chapter 19 im 10th ed

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CHAPTER 19

Cash and MarketableSecurities Management

CHAPTER ORIENTATION

This chapter initiates our study of cash management, focusing on the cash flow process andthe reasons why a firm holds cash balances. Cash management systems are explored, as is thetopic of investing excess cash in marketable securities.

CHAPTER OT!INE

I. Why a company holds cash

A. ound cash management techni!ues are based on a thorough understanding of the cash flow process.

". Cash holdings are increased from several external sources on anirregular basis.

#. Irregular cash outflows reduce the firm$s cash balance.

%. &ther ma'or sources of cash arising from internal operations occur ona rather regular basis, i.e., accounts receivable collections.

(. Three motives for holding cash balances have been identified by )eynes.

". The transactions motive

#. The precautionary motive

%. The speculative motive

II. Cash management ob'ectives and decisions

A. The risk return trade*off

". trike an acceptable balance between holding too much cash andholding too little cash.

#. A large cash investment minimi+es insolvency, but penali+es profitability.

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

(. The ob'ectives

#"



". &n*hand cash must be sufficient to meet disbursal needs.

#. Idle cash balances must be reduced to a minimum.

C. The decisions

". -ow to speed up cash collections and slow down cash outflows

#. What should be the composition of the marketable securities portfolio

%. -ow should the investment in li!uid assets be split between actual cashholdings and marketable securities

/. 0erspective on collection and disbursement procedures

III. Collection and disbursement procedures

A. Cash acceleration and deceleration techni!ues revolve around the concept of float.

". 1ail float

#. 0rocessing float

%. Transit float

. /isbursing float

(. 2loat reduction can result in 3l4 usable funds that are released for companyuse and 3#4 increased returns produced on these freed*up balances.

C. everal techni!ues are available to improve the management of the firm$s cashinflows and may also provide for a reduction in float.

". The lock*box arrangement expedites cash gathering.

a. The ob'ective is to reduce both mail and processing float.

b. The procedure includes rental of a local post office box and

authori+ation of a local bank, in which a demand depositaccount 3//A4 is maintained, to pick up remittances from the box.

c. The arrangement provides for 3l4 increased working cash, 3#4elimination of clerical functions, and 3%4 early knowledge of dishonored checks.

d. Added costs must be evaluated.

#. 0re*authori+ed checks 30ACs4 also speed up the conversion of receiptsinto working cash.

a. The ob'ective is to reduce mail and processing float. b. A 0AC 3l4 is created with the individual$s legal authori+ation,

3#4 resembles an ordinary check, and 3%4 does not contain thesignature of the person on whose account it is being drawn.

c. 0AC systems are most useful to firms that regularly receive alarge volume of payments of a fixed amount from the samecustomers.

#"5



%. /epository transfer checks 3/TCs4 are used in con'unction withconcentration banking.

1a'or ob'ectives of using /TCs are 3"4 elimination of excess cash balances held in several regional banks and 3#4 reduction of float.

. Wire transfers offer the fastest method for moving funds betweencommercial banks. Two ma'or communication facilities accommodatewire transfers6 3"4 (ank Wire, and 3#4 2ederal 7eserve Wire ystem.

/. Techni!ues used by firms that hope to improve the management of their cashflow

". 8ero balance accounts 38(As4 permit centrali+ed control, but alsoallow the firm to maintain disbursing authority at the local level. Thema'or ob'ective is to achieve better control over cash payments. Itmight also increase disbursement float.

#. 0ayable*through drafts 30T/s4 have the physical appearance of ordinary checks but they are drawn on and paid by the issuing firminstead of the bank.

a. The ob'ective of a 0T/ system is to provide for effectivecontrol of field*authori+ed payments.

b. top payment orders can be initiated on any drafts consideredinappropriate.

c. 9egal payment of individual drafts takes place after review andapproval of the drafts by the company. /isbursing float isusually not increased by the use of drafts.

I:. ;lectronic funds transfer systems 3;2T4 reduce transit, mail, and processing float.

A. Transactions are immediately reflected on the books and bank accounts of

firms doing business.

(. This ideal has not yet been fully reached.

C. The purpose of the ;2T is the elimination of the check as a method of transferring funds.

/. 0erspective on evaluating costs.

#"<



:. ;valuating the costs of cash management services

A. Whether a cash management system will provide an economic benefit can beevaluated by6

added costs = added benefits

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

C. &n a per unit basis, this relationship can be expressed as follows6

0 = 3/4 34 3i4

where 0 = increase in per*check processing cost, if new system is adopted

/ = days saved in the collection process

= average check si+e in dollars

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

/. The product of 3/4 x 34 x 3i4 must exceed 0 for the system to be beneficial tothe firm.

;. 0erspective on the marketable securities portfolio.

:I. Composition of marketable securities portfolio

A. 2ive factors to consider when selecting a proper marketable securities mix

". 2inancial risk

#. Interest rate risk

%. 9i!uidity

. Taxability of interest income and capital gains

5. >ield criterion

(. 1arketable security alternatives

". A Treasury bill is a direct obligation of the ?.. government.

a. 1ay be purchased in denominations of @", and higher 3@",, @"5,, @5,, @",, @5,, and@",,4.

b. Currently offered with maturities of B", "#, and %<5 days.

c. ince 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 thanother marketable securities of like maturity.

e. Income from Treasury bills is sub'ect to the federal income taxand is taxed as ordinary income.

#. 2ederal agency securities represent debt obligations of corporationsand agencies that have been created to manage the various lending programs of the ?.. government.

#"D



%. (ankers$ acceptances are drafts drawn on a specific bank by anexporter in order to obtain payment for goods shipped to a customer who maintains an account with that bank.

a. 1aturities run mostly from % to " days.

b. Acceptances are sold on a discount basis.

c. Income generated is fully taxable at all levels.d. 0rovide investors with a higher yield than do Treasury bills.

. A negotiable certificate of deposit 3C/4 is a marketable receipt for funds that have been deposited in a bank for a fixed time period at afixed interest rate.

a. C/s are offered in denominations ranging from @#5, to@",,

b. 1aturities range from " to " months.

c. >ields are higher than those of Treasury bills.

d. Income received is taxed at all governmental levels.

5. Commercial paper refers to short*term, unsecured promissory notes.

a. 0aper ranges from @5, up to @5,,.

b. The notes are generally sold on a discount basis with maturitiesranging from % to #D days.

c. 0aper has no active trading in a secondary market.

d. 7eturn received is taxable at all governmental levels.

<. 7epurchase 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 interestcharge.

a. These agreements are usually executed in si+es of @5, or more.

b. There is a specified maturity date or time period.

c. >ields are higher than for Treasury bills and are taxable at allgovernmental levels.

D. 1oney market mutual funds usually invest in a diversified portfolio of short*term, high*grade debt instruments.

a. hares are sold to a large number of small investors.

b. 2unds offer a high degree of li!uidity.

c. 7eturns are usually taxable at all governmental levels.

IE. ummary

#"



"B*D. 3"4 Choosing among various methods available for speeding up cash receipts,slowing down cash payments, and providing for more effective control over cash outflows.

3#4 plitting the firm$s li!uid asset holdings among cash and marketable securities.

3%4 Choosing the appropriate marketable securities mix.

"B*. 3"4 1ail float6 this represents funds which are not usable to the firm because of the time necessary for a customer$s remittance check to travel through themails to a company collection center.

3#4 0rocessing float6 this represents funds tied up due to the time needed for thecompany to process the remittance checks and get them ready for deposit in ademand deposit account.

3%4 Transit float6 this represents funds tied up because of the time necessary for adeposited check to clear through the commercial banking system and becomeGgoodG funds to the firm.

34 /isbursing float6 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.

"B*B. In the context of cash management, financial risk is the uncertainty of future returnsfrom 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 calleddefault risk. &n the other hand the uncertainty related to the expected returns from afinancial asset caused by changes in interest rates is called interest rate risk.

"B*". 9i!uidity is the ability to change a security into cash. A money market instrument thatis highly li!uid can be converted into cash !uickly and at a price near its prevailingmarket price.

"B*"". Commercial paper "B*"#. (ills**5.BH

Agencies**<."H

0aper**<.#5H

"B*"%. 3"4 1aturity periods on repurchase agreements can be individually tailored to theneeds of the investor.

3#4 The price at which the repo will be li!uidated is set at the time the contract isfinali+ed.

##



SO!TIONS TOEN#$O%$CHAPTER PRO'!EMS

olutions to 0roblem et A

"B*"A.

Average daily float =>ear in/ays

7evenuesAnnual=

%<5

AAA,AAA,A@=

@"B,5B

3Average daily float4 x 3Jumber of days of float reduction4K = Amount that can beinvested

3@"B,5B4 x 3D4K = @D<D,"#%

3Amount that can be invested4 x Interest rate on investment4K = Annual interest

forgone

3@D<D,"#%4 x 3.54K = @%,%5

Thus, the cost of the -ealthy -erbal$s current billing system is6

Annual interest forgone @%,%5<0lus6 Clerical costs %5,Cost of current system @D%,%5<

And, the net annual gain from adoption of the proposed concentration banking system is6

Cost of current system @D%,%5<9ess6 cost of concentration banking system , Jet annual gain from proposed system @%%,%5<

"B*#A.

Analysis of the two alternatives re!uires that the net earnings be computed for eachalternative for each of the specified time periods as follows6

Invest in 1oney 1arket 2und6

Cash Interest -olding Annual Annual Jet

Available 7ate 0eriod ;arnings Cost ;arnings

@D5, .5 "mo. @%,"#5 @%,"#5@D5, .5 # mo. <,#5 <,#5@D5, .5 < mo. ",D5 ",D5@D5, .5 "# mo. %D,5 %D,5

##"



Invest directly in marketable securities6

Cash Interest -olding Annual Annual JetAvailable 7ate 0eriod ;arnings Cost ;arnings

@D5, .D5 "mo. @,< "5 *@",%"#

@D5, .D5 # mo. B,%D5 "5 *5,<#5@D5, .D5 < mo. #,"#5 "5 "%,"#5@D5, .D5 "# mo. 5<,#5 "5 ",#5

Accordingly, a comparison of the net earnings of the two alternatives indicates the following6

1oney 1arket 2und /irect Investment 7ecommendation

" mo. @%,"#5 *@",%"# 1oney 1arket 2und# mo. <,#5 *5,<#5 1oney 1arket 2und

< mo. ",D5 "%,"#5 1oney 1arket 2und"# mo. %D,5 ",#5 /irect Investment

"B*%A.

Annual collection = 3@<,#%#,%D54 3"# regions4 = @D,D,5

/aily collections = @D,D,5 L %<5 = @#,B

?se of the lock*box system will reduce 1arino 7ug Company$s float by % days according tothe study done by Jational (ank of 1iami. The value of the float reduction is found by

presuming the freed funds will be added to the marketable securities portfolio and will earnthe B.D5H yield noted in the text of the problem. The gross annual savings from the systemare6

3@#,B4 3%4 3.BD54 = @5B,B%%

The annual cost of operating the lock*box system is6

3@%#5 per month4 3"# regions4 3"# months4 = @<,

The net annual savings are6

3@5B,B%%4 * 3@<,4 = @"%,"%%

1arino$s management should approve the use of the proposed lock*box system and, thereby,save @"%,"%% per year.

###



"B*A.3a4 The average accrued wages under the monthly payment system are6

#

4,<D53@ = @",%5,

This means the firm has, on average, @","#,5 3i.e., @",%5, * @%%D,54more to invest. This provides an annual return of 3@","#,54 3.54 =@<,<%. Therefore, 1ac$s Tennis 7acket should move to the monthly payment system since it will generate @<,<% * @5,DD5 = @%5,# in netannual savings.

3b4 9et r = the break*even rate of return on the near cash portfolio6

@","#,5 3r4 = @5,DD5

r = 5."H

A reasonable margin of safety favoring adoption of the monthly payment

proposal is present.

"B*5A.3a4 7eduction in mail float6

3".5 days4 3@D5,4 = @","#5,M reduction in processing float63#. days4 3@D5,4 = ",5,= Total 2loat 7eduction @#,<#5,

3b4 The opportunity cost of maintaining the current banking arrangement is6

3.B#4 3@#,<#5,4 = @#",5

3c4 The average number of checks to be processed each day through the lock*boxarrangement is6

si+echeckAverage

sremittance/aily=

D5A,%@

AAA,D5A@ = # checks per day

Jow we can calculate the cost of the lock*box system on an annual basis asfollows6

3# checks4 3@.%54 3#D days4 = @",B

Jext, we compute the cost of the automated depository transfer check 3A/TC4 system. econd Jational (ank will not contribute to the cost of theA/TC arrangement because it is the lead concentration bank and, thereby,receives the transferred data. Thus, Names Waller will be charged for sixA/TCs 3or, three locations O # checks each4 each business day. The cost of the A/TC system is6

3< daily transfers4 3@#D each4 3#D days4 = @%,D

##%



The total cost of the proposed system will be6

9ock*box cost @",B

A/TC cost %,D

Total cost @<#,<

3d4 Waller Jail Corp. should adopt the proposed system. The pro'ected netannual gain will be @"D,<.

0ro'ected return on freed balances @#",5

9ess6 Cost of new system <#,<

Jet annual gain @"D,<

"B*<A. Initially, compute the firm$s average remittance check si+e and daily opportunity costof carrying cash. The average check si+e is6

AAA,"5

AAA,AAA,A@ = @#,<<<.<D

The daily opportunity cost of carrying cash is6

%<5

AB. = .#<< per day

Jext, the days saved in the collection process can be evaluated according to thisformat6

Added costs = Added benefits

or

0 = 3/4 34 3i4

@.%5 = 3/4 3#,<<<.<D4 3.#<<4

.5%## days = /

We know 1ountain 2urniture will experience a financial gain if it adopts the lock*box

system and, thereby, speeds up its collections by more than .5%## days.

##



"B*DA.year in/ays

revenuesAnnual =

%<5

,,CB@=

day persales@#,%C,%5<

3A.AB<4yield43assumed

<43@#,%C,%5 day4 per3sales

= @#%,#

"B*A. 3a4 2irst, it is necessary to compute 1ustang$s average remittance check si+e andthe daily opportunity cost of carrying cash. The average check si+e is6

AAA,<

AAA,AAA,"#@ = @#, per check.


%<5

AD.A = ."B" per day

econd, the days saved in the collection process can be evaluated according tothe general format of

Added Costs = Added (enefits

or

0 = 3/4 34 3i4

.# = 3/4 3@#,4 3."B"4

.5#" days = /.

Therefore, 1ustang ki*Wear will experience a financial gain if it adopts thelock*box system and speeds up its collections by more than .5#" days.

3b4 In this situation the daily opportunity cost of carrying cash is6

%<5

A5.A = ."#%% per day

2or 1ustang to break even should it choose to install the lock*box system, thecash collections must be accelerated by ."" days as follows6

@.# = 3/4 3@#,4 3."#%%4

."" days = /.

##5



3c4 The break*even cash acceleration period of ."" days is greater than the.5#" days found in part 3a4. This is due to the lower yield available on near*cash assets 3or .5 percent annually versus D. percent4. ince the alternativerate of return on the freed*up balances is lower in the second situation, morefunds must be invested to cover the costs of operating the lock*box system.The greater cash acceleration period generates this increased level of re!uiredfunds.

"B*BA. The value of one day of processing float is6

#DA

AAA,AAA,"C@ = @<<,<<D

The annual savings at H are6

3# days4 3@<<,<<D4 3.4 = @",<<D

"B*"A.

Annual collections = 3@5,#,4 3"#4 = @<#,,

/aily collections = @<#,,L%<5 = @"D,B5B

The opportunity cost of the mail and processing float is6

3@"D,B5B4 3.4 3.B4 = @<",55

"B*""A.

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. (eforeevaluating the 5 day and < day payment alternatives it is necessary to calculate theamount of purchases that are actually discounted and the value of the annual purchasediscount earned by (radford Construction. These amounts are calculated below6

0urchases discounted3@%D,5, annual purchases4 3.#54 = @B,%D5,

0urchase discounts earned3@B,%D5,4 3.%4 = @#",#5

with @#",#5 in purchase discounts earned. (radford actually pays6

3@B,%D5,4 * 3@#",#54 = @B,B%,D5, " days after purchase.

The annual amount not discounted is 3@%D,5,4 * 3@B,%D5,4 = @#,"#5,.

We are now in a position to evaluate first the 5 day proposal and, second, the < day proposal.

5 day alternative6

##<



3"4 3#4 3%4 34 = 3"4 x 3#4 x 3%40rincipal ;xtra time Interest Interestamount available rate earned

@ #,"#5, "5 days ."# P %<5 = @"%,<BB B,B%,D5 %5 days ."# P %<5 = ",<

Total added return @#%,%%B

* @#",#5 9ost discounts earned

M #%,%%B Total added return

@ %D,B"" 9oss to (radford by stretching payables to 5 days.

< day alternative6

3"4 3#4 3%4 34 =3"4x3#4x3%40rincipal ;xtra time Interest Interestamount available rate earned

@#,"#5, % days ."# P %<5 = @#DD,%BD B,B%,D5 5 days ."# P %<5 = "B,<

Total added return @#<,%

*@#",#5 9ost discounts earned

M@#<,% Total added return

@"5,<%% Qained by (radford by stretching payables to < days

2inally, we can evaluate the effect of the pro'ected price increase to (radford that is

associated with the < day alternative.

0rice Increase6

@%D,5, 0urchases

.5

@ "D,5 0rice increase

@"D,5 0rice increase

*"5,<%% Jet added return

@ ",<D 9oss to (radford

?ltimately, none of the proposed courses of action would benefit the firm.

##D



"B*"#A.

3a4 0 = T

"C

"T 3".AB4

@CA ∑

=

M "C4AB."3

AAA,"@ = @B"#.

The bond can be sold for @B"#.. This was developed as follows6

@ 3.D55<4 M @", 3.#""BB4 = @B"#.3b4 @", * @B"#. = @D.5<

3c4 2irst, we find the price of the *year bond, which now has # years remaining tomaturity6

0 = T

#

"T 3".AB4

@CA ∑

=

M #4AB."3

AAA,"@ = @B#."

Then we can determine the expected capital loss on the shorter*term bond asfollows6

@", * @B#." = @"D.5B

The capital loss on the shorter*term bond is much less than that suffered on thelonger*term instrument.

3d4 Interest rate risk.

"B*"%A.The easiest way to visuali+e the appropriate responses to all three parts of this problem is to calculate the income that would be generated if the entire @,,was invested in each separate maturity category. This is shown below6

Amount >ield Income (rokerage Jet". @,, 3.<#4 "L"# @ #,<<D @", @ ",<<D#. @,, 3.<4 #L"# @ #,<<D @", @ %#,<<D

%. @,, 3.<54 %L"# @ <5, @", @ 55,. @,, 3.<D4 L"# @ B,%%% @", @ DB,%%%5. @,, 3.<B4 5L"# @""5, @", @"5,<. @,, 3.D4 <L"# @", @", @"%,

2rom this table we can see that the @", brokerage fee is exceeded by theincremental return from the investment in all maturity categories. ince the availableyield rises with each successive increase in the maturity period, investment in longer maturities increases return. Jow, we can proceed to answer the specific parts of this problem.

3a4 7eturn from investing6

@#,, for three months @%#,5

@#,, for six months @D, * brokerage fee @",

@B#,5

(y investing half of the excess for three months and half for six months the return will be maximi+ed at @B#,5F this approach adheres to the wishes of the company president.

##



3b4 ?nder this circumstance all @,, should be invested in securities withmaturity periods of six months. The added income will be @"%,.

3c4 This solution is developed from the table above6

3"4<

<<D,#= @ %,5

3#4<

<<D,#= @ D,"""

3%4<

AAA,<5= @",%%

34<

%%%,CB= @",B

354<

AAA,""5= @"B,"<D

3<4<AAA,"A = @#%,%%%

Total D,DD(rokerage fee *", Jet @<,DD

"B*"A.

3a4 The after*tax yield to Aggieland 2ireworks on the (((*rated bond is 3.B43"*.<4 = .< = .<H. ince the yield on the tax*exempt issue isalready stated on an after*tax basis, we can conclude the 5 "L# percent return

on the municipal is preferable.

3b4 r =T43"

Rr

−

r =4<.A"3

A55.A

− =

5.A

A55.A = "."5H

##B



SO!TION TO INTE(RATI)E PRO'!EM

". The amount of cash balances that will be freed if Jew Wave urfing tuff, Inc. adoptsthe system proposed by the (ank of the ?..6

Cash balances freed due to reduction in mail float6

3Jumber of days eliminated4 x 3Average daily cash remittances4K3%.54 x 3@",4K = @%5,

Cash balances freed due to reduction in processing float6

3Jumber of days eliminated4 x 3Average daily cash remittances4K

34 x 3@",4K = @,

Total float reduction @D5,

#. &pportunity cost of maintaining the current banking arrangement6

32orecast yield on marketable securities portfolio4 x 3Total float reduction4

= 3&pportunity Cost**Interest4

3.<4 x 3@D5,4K = @5,

&pportunity cost**interest @5,

&pportunity cost**clerical expense 5,

Total &pportunity cost @B5,

%. 0ro'ected annual cost of operating the proposed system6

Average number of checks to be processed each day through the lock*boxarrangement6

si+echeckAverage

sremittance/aily=

AAA,"@

AAA,"AA@= " checks

7esulting cost of lock*box system on an annual basis6

3Average number of checks4 x 30rocessing cost per check4 x 3Jumber of business days per year4K = Cost

3"4 x 3@.#54x 3#D4K = @<,D5

Jext, the estimated cost of the A/TC system must be calculated. The (ank of the?.. will not contribute to the cost of the A/TC because it is the lead concentration bank and thereby receives the transferred data. As a result, Jew Wave will becharged for six A/TCs 3three locations O two checks each4 each business day. TheA/TC system, therefore, costs6

#%



3Jo. of daily transfers4 x 3Cost per transfer4 x 3Jo. of business days per year4K =Cost

3<4 3@#54 x 3#D4K = @,5

Accordingly, the total cost of the proposed system is6

9ock*box cost @ <,D5

A/TC cost ,5

Total Cost @D,#5

. The net annual gain associated with adopting the proposed system is6

&pportunity cost of current system from G#G aboveK @B5,

9ess6 Total cost of new system from G%G aboveK D,#5

Jet annual gain 3loss4 @D,D5

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

olutions to 0roblem et (

"B*"(.

Average daily float =>ear in/ays

7evenuesAnnual=

%<5

AAA,AAA,CA@= @#"B,"D

3Average daily float4 x 3Jo. of days of float reduction4K = Amount that can beinvested

3@#"B,"D4 x 354K = @",B5,B

3Amount that can be invested4 x 3Interest rate on investment4K = Annualinterest forgone

3@",B5,B4 x 3.554K = @<,#D

Thus, the cost of the prightly tep$s current billing system is6

Annual interest forgone @ <,#D

0lus6 Clerical costs 5,

Cost of current system @"",#D

And, the net annual gain from adoption of the proposed concentration banking system is6

Cost of current system @"",#D

9ess6 cost of concentration banking system ,

Jet annual gain from proposed system @ %,#D

#%"



"B*#(.

Analysis of the two alternatives re!uires that the net earnings be computed for eachalternative for each of the specified time periods as follows6Invest in 1oney 1arket 2und6


@",", .55 " mo. @5,# @5,#

@",", .55 # mo. ",% ",%

@",", .55 < mo. %,#5 %,#5

@",", .55 "# mo. <,5 <,5

Invest directly in marketable securities6


@",", . " mo. @D,%%% @"5, *@D,<<D@",", . # mo. ",<<D "5, * %%%

@",", . < mo. , "5, #B,

@",", . "# mo. , "5, D%,

Accordingly, a comparison of the net earnings of the two alternatives indicates the following6

1oney 1arket 2und /irect Investment 7ecommendation

" mo. @5,# *@D,<<D 1oney 1arket 2und

# mo. ",% *%%% 1oney 1arket 2und

< mo. %,#5 #B, 1oney 1arket 2und"# mo. <,5 D%, /irect Investment

"B*%(.

3a4 7eduction in mail float6

3".5 days4 3@,4 = @",#,

M reduction in processing float6

3#. days4 3@,4 = ",<,

= Total 2loat 7eduction @#,,

#%#



3b4 The opportunity cost of maintaining the current banking arrangement is6

3.B54 3@#,,4 = @#<<,

3c4 The average number of checks to be processed each day through the lock*boxarrangement is6

si+echeckAverage

sremittance/aily=

AAA,@

AAA,CAA@= # checks per day

Jow we can calculate the cost of the lock*box system on an annual basis asfollows6

3# checks4 [email protected] 3#D days4 = @#",<

Jext, we compute the cost of the automated depository transfer check 3A/TC4 system. 2irst Citi+ens (ank will not contribute to the cost of theA/TC arrangement because it is the lead concentration bank and, thereby,receives the transferred data. Thus, Charles )obrin will be charged for sixA/TCs 3or, three locations O # checks each4 each business day. The cost of the A/TC system is6

3< daily transfers4 3@% each4 3#D days4 = @,<

The total cost of the proposed system will be6

9ock*box cost @#",<A/TC cost ,<Total cost @D,#

3d4 )obrin /oor S Qlass, Inc. should adopt the proposed system. The pro'ectednet annual gain will be @"B5,.

0ro'ected return on freed balances @#<<,9ess6 Cost of new system 3D,# 4 Jet annual gain @"B5,

"B*(. Annual collections = @",, 35 regions4 = @5,,

/aily collections = @5,,L%<5 = @"%<,B<

The value of the %. days$ float reduction is found by presuming the freed balances will be added to the marketable securities portfolio and will earn "".H 3see text of problem4. The gross annual savings from the system are6

3@"%<,B<4 3%. days4 3.""4 = @5,#5

#%%



The annual cost of operating the lock*box system is6

3@< per month4 35 regions4 3"# months4 = @%<,

The net annual savings are6 @5,#5

* %<,

@B,#5 avings

The data indicate that 7egency Components should adopt the lock*box system.

"B*5(. Initially, compute the firm$s average remittance check si+e and daily opportunity costof carrying cash. The average check si+e is6

AAA,#A

AAA,AAA,5A@ = @#,5


%<5

AB.= .#<< per day

Jext, the days saved in the collection process can be evaluated according to thisformat6

Added costs = Added benefits

or

0 = 3/4 34 3i4

@.%D = 3/4 3#,54 3.#<<4

.<# days = /

We know -allmark Technology will experience a financial gain if it adopts the lock* box system and, thereby, speeds up its collections by more than .<# days.

"B*<(.year in/ays

revenuesAnnual =

%<5

,,B@ =

day persales#,<5,D5%

3A.AB54yield43assumed

%43@#,<5,D5

day4 per3sales = @#%,#D

"B*D(. 3a4 2irst, it is necessary to compute Colorado Comm$s average remittance checksi+e and the daily opportunity cost of carrying cash. The average check si+e is6

AAA,D

AAA,AAA,"A@ = @",#B per check.

#%




%<5

AD.A = ."B" per day

econd, the days saved in the collection process can be evaluated according to

the general format of

Added Costs = Added (enefits

or

0 = 3/4 34 3i4

.% = 3/4 3@",#B4 3."B"4

".B< days = /

Therefore, Colorado Comm will experience a financial gain if it adopts thelock*box system and speeds up its collections by more than ".B< days.

3b4 In this situation the daily opportunity cost of carrying cash is6

%<5

A5.A = ."#%% per day

2or Colorado Comm to break even should it choose to install the lock*boxsystem, the cash collections must be accelerated by ".D#D days as follows6

@.% = 3/4 3@",#B4 3."#%%4

".D#D days = /

3c4 The break*even cash acceleration period of ".D#D days is greater than the".B< days found in part 3a4. This is due to the lower yield available on near*cash assets 3or .5 percent annually versus D. percent4. ince the alternativerate of return on the freed*up balances is lower in the second situation, morefunds must be invested to cover the costs of operating the lock*box system.The greater cash acceleration period generates this increased level of re!uiredfunds.

"B*(.The value of one day of processing float is6

#DA

AAA,AAA,"D@ = @<#,B<%

The annual savings at BH are6

3# days4 3@<#,B<%4 3.B4 = @"",%%%

"B*B(. 3a4 The average accrued wages under the monthly payment system are6

#%5



"B*"#(.

3a4 0 = T3".B4

@C"C

"T ∑=

M "C4AB."3

AAA,"@ = @B"#.

The bond can be sold for @B"#.. This was developed as follows6

@ 3.D55<4 M @", 3.#""BB4 = @B"#.

3b4 @", * @B"#. = @D.5<

3c4 2irst, we find the price of the *year bond, which now has # years remaining tomaturity6

0 = T3".B4

@C#

"T ∑=

M #4AB."3

AAA,"@ = @B#."

Then we can determine the expected capital loss on the shorter*term bond asfollows6

@", * @B#." = @"D.5B

The capital loss on the shorter*term bond is much less than that suffered on thelonger*term instrument.

3d4 Interest rate risk.

"B*"%(.

The easiest way to visuali+e the appropriate responses to all three parts of this problem is to calculate the income that would be generated if the entire @%,5,was invested in each separate maturity category. This is shown below6

Amount >ield Income (rokerage Jet

". @%,5, 3.<#4 "L"# @ ",% @"5, @ %,%

#. @%,5, 3.<4 #L"# @ %D,%%% @"5, @ ##,%%%

%. @%,5, 3.<54 %L"# @ 5<,D5 @"5, @ ",D5

. @%,5, 3.<D4 L"# @ D,"<D @"5, @ <%,"<D

5. @%,5, 3.<B4 5L"# @",<#5 @"5, @5,<#5

<. @%,5, 3.D4 <L"# @"##,5 @"5, @"D,5

2rom this table we can see that the @"5, brokerage fee is exceeded by theincremental return from the investment in all maturity categories. ince the availableyield rises with each successive increase in the maturity period, investment in longer maturities increases return. Jow, we can proceed to answer the specific parts of this problem.

#%



3a4 7eturn from investing6

@",D5, for three months @#,%

@",D5, for six months @<",#5

* brokerage fee @"5,

@D,<

(y investing half of the excess for three months and half for six months thereturn will be maximi+ed at @D,<F this approach adheres to the wishes of the company president.

3b4 ?nder this circumstance all @%,5, should be invested in securities withmaturity periods of six months. The added income will be @"D,5.

3c4 This solution is developed from the table above6

3"4<

AC%,"C= @ %,"

3#4<%%%,%D = @ <,###

3%4<

CD5,5<= @B,DB

34<

"<D,DC= @"%,#

354<

<#5,"AA= @"<,DD"

3<4

<

5AA,"##= @#,"D

Total <,B%"

(rokerage *"5,

Jet @5%,B%"

"B*"(.

3a4 The after*tax yield to Ward Qrocers on the (((*rated bond is 3.4 3"*.<4= .%# = .%#H. ince the yield on the tax*exempt issue is already statedon an after*tax basis, we can conclude the 5 "L# percent return on themunicipal is preferable.

3b4 r =T43"Rr −

r =4<.A"3

A55.A

− =

5.A

A55.A= "."5H

chapter 19 im 10th ed

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