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2 These usually involve linear programming. Linear programming is an efficient method of hunting through
the possible solutions to find the optimal one.

Midland, Texas; or Wilmington, Delaware. In these cases, it may take 3 or 4 days before
each check is presented for payment. United Carbon thus gains several days of addi-
tional float. Some firms even maintain disbursement accounts in different parts of the
country. The computer looks up each supplier™s zip code and automatically produces a
check on the most distant bank.
The suppliers won™t object to these machinations because the Federal Reserve guar-
antees a maximum clearing time of 2 days on all checks cleared through the Federal Re-
serve system. Therefore, the supplier never gives up more than 2 days of float. Instead,
the victim of remote disbursement is the Federal Reserve, which loses float if it takes
more than 2 days to collect funds. The Fed has been trying to prevent remote disburse-

Zero-Balance Accounts. A New York City bank receives several check deliveries
each day. Thus if United Carbon uses a New York City bank for paying its suppliers, it
will not know at the beginning of the day how many checks will be presented for pay-
ment. Either it must keep a large cash balance to cover contingencies, or it must be pre-
pared to borrow.
However, instead of having a disbursement account with, say, Morgan Guaranty
ZERO-BALANCE Trust in New York, United Carbon could open a zero-balance account with Morgan™s
ACCOUNT Regional affiliated bank in Wilmington, Delaware. Because it is not in a major banking center,
bank account to which just this affiliated bank receives almost all check deliveries in the form of a single, early-
enough funds are transferred morning delivery from the Federal Reserve. Therefore, it can let the cash manager at
daily to pay each day™s bills. United Carbon know early in the day exactly how much money will be paid out that day.
The cash manager then arranges for this sum to be transferred from the company™s con-
centration account to the disbursement account. Thus by the end of the day (and at the
start of the next day), United Carbon has a zero balance in the disbursement account.
United Carbon™s Wilmington account has two advantages. First, by choosing a re-
mote location, the company has gained several days of float. Second, because the bank
can forecast early in the day how much money will be paid out, United Carbon does not
need to keep extra cash in the account to cover contingencies.

Many cash payments involve pieces of paper, such as dollar bills or a check. But the use
of paper transactions is on the decline. For consumers, paper is being replaced by credit
cards or debit cards. In the case of companies, payments are increasingly made elec-
When banks in the United States make large payments to each other, they do so elec-
tronically, using an arrangement known as Fedwire. This is operated by the Federal Re-
serve system and connects more than 10,000 financial institutions in the United States
to the Fed and so to each other. Suppose Bank A instructs the Fed to transfer $1 million
from its account with the Fed to the account of Bank B. Bank A™s account is then re-
duced by $1 million immediately and Bank B™s account is increased at the same time.
Fedwire is used to make high-value payments. Bulk payments such as wages, divi-
dends, and payments to suppliers generally travel through the Automated Clearinghouse
(ACH) system and take 2 to 3 days. In this case the company simply needs to provide a
computer file of instructions to its bank, which then debits the corporation™s account
and forwards the payments to the ACH system.
For companies that are “wired” to their banks, these electronic payment systems
have several advantages:
Cash and Inventory Management 211

• Record keeping and routine transactions are easy to automate when money moves
electronically. For example, the Campbell Soup Company discovered it could handle
cash management and short-term borrowing and lending with a total staff of seven.3
The company™s domestic cash flow was about $5 billion.
• The marginal cost of transactions is very low. For example, it costs less than $10 to
transfer huge sums of money using Fedwire and only a few cents to make each ACH
• Float is drastically reduced. This can generate substantial savings. For example, cash
managers at Occidental Petroleum found that one plant was paying out about $8 mil-
lion per month several days early to avoid any risk of late fees if checks were delayed
in the mail. The solution was obvious: The plant™s managers switched to paying large
bills electronically; that way they could ensure checks arrived exactly on time.4

Inventories and Cash Balances
So far we have focused on managing the flow of cash efficiently. We have seen how ef-
ficient float management can improve a firm™s income and its net worth. Now we turn
to the management of the stock of cash that a firm chooses to keep on hand and ask:
How much cash does it make sense for a firm to hold?

Recall that cash management involves a trade-off. If the cash were invested in
securities, it would earn interest. On the other hand, you can™t use securities
to pay the firm™s bills. If you had to sell those securities every time you
needed to pay a bill, you would incur heavy transactions costs. The art of
cash management is to balance these costs and benefits.

If that seems more easily said than done, you may be comforted to know that pro-
duction managers must make a similar trade-off. Ask yourself why they carry invento-
ries of raw materials, work in progress, and finished goods. They are not obliged to
carry these inventories; for example, they could simply buy materials day by day, as
needed. But then they would pay higher prices for ordering in small lots, and they would
risk production delays if the materials were not delivered on time. That is why they
order more than the firm™s immediate needs. Similarly, the firm holds inventories of fin-
ished goods to avoid the risk of running out of product and losing a sale because it can-
not fill an order.
But there are costs to holding inventories: money tied up in inventories does not earn
interest; storage and insurance must be paid for; and often there is spoilage and deteri-
oration. Production managers must try to strike a sensible balance between the costs of
holding too little inventory and those of holding too much.
In this sense, cash is just another raw material you need for production. There are
costs to keeping an excessive inventory of cash (the lost interest) and costs to keeping
too small an inventory (the cost of repeated sales of securities).

3 J. D. Moss, “Campbell Soup™s Cutting-Edge Cash Management,” Financial Executive 8 (September/Octo-
ber 1992), pp. 39“42.
4 R. J. Pisapia, “The Cash Manager™s Expanding Role: Working Capital,” Journal of Cash Management 10

(November/December 1990), pp. 11“14.

Let us take a look at what economists have had to say about managing inventories and
then see whether some of these ideas can help us manage cash balances. Here is a sim-
ple inventory problem.
A builders™ merchant faces a steady demand for engineering bricks. When the mer-
chant every so often runs out of inventory, it replenishes the supply by placing an order
for more bricks from the manufacturer.
There are two costs associated with the merchant™s inventory of bricks. First, there is
the order cost. Each order placed with a supplier involves a fixed handling expense and
delivery charge. The second type of cost is the carrying cost. This includes the cost of
space, insurance, and losses due to spoilage or theft. The opportunity cost of the capi-
tal tied up in the inventory is also part of the carrying cost.
Here is the kernel of the inventory problem:

As the firm increases its order size, the number of orders falls and therefore
the order costs decline. However, an increase in order size also increases the
average amount in inventory, so that the carrying cost of inventory rises. The
trick is to strike a balance between these two costs.

Let™s insert some numbers to illustrate. Suppose that the merchant plans to buy 1
million bricks over the coming year. Each order that it places costs $90, and the annual
carrying cost of the inventory is $.05 per brick. To minimize order costs, the merchant
would need to place a single order for the entire 1 million bricks on January 1 and
would then work off the inventory over the remainder of the year. Average inventory
over the year would be 500,000 bricks and therefore carrying costs would be 500,000 —
$.05 = $25,000. The first row of Table 2.10 shows that if the firm places just this one
order, total costs are $25,090:
Total costs = order costs + carrying costs
$25,090 = $90 + $25,000
To minimize carrying costs, the merchant would need to minimize inventory by
placing a large number of very small orders. For example, the bottom row of Table 2.10

TABLE 2.10
How inventory costs vary with the number of orders

Order Size Orders per Year Average Inventory Order Costs Carrying Costs Total Costs
= = = = = =
Order Costs
Annual Purchases Order Size
Bricks per Order $90 per Order $.05 per Brick Carrying Costs
Bricks per Order 2
1,000,000 1 500,000 $ 90 $ 25,000 $ 25,090
500,000 2 250,000 180 12,500 12,680
200,000 5 100,000 450 5,000 5,450
100,000 10 50,000 900 2,500 3,400
60,000 16.7 30,000 1,500 1,500 3,000
50,000 20 25,000 1,800 1,250 3,050
20,000 50 10,000 4,500 500 5,000
10,000 100 5,000 9,000 250 9,250
Cash and Inventory Management 213

Determination of optimal
order size.
Total costs
Carrying costs

Inventory costs, dollars


Order costs

Optimal order Order size
size 60,000 bricks

shows the costs of placing 100 orders a year for 10,000 bricks each. The average in-
ventory is now only 5,000 bricks and therefore the carrying costs are only 5,000 — $.05
= $250. But the order costs have risen to 100 — $90 = $9,000.
Each row in Table 2.10 illustrates how changes in the order size affect the inventory
costs. You can see that as the order size decreases and the number of orders rises, total
inventory costs at first decline because carrying costs fall faster than order costs rise.
Eventually, however, the curve turns up as order costs rise faster than carrying costs fall.
Figure 2.6 illustrates this graphically. The downward-sloping curve charts annual order
costs and the upward-sloping straight line charts carrying costs. The U-shaped curve is
the sum of these two costs. Total costs are minimized in this example when the order
size is 60,000 bricks. About 17 times a year the merchant should place an order for
60,000 bricks and it should work off this inventory over a period of about 3 weeks. Its
inventory will therefore follow the sawtoothed pattern in Figure 2.7.
Note that it is worth increasing order size as long as the decrease in total order

The builders™ merchant
minimizes inventory costs by
Inventory, thousands of bricks

placing about 17 orders a
year for 60,000 bricks each. 60
That is, it places orders at
about 3-week intervals.
Average inventory

0 3 6 9 12

costs outweighs the increase in carrying costs. The optimal order size is the point at
which these two effects offset each other. This order size is called the economic order
quantity. There is a neat formula for calculating the economic order quantity. The for-
QUANTITY Order size
mula is
that minimizes total inventory
2 annual sales cost per order
Economic order quantity =
carrying cost
In the present example,
2 — 1,000,000 — 90
Economic order quantity = = 60,000 bricks
You have probably already noticed several unrealistic features in our simple exam-
ple. First, rather than allowing inventories of bricks to decline to zero, the firm would
want to allow for the time it takes to fill an order. If it takes 5 days before the bricks can
be delivered and the builders™ merchant waits until it runs out of stock before placing
an order, it will be out of stock for 5 days. In this case the firm should reorder when its
stock of bricks falls to a 5-day supply.
The firm also might want to recognize that the rate at which it sells its goods is sub-
ject to uncertainty. Sometimes business may be slack; on other occasions the firm may
land a large order. In this case it should maintain a minimum safety stock below which
it would not want inventories to drop.
The number of bricks the merchant plans to buy in the course of the year, in this case
1 million, is also a forecast that is subject to uncertainty. The optimal order size is pro-
portional to the square root of the forecast of annual sales.

These are refinements: the important message of our simple example is that
the firm needs to balance carrying costs and order costs. Carrying costs
include both the cost of storing the goods and the cost of the capital tied up in
inventory. So when storage costs or interest rates are high, inventory levels
should be kept low. When the costs of restocking are high, inventories should
also be high.

In recent years a number of firms have used a technique known as just-in-time in-
ventory management to make dramatic reductions in inventory levels. Firms that use the
just-in-time system receive a nearly continuous flow of deliveries, with no more than 2


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