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4.4

year. Average daily collections are $450,000. As a result of the system, the float time will be

reduced by 3 days. The rate of return is 14 percent. Should the lockbox arrangement be

instituted?

SOLUTION

cost $216,000

Return on freed cash (0.14 X 3 X $450,000) 189,000

$ 27,000

Disadvantage of lockbox

The lockbox should not be used.

118 THE MANAGEMENT OF WORKING CAPITAL [CHAP. 4

Dividing of Region. Boston Corporation has an arrangement with XYZ Bank in which the bank

4.5

handles $5 million a day in collections but requires a $420,000 compensating balance. The

company is considering withdrawing from the arrangement and dividing its southern region so

that two other banks will handle the business instead. Bank S will handle $3 million a day of

collections and require a $450,000 compensating balance, and bank T will handle the other $2

million a day and require a compensating balance of $350,000. By dividing the southern region,

collections will be accelerated by 4 day. The rate of return is 17 percent. Should the southern

region be divided?

SOLUTION

Accelerated cash inflow

$5 million per day X day $2,500,000

Incremental compensating balance

required 380,000

$2,120 ,Ooo

Increased cash flow

Rate of return X 0.17

Net annual savings $ 360,400

Yes, the southern region should be divided, as doing so will save the company $360,400 per year.

Average Cash Balance. Dane Companyâ€™s weekly average cash balances are:

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Week Average Cash Balance

1 $15,000

2 19,000

3 12,000

4 17,000

Total $63,000

(a) What is the monthly average cash balance? (6) Assuming an annual interest rate of 15

percent, what is the monthly rate of return earned on the average cash balance?

SOLUTl0N

-- -

$639000 $15,750

4

$15,750 X (0.15 + 12) = $196.88

(b)

Book Balance versus Bank Balance. Company P writes checks averaging $30,000per day that

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require 4 days to clear. By what amount will its book balance be less than its bank balance?

SOLUTl0N

$30,000 X 4 days = $120,000

Opportunity Cost of Not Taking Discount.What is the opportunity cost of not taking a discount

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when the terms are 2/20, net/45?

SOLUTION

discount percent 360 2 360

Opportunity cost -=29.4%

= X-=-

N

100 - discount percent 98 25

119

CHAP. 41 THE MANAGEMENT OF WORKING CAPITAL

Optimal Cash Tkansaction Size. Green Corporation anticipates a cash requirement of $1,000over

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a 1-month period. It is expected that cash will be paid uniformly. The annual interest rate is 24

percent. The transaction cost of each borrowing or withdrawal is $30. (a) What is the optimal

transaction size? ( b )What is the average cash balance?

SOLUTION

E

(a) The optimum transaction size is:

/g

JZ(30)o

C= = $1,732.05

= =

0.24 + 12"

(b) The average cash balance is:

0.24 annual interest rate

= 0.02

Monthly interest rate =

a

12 months

The Miller-Orr Model. Heavenly Company has experienced a stochastic demand for its product,

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which results in fluctuating cash balances randomly. The following information is supplied:

$100

Fixed cost of a securities transaction

$1,000

Variance of daily net cash flows

Daily interest rate on securities (6%/360) 0.000167

Determine the optimal cash balance, upper and lower limit of cash needed, and average cash

balance.

SOLUTION

The optimal cash balance, the upper limit of cash needed, and the average cash balance follow:

3 3( 100)( 1000)

= J4(0.000167)

= 3˜449,910,000,000= $7,663

The optimal cash balance is $7,663. The upper limit is $22,989 (3 X $7,663). The lower limit is zero. The

average cash balance is

($7,663 + $22,989) = $10,217.33

3

When the upper limit of $22,989 is reached, $15,326 of securities ($22,989 - $7,663) will be purchased to

bring you to the optimal cash balance of $7,663. When the lower limit of zero dollars is reached, $7,663 of

securities will be sold to again bring you to the optimal cash balance of $7,663.

41

.1 Date of Cash Receipt. The terms of sale are 3/20,net/45, May 1dating. What is the last date the

customer may pay in order to receive the discount?

SOLUTION

May 20.

4n Average Investment in Accounts Receivable. Milch Corporation sells on terms of net/90. Their

.

accounts receivable are on average 20 days past due. If annual credit sales are $800,000,what is

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