Management Accounting
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. An increase in the per unit cost of finished goods.
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
production activity from the purchase of raw materials to the delivery of finished goods
inventory to the customer. The financial accounting for inventory is concerned primarily
with determining the correct count and the assignment of historical cost. However,
from a management accounting viewpoint, the central focus is on manufacturing the
right amounts at the lowest cost consistent with a quality product. From a financial
viewpoint, 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
to a reduced cash flow, the effect of poor inventory management can be a lower rate
of return.
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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,
including finished goods, is often reflected in the use of terms such as such as stock
outs, 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 costs
2. Purchasing costs.
Inventory is a term that may mean finished goods, materials, and work in process.
In a manufacturing business, there is a logical connection between these three types
of inventory:
Materials
Labor
Overhead
Æ Work in Process
Æ Finished goods
Æ Cost of goods sold
To have finished goods inventory, production must take place at a rate greater
than 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
a financial accounting viewpoint, the main accounting problems concern:
1.
2.
3.
4.
The flow of costs (FIFO, LIFO, average cost)
Use of a type of inventory costing method (periodic or perpetual)
Taking of physical inventories.
Techniques for estimating inventory
From a financial accounting viewpoint, the cost assigned to inventory directly
affects 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
can be placed in two general categories: (1) those decisions that affect the quantity
of inventory and (2) those decisions that affect the per unit cost of inventory.
Decisions that affect the quantity of inventory
1. Order size
2. Number of orders
3. Safety stock
4. Lead time
5. Planned production
Management Accounting
Decisions that affect the cost per unit of inventory
1. Suppliers of raw material (list price and discounts)
2. Order size (quantity discounts)
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 budget
2. Order size for raw materials
3. Number of times to order for raw materials
4. Reorder point
5. Safety stock
Production Budget Decision
The 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
Back orders
Desired
ending Finished Goods Inventory
Finished goods (BI)
$100,000
5,000
20,000
________
25,000
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
significant negative impact on sales. A good production budget is one that meets the
current 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.
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Purchase of Materials Decision
The 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
decisions regarding the materials inventory: (1) orders size and (2) number of orders.
There are consequently two major questions:
1. How many units should be purchased each time a purchase is made
(order size)?
2. How many purchases should be made (number of orders)?
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
Units
18,000
Average
Inventory
9,000
0
60
120
180
240
300
360
Work Days
In terms of dollars, the amount invested in inventory would fluctuate between
$90,000 and zero. In this example, the average inventory would be 9,000 computed
as follows:
Order size
Average Inventory = –––––––––
(1)
2
Management Accounting
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 = 9,000
The major factor here that affects the level of inventory is order size ( the number
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
could be as low as .5 unit (1 /2) or as large as 54,000 (108,000 / 2). The best order
size, as will be explained and illustrated now, is determined by the cost of ordering
(purchasing) and the cost of carrying inventory.
Purchasing Cost
The 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
requisition and finally ends with payment of the materials purchases. This process
may be illustrated as follows:
Purchase
Requisition
Æ
Purchase
Order
Delivery
of
Æ
Order
Receiving and
Preparation
Inspection of
of Voucher
Æ
Æ
order
Payment of
Purchase
Æ
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. Delivery of order (postage, telephone time, filing)
4. Receiving of purchased materials (inspection, storing, receiving
report.
5. Accounting costs (preparing vouchers and recording time)
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
present themselves. The first one is to simply buy one unit at a time and purchase
100,000 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
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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
had sufficient space for 52 loaves of bread and sliced ham. The cost of storing a
year’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 that are needed for a specified period of time, for example a year, as order
size increases the number of times required to purchase decreases. To illustrate
mathematically
Let:
A represent the total material in units needed for a defined period
of time
E represent the order size.
The number of orders that would result may be computed as follows;
A
Number of orders = ––
(2)
E
If order size were 1,000 and the annual requirement for materials is 120,000, then
the number of orders would 120 (120,000 / 1,000). If we assume that each order has
a 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:
A
TPC = ––– (P)
(3)
E
TPC - total purchasing cost
A
- periodic demand for material
P
- 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
purchasing cost would be $1,200 (120,000/10,000 x $100).
Management Accounting
The cost of various order sizes may be illustrated as follows:
A = 120,000
P =
$100
Order Size
Order 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
Total Purchasing Cost
7000
6000
5000
$
4000
Total
Purchasing
Cost
3000
2000
1000
0
0
20000
40000
60000
80000
100000
120000
140000
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
to first discuss carrying costs.
Carrying Cost
The purchase of materials or the production of finished goods normally requires that
the materials or finished goods be stored until used or sold. The storage of materials
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or finished goods obviously requires storage space. The greater the purchase lot
at 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 (a big order size requires an investment of money).
2. Taxes (inventory is typically subject to a property tax).
3. Insurance (inventory is always at risks like theft or fire or damage).
4. Storage costs (inventory requires building space and is subject to the
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
level of inventory (reorder point), a new order must be placed. The inventory at its
maximum 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,
If
then:
Carrying cost =
E
-
S
-
TCC -
TCC =
Order size
––––––––––
2
x (Carrying cost per unit)
represents order size
represents carrying cost per unit
denotes total carrying cost
E
––––– (S)
2
(4)
The cost of carrying inventory sizes may be illustrated the following table:
A = 120,000
S = $5.00
Order Size
Order 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
Management Accounting
Total carrying cost may be graphically illustrated as shown in figure 11.3:
Figure 11-3 • Graph of Total Carrying Costs
Total Carrying Cost
350000
300000
250000
$
200000
Total
Carrying
Cost
150000
100000
50000
0
0
50000
100000
150000
Order Size
Figure 11-4 • Graph of Total Inventory Costs
EOQ Costs
35000
30000
Total
Purchasing
Cost
25000
$
20000
Total
Carrying
Cost
15000
10000
Total Cost
5000
0
0
1000
2000
3000
4000
5000
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:
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204 | CHAPTER ELEVEN • Inventory Decision-Making
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 made
1. As order size increases, total purchasing cost decreases.
2. As order size increases, total carrying cost increases
3. 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 Formula
Earlier total purchasing cost was defined as follows:
TPC
=
TPC
A
P
E
-
-
-
-
A
––– (P)
E
total purchasing cost
periodic demand for material
cost of placing each order
order size
Also, earlier total carrying cost was defined as follows:
E
TCC = –––(S)
2
S
-
carrying cost per unit of inventory
Total cost can then be defined as follows:
TC
A
= –––– (P) +
E
E
–––– (S)
2
(5)
Management Accounting
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
Solving for E using basic algebra (see appendix to this chapter), we then get:
E =
2 A P
(6)
2
Given the same values used previously as follows:
A = 120,000
P = $100
S = $5.00
The order size that minimizes total cost then is :
E =
2 (120,000) ($100)
$5.00
= 2,191
If this is the correct answer, then TPC should equal TCC
120,000
TPC = –––––––– ($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 Problem
The L. K. Widget Company’s accountant presented the following information
based on a cost analysis:
Annual demand for materials (units)
(A) 100
Cost of placing an order
(P) $10.00
Cost per unit of carrying inventory
(S) $5.00
Based on the above information, economic order quantity may be computed as
follows:
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E =
2 (100) ($10)
$5.00
= 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
1
100.00
2
20.00
10
15
Average
Inventory
.50
Total
Purchasing
Total
Carrying
Total
Cost
$1,000.00
$ 2.50
$1,002.50
1.0
$ 200.00
$ 12.50
$ 212.50
10.00
5.0
$ 100.00
$ 25.00
$ 125.00
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.
Extreme and frequent fluctuations in demand requires other approaches to the order
size decision. Secondly, The EOQ model requires fairly accurate estimates of carrying
and purchasing costs. Multiple products and numerous types of material for a single
product may make the computation of these costs very difficult.
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
be placed? Obviously, if inventory has reached zero, then the time to place an order
has been missed. In formulating an answer to this question, a number of factors must
Management Accounting
be considered including:
1. Lead time
2. Average usage per day
3. 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
is required to manufacture finished goods. A primary objective in the management
of the production process is to main a steady flow with minimal interruptions. A
consistent 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
500,000
AUPD = –––––––––––––––––––––––––––– = –––––––– = 2,000 Work days
250
There is a connection between lead time and average usage per day. To avoid
a stock out, the level of inventory at the time an order is placed must be sufficient to
last 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 the
production process, it is normally desirable to carry some safety stock. The question
as to how much safety stock to carry is a difficult question to answer. If safety stock is
too 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.
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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 Problem
Assume the following:
Annual demand for raw materials
Number of work days
Desired safety stock level
Lead time (days)
25,000
250
100
5
Computing the reorder point requires, first of all, determining the average usage
per day:
25,000
AUPD = ––––––– = 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 Discounts
The 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
$2.50
300 +
When quantity discounts are available, the basic EOQ formula can not be used
to directly solve for the best order size. However, it must be used on an iterative (trial
and error) basis to find the best order size.
When quantity discounts were not available, the cost of inventory itself,
(purchases), was not relevant and could be ignored. However, because now the
order size affects the cost per unit, the total cost of inventory purchases must be
Management Accounting
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
E
TC = –––– (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 size
S
- represents carrying cost per unit
TCC - denotes total carrying cost
TPC - total purchasing cost
A
- periodic demand for material
P
- cost of placing each order
Equation (9) above cannot be used to directly solve for order size (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
figures 11-7 and 11-8.
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 range which minimizes total cost. (In many
cases the best order size is a price break quantity.)
Figure 11.5 • Total Purchasing Cost
$
Figure 11.6 • Total Carrying Cost
$
Total Purchasing Cost
4,000
4,000
3,500
3,500
3,000
3,000
2,500
2,500
2,000
2,000
1500
1500
1,000
1,000
500
500
50
100
150
200
Order Size
250
300
Total Carrying Cost
50
100
150
200
Order Size
250
300
| 209
210 | CHAPTER ELEVEN • Inventory Decision-Making
Figure 11-7 • Cost of Purchases
Figure 11-8 • Total Cost
$
$
4,000
4,000
3,500
3,500
3,000
2,500
2,000
2,000
1500
1500
1,000
1,000
500
500
100
150
200
Order Size
250
Total Cost
3,000
Purchases
2,500
50
Total Purchasing Cost
Purchases
Total Carrying Cost
300
50
100
150
200
Order Size
250
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
$4.70
50 +
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)
Total
Carrying
Cost
(E/2)S
Inventory
Cost
C( 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
300
Management Accounting
Step 1
Based on equation (2) the above work sheet was prepared.
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 $514.22
Total cost if order size is 31 $525.12
If an order size greater than 30 is used, then the total cost is
greater as seen above.
Step 4
Occasionally, the best order size can be found by using equation (6). In
other words, a better solution can be found than the one indicated by the
trial and error work sheet method.
E =
2 (100) ($1.00)
$2.00
= 10
However, if an order size of 10 is made, the total cost is $520. Clearly, this is not
the best solution since at an order size of 30 units the total cost is less ($513.30). The
use of the equation (1), therefore, did not find a better solution.
Summary
Good 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 stock
2. Purchasing costs
9. Reorder point
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212 | CHAPTER ELEVEN • Inventory Decision-Making
3.
4.
5.
7.
Inventory cost
Demand for inventory
Number of orders
Average inventory
10. Lead time
11. Average usage per day
12. Work days
Appendix: Derivation of the EOQ Formula
Derivation of EQO Formula
Algebraic Derivation
AP
–––– =
E
ES
––––
2
AP
–––– =
1
E 2S
––––
2
2AP
––––
S
E =
=
E2
2AP
S
Calculus Derivation
TIC =
AP
–––– +
E
ES
––––
2
d(TIC) d(AP/E)
––––– = ––––––– +
d E
dE
d(TIC) d (APE-1) ) d(.5ES)
––––– = –––––––– + –––––––
d E
dE
dE
d(TIC) d- (APE-2) )
––––– = ––––––––– +
d E
dE
d(.5ES)
––––––
dE
d(TIC)
–––––– =
dE
(.5S)
- (APE-2) )
- (APE-2) )
+
+
d(.ES)
––––––
dE
(.5S) = 0
- (APE-2) ) = - (.5S)
AP
––––
=
E-2
AP
––––
.5S
E =
=
.5S
- ––––
AP
E2
2AP
S
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 total purchasing cost = total carrying cost. The calculus approach finds the
first derivative of the total cost equation and then sets that equation to zero in order
to solve for E, the order size.
Management Accounting
Q. 11.1
Define the following terms:
a. Purchasing cost
b. Carrying cost
c. Economic order quantity
d. Safety stock
e. Reorder point
f. Average lead time
g. Average usage during lead time
h. Workdays per year
i. Average inventory
j. Forgone discounts
k. Stock outs
What are four basic decisions that must be made concerning
inventory?
Q. 11.2
Q. 11.3
Explain how the order size decision determines average inventory?
Q. 11.4
Defined mathematically the total cost of carrying and purchasing
inventory
Q. 11.5
Illustrate graphically total carrying cost.
Q. 11.6
Illustrate graphically total purchasing cost.
Q. 11.7
List five examples of purchasing cost.
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/E
b. A/E (P)
c. E/2
d. E/2 (S)
e. C(A)
f. E/2(IC)
f. AUPD x LT
What inventory management cost is relevant when quantity discounts
are available that is otherwise irrelevant?
Q. 11.12
Q. 11.13
What is the total cost equation when quantity discounts are available?
Q.11.14.
What is the major disadvantage of taking a quantity discount?
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214 | CHAPTER ELEVEN • Inventory Decision-Making
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
quantity discounts are available?
Q. 11.17
Prepare a work sheet with the proper headings that may be used to find
the 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:
Material requirements (units)
6,000
Carrying cost (per unit)
$ .50
Purchasing cost (per order)
$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.
Exercise 11.2 • Optimum Order Size-No Quantity Discounts
You have been provided the following information:
Material requirements (units)
8,000
Carrying cost (per unit)
$ .85
Purchasing cost (per order)
$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.
Exercise 11.3 • Optimum Order Size-No Quantity Discounts
The Acme Manufacturing Company does not have a systematic or scientific
approach 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:
Management Accounting
Annual required units of material
Cost of placing each order:
Stationery
Clerical
10,000
$ .10
$ .30
Basic time preparing for loading/storing
$2.00
Carrying costs per unit (annual)
Taxes
Insurance
Storage
Interest
$
$
$
$
.05
.10
.45
.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 Discount
The 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:
Determine whether the company should take advantage of the quantity discount?
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
Price
1
-
1,499
$.20
1,500
-
2,999
$.19
3,000
-
4,999
$.18
4,500
+
$.17
Required:
In what quantities should the ABC Manufacturing Company order?
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216 | CHAPTER ELEVEN • Inventory Decision-Making
Exercise 11.6 • Reorder Point and Safety Stock
You have been provided the following information:
Order size
200
Lead time
10 days
Number of work days per year
250
Annual material requirements
2,000
Safety; stock (units)
20
Required:
1.
a.
b.
c.
d.
e.
2.
Based on the above information (assuming conditions of certainty)
compute the following:
The number of orders per year
Average usage per day
Average inventory
Number of work days between orders
Usage during lead time
Prepare a graph which shows (1) maximum level of inventory, (2) lead
time and (3) reorder point.