ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 4: Management of working capital: inventory control
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Conclusion
The order quantity that minimises total costs is 40,000 units. This is over $23,000
cheaper than buying the economic order quantity.
Workings
(W1) Annual purchase costs
Orderquantity Annualpurchasecost
Units $
22,000(=EOQ) 120,000×$3 360,000
25,000 120,000×$(3–0.10) 348,000
40,000 120,000×$(3–0.20) 336,000
(W2) Annual ordering costs
Orderquantity Annualorderingcosts
Units $
22,000(=EOQ) (120,000/22,000)×$605 3,300
25,000 (120,000/25,000)×$605 2,904
40,000 (120,000/40,000)×$605 1,815
(W3) Annual holding costs
Orderquantity Annualholdingcosts
Units $
22,000(=EOQ) (22,000/2)×$0.3 3,300
25,000 (25,000/2)×$0.29 3,625
40,000 (40,000/2)×$0.28 5,600
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Reorder level and buffer stock
Minimising materials costs
Holding costs and ordering costs
Economic order quantity (EOQ)
EOQ: changes in the variables in the formula
2 Reorder level and buffer stock
2.1 Inventory reorder level and other warning levels
So far, it has been assumed that when an item of materials is purchased from a
supplier, the delivery from the supplier will happen immediately. In practice,
however, there is likely to be some uncertainty about when to make a new order for
materials in order to avoid the risk of running out of inventory before the new order
arrives from the supplier. There are two reasons for this.
There is a supply ‘lead time’. This is the period of time between placing a new
order with a supplier and receiving the delivery of the purchased items. The
length of this supply lead time might be uncertain and might be several days,
weeks or even months.
The daily or weekly usage of the material might not be a constant amount.
During the supply lead time, the actual usage of the material may be more than
or less than the average usage.
If demand for an inventory item exceeds the available quantity of inventory during
the reorder period, there will be a stock-out (inventory-out). When there is a stock-
out of a key item of materials, there might be a hold-up in production and a
disruption to the production schedules. This in turn may lead to a loss of sales and
profits. Stock-outs therefore have a cost.
Management responsible for inventory control might to know:
what the reorder level should be for each item of materials, in order to avoid any
stock-out: the reorder level is the level of inventory at which a new order for the
item should be placed with the supplier
whether the inventory level for each item of material appears to be too high or
too low
what the reorder level should be for each item of materials, if stock-outs can be
allowed to happen.
In an inventory control system, if there is uncertainty about the length of the supply
lead time and demand during the lead time there might be three warning levels for
inventory, to warn management that:
the materials item should now be reordered (the reorder level)
the inventory level is too high (a maximum inventory level) or
the inventory level is getting dangerously low (a minimum inventory level).
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2.2 Reorder level avoiding stock-outs and buffer stock
If the management policy is to avoid stock-outs entirely, the reorder level should be
high enough to ensure that no stock-out occurs during the supply lead time. A new
quantity of materials should be ordered when current inventory reaches the reorder
level for that material.
If the supply lead time (time between placing an order and receiving delivery) is
certain and demand during the lead time is constant, the reorder level is:
[Demand for the material item per day/week] × [Lead time in days/weeks]
If the supply lead time is uncertain, and demand during the lead time is also
uncertain, there should be a safety level of inventory. The
reorder level should
be
:
[Maximum demand for the material item per day/week] × [Maximum supply
lead time in days/weeks]
Safety inventory (‘buffer stock’ or ‘safety stock’)
The reorder level is therefore set at the maximum expected consumption of the
material item during the supply lead time. This is more than the average usage
during the supply lead time. As a result, more inventory is held that is needed on
average.
If the order quantity is Q, the average inventory level is Q/2 + ‘safety inventory’.
Safety inventory is the average amount of inventory held in excess of average
requirements in order to remove the risk of a stock-out (or ‘inventory out’). The size
of the safety inventory is calculated as follows:
Units
Reorder level (Maximum demand per day
× Maximum lead time)
A
Average usage in the lead time period (Average demand per day
× Average lead time)
B
Safety inventory (A – B)
The cost of holding safety inventory is the size of the safety inventory multiplied by
the holding cost per unit.
2.3 Maximum inventory level
The inventory level should never exceed a maximum level. If it does, something
unusual has happened to either the supply lead time or demand during the supply
lead time.
When demand during the supply lead time is uncertain and the supply lead time is
also uncertain, the maximum inventory level is:
Reorder level + Reorder quantity – [Minimum demand for the material item per
day/week × Minimum supply lead time in days/weeks]
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This maximum level should occur at the time that a new delivery of the item has
been received from the supplier. The supply lead time is short; therefore there are
still some units of inventory when the new delivery is received.
2.4 Minimum inventory level
The inventory level could be dangerously low if it falls below a minimum warning
level. When inventory falls below this amount, management should check that a
new supply will be delivered before all the inventory is used up, so that there will
be no stock-out.
When demand during the supply lead time is uncertain and the supply lead time is
also uncertain, the minimum (warning) level for inventory is:
Reorder level – [Average demand for the material item per day/week × Average
lead time in days/weeks]
Example
A company uses material item BC67. The reorder quantity for this material is 12,000
units. There is some uncertainty about the length of the lead time between ordering
more materials and receiving delivery from the supplier. There is also some
variability in weekly demand for the item.
Supply lead time (weeks)
Average 2.5
Maximum 3
Minimum 1
Demand per week (units)
Average 1,200
Maximum 1,500
Minimum 800
Required
Calculate the reorder level, the maximum inventory level and the minimum
inventory level for material item BC67.
Answer
Re-order level
= [Maximum demand for the material item per day/week] ×
[Maximum lead time in days/weeks]
Maximum demand per week 1,500 units
Maximum lead time (weeks) 3 weeks
Re-order level 4,500 units
Buffer stock (safety inventory)
= Reorder level - [Average demand for the material
item per week] × [Average lead time in weeks]
= 4,500 – (1,200
× 2.5) = 1,500 units.
Chapter 4: Management of working capital: inventory control
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The annual cost of having the buffer stock = 1,500 units × Holding cost per unit per
year.
Maximum inventory level
= Reorder level + Reorder quantity - [Minimum demand
for the material item per day/week × Minimum lead time in days/weeks]
Units
Re-order level 4,500
Reorder quantity 12,000
Minimum demand per week 800 units
Minimum lead time (weeks) × 1 week
(800)
Maximum inventory level 15,700
Minimum inventory level = Reorder level - [Average demand for the material item
per day/week × Average lead time in days/weeks]
Units
Re-order level 4,500
Average demand per week 1,200 units
Average lead time (weeks) × 2.5 weeks
Subtract:
(3,000)
Minimum inventory level 1,500
The minimum inventory level is the buffer stock quantity.
Example
An examination question on inventory management might combine a test of your
understanding of the EOQ model and reorder level or buffer stock. Here is an
example.
A company orders 50,000 units of an item when the inventory level falls to 100,000
units. Annual consumption of the item is 1,800,000 units per year. The holding cost
per unit is $1.50 per unit per year and the cost of making an order for delivery of the
item is $375 per order. The supply lead time is 2 weeks and you should assume a 50-
week year and constant weekly demand for the item.
Required
Calculate the cost of the current ordering policy and calculate how much annual
savings could be obtained using the EOQ model.
Answer
Weekly demand = 1,800,000/50 weeks = 36,000 units.
Current policy
The reorder level is 100,000 units, therefore there is buffer stock.
Buffer stock = 100,000 units – (36,000 units
× 2 weeks) = 28,000 units.
Average inventory = 50,000 units/2 + Buffer stock = 25,000 + 28,000 = 53,000 units.
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Annual cost of current policy
$
Order costs: $375
× (1,800,000/50,000)
13,500
Holding costs: 53,000 × $1.50
79,500
93,000
EOQ
It is assumed that the company intends to maintain a buffer stock of 28,000 units.
EOQ =
⎟
⎠
⎞
⎜
⎝
⎛
××
1.5
3751,800,0002
= 0900,000,00 = 30,000 units
Annual cost of EOQ policy
$
Order costs: $375
× (1,800,000/30,000)
22,500
Holding costs of EOQ : (30,000/2) × $1.50
22,500
Holding cost of buffer stock: 28,000 × $1.50
42,000
87,000
Cost of current policy 93,000
Annual saving by ordering EOQ 6,000
2.5 Using a probability table to decide the optimal reorder level
When a company is prepared to accept the risk of stock-outs, the optimal reorder
level might be estimated using probabilities of demand (and probabilities of the
supply lead time) to calculate the reorder level that has the lowest expected value of
total cost.
A probability table can be prepared. For each possible reorder level under
consideration, we can calculate:
the probable demand in the lead time between order and delivery
the risk of having excess inventory (buffer stock) and its cost
the risk of stock-outs, and their cost.
The reorder level selected might be the reorder level at which the expected value
(EV) of cost is minimised.
Example
Entity X uses item Z in its production process. It purchases item Z from an external
supplier, in batches.
For item Z, the following information is relevant:
Holding cost
$15 per unit per year
Stock out cost $5 for each stock-out
Lead-time 1 week
EOQ 270 units
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Entity X operates for 48 weeks each year. Weekly demand for unit Z for production
is variable, as follows:
Units demanded
during the lead time
Probability
70 10%
80 20%
90 30%
100 40%
Required
Suggest whether a reorder level of 90 units or 100 units would be more appropriate.
Answer
The average demand in the lead-time is:
[(70 × 10%) + (80 × 20%) + (90 × 30%) + (100 × 40%)] = 90 units
Average annual demand is 48 weeks × 90 units = 4,320 units.
Since the EOQ is 270 units, entity X will expect to place
4, 320
270
orders = 16 orders
each year. Therefore there will be 16 lead times each year.
Setting up the probability table
Reorder
level
Average
buffer
stock
Stock‐outsand
probability
EVofannual
stock‐outs
Annual
holdingcost
ofbuffer
stock
Total
EV
of
cost
units units $ $ $
90 0 0.4probabilityof10
stock‐outseach
lead‐time.
EVofstockouts
=0.4×10×16leadtimes
=64stock‐outs
64×$5=$320 0 320
100 10 0stock‐outs $0 10×£15=$150 150
Note:
Average buffer stock is estimated as = Reorder level minus average demand
in the lead time.
Other reorder levels (110 units, 80 units, 70 units, and so on) could be tested until
the least-cost reorder level is found.
In comparing reorder levels of 90 and 100 units, a reorder level of 100 units is
preferable, because it has a lower EV of cost. When inventory falls to 100 units,
Entity X would place a new order for 270 units.
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Just-in-Time (JIT) and other inventory management methods
Minimising materials costs
Holding costs and ordering costs
Economic order quantity (EOQ)
EOQ: changes in the variables in the formula
3 Just-in-time (JIT) and other inventory management
methods
3.1 JIT production and JIT purchasing
Just-in-Time (JIT) management methods originated in Japan in the 1970s. JIT is a
radically different approach to inventory management compared with management
using the EOQ model and reorder levels.
The principle of JIT is that producing items for inventory is wasteful, because
inventory adds no value, and holding inventory is therefore an expense for which
there is no benefit.
If there is no immediate demand for output from any part of the system, a
production system should not produce finished goods output for holding as
inventory. There is no value in achieving higher volumes of output if the extra
output goes into inventory as has no immediate use.
Similarly, if there is no immediate demand for raw materials, there should not be
any of the raw materials in inventory. Raw materials should be obtained only when
they are actually needed.
It follows that in an ideal production system:
there should be no inventory of finished goods: items should be produced just in
time to meet customer orders, and not before (=
just in time production)
there should be no inventories of purchased materials and components:
purchases should be delivered by external suppliers just in time for when they
are needed in production (=
just in time purchasing).
‘Just-in-time purchasing is a purchasing system in which material purchases are
contracted so that the receipt and usage of the materials, to the maximum extent,
coincide’ (CIMA Official Terminology).
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3.2 Practical implications of JIT
JIT production
It is important that items should be available when required. Finished goods must
be available when customers order them, and raw materials and components must
be supplied when they are needed for production.
In practice, this means that:
Production times must be very fast. If there is no inventory of finished goods,
production has to be fast in order to meet new customer orders quickly.
Production must be reliable, and there must be no hold-ups, stoppages or
bottlenecks. Poor quality production, leading to rejected items and scrap, is
unacceptable.
Deliveries from suppliers must be reliable: suppliers must deliver quickly and
purchased materials and components must be of a high quality (so that there
will be no scrapped items or rejected items in production).
JIT purchasing
JIT depends for its success not only on highly efficient and high-quality production,
but also on efficient and reliable supply arrangements with key suppliers. For
successful JIT purchasing, there must be an excellent relationship with key
suppliers. Collaborative long-term relationships should be established with major
suppliers, and purchasing should not be based on selecting the lowest price offered
by competing suppliers.
By implementing a JIT system, an entity will be working with its key (‘strategic’)
suppliers to implement a manufacturing system that will:
reduce or eliminate inventories and WIP
reduce order sizes, since output is produced to meet specific demand and raw
material deliveries should be timed to coincide with production requirements
ensure deliveries arrive in the factory exactly at the time that they are needed.
The overall emphasis of a JIT purchasing policy is on consistency and quality, rather
than looking for the lowest purchase price available.
3.4 Problems with JIT
There might be several problems with using JIT in practice.
Zero inventories cannot be achieved in some industries, where customer
demand cannot be predicted with certainty and the production cycle is quite
long. In these situations, it is necessary to hold some inventories of finished
goods.
It might be difficult to arrange a reliable supply system with key suppliers,
whereby suppliers are able to deliver materials exactly at the time required.
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If the EOQ model succeeds in minimising total costs of holding costs and
ordering costs, this suggests that with a JIT purchasing system, ordering costs
might be very high.
3.5 Other inventory control systems
EOQ and JIT are two methods of managing and controlling inventory and
purchasing quantities. Other systems might be used.
Two bin system
When a two-bin system is used in a warehouse or stores department, each item of
inventory is stored in two bins or large containers. Inventory is taken from Bin 1
until it is empty, and a new order is placed sufficient to fill Bin 1 again.
However, the delivery of more units of the item will take time, and since Bin 1 is
empty, units are now taken from Bin 2. Bin 2 is large enough to continue supplying
the item until the new delivery arrives. On delivery both bins are replenished and
units are once again supplied from Bin 1.
This cycle continues indefinitely.
Periodic review system
In a periodic review system, there is a reorder quantity and a reorder level for each
item of inventory.
Inventory levels are checked periodically, say every one, two, three or four weeks. If
the inventory level for any item has fallen below its reorder level, a new order for
the reorder quantity is placed immediately.
Example
Suppose that the demand for an inventory item each week is 400 units, and
inventory control is applied by means of a three-weekly periodic review. The lead-
time for a new order is two weeks.
The minimum inventory level should therefore be (3 weeks + 2 weeks) = 5 weeks ×
400 units = 2,000 units. If the inventory level is found to be lower than this level at
any periodic review, a new order for the item should be made.
ABC method of inventory control
With the ABC method of inventory control, it is recognised that some items of
inventory cost much more than others to hold. Inventory can perhaps be divided
into three broad categories:
Category A inventory items, for which inventory holding costs are high.
Category B inventory items, for which inventory holding costs are fairly high,
but not as high as for category A items.