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A B C D E F G H I
10/28/2015
C = annual carrying cost as a percentage of inventory value.
P = purchase price per unit.
Q = number of units in each order.
F = fixed costs per order.
S = annual usage in units.
Solving for Q gives us:
TIC = CP(Q/2) + F(S/Q)
Chapter 28. 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
its laptop computer. Each chip costs Webster $200, and in addition it must pay its supplier a $1,000 setup fee on each
order. Further, the minimum order size is 250 units; Webster's annual usage forecast is 5,000 units; and the annual
carrying cost of this item is estimated to be 20 percent of the average inventory value.
Andria plans to begin her session with the senior executives by reviewing some basic inventory concepts, after which
she will apply the EOQ model to Webster's microchip inventory. As her assistant, you have been asked to help her by
answering the following questions:
a. Why is inventory management vital to the health of most firms?
Note that S/Q is the number of orders placed each year, and, if no safety stocks are carried, Q/2 is the average number of
units carried in inventory during the year.
The economic (optimal) order quantity (EOQ) is that order quantity which minimizes total inventory costs. Thus, we have a
standard optimization problem, and the solution is to take the first derivative of the TIC with respect to quantity and set it
equal to zero:
b. What assumptions underlie the EOQ Model?
The standard form of the EOQ model requires the following assumptions:
· 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
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 sales. Conversely, if excess inventories are carried, a firm will incur higher costs than necessary. Worst of all, if a firm
carries large inventories, but of the wrong items, it will incur high costs and still lose sales.
These assumed conditions are not met in the real world, and, as a result, safety stocks are carried, and these stocks raise
c. Write out the formula for the total costs of carrying and ordering inventory, and then use the formula to derive the EOQ
model.
· 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
d. What is the EOQ for custom microchips? What are total inventory costs if the EOQ is ordered?
0
Q
)S)(F(
2
)P)(C(
dQ
)TIC(d
2=-=
)P)(C(
)S)(F(2
)P)(C(
)S)(F(2
Q
Q
)S)(F(
2
)P)(C(
2
2
=
=
units500
)200($2.0
)000,5)(000,1($2
EOQ ==
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A B C D E F G H I
= 0.2($200)(500/2) + $1,000(5,000/500)
= $40(250) + $1,000(10) = $10,000 + $10,000 = $20,000.
C = 20%
P = $ 200
F = $ 1,000
S = 5,000
EOQ = 500
TIC = 20,000$
C = 20%
P = $ 200
F = $ 1,000 @400, TIC = 20,500
S =
5,000 @600, TIC = 20,333
Order quantity = 600 plug in 400 and 600
TIC = 20,333$
TIC = CP(average inventory) + F(S/Q)
= 0.2($200)(450) + $1,000(5,000/500)
TIC = CP(Q/2) + F(S/Q)
= 0.2($198)(1,000/2) + $1,000(5,000/1,000) = $19,800 + $5,000
= $24,800.
Note that we have reduced the unit price by the amount of the discount. Since total costs are $24,800 if Webster orders
1,000 chips at a time, the incremental annual cost of taking the discount is $24,800 - $20,000 = $4,800. However, Webster
would save 1 percent on each chip, for a total annual savings of 0.01($200)(5,000) = $10,000. Thus, the net effect is that
Webster would save $10,000 - $4,800 = $5,200 if it takes the discount, and hence it should do so.
First, note that since the discount will only affect the orders for the operating inventory, the discount decision need not take
account of the safety stock. Webster's current total cost of its operating inventory is $20,000 (see part d). If Webster
increases its order quantity to 1,000 units, then its total costs for the operating inventory would be $24,800:
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?
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
which usage is approximately constant. For example, assume that the usage rate is constant, but different, during the
There are two ways to view the impact of safety stocks on total inventory costs. Webster's total cost of carrying the
operating inventory is $20,000 (see part d). Now the cost of carrying an additional 200 units is CP(safety stock) =
0.2($200)(200) = $8,000. Thus, total inventory costs are increased by $8,000, for a total of $20,000 + $8,000 = $28,000.
Another approach is to recognize that, with a 200-unit safety stock, Webster's average inventory is now (500/2) + 200 = 450
units. Thus, its total inventory cost, including safety stock, is $28,000:
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?
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,
then Webster must reorder each time its inventory reaches 2(96) = 192 units. Then, after 2 weeks, as it uses its last
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?
Webster must still reorder when the operating inventory reaches 192 units. However, with a safety stock of 200 units in
addition to the operating inventory, the reorder point becomes 200 + 192 = 392 units. Since Webster will reorder when its
microchip inventory reaches 392 units, and since the expected delivery time is 2 weeks, Webster's normal 96 unit usage
could rise to 392/2 = 196 units per week over the 2-week delivery period without causing a stockout. Similarly, if usage
remains at the expected 96 units per week, Webster could operate for 392/96 » 4 weeks versus the normal two weeks while
awaiting delivery of an order.
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.
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A B C D E F G H I
Monthly cash deficit (cash needs) 100,000.00
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
carrying--or opportunity--cost
cost 70 74,833 57,966 48,990 43,205 39,080
90 84,853 65,727 55,549 48,990 44,313
110 93,808 72,664 61,412 54,160 48,990
Optimal cash transfer size for various order costs and carrying costs
(2.) The use of air freight for deliveries.
(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
costs. This reduces inventory holdings of final goods.
Air freight would presumably shorten delivery times and reduce the need for safety stocks. It might or might not affect the
EOQ.
(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.
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:
(1.) The use of just-in-time procedures.
The EOQ model can still be used if there are seasonal variations in usage, but it must be applied to shorter periods during
which usage is approximately constant. For example, assume that the usage rate is constant, but different, during the
summer and winter periods. The EOQ model could be applied separately, using the appropriate annual usage rate, to each
period, and during the transitional fall and spring seasons inventories would be either run down or built up with special
seasonal orders.
j. How would these factors affect an EOQ analysis?
Just-in-time procedures are designed specifically to reduce inventories. If a just in time system were put in place, it would
largely obviate the need for using the EOQ model.
