 The last class we familiarize ourselves with the economic order quantity which gives some insights on what should be the actual level of inventory that needs to be maintained and how inventory as a cost is very critical when we actually understand the concepts of budgeting and to that extend how a proper inventory planning model would help in reducing the associated cost so that the actual cost is in line with the budgeted cost as a result of which the variance is zero or as much as possible the variance could be minimized. The graphical illustration of the model that we saw last class related two variables that is the order size the inventory order size and the cost associated with the ordering and we saw that there are two types of cost that are associated when it comes to inventory one is the ordering cost itself which decreases as the order size increases and the other one is the carrying cost of the inventory so if you look at the relationship this we saw is the ordering cost and how it behaves with order size and the carrying cost and how it behaves with the order size and we found that at this point of intersection is where we find the total inventory cost which is the carrying cost plus the ordering cost is minimum which means we found that if this is the representation of the total inventory cost let us say this is total inventory cost this is minimum at this point and the order size that corresponds to that point where the total inventory cost is minimum is what we saw is the economic order quantity and we related the economic order quantity with a formula which is two times Fs by Cp where Eoq is the economic order quantity and F is the fixed cost of ordering placing and receiving the inventory S is the annual sales C is the annual carrying cost which is which was in our example represent as a percentage of the average inventory value and P is the purchase price that the firm pays per unit of the inventory so this is how the economic order quantity was related to these four variables. Now before we proceed further we would like to I would like to understand this model with the help of an illustrative example that broadly covers various special cases and then we will understand how there are different concepts that are associated with the economic order quantity for example we made an assumption that we are basically trying to plan our inventory on a very pragmatic approach either based on historical experiences of handling inventory as a result of which we know that this is the carrying cost this is the ordering cost and the annual sales is this much so the average expected inventory is this much and we found this relationship based on which we found the economic order quantity. Now using the same formula with some numerical examples let us just try to understand with a few more additional concepts let us say that the situation is not as simple as the formula suggests let us say as an entity I need to also have something called a safety stock safety stock to meet sudden requirements a surge in demand or let us say that inventory is not just easily available that I place an order now and then immediately I get it tomorrow let us say there is also a need time for me to get the inventory from the time that I order now if these two are the additional dimensions that need to be factored now how will that change the inventory planning or how will that change the order quantity that we will understand by taking an example and I will use a numerical example so that the numbers give you a better understanding now let us say yes which is the annual sales is around 26,000 let us say we are talking about textile unit so I am selling around 26,000 shirts let us say so the annual sales is 26,000 units now see as I told you it is a percentage carrying cost which is expressed as a percentage of the inventory value and let us say that is 25% now P is the purchase price of one unit of the inventory let us say it is 4.92 rupees per unit of inventory and let us say the fixed ordering cost is 1000 so for every order that we need to place the fixed ordering cost is 1000 these are the numerical examples now let us begin with the fundamental equation that economic order quantity is square root of 2fs by cp now the question is first let us calculate the economic order quantity for this entity whose annual sales is so much the ordering cost is so much the carrying cost is so much and the purchase price is 4.92 fitting it into this formula 26,000 was here annual sales 25% times 4.92 so the economic order quantity is 6,500 units so it means for an annual sales of 26,000 shirts that we assume that this entity is going to make and with an economic order quantity of 6,500 the next data that we can arrive is the total number of times that we have to place an order during this period and assuming that each of the order is equally sized then the number of orders that we are going to place in this year in one year will be 26,000 by 6,500 which is very simple 4 this is one data point I am just trying to present you various data points so that let us see how we can get more information using this simple formula and how a different circumstances using the same formula how we would plan our inventory in a different way so we know now that we will be placing 4 orders in a given particular year now let us next go to average inventory what is average inventory we are assuming that the inventory consumption is uniform which means the average inventory at any point of time between 2 successive order points is the opening inventory plus closing inventory divided by 2 in this case at every time that we order and every time we receive an order so let us say at the time we receive the order in this case 6,500 units are there and then it is uniformly used after which it reaches 0 and then we order again again we get 6,500 units now the average inventory in this case would hence be just 6,500 divided by 2 why because it is 6,500 plus 0 divided by 2 now this assumption holds good because we are assuming that the inventory is consumed at a uniform rate now let us say the sales is also uniform let us say the sales is also uniform which means the sales rate if I need to calculate the sales rate then for a year which has 52 weeks I would be selling around 500 units every year this is another data point now at a cost of we know that the purchase price of an inventory is 4.92 and the average inventory is 3,250 average inventory is 3,250 purchase price is 4.92 per unit now let us bring in a little bit of working capital remember when we dealt with accounting I was telling you that there is something called working capital which needs to meet the immediate requirements of financing not long term but more short term in this case this is a classic example for a working capital requirement which means I need around 3,250 units of inventory and when the purchase price is 4.92 it means that the average investment that I have to make in purchasing inventory is 3,250 into 4.92 so the average investment in inventory will be 3,250 times 4.92 which is 16,000 rupees so let us say this working capital requirement I am financing it through a bank loan so suppose I am doing a working capital requirement analysis I need to forecast what would be the working capital requirement this gives me an understanding that the average requirement is 16,000 or it could be as high as 32,000 because the peak demand is the average inventory 3,250 is the average inventory but actually the peak inventory is 6,500 as a result of which the working capital requirement will also vary from the highest possible 32,000 which is 6,500 into 4.92 to as low as 0 which means I do not need any working capital. So if the question is what is the average working capital requirement it is average inventory times the purchase price and then based on that we would come to an understanding that this is the average working capital requirement and then the cost of financing that working capital is also calculated that is again as a different subject matter by itself but this is just to give you a data point that with average inventory I can also calculate my average working capital or in this case the average investment that is required in inventory which is 16,000 now you should also notice one more relationship the EOQ is square root of 2 FS by CD. So we will understand that the given increase in sales with a given increase in sales will result in a less than proportionate increase in inventories because the relationship between the EOQ and sales is not directly linear but it is a square root relationship which means let us say the sales which is 26,000 now increases to 52,000 let us say there is a 100 percent increase in sales. Now the sales increase by 100 percent and since this is a square root relationship you will understand that the economic order quantity will not increase by the same 100 percent but definitely will increase but the increase is less proportionate than 100 percent which would be if you calculate the EOQ at this sales level the EOQ at 52,000 will be somewhere around 9,000 which is close to another 40 percent let us say 40 percent increase in EOQ. So 100 percent increase in sales results in a 40 percent increase in the economic order quantity and also the average inventory that is also required will raise by the same percentage. Now you will understand when I was talking about the need for maintaining economies of scale now this example suggest that economies of scale when it comes to holding inventories makes a lot of sense because the relationship between the economic order quantity and sales since it is not linear but through a square root it means that the economies of scale will help in reducing the total inventory cost. Now let us just split this total inventory cost as we saw in the previous class we know that it is a sum of the total carrying cost plus the total ordering cost and for the same example we are expressing the total carrying cost and the total ordering cost based on the data that we have and substituting the value at economic order quantity so Q is 6,500 plus 26,000 into 1000 divided by now notice here that the total inventory cost at the economic order quantity is 8,000 now this 8,000 could be 2000 plus 6000 or 3000 plus 5000 or 4000 plus 4000 but it is necessarily 4000 plus 4000 in this case because Q here is the economic order quantity and this is no rocket science add economic order quantity because our total carrying cost is equal to the total ordering cost this 8,000 has to be necessarily be split into 4000 and 4000 each for ordering and carrying cost and this is true in all examples where the total ordering cost and the total carrying cost will be equal at the economic order quantity and that is what I just illustrated in this example. Now in reality things are not as simple as this example suggest I told you in one example that suppose I order an inventory and it is going to take two weeks for me to get the inventory so after I make an order let us assume that I have to wait for two weeks then as somebody who has to plan the inventory to ensure that the inventory is available just at the time that it is required we need to have some trigger points the moment the inventory level falls to a certain level there is a trigger and hence we order the inventory. So that should be something called an inventory ordering point now this is what a lot of people who do the inventory planning will set based on their requirements now let us say in this case since I told you it is a two week lead time that is required for inventory to arrive which means the 6500 order quantity that I expect will take two weeks for it to arrive which means we need to set this trigger two weeks before the inventory drops to zero that is the point now graphically we can represent this now let us say this is the lead time we will denote them in weeks and let us say this is the inventory units so we begin with zero weeks 4 weeks 6 8 10 12 14 and so on 26 28 30 and so on and let us retain the same example that we used before which means let us say this is 1000 2000 3000 4000 this inventory is in 1000 5 6 7 8 now in this example we are assuming that the sales rate is uniform the inventory consumption is uniform which means 500 units is being sold every week and the 6500 economic order quantity which is ordered four times a year is used uniformly which means 6500 over a 13 week period is consumed at a uniform rate of 6500 divided by 13 that will be the number of inventory units that is consumed every week now if that assumption is made let us see how the behavior of inventory with lead time gives us an understanding of when we should order the inventory now in this case I have told you that it requires two weeks time for the inventory to be delivered from the time that it is ordered and since the average sales rate is uniform which means 500 units is being sold every year then every week so every week 500 units are being sold so what will be the order point now the order point is in this case because it requires two weeks for the inventory to arrive and in addition I am just giving an extra dimension and let us say that that is not also the only condition there is also another condition that I also need to maintain a safety stock of 1000 units of inventory or two weeks of inventory which means that not only should I have to at order in order two weeks in advance but also order in such a way that it also ensures that there is a minimum safety stock of 1000 units that can be used when there is a likely event where there is going to be a surge in the demand in this case we are saying that we are going to sell 500 units every week but let us assume that the maximum there is a likelihood that the sales rate is twice this amount so 1000 units each week and I want to set the safety stock to be 1000 in that case instead of 6500 being the economic order quantity my maximum inventory that I will be holding is not 6500 but it will be 6500 plus a safety stock of 1000 so the maximum inventory that I will be holding now will be 7500 and given that the sales rate is uniform the average sales rate is uniform this is 11th week, 13th week my order point here now is the moment the inventory level touches to 2000 when will that happen it happens here I will have to order because it takes two weeks for me to this is the lead time this two weeks is my lead time on this week axis it takes two weeks for me to get my 1000 units of inventory so what will happen at the 13th week this will go down and I have also internally set a condition that I have to have a minimum stock of 1000 now are we meeting this condition yes the order point was when the inventory level dropped to 2000 I placed an order while the sales went the regular sales was 1000 and after two weeks it is here and by the time whatever I ordered during the 11th week I would have received and suppose there was a surge in the demand I would have met this demand because of my safety stock level then it would have later come down to 0 the 15th week this is in the even that there is a surge in the demand assuming that there is no surge in the demand and that the safety stock is not utilized then at the end of the 13th week my inventory once again reaches to the 7500 and that keeps 26th week so this relationship continues for every quarter since the number of orders that we make in the year is for this in this case so you will find that this will be my economic order of quantity this is 7500,000,6500 this is my safety stock so I am just presenting everything in this graph so that this is better understood instead of taking a example and working it out so this will be the economic order of quantity. Now what I have done in this graph is just trying to mix both the parameters that I have internally said one is that I need to have a safety stock of 1000 units of saleable inventory at any point of time and that also the information is that it takes two weeks for me to get my inventory whenever I need to order that which means every time I order an EOQ it takes two weeks and in this example our EOQ was 6500 and we knew that we are going to order four times which means at the end of the 13th week we place an order and we know that it takes two weeks so what do I do when do I order 6500 units at the end of the 11th week of every quarter so I place an order and in this case I am ordering it when the inventory level is at 2000 because I know that I need to maintain a safety stock of 1000 and that the incremental 1000 is for the to take care of the lead time so that is the additional dimension that I have given so this graph represents how decisions are taking when it comes to inventory planning level to set the trigger points for us to order the inventory to ensure that it not only meets the criteria of the economic order quantity being available just at the time that I require it so that we do not have to carry excess inventory nor have to incur additional cost for not having inventory because at times when you do not have inventory when you actually need it you also end up buying inventory at extra price extra cost remember when we did this in the material variance analysis at times we also pay more for the raw material inventory as a result of which we end up having an unfavorable variance so two things one we also need to ensure that we have the optimum inventory and secondly we suppose we anticipate at times there is a good possibility that there will be a surge in demand and that we will have to meet the demand through safety stock we should also have some safety stock but safety stock is also additional cost so the question is whether the benefit of incurring that additional cost of holding safety stock whether that will be outweighed by the incremental sales is something that we have to satisfy ourselves if we feel that the safety stock holding safety stock is going to be beneficial then we will incur the additional cost of holding the safety stock in this case the increase in the average inventory causes an increase in the average inventory carrying cost because of the safety stock to the extent that this is in this case the safety stock is 1000 we know that the inventory value is 4.92 and the carrying cost is 25 percent of the purchase price so this will be the additional cost that we will have to incur for holding the safety stock so this 1230 will be the additional cost that we will be incurring in addition to holding the economic order quantity now if this if the incremental sales outweighs this benefit then there is some sense in holding the extra stock. Now this illustrative model that gives you an understanding of what is the economic order quantity and also the timing from the timing perspective when should we order this economic order quantity this is important for us to know from the perspective of understanding how we can reduce the total inventory costs remember when in last class we were talking about the cash conversion cycle three important parameters emerged one is the collection period the other is the payment deferral period and the other is the inventory conversion period while the collection period which is got something to do with the accounts receivable that can be shortened by employing good or better practices that ensures faster collection there is something called accounts receivable management we can reduce the collection period likewise the deferral period as much as possible we would try to elongate by better negotiating terms with the vendor but one thing is the inventory conversion period which can also be shortened either by having better processes about which accounting does not play a major role or the management accounting does not play a major role but it can be the inventory conversion period when it is converted into cost can be reduced if we have better inventory planning in place which means there should be a scientific approach that ensures that we are holding only the right level of inventory as a result of which the cost of holding that inventory is minimized and which it is with that understanding that we study this economic order quantity model and this will give you a very clear understanding on how much is the optimum inventory that we need to hold as a result of which the cost of holding such inventory is minimized and if the cost of holding such inventory is minimized in the overall scheme of budgeting we are trying to as much as possible achieve the total cost very much within the budgeted estimates otherwise what will happen is it will be more the actual cost will be more than the budget as a result of which we get unfavorable variances it is only with that perspective I thought I should just give you this introductory concept on economic order quantity. Now what we have done in the first part when I began this course I said that I will be handling the three C's of business analysis one was the code the other was the conduct and the other was the climate code conduct and climate. Now as we draw close to finishing the first C which is the code I would like to begin the next class by giving by working out a comprehensive case that covers the fundamentals of accounting and also tries to give you an understanding on how to prepare a balance sheet income statement and as we work we will also understand some nuances of certain concepts when it actually comes into real time application and then with that I will be finishing the first C after which we will enter into the other two C's which is the climate and the conduct there I will be talking about strategy economy how to understand the economic principles theory of demand and supply how do companies come out with strategies these are things that I will be talking into the when I talk about the other two C's which namely the code and the conduct and the climate. Next class I will be giving inputs will be working out a problem on the fundamentals of accounting that we have gathered so far. So what we will be doing is we will go through a series of transactions and these are I will pick a live real case study examples so that you will understand how these accounting concepts are employed in for real time purposes how certain principles of accounting if interpreted in different ways result in different ways of recording these transactions and communicating it in a different way. So this we will understand when we actually work real time case so next class I will be coming with a case study which I will start working out myself so that you will have a better understanding and that in my opinion will form the comprehensive summary for these first 20 sessions on accounting both financial accounting and management accounting so next class we will begin working a small case study thank you.