Ch 16 InventoryManagement

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Tata McGraw-Hill Publishing Company Limited, Management Accounting 16-1

Chapter 16

Inventory Management


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INVENTORY MANAGEMENT

Objectives

Techniques

Solved Problems


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Inventory

Inventory refers to the stockpile of the products a firm

would sell in future in the normal course of business

operations and the components that make up the product.

The firm stores three types of inventories, namely, rawmaterials, work-in-process/semi-finished goods and

finished good.

The management of inventory is different from the

management of other current assets in that virtually all the

functional areas are involved. The job of the finance

manager is to reconcile the conflicting viewpoints of the

various functional areas regarding the appropriate inventory

levels.


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Objectives

The objectives of inventory management consists of two

counterbalancing parts:

1) to minimise investments in inventory and2) to meet the demand for products by efficiently

organising the production and sales operations.

In operational terms, the goal of inventory management is to

have a trade-off between these two conflicting objectives

which can be expressed in terms of costs and benefits

associated with different levels of inventory.


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Costs of Holding Inventory

The costs of holding inventory are ordering costs and

carrying costs.

Ordering cost is the fixed cost of placing and receiving an

inventory order.

Carrying costs are the variable costs per unit of holding an

item in inventory for a specified time period.


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The cost of holding inventory may be divided into two categories:

(1) Those that Arise Due to the Storing of Inventory The main components of thiscategory of carrying costs are

1. storage cost, that is, tax, depreciation, insurance, maintenance of the

building, utilities and janitorial services;2. insurance of inventory against fire and theft;

3. deterioration in inventory because of pilferage, fire, technical obsolescence,style obsolescence and price decline;

4. serving costs, such as, labour for handling inventory, clerical andaccounting costs.

(2) The Opportunity Cost of Funds This consists of expenses in raising funds(interest on capital) to finance the acquisition of inventory

Benefits of Holding Inventory

The second element in the optimum inventory decision deals with the benefits

associated with holding inventory. The major benefits of holding inventory are thebasic functions of inventory. The basic function of inventories is to act as abuffer to decouple or uncouple the various activities of a firm so that all do nothave to be pursued at exactly the same rate.

The key activities are (1) purchasing, (2) production, and (3) selling. The termuncoupling means that these interrelated activities of a firm can be carried onindependently. The effect of uncoupling (maintaining inventory) are as follows.


7/29 Tata McGraw-Hill Publishing Company Limited, Management Accounting 16-7

Benefits in Purchasing If the purchasing of raw materials and other goods is not

tied to production/sales, that is, a firm can purchase independently to ensure the

most efficient pur-chase, several advantages would become available. In the first

place, a firm can purchase larger quantities than is warranted by usage in

production or the sales level. This will enable it to avail of discounts that are

available on bulk purchases. Moreover, it will lower the ordering cost as feweracquisitions would be made.

Benefits in Production Finished goods inventory serves to uncouple production

and sale. This enables production at a rate different from that of sales. That is,

production can be carried on at a rate higher or lower than the sales rate. This

would be of special advantage to firms with seasonal sales pattern

Benefits in Work-in-Process The inventory of work-in-process performs two

functions. In the first place, it is necessary because production processes are not

instantaneous. The amount of such inventory depends upon technology and the

efficiency of production. In a multi-stage production process, the work-in-process

inventory serves a second purpose also. It uncouples the various stages of

production so that all of them do not have to be performed at the same rate. The

stages involving higher set-up costs may be most efficiently performed inbatches with a work-in-process inventory accumulated during a production run.5

Benefits in Sales The maintenance of inventory also helps a firm to enhance its

sales efforts. For one thing, if there are no inventories of finished goods, the level

of sales will depend upon the level of current production.


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Techniques

1) ABC Analysis

2) Economic Order Quantity3) Reorder-Point

4) Safety Stock


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TABLE 1 Inventory Breakdown between Number of Items and Inventory Value

Group Number of items (per cent) Inventory value (per cent)

A 15 70

B 30 20

C 55 10

Total 100 100

Some points stand out from Table 1. While group A is the least important interms of the number of items, it is by far the most important in terms of the

investments involved. With only 15 per cent of the number, it accounts for as

much as 70 per cent of the total value of inventory. The firm should direct most

of its inventory control efforts to the items included in this group. The items

comprising B group account for 20 per cent of the investments in inventory.

They deserve less attention than A, but more than C, which involves only 10

per cent of the total value although number-wise its share is as high as 55 per

cent. The A B C analysis is illustrated in Example 1.


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Example 1 A firm has 7 different items in its inventory. The average number of

each of these items held, alongwith their units costs, is listed below. The firm

wishes to introduce an A B C inventory system. Suggest a breakdown of the

items into A, B, and C classifications.

Item number Average number of units in inventory Average cost per unit

1

2

3

4

5

6

7

20,000

10,000

32,000

28,000

60,000

30,000

20,000

Rs 60.80

102.40

11.00

10.28

3.40

3.00

1.3

Solution The A B C analysis is presented in Table 2.


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TABLE 2 ABC Analysis

Item Units Per cent of

total

Unit cost Total cost Per cent of

total

(1) (2) (3) (4) (5) (6)

1 20,000 10 Rs 60.80 Rs 12,16,000 38.00 70

2 10,000 5 15 102.40 10,24,000 32.00

3 32,000 16 11.00 3,52,000 11.00 20

4 28,000 14 30 10.28 2,88,000 9.00

5 60,000 30 3.40 2,04,000 6.38 106 30,000 15 55 3.00 90,000 2.80

7 20,000 10 1.30 26,000 0.82

Total 2,00,000 100 32,00,000 100.00

The A B C system of classification should, however, be used with caution. For

example, an item of inventory may be very inexpensive. Under the A B C system itwould be classified into C category. But it may be very critical to the production

process and may not be easily available. It deserves the special attention of

management. But in terms of the A B C framework, it would be included in the

category which requires the least attention. This is a limitation of the A B C

analysis.


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Economic Order Quantity (EOQ)

EOQ refers to the level of inventory at which the total cost of

inventory comprising

1) Order/Setup cost, and2) Carrying cost is the minimum.

Carrying Costs are cost associated with the

maintenance/holding

of inventory.

Ordering Costs are costs associated with acquisition

of/placing

order for inventory.


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Solution

Table 3: Inventory Cost for Different Order Quantities

1. Size of order (units)

2. Number of orders

3. Cost per order

4. Total ordering cost (2 3)

5. Carrying cost per unit

6. Average inventory (units)

7. Total carrying cost (5 6)

8. Total cost (4 + 7)

1,600

1

Rs 50

50

1

800

800

850

800

2

Rs 50

100

1

400

400

500

400

4

Rs 50

200

1

200

200

400

200

8

Rs 50

400

1

100

100

500

100

16

Rs 50

800

1

50

50

850

Example 2

A firms inventory planning period is one year. Its inventory requirement for this period is 1,600

units. Assume that its acquisition costs are Rs 50 per order. The carrying costs are expected to be

Re 1 per unit per year for an item.

The firm can procure inventories in various lots as follows: (i) 1,600 units, (ii) 800 units, (iii) 400

units, (iv) 200 units, and (v) 100 units. Which of these order quantities is the economic order

quantity?

Working Notes

(i) Number of orders = Total inventory requirement/ Order size, (ii) Average inventory = Order size/2


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Example 3 The following details are available in respect of a firm:

1. Inventory requirement per year, 6,000 units2. Cost per unit (other than carrying and ordering costs), Rs 53. Carrying costs per item for one year, Re 14. Cost of placing each order, Rs 605. Alternative order sizes: (units) 6,000, 3,000, 2,000, 1,200, 1,000, 600 and 200.

Determine the economic order quantity.

Solution The EOQ is determined in Table 4.

TABLE 4 Determination of Economic Order Quantity

1.

2.

3.4.5.6.7.

8.

Cost of items purchasedeach year (Rs)Order size (units)

Number of ordersAverage inventory (units)Total carrying costs (Rs)Total ordering costs (Rs)Total cost (carrying plusordering cost) (Rs)Total cost (Rs)

30,000

6,000

13,0003,000

603,060

33,060

30,000

3,000

21,5001,500

1201,620

31,620

30,000

2,000

31,0001,000

1801,180

31,180

30,000

1,200

5600600300900

30,900

30,000

1,000

6500500360860

30,860

30,000

600

10300300600900

30,900

30,000

200

30100100

1,8001,900

31,900

Clearly, the EOQ is 1,000 units.Working Notes

(i) Number of orders = Demand per year/order size(ii) Average inventory = Order size/2(iii) Total carrying cost = Average inventory Carrying cost per unit(iv) Total ordering cost = Number of orders Cost per order(v) Total cost = Cost of items purchased + Total carrying and ordering costs


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Mathematical (Short-cut) Approach

The economic order quantity can, using a short-cut method, be

calculated by the following equation:

EOQ = 2 AB/C

Where A = Annual usage of inventory in units,

B = Buying cost per order,C = Carrying cost per unit per year.

Example 4 Using the facts in Example 2, find out the EOQ by

applying the short-cut mathematical approach.

EOQ =2 1,600 50

= 400 units.1


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Reorder Point

The re-order point is that level of inventory when a fresh order

should be placed with suppliers. It is that inventory level which is

equal to the consumption during the lead time or procurement time.

Re-order level = (Daily usage Lead time) + Safety stock.

Minimum level = Re-order level (Normal usage Average delivery

time).

Maximum level = Reorder level (Minimum usage Maximum delivery

time) + Re-order quantity.Average stock level = Minimum level + (Re-order quantity)/2.

Danger level = (Average consumption per day Lead time in days for

emergency purchases).


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Safety Stock

The safety stock are the minimum additional inventory which serve

as a safety margin to meet an unanticipated increase in usage.

The first step is to estimate the probability of being out of stock,

as well as the size of stock-out.

Stock-out costs are costs associated with the shortage

(stock-out) of inventory.

After the determination of the size and probability of stock-out,

the next step is the calculation of the stock-out cost.

Then, the carrying cost should be calculated.

Finally, the carrying costs and the expected stock-out costs at each safety

level should be added.

The optimum safety stock would be that level of inventory at which the

total of these two costs is the lowest.


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Example 5 The experience of a firm being out of stock is summarised below:

(a) Stock-out (number of units) Number of times

500400

250

100

50

0Total

1(1)2(2)

3(3)

4(4)

10(10)

80(80)100(100)

Figures in brackets represents percentage of time the firm has been out of

stock.

(b) Assume that the stock-out costs are Rs 40 per unit.

(c) The carrying cost of inventory per unit is Rs 20.

Determine the optimum level of stock-out inventory.

Solution

TABLE 5 C t ti f E t d St k t C t


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TABLE 5 Computation of Expected Stock-out Costs

Safety stocklevel (units)

Stock-out(units)

Stock-outcosts

(Rs 40 perunit)

Probabilityof stock-out

Expectedstock-out

cost atthis level

Totalexpectedstock-out

cost

(1) (2) (3) (4) (5) (6)

500 0 0 0 0 0

400 100 Rs 4,000 0.01 Rs 40 Rs 40

250 250 10,000 0.01 100

150 6,000 0.02 120 220

100 400 16,000 0.01 160

300 12,000 0.02 240150 6,000 0.03 180 580

50 450 18,000 0.01 180

350 14,000 0.02 280

200 8,000 0.03 240

50 2,000 0.04 80 780

0 500 20,000 0.01 200

400 16,000 0.02 320

250 10,000 0.03 300

100 4,000 0.04 160

50 2,000 0.10 200 1,180


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Working Notes

(i) The determination of the optimum safety stock involves dealing withuncertain demand. The first step, therefore, is to estimate the probability ofbeing out of stock as well as the size of stock-out in terms of the shortage of

inventory at different levels of safety stock.Size of stock-out (units) The shortage of inventory at different levels of safetystock can be computed as follows:

a) The firms experience has been that it has been short of inventory by 500units only once in 100 times. If, therefore, the level of safety stock is 500units, it will never be short of inventory. It means that with 500 units of

safety stock, the size of stock-out would be zero.b) When the firm has a safety stock of 400 units, it could be short by 100

units.c) Further, with 250 units of safety stock, the firm could be short by 250

units if the actual demand turns out to be 500 units greater thanexpected; 150 units short if the demand turn out to be 400 units greater

than expected. Thus, the size of stock-out could be 250 units or 150 unitsdepending upon the level of actual demand.

d) It should be obvious that the size of stock-out increases with a decreasein the level of safety stock. The size of the stock-out for safety stocklevels of 100 units, 50 units and 0 units can be computed on the lines ofstep (c).


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The stock-out size at different safety stock levels is computed in column (2) of Table 5.

Probability of Stock-out The probability of stock-out at different levels of safety stock

can be computed as follows:

a) If the safety stock of the firm is 500 units, there is no chance of the firm being out

of stock. The probability of stock-out is, therefore, zero.

b) When the safety stock is 400 units, there is 1 per cent chance that the firm will be

short of inventory. The probability of stock-out is, therefore, 0.01.

c) The probability of stock-out for other levels of safety stock is similarly computed

in column (4) of Table 5.(ii) After the determination of the size and probability of stock-out, the next

step is the calculation of the stock-out cost. The expected stock-out cost can

be found out by multiplying the stock-out cost and the probability of stock-out.

When the stock-out is expected to be 100 units (safety stock being 400 units),

the stock-out cost would be 100

Rs 40 = Rs 4,000. But the probability ofstock-out of this size is only 0.01. Therefore, the expected cost stock-out

would be Rs 4,000 0.01 = Rs 40. For other levels of safety stock, the expected

stock-out cost can be similarly computed (column 5 of Table 5).


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(iii) The next step is to compute the total expected stock-out costs (column 6

of Table 5).

(iv) Then, the carrying costs should be calculated. The carrying costs are

equal to the safety stock multiplied by the carrying costs per unit. (Table 6

column 3).TABLE 6 Computation of Total Safety Stock Costs

Safety stock

level (units)

Expected stock-

out costs*

Carrying costs

(Rs 20 per unit)

Total safety

stock cost

(1) (2) (3) (4) (2 + 3)

050

100

250

400

500

Rs 1,180780

580

220

40

0

0Rs 1,000

2,000

5,000

8,000

10,000

Rs 1,1801,780

2,580

5,220

8,040

10,000

*from Table 5 column 6.

(v) Finally, the carrying costs and the expected stock-out costs at each safety

stock level should be added (Table 6, column 4). The optimum safety stock

would be that level of inventory at which total of these two costs is the lowest.

Thus, the optimum safety stock is zero units.


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SOLVED PROBLEM 1

M/s Tubes Ltd are the manufacturers of picture tubes for T.V. The following are

the details of the operation during the current year.

Average monthly market demand (tubes) 2,000

Ordering cost (per order) Rs 100

Inventory carrying cost (per cent per annum) 20

Cost of tubes (per tube) 500

Normal usage (tubes per week) 100

Minimum usage (tubes per week) 50

Maximum usage (tubes per week) 200

Lead time to supply (weeks) 6-8

Compute from the above:

1. Economic order quantity. If the supplier is willing to supply quarterly 1,500

units at a discount of 5 per cent, is it worth accepting?

2. Maximum level of stock

3. Minimum level of stock

4. Reorder level


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Solution

1. Economic order quantity

Annual demand (A) = Normal usage per week 52 weeks = 100 tubes 52 =5,200 tubes. Ordering cost per order (B) = Rs 100 per order

Inventory carrying cost per unit per annum (C) = Rs 500 0.20 = Rs 100 per unitper annum

If supplier is willing to supply 1,500 units at a discount of 5 per cent:

Total cost (When order size is 1,500 units) = Cost of 5,200 units + Ordering cost+ Carrying cost

= [5,200 (500 0.95)] +[ (5,200/1,500) Rs 100) + ((1/2) 1,500 0.20 475)]

= Rs 24,70,000 + Rs 346.67 + Rs 71,250 = Rs 25,41,596.67

Total cost (when order size is 102 units) = (5,200 500) + (5,200/102 Rs 100) +(1/2 102 0.20 500)

= Rs 26,00,000 + Rs 5,098.03 + Rs 5,100 = Rs 26,10,198.03

Since the total cost under quarterly supply of 1,500 units with 5 per centdiscount is lower than when order size is 102 units, the offer should beaccepted. While accepting this offer, consideration of capital blocked on ordersize of 1,500 units per quarter has been ignored.

tubes102100Rs100Rsunits2005,2AB/C2EOQ


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SOLVED PROBLEM 2

The purchase department of an organisation has received an offer of quantity

discounts on its order of materials as under:

Price per tonne Tonnes

Rs 1,400 Less than 500

1,380 500 and less than 1,000

1,360 1,000 and less than 2,000

1,340 2,000 and less than 3,000

1,320 3,000 and above

The annual requirement of the material is 5,000 tonnes. The delivery cost per

order is Rs 1,200 and the annual stock holding cost is estimated at 20 per cent

of the average inventory.

The purchase department wants you to consider the following purchaseoptions and advise which among them will be the most economical order

quantity, presenting the information in a tabular form:

The purchase quantity options to be considered are: 400 tonnes, 500 tonnes,

1,000 tonnes, 2,000 tonnes, and 3,000 tonnes


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Tata McGraw-Hill Publishing Company Limited Management Accounting 16-29

Solution

Determination of economic order quantity (EOQ)

1. Annual requirements (tonnes) 5,000 5,000 5,000 5,000 5,000

2. Order size (tonnes) 400 500 1,000 2,000 3,000

3. Number of orders (1 2)* 12.5 10 5 2.5 1.67

4. Price per tonne (Rs) 1,400 1,380 1,360 1,340 1,320

5. Cost of inventory (1 4) Rs lakh 70 69 68 67 66

6. Ordering cost (Rs) (No. of orders

Rs 1,200)

15,000 12,000 6,000 3,000 2,004

7. Average inventory (tonnes) 200 250 500 1,000 1,500

8. Average inventory (Rs lakh) 2.8 3.45 6.8 13.4 19.8

9. Carrying cost

(0.20 Average inventory) (Rs

lakh)

0.56 0.69 1.36 2.68 3.96

10. Total cost (5 + 6 + 9) (Rs lakh) 70.71 69.81 69.42 69.71 69.98

* Number of orders can be in fraction figure as per going concern concept.

Recommendation The purchase department is advised to have order size of 1,000

tonnes as at this order size total cost is minimum.

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Ch 16 InventoryManagement

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