im -section b - solutions_ch20

8/10/2019 IM -Section B - Solutions_Ch20

1/13

B-42 SOLUTIONS

CHAPTER 20

CASH AND LIQUIDITY MANAGEMENT

Answers to Concepts Review and Critical Tin!in" Q#estions

$% Yes. Once a firm has more cash than it needs for operations and planned expenditures, the excesscash has an opportunity cost. It could be invested (by shareholders) in potentially more profitableways. Question 1 discusses another reason.

&% If it has too much cash it can simply pay a dividend, or, more li!ely in the current financialenvironment, buy bac! stoc!. It can also reduce debt. If it has insufficient cash, then it must eitherborrow, sell stoc!, or improve profitability.

'% "robably not. #reditors would probably want substantially more.

(% In the case of $icrosoft, the company%s reason &iven for holdin& cash was to pay for potentialsettlements in its monopoly cases brou&ht by the '.. &overnment and the uropean 'nion. *$&enerally ar&ued that it held cash to &uard a&ainst future economic downturns.

)% #ash mana&ement is associated more with the collection and disbursement of cash. +iuiditymana&ement is broader and concerns the optimal level of liuid assets needed by a firm. -hus, forexample, ord and #hrysler%s stoc!pilin& of cash was liuidity mana&ement/ whereas, evaluatin& aloc!box system is cash mana&ement.

*% uch instruments &o by a variety of names, but the !ey feature is that the dividend ad0usts, !eepin&

the price relatively stable. -his price stability, alon& with the dividend tax exemption, ma!es socalled ad0ustable rate preferred stoc! very attractive relative to interestbearin& instruments.

+% 2et disbursement float is more desirable because the ban! thin!s the firm has more money than itactually does, and the firm is, therefore, receivin& interest on funds it has already spent.

,% -he firm has a net disbursement float of 34,. If this is an on&oin& situation, the firm may betempted to write chec!s for more than it actually has in its account.

-% a. 5bout the only disadvanta&e to holdin& -bills are the &enerally lower yields compared toalternative money mar!et investments.

b. ome ordinary preferred stoc! issues pose both credit and price ris!s that are not consistentwith most shortterm cash mana&ement plans.

c. -he primary disadvanta&e of 2#6s is the normally lar&e transactions si7es, which may not befeasible for the shortterm investment plans of many smaller to mediumsi7ed corporations.

d. -he primary disadvanta&es of the commercial paper mar!et are the hi&her default ris!characteristics of the security and the lac! of an active secondary mar!et which mayexcessively restrict the flexibility of corporations to meet their liuidity ad0ustment needs.


2/13

B-43 SOLUTIONS

e. -he primary disadvanta&es of 852s is that some possess nontrivial levels of default ris!, andalso, corporations are somewhat restricted in the type and amount of these taxexempts thatthey can hold in their portfolios.

f. -he primary disadvanta&e of the repo mar!et is the &enerally very short maturities available.

$.% -he concern is that excess cash on hand can lead to poorly thou&htout investments. -he thou&ht isthat !eepin& cash levels relatively low forces mana&ement to pay careful attention to cash flow andcapital spendin&.

$$% 5 potential advanta&e is that the uic!er payment often means a better price. -he disadvanta&e isthat doin& so increases the firm%s cash cycle.

$&% -his is really a capital structure decision. If the firm has an optimal capital structure, payin& off debtmoves it to an underlevera&ed position. 9owever, a combination of debt reduction and stoc! buybac!s could be structured to leave capital structure unchan&ed.

$'% It is unethical because you have essentially tric!ed the &rocery store into ma!in& you an interestfree

loan, and the &rocery store is harmed because it could have earned interest on the money instead ofloanin& it to you.

Sol#tions to Q#estions and /ro0le1s

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple

steps. ue to space and readability constraints! when these intermediate steps are included in this

solutions manual! rounding may appear to have occurred. "owever! the final answer for each problem is

found without rounding during any step in the problem.

#asic

$% -he avera&e daily float is the avera&e amount of chec!s received per day times the avera&e numberof days delay, divided by the number of days in a month. 5ssumin& : days in a month, the avera&edaily float is;

5vera&e daily float < =(66>?,)@:5vera&e daily float < 661AB,

&% a. -he disbursement float is the avera&e monthly chec!s written times the avera&e number of daysfor the chec!s to clear, so;

6isbursement float < B(344,)6isbursement float < 3??,

-he collection float is the avera&e monthly chec!s received times the avera&e number of daysfor the chec!s to clear, so;

#ollection float < ?(C3A,)#ollection float < C31=,


3/13

CHAPTER 20 B-44

-he net float is the disbursement float plus the collection float, so;

2et float < 3??, C 1=,2et float < 3=,

b. -he new collection float will be;

#ollection float < 1(C3A,)#ollection float < C3A,

5nd the new net float will be;

2et float < 3??, C A,2et float < 31B,

'% a. -he collection float is the avera&e daily chec!s received times the avera&e number of days forthe chec!s to clear, so;

#ollection float < B(8'8?D,)#ollection float < 8'81A,

b. -he firm should pay no more than the amount of the float, or 8'81A,, to eliminate thefloat.

c. -he maximum daily char&e the firm should be willin& to pay is the collection float times thedaily interest rate, so;

$aximum daily char&e < 8'81A,(.?4)$aximum daily char&e < 8'8?D.

(% a. -otal float < B(3?,) E 4(34,)-otal float < 314,

b. -he avera&e daily float is the total float divided by the number of days in a month. 5ssumin&: days in a month, the avera&e daily float is;

5vera&e daily float < 314,@:5vera&e daily float < 3:,4

c. -he avera&e daily receipts are the avera&e daily chec!s received divided by the number of daysin a month. 5ssumin& a : day month;

5vera&e daily receipts < (3?, E 4,)@:5vera&e daily receipts < 3A::.::

-he wei&hted avera&e delay is the sum of the days to clear a chec!, times the amount of thechec! divided by the avera&e daily receipts, so;

Fei&hted avera&e delay < B(3?,@3?4,) E 4(34,@3?4,)Fei&hted avera&e delay < B.? days


4/13

B-45 SOLUTIONS

)% -he avera&e daily collections are the number of chec!s received times the avera&e value of a chec!,so;

5vera&e daily collections < GA(14,)5vera&e daily collections < G1,?,

-he present value of the loc!box service is the avera&e daily receipts times the number of days thecollection is reduced, so;

"H < (? day reduction)(G1,?,)"H < G?,B,

-he daily cost is a perpetuity. -he present value of the cost is the daily cost divided by the dailyinterest rate. o;

"H of cost < [email protected]="H of cost < G1,?4,

-he firm should ta!e the loc!box service. -he 2"H of the loc!box is the cost plus the present valueof the reduction in collection time, so;

2"H < CG?,B, E 1,?4,2"H < G1,14,

-he annual net savin&s excludin& the cost would be the future value of the savin&s minus thesavin&s, so;

5nnual savin&s < G?,B,(1.1=):=4C ?,B,5nnual savin&s < G1BB,:?1.=:

5nd the annual cost would be the future value of the daily cost, which is an annuity, so;

5nnual cost < G?(HI5:=4,.1=)5nnual cost < GD4,1=D.4?

o, the annual net savin&s would be;

5nnual net savin&s < G1BB,:?1.=: C D4,1=D.4?5nnual net savin&s < G=>,14B.1?

*% a. -he avera&e daily float is the sum of the percenta&e each chec! amount is of the total chec!sreceived times the number of chec!s received times the amount of the chec! times the number

of days until the chec! clears, divided by the number of days in a month. 5ssumin& a : daymonth, we &et;

5vera&e daily float < J.=4(D,)(34)(?) E .:4(D,)(3D)(:)K@:5vera&e daily float < 3:?,:1D

On avera&e, there is 3:?,:1D that is uncollected and not available to the firm.


5/13

CHAPTER 20 B-46

b. -he total collections are the sum of the percenta&e of each chec! amount received times thetotal chec!s received times the amount of the chec!, so;

-otal collections < .=4(D,)(34) E .:4(D,)(3D)-otal collections < 3??D,4 E 1D1,4-otal collections < 3:>>,

-he wei&hted avera&e delay is the sum of the avera&e number of days a chec! of a specificamount is delayed, times the percenta&e that chec! amount ma!es up of the total chec!sreceived, so;

Fei&hted avera&e delay < ?(3??D,4@3:>>,) E :(31D1,4@3:>>,)Fei&hted avera&e delay < ?.B: days

-he avera&e daily float is the wei&hted avera&e delay times the avera&e chec!s received perday. 5ssumin& a : day month, we &et;

5vera&e daily float < ?.B:(3:>>,@: days)

5vera&e daily float < 3:?,:1D

c. -he most the firm should pay is the total amount of the avera&e float, or 3:?,:1D.

d. -he avera&e daily interest rate is;

1.D < (1 E 8):=48 < .1A4B per day

-he daily cost of float is the avera&e daily float times the daily interest rate, so;

6aily cost of the float < 3:?,:1D(.1A4B)

6aily cost of the float < 34.>>

e. -he most the firm should pay is still the avera&e daily float. 'nder the reduced collection timeassumption, we &et;

2ew avera&e daily float < 1.4(3:>>,@:)2ew avera&e daily float < 31>,>4

+% a. -he present value of adoptin& the system is the number of days collections are reduced timesthe avera&e daily collections, so;

"H < :(B)(L1?,)

"H < 31BB,,

b. -he 2"H of adoptin& the system is the present value of the savin&s minus the cost of adoptin&the system. -he cost of adoptin& the system is the present value of the fee per transaction timesthe number of transactions. -his is a perpetuity, so;

2"H < L1BB$ C JL.A(B)@.?K2"H < L1B?,B,


6/13

B-47 SOLUTIONS

c. -he net cash flows is the present value of the avera&e daily collections times the daily interestrate, minus the transaction cost per day, so;

2et cash flow per day < L1BB$(.?) C L.A(B)2et cash flow per day < L?A,BA

-he net cash flow per chec! is the net cash flow per day divided by the number of chec!sreceived per day, or;

2et cash flow per chec! < L?A,BA@B2et cash flow per chec! < LD1.?

5lternatively, we could find the net cash flow per chec! as the number of days the systemreduces collection time times the avera&e chec! amount times the daily interest rate, minus thetransaction cost per chec!. 6oin& so, we confirm our previous answer as;

2et cash flow per chec! < :(L1?,)(.?) C L.A2et cash flow per chec! < LD1.? per chec!

,% a. -he reduction in cash balance from adoptin& the loc!box is the number of days the systemreduces collection time times the avera&e daily collections, so;

#ash balance reduction < ?(M584,)#ash balance reduction < M581,,

b. -he dollar return that can be earned is the avera&e daily interest rate times the cash balancereduction. -he avera&e daily interest rate is;

5vera&e daily rate < 1.>1@:=4C 15vera&e daily rate < .?:= per day

-he daily return that can be earned from the reduction in days to clear the chec!s is;

6aily return < M581,,(.?:=)6aily return < M58?:=.1:

c. If the company ta!es the loc!box, it will receive three payments early, with the first paymentoccurrin& today. Fe can use the daily interest rate from part b, so the savin&s are;

avin&s < M584, E M584,("HI5.?:=,?)avin&s < M581,B>>,=B4.>1

If the loc!box payments occur at the end of the month, we need the effective monthly interestrate, which is;

$onthly interest rate < 1.>1@1?C 1$onthly interest rate < .D?D


7/13

CHAPTER 20 B-48

5ssumin& the loc!box payments occur at the end of the month, the loc!box payments, which are aperpetuity, will be;

"H < #@8M581,B>>,=B4.>1 < # @ .D?D# < M581,AA.B:

It could also be assumed that the loc!box payments occur at the be&innin& of the month. If so,we would need to use the "H of a perpetuity due, which is;

"H < # E # @ 8

olvin& for #;

# < ("H N 8) @ (1 E 8)# < (M581,B>>,=B4.>1 N .D?D) @ (1 E .D?D)# < M581,D:1.>

-% -he interest that the company could earn will be the amount of the chec!s times the number of daysit will delay payment times the number of wee!s that chec!s will be disbursed times the dailyinterest rate, so;

Interest < 3=B,(=)(4?@?)(.?)Interest < 31,>>=.A

$.% -he benefit of the new arran&ement is the 31 million in accelerated collections since the newsystem will speed up collections by one day. -he cost is the new compensatin& balance, but thecompany will recover the existin& compensatin& balance, so;

2"H < 31,, C (3=, C 4,)

2"H < 3>,>,

-he company should proceed with the new system. -he savin&s are the 2"H times the annualinterest rate, so;

2et savin&s < 3>,>,(.4)2et savin&s < 3B>4,

$ntermediate

$$% -o find the 2"H of ta!in& the loc!box, we first need to calculate the present value of the savin&s.-he present value of the savin&s will be the reduction in collection time times the avera&e daily

collections, so;

"H < ?(D)(31,1)"H < 31,4B,

5nd the daily interest rate is;

6aily interest rate < 1.=11@:=4C16aily interest rate < .1= or .1= per day


8/13

B-49 SOLUTIONS

-he transaction costs are a perpetuity. -he cost per day is the cost per transaction times the numberof transactions per day, so the 2"H of ta!in& the loc!box is;

2"H < 31,4B, C J3.:4(D)@.1=K2"H < 34,B?D.4:

Fithout the fee, the loc!box system should be accepted. -o calculate the 2"H of the loc!box withthe annual fee, we can simply use the 2"H of the loc!box without the annual fee and subtract theaddition cost. -he annual fee is a perpetuity, so, with the fee, the 2"H of ta!in& the loc!box is;

2"H < 34,B?D.4: C J31,@.=K2"H < C311,?:>.1B

Fith the fee, the loc!box system should not be accepted.

$&% -o find the minimum number of payments per day needed to ma!e the loc!box system feasible is thenumber of chec!s that ma!es the 2"H of the decision eual to 7ero. -he avera&e daily interest rateis;

6aily interest rate < 1.41@:=4C 16aily interest rate < .1:B per day

-he present value of the savin&s is the avera&e payment amount times the days the collection periodis reduced times the number of customers. -he costs are the transaction fee and the annual fee. othare perpetuities. -he total transaction costs are the transaction costs per chec! times the number ofchec!s. -he euation for the 2"H of the pro0ect, where 2 is the number of chec!s transacted per day,is;

2"H < < (34,4)(1)2 C J3.1?(2)@.1:BK C J3?4,@.4K34, < 34,42 C 3A>4.4?2

3B,=B.BA2 < 34,2 < 1A.4> 1> customers per day

%hallenge

$'% a. -he amount the company will have available is the future value of the transfers, which are anannuity. -he amount of each transfer is one minus the wire transfer cost, times the number oftransfers, which is four since there are four ban!s, times the amount of each transfer. o, thetotal available in two wee!s will be;

5mount available < (1 C .14)(B)(314,)(HI5.14,1B)5mount available < 3A,:>4,4A?.=?

b. -he ban! will accept the 5#9 transfers from the four different ban!s, so the company incurs atransfer fee from each collection center. -he future value of the deposits now will be;

Halue of 5#9 < JB(314, C D)(HI5.14,1B)[email protected] of 5#9 < 3A,:=D,D1.4?

-he company should not &o ahead with the plan since the future value is lower.


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CHAPTER 20 B-50

c. -o find the cost at which the company is indifferent, we set the amount available we found inpart aeual to the cost euation we used in part b. ettin& up this euation where P stands forthe 5#9 transfer cost, we find;

JB(314, C 3P)(HI5.14,1B)[email protected] < 3A,:>4,4A?.=?P < 3??.4:


10/13

B-51 SOLUTIONS

APPENDIX 20A

$% a. Increase. -his will increase the tradin& costs, which will cause an increase in the tar&et cashbalance.

b. 6ecrease. -his will increase the holdin& cost, which will cause a decrease in the tar&et cash

balance.

c. Increase. -his will increase the amount of cash that the firm has to hold in noninterest bearin&accounts, so they will have to raise the tar&et cash balance to meet this reuirement.

d. 6ecrease. If the credit ratin& declines, then it is more difficult for the firm to borrow, forcin& itto increase the tar&et cash balance.

e. Increase. If the cost of borrowin& increases, the firm will need to hold more cash to protecta&ainst cash shortfalls as its borrowin& costs become more prohibitive.

f. 6ecrease. -his depends somewhat on what the fees apply to, but if direct fees are established,

then the compensatin& balance may be lowered, thus lowerin& the tar&et cash balance. If, on theother hand, fees are char&ed on the number of transactions, then the firm may wish to hold ahi&her cash balance so they are not transferrin& money into the account as often.

&% -he tar&et cash balance usin& the 5- model is;

#< J(?- N )@8K1@?#< J?(34,)(31?)@.DK1@?#< 31,:>.:1

-he initial balance should be 31,:>.:1, and whenever the balance drops to 3, another 31,:>.:1should be transferred in.

'% -he holdin& cost is the avera&e daily cash balance times the interest rate, so;

9oldin& cost < (#564)(.4)9oldin& cost < #56?4.

-he tradin& costs are the total cash needed times the replenishin& costs, divided by the avera&e dailybalance times two, so;

-radin& cost < J(#56:,)(#56D)K@J(#564)(?)K-radin& cost < #56?1.

-he total cost is the sum of the holdin& cost and the tradin& cost, so;

-otal cost < #56?1. E ?4.-otal cost < #56?:4.


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CHAPTER 20 B-52

-he tar&et cash balance usin& the 5- model is;

#< J(?- N )@8K1@?#< J?(#56:,)(#56D)@.4K1@?#< #56?,A>A.?A

-hey should increase their avera&e daily cash balance to;

2ew avera&e cash balance < #56?,A>A.?A@?2ew avera&e cash balance < #561,BB>.1B

-his would minimi7e the costs. -he new total cost would be;

2ew total cost < (#561,BB>.1B)(.4) E J(#56:,)(#56D)K@J?(#561,BB>.1B)K2ew total cost < #561BB.>1

(% a. -he opportunity costs are the amount transferred times the interest rate, divided by two, so;

Opportunity cost < (34)(.=)@?Opportunity cost < 314.

-he tradin& costs are the total cash balance times the tradin& cost per transaction, divided by theamount transferred, so;

-radin& cost < (3B,)(3?4)@34-radin& cost < 3?.

-he firm !eeps too little in cash because the tradin& costs are much hi&her than the opportunitycosts.

b. -he tar&et cash balance usin& the 5- model is;

#< J(?- N )@8K1@?#< J?(3B,)(3?4)@.=K1@?#< 31,A?4.DB

)% -he total cash needed is the cash shorta&e per month times twelve months, so;

-otal cash < 1?(#2Y:.4$)-otal cash < #2YB?,,

-he tar&et cash balance usin& the 5- model is;

#< J(?- N )@8K1@?#< J?(#2YB?$)(#2Y4,)@.=4K1@?#< #2Y?,4B1,>44.=B


12/13

B-53 SOLUTIONS

-he company should invest;

Invest < #2YD,, C ?,4B1,>44.=BInvest < #2YB,B4A,BB.:=

of its current cash holdin&s in mar!etable securities to brin& the cash balance down to the optimal

level. Over the rest of the year, sell securities;

ell securities < #2YB?$@#2Y?,4B1,>44.=B

ell securities < 1=.4? 1D times.

*% -he lower limit is the minimum balance allowed in the account, and the upper limit is the maximumbalance allowed in the account. Fhen the account balance drops to the lower limit;

+ower limit < 3=, C B,+ower limit < 3?,

in mar!etable securities will be sold, and the proceeds deposited in the account. -his moves the

account balance bac! to the tar&et cash level. Fhen the account balance rises to the upper limit, then;

'pper limit < 31?4, C =,'pper limit < 3=4,

of mar!etable securities will be purchased. -his expenditure brin&s the cash level bac! down to thetar&et balance of 3=,.

+% -he tar&et cash balance usin& the $illerOrr model is;

#< + E (:@B N N ?@ 8K1@:

#< 31,1 E J:@B(3D4)(3=)?@.?1K1@:

#< 3?,AD.>4

-he upper limit is;

'< : N #C ? N +'< :(3?,AD.>4) C ?(31,1)'< 3B,=:.A4


13/13

CHAPTER 20 B-54

Fhen the balance in the cash account drops to 31,1, the firm sells;

ell < 3?,AD.>4 C 1,1ell < 3>AD.>4

of mar!etable securities. -he proceeds from the sale are used to replenish the account bac! to the

optimal tar&et level of #. #onversely, when the upper limit is reached, the firm buys;

uy < 3B,=:.A4 C ?,AD.>4uy < 31,>D4.>

of mar!etable securities. -his expenditure lowers the cash level bac! down to the optimal level of3?,AD.>4.

,% 5s variance increases, the upper limit and the spread will increase, while the lower limit remainsunchan&ed. -he lower limit does not chan&e because it is an exo&enous variable set by mana&ement.5s the variance increases, however, the amount of uncertainty increases. Fhen this happens, thetar&et cash balance, and therefore the upper limit and the spread, will need to be hi&her. If the

variance drops to 7ero, then the lower limit, the tar&et balance, and the upper limit will all be thesame.

-% -he avera&e daily interest rate is;

6aily rate < 1.D1@:=4C 16aily rate < .1A4 or .1A4 per day

-he tar&et cash balance usin& the $illerOrr model is;

#< + E (:@B N N ?@ 8K1@:

#< 8+1,D4, E J:@B(8+11,B,)(8+4,)@.1A4K1@:

#< 8+1,A11,:??.DA

-he upper limit is;

'< : N #C ? N +'< :(8+1,A11,:??.DA) C ?(8+1,D4,)'< 8+1,>::,>=A.::

$.% 'sin& the 5- model and solvin& for 8, we &et;

#< J(?- N )@8K1@?

3?,? < J?(3?4,)(31?)@8K1@?

8 < J?(3?4,)(31?)K@3?,??8 < .1?B or 1?.B

im -section b - solutions_ch20

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