CHAPTER 19

Cash and Marketable
Securities Management
CHAPTER ORIENTATION
This chapter initiates our study of cash management, focusing on the cash flow process
and the reasons why a firm holds cash balances. Cash management systems are explored,
as is the topic of investing excess cash in marketable securities.

CHAPTER OUTLINE
I.

Why a company holds cash
A.

B.

II.

Sound cash management techniques are based on a thorough understanding
of the cash flow process.
1.

Cash holdings are increased from several external sources on an
irregular basis.

2.

Irregular cash outflows reduce the firm's cash balance.

3.

Other major sources of cash arising from internal operations occur
on a rather regular basis, i.e., accounts receivable collections.

Three motives for holding cash balances have been identified by Keynes.
1.

The transactions motive

2.

The precautionary motive

3.

The speculative motive

Cash management objectives and decisions
A.

B.

The risk return trade-off
1.

Strike an acceptable balance between holding too much cash and
holding too little cash.

2.


A large cash investment minimizes insolvency, but penalizes
profitability.

3.

A small cash investment frees excess balances for investment in
more profitable assets, which increase profitability.

The objectives
214


C.

D.
III.

1.

On-hand cash must be sufficient to meet disbursal needs.

2.

Idle cash balances must be reduced to a minimum.

The decisions
1.

How to speed up cash collections and slow down cash outflows?


2.

What should be the composition of the marketable securities
portfolio?

3.

How should the investment in liquid assets be split between actual
cash holdings and marketable securities?

Perspective on collection and disbursement procedures

Collection and disbursement procedures
A.

Cash acceleration and deceleration techniques revolve around the concept of
float.
1.

Mail float

2.

Processing float

3.

Transit float

4.


Disbursing float

B.

Float reduction can result in (l) usable funds that are released for company
use and (2) increased returns produced on these freed-up balances.

C.

Several techniques are available to improve the management of the firm's
cash inflows and may also provide for a reduction in float.
1.

2.

The lock-box arrangement expedites cash gathering.
a.

The objective is to reduce both mail and processing float.

b.

The procedure includes rental of a local post office box and
authorization of a local bank, in which a demand deposit
account (DDA) is maintained, to pick up remittances from
the box.

c.


The arrangement provides for (l) increased working cash, (2)
elimination of clerical functions, and (3) early knowledge of
dishonored checks.

d.

Added costs must be evaluated.

Pre-authorized checks (PACs) also speed up the conversion of
receipts into working cash.
a.

The objective is to reduce mail and processing float.

b.

A PAC (l) is created with the individual's legal authorization,
(2) resembles an ordinary check, and (3) does not contain the
signature of the person on whose account it is being drawn.

215


c.

3.

PAC systems are most useful to firms that regularly receive a
large volume of payments of a fixed amount from the same
customers.


Depository transfer checks (DTCs) are used in conjunction with
concentration banking.
Major objectives of using DTCs are (1) elimination of excess cash
balances held in several regional banks and (2) reduction of float.

4.

D.

IV.

Wire transfers offer the fastest method for moving funds between
commercial banks.
Two major communication facilities
accommodate wire transfers: (1) Bank Wire, and (2) Federal
Reserve Wire System.

Techniques used by firms that hope to improve the management of their cash
flow
1.

Zero balance accounts (ZBAs) permit centralized control, but also
allow the firm to maintain disbursing authority at the local level. The
major objective is to achieve better control over cash payments. It
might also increase disbursement float.

2.

Payable-through drafts (PTDs) have the physical appearance of

ordinary checks but they are drawn on and paid by the issuing firm
instead of the bank.
a.

The objective of a PTD system is to provide for effective
control of field-authorized payments.

b.

Stop payment orders can be initiated
considered inappropriate.

c.

Legal payment of individual drafts takes place after review
and approval of the drafts by the company. Disbursing float is
usually not increased by the use of drafts.

on any drafts

Electronic funds transfer systems (EFT) reduce transit, mail, and processing float.
A.

Transactions are immediately reflected on the books and bank accounts of
firms doing business.

B.

This ideal has not yet been fully reached.


C.

The purpose of the EFT is the elimination of the check as a method of
transferring funds.

D.

Perspective on evaluating costs.

216


V.

Evaluating the costs of cash management services
A.

Whether a cash management system will provide an economic benefit can
be evaluated by:
added costs = added benefits

B.

If the benefits exceed the costs, the system is economically feasible.

C.

On a per unit basis, this relationship can be expressed as follows:
P
where P


VI.

= (D) (S) (i)
= increase in per-check processing cost, if new system is
adopted

D

= days saved in the collection process

S

= average check size in dollars

i

= the daily, before-tax opportunity cost of carrying cash.

D.

The product of (D) x (S) x (i) must exceed P for the system to be beneficial
to the firm.

E.

Perspective on the marketable securities portfolio.

Composition of marketable securities portfolio
A.


B.

Five factors to consider when selecting a proper marketable securities mix
1.

Financial risk

2.

Interest rate risk

3.

Liquidity

4.

Taxability of interest income and capital gains

5.

Yield criterion

Marketable security alternatives
1.

2.

A Treasury bill is a direct obligation of the U.S. government.

a.

May be purchased in denominations of $1,000 and higher
($10,000, $15,000, $50,000, $100,000, $500,000, and
$1,000,000).

b.

Currently offered with maturities of 91, 182, and 365 days.

c.

Since Treasury bills are sold on a discount basis, the investor
does not receive an actual interest payment.

d.

The bills are considered risk-free and sell at lower yields than
other marketable securities of like maturity.

e.

Income from Treasury bills is subject to the federal income
tax and is taxed as ordinary income.

Federal agency securities represent debt obligations of corporations
and agencies that have been created to manage the various lending
programs of the U.S. government.
217



3.

4.

5.

6.

7.

IX.

Bankers' acceptances are drafts drawn on a specific bank by an
exporter in order to obtain payment for goods shipped to a customer
who maintains an account with that bank.
a.

Maturities run mostly from 30 to 180 days.

b.

Acceptances are sold on a discount basis.

c.

Income generated is fully taxable at all levels.

d.


Provide investors with a higher yield than do Treasury bills.

A negotiable certificate of deposit (CD) is a marketable receipt for
funds that have been deposited in a bank for a fixed time period at a
fixed interest rate.
a.

CDs are offered in denominations ranging from $25,000 to
$10,000,000

b.

Maturities range from 1 to 18 months.

c.

Yields are higher than those of Treasury bills.

d.

Income received is taxed at all governmental levels.

Commercial paper refers to short-term, unsecured promissory notes.
a.

Paper ranges from $5,000 up to $5,000,000.

b.

The notes are generally sold on a discount basis with

maturities ranging from 3 to 270 days.

c.

Paper has no active trading in a secondary market.

d.

Return received is taxable at all governmental levels.

Repurchase agreements involve the actual sale of securities by a
borrower to the lender, with a commitment on the part of the
borrower to repurchase the securities at the contract price plus a
stated interest charge.
a.

These agreements are usually executed in sizes of $500,000
or more.

b.

There is a specified maturity date or time period.

c.

Yields are higher than for Treasury bills and are taxable at all
governmental levels.

Money market mutual funds usually invest in a diversified portfolio
of short-term, high-grade debt instruments.

a.

Shares are sold to a large number of small investors.

b.

Funds offer a high degree of liquidity.

c.

Returns are usually taxable at all governmental levels.

Summary

218


ANSWERS TO
END-OF-CHAPTER QUESTIONS
19-1. The procedure by which funds generated from company activity are accommodated
(directed) through the firm from the time of their initial receipt until their ultimate
disposition. Over the long run, accounts receivable collections account for the
largest regular source of cash in the typical manufacturing company. Payment of
accounts payable, payroll expenses, and the distribution of income to the owners
(cash dividends) are the major forms of cash disbursal. Other sources of cash for a
company may include receipts from the sale of assets, assumption of additional
debt, issuance of new stock, or gains realized from investments. While these are
important sources of cash to a company, the proceeds are not available on a regular
basis. Major capital expenditure programs, new company acquisitions, and
inventory stockpiling are examples of irregular disbursals of cash outside the

normal course of everyday business.
19-2. The three classical motives for holding cash and near-cash balances are: (1) the
transactions motive; (2) the precautionary motive; (3) the speculative motive.
Transactions balances allow the firm to make payments that arise in the ordinary
course of doing business. Precautionary balances provide a buffer stock of liquid
assets that can be drawn down if unexpected demands for cash arise. Speculative
balances permit the economic unit to take advantage of future profit-making
situations.
19-3. Concentration banking involves the use of multiple cash collection centers and the
deposit of funds in regional banks located near the collection centers. Funds are
then transferred from the regional commercial banks to a concentration bank. A
concentration bank is one where the firm maintains a major cash disbursing
account. Concentration banking may permit the firm to: (1) operate with lower
levels of excess cash; (2) maintain more effective control over the firm's cash
resources;
(3) make prudent decisions concerning marketable securities
transactions. Moreover, concentration banking will reduce both mail float and
transit float.
19-4. The "regular" depository transfer check is a pre-printed form that is filled out and
mailed by a company employee in order to move demand deposit balances from one
bank to another. The automated depository transfer check (ADTC) eliminates the
mail delay associated with the "regular" depository transfer check. The deposit
information in this latter case is telephoned by a company employee to a regional
data collection center. The data collection center transmits the information to the
firm's concentration bank. Ordinarily, both of these systems are used in conjunction
with a concentration banking arrangement.
19-5. The firm which regularly receives a large volume of payments from the same
customers will find the pre-authorized check system a useful device. Common
examples are insurance companies, savings and loan associations, consumer credit
firms, leasing enterprises and charitable and religious organizations.

19-6. The firm must: (1) maintain adequate cash balances that will permit it to meet the
disbursal needs that occur in the course of doing business; (2) reduce idle cash
balances to a minimum.
219


19-7. (1)

Choosing among various methods available for speeding up cash receipts,
slowing down cash payments, and providing for more effective control over
cash outflows.

(2)

Splitting the firm's liquid asset holdings among cash and marketable
securities.

(3)

Choosing the appropriate marketable securities mix.

19-8. (1)

Mail float: this represents funds which are not usable to the firm because of
the time necessary for a customer's remittance check to travel through the
mails to a company collection center.

(2)

Processing float: this represents funds tied up due to the time needed for the

company to process the remittance checks and get them ready for deposit in
a demand deposit account.

(3)

Transit float: this represents funds tied up because of the time necessary for
a deposited check to clear through the commercial banking system and
become "good" funds to the firm.

(4)

Disbursing float: this refers to funds available in the firm's demand deposit
account due to the time needed for a payment check to clear through the
banking system.

19-9. In the context of cash management, financial risk is the uncertainty of future
returns from a security caused by possible changes in the financial capability of the
security-issuer to make future payments to the security-owner. This is sometimes
called default risk. On the other hand the uncertainty related to the expected
returns from a financial asset caused by changes in interest rates is called interest
rate risk.
19-10. Liquidity is the ability to change a security into cash. A money market instrument
that is highly liquid can be converted into cash quickly and at a price near its
prevailing market price.
19-11. Commercial paper
19-12. Bills--5.90%
Agencies--6.10%
Paper--6.25%
19-13. (1)


Maturity periods on repurchase agreements can be individually tailored to
the needs of the investor.

(2)

The price at which the repo will be liquidated is set at the time the contract
is finalized.

220


SOLUTIONS TO
END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A
19-1A.
Average daily float
[(Average daily float) x
invested
[($109,589)

Annual Revenues
Days in Year

=

=

$40,000,000
=
365


$109,589

(Number of days of float reduction)] = Amount that can be

x

(7)]

[(Amount that can be invested) x
forgone
[($767,123)

=

$767,123

Interest rate on investment)] = Annual interest

x

(.05)]

=

$38,358

Thus, the cost of the Healthy Herbal's current billing system is:
Annual interest forgone
Plus: Clerical costs

Cost of current system

$38,356
35,000
$73,356

And, the net annual gain from adoption of the proposed concentration banking system is:
Cost of current system
Less: cost of concentration banking system
Net annual gain from proposed system

$73,356
40,000
$33,356

19-2A.
Analysis of the two alternatives requires that the net earnings be computed for each
alternative for each of the specified time periods as follows:
Invest in Money Market Fund:
Cash
Available

Interest
Rate

Holding
Period

Annual
Earnings


$750,000
$750,000
$750,000
$750,000

0.05
0.05
0.05
0.05

1mo.
2 mo.
6 mo.
12 mo.

$3,125
6,250
18,750
37,500

Invest directly in marketable securities:
221

Annual
Cost
0
0
0
0


Net
Earnings
$3,125
6,250
18,750
37,500


Cash
Available

Interest
Rate

Holding
Period

Annual
Earnings

Annual
Cost

$750,000
$750,000
$750,000
$750,000

0.075

0.075
0.075
0.075

1mo.
2 mo.
6 mo.
12 mo.

$4,688
9,375
28,125
56,250

15000
15000
15000
15000

Net
Earnings
-$10,312
-5,625
13,125
41,250

Accordingly, a comparison of the net earnings of the two alternatives indicates the
following:
Money Market Fund
1 mo.

2 mo.
6 mo.
12 mo.

$3,125
6,250
18,750
37,500

Direct Investment
-$10,312
-5,625
13,125
41,250

Recommendation
Money Market Fund
Money Market Fund
Money Market Fund
Direct Investment

19-3A.
Annual collection = ($6,232,375) (12 regions) = $74,788,500
Daily collections = $74,788,500 / 365 = $204,900
Use of the lock-box system will reduce Marino Rug Company's float by 3 days according
to the study done by National Bank of Miami. The value of the float reduction is found by
presuming the freed funds will be added to the marketable securities portfolio and will earn
the 9.75% yield noted in the text of the problem. The gross annual savings from the system
are:
($204,900) (3) (.0975) = $59,933

The annual cost of operating the lock-box system is:
($325 per month) (12 regions) (12 months) = $46,800
The net annual savings are:
($59,933) - ($46,800) = $13,133
Marino's management should approve the use of the proposed lock-box system and,
thereby, save $13,133 per year.

222


19-4A.
(a)

The average accrued wages under the monthly payment system are:
4($675,000)
= $1,350,000
2
This means the firm has, on average, $1,012,500 (i.e., $1,350,000 $337,500) more to invest. This provides an annual return of ($1,012,500)
(.085) = $86,063. Therefore, Mac's Tennis Racket should move to the
monthly payment system since it will generate $86,063 - $50,775 = $35,288
in net annual savings.

(b)

Let r = the break-even rate of return on the near cash portfolio:
$1,012,500 (r) = $50,775
r = 5.01%
A reasonable margin of safety favoring adoption of the monthly payment
proposal is present.


19-5A.
(a)

Reduction in mail float:
(1.5 days) ($750,000) =
+ reduction in processing float:
(2.0 days) ($750,000) =
= Total Float Reduction

(b)

1,500,000
$2,625,000

The opportunity cost of maintaining the current banking arrangement is:
(.092) ($2,625,000) =

(c)

$1,125,000

$241,500

The average number of checks to be processed each day through the lockbox arrangement is:
Daily remittances
Average check size

=

$750,000

= 200 checks per day
$3,750

Now we can calculate the cost of the lock-box system on an annual basis as
follows:
(200 checks) ($0.35) (270 days) = $18,900
Next, we compute the cost of the automated depository transfer check
(ADTC) system. Second National Bank will not contribute to the cost of the
ADTC arrangement because it is the lead concentration bank and, thereby,
receives the transferred data. Thus, James Waller will be charged for six
ADTCs (or, three locations @ 2 checks each) each business day. The cost
of the ADTC system is:
(6 daily transfers) ($27 each) (270 days) = $43,740

223


The total cost of the proposed system will be:
Lock-box cost

$18,900

ADTC cost

43,740

Total cost
(d)

$62,640


Waller Nail Corp. should adopt the proposed system. The projected net
annual gain will be $178,860.
Projected return on freed balances
Less: Cost of new system
Net annual gain

$241,500
62,640
$178,860

19-6A. Initially, compute the firm's average remittance check size and daily opportunity
cost of carrying cash. The average check size is:
$40,000,000
= $2,666.67
15,000
The daily opportunity cost of carrying cash is:
.09
365

= .0002466 per day

Next, the days saved in the collection process can be evaluated according to this
format:
Added costs = Added benefits
or
P = (D) (S) (i)
$0.35 = (D) (2,666.67) (.0002466)
0.5322 days = D
We know Mountain Furniture will experience a financial gain if it adopts the lockbox system and, thereby, speeds up its collections by more than 0.5322 days.


224


Annual revenues
$890,000,000
=
Days in year
365

19-7A.

(sales per day) (assumed yield)
($2,438,356)
(0.096)
19-8A. (a)

=

=

$2,438,356 sales
per day
$234,082

First, it is necessary to compute Mustang's average remittance check size
and the daily opportunity cost of carrying cash. The average check size is:
$12,000,000
6,000


= $2,000 per check.

The daily opportunity cost of carrying cash is:
0.07
365

=

0.0001918 per day

Second, the days saved in the collection process can be evaluated according
to the general format of
Added Costs = Added Benefits
or
P = (D) (S) (i)
0.20 = (D) ($2,000) (0.0001918)
0.5214 days = D.
Therefore, Mustang Ski-Wear will experience a financial gain if it adopts the
lock-box system and speeds up its collections by more than 0.5214 days.
(b)

In this situation the daily opportunity cost of carrying cash is:
0.045
= 0.0001233 per day
365
For Mustang to break even should it choose to install the lock-box system,
the cash collections must be accelerated by 0.8110 days as follows:
$0.20 = (D) ($2,000) (0.0001233)
0.8110 days = D.


225


(c)

The break-even cash acceleration period of 0.8110 days is greater than the
0.5214 days found in part (a). This is due to the lower yield available on
near-cash assets (or 4.5 percent annually versus 7.0 percent). Since the
alternative rate of return on the freed-up balances is lower in the second
situation, more funds must be invested to cover the costs of operating the
lock-box system. The greater cash acceleration period generates this
increased level of required funds.

19-9A. The value of one day of processing float is:
$18,000,000
= $66,667
270
The annual savings at 8% are:
(2 days) ($66,667) (0.08) = $10,667
19-10A.
Annual collections = ($5,200,000) (12) = $62,400,000
Daily collections = $62,400,000/365 = $170,959
The opportunity cost of the mail and processing float is:
($170,959) (4.0) (0.09) = $61,545
19-11A.
This exercise attempts to illustrate that a change in the firm's accounts payable
policy can properly be viewed as a part of the overall problem of cash management.
Before evaluating the 45 day and 60 day payment alternatives it is necessary to
calculate the amount of purchases that are actually discounted and the value of the
annual purchase discount earned by Bradford Construction. These amounts are

calculated below:
Purchases discounted
($37,500,000 annual purchases) (0.25) = $9,375,000
Purchase discounts earned
($9,375,000) (0.03) = $281,250
with $281,250 in purchase discounts earned. Bradford actually pays:
($9,375,000) - ($281,250) = $9,093,750, 10 days after purchase.
The annual amount not discounted is ($37,500,000) - ($9,375,000) = $28,125,000.
We are now in a position to evaluate first the 45 day proposal and, second, the 60
day proposal.

226


45 day alternative:
(1)
(2)
Principal
Extra time
amount
available
$ 28,125,000
9,093,750

15 days
35 days

(3)
Interest
rate


(4) = (1) x (2) x (3)
Interest
earned

0.12 ÷ 365 =
$138,699
0.12 ÷ 365 =
104,640
Total added return $243,339

- $281,250 Lost discounts earned
+ 243,339 Total added return
$ 37,911 Loss to Bradford by stretching payables to 45 days.
60 day alternative:
(1)
Principal
amount

(2)
Extra time
available

$28,125,000
9,093,750

30 days
50 days

(3)

Interest
rate

(4) =(1)x(2)x(3)
Interest
earned

0.12 ÷ 365 =
$277,397
0.12 ÷ 365 =
149,486
Total added return $426,883

-$281,250 Lost discounts earned
+$426,883 Total added return
$145,633 Gained by Bradford by stretching payables to 60 days
Finally, we can evaluate the effect of the projected price increase to Bradford that is
associated with the 60 day alternative.
Price Increase:
$37,500,000 Purchases
.005
$

187,500 Price increase

$187,500 Price increase
-145,633 Net added return
$ 41,867 Loss to Bradford
Ultimately, none of the proposed courses of action would benefit the firm.


227


19-12A.
18

(a)

P =

∑

T =1

$80
$1,000
= $912.44
T +
(1.09)
(1.09)18

The bond can be sold for $912.44. This was developed as follows:
$80 (8.7556) + $1,000 (.21199) = $912.44
(b)

$1,000 - $912.44 = $87.56

(c)

First, we find the price of the 4-year bond, which now has 2 years remaining

to maturity:
2

P =

∑

T =1

$80
$1,000
+
= $982.41
(1.09)T
(1.09) 2

Then we can determine the expected capital loss on the shorter-term bond as
follows:
$1,000 - $982.41 = $17.59
The capital loss on the shorter-term bond is much less than that suffered on
the longer-term instrument.
(d)

Interest rate risk.

19-13A.The easiest way to visualize the appropriate responses to all three parts of this
problem is to calculate the income that would be generated if the entire $4,000,000
was invested in each separate maturity category. This is shown below:
1.
2.

3.
4.
5.
6.

Amount
$4,000,000
$4,000,000
$4,000,000
$4,000,000
$4,000,000
$4,000,000

Yield
(.062) 1/12
(.064) 2/12
(.065) 3/12
(.067) 4/12
(.069) 5/12
(.070) 6/12

Income
$ 20,667
$ 42,667
$ 65,000
$ 89,333
$115,000
$140,000

Brokerage

$10,000
$10,000
$10,000
$10,000
$10,000
$10,000

Net
$ 10,667
$ 32,667
$ 55,000
$ 79,333
$105,000
$130,000

From this table we can see that the $10,000 brokerage fee is exceeded by the
incremental return from the investment in all maturity categories. Since the
available yield rises with each successive increase in the maturity period,
investment in longer maturities increases return. Now, we can proceed to answer
the specific parts of this problem.
(a)
Return from investing:
$2,000,000 for three months
$32,500
$2,000,000 for six months
$70,000
- brokerage fee
$10,000
$92,500
By investing half of the excess for three months and half for six months the return

will be maximized at $92,500; this approach adheres to the wishes of the company
president.

228


(b)

Under this circumstance all $4,000,000 should be invested in securities with
maturity periods of six months. The added income will be $130,000.

(c)

This solution is developed from the table above:
(1)

20,667
6

=

$ 3,445

(2)

42,667
6

=


$ 7,111

(3)

65,000
6

=

$10,833

(4)

89,333
6

=

$14,889

(5)

115,000
6

=

$19,167

(6)


140,000
6

=

$23,333

Total
Brokerage fee
Net

78,778
-10,000
$68,778

19-14A.
(a)

The after-tax yield to Aggieland Fireworks on the BBB-rated bond is (0.09)
(1-0.46) = .0486 = 4.86%. Since the yield on the tax-exempt issue is
already stated on an after-tax basis, we can conclude the 5 1/2 percent return
on the municipal is preferable.

(b)

r =

r*
(1 − T)


r =

0.055
0.055
=
(1 − 0.46)
0.54

=

229

10.185%


SOLUTION TO INTEGRATIVE PROBLEM
1.

The amount of cash balances that will be freed if New Wave Surfing Stuff, Inc.
adopts the system proposed by the Bank of the U.S.:
Cash balances freed due to reduction in mail float:
[(Number of days eliminated)
[(3.5)

x

(Average daily cash remittances)]

x


($100,000)]

=

$350,000

Cash balances freed due to reduction in processing float:
[(Number of days eliminated)

x

(Average daily cash remittances)]

[(4)

x

($100,000)]

=

Total float reduction
2.

$750,000

Opportunity cost of maintaining the current banking arrangement:
(Forecast yield on marketable securities portfolio) x
=


(Total float reduction)

(Opportunity Cost--Interest)

[(.06)

x

Opportunity cost--interest

($750,000)]

= $45,000

$45,000

Opportunity cost--clerical expense

50,000

Total Opportunity cost
3.

$400,000

$95,000

Projected annual cost of operating the proposed system:
Average number of checks to be processed each day through the lock-box

arrangement:
Daily remittances
Average check size

=

$100,000
$1,000

=

100 checks

Resulting cost of lock-box system on an annual basis:
[(Average number of checks) x (Processing cost per check) x (Number of
business days per year)]
=
Cost
[(100) x

($0.25)x

(270)] =

$6,750

Next, the estimated cost of the ADTC system must be calculated. The Bank of the
U.S. will not contribute to the cost of the ADTC because it is the lead concentration
bank and thereby receives the transferred data. As a result, New Wave will be
charged for six ADTCs (three locations @ two checks each) each business day.

The ADTC system, therefore, costs:

230


[(No. of daily transfers) x (Cost per transfer) x (No. of business days per year)] =
Cost
[(6)

($25)

x

(270)]

=

$40,500

Accordingly, the total cost of the proposed system is:
Lock-box cost
ADTC cost
Total Cost
4.

$ 6,750
40,500
$47,250

The net annual gain associated with adopting the proposed system is:

Opportunity cost of current system [from "2" above]
Less: Total cost of new system [from "3" above]
Net annual gain (loss)

$95,000
47,250
$47,750

As a result, the analysis suggests the company should adopt the proposed cash
receipts acceleration system.

Solutions to Problem Set B
19-1B.
Annual Revenues
Days in Year

Average daily float =
[(Average daily float)
invested
[($219,178)

=

$80,000,000
365

x (No. of days of float reduction)]
x

(5)]


[(Amount that can be invested)
interest forgone
[($1,095,890) x

=
x

(.055)] =

= $219,178

= Amount that can be

$1,095,890
(Interest rate on investment)]

= Annual

$60,274

Thus, the cost of the Sprightly Step's current billing system is:
Annual interest forgone

$ 60,274

Plus: Clerical costs

50,000


Cost of current system

$110,274

And, the net annual gain from adoption of the proposed concentration banking system is:
Cost of current system
Less: cost of concentration banking system
Net annual gain from proposed system

231

$110,274
80,000
$ 30,274


19-2B.
Analysis of the two alternatives requires that the net earnings be computed for each
alternative for each of the specified time periods as follows:
Invest in Money Market Fund:
Cash
Available
Earnings
$1,100,000
$1,100,000
$1,100,000
$1,100,000

Interest
Rate


Holding
Period

Annual
Earnings

Annual
Cost

Net

0.055
0.055
0.055
0.055

1 mo.
2 mo.
6 mo.
12 mo.

$5,042
10,083
30,250
60,500

0
0
0

0

$5,042
10,083
30,250
60,500

Invest directly in marketable securities:
Cash
Available
$1,100,000
$1,100,000
$1,100,000
$1,100,000

Interest
Rate
0.08
0.08
0.08
0.08

Holding
Period
1 mo.
2 mo.
6 mo.
12 mo.

Annual

Earnings
$7,333
14,667
44,000
88,000

Annual
Cost
$15,000
15,000
15,000
15,000

Net
Earnings
-$7,667
- 333
29,000
73,000

Accordingly, a comparison of the net earnings of the two alternatives indicates the
following:
Money Market Fund
1 mo.
$5,042
2 mo.
10,083
6 mo.
30,250
12 mo.

60,500

Direct Investment
-$7,667
-333
29,000
73,000

19-3B.
(a)

Reduction in mail float:
(1.5 days) ($800,000) =

$1,200,000

+ reduction in processing float:
(2.0 days) ($800,000) =

1,600,000

= Total Float Reduction

$2,800,000

232

Recommendation
Money Market Fund
Money Market Fund

Money Market Fund
Direct Investment


(b)

The opportunity cost of maintaining the current banking arrangement is:
(.095) ($2,800,000) =

(c)

$266,000

The average number of checks to be processed each day through the lockbox arrangement is:
Daily remittances
$800,000
=
= 200 checks per day
Average check size
$4,000
Now we can calculate the cost of the lock-box system on an annual basis as
follows:
(200 checks) ($0.40) (270 days) = $21,600
Next, we compute the cost of the automated depository transfer check
(ADTC) system. First Citizens Bank will not contribute to the cost of the
ADTC arrangement because it is the lead concentration bank and, thereby,
receives the transferred data. Thus, Charles Kobrin will be charged for six
ADTCs (or, three locations @ 2 checks each) each business day. The cost
of the ADTC system is:
(6 daily transfers) ($30 each) (270 days) = $48,600

The total cost of the proposed system will be:
Lock-box cost
ADTC cost
Total cost

(d)

$21,600
48,600
$70,200

Kobrin Door & Glass, Inc. should adopt the proposed system. The projected
net annual gain will be $195,800.
Projected return on freed balances
Less: Cost of new system
Net annual gain

19-4B.

$266,000
(70,200)
$195,800

Annual collections = $10,000,000 (5 regions) = $50,000,000
Daily collections = $50,000,000/365 = $136,986
The value of the 3.0 days' float reduction is found by presuming the freed balances
will be added to the marketable securities portfolio and will earn 11.0% (see text of
problem). The gross annual savings from the system are:
($136,986) (3.0 days) (.11) = $45,205


233


The annual cost of operating the lock-box system is:
($600 per month) (5 regions) (12 months) = $36,000
The net annual savings are:

$45,205
- 36,000
$9,205

Savings

The data indicate that Regency Components should adopt the lock-box system.
19-5B. Initially, compute the firm's average remittance check size and daily opportunity
cost of carrying cash. The average check size is:
$50,000,000
20,000

= $2,500

The daily opportunity cost of carrying cash is:
.09
= .0002466 per day
365
Next, the days saved in the collection process can be evaluated according to this
format:
Added costs = Added benefits
or
P = (D) (S) (i)

$0.37 = (D) (2,500) (.0002466)
0.6002 days = D
We know Hallmark Technology will experience a financial gain if it adopts the
lock-box system and, thereby, speeds up its collections by more than 0.6002 days.
19-6B.

Annual revenues
$900,000,000
=
Days in year
365

=

2,465,753 sales
per day

(sales per day) (assumed yield)
= $234,247
($2,465,753)
(0.095)
19-7B. (a)

First, it is necessary to compute Colorado Comm's average remittance check
size and the daily opportunity cost of carrying cash. The average check size
is:
$10,000,000
7,000

= $1,429 per check.


234


The daily opportunity cost of carrying cash is:
0.07
365

= 0.0001918 per day

Second, the days saved in the collection process can be evaluated according
to the general format of
Added Costs = Added Benefits
or
P = (D) (S) (i)
0.30 = (D) ($1,429) (0.0001918)
1.0946 days = D
Therefore, Colorado Comm will experience a financial gain if it adopts the
lock-box system and speeds up its collections by more than 1.0946 days.
(b)

In this situation the daily opportunity cost of carrying cash is:
0.045
= 0.0001233 per day
365
For Colorado Comm to break even should it choose to install the lock-box
system, the cash collections must be accelerated by 1.7027 days as follows:
$0.30 = (D) ($1,429) (0.0001233)
1.7027 days = D


(c)

The break-even cash acceleration period of 1.7027 days is greater than the
1.0946 days found in part (a). This is due to the lower yield available on
near-cash assets (or 4.5 percent annually versus 7.0 percent). Since the
alternative rate of return on the freed-up balances is lower in the second
situation, more funds must be invested to cover the costs of operating the
lock-box system. The greater cash acceleration period generates this
increased level of required funds.

19-8B.
The value of one day of processing float is:
$17,000,000
270

= $62,963

The annual savings at 9% are:
(2 days) ($62,963) (0.09) = $11,333

235


19-9B. (a)

The average accrued wages under the monthly payment system are:
4($500,000)
2

= $1,000,000


This means that the firm has, on the average, $750,000 (i.e., $1,000,000 $250,000) more to invest. This provides an annual return of ($750,000)
(0.08) = $60,000. Therefore, Katz Jewelers should move to the monthly
payment system since it will generate $60,000 - $40,000 = $20,000 in net
annual savings.
(b)

Let r = the break-even rate of return on the near-cash portfolio:
$750,000

(r) = $40,000
r

=

5.33%

A reasonable margin of safety favoring adoption of the monthly payment
proposal is present.
19-10B.
Annual collections = ($5,000,000) (10) = $50,000,000
Daily collections = $50,000,000/365 = $136,986
The opportunity cost of the mail and processing float is:
($136,986) (4.0) (0.09) = $49,315
19-11B.
This exercise attempts to illustrate that a change in the firm's accounts payable
policy can properly be viewed as a part of the overall problem of cash management.
Before evaluating the 45 day and 60 day payment alternatives it is necessary to
calculate the amount of purchases that are actually discounted and the value of the
annual purchase discount earned by Meadowbrook. These amounts are calculated

below:
Purchases discounted
($40,000,000 annual purchases) (0.25) = $10,000,000
Purchase discounts earned
($10,000,000) (0.03) = $300,000
with $300,000 in purchase discounts earned. Meadowbrook actually pays:
($10,000,000) - ($300,000) = $9,700,000, 10 days after purchase.
The annual amount not discounted is ($40,000,000) - ($10,000,000) =
$30,000,000.
We are now in a position to evaluate first the 45 day proposal and, second, the 60
day proposal.
236


45 day alternative:
(1)
Principal
amount

(2)
Extra time
available

$30,000,000
9,700,000
- $300,000
+ 237,931
- $ 62,069

15 days

35 days

(3)
Interest
rate

(4) = (1) x (2) x (3)
Interest
earned

0.11 ÷ 365 =
$135,616
0.11 ÷ 365 =
102,315
Total added return $237,931

Lost discounts earned
Total added return
Loss to Meadowbrook by stretching payables to 45 days.

60 day alternative:
(1)
Principal
amount
$30,000,000
9,700,000

(2)
Extra time
available

30 days
50 days

(3)
Interest
rate

(4) =(1)x(2)x(3)
Interest
earned

0.11 ÷ 365
=
$271,233
0.11 ÷ 365
=
146,164
Total added return $417,397

-$300,000 Lost discounts earned
+$417,397 Total added return
$117,397 Gained by Meadowbrook by stretching payables to 60 days
Finally, we can evaluate the effect of the projected price increase to Meadowbrook
that is associated with the 60 day alternative.
Price Increase:
$40,000,000 Purchases
.005
$ 200,000 Price increase
$200,000 Price increase
-117,397 Net added return

-$ 82,603 Loss to Meadowbrook
Ultimately, none of the proposed courses of action would benefit the firm.

237


19-12B.
(a)

P =

18 $80
$1,000
∑
= $912.44
T +
(1.09)18
T = 1 (1.09)

The bond can be sold for $912.44. This was developed as follows:
$80 (8.7556) + $1,000 (.21199) = $912.44
(b)

$1,000 - $912.44 = $87.56

(c)

First, we find the price of the 4-year bond, which now has 2 years remaining
to maturity:
P =


2
$1,000
$80
∑
= $982.41
T +
(1.09) 2
T = 1 (1.09)

Then we can determine the expected capital loss on the shorter-term bond as
follows:
$1,000 - $982.41 = $17.59
The capital loss on the shorter-term bond is much less than that suffered on
the longer-term instrument.
(d)

Interest rate risk.

19-13B.
The easiest way to visualize the appropriate responses to all three parts of this
problem is to calculate the income that would be generated if the entire $3,500,000
was invested in each separate maturity category. This is shown below:
1.
2.
3.
4.
5.
6.


Amount
$3,500,000
$3,500,000
$3,500,000
$3,500,000
$3,500,000
$3,500,000

Yield
(.062) 1/12
(.064) 2/12
(.065) 3/12
(.067) 4/12
(.069) 5/12
(.070) 6/12

Income
$ 18,083
$ 37,333
$ 56,875
$ 78,167
$100,625
$122,500

Brokerage
$15,000
$15,000
$15,000
$15,000
$15,000

$15,000

Net
$ 3,083
$ 22,333
$ 41,875
$ 63,167
$85,625
$107,500

From this table we can see that the $15,000 brokerage fee is exceeded by the
incremental return from the investment in all maturity categories. Since the
available yield rises with each successive increase in the maturity period,
investment in longer maturities increases return. Now, we can proceed to answer
the specific parts of this problem.

238