· All values are known with certainty and constant over time.
· All carrying costs are variable, so carrying costs change proportionally with changes in inventory levels
These assumed conditions are not met in the real world, and, as a result, safety stocks are carried, and these stocks raise
· Inventory usage is uniform over time. For example, a retailer would sell the same number of units each day.
· All ordering costs are fixed per order; that is, the company pays a fixed amount to order and receive each shipment of
P = purchase price per unit.
Q = number of units in each order.
F = fixed costs per order.
S = annual usage in units.
The economic (optimal) order quantity (EOQ) is that order quantity which minimizes total inventory costs. Thus, we have a
equal to zero:
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1/13/2015
C = annual carrying cost as a percentage of inventory value.
Chapter 23. Mini Case for Advanced Issues in Cash Management and Inventory Control
Andria Mullins, financial manager of Webster Eelectronics, has been asked by the firm’s CEO, Fred Weygandt, to evaluate
the company’s inventory control techniques and to lead a discussion of the subject with the senior executives. Andria
a. Why is inventory management vital to the health of most firms?
b. What assumptions underlie the EOQ Model?
The standard form of the EOQ model requires the following assumptions:
TIC = total carrying costs + total ordering costs = CP(Q/2) + F(S/Q)
Inventory management is critical to the financial success of most firms. If insufficient inventories are carried, a firm will lose
c. Write out the formula for the total costs of carrying and ordering inventory, and then use the formula to derive the EOQ
model.
carries large inventories, but of the wrong items, it will incur high costs and still lose sales.
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S = 5,000
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P = $ 200
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C = 20%
P = $ 200
C = 20%
d. What is the EOQ for custom microchips? What are total inventory costs if the EOQ is ordered?
f. Suppose it takes 2 weeks for Webster’s supplier to set up production, make and test the chips, and deliver them to
Webster’s plant. Assuming certainty in delivery times and usage, at what inventory level should Webster reorder? (assume
a 52-week year, and assume that Webster orders the EOQ amount.
e. What is Webster’s added cost if it orders 400 units at a time rather than the EOQ quantity? What if it orders 600 per
order?
There are two ways to view the impact of safety stocks on total inventory costs. Webster’s total cost of carrying the
With an annual usage of 5,000 units, Webster’s weekly usage rate is 5,000/52 ~ 96 units. If the order lead time is 2 weeks,
g. Of course, there is uncertainty in Webster’s usage rate as well as in delivery times, so the company must carry a safety
stock to avoid running out of chips and having to halt production. If a 200-unit safety stock is carried, what effect would
this have on total inventory costs? What is the new reorder point? What protection does the safety stock provide if usage
increases, or if delivery is delayed?
units500
)000,5)(000,1($2
EOQ ==
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addition to the operating inventory, the reorder point becomes 200 + 192 = 392 units. Since Webster will reorder when its
could rise to 392/2 = 196 units per week over the 2-week delivery period without causing a stockout. Similarly, if usage
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summer and winter periods. The EOQ model could be applied separately, using the appropriate annual usage rate, to each
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(2.) The use of air freight for deliveries.
(3.) The use of a computerized inventory control system, wherein as units were removed from stock, an electronic
system automatically reduced the inventory account and, when the order point was hit, automatically sent an electronic
message to the supplier placing an order. The electronic system ensures that inventory records are accurate, and that
orders are placed promptly.
Webster must still reorder when the operating inventory reaches 192 units. However, with a safety stock of 200 units in
First, note that since the discount will only affect the orders for the operating inventory, the discount decision need not take
(1.) The use of just-in-time procedures.
i. For many firms, inventory usage is not uniform throughout the year, but, rather, follows some seasonal pattern. Can the
EOQ model be used in this situation? If so, how?
The EOQ model can still be used if there are seasonal variations in usage, but it must be applied to shorter periods during
h. Now suppose Webster’s supplier offers a discount of 1 percent on orders of 1,000 or more. Should Webster take the
discount? Why or why not?
j. How would these factors affect an EOQ analysis?
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Opportunity cost for cash 7%
Brokerage costs for each transaction 32
Total cash needs per year 1,200,000.00
EOQ = Optimal cash transfer 33,123
Number of times to liquidate per year 36.2
Number of weeks between liquidations 1.435
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32 50,596 39,192 33,123 29,212 26,423
90 84,853 65,727 55,549 48,990 44,313
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Monthly cash deficit (cash needs) 100,000.00
carrying–or opportunity–cost
33,123 3% 5% 7% 9% 11%
10 28,284 21,909 18,516 16,330 14,771
Optimal cash transfer size for various order costs and carrying costs
(4.) The manufacturing plant is redesigned and automated. Computerized process equipment and state-of-the-art
robotics are installed, making the plant highly flexible in the sense that the company can switch from the production of
one item to another at a minimum cost and quite quickly. This makes short production runs more feasible than under the
old plant setup.
The trend in manufacturing is toward flexibly designed plants, which permit small production runs without high setup
Computerized control systems would, generally, enable the company to keep better track of its existing inventory. This
would probably reduce safety stocks, and it might or might not affect the EOQ.
Applying this to cash management:
costs. This reduces inventory holdings of final goods.