ACCA paper f9 financial management study materials F9FM session14 d08

Ü EOQ graph $ Cost Total cost holding cost ordering cost EOQ Ü Assumption of EOQ: ̌ purchase price per unit is constant; ̌ constant demand; ̌ no risk of stockouts... must rent sufficient

OVERVIEW

Objective

Ü To understand the costs and benefits of holding inventory and determine the Economic Order Quantity (EOQ) which minimises costs

Ü To appreciate other possible inventory control systems

INVENTORY CONTROL

OTHER INVENTORY SYSTEMS EOQ MODEL

Ü Definition

Ü Reasons for holding inventory

Ü Costs associated with inventory

Ü Definition

Ü Determination of EOQ

Ü Complications

Ü Quantity discounts

RE-ORDER LEVEL

Ü Definitions

Ü Constant demand

during lead time

Ü Uncertain demand

during lead time

Ü Service levels

Ü Periodic review system

Ü ABC system

Ü Just-in-time (JIT)

Ü Perpetual inventory

Ü MRP

1 INVENTORY CONTROL

1.1 Definition

The systematic regulation of inventory levels

Ü If inventory is too high

Inefficient ⇒ profit reduced

Ü If inventory is too low

Insufficient to satisfy customers ⇒ profit reduced

1.2 Reasons for holding inventory

Ü To meet demand by acting as a buffer in times of unusually high consumption, i.e to

reduce the risk of stockouts

Ü To ensure continuous production

Ü To take advantage of quantity discounts

Ü To buy in ahead of a shortage or ahead of a price rise

Ü For technical reasons (e.g maturing whisky in casks or keeping oil in pipelines)

Ü To reduce ordering costs

1.3 Costs associated with inventory

Ü Purchase price;

Ü Holding costs:

̌ cost of capital tied up;

̌ insurance;

̌ deterioration, obsolescence and theft;

̌ warehousing;

̌ stores administration

Ü Re-order costs:

̌ transport costs;

̌ clerical and administrative expenses;

batch set-up costs for goods produced internally

Ü Shortage costs:

̌ production stoppages caused by lack of raw materials;

̌ stockout costs for finished goods – anything from a delayed sale to a lost customer;

̌ emergency re-order costs

Ü Systems costs – people and computers

The benefits of holding inventory must outweigh the costs

2.1 Definition

Ü The Economic Order Quantity (EOQ) is the quantity of inventory that should be ordered

each time a purchase order is made

Ü EOQ aims to minimise the costs which are relevant to ordering and holding inventory

2.2 Determination of EOQ

x = order quantity

CH = cost of holding one unit for one year

D = annual demand

CO = cost of placing an order

Ü The total annual relevant cost to be minimised

= annual holding cost + annual order cost

= the cost of holding one

unit in inventory for one

year × the average number

of units held

+ the cost of an order × the number of orders in a year

=

2

x

The total cost is minimized when:

x =

H

0

C

D

C

2

Ü EOQ graph

$

Cost

Total cost

holding cost

ordering cost

EOQ

Ü Assumption of EOQ:

̌ purchase price per unit is constant;

̌ constant demand;

̌ no risk of stockouts

Example 1

Ü Using the following data calculate the EOQ

D = 40,000 units

CO = $2

CH = $1

Solution

EOQ =

2.3 Complications

2.3.1 Warehouse rental

Ü The EOQ model assumes that holding costs vary with the average inventory level

Ü However if a warehouse is rented on a long-term contract (rather than daily) then it

needs to be large enough to hold the maximum level of stock, rather than the average

must rent sufficient floor space to meet this quantity rather than

2

x

(x/2)

x

Ü deal with this by doubling the floor space used by one unit when calculating holding cost,

and then use the normal EOQ formula

Example 2

Annual demand = 3,000 units

Reorder cost = $5

Holding cost = $3.33 per unit + rental of warehouse

Each unit occupies 3m2 rented on annual contracts for $5 per m2

Solution

D =

CO =

CH =

3,000

5

EOQ =

2.3.2 Cost of capital

Ü Inventory, like any other asset, must be matched by a liability Therefore there must be a cost of financing inventory

Ü This is a type of holding cost

Illustration 1

Cost of Capital = 10%

Price per unit = $100

∴ Holding cost = $100 × 0.1 = $10

This is in addition to any other holding costs you are given

2.4 Quantity discounts

Ü The supplier may offer a “bulk-buying” discount on each unit purchased for specified

quantities above the EOQ

Ü In this case the purchase price obviously becomes a relevant factor in the decision

Ü To deal with this, calculate

Total annual cost =

cost purchase

Annual cost

order Annual cost

holding Annual

+ +

for each order quantity where discounts are available and at the order level calculated

by the EOQ

Ü Choose the order quantity with the lowest total cost

Example 3

Annual demand = 5,000

Holding cost = $7.50

Reorder cost = $30

Purchase price = $1.10

A discount of 3% is available on orders of 300 units or more

Required:

Determine whether or not the discount is worthwhile

Solution

EOQ =

Holding

2x CH =

Reorder

x

D CO =

Purchase cost

Total

_

–––––

Total cost at order quantity = 300 units

Holding

2

x CH =

Reorder

x

D CO =

–––––

Conclusion:

3 RE-ORDER LEVEL

3.1 Definitions

Ü Re-order level (ROL) is the level to which inventory should fall before a purchase order

is made

Ü Lead time is the time between placing and receiving an order

Ü There are two possible situations to be dealt with:

(1) Constant demand in lead time

(2) Uncertain demand in lead time

3.2 Constant demand during lead time

Ü Re-order level (ROL) = lead time (days) × demand per day

Ü For example if demand is 40 units per day and lead time is two days - when inventory levels fall to 80 units then inventory would be re-ordered This can be shown

graphically:

INVENTORY

LEVEL

ROL

TIME

{ Lead time

3.3 Uncertain demand during lead time

Ü There will be an expected level of demand, not a known level of demand

Ü A “buffer” or “safety” inventory will need to be held to reduce the risk of a stockout

Method

(1) Calculate expected demand in the lead time

Expected lead time demand = ∑xi p(xi)

where

xi = level of demand

p (xi) = probability of level of demand

(2) Take each level of demand ≥ expected lead time demand as a possible

reorder level and calculate the expected annual stockout cost

(3) For each possible ROL calculate the expected annual buffer holding

cost

(4) Choose the ROL with the lowest sum of stock out and holding cost

Example 4

The following information relates to inventory levels of component XL5:

Holding cost = $8

Stockout cost = $3

Lead time = 1 week

The company operates for 50 weeks per annum and weekly demand is given

by:

x i p(x i ) Demand Probability

Required:

Solution

Average demand in the lead time =

Average annual demand =

orders per annum =

ROL Buffer Demand Units

short Probability units Ave

short

Exp annual stock-out cost

Exp annual buffer holding cost

Total annual cost

$

80

Average =

Average =

The optimum ROL is therefore

3.4 Service levels

Ü Setting a “service level” of 98% implies that the firm accepts a 2% chance of a stock-out

Example 5

Average weekly demand for an item of inventory is 300 units with a standard

deviation of 40 units The lead time is one week

Required:

What ROL is needed to provide a service level of 95%? Normal distribution

tables show that 5% of observations lie 1.645 standard deviations above the

mean

4 OTHER INVENTORY SYSTEMS

4.1 Periodic review system

The inventory levels are reviewed at fixed time intervals, and variable quantities will be ordered

as appropriate

The order size made is sufficient to return inventory levels to a pre-determined level

A very simple method of inventory control – ideal where inventory control is only one of a

person’s responsibilities

4.2 ABC system of inventory control

The aim is to reduce the work involved in inventory control in a business which may have

several thousand types of inventory items

The inventory is categorised into class A, B or C according to the annual cost of the usage of

that inventory item, or the difficulty of obtaining replacements, or the importance to the

production process

Class A will then take most of the inventory control effort, Class B less and Class C less still

Commentary

Whilst this seems acceptable for inventory of finished goods, it may cause problems for

raw materials There may be an item which has a very small cost but which is vital for

the manufacture of the finished product Such an item would have to be included in

with the Class A items because of its inherent importance, rather than its cost

4.3 Just-in-time (JIT)

In a JIT system production and purchasing are linked closely to sales demand on a

week-to-week basis The aim is to create a continuous flow of raw materials inventory into work in

progress, which becomes finished goods to go immediately to the customer This means

that negligible inventory needs to be held

Conditions necessary include the following:

Ü Flexibility of both suppliers and internal workforce to expand and contract output at

short notice

Ü Raw material inventory must be of guaranteed quality – indeed, quality must be

maintained at every stage

Ü Close working relationship with suppliers and, if possible, geographically proximity in

Ü The workforce must be willing to increase or decrease its working hours from one

period to another This could be done by having a core workforce with a group of

part-time or freelance workers

Ü The design of the factory must be such that JIT deliveries to all areas are possible

Ü Total reliance on suppliers for quality and delivery, and therefore very tight contracts

with penalty clauses

Ü Significant investment by suppliers, and therefore long-term contracts

4.4 Perpetual inventory methods

Where a firm keeps perpetual inventory records, there will frequently be a replenishment

point that triggers an order Such a system relies upon the accuracy of the records, not on

physical counts

It is possible to use point of sale (POS) terminals that automatically update inventory

records as each successive sale is made

One advantage of such a system is the data it provides to management to determine which

product lines are moving rapidly Sales managers may also use the data to make tactical

decisions on special prices to sell slow-moving items

4.5 Material requirements planning (MRP)

A system that uses the production schedule to decide what is needed and when This is then

linked in with suppliers’ discounts, lead times, etc to devise an optimal inventory holding

and ordering policy

Key points

ÐThey formula for the Economic order Quantity is provided in the exam –

the key is to identify the relevant data

ÐDo not confuse the Economic Order Quantity (EOQ) with the Re –Order

Level (ROL) EOQ tells us how large each order should be, ROL tells us

when we should place on order for inventory

ÐJust-In-Time (JIT) is the other main inventory system to be familiar with

FOCUS

EXAMPLE SOLUTIONS

Solution 1 — EOQ

EOQ =

1

000 , 40 2

2× ×

x = 400 units

Solution 2 — Floor space

D =

CO =

CH =

3,000

5

$3.33 + (2 × 3 × 5) = $33.33

EOQ =

33 33

000 , 3 5

2× ×

= 30 units

Solution 3 — Quantity discount

EOQ =

50 7

000 , 7 30

2× ×

= 200 units

Holding

2

x CH =

2

Reorder

x

D CO =

200

Total

_

7,000 _

Total cost at order quantity = 300 units

Holding

2

x CH =

2

Reorder

x

D CO =

300

Purchase cost 5,000 × 1.10 × 0.97 _ 5,335

6,960 _

Solution 4 — Re-order level

Average demand in the lead time = 60 units

Average annual demand = 60 × 50 = 3,000 units

Since the EOQ = 150, there will be 1503,000= 20 orders per annum

ROL Buffer Demand Units

short Prob units Ave

short

Exp annual inventory out

cost

Exp annual buffer holding cost

Total annual cost

$

The optimum ROL is therefore 70 units

Solution 5 — Service level

ROL

SD = 40

300

45%

5%

z = 1.645 (using normal distribution tables)