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or 3 hours™ worth of parts inventory on hand at any time. For these firms the extra cost
of restocking is completely outweighed by the saving in carrying cost. Just-in-time in-
ventory management requires much greater coordination with suppliers to avoid the
costs of stock-outs, however.
Just-in-time inventory management also can reduce costs by allowing suppliers to
produce and transport goods on a steadier schedule. However, just-in-time systems rely
heavily on predictability of the production process. A firm with shaky labor relations,
for example, would adopt a just-in-time system at its peril, for with essentially no in-
ventory on hand, it would be particularly vulnerable to a strike.

The builders™ merchant has experienced an increase in demand for engineering bricks.
Self-Test 4
It now expects to sell 1.25 million bricks a year. Unfortunately, interest rates have risen
and the annual carrying cost of the inventory has increased to $.09 per brick. Order
costs have remained steady at $90 per order.
Cash and Inventory Management 215

a. Rework Table 20.1 for each of the eight order sizes shown in the table.
b. Has the optimal inventory level risen or fallen? Explain why.

William Baumol was the first to notice that this simple inventory model can tell us
something about the management of cash balances.5 Suppose that you keep a reservoir
of cash that is steadily drawn down to pay bills. When it runs out, you replenish the cash
balance by selling short-term securities. In these circumstances your inventory of cash
also follows a sawtoothed pattern like the pattern for inventories we saw in Figure 2.7.
In other words, your cash management problem is just like the problem of finding
the optimal order size faced by the builders™ merchant. You simply need to redefine the
variables. Instead of bricks per order, the order size is defined as the value of short-term
securities that are sold whenever the cash balance is replenished. Total cash outflow
takes the place of the total number of bricks sold. Cost per order becomes the cost per
sale of securities, and the carrying cost is just the interest rate. Our formula for the
amount of securities to be sold or, equivalently, the initial cash balance is therefore
2 annual cash outflows cost per sale of securities
Initial cash balance =
interest rate

The optimal amount of short-term securities sold to raise cash will be higher
when annual cash outflows are higher and when the cost per sale of
securities is higher. Conversely, the initial cash balance falls when the interest
rate is higher.

The Optimal Cash Balance
Suppose that you can invest spare cash in U.S. Treasury bills at an interest rate of 8 per-
cent, but every sale of bills costs you $20. Your firm pays out cash at a rate of $105,000
per month, or $1,260,000 per year. Our formula for the initial cash balance tells us that
the optimal amount of Treasury bills that you should sell at one time is
2 — 1,260,000 — 20
= $25,100
Thus your firm would sell approximately $25,000 of Treasury bills four times a
month”about once a week. Its average cash balance will be $25,000/2, or $12,500.

In Baumol™s model a higher interest rate implies smaller sales of bills. In other
words, when interest rates are high, you should hold more of your funds in interest-
bearing securities and make small sales of these securities when you need the cash. On
the other hand, if you use up cash at a high rate or there are high costs to selling secu-
rities, you want to hold large average cash balances. Think about that for a moment. You

5 SeeW. J. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Jour-
nal of Economics 66 (November 1952), pp. 545“556.

can hold too little cash. Many financial managers point with pride to the extra interest
that they have earned. Such benefits are highly visible. The costs are less visible but
they can be very large. When you allow for the time that the manager spends in moni-
toring the cash balance, it may make some sense to forgo some of that extra interest.

Suppose now that the interest rate is only 4 percent. How will this affect the optimal ini-
Self-Test 5
tial cash balance derived in Example 4? What will be the average cash balance? What
will be annual trading costs? Explain why the optimal cash position now involves fewer

Baumol™s model stresses the essential similarity between the inventory problem and the
cash management problem. It also demonstrates the relationship between the optimal
cash balance on the one hand and the level of interest rates and the cost of transactions
on the other. However, it is clearly too simple for practical use. For example, firms do
not pay out cash at a steady rate day after day and week after week. Sometimes the firm
may collect a large unpaid bill and therefore receive a net inflow of cash. On other oc-
casions it may pay its suppliers and so incur a net outflow of cash.
Economists and management scientists have developed a variety of more elaborate
and realistic models that allow for the possibility of both cash inflows and outflows. For
example, Figure 2.8 illustrates how the firm should manage its cash balance if it can-
not predict day-to-day cash inflows and outflows. You can see that the cash balance me-
anders unpredictably until it reaches an upper limit. At this point the firm buys enough
securities to return the cash balance to a more normal level. Once again the cash bal-
ance is allowed to meander until this time it hits a lower limit. This may be zero, some
minimum safety margin above zero, or a balance necessary to keep the bank happy.
When the cash balance hits the lower limit, the firm sells enough securities to restore
the balance to a normal level. Thus the rule is to allow the cash holding to wander freely
until it hits an upper or lower limit. When this happens, the firm should buy or sell se-
curities to regain the desired balance.

If cash flows are
unpredictable, the cash
Upper limit
balance should be allowed to
meander until it hits an
upper or lower limit. At this
Cash balance

point the firm buys or sells
securities to restore the
balance to the return point, Return point
which is the lower limit plus
one-third of the spread
between the upper and lower Lower limit

Cash and Inventory Management 217

How far should the firm allow its cash balance to wander? The answer depends on
three factors. If the day-to-day variability in cash flows is large or if the cost of buying
and selling securities is high, then the firm should set the upper and lower limits far
apart. The firm allows wider limits when cash-flow volatility is high to keep down the
frequency of costly security sales and purchases. Similarly, the firm tolerates wider lim-
its if the cost of security transactions is high. Conversely, if the rate of interest is high
and the incentives to manage cash are correspondingly more important, the firm will
set the limits close together.6
Have you noticed one odd feature about Figure 2.8? The cash balance does not re-
turn to a point halfway between the lower and upper limits. It always comes back to a
point one-third of the distance from the lower to the upper limit. Always starting at this
return point means the firm hits the lower limit more often than the upper limit. This
does not minimize the number of transactions”that would require always starting ex-
actly at the middle of the spread. However, always starting at the middle would mean a
larger average cash balance and larger interest costs. The lower return point minimizes
the sum of transaction costs and interest costs.
Recognizing uncertainty in cash flows adds some extra realism, but few managers
would concede that cash inflows and outflows are entirely unpredictable. The manager
of Toys ˜R™ Us knows that there will be substantial cash inflows around Christmas. Fi-
nancial managers know when dividends will be paid and when taxes will be due. Ear-
lier we described how firms forecast cash inflows and outflows and how they arrange
short-term investment and financing decisions to supply cash when needed and put cash
to work earning interest when it is not needed.
This kind of short-term financial plan is usually designed to produce a cash balance
that is stable at some lower limit. But there are always fluctuations that financial man-
agers cannot plan for, certainly not on a day-to-day basis. You can think of the decision
rule depicted in Figure 2.8 as a way to cope with the cash inflows and outflows which
cannot be predicted, or which are not worth predicting. Trying to predict all cash flows
would chew up enormous amounts of management time.
You should therefore think of these cash management rules as helping us understand
the problem of cash management. But they are not generally used for day-to-day man-
agement and would probably not yield substantial savings compared with policies based
on a manager™s judgment, providing of course that the manager understands the trade-
offs we have discussed.

How would you expect the firm™s cash balance to respond to the following changes?
Self-Test 6
a. Interest rates increase.
b. The volatility of daily cash flow decreases.
c. The transaction cost of buying or selling marketable securities goes up.

For very large firms, the transaction costs of buying and selling securities become triv-
ial compared with the opportunity cost of holding idle cash balances. Suppose that the
6See M. H. Miller and D. Orr, “A Model of the Demand for Money by Firms,” Quarterly Journal of Eco-
nomics 80 (August 1966), pp. 413“435.

interest rate is 4 percent per year, or roughly 4/365 = .011 percent per day. Then the
daily interest earned on $1 million is .00011 — $1,000,000 = $110. Even at a cost of $50
per transaction, which is generous, it pays to buy Treasury bills today and sell them to-
morrow rather than to leave $1 million idle overnight.
A corporation with $1 billion of annual sales has an average daily cash flow of
$1,000,000,000/365, about $2.7 million. Firms of this size end up buying or selling se-
curities once a day, every day, unless by chance they have only a small positive cash bal-
ance at the end of the day.
Why do such firms hold any significant amounts of cash? For two reasons. First,
cash may be left in non“interest-bearing accounts to compensate banks for the services
they provide. Second, large corporations may have literally hundreds of accounts with
dozens of different banks. It is often less expensive to leave idle cash in some of these
accounts than to monitor each account daily and make daily transfers between them.
One major reason for the proliferation of bank accounts is decentralized manage-
ment. You cannot give a subsidiary operating freedom to manage its own affairs with-
out giving it the right to spend and receive cash.
Good cash management nevertheless implies some degree of centralization. You
cannot maintain your desired inventory of cash if all the subsidiaries in the group are
responsible for their own private pools of cash. And you certainly want to avoid situa-
tions in which one subsidiary is investing its spare cash at 8 percent while another is
borrowing at 10 percent. It is not surprising, therefore, that even in highly decentralized
companies there is generally central control over cash balances and bank relations.

We have seen that when firms have excess funds, they can invest the surplus in interest-
bearing securities. Treasury bills are only one of many securities that might be appro-
priate for such short-term investments. More generally, firms may invest in a variety of
securities in the money market, the market for short-term financial assets.
Only fixed-income securities with maturities less than 1 year are considered to be
Market for short-term
part of the money market. In fact, however, most instruments in the money market have
financial assets.
considerably shorter maturity. Limiting maturity has two advantages for the cash man-
ager. First, short-term securities entail little interest-rate risk. Recall that price risk due
to interest-rate fluctuations increases with maturity. Very-short-term securities, there-
fore, have almost no interest-rate risk. Second, it is far easier to gauge financial stabil-
ity over very short horizons. One need not worry as much about deterioration in finan-
cial strength over a 90-day horizon as over the 30-year life of a bond. These
considerations imply that high-quality money-market securities are a safe “parking
spot” to keep idle balances until they are converted back to cash.
Most money-market securities are also highly marketable or liquid, meaning that it
is easy and cheap to sell the asset for cash. This property, too, is an attractive feature of
securities used as temporary investments until cash is needed. Treasury bills are the
most liquid asset. Treasury bills are issued by the United States government with orig-
inal maturities ranging from 90 days to 1 year.
Some of the other important instruments of the money market are
Commercial paper. This is the short-term, usually unsecured, debt of large and well-
known companies. While maturities can range up to 270 days, commercial paper usu-
ally is issued with maturities of less than 2 months. Because there is no active trading
in commercial paper, it has low marketability. Therefore, it would not be an appro-
Cash and Inventory Management 219

priate investment for a firm that could not hold it until maturity. Both Moody™s and
Standard & Poor™s rate commercial paper in terms of the default risk of the issuer.
Certificates of deposit. CDs are time deposits at banks, usually in denominations
greater than $100,000. Unlike demand deposits (checking accounts), time deposits
cannot be withdrawn from the bank on demand: the bank pays interest and principal
only at the maturity of the deposit. However, short-term CDs (with maturities less
than 3 months) are actively traded, so a firm can easily sell the security if it needs
Repurchase agreements. Also known as repos, repurchase agreements are in effect col-
lateralized loans. A government bond dealer sells Treasury bills to an investor, with
an agreement to repurchase them at a later date at a higher price. The increase in
price serves as implicit interest, so the investor in effect is lending money to the
dealer, first giving money to the dealer and later getting it back with interest. The
bills serve as collateral for the loan: if the dealer fails, and cannot buy back the bill,
the investor can keep it. Repurchase agreements are usually very short term, with
maturities of only a few days.

What is float and why can it be valuable?
The cash shown in the company ledger is not the same as the available balance in its bank
account. When you write a check, it takes time before your bank balance is adjusted
downward. This is payment float. During this time the available balance will be larger than
the ledger balance. When you deposit a check, there is a delay before it gets credited to your
bank account. In this case the available balance will be smaller than the ledger balance. This
is availability float. The difference between payment float and availability float is the net
float. If you can predict how long it will take checks to clear, you may be able to “play the
float” and get by on a smaller cash balance. The interest you can thereby earn on the net


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