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float is a source of value.

What are some tactics to increase net float?
You can manage the float by speeding up collections and slowing down payments. One way
to speed collections is by concentration banking. Customers make payments to a regional
office, which then pays the checks into a local bank account. Surplus funds are transferred
from the local account to a concentration bank. A related technique is lock-box banking. In
this case customers send their payments to a local post office box. A local bank empties the
box at regular intervals and clears the checks. Concentration banking and lock-box banking
reduce mailing time and the time required to clear checks. Finally, a zero-balance account
is a regional bank account to which just enough funds are transferred each day to pay that
day™s bills.

What are the costs and benefits of holding inventories?
The benefit of higher inventory levels is the reduction in order costs associated with
restocking and the reduced chances of running out of material. The costs are the carrying
costs, which include the cost of space, insurance, spoilage, and the opportunity cost of the
capital tied up in inventory. The economic order quantity is the order size that minimizes
the sum of order costs plus carrying costs.

What are the costs and benefits of holding cash?
Cash provides liquidity, but it doesn™t pay interest. Securities pay interest, but you can™t use
them to buy things. As financial manager you want to hold cash up to the point where the
incremental or marginal benefit of liquidity is equal to the cost of holding cash, that is, the
interest that you could earn on securities.

Why is an understanding of inventory management useful for cash management?
Cash is simply a raw material”like inventories of other goods”that you need to do
business. Capital that is tied up in large inventories of any raw material rather than
earning interest is expensive. So why do you hold inventories at all? Why not order
materials as and when you need them? The answer is that placing many small orders is also
expensive. The principles of optimal inventory management and optimal cash management
are similar.
Try to strike a balance between holding too large an inventory of cash (and losing
interest on the money) and making too many small adjustments to your inventory (and
incurring additional transaction or administrative costs). If interest rates are high, you want
to hold relatively small inventories of cash. If your cash needs are variable and your
transaction or administrative costs are high, you want to hold relatively large inventories.

Where do firms invest excess funds until they are needed to pay bills?
Firms can invest idle cash in the money market, the market for short-term financial assets.
These assets tend to be short-term, low risk, and highly liquid, making them ideal
instruments in which to invest funds for short periods of time before cash is needed.

www.sb.gov.bc.ca/smallbus/workshop/cashflow.html Guide to preparing a cash-flow forecast
Related Web www.fpsc.com/firstunion/ First Union™s quarterly magazine with a focus on cash management
Links www.ioma.com/mgmtlib/ An on-line “management library” with some articles on cash man-
www.nacha.org/ Automated collection systems for cash management

payment float concentration banking economic order quantity
Key Terms availability float lock-box system money market
net float zero-balance account

1. Float. On January 25, Coot Company has $250,000 deposited with a local bank. On Janu-
Quiz ary 27, the company writes and mails checks of $20,000 and $60,000 to suppliers. At the
end of the month, Coot™s financial manager deposits a $45,000 check received from a cus-
tomer in the morning mail and picks up the end-of-month account summary from the bank.
The manager notes that only the $20,000 payment of the 27th has cleared the bank. What
are the company™s ledger balance and payment float? What is the company™s net float?
2. Float. A company has the following cash balances:

Company™s ledger balance = $600,000
Bank™s ledger balance = $625,000
Available balance = $550,000
Cash and Inventory Management 221

a. Calculate the payment float and availability float.
b. Why does the company gain from the payment float?
c. Suppose the company adopts a policy of writing checks on a remote bank. How is this
likely to affect the three measures of cash balance?

3. Float. General Products writes checks that average $20,000 daily. These checks take an av-
erage of 6 days to clear. It receives payments that average $22,000 daily. It takes 3 days be-
fore these checks are available to the firm.

a. Calculate payment float, availability float, and net float.
b. What would be General Products™s annual savings if it could reduce availability float to
2 days? The interest rate is 6 percent per year. What would be the present value of these

4. Lock Boxes. Anne Teak, the financial manager of a furniture manufacturer, is considering
operating a lock-box system. She forecasts that 300 payments a day will be made to lock
boxes with an average payment size of $1,500. The bank™s charge for operating the lock
boxes is $.40 a check. The interest rate is .015 percent per day.

a. If the lock box saves 2 days in collection float, is it worthwhile to adopt the system?
b. What minimum reduction in the time to collect and process each check is needed to jus-
tify use of the lock-box system?

5. Cash Management. Complete the following passage by choosing the appropriate term from
the following list: lock-box banking, wire transfer, payment float, concentration banking,
availability float, net float, depository transfer check.
The firm™s available balance is equal to its ledger balance plus the ________ and minus the
________. The difference between the available balance and the ledger balance is often
called the ________. Firms can increase their cash resources by speeding up collections.
One way to do this is to arrange for payments to be made to regional offices which pay the
checks into local banks. This is known as ________. Surplus funds are then transferred from
the local bank to one of the company™s main banks. Transfer may be by the quick but ex-
pensive ________ or by the slightly slower but cheaper ________. Another technique is to
arrange for a local bank to collect the checks directly from a post office box. This is known
as ________.

6. Lock Boxes. Sherman™s Sherbet currently takes about 6 days to collect and deposit checks
Practice from customers. A lock-box system could reduce this time to 4 days. Collections average
Problems $10,000 daily. The interest rate is .02 percent per day.

a. By how much will the lock-box system reduce collection float?
b. What is the daily interest savings of the system?
c. Suppose the lock-box service is offered for a fixed monthly fee instead of payment per
check. What is the maximum monthly fee that Sherman™s should be willing to pay for this
service? (Assume a 30-day month.)
7. Lock Boxes. The financial manager of JAC Cosmetics is considering opening a lock box in
Pittsburgh. Checks cleared through the lock box will amount to $300,000 per month. The
lock box will make cash available to the company 3 days earlier.

a. Suppose that the bank offers to run the lock box for a $20,000 compensating balance. Is
the lock box worthwhile?

b. Suppose that the bank offers to run the lock box for a fee of $.10 per check cleared in-
stead of a compensating balance. What must the average check size be for the fee alter-
native to be less costly? Assume an interest rate of 6 percent per year.
c. Why did you need to know the interest rate to answer (b) but not to answer (a)?

8. Collection Policy. Major Manufacturing currently has one bank account located in New
York to handle all of its collections. The firm keeps a compensating balance of $300,000 to
pay for these services (see Section 19.7). It is considering opening a bank account with West
Coast National Bank to speed up collections from its many California-based customers.
Major estimates that the West Coast account would reduce collection time by 1 day on the
$1 million a day of business that it does with its California-based customers. If it opens the
account, it can reduce the compensating balance with its New York bank to $200,000 since
it will do less business in New York. However, West Coast also will require a compensating
balance of $200,000. Should Major open the new account?
9. Economic Order Quantity. Assume that Everyman™s Bookstore uses up cash at a steady
rate of $200,000 a year. The interest rate is 2 percent and each sale of securities costs $20.

a. How many times a year should the store sell securities?
b. What is its average cash balance?

10. Economic Order Quantity. Genuine Gems orders a full month™s worth of precious stones
at the beginning of every month. Over the course of the month, it sells off its stock, at which
point it restocks inventory for the following month. It sells 200 gems per month, and the
monthly carrying cost is $1 per gem. The fixed order cost is $20 per order. Should the firm
adjust its inventory policy? If so, should it order smaller stocks more frequently or larger
stocks less frequently?
11. Economic Order Quantity. Patty™s Pancakes orders pancake mix once a week. The mix is
used up by the end of the week, at which point more is reordered. Each time Patty orders
pancake mix, she spends about a half hour of her time, which she estimates is worth $20.
Patty sells 200 pounds of pancakes each week. The carrying cost of each pound of the
mix is 5 cents per week. Should Patty restock more or less frequently? What is the cost-
minimizing order size? How many times per month should Patty restock?
12. Economic Order Quantity. A large consulting firm orders photocopying paper by the car-
ton. The firm pays a $30 delivery charge on each order. The total cost of storing the paper,
including forgone interest, storage space, and deterioration, comes to about $1.50 per carton
per month. The firm uses about 1,000 cartons of paper per month.

a. Fill in the following table:

Order Size
100 200 250 500
Orders per month ________ ________ ________ ________
Total order cost ________ ________ ________ ________
Average inventory ________ ________ ________ ________
Total carrying costs ________ ________ ________ ________
Total inventory costs ________ ________ ________ ________

b. Calculate the economic order quantity. Is your answer consistent with your findings in
part (a)?
Cash and Inventory Management 223

13. Economic Order Quantity. Micro-Encapsulator Corp. (MEC) expects to sell 7,200 minia-
ture home encapsulators this year. The cost of placing an order from its supplier is $250.
Each unit costs $50 and carrying costs are 20 percent of the purchase price.
a. What is the economic order quantity?
b. What are total costs”order costs plus carrying costs”of inventory over the course of the

14. Inventory Management. Suppose now that the supplier in the previous problem offers a 1
percent discount on orders of 1,800 units or more. Should MEC accept the supplier™s offer?
15. Inventory Management. A just-in-time inventory system reduces the cost of ordering ad-
ditional inventory by a factor of 100. What is the change in the optimal order size predicted
by the economic order quantity model?
16. Cash Management. A firm maintains a separate account for cash disbursements. Total dis-
bursements are $100,000 per month spread evenly over the month. Administrative and trans-
action costs of transferring cash to the disbursement account are $10 per transfer. Mar-
ketable securities yield 1 percent per month. Determine the size and number of transfers that
will minimize the cost of maintaining the special account.
17. Float Management. The Automated Clearinghouse (ACH) system uses electronic commu-
nication to provide next-day delivery of payments. The processing cost of making a payment
through the ACH system is roughly half the cost of making the same payment by check. Why
then do firms often rationally choose to make payments by check?
18. Float Management. A parent company settles the collection account balances of its sub-
sidiaries once a week. (That is, each week it transfers any balances in the accounts to a cen-
tral account.) The cost of a wire transfer is $10. A depository transfer check costs $.80. Cash
transferred by wire is available the same day, but the parent must wait 3 days for depository
transfer checks to clear. Cash can be invested at 12 percent per year. How much money must
be in a collection account before it pays to use a wire transfer?
19. Float Management. Knob, Inc., is a nationwide distributor of furniture hardware. The com-
pany now uses a central billing system for credit sales of $182.5 million annually. First Na-
tional, Knob™s principal bank, offers to establish a new concentration banking system for a
flat fee of $100,000 per year. The bank estimates that mailing and collection time can be re-
duced by 3 days.

a. By how much will Knob™s availability float be reduced under the new system?
b. How much extra interest income will the new system generate if the extra funds are used
to reduce borrowing under Knob™s line of credit with First National? Assume the interest
rate is 12 percent.
c. Finally, should Knob accept First National™s offer if collection costs under the old system
are $40,000 per year?

20. Cash Management. If cash flows change unpredictably, the firm should allow the cash bal-
ance to move within limits.
a. What three factors determine how far apart these limits are?
b. How far should the firm adjust its cash balance when it reaches the upper or lower limit?
c. Why does it not restore the cash balance to the halfway point?
21. Optimal Cash Balances. Suppose that your weekly cash expenses are $80. Every time you
withdraw money from the automated teller at your bank, you are charged 15 cents. Your bank
account pays interest of 3 percent annually.

a. How often should you withdraw funds from the bank?
b. What is the optimal-sized withdrawal?
c. What is your average amount of cash on hand?

22. Cash Management. Suppose that the rate of interest increases from 4 to 8 percent per year.
Would firms™ cash balances go up or down relative to sales? Explain.
23. Cash and Inventory Management. According to the economic order quantity inventory
model and the Baumol model of cash management, what will happen to cash balances and
inventory levels if the firm™s production and sales both double? What is the implication of
your answer for percentage of sales financial planning models (see Section 18.2)?

24. Float Management. Some years ago, Merrill Lynch increased its float by mailing checks
drawn on West Coast banks to customers in the East and checks drawn on East Coast banks
Problem to customers in the West. A subsequent class action suit against Merrill Lynch revealed that
in 28 months from September 1976 Merrill Lynch disbursed $1.25 billion in 365,000 checks
to New York State customers alone. The plaintiff™s lawyer calculated that by using a remote
bank Merrill Lynch had increased its average float by 11„2 days.7

a. How much did Merrill Lynch disburse per day to New York State customers?
b. What was the total gain to Merrill Lynch over the 28 months, assuming an interest rate
of 8 percent?
c. What was the present value of the increase in float if the benefits were expected to be per-
d. Suppose that the use of remote banks had involved Merrill Lynch in extra expenses. What
was the maximum extra cost per check that Merrill Lynch would have been prepared to

1 a. The ledger balance is $940 + $100 “ $40 = $1,000.
Solutions to b. Availability float is $100, since you do not yet have access to the funds you have de-


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