? Well, I will need 600 divided by 89.44. I'm ordering a little bit more than six times. So I need to order a little bit more, okay? 6.71, 6.71 rather than six. Now, so what is the total restocking cost? Well, if I'm ordering 6.7 times, again, this is rounding. Don't worry about the rounding. The point is trying to be as close as possible. You cannot order 6.7 times, times $20. It's $134.16. Now, the average inventory now, rather than 100 divided by two, my average inventory is around 90 pears divided by two equal to 44.72 or 45. I multiply this by my carrying cost equal to 134.16. Notice, now my restocking cost is 134. My carrying cost is 134. Simply put, when I did this, when I was not taking the EOQ into account, the carrying cost was a little bit too much. Now, the carrying cost went down and my, I'm sorry, yeah, the carrying cost went from 150 to 134, and the ordering cost went from 120 to 134 because I'm ordering more than six times. I'm ordering 6.71 times, but this is the optimal. This is the optimal point. This is the optimal point where I'm minimizing the cost. Therefore, the total will be 268 versus 270, which is not that much. 268 here versus 270. Close, very close to each other because notice what I did is I reduced my carrying cost, but I increased my restocking cost. I increased my restocking cost. So this is basically how you would use the EOQ or how you would use the formula. Again, this example cannot be that realistic because again, 6.71 is not, you cannot order 6.71 times, but the point is hopefully, now you have a better understanding about the formula and where it came from. It's where the carrying cost and the restocking cost, the ordering cost are minimized. They equal to each other. 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