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Management Accounting | 195

Inventory Decision-Making

To be successful, most businesses other than service businesses are required to carry inventory. In these businesses, good management of inventory is essential. The management of inventory requires a number of decisions. Poor decision making regarding inventory can cause:

1. Loss of sales because of stock outs.2. Depending on circumstances, inadequate production for a period of time.3. Increases in operating expenses due to unnecessary carrying costs or

loss from discarding obsolete inventory.4. Anincreaseintheperunitcostoffinishedgoods.

Of all the activities in a manufacturing business, inventory creation is the most dynamic and certainly the most visible activity. In one sense, inventory involves all productionactivityfromthepurchaseofrawmaterialstothedeliveryoffinishedgoodsinventorytothecustomer.Thefinancialaccountingforinventoryisconcernedprimarilywith determining the correct count and the assignment of historical cost. However, from a management accounting viewpoint, the central focus is on manufacturing the rightamountsatthelowestcostconsistentwithaqualityproduct.Fromafinancialviewpoint, poor management of inventory can adversely affect cash flow. Also,excessive inventory can cause a decrease in ROI. An over stock of inventory causes total assets to be larger and certain expenses to increase. Consequently, in addition toareducedcashflow,theeffectofpoorinventorymanagementcanbealowerrateof return.

196 | CHAPTER ELEVEN • Inventory Decision-Making

Finished goods inventory represents the company’s product for available for sale at a given point in time. A certain amount of inventory must be available at all times in order to have an effective marketing operation. The poor management of inventory, includingfinishedgoods,isoftenreflectedintheuseoftermssuchassuchasstockouts, back orders, decrease in inventory turnover, lost sales, and inadequate safety stock.

The existence of inventory results in expenses other than the cost of inventory itself which typically are categorized as:

1. Carrying costs2. Purchasing costs.

Inventoryisatermthatmaymeanfinishedgoods,materials,andworkinprocess.In a manufacturing business, there is a logical connection between these three types of inventory:

MaterialsLaborOverhead

Æ Work in Process Æ Finished goods Æ Cost of goods sold

Tohavefinishedgoodsinventory,productionmusttakeplaceatarategreaterthan sales. Inventory decisions have a direct impact on production. For example, a decision to increase safety stock means that the production rate must increase until the desired level of safety stock is achieved.

From an accounting standpoint, there are two main areas of concern. First, from afinancialaccountingviewpoint,themainaccountingproblemsconcern:

1. Theflowofcosts(FIFO, LIFO, average cost)2. Useofatypeofinventorycostingmethod(periodicorperpetual)3. Taking of physical inventories.4. Techniques for estimating inventory

From a financial accounting viewpoint, the cost assigned to inventory directlyaffects net income. If ending inventory is overstated, then net income is overstated and conversely, if ending inventory is understated then net income is understated. Also, the use of direct costing rather than absorption costing can affect net income as discussed in chapter 6. From a management accounting viewpoint, there are variety of inventory decisions that affect net income. Decisions regarding inventory canbeplacedintwogeneralcategories:(1)thosedecisionsthataffectthequantityofinventoryand(2)thosedecisionsthataffecttheperunitcostofinventory.

Decisions that affect the quantity of inventory1. Order size2. Number of orders3. Safety stock4. Lead time5. Planned production


Decisions that affect the cost per unit of inventory1. Suppliersofrawmaterial(listpriceanddiscounts)2. Ordersize(quantitydiscounts)3. Freight

In addition, decisions pertaining to labor and overhead also indirectly affect the per unit cost of inventory. In a manufacturing business, the costs of labor and overhead do not become operating expenses until the manufacturing costs appear as part of cost of goods sold. Labor and overhead costs are deferred in inventory until the inventory has been sold.

In this chapter, the main focus of discussion will be the following inventory decisions:

1. Production budget2. Order size for raw materials3. Number of times to order for raw materials4. Reorder point 5. Safety stock

Production Budget DecisionThe production budget was discussed in some detail in chapter 8. The production

budget decision is of utmost importance. If the production budget is inadequate, then stock outs will occur. If the production budget is too large, then unnecessary carrying costs will be incurred. The production budget format as presented previously was:

Production Budget For the Quarter Ending March 31, 20xx

Sales forecast $100,000Back orders 5,000Desired ending Finished Goods Inventory 20,000 ________ 25,000Finishedgoods(BI) 10,000 ________ $115,000

The key to a good production management is an accurate sales forecast. Without a reliable sales forecast, the production process is likely to be chaotic and have a significantnegativeimpactonsales.Agoodproductionbudgetisonethatmeetsthecurrent sales demand plus provides for an adequate planned safety stock. Also, in the preparation of the purchases budget, decisions for the desired levels of safety stock in materials must be made. The production budget determines the need for plant capacity. If the current production budget exceeds existing plant capacity, then ways to increase plant capacity must be considered. Increasing plant capacity may involve scheduling overtime or a second shift or even purchasing and installing more production equipment and hiring additional labor.


Purchase of Materials DecisionThe main management accounting tool that may be used to make inventory

purchase decisions is the EOQ model. This tool recognizes that there are two major decisionsregardingthematerialsinventory:(1)orderssizeand(2)numberoforders.There are consequently two major questions:

1. How many units should be purchased each time a purchase is made (ordersize)?

2. Howmanypurchasesshouldbemade(numberoforders)?

To understand an EOQ model, it is essential that the concept of average inventory be understood. Inventory is never static and is constantly rising and falling over time, even in the very short term. Inventory, for example, rises when raw materials are purchased and falls when raw material is used. Because inventory in a business is constantly changing, it is necessary to think in terms of average inventory levels. The high points and low points of inventory are easy to explain and illustrate, if a purchasing policy is consistently applied and the rate of usage of raw material is uniform. Inventory is at its highest and lowest levels when a new shipment of material arrives. Theoretically, in absence of a need for safety stock, a new shipment should arrive at the moment inventory reaches zero. Immediately, upon arrival of a new shipment, inventory is then at its highest level again. To illustrate, assume that each purchase order placed is for 18,000 units at $5.00 per unit and that usage of raw materials is uniform at 300 units of material per day. If production and usage of material takes place every day, then a shipment of material should last 60 days. These conditions may be illustrated as follows:

Figure 11-1 • Graphical Illustration of Average Inventory

60 120 180 240 300 360 Work Days

AverageInventory

Units

18,000

9,000

0

In termsof dollars, theamount invested in inventorywould fluctuate between$90,000 and zero. In this example, the average inventory would be 9,000 computed as follows:

Order sizeAverage Inventory = ––––––––– (1) 2


At its highest level inventory would be 18,000 units and at its lowest level inventory would be 0. Based on the above equation average inventory is:

AI = (18,000 + 0)/ 2 = 9,000Themajorfactorherethataffectsthelevelofinventoryisordersize(thenumber

of units purchased in each order). If demand for materials for a full year is 108,000 units, then the extremes for purchasing could be one large order of 108,000 or 108,000 orders of one unit per order. Given these extremes, then average inventory couldbeaslowas.5unit(1/2)oraslargeas54,000(108,000/2).Thebestordersize, as will be explained and illustrated now, is determined by the cost of ordering (purchasing)andthecostofcarryinginventory.

Purchasing CostThe purchase of materials or parts necessary to make a finished product

involves a process that needs to be understood. The process begins with a purchase requisitionandfinallyendswithpaymentofthematerialspurchases.Thisprocessmay be illustrated as follows:

PurchaseRequisition Æ

PurchaseOrder Æ

Delivery ofOrder

Æ

Receiving and Inspection of order

Æ

Preparation of Voucher Æ

Payment of Purchase and Accounting

The cost of placing an order, therefore, consists of the following:

1. Cost of preparing purchase requisition

2. Cost of preparing purchase order

3. Deliveryoforder(postage,telephonetime,filing)

4. Receiving of purchased materials (inspection, storing, receiving report.

5. Accountingcosts(preparingvouchersandrecordingtime)

It is important to remember that the cost of the inventory itself is not a purchasing cost. The purchase of inventory is typically recorded to the materials purchases account and is treated as a separate and distinct cost.

The number of times an order is placed is to some extent discretionary. To illustrate, assume that the K. L. Widget Company has determined that for the current quarter 100,000 units of raw material Y need to be purchased. Two extreme possibilities presentthemselves.Thefirstoneistosimplybuyoneunitatatimeandpurchase100,000 times. The second extreme is to make 1 large order of 100,000 units. Between purchasing one unit at a time or buying one unit at a time 100,000 times, there is a large number of possibilities between an order size of 1 and 100,000.

It is obvious that each time an order is placed some purchasing costs are incurred, and that as the number of orders placed increases, the total cost of purchasing increases. To use a simple example, if you enjoy eating a sandwich at lunch each


day and you make your own sandwiches, then you must purchase bread and say a package of sliced ham. Then, at a minimum, you must purchase one loaf of bread and a package of sliced ham which, for example purposes here, can last for one week. You must then visit your grocery store once a week. This means that for a full year you would make a minimum of 52 trips a year. However, the other extreme alternative would be to purchase a full year’s worth of bread and ham and, therefore, make only one trip per year. If the grocery store was 5 miles away and at a cost of 50¢ per mile, each trip will cost you $5.00 per trip or $260 per year. However, purchasing one time per year, then means you have a carrying or storage problem. You would have to have space to store 52 loaves of bread and packages of sliced him. Assuming you had this space, then you face the problem of spoilage which for bread is most likely to happen within a few weeks, unless you had a freezer which hadsufficientspace for52 loavesofbreadandslicedham.Thecostofstoringayear’s supply would most likely exceed the reduced cost in purchasing. In business, the same principle applies. As the size of the order increases, the cost of carrying or storing inventory increases in total.

The basic principle of purchasing then is this: Given the amount of material or parts thatareneeded foraspecifiedperiodof time, forexampleayear,asordersize increases the number of times required to purchase decreases. To illustrate mathematically

Let: A representthetotalmaterialinunitsneededforadefinedperiod

of time E represent the order size.

The number of orders that would result may be computed as follows; ANumber of orders = –– (2) E

If order size were 1,000 and the annual requirement for materials is 120,000, then thenumberoforderswould120(120,000/1,000).Ifweassumethateachorderhasa measurable cost, and if we let this cost be represented by the letter P, then the total cost of purchasing may be computed as follows:

ATPC = ––– (P) (3) ETPC - total purchasing costA - periodic demand for materialP - cost of placing each order

This equation may be read as the number of orders times the cost of placing one order.

If P is $100, then given that the number of orders is 120, then total purchasing cost would be $12,000. If the same values assumed before are used and, if 10,000 units were purchased each time then only 12 orders would be placed and the total purchasingcostwouldbe$1,200(120,000/10,000x$100).


The cost of various order sizes may be illustrated as follows: A = 120,000 P = $100

Order SizeOrder size 1 10,000 30,000 50,000 70,000 90,000 10,000 120,000

Number of orders 120,000 12 4 2.4 1.7 1.33 1.09 1

Total purchasing cost

$12,000,000 $1,200 $400 $240 $170 $133 $109 100

Graphically, the cost of purchasing may be presented as follows:

Figure 11-2 • Graph of Total Purchasing Cost

7000

6000

5000

4000

3000

2000

1000

00 20000 40000 60000 80000 100000 120000 140000

Total Purchasing Cost

TotalPurchasingCost

Order Size

$

An order size of one unit per order results in a total and most likely unacceptable cost of $12,000,000. While an order size of 120,000 minimizes total purchasing cost at $100, this order size is also most likely to be unacceptable, because of the high carrying cost that would inevitably result due to the high average carrying cost that would invariably follow. The main point to observe is that as order size increases total purchasing cost decreases.

There has been developed a tool that can determine the right order size and, therefore, the right number of times to purchase. This tool is commonly called an EOQ model. However, before this tool is mathematically introduced, it is necessary tofirstdiscusscarryingcosts.

Carrying CostThepurchaseofmaterialsortheproductionoffinishedgoodsnormallyrequiresthat

thematerialsorfinishedgoodsbestoreduntilusedorsold.Thestorageofmaterials


or finishedgoodsobviously requires storagespace.Thegreater thepurchase lotat any given time, the greater is the storage space required. How long inventory is stored varies directly with the rate at which it is used. In a restaurant where one loaf of bread is purchased each time and a new loaf immediately purchased when the last loaf is used up, not much space would be require. On the other hand, if 144 loaves are purchased at a time, then considerably more space would be required. Depending on the type of raw materials, some or all of the carrying costs could be incurred:

1. Interest(abigordersizerequiresaninvestmentofmoney).2. Taxes(inventoryistypicallysubjecttoapropertytax).3. Insurance(inventoryisalwaysatrisksliketheftorfireordamage).4. Storagecosts(inventoryrequiresbuildingspaceandissubjecttothe

costs associated with a building such as depreciation,5. Salary of storekeeper and helpers, if required.6. Spoilage.

The basic principle of carrying inventory may be explained as follows: At a certain levelofinventory(reorderpoint),anewordermustbeplaced.Theinventoryatitsmaximum would be equal to the order size and at a minimum would be zero if no safety stock is being carrying. Inventory is at a maximum when a new shipment is received, and at its lowest moments before the new order arrives. As explained earlier in this chapter, the inventory is not a constant amount and is best numerically described as an average.

Mathematically, total carrying cost is simply the average inventory for a period of time times the cost of carrying a single unit of inventory: Therefore, mathematically,

Order sizeCarrying cost = –––––––––– x (Carrying cost per unit) 2

IfE - represents order sizeS - represents carrying cost per unitTCC - denotes total carrying cost

then: ETCC = ––––– (S) (4) 2

The cost of carrying inventory sizes may be illustrated the following table:A = 120,000 S = $5.00

Order SizeOrder size 1 10,000 30,000 50,000 70,000 90,000 110,000 120,000

Average inventory .5 5,000 15,000 25,000 35,000 45,000 55,000 60,000

Total carrying cost $2.50 $25,000 $75,000 $125,000 $175,000 $225,000 $275,000 $300,000


Totalcarryingcostmaybegraphicallyillustratedasshowninfigure11.3:

Figure 11-3 • Graph of Total Carrying Costs

350000

300000

250000

200000

150000

100000

50000

00 50000 100000 150000

Total Carrying Cost

TotalCarryingCost

Order Size

$

Figure 11-4 • Graph of Total Inventory Costs

35000

30000

25000

20000

15000

10000

5000

00 1000 2000 3000 4000 5000

EOQ Costs

TotalPurchasingCost

TotalCarryingCost

Total Cost

Order Size

$

As order size increases, the total carrying cost increases. With an order size of 1 unit carrying cost for the entire period is only $2.50. However, if the entire periodic need for material is purchased one time, then the total carrying cost is $300,000, the maximum cost that can be incurred.

Close observation of the above schedule reveals that as order size increases, total carrying cost also increases directly, just the opposite of total purchasing cost. A paradox then exists. Any attempt to minimize total purchasing cost, then increases total carrying cost and vice versus. The goal of inventory management becomes apparent: The goal should be then to minimize total purchasing cost and carrying cost and not each cost separately. The two illustrations above concerning total purchasing cost and total carrying cost can now be combined as follows:


Order Size

Order size 1 10,000 30,000 50,000 70,000 90,000 110,000 120,000

Total purchasing cost

$12 M $1,200 $400 $240 $170 $133 $109 100

Total carrying cost

$2.50 $25,000 $75,000 $125,000 $175,000 $225,000 $275,000 $300,000

Total cost $12 m $26,200 $75,400 $125,240 $175,170 $225133 $275,109 $300,100

It is apparent by observation that the order size of 10,000 shows the lowest total cost of carrying and purchasing inventory. However, whether an order size of 10,000 is the best order size has not been yet determined. An order size less than 10,000 might result in lower costs. This table may be graphically presented as shown above.

From this graph the following observations may be made1. As order size increases, total purchasing cost decreases.2. As order size increases, total carrying cost increases3. Total cost is minimized where total purchasing cost equals total carrying

cost.

The observation that total cost of managing inventory can be minimized where total purchasing cost equals total carrying cost allows us later to derive a formula for determining the best economic order size.

EOQ FormulaEarliertotalpurchasingcostwasdefinedasfollows:

ATPC = ––– (P) E

TPC - total purchasing costA - periodic demand for materialP - cost of placing each orderE - order size

Also,earliertotalcarryingcostwasdefinedasfollows: ETCC = ––– (S) 2

S - carrying cost per unit of inventory

Totalcostcanthenbedefinedasfollows:

A ETC = –––– (P) + –––– (S) (5) E 2


Since the best order size is where TPC = TCC, we can mathematically solve for the best order size as follows:

A E –––– (P) = –––– (S) E 2

SolvingforEusingbasicalgebra(seeappendixtothischapter),wethenget:

2 A P

2E = (6)

Given the same values used previously as follows:A = 120,000P = $100S = $5.00

The order size that minimizes total cost then is :

2 (120,000) ($100)

$5.00E = = 2,191

If this is the correct answer, then TPC should equal TCC

120,000TPC = –––––––– ($100) = $5,475 2,190.9

2,190 TCC = –––––––– ($5) = $5,475 2

Since TPC = TCC, the best order size is 2,191 units.

Illustrative ProblemThe L. K. Widget Company’s accountant presented the following information

based on a cost analysis:Annualdemandformaterials(units) (A) 100Costofplacinganorder (P) $10.00Costperunitofcarryinginventory (S) $5.00

Based on the above information, economic order quantity may be computed as follows:


2 (100) ($10)

$5.00E = = 20

Using the same values given above, the following schedule may be prepared:

Schedule of Costs of Carrying and Purchasing Inventory

Order size

Number of Orders

Average Inventory

Total Purchasing

Total Carrying

TotalCost

1 100.00 .50 $ 1,000.00 $ 2.50 $ 1,002.50

2 20.00 1.0 $ 200.00 $ 12.50 $ 212.50

10 10.00 5.0 $ 100.00 $ 25.00 $ 125.00

15 6.67 7.5 $ 66.67 $ 37.50 $ 104.17

20 5.00 10.0 $ 50.00 $ 50.00 $ 100.00

25 4.00 12.5 $ 40.00 $ 62.50 $ 102.50

30 3.30 15.0 $ 33.00 $ 75.00 $ 108.00

35 2.85 17.5 $ 28.50 $ 87.50 $ 116.00

40 2.22 20.0 $ 22.00 $ 100.00 $ 122.00

45 2.50 22.5 $ 25.00 $ 112.50 $ 137.50

50 2.00 25.0 $ 20.00 $ 125.00 $ 145.00

The most economical order size is 20. When order size is 20, then total carrying cost equals total purchasing costs and total cost is minimized at $100.

The EOQ formula just discussed is based on several assumptions which if not true may result in values that are not helpful in making order size decisions. First, this EOQ model requires an accurate estimate of demand under conditions of certainty. Extremeandfrequentfluctuationsindemandrequiresotherapproachestotheordersize decision. Secondly, The EOQ model requires fairly accurate estimates of carrying and purchasing costs. Multiple products and numerous types of material for a single productmaymakethecomputationofthesecostsverydifficult.

Making the Reorder Point Decision When to reorder materials or parts is a decision that must be thoughtfully

considered. If the decision to reorder is made too late, then undesirable consequences such as stock outs and delays in production may happen. If the decision to reorder is made too soon, then unnecessary carrying costs will be incurred. The important question then concerning reordering is: at what level of inventory should a new order beplaced?Obviously,ifinventoryhasreachedzero,thenthetimetoplaceanorderhas been missed. In formulating an answer to this question, a number of factors must


be considered including:1. Lead time2. Average usage per day3. Desired safety

Lead Time -Lead time is time between placing and order and receiving an order. Lead time can vary greatly depending on a number of factors. It could be as little as a few hours or as great as many months. Lead time can be affected by factors or conditions such as bad weather, strikes on the part of the supplier’s workers, production problems on the part of the suppliers, and unexpected problems in shipping. Because lead time can vary with each order placed, the normal approach to developing a reorder point is to use average lead time. When the variations are small, the use of average lead time is workable. Lead time should be measured in terms of work days rather than calendar days. If lead time is one day but the supplier of the material in question is closed on Saturdays and Sundays, then a order placed on Friday might not be received until Tuesday of the next week. The problem of unpredictable variations in lead time can usually be solved by carrying safety stock.Average Usage per Day - It goes without saying that some level of materials inventory isrequiredtomanufacturefinishedgoods.Aprimaryobjectiveinthemanagementof the production process is to main a steady flow with minimal interruptions.Aconsistent daily production rate is highly desirable. If this goal is achieved, then the amount of material used each day is easily computed. Average usage per day will tend to be the same.

To illustrate, if the production budget shows a planned production of 50,000 widgets per year and each widget requires 10 units of material Z, then 500,000 units of material Z need to be purchased annually. If the year consists of 250 work days, then the following simple equation can be used to compute average usage per day

Annual requirement for material 500,000AUPD = –––––––––––––––––––––––––––– = –––––––– = 2,000 Work days 250

There is a connection between lead time and average usage per day. To avoid astockout,thelevelofinventoryatthetimeanorderisplacedmustbesufficienttolast until the new shipment arrives. This level of inventory, assuming no safety stock, can be computed simply by multiplying lead time times average usage per day

Reorder point = Lead time x Average Usage per Day(7)Safety Stock - Because both lead time and average usage per day can vary significantly in the short run and to avoid stock outs during a critical time in theproduction process, it is normally desirable to carry some safety stock. The question astohowmuchsafetystocktocarryisadifficultquestiontoanswer.Ifsafetystockistoo small, then stock outs can still occur. If safety stock is to large, then unnecessary carrying cost will be incurred. When average usage during lead time tends to be volatile, safety stock models tend to be based on probability theory and requires knowing the probability of different levels of demand during lead time. The use of probability models for safety stock is beyond the scope of this chapter.


However, giving that a decision had been made regarding safety stock by whatever method, the equation for reorder point then becomes:

Reorder point = Lead time x Average Usage Per Day + Safety Stock (8)

Illustrative ProblemAssume the following:

Annual demand for raw materials 25,000Number of work days 250Desired safety stock level 100Leadtime(days) 5

Computingthereorderpointrequires,firstofall,determiningtheaverageusageper day:

25,000AUPD = ––––––– = 100 250

Reorder point then may be computed as follows:

RP = AUPD x Lead time + safety stock = (100 x 5) + 100 = 600

When inventory level becomes 600, then a new order should be placed. Theoretically, the new order should be received on the day the inventory reaches the safety stock level of 100 units.

Economic Order Quantity and Quantity DiscountsThe previous discussion on order size was based on the assumption that quantity

discounts were not available. The EOQ formula as explained above is not able to determine the most economic order size, given the availability of quantity discounts. Suppliers will often provide incentives to purchasers to buy in bigger quantities. A typical discount schedule might look as follows:

Quantity Discount Schedule for Material Z

Order Size Price

1 - 99 $5.00

100 - 199 $4.00

200 - 299 $3.00

300 + $2.50

When quantity discounts are available, the basic EOQ formula can not be used todirectlysolveforthebestordersize.However,itmustbeusedonaniterative(trialanderror)basistofindthebestordersize.

When quantity discounts were not available, the cost of inventory itself, (purchases),wasnot relevantandcouldbe ignored.However,becausenow theorder size affects the cost per unit, the total cost of inventory purchases must be


taken into account. Without quantity discounts, the total cost of inventory purchased remained the same regardless of order size. In order to solve for the best order size, the following equation must be used.

A ETC = –––– (P) + –––– (S) + C(A) (9) E 2

The EOQ formula now has C(A), the total inventory purchase cost, as a cost element. When quantity discounts exists, the cost of inventory becomes relevant in the order

size decision. C represents the cost of one unit of inventory. The other mathematical symbols have the same meaning as before:

E - represents order sizeS - represents carrying cost per unitTCC - denotes total carrying costTPC - total purchasing costA - periodic demand for materialP - cost of placing each order

Equation(9)abovecannotbeusedtodirectlysolveforordersize(E). The reason is that there are two unknowns: (1) order size and (2) cost per unit of inventory.Order size affects cost per unit and cost per unit affects order size. Because of the dependency of price on order size and order size on cost per unit of inventory, the total carrying cost curve and the total cost curve is now discontinuous as shown in figures11-7and11-8.

The trial and error procedure based on equation 9 that must be used is as follows:

Step 1 Prepare a work sheet based on the total cost equation.

Step 2 Compute total cost at each price break, including an order size of one unit.

Step 3 Determine the order size rangewhichminimizes total cost. (Inmanycases the best order size is a price break quantity.)

50 100 150 200 250 300

$

4,000

3,500

3,000

2,500

2,000

1500

1,000

500

50 100 150 200 250 300

$

4,000

3,500

3,000

2,500

2,000

1500

1,000

500

Order Size Order Size


Total Carrying Cost

Figure 11.5 • Total Purchasing Cost Figure 11.6 • Total Carrying Cost


Step 4 Use the basic EOQ model to see if a better order size exists.Illustration

The K. L. Widget Company may purchase Material Z at a quantity discount. The company annually purchases 100 units. The cost of placing 1 order is $1. Carrying cost is $2.00 per unit. The following discount schedule is available:

Quantity Discount Schedule for Material Z

Order Size Price

1 - 19 $5.00

20 - 29 $4.90

30 - 49 $4.80

50 + $4.70

Work Sheet for Determining Best Order Size (Quantity Discounts Available)

Order Size(E)

Number of

Orders (A/E)

Total Purchasing

Cost(A/E) P

Average Inventory

( E/2)

TotalCarrying

Cost(E/2)S

Inventory CostC( A)

Total Cost

1 100 $ 100.00 .5 $ 1.00 $500 $601.00

20 5 $ 5.00 10 $ 20.00 $490 $515.00

30 3.3 $ 3.30 15 $ 30.00 $480 $513.30

50 2 $ 2.00 25 $ 50.00 $470 $522.00

EOQ Order size

10 $ 10.00 5 $ 10.00 $500 $520.00

50 100 150 200 250 300

$

4,000

3,500

3,000

2,500

2,000

1500

1,000

500

50 100 150 200 250 300

$

4,000

3,500

3,000

2,500

2,000

1500

1,000

500

Order Size Order Size

Total Carrying Cost

Total Cost

Purchases Purchases


Figure 11-7 • Cost of Purchases Figure 11-8 • Total Cost


Step 1 Basedonequation(2)theaboveworksheetwasprepared.

Step 2 The price break quantities are 1, 20,30 and 50. For example, when 20 units or more are ordered, then price decreases from $5.00 to $4.90 per unit. In the above work sheet, then at each price break quantity, total cost was computed.

Step 3. The range that results in the lowest cost is the range between 30 and 50 units. At an order size of 30 units, the total cost is $513.30. Normally, in this range the lowest cost results in the smallest order size in this range, which in this case would be 30 units.

Total cost if order size is 30 $514.22Total cost if order size is 31 $525.12If an order size greater than 30 is used, then the total cost is greater as seen above.

Step 4 Occasionally,thebestordersizecanbefoundbyusingequation(6).Inother words, a better solution can be found than the one indicated by the trial and error work sheet method.

2 (100) ($1.00)

$2.00E = = 10

However, if an order size of 10 is made, the total cost is $520. Clearly, this is not thebestsolutionsinceatanordersizeof30unitsthetotalcostisless($513.30).Theuseoftheequation(1),therefore,didnotfindabettersolution.

SummaryGood inventory decisions are critical to the success of a business. Excessive

inventory levels may lead to inventory write-off losses, and even if eventually sold, excessive inventory levels will result in unnecessary carrying costs. Inadequate inventory on the other hand can result in stock outs and production delays. In modern business, some products involve hundreds of different parts and material. Consequently, the purchasing of parts and materials at the appropriate time is highly critical. The purchasing function in many business is extremely important.

Order size is one of the more important inventory decisions. Improper management of the order size will result in excessive total inventory management costs. The use of EOQ models provide a valuable insight as to factors that must be considered in making inventory decisions. Both management and the management accountant need a solid understanding of inventory management principles.

Making good inventory decisions required considerable knowledge and skill. To make good inventory decisions requires understanding of the follow terms.

1. Carrying cost 8. Safety stock2. Purchasing costs 9. Reorder point


3. Inventory cost 10. Lead time4. Demand for inventory 11. Average usage per day5. Number of orders 12. Work days7. Average inventory

Appendix: Derivation of the EOQ Formula

Derivation of EQO Formula

Algebraic Derivation Calculus Derivation

AP ES –––– = –––– E 2

AP E2S –––– = –––– 1 2

2AP –––– = E2

S

2 A P

SE =

AP ESTIC = –––– + –––– E 2

d(TIC) d(AP/E) d(.ES) ––––– = ––––––– + –––––– d E dE dE

d(TIC) d (APE-1) ) d(.5ES) ––––– = –––––––– + ––––––– d E dE dE

d(TIC) d- (APE-2) ) d(.5ES) ––––– = ––––––––– + –––––– d E dE dE

d(TIC) –––––– = - (APE-2) ) + (.5S) d E

- (APE-2) ) + (.5S) = 0

- (APE-2) ) = - (.5S)

AP .5S –––– = - –––– E-2 AP

AP –––– = E 2 .5S

2 A P

SE =

As illustrated above the EOQ formula can be derived using either calculus or algebra. Actually, for his version of the EOQ formulas using simply algebra is much easier. The algebra approach begins with recognizing that optimum order size is where totalpurchasingcost= totalcarryingcost.Thecalculusapproachfinds thefirstderivativeofthetotalcostequationandthensetsthatequationtozeroinorderto solve for E, the order size.


Q.11.1 Definethefollowingterms:

a. Purchasing costb. Carrying costc. Economic order quantityd. Safety stocke. Reorder pointf. Average lead timeg. Average usage during lead timeh. Workdays per yeari. Average inventoryj. Forgone discountsk. Stock outs

Q. 11.2 What are four basic decisions that must be made concerning inventory?

Q.11.3 Explainhowtheordersizedecisiondeterminesaverageinventory?

Q.11.4 Defined mathematically the total cost of carrying and purchasinginventory

Q. 11.5 Illustrate graphically total carrying cost.

Q. 11.6 Illustrate graphically total purchasing cost.

Q.11.7 Listfiveexamplesofpurchasingcost.

Q. 11.8 List six examples of carrying cost.

Q. 11.9 Explain the effect that quantity discounts have on the EOQ model.

Q. 11.10 Draw a graph showing or illustrating economic order quantity, reorder point, lead time, and safety stock.

Q. 11.11 Identify these equations:

a. A/Eb. A/E (P)c. E/2d. E/2 (S)e. C(A)f. E/2(IC)f. AUPD x LT

Q. 11.12 What inventory management cost is relevant when quantity discounts areavailablethatisotherwiseirrelevant?

Q.11.13 Whatisthetotalcostequationwhenquantitydiscountsareavailable? Q.11.14. Whatisthemajordisadvantageoftakingaquantitydiscount?


Q.11.15 Explain why a basic EOQ equation can’t be derived when quantity discounts are available.

Q.11.16 What procedure must be used to identify the best order size when quantitydiscountsareavailable?

Q.11.17 Prepareaworksheetwiththeproperheadingsthatmaybeusedtofindthe optimum order size when quantity discounts are available.

Q. 11.18 For what order sizes should total cost be computed on the work sheet?

Exercise 11.1 • Optimum Order Size-No Quantity Discounts

You have been provided the following information:Materialrequirements(units) 6,000Carryingcost(perunit) $.50Purchasingcost(perorder) $5.00

Required:

1. Determine the optimum order size that minimizes total purchasing and carrying cost.

2. Prepare a graph illustrating the behavior of total carrying cost, total purchasing cost, and total cost.


You have been provided the following information:Materialrequirements(units) 8,000Carryingcost(perunit) $.85Purchasingcost(perorder) $10.00

Required: 1. Determine the optimum order size that minimizes total purchasing and carrying

cost.

2. Prepare a graph illustrating the behavior of total carrying cost, total purchasing cost, and total cost.


TheAcme Manufacturing Company does not have a systematic or scientificapproach to the planning and control of inventory; however, the Acme Manufacturing Company is considering installing a formal planning and control system which includes the use of economic order quantity models. In regard to a proposed procedure for the control of raw materials, the following cost study was made:


Annual required units of material 10,000 Cost of placing each order: Stationery $ .10 Clerical $ .30

Basictimepreparingforloading/storing $2.00

Carryingcostsperunit(annual) Taxes $ .05 Insurance $ .10 Storage $ .45 Interest $ .20

Required:

1. Compute the optimum order size that minimizes total cost.

2. Graphically illustrate the above data.

Exercise 11.4 • Optimum Order Size-Quantity Discounts

Single DiscountThe ABC Manufacturing Company annually purchases 10,000 units of material

X. The company’s accountant has determined that it costs the company $10.00 each time an order is placed and that the cost of carrying inventory is $1.00 per unit per year. ‘The company has been purchasing material X at a cost of $25.00 per unit. If material X is purchased in quantities of 5,000 or more, then material X can be purchased at $20.00 per unit.. Required:

Determinewhetherthecompanyshouldtakeadvantageofthequantitydiscount?

Exercise 11.5 • Optimum Order Size-Quantity Discounts

The ABC Manufacturing Company annually purchases 10,000 units of material Y. The company’s accountant has determined that it costs the company $5.00 each time an order is placed and that the cost of carrying inventory is $ .30 per unit. The company has been purchasing material Y at a cost of $.20 per unit; however, the supplier of Y has offered the following discounts:

Quantity Range Price1 - 1,499 $.201,500 - 2,999 $.193,000 - 4,999 $.184,500 + $.17

Required: InwhatquantitiesshouldtheABCManufacturingCompanyorder?


Exercise 11.6 • Reorder Point and Safety Stock

You have been provided the following information:Order size 200Lead time 10 daysNumber of work days per year 250Annual material requirements 2,000Safety;stock(units) 20

Required:1. Based on the above information (assuming conditions of certainty)

compute the following:

a. The number of orders per yearb. Average usage per dayc. Average inventoryd. Number of work days between orderse. Usage during lead time

2. Prepareagraphwhichshows(1)maximumlevelofinventory,(2)leadtimeand(3)reorderpoint.

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