ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1 18/08/1418/08/14 2:092:09 PMPM user1user1 //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles APPENDIXA INVENTORYDECISIONS Inventory planning and control decisions are an important aspect of the manage- ment of many organizations and, as discussed in Chapter 9, play an integral role in LEARNINGOBJECTIVE 6 preparing the master budget. Inventory levels are not left to chance but rather are Compute the optimal carefully planned. The major issues that must be addressed are as follows: How does inventory level and order size. the manager know what inventory level is appropriate for the firm? Will the appro- priate level vary from organization to organization? Specifically, inventory decisions involve how much to order—the economic order quantity —when to order, the amount of safety (backup) stock to keep on hand, and special considerations associated with perishable products. Cost factors, uncer- tainty, and revenues all contribute to the decision analysis. The purpose of this appendix is to examine the inventory control methods available to the manager to manage inventory levels, and the costs related to these decisions. These methods are relevant both in preparing the master budget and in managing inventory levels throughout the year. Costs Associated with Inventory Three groups of costs are associated with inventory. The first group, inventory Inventory ordering costs ordering costs , consists of costs associated with the acquisition of inventory. Costs associated with the Examples are acquisition of inventory, such as clerical costs and transportation 1. Clerical costs. costs. 2. Transportation costs. The second group, inventory carrying costs , consists of costs that arise from Inventory carrying costs having inventory on hand. Examples are Costs associated with the storage of inventory, such as 1. Storage space costs. storage space, property taxes, 2. Handling costs. insurance, and interest on funds. 3. Property taxes. 4. Insurance. 5. Obsolescence losses. 6. Interest on capital invested in inventory. The third group, the costs of not carrying sufficient inventory , consists of Costs of not carrying costs that result from not having enough inventory on hand to meet customers’ sufficient inventory needs. Costs in this group are more difficult to quantify than costs in the other two Costs that result from not having groups, but nevertheless they can be very significant to a firm. Examples of costs in enough inventory on hand to this group are meet customers' needs, including customer dissatisfaction and lost 1. Customer dissatisfaction (resulting in lost future sales). sales, forgone quantity discounts, 2. Quantity discounts forgone. uneven production, and additional 3. Uneven production (expediting of goods, extra setup, overtime, etc.). transportation charges. 4. Inefficient production runs. 5. Additional transportation charges. Conceptually, the appropriate level of inventory to carry is the level that mini- mizes the total of these three groups of costs. Such minimization is difficult to achieve, however, because some of the costs involved are in direct conflict with one another. For example, as inventory levels increase, the costs of carrying inventory also increase, but the costs of not carrying sufficient inventory decrease. To mini- mize cost, managers must balance the three groups of costs. The problem really has two dimensions—how much to order (or how much to produce in a production run) and how often to order. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 2 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles 9A-2 Appendix 9A Inventory Decisions Computing the Economic Order Quantity Economic order quantity The concept of how much to order is commonly referred to as the economic order (EOQ) quantity (EOQ) . Simply put, it is the order size that minimizes the first two groups The order size for materials that of costs just described. We consider two approaches to computing the EOQ—the minimizes the costs of ordering tabular approach and the formula approach. and carrying inventory. The Tabular Approach For a given level of annual consumption of an inventory item, a firm might place a few large-quantity orders each year, or it might place many small-quantity orders. Placing only a few orders results in low inventory ordering costs but high inventory carrying costs, as the average inventory level on hand is very large. Conversely, placing many orders results in high inventory ordering costs but low inventory car- rying costs because the average inventory level is relatively small. The EOQ represents the order size that balances these two groups of costs. To demonstrate how it is computed, we assume that a manufacturer uses 3,000 subassem- blies (manufactured parts inserted into other manufactured items) in the manufactur- ing process each year. The subassemblies are purchased from a supplier at a cost of $20 each. Other cost data are given below: Inventory carrying costs, per unit, per year . $ 0.80 Cost of processing a purchase order . $10.00 Exhibit 9A–1 tabulates the total costs associated with various order sizes for the subassemblies. Notice that the total annual cost is lowest (and is equal) at the 250-unit and 300-unit order sizes. The EOQ lies somewhere between these two points. By adding more columns to the table, we could identify 274 units as being the exact EOQ. The cost relationships from this tabulation are presented graphically in Exhibit 9A–2. Notice from the graph that total annual cost is minimized at that point when annual carrying costs and annual purchase order costs are equal. The same point identifies the EOQ, because the purpose of the computation is to find the point of exact trade-off between these two classes of costs. Observe from the graph that total cost tends to flatten out between 200 and 400 units. Most firms look for this minimum cost range and choose an order size that falls within it, rather than choosing the exact EOQ. The primary reason is that suppliers will often ship goods only in round-lot sizes. EXHIBIT9A–1 Tabulation of Costs Associated with Various Order Sizes Order Size in Units Symbol* 25 50 100 200 250 300 400 1,000 3,000 E/2 Average inventory in units . 12.5 25 50 100 125 150 200 500 1,500 Q/E Number of purchase orders . 120 60 30 15 12 10 7.5 3 1 C(E/2) Annual carrying cost at $0.80 per unit . $ 10 $ 20 $ 40 $ 80 $100 $ 120 $ 160 $400 $1,200 P(Q/E) Annual purchase order cost at $10 per order . 1,200 600 300 150 120 100 75 30 10 T Total annual cost . $1,210 $620 $340 $230 $220 $220 $235 $ 430 $ 1,210 *Symbols: E = Order size in units (see headings above). Q = Annual quantity used in units (3,000 in this example). C = Annual cost of carrying one unit in inventory. P = Cost of placing one order. T = Total annual cost = P(Q/E) + C(E/2) ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 3 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles Appendix 9A Inventory Decisions 9A-3 EXHIBIT9A–2 Graphic Solution to Economic Order $500 Quantity 400 Total cost 300 Cost Annual carrying cost at $0.80 per unit 200 Annual ordering cost 100 at $10 per order 0 0 200 400 600 800 1,000 Order size (units) Economic order quantity The table in Exhibit 9A–1 is based on the formula T = P 1Q/E2 + C 1E/22 where P is the constant cost per order and C is the cost of carrying one unit of inventory for the period of time under consideration. If quantity discounts can be obtained for orders of a certain size, another term representing the purchase costs of the particular lot size should be added to the formula or another line should be added to the table. Other complications arise where annual or period demand is not known, lead times vary, or multiple deliveries are necessary for each order. We do not incorporate these additional complexities in our examples. The Formula Approach The EOQ can also be determined using the formula 2QP E = B C where E = Order size in units. Q = Annual quantity used in units. P = Cost of placing one order. C = Annual cost of carrying one unit in stock. Substituting with the data used in our preceding example, we have Q = 3,000 subassemblies used per year. P = $10 cost to place one order. C = $0.80 cost to carry one subassembly in inventory for one year. 213,00021$102 $60,000 E = = = 275,000 B $0.80 B $0.80 E = 274 1the EOQ2 ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 4 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles 9A-4 Appendix 9A Inventory Decisions Although the solution can easily be obtained using the formula approach, it has the drawback of not providing the range of information produced using the tabular approach; also, it cannot be used where changes in purchase prices occur with changes in lot sizes. It is worth pointing out that if carrying costs could be determined for a period of time shorter than a year, say a month, then Q could be determined for that same period of time, as could the EOQ, using either the tabular or the formula approach. Just-in-Time and the Economic Order Quantity The EOQ will decrease under either of these circumstances: 1. The cost of placing an order decreases. 2. The cost of carrying inventory increases. Managers who advocate JIT purchasing argue that the cost of carrying inventory is much greater than generally realized because of the waste and inefficiency that inventories create.