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marketable securities or the interest rate applicable to short-term debt).

EXAMPLE 4.6 A firmвЂ™sweekly average cash balances are as follows:

Average Cash Balance

Week

$12,000

1

2 17,000

3 10,000

4 15,000

Total $54,000

The monthly average cash balance is:

--

$549000 - $13,500

4

If the annual interest rate is approximated at 12 percent, the monthly return earned on the average cash

balance is:

$13,500X 0.1 = $135

For a cash acceleration system to be feasible, the return earned on the freed cash must exceed the

cost of the system.

Delay of Cash Oufflow

There are various ways to delay cash disbursements, including:

1. Using drafts to pay bills since drafts are not due on demand. When a bank receives a draft it

must return the draft to the issuer for acceptance prior to payment. When the company accepts

the draft, it then deposits the required funds with the bank; hence, a smaller average checking

balance is maintained.

2. Mailing checks from post offices having limited service or from locations where the mail must

go through several handling points, lengthening the payment period.

3. Drawing checks on remote banks or establishing cash disbursement centers in remote locations

so that the payment period is lengthened. For example, someone in New York can be paid with

a check drawn on a California bank.

4. Using credit cards and charge accounts in order to lengthen the time between the acquisition

of goods and the date of payment for those goods.

The cash disbursements of a firm may be controlled by centralizing its payable operation so that it

satisfies its obligations at optimum times. Centralization will also facilitate the prediction of the

disbursement float.

Payments to vendors should be delayed to the maximum as long as there is no associated finance

charge or impairment of the companyвЂ™s credit rating. Of course, bills should not be paid prior to their

due dates because of the time value of money.

A company can minimize its cash balances by using probabilities related to the expected time that

checks will clear. Deposits, for example, may be made to a payroll checking account based on the

expected time needed for the checks to clear.

102 THE MANAGEMENT OF WORKING CAPITAL [CHAP. 4

Although not a delay of cash outflow, a company may reduce its cash outflow by the early repayment

of a loan, thus avoiding some payment of interest. The company should consider the wire transfer of funds

if a quick payment method is called for, especially if the payment is to be made to a distant location.

EXAMPLE 4.7 Every 2 weeks, company X disburses checks that average $500,000and take 3 days to clear. How

much money can the company save annually if it delays transfer of funds from an interest-bearing account that pays

0.0384 percent per day (annual rate of 14 percent) for those 3 days?

The interest for 3 days is:

$500,000 X (0.000384 X 3) = $576

The number of 2-week periods in a year is:

52 weeks

-= 26

2 weeks

The savings per year is:

$576 X 26 = $14,976

Opportunity Cost of Forgoing a Cash Discount

An opportunity cost is the net revenue lost by rejecting an alternative action. A firm should typically

take advantage of a discount offered by a creditor because of the associated high opportunity cost. For

example, if the terms of sale are 2/10, netl30, the customer has 30 days to pay the bill but will get a 2

percent discount if he or she pays in 10days. Some companies use seasonal datings such as 2/10, netl30,

July 1dating. Here, with an invoice dated July 1,the discount can be taken until July 10.

The following formula may be used to compute the opportunity cost in percentage, on an annual

basis, of not taking a discount:

discount percent 360

Opportunity cost = X-

N

100 - discount percent

where N = the number of days payment can be delayed by forgoing the cash discount

= days credit is outstanding - discount period

The numerator of the first term (discount percent) is the cost per dollar of credit, whereas the

denominator (100 - discount percent) represents the money made available by forgoing the cash

discount. The second term represents the number of times this cost is incurred in a year.

EXAMPLE 4.8 The opportunity cost of not taking a discount when the terms are 3/15, net/60 is computed as

follows:

3 360 3 360

Opportunity cost = - - - -= 24.7%

x =

97 45

100-3 60-15

Determination of the Optimal Cash Balance

There are two techniques for deciding how much cash to maintain at any given point, considering

that both holding cash and investing it have both advantages and disadvantages. The purpose of cash

models is to satisfy cash requirements at the least cost.

BaumolвЂ™s Model

It attempts to determine the optimum amount of transaction cash under conditions of certainty. The

objective is to minimize the sum of the fixed costs of transactions and the opportunity cost of holding

cash balances. These costs are expressed as:

103

THE MANAGEMENT OF WORKING CAPITAL

CHAP. 41

where 6 = the fixed cost of a transaction, T = the total cash needed for the time period involved, i = the

interest rate on marketable securities, and C = cash balance.

The optimal level of cash is determined using the following formula:

EXAMPLE4.9 You estimate a cash need for $4,0o0,000 over a 1-month period where the cash account is expected

to be disbursed at a constant rate. The opportunity interest rate is 6% per annum, or 0.5 percent for a 1-month

period. The transaction cost each time you borrow or withdraw is $100.

The optimal transaction size (the optimal borrowing or withdrawal lot size) and the number of transactions

you should make during the month follow:

The optimal transaction size is $400,000. The average cash balance is:

The number of transactions required are:

M9000вЂ™000 = 10 transactions during the month.

$400,000

The Miller-Orr Model

The Miller-Orr model is a stochastic model for cash management where uncertainty exists for cash

payments. In other words, there is irregularity of cash payments. The Miller-Orr model places an upper

and lower limit for cash balances. When the upper limit is reached a transfer of cash to marketable

securities or other suitable investments is made. When the lower limit is reached a transfer from securities

to cash occurs. A transaction will not occur as long as the cash balance falls within the limits.

The Miller-Orr model takes into account the fixed costs of a securities transaction ( b ) ,assumed to

be the same for buying as well as selling, the daily interest rate on marketable securities ( i ) , and the

variance of daily net cash flows (s2). A major assumption is the randomness of cash flows. The two control

limits in the Miller-Orr model may be specified as вЂњhвЂќ dollars as an upper limit and zero dollars at the

lower limit. When the cash balance reaches the upper level, h less z dollars of securities are bought and

the new balance equals zero, z dollars of securities are sold and the new balance again reaches z .

The optimal cash balance z is computed as follows:

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