Costs Associated with Inventory Three Groups of Costs Are Associated with Inventory

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APPENDIXA INVENTORYDECISIONS

Inventory planning and control decisions are an important aspect of the management 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 appropriate 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, uncertainty, 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 minimizes 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 minimize 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 carrying 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 subassemblies (manufactured parts inserted into other manufactured items) in the manufacturing 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. These managers argue that this fact, combined with the fact that JIT purchasing dramatically reduces the cost of placing an order, is solid evidence that companies should purchase more frequently in smaller amounts. Assume, for example, that a company has used the following data to compute its EOQ: Q = 1,000 units needed each year. P = $60 cost to place one order. C = $3 cost to carry one unit in inventory for one year. Given these data, the EOQ is 2QP 211,00021$602 E = = = 240,000 B C B $3 E = 200 units Now assume that as a result of JIT purchasing, the company is able to decrease the cost of placing an order to only $10. Also assume that because of the waste and inefficiency caused by inventories, the true cost of carrying a unit in inventory is $8 per year. The revised EOQ is 2QP 211,00021$102 E = = = 22,500 B C B $8 E = 50 units Under JIT purchasing, the company would not necessarily order in 50-unit lots since purchases would be geared to current demand. However, this example shows how significantly the factors underlying the JIT concept can affect the purchasing decision. Production Lot Size Economic production lot The EOQ concept can also be applied to the problem of determining the economic (batch) size production lot (batch) size . Deciding when to start and when to stop production The number of units produced in runs is a problem that has challenged manufacturers for years. The problem can be a production lot that minimizes solved quite easily by inserting the setup costs for a new production lot (batch) setup costs and the costs of into the EOQ formula in place of the purchase order cost. The setup cost includes carrying inventory. the incremental labour and other costs involved in making facilities ready to produce a batch of a particular production item. Setup costs To illustrate, assume that Robson Company has determined that the following Labour and other costs involved costs are associated with one of its product lines: in getting facilities ready to produce a batch of a particular Q = 15,000 units produced each year. production item. P = $150 setup costs to change production from one product to another. C = $2 to carry one unit in inventory for one year. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 5 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-5

What is the optimal production lot size for this product line? It can be determined by using the same formula used to compute the EOQ:

2115,00021$1502 $4,500,000 O = = = 22,250,000 B $2 B $2 O = 1,500 1economic production lot size in units2

The Robson Company will minimize its overall costs by producing in lots of 1,500 units each. Tabular analysis can be used to provide a more flexible model for the planning of production lot sizes. Managers involved in constrained operations would go even further in reducing lot sizes.1 When a particular work centre is not a constraint, the only significant cost involved in setups is typically direct labour wages. However, since direct labour wages are considered to be a fixed cost rather than a variable cost in the theory of constraints (discussed in Chapter 12), the incremental cost of setups is considered to be zero. Therefore, at work centres that are not a constraint, the economic lot size in the theory of constraints is as small as a single unit. At a work centre that is a constraint, setup time is very costly, since each minute spent setting up is a minute taken away from producing output that could be sold. Therefore, setup reduction efforts should focus on the constraint work centre, and lot sizes should be larger at the constraint than at other work centres. Managers should be extremely cautious when applying the results of activity- based costing (ABC) analyses to computation of the economic lot size. Typically, one of the results of an ABC analysis is a dramatic increase in the apparent costs of setups. This is because under conventional costing systems, many of the costs that might be attributed to switching over from one product to another are lumped into the general manufacturing overhead cost pool and distributed to products based on direct labour-hours or some other measure of volume. However, when an ABC analysis is done, these costs are separately identified as setup costs. As a consequence, setup costs appear to increase, implying that the economic lot size should be increased. However, a close examination of the costs attributed to setups in the ABC analysis will usually reveal that most of the costs are fixed and cannot be avoided by reducing the number of setups. For example, machinery depreciation may be included in setup costs. However, reducing the number of setups will have no impact on the amount of machinery depreciation actually incurred. JIT production philosophy, when it was originated, carefully examined the assumptions in economic production lot size analysis. The typical analysis assumes that setup time is a known fixed cost, for example, $150 per setup in the preceding example. JIT approached this production lot size problem by attempting to reduce setup costs to zero. If setup costs in the Robson Company example were reduced to, say, $1, the economic production lot size in units would only be 122 units, which is much closer to a JIT production approach. The lower the setup cost, the smaller the production lots. Production approaches have been redesigned in some operations so that many different products can be manufactured at little or no setup cost.

Reorder Point and Safety Stock We stated earlier that the inventory problem has two dimensions—how much to order and how often to order. Determining how often to order involves two concepts, termed the reorder point and safety stock , and involves finding the optimal trade-off between the second two groups of inventory costs outlined earlier (the costs of carrying inventory and the costs of not carrying sufficient inventory). First, we will discuss the reorder point and the factors involved in its computation. Then we will discuss the circumstances under which a safety stock must be maintained. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 6 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

9A-6 Appendix 9A Inventory Decisions

Reorder point The reorder point indicates to managers when to place an order or when to The point in time when an order initiate production to replenish depleted inventory. It depends on three factors—the must be placed to replenish EOQ (or economic production lot size), the lead time , and the rate of usage during depleted inventory; it is the lead time. The lead time can be defined as the interval between the time that determined by multiplying the an order is placed and the time that the order is actually received from the supplier lead time by the average daily or production is completed. or weekly usage.

Lead time Constant Usage during the Lead Time If the rate of usage during the lead The interval between the time time is known with certainty, the reorder point can be determined by the follow- that an order is placed and the ing formula: time that the order is actually received from the supplier or Reorder point = Lead time × Average daily or weekly usage production is completed. To illustrate the formula’s use, assume that a company’s EOQ is 500 units, that the lead time is 3 weeks, and that the average weekly usage is 50 units. Reorder point = 3 weeks × 50 units per week = 150 units The reorder point would be 150 units. That is, the company automatically places a new order for 500 units when inventory stock drops to a level of 150 units, or three weeks’ supply, left on hand.

Variable Usage during the Lead Time The previous example assumed that the 50 units per week usage rate was constant and was known with certainty. Although some firms enjoy the luxury of such certainty, it is more common to observe considerable variation in the rate of usage from period to period. If usage varies from period to period, the firm that reorders in the way computed earlier will sometimes find itself out of inventory. A sudden increase in demand, a delay in delivery, or a problem in processing an order may cause inventory levels to be depleted before a new order arrives. Companies that experience problems in demand, delivery, or the processing of orders have found that they need some type of buffer to guard against stock-outs. Safety stock Such a buffer is usually called a safety stock . A safety stock serves as insurance The difference between average against greater than usual demand and against problems in the ordering and deliv- usage of materials and ery of goods. Its size is determined by deducting average usage from the maximum maximum usage of materials usage that can reasonably be expected during a period. For example, if the firm in that can reasonably be expected the preceding example were faced with a situation of variable demand for its prod- during the lead time. uct, it could compute a safety stock as follows:

Maximum expected usage per week ...... 75 units Average usage per week ...... 50 Excess...... 25 units Lead time...... × 3 weeks Safety stock...... 75 units

The reorder point is then determined by adding the safety stock to the average usage during the lead time . In formula form, the reorder point is Reorder point = 1Lead time × Average daily or weekly usage2 + Safety stock Computation of the reorder point using this approach is shown both numerically and graphically in Exhibit 9A–3. As shown in the exhibit, the company places a new order for 500 units when inventory stocks drop to a level of 225 units remaining. If management does not want to assume the worst-case situation by using the maximum expected usage per week, then a slightly more complex calculation of the safety stock is necessary, as shown in Exhibit 9A–4, which is based on the data that follow. Assume that management makes the following estimates for a yearly period: ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 7 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-7

Carrying cost per year ...... $1 per unit Stock-out cost per unit ...... $0.60 Average usage per week ...... 50 Orders placed per year ...... 12

Demand Probability 80 0.05 120 0.06 140 0.20 150 0.38 160 0.20 180 0.06 220 0.05 1.00

These estimates reflect the uncertainty experienced by management when fac- ing the various demand possibilities. The table of demand levels and corresponding probabilities presents how management has estimated the uncertainty it faces, which can be incorporated into the safety stock calculation. The calculation of the optimal safety stock begins by computing the various inventory quantities that the demand probabilities indicate could be satisfied by the safety stock. These are the demand quantities in excess of the expected demand of 150 units during the lead time period. Calculation (a ) in Exhibit 9A–4 illustrates the amounts. Each unit of safety stock inventory will be on hand for the year (the typical time period used), so the carrying cost per unit of inventory per year is used to determine the first cost element: the total carrying cost of the safety stock per year. The second set of calculations computes the stock-out costs caused when demand exceeds the safety stock quantity. Column (b ) in Exhibit 9A–4 reflects the excess demand possibilities above the safety stock and the average demand during the lead time, in other words, the stock-out quantity. The stock-out in units is multiplied by the stock-out cost of $0.60 per unit to give the stock-out cost for each time an order is placed. Knowledge of the average inventory usage per year and the order size is used to determine the number of times that orders are placed in a year. To determine the stock-out total costs, the stock-out cost per order is multiplied by

EXHIBIT9A–3 Determining the Reorder Point—Variable Usage

575 Average usage

Economic Maximum order quantity Reorder point 225 expected usage

Inventory (units) Safety stock 75 0 5 weeks 10 weeks 15 weeks 20 weeks

Lead time 3 weeks Economic order quantity. . . . 500.units Lead time ...... 3.weeks Average weekly usage . . . . . 50.units Maximum weekly usage . . . . 75.units Safety stock ...... 75.units

Reorder point = (3 weeks 3 50 units per week) + 75 units = 225 units ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 8 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

9A-8 Appendix 9A Inventory Decisions

EXHIBIT9A–4 Safety Stock Level

(a) (b) (c) (d) (e) Total Number of Expected Safety Carrying Stock-Out Times Probability Stock-Out Total Stock Level Cost per Stock-Out Cost per Orders of Stock- Cost per Cost per in Units Year in Units Order Time Placed Out Year Year –0– $–0– 10 $ 6.00 12 0.20 $ 14.40 30 18.00 12 0.06 12.96 70 42.00 12 0.05 25.20 $52.56 10 10 20 12.00 12 0.06 8.64 60 36.00 12 0.05 21.60 40.24 30 30 40 24.00 12 0.05 14.40 44.40 70 70 0 0.00 12 0.00 0.00 70.00

a. Safety stock level is possible demand minus expected demand (e.g., 180 - 150 = 30). Carrying cost of safety stock is units times cost per unit to carry (e.g., 30 × $1 = $30). b. Stock-out in units is possible demand minus expected demand minus safety stocks (e.g., 220 - 150 - 10 = 60). c. Stock-out cost per order time is stock-out in units times stock-out cost per unit (e.g., 30 × $0.60 = $18.00). d. Expected stock-out cost per year is stock-out cost per order time, times the number of orders placed per year, times the probability of a stock-out (e.g., $6 × 12 × 0.20 = $14.40). The probability of a stock-out is obtained from the data for various demand levels in excess of the expected amount of 150 units plus the safety stock. e. Total cost per year is the carrying cost of the safety stock plus the expected stock-out cost per year for the appropriate demand levels (e.g., the cost of having a safety stock level of 10 units is $10 + $8.64 + $21.60 = $40.24).

the number of orders per year and by the probability of each possible demand level to yield column ( d ). The sum of the total carrying cost for the safety stock and the expected stock-out costs gives the cost for each safety stock level. The lowest expected total costs provide the optimal level of safety stock. Notice that Exhibit 9A–4 suggests that 10 is the optimal level of safety stock, with a total cost of $40.24.

Perishable Products Inventory for perishable products or services such as hotel rooms poses an interest- ing and somewhat different type of problem. Basically, if too much or too many are ordered, the cost of the inventory is similar to a carrying cost, while ordering too few has the cost of contribution forgone from the lost sale. A firm cannot sell what it does not have, while it loses what it purchased but did not sell. Assume the following: Purchase cost, $3 per unit. Selling price, $5 per unit. Remember: You cannot sell what you do not have. What you buy but cannot sell is lost. Carefully review the calculations in Exhibit 9A–5 to see how the information can be combined to select the optimal inventory level. For perishable products, each unsold unit of inventory is generally lost; at best, a rebate may be received from the inventory supplier. Comparison of the total revenue based on demand quantities times selling prices, with the purchase cost of the inventory adjusted for any rebates or returns, determines the profit or loss for each combination of demand and inventory shown in Exhibit 9A–5. Because the demand levels are uncertain, each possible profit or loss before income taxes for the particular inventory level is multiplied by the probability of the demand level to yield the expected profits. The maximum expected profit is considered to be the indicator of the optimum inventory level. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 9 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-9

Profitability of Order/Demand Combinations EXHIBIT9A–5 Calculation of and Demand Probabilities Optimal Inventory 0.10 0.15 0.05 0.40 0.30 Inventory 1 2 3 4 5 Expected Profit 1 ...... $2 $2 $2 $2 $2 $2.00 2 ...... -1 4 4 4 4 3.50 3 ...... -4 1 6 6 6 4.25 4...... -7 -2* 3 8 8 4.75 5 ...... -10 -5 -0- 5 10 3.25**

Note: Four units is the optimum level of inventory because it has the greatest expected profit, $4.75. * Profit = Revenues - Costs: [($5 × 2) - ($3 × 4)]. Revenue is based on estimated demand, while costs are based on the units in inventory. ** Profit × Probability; for example, [0.10(-$10) + 0.15(-$5) + 0.05($0) + 0.40($5) + 0.30($10)] = $3.25.

GLOSSARY

Review key terms and definitions on Connect.

APPENDIXAQUESTIONSEXERCISES ANDPROBLEMS

9A–1 What are inventory ordering costs? 9A–2 What trade-offs in costs are involved in computing the EOQ? 9A–3 What is the reorder point and how is it determined? 9A–4 List at least three costs associated with a company’s inventory policy that do not appear as an expense on the income statement. 9A–5 List the three factors on which the reorder point depends. 9A–6 Will reducing the number of setups always lead to a reduction in setup costs? Explain. 9A–7 How can variable usage of inventory items be accommodated in the calculation of safety stock? 9A–8 What inventory costs are associated with perishable products?

EXERCISE 9A–1 Economic Production Lot Size [LO6] Jones Limited manufactures a variety of apparel and safety gear for motorcycles. One of its most popular products is the R-250 motorcycle helmet, with 30,000 units produced each year. Setup costs are $200 to switch production from one product to another. It costs $3 to carry one R-250 helmet in inventory for a year. Required: 1. Compute the economic production lot size for the R-250. 2. Assume that the company has been able to reduce setup costs for each production switch from one product to another to $100. Also assume that when the waste and inefficiency caused by inventories is also considered, the cost to carry a helmet in inventory jumps to $6 per unit. Under these conditions, what is the economic production lot size for the R-250?

EXERCISE 9A–2 Reorder Point and Safety Stock [LO6] Medical Lab Supplies distributes medical supplies and equipment throughout North America. Selected information related to a quick-developing X-ray film carried by the company is given below:

Economic order quantity ...... 1,400 units Maximum weekly usage ...... 168 units Lead time...... 4 weeks Average weekly usage...... 140 units

Management is trying to determine the proper safety stock to carry on this inventory item and to determine the proper reorder point. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1010 30/07/1430/07/14 7:327:32 PMPM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

9A-10 Appendix 9A Inventory Decisions

Required: 1. Assume that no safety stock is to be carried. What is the reorder point? 2. Assume that a full safety stock is to be carried. a. What is the size of the safety stock in units? b. What is the reorder point?

EXERCISE 9A–3 Economic Order Quantity [LO6] Carlson Limited uses 12,000 units of part CRF-2 each year. To improve control over its inventories, the company wants to calculate the EOQ for this part. Required: 1. The company has determined that the cost to place an order for the part is $15, and it has determined that the cost to carry one part in inventory for one year is $1.00. Compute the EOQ for the part. 2. Assume that the cost to place an order decreases from $15 to $12 per order. Will the EOQ increase or decrease? Calculate the new EOQ . 3. Now assume that the cost to carry a part in inventory decreases from $1.00 to $0.80 per part. (Ordering costs remain unchanged at $15 per order.) What will be the effect on the EOQ? Show computations. 4. In (2) and (3) above, explain why a decrease in cost causes the EOQ to go down in one case and to go up in the other.

EXERCISE 9A–4 Inventory Costs [LO6] Classify the following as either (a ) costs of carrying inventory or (b ) costs of not carrying sufficient inventory: 1. Courier charges on a rush order of a critical part needed in production. 2. Interest paid on a working capital loan. 3. Municipal taxes on inventory. 4. Spoilage of perishable goods. 5. Overtime paid to employees to expedite the setup for a rush order. 6. Customers lost through inability of the company to make prompt delivery. 7. Quantity discounts lost as a result of purchasing in small lots. 8. Theft insurance on inventory. 9. Loss sustained when a competitor comes out with a less expensive, more efficient product. 10. A general feeling of ill will among customers due to the late delivery of orders during a peak period.

PROBLEM 9A–5 Economic Order Quantity; Safety Stock; Just-in-Time Purchasing Impact [LO6] Jones Metal Works Inc. uses a small casting in one of its finished products. The castings are purchased from a foundry located in another province. In total, Jones Metal Works Inc. purchases 54,000 castings per year at a cost of $32 per casting. The castings are used evenly in the production process throughout a 360-day production year. The company estimates that it costs $45 to place a single purchase order and about $6.00 to carry one part in inventory for a year. Delivery from the supplier generally takes 6 days, but it can take as many as 10 days. The days of delivery time and the percentage of their occurrence are shown in the following tabulation:

Delivery Time Percentage (Days) of Occurrence 6...... 75 7...... 10 8...... 5 9...... 5 10...... 5 100 ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1111 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-11

Required: 1. Compute the EOQ. 2. Assume that the company is willing to assume a 15% risk of being out of stock. What is the safety stock? The reorder point? 3. Assume that the company is willing to assume only a 5% risk of being out of stock. What is the safety stock? The reorder point? 4. Assume a 5% stock-out risk as stated in (3) above. What is the total cost of ordering and carrying inventory for one year? 5. Refer to the original data. Assume that the company decides to adopt JIT purchasing policies. This change allows the company to reduce its cost of placing a purchase order to only $15. Also, the company estimates that when the waste and inefficiency caused by inventories are considered, the true cost of carrying a unit in stock is $8.00 per year. a. Compute the EOQ. b. How frequently would the company place an order, as compared to the old purchasing policy?

PROBLEM 9A–6 Tabulation Approach; Economic Order Quantity; Reorder Point [LO6] You have been hired to install an inventory control system for Dooly Company. Among the inventory control features that Dooly wants are indicators of how much to order and when . The following information is furnished for one item, called a duosonic , that is carried in inventory: a. Duosonics are sold by the gross (12 dozen, or 144) at a list price of $800 per gross, FOB shipper. Dooly receives a 40% trade discount off list price on purchases in gross lots. b. Freight cost is $20 per gross from the shipping point to Dooly’s plant. c. Dooly uses about 5,000 duosonics during a 259-day production year but must purchase a total of 36 gross per year to allow for normal breakage. Minimum and maximum usages are 12 and 28 duosonics per day, respectively. d. Normal delivery time to receive an order is 20 working days from the date that a purchase request is initiated. A stock-out (complete exhaustion of the inventory) of duosonics would stop production, and Dooly would purchase duosonics locally at list price rather than shut down. e. The cost of placing an order is $30. f. Storage space cost is $24 per year per gross. g. Insurance and taxes are approximately 12% of the net delivered cost of average inventory, and Dooly expects a return of at least 8% on its average investment. (Ignore ordering costs and carrying costs in making these computations.) Required: 1. Prepare a schedule computing the total annual cost of duosonics based on uniform order lot sizes of one, two, three, four, and five gross of duosonics. (The schedule should show the total annual cost according to each lot size.) Indicate the EOQ. 2. Prepare a schedule computing the minimum stock reorder point for duosonics. This is the point below which reordering is necessary to guard against a stock-out. Factors to be considered include average lead period usage and safety stock requirements. (CPA, adapted) PROBLEM 9A–7 Economic Order Quantity; Safety Stock; Just-in-Time Purchasing Impact [LO6] Lownie Limited uses 7,200 units of material T-95 each year. The material is used evenly throughout the year in the company’s production process. A recent cost study indicates that it costs $3.20 to carry one unit in inventory for a year. The company estimates that the cost of placing an order for material T-95 is $45. On average, it takes 7 days to receive an order from the supplier. Sometimes orders do not arrive for 10 days, and at rare intervals (about 2% of the time) they do not arrive for 12 days. Each unit of material T-95 costs the company $15. Lownie Limited works an average of 360 days per year. Required: 1. Compute the EOQ. 2. What size safety stock would you recommend for material T-95? Why? 3. What is the reorder point for material T-95 in units assuming (a ) 3-day safety stock, and ( b ) 5-day safety stock? 4. Compute the total cost associated with ordering and carrying material T-95 in inventory for a year assuming (a ) 3-day safety stock, and (b ) 5-day safety stock. (Do not include the $30 purchase cost in this computation.) ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1212 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

9A-12 Appendix 9A Inventory Decisions

5. Refer to the original data. Assume that as a result of adopting JIT purchasing policies, the company is able to reduce the cost of placing a purchase order to only $20. Also assume that after considering the waste and inefficiency caused by inventories, the actual cost of carrying one unit of material T-95 in inventory for a year is $6. a. Compute the new EOQ . b. How frequently would the company place a purchase order, as compared to the old purchasing policy? PROBLEM 9A–8 Integration of Purchases Budget; Reorder Point; Safety Stock [LO6] The Miller Company manufactures and sells industrial components. The Christo plant is responsible for producing two components, AD-5 and FX-3. Plastic, brass, and aluminum are used in the production of these two products. The Miller Company has adopted a 13-period reporting cycle in all of its plants for bud- geting purposes. Each period is four weeks long and has 20 working days. Experience has shown that adequate inventory levels for AD-5 and FX-3 can be maintained if 40% of the next period’s projected sales are on hand at the end of a reporting period. Based on this experience and the projected sales, the Christo plant has budgeted production of 8,000 units of AD-5 and 6,000 units of FX-3 in the eighth period. Production is assumed to be uniform for both products within each four-week period. The raw material specifications for AD-5 and FX-3 are as follows:

AD-5 FX-3 (kilograms) (kilograms)

Plastic...... 2.0 1.0 Brass...... 0.5 — Aluminum...... — 1.5

Data relating to the purchase of raw materials are as follows:

Projected Inventory Status at the End of the Seventh Period Standard Lead (kilograms) Purchase Purchase Reorder Time in Price per Lot Point On On Working Kilogram (kilograms) (kilograms) Hand Order Days

Plastic...... $0.40 15,000 12,000 16,000 15,000 10 Brass...... 0.95 5,000 7,500 9,000 — 30 Aluminum...... 0.55 10,000 10,000 14,000 10,000 20

The sales of AD-5 and FX-3 vary somewhat from month to month. However, the safety stock incorporated into the reorder point for each of the raw materials is adequate to compensate for variations in the sales of the finished products. Raw material orders are placed the day the quantity on hand falls below the reorder point. Christo plant’s suppliers are very dependable, so the given lead times are reliable. The outstanding orders for aluminum and plastic are due to arrive on the fourth and tenth working days of the eighth period, respectively. Payments for all raw material orders are remitted in the month of delivery. Required: The Christo plant is required to submit a report to Miller Company corporate headquarters, summarizing the projected raw materials activities, before each period commences. The data for the eighth-period report are being assembled. Determine the following items for plastic, brass, and aluminum for inclusion in the eighth-period report: 1. Projected quantities (in kilograms) of each raw material to be issued to the Production Department. 2. Projected quantities (in kilograms) of each raw material ordered and the date (in terms of working days) the order is to be placed. ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1313 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-13

3. The projected inventory balance (in kilograms) of each raw material at the end of the period. 4. The payments for purchases of each raw material. (CMA, adapted)

PROBLEM 9A–9 Economic Order Quantity Computations [LO6] Golf Supplies Limited buys golf balls at $20 per dozen from its wholesaler. All purchase orders are authorized by the respective department managers, who are paid weekly salaries of $1,000 to work 40 hours. On average, it takes a manager about 15 minutes to gather the information required to produce a purchase order. When not performing administrative tasks, such as placing orders, hiring, scheduling and training staff, and attending meetings, managers spend their time selling. Once the purchase order information is collected, it is entered into a computerized purchase order form by a part-time employee hired on an hourly basis, at $15 per hour, to do data entry. On average it takes this person 10 minutes to enter an order and produce a printed copy. The order form costs $0.25 and mailing costs are $1.50. When the order arrives, it is unloaded from the truck and placed in inventory by the stock supervisor, who is paid $18 per hour. It takes 20 minutes to unload and store each order. Rent, insurance, and taxes for each dozen golf balls in inventory amounts to $1.00 per year. Golf Supplies will sell about 12,000 dozen golf balls evenly throughout the year in its busy store, where each salesperson generates weekly sales with a contribution margin of $4,000. In fact, the store is so busy that part-time employees, who are paid $15 per hour, are constantly used to help with sales. Golf Supplies desires a 10% return on any investment that it makes. Required: 1. What is the EOQ in dozens? 2. Notwithstanding the answer to (1), and assuming that Golf Supplies places order sizes of 400 dozen evenly throughout the year, what are the total annual inventory expenses to sell 12,000 dozen golf balls? 3. Suppose that by integrating its ordering system with its main supplier and improving the inventory receiving process, Golf Supplies can lower its total cost of placing each order to $10. Recalculate the EOQ and the total annual inventory expenses to sell 12,000 dozen golf balls. (CGA–Canada, adapted)

PROBLEM 9A–10 Economic Order Quantity; Safety Stock [LO6] Brown Ltd. has obtained the following costs and other data pertaining to one of its raw materials: Working days per year, 250 days Normal use per day, 400 units Maximum use per day, 600 units Minimum use per day, 100 units Lead time, 8 days Cost of placing one order, $20.00 Carrying cost per unit per year, $0.30 Required: Compute the following: 1. EOQ. 2. Safety stock. 3. Reorder point. 4. Normal maximum inventory. 5. Absolute maximum inventory. 6. Average inventory. 7. Assume use per day can occur with the following probabilities:

Daily Demand Probability 400 ...... 0.40 450...... 0.30 500 ...... 0.20 550 ...... 0.05 600 ...... 0.05 ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1414 14/07/1414/07/14 11:5311:53 AMAM useruser //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

9A-14 Appendix 9A Inventory Decisions

Stock-out costs are estimated to be $0.05 per unit. Determine the safety stock amount that minimizes the expected costs involved. (CGA–Canada, adapted)

PROBLEM 9A–11 Inventory of Perishable Products [LO6] A newsstand receives its weekly order of View magazine on Monday and cannot reorder during the week. Each copy costs $1.80 and sells for $3.00. Unsold copies may be returned the following week for a $1.20 rebate. When the newsstand runs out of copies, the owner knows from experience that customers will purchase View magazine elsewhere for an average of two weeks; therefore, the estimated goodwill loss from stock-outs is $2.40 per unsatisfied customer. Demand has been remarkably constant, ranging from 7 to 10 copies per week, as shown below:

Demand (in copies) 7 8 9 10

Probability 0.30 0.40 0.20 0.10

Required: 1. Determine the optimal number of copies to keep in inventory and the expected profit. 2. What is the expected opportunity loss from keeping seven copies on hand? (CMA–Canada, adapted)

PROBLEM 9A–12 Inventory of Perishable Products [LO6] Faye’s Flowers stocks fresh-cut roses on a weekly basis that sell for $30 per dozen and have a purchase cost of $20 per dozen. Unsold week-old roses are reduced in price to $15 per dozen and are always completely sold without affecting the current week’s demand for fresh-cut roses. Faye, the owner of the florist, estimates weekly demand characteristics for fresh-cut roses as follows:

Demand Demand (dozens) Probability

150 ...... 0.1 160...... 0.2 170 ...... 0.3 180...... 0.3 190...... 0.1

Required: How many dozen roses should Faye’s Flowers order each week to maximize net income? Support your decision by preparing an appropriate payoff table. (CMA–Canada, adapted)

PROBLEM 9A–13 Economic Order Quantity Computations [LO6] Francq Company is a regional distributor of automobile window glass. With the growing level of consumer demand for fuel-efficient subcompact cars, management recognizes a need to determine the total inventory cost associated with maintaining an optimal supply of replace- ment windshields that will fit these vehicles. Francq is expecting a daily demand for 100 windshields. The purchase price of each windshield is $200. Other costs associated with ordering and maintaining an inventory of these windshields are as follows: a. The historical ordering costs incurred in the Purchase Order Department for placing and processing orders are shown below:

Year Orders Placed and Processed Total Ordering Costs

1 56 $34,440 2 154 34,930 3 280 35,560 ggar24903_app9a_001-015.inddar24903_app9a_001-015.indd PagePage 1515 18/08/1418/08/14 2:092:09 PMPM user1user1 //207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles207/MHR00249/gar24903_disk1of1/1259024903/gar24903_pagefiles

Appendix 9A Inventory Decisions 9A-15

Management expects the order costs to increase 20% over the amounts and rates experienced during the past three years. b. The windshield manufacturer charges Francq a $104 shipping fee per order. c. A clerk in the Receiving Department receives, inspects, and secures the windshields as they arrive from the manufacturer. This activity requires eight hours per order received. This clerk has no other responsibilities and is paid at a rate of $15.00 per hour. Related variable overhead costs in this department are applied at the rate of $2.50 per hour. d. Additional warehouse space will have to be rented to store the new windshields. Space can be rented as needed in a public warehouse at an estimated cost of $5,000 per year plus $5.00 per windshield. e. Breakage cost is estimated to be 10% of the cost per windshield. f. Taxes and fire insurance on the inventory are $5.00 per windshield. g. The desired rate of return on the investment in inventory is 15% of the purchase price. Five working days are required from the time an order is placed with the manufacturer until it is received. Francq uses a 300-day work-year when making EOQ computations. Required: Calculate the following values for Francq Company: 1. Value for ordering cost that should be used in the EOQ formula. 2. Value for storage cost that should be used in the EOQ formula. 3. EOQ. 4. Minimum annual total storage and carrying costs at the EOQ point. 5. Reorder point in units. (CMA, adapted)

ENDNOTE

1. The theory of constraints deals with issues such as limited availability of raw materials or machine time, which restrict the company's ability to meet demand.