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Chapter 9

Cash Collection SystemsTHIS IS A PRELIMINARY DRAFT OF THE 3rd EDITION IM AND ISSUBJECT TO CORRECTION AND REVISION. IF YOU FINDERRORS IN THE TEXT OR CALCULATIONS, OR HAVEOBSERVATIONS REGARDING THE CONCEPTS PRESENTED,PLEASE E-MAIL THE IM AUTHOR AT: [email protected] .

--Karl BordenProfessor of Financial EconomicsUniversity of NebraskaKearney, NE

Contents

Cash Flow Timeline and Cash CollectionThe Cost of FloatTypes of Collection SystemsThe Lockbox Location StudyThe Lockbox ModelLockbox Bank SelectionA Lockbox Study Case Example

Appendix 9A: A Linear Programming Formulation ofthe Lockbox Model

Page 155
mailto:[email protected]:[email protected]

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Chapter 9 - Page 156

Answers to Questions:1. a.) Mail float: the time delay from the time a check is mailed to the time it

reaches its destination.b.) Processing float: the time delay from receipt of the check until the check is

entered into the clearing process.c.) Availability float: the time delay from when the check is entered into the

clearing process until good funds are credited to the deposit account.

2. a.) Decentralized collection systems:

Advantage - mail and availability delay is minimal.Disadvantages - 1.) the field office may not be very efficient at depositing thechecks, 2.) the deposits may remain at the field office's bank account earningminimal rates of return if any.

b.) Centralized collection systems:

Advantage - A centralized collection system would generally have highspeed processing equipment to ensure quick depositing of checks. Also the cashmanager has more control since there are far fewer deposit accounts compared tothe decentralized alternative.Disadvantages - mail and availability time would generally be greater than for adecentralized system.

c.) Lockbox collection system:

The lockbox system is similar to the decentralized collection system in that there

are dispersed collection sites to reduce the mail and availability delays. It issimilar to the centralized collection system in that there is enhanced corporatecontrol by having the funds deposited in the collection banks transferred on afrequent basis to a few concentration accounts at the firm's credit or disbursingbanks.

3. A lockbox collection system helps the cash cycle by reducing collection float

thus speeding up the cash cycle.4. A retail lockbox is characterized by processing a large volume of relatively low

face value items with standardized remittance information. A wholesale lockbox

is characterized by processing a relatively low volume of high face value itemswith non-standardized remittance information.

5. The variables include: number of items, average face value, days of collection

float, variable processing cost per item, and fixed cost.6. Customer groups versus individual customers. Remittance sample. Mail and

availability times

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7. A lockbox collection system reduces mail delay by placing collection sites

relatively close to the customer mailing site. It reduces processing delay bymaking several pickups daily from the local post office, by using unique zipcodes which speeds up sorting, and by using trained staff and state of the artprocessing equipment and finally by working 24 hours daily. Availability delayis reduced because the collection site is relatively close to the mail site and thebank selection process considers mail float as well as availability float.

8. It will definitely increase the efficiency of collection systems by reducing the

number of banks that a company will need to deal with. Increasing efficiencywill reduce the costs associated with collections and it will also tend to speed upthe receipt of cash.

Answers to Questions:

1. a.) Mail float: the time delay from the time a check is mailed to the time itreaches its destination.b.) Processing float: the time delay from receipt of the check until the check isentered into the clearing process.c.) Availability float: the time delay from when the check is entered into theclearing process until good funds are credited to the deposit account.

2. a.) Decentralized collection systems:Advantage - mail and availability delay is minimal.Disadvantages - 1.) the field office may not be very efficient at depositing thechecks, 2.) the deposits may remain at the field office's bank account earningminimal rates of return if any.

b.) Centralized collection systems:Advantage - A centralized collection system would generally have highspeedprocessing equipment to ensure quick depositing of checks. Also the cashmanage has more control since there are far fewer deposit accounts compared tothe decentralized alternative.Disadvantages - mail and availability time would generally be greater than for adecentralized system.

c.) Lockbox collection system:The lockbox system is similar to the decentralized collection system in that thereare dispersed collection sites to reduce the mail and availability delays. It issimilar to the centralized collection system in that there is enhanced corporate

control by having the funds deposited in the collection banks transferred on afrequent basis to a few concentration accounts at the firm's credit or disbursingbanks.

3. A lockbox collection system helps the cash cycle by reducing collection float thusspeeding up the cash cycle.

4. A retail lockbox is characterized by processing a large volume of relatively lowface value items with standardized remittance information. A wholesale lockbox

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is characterized by processing a relatively low volume of high face value itemswith non-standardized remittance information.

5. The variables include: number of items, average face value, days of collectionfloat, variable processing cost per item, and fixed cost.

6. Customer groups versus individual customers. Remittance sample. Mail andavailability times

7. They both use the same data variables and they both start out with the one-sitecollection point with similar calculations. However, then the completeenumeration model begins to assess ALL possible combinations of collectionsites while the greedy algorithm evaluates combinations of ever increasingcollections sites that only include previous optimal combinations of sites.

8. A lockbox collection system reduces mail delay by placing collection sitesrelatively close to the customer mailing site. It reduces processing delay bymaking several pickups daily from the local post office, by using unique zipcodes which speeds up sorting, and by using trained staff and state of the art

processing equipment and finally by working 24 hours daily. Availability delayis reduced because the collection site is relatively close to the mail site and thebank selection process considers mail float as well as availability float.

9. It will definitely increase the efficiency of collection systems by reducing thenumber of banks that a company will need to deal with. Increasing efficiencywill reduce the costs associated with collections and it will also tend to speed upthe receipt of cash.

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Solutions to Problems: Chapter 9

1. Calculating float and the cost of float.

ASSUMPTIONS:Remittance Mail Availability Dollar-Day

per month Float Float Float$100,000 2 1 $300,000$5,000 7 2 $45,000$300,000 1 1 $600,000$10,000 5 1 $60,000$150,000 4 2 $900,000

Total $565,000 $1,905,000=Total

Annual opportunity rate 4%Days in month 30

a.) Calculating the total dollar-day float for the month

Total dollar day float = S [remittances*(mail + availability float)] =$1,905,000=

b.) Calculating the average dollar-day float

Average Dollar-Day Float = Total Dollar-Day Float / Days in month= $1.905 mil / 30 = $63,500

c.) Calculating the average collection float (in days)

Average Collection Float = Total Dollar-Day Float / Total Remittance= $1.905 mil / $565K = 3.37 days

d.) Calculating the annual cost of float

Annual Cost of Float = Average Dollar-Day Float * Discount Rate= $63,500 *.04 = $2,540

2. Calculating float and the cost of float.

ASSUMPTIONS:Remittances Mail Processing Availability Dollar-Day per month Float Float Float Float$500,000 5 1 2 $4,000,000$100,000 2 2 1 $500,000

$50,000 5 1 2 $400,000$1,000,000 3 0.5 0 $3,500,000$25,000 1 2 2 $125,000$1,675,000 $8,525,000

Annual opportunity rate 5%Days in month 30

a.) Calculating the total dollar-day float for the month

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Total dollar day float = S [remittances*(mail + availability float)] =$8,525,000

b.) Calculating the average dollar-day float

Average Dollar-Day Float = Total Dollar-Day Float / Days in month= $8.525 mil / 30 = $284,167

c.) Calculating the average collection float (in days)

Average Collection Float = Total Dollar-Day Float / Total Remittance= $8.525 mil / $1,675K = 5.09 days

d.) Calculating the annual cost of float

Annual Cost of Float = Average Dollar-Day Float * Discount Rate

= $284,167 * 0.05 = $14,208

3. Comparing costs of cash collection systems.

ASSUMPTIONS:Average number of remittances per month, N 5,000Average face value, F $10,000Mail float 3Processing float 2Availability float 2Total days of float, D 7Annual opportunity rate, k 5%Fixed cost, FC $150Variable cost, VC $0.35

a.) Calculating the monthly total cost for a cash collection system

TC = Total cost

N= # of remittancesF= Average face value ofremittances

D= Total days of float

i= Daily opportunity cost

VC= Variable cost

FC= Fixed cost

TC per month = N * ((F*D*i) + VC) + FC= 5000*((10,000*7*0.05 / 365) + 0.35) + $150

TC per month = $49,845

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b.) Changing to a lockbox system

ASSUMPTIONSAverage number of remittances per month, N 5,000Average face value, F $10,000Mail float 1Processing float 0Availability float 1Total days of float, D 2Annual opportunity rate, k 5%Fixed cost, FC $500Variable cost, VC $0.80TC per month = N * ((F*D*i) + VC) + FCTC per month = $18,199Yes, change to the lockbox system. The monthly cost drops substantially (overhalf !).

4. Comparing costs of cash collection systems.

ASSUMPTIONSAverage number of remittances per month, N 130,000Average face value, F $285Mail float 3Processing float 1Availability float 1.5Total days of float, D 5.5Annual opportunity rate, k 4%Fixed cost, FC $125Variable cost, VC $0.25

Total Cost for cashcollection system

TC = Total cost

N= # of remittancesF= Average face value ofremittances

D= Total days of float

i= Daily opportunity cost

VC= Variable cost

FC= Fixed cost

a.) Calculating the monthly total cost for a cash collection system

TC per month = N * ((F*D*i) + VC) + FCTC per month = $54,957

b.) Changing to a lockbox system

ASSUMPTIONS

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Average number of remittances per month, N 130,000Average face value, F $285Mail float 1Processing float 0Availability float 1Total days of float, D 2Annual opportunity cost, k 4%Fixed cost, FC $425Variable cost, VC $0.75

TC per month = N * ((F*D*i) + VC) + FC

TC per month = $106,046

No, do not switch to the lockbox system since monthly costs increase.

5. Determining the optimal number of lockboxes and customer allocation.

ASSUMPTIONS:Annual opportunity rate = 8.00%

AverageCustomer Monthly

Group Remittances Remittances Days of FloatNumber Face Value Bank A Bank B Bank C

1 2,000 $50,000 5 3 12 4,000 30,000 1 6 43 1,000 18,000 3 7 54 200 20,000 7 1 3

Variable Processing Costs $0.30 $0.60 $0.80Fixed Costs $300 $400 $150

1-Bank Solution:

Variable Costs = N*(F*d*i + VC)Example: for Bank A in Group 1, Variable Costs =2000 * [(50000 * 5 * 0.08 / 365) + 0.30]

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1-Bank Solution:

Group Bank A Bank B Bank C

1$110,18

9 $66,953 $23,518

2 $27,501$160,20

8$108,40

5

3 $12,136 $28,216 $20,526

4 $6,197 $997 $2,790FixedCost $300 $400 $150TotalCost

$156,323

$256,775

$155,389

minimum cost for a 1-bank system

2-Bank Solution:

2-Bank Solution:Combinatio

n 1Combination

2 Combination 3

Group Bank A Bank B Bank A Bank C Bank B Bank C

1 $66,953 $23,518 $23,518

2$27,50

1 $27,501$108,40

5

3$12,13

6 $12,136 $20,526

4 $997 $2,790 $997

Total VC$39,63

7 $67,950 $39,637 $26,308 $997$152,44

9

Fixed Cost $300 $400 $300 $150 $400 $150

Total Cost$108,28

7$66,39

5$153,99

6minimum cost for a 2-bank system

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3-Bank Solution:

3-Bank Solution: Combination 1


1 $23,518

2$27,50

1

3$12,13

6

4 $997

Total VC

$39,63

7 $997 $23,518Fixed Cost $300 $400 $150

$65,002

Select the 3-bank system since it minimizes total costs. As for customer allocation,customer group 1 remits to Bank C. Customer group 2 remits to Bank A. Customergroup 3 remits to Bank A. Customer group 4 remits to Bank B.


Assumptions

Opportunity rate 8.00%

Customer Average monthly

GroupRemittances Remittances Days of Float

---------

NumberFaceValue

BankA Bank B Bank C

1 500 $50,000 5 2 1

2 1,000 30,000 1 5 4

3 100 18,000 3 4 5

4 50 20,000 7 1 3

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Variable Processing Costs $0.25 $0.70 $0.50FixedCosts $500 $600 $400

1-Bank Solution:


1$27,52

2 $11,309 $5,729

2 $6,825 $33,577 $26,801

3 $1,209 $1,648 $2,023

4 $1,547 $254 $683Fixed Cost $500 $600 $400

Total Cost$37,60

3 $47,388$35,63

6

2-Bank Solution:Combinati

on 1Combinati

on 2Combination

3


1$11,30

9 $5,729 $5,729

2 $6,825 $6,825$26,80

1

3 $1,209 $1,209 $1,648

4 $254 $683 $254

Total VC $8,034$11,56

3 $8,034 $6,412 $1,902$32,53

1Fixed

Cost $500 $600 $500 $400 $600 $400

TotalCost

$20,697

$15,346

$35,433

3-Bank Solution:Combination

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1


1 $5,729

2 $6,825

3 $1,2094 $254

TotalVC $8,034 $254 $5,729FixedCost $500 $600 $400

$15,518

Minimum CostSolution=

$15,346 Select the two-bank system, A & C


Assumptions




------

Number FaceValue Bank A Bank B Bank C

1 2,000 $500 6 2 1

2 10,000 900 5 1 3

3 4,000 1,500 1 4 6


1-Bank Solution:


1 $2,415 $838 $1,619

2$15,36

3 $3,973 $12,918

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3 $3,515 $6,060 $10,690

Fixed Cost $350 $550 $250

Total Cost$21,64

3$11,42

1 $25,477


1Combination

2Combination

3


1 $838 $1,619 $838

2 $3,973$12,91

8 $3,973

3 $3,515 $3,515 $6,060

TotalVC $3,515 $4,811 $3,515

$14,537

$10,871 $0

FixedCost $350 $550 $350 $250 550 $250

Tot.Cost $9,226

$18,652

$11,671

3-BankSolution:

Combination 1

GroupBank

ABank

B Bank C

1 $838

2$3,97

3

3$3,51

5TotalVC

$3,515

$4,811 $0

FixedCost $350 $550 $250

$9,476

Minimum CostSolution =

$9,226 Select the two-bank system, A & B

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Assumptions




---------

Number Face ValueBank

A Bank B Bank C

1 50,000 $98 5 6 1

2 100,000 55 1 4 3

3 75,000 125 3 5 4


1-Bank Solution:


1 $34,212 $28,055 $36,342

2 $56,507 $46,027 $74,521

3 $48,955 $42,842 $62,774FixedCost $350 $500 $250TotalCost

$140,025

$117,425

$173,887

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1Combination

2Combination 3


1$28,05

5$34,21

2$28,05

5

2$46,02

7$56,50

7$46,02

7

3$42,84

2$48,95

5$42,84

2

Total VC $0$116,9

25$139,6

75 $0$116,9

25 $0Fixed

Cost $350 $500 $350 $250 500 $250

TotalCost

$117,775

$140,275

$117,675

3-Bank Solution:

Combination 1

GroupBank

A Bank B Bank C

1 $28,055

2 $46,027

3 $42,842

Total VC $0$116,92

5 $0FixedCost $350 $500 $250

$118,025

Minimum Cost Solution= $117,425

Select the one-bank system,B

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