Chapter 9

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					                                     Chapter 9
                              Cash Collection Systems
THIS IS A PRELIMINARY DRAFT OF THE 3rd EDITION IM AND IS SUBJECT
TO CORRECTION AND REVISION. IF YOU FIND ERRORS IN THE TEXT
OR CALCULATIONS, OR HAVE OBSERVATIONS REGARDING THE
CONCEPTS PRESENTED, PLEASE E-MAIL THE IM AUTHOR AT:
bordenk@unk.edu .

--Karl Borden
Professor of Financial Economics
University of Nebraska
Kearney, NE




                                       Contents

                    Cash Flow Timeline and Cash Collection
                    The Cost of Float
                    Types of Collection Systems
                    The Lockbox Location Study
                    The Lockbox Model
                    Lockbox Bank Selection
                    A Lockbox Study Case Example
                    Appendix 9A: A Linear Programming Formulation of
                    the Lockbox Model




                                       Page 155
                                  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 the
     checks, 2.) the deposits may remain at the field office's bank account earning
     minimal 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 cash manage
     has more control since there are far fewer deposit accounts compared to the
     decentralized alternative.
     Disadvantages - mail and availability time would generally be greater than for a
     decentralized 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 is
     similar to the centralized collection system in that there is enhanced corporate
     control by having the funds deposited in the collection banks transferred on a
     frequent basis to a few concentration accounts at the firm's credit or disbursing
     banks.

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 items
     with 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

7.   They both use the same data variables and they both start out with the one-site
     collection point with similar calculations. However, then the complete
     enumeration model begins to assess ALL possible combinations of collection sites
     while the greedy algorithm evaluates combinations of ever increasing collections
     sites that only include previous optimal combinations of sites.
8.   A lockbox collection system reduces mail delay by placing collection sites
     relatively close to the customer mailing site. It reduces processing delay by
     making several pickups daily from the local post office, by using unique zip codes
                                   Chapter 9 - Page 157


     which speeds up sorting, and by using trained staff and state of the art processing
     equipment and finally by working 24 hours daily. Availability delay is reduced
     because the collection site is relatively close to the mail site and the bank selection
     process considers mail float as well as availability float.

9.   It will definitely increase the efficiency of collection systems by reducing the
     number of banks that a company will need to deal with. Increasing efficiency will
     reduce the costs associated with collections and it will also tend to speed up the
     receipt of cash.
                                   Chapter 9 - Page 158



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
                                   Chapter 9 - Page 159


a.)   Calculating the total dollar-day float for the month
      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           5,000
      Average face value, F                                $10,000
      Mail float                                           3
      Processing float                                     2
      Availability float                                   2
      Total days of float, D                               7
      Annual opportunity rate, k                           5%
      Fixed cost, FC                                       $150
      Variable cost, VC                                    $0.35

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


          TC = Total cost
          N= # of remittances
          F= Average face value of remittances
          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
                                  Chapter 9 - Page 160


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

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

      Total Cost for cash collection
      system
      TC = Total cost
      N= # of remittances
      F= Average face value of
      remittances
      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) + FC
      TC per month = $54,957
                                   Chapter 9 - Page 161


b.)    Changing to a lockbox system
       ASSUMPTIONS
       Average number of remittances per month, N         130,000
       Average face value, F                              $285
       Mail float                                         1
       Processing float                                   0
       Availability float                                 1
       Total days of float, D                             2
       Annual opportunity cost, k                         4%
       Fixed cost, FC                                     $425
       Variable 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%
                            Average
            Customer        Monthly
Group       Remittances Remittances                Days of Float
            Number          Face Value       Bank A       Bank B         Bank C
1           2,000           $50,000          5            3              1
2           4,000           30,000           1            6              4
3           1,000           18,000           3            7              5
4           200             20,000           7            1              3

Variable Processing Costs                    $0.30        $0.60          $0.80
Fixed Costs                                  $300         $400           $150
                                    Chapter 9 - Page 162


        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]

        1-Bank Solution:

        Group            Bank A       Bank B         Bank C

                     1   $110,189      $66,953        $23,518
                     2    $27,501     $160,208       $108,405
                     3    $12,136      $28,216        $20,526
                     4     $6,197         $997         $2,790
        Fixed Cost           $300         $400           $150
        Total Cost       $156,323     $256,775       $155,389
                                                     minimum cost for a 1-bank system




        2-Bank Solution:

2-Bank Solution:
                      Combination 1              Combination 2              Combination 3
Group              Bank A    Bank B            Bank A     Bank C             Bank B      Bank C

             1                 $66,953                      $23,518                      $23,518
             2     $27,501                    $27,501                                   $108,405
             3     $12,136                    $12,136                                    $20,526
             4                    $997                       $2,790            $997
Total VC           $39,637     $67,950        $39,637       $26,308            $997     $152,449
Fixed Cost            $300        $400           $300          $150            $400         $150

Total Cost                    $108,287                     $66,395                     $153,996
                                                      minimum cost for a 2-bank system
                                     Chapter 9 - Page 163


3-Bank Solution:

        3-Bank Solution:
                                  Combination      1
               Group       Bank A    Bank B            Bank C

                     1                                 $23,518
                     2     $27,501
                     3     $12,136
                     4                    $997
        Total VC           $39,637        $997         $23,518
        Fixed 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. Customer
group 3 remits to Bank A. Customer group 4 remits to Bank B.




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

     Assumptions
     Opportunity rate                8.00%

                  Customer    Average monthly
     Group        Remittances Remittances                   Days of Float
                                                               ---------
                    Number     Face Value        Bank A           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
     Variable Processing Costs                    $0.25             $0.70     $0.50
     Fixed
     Costs                                         $500             $600       $400
                                       Chapter 9 - Page 164


1-Bank Solution:

Group              Bank A      Bank B           Bank C

             1     $27,522       $11,309          $5,729
             2      $6,825       $33,577         $26,801
             3      $1,209        $1,648          $2,023
             4      $1,547          $254            $683
Fixed Cost            $500          $600            $400
Total Cost         $37,603       $47,388         $35,636



2-Bank Solution:
                    Combination 1             Combination 2         Combination 3
Group            Bank A Bank B             Bank A Bank C          Bank B      Bank C

         1                   $11,309                     $5,729               $5,729
         2        $6,825                    $6,825                           $26,801
         3        $1,209                    $1,209                  $1,648
         4                      $254                       $683       $254
Total VC          $8,034     $11,563        $8,034       $6,412     $1,902   $32,531
Fixed Cost          $500        $600          $500         $400       $600      $400

Total Cost                   $20,697                   $15,346               $35,433


3-Bank Solution:
                    Combination 1
   Group     Bank A   Bank B Bank C

        1                                  $5,729
        2        $6,825
        3        $1,209
        4                      $254
Total VC         $8,034        $254        $5,729
Fixed
Cost              $500         $600          $400

                                         $15,518

Minimum Cost
Solution=                                $15,346 Select the two-bank system, A & C
                                        Chapter 9 - Page 165


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

       Assumptions
       Opportunity rate                 8.00%

                   Customer    Average monthly
       Group       Remittances Remittances                      Days of Float
                                                                    ------
                     Number Face Value             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
       Variable Processing Costs                    $0.55            $0.20          $0.70
       Fixed
       Costs                                          $350            $550           $250



      1-Bank Solution:

               Group    Bank A         Bank B        Bank C

                    1      $2,415          $838        $1,619
                    2     $15,363        $3,973       $12,918
                    3      $3,515        $6,060       $10,690
      Fixed Cost             $350          $550          $250
      Total Cost          $21,643       $11,421       $25,477



     2-Bank Solution:
                    Combination 1                Combination 2          Combination 3
        Group      Bank A     Bank B            Bank A     Bank C      Bank B Bank C

             1                        $838                  $1,619        $838
             2                      $3,973                 $12,918      $3,973
             3       $3,515                     $3,515                  $6,060
     Total VC        $3,515         $4,811      $3,515     $14,537     $10,871              $0
     Fixed
     Cost               $350         $550         $350         $250          550       $250

     Tot. Cost                      $9,226                 $18,652                  $11,671
                                      Chapter 9 - Page 166


 3-Bank Solution:
                   Combination       1
      Group   Bank A Bank B          Bank C

         1                 $838
         2               $3,973
         3     $3,515
 Total VC      $3,515    $4,811           $0
 Fixed
 Cost            $350        $550       $250

                                      $9,476

 Minimum Cost Solution =              $9,226 Select the two-bank system, A & B




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


     Assumptions
     Opportunity rate                  10.00%

               Customer       Average monthly
     Group     Remittances    Remittances                    Days of Float
                                                                   ---------
                   Number           Face Value    Bank 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
     Variable Processing Costs                     $0.55                 $0.40    $0.70
     Fixed
     Costs                                           $350                $500      $250
                                       Chapter 9 - Page 167




                 1-Bank Solution:

                         Group         Bank A        Bank B         Bank C

                               1      $34,212       $28,055         $36,342
                               2      $56,507       $46,027         $74,521
                               3      $48,955       $42,842         $62,774
                 Fixed Cost              $350          $500            $250
                 Total Cost          $140,025      $117,425        $173,887



   2-Bank Solution:

                    Combination 1                Combination 2   Combination 3
       Group       Bank A    Bank B             Bank A    Bank C   Bank B    Bank C

             1                      $28,055    $34,212                    $28,055
             2                      $46,027    $56,507                    $46,027
             3                      $42,842    $48,955                    $42,842
   Total VC               $0       $116,925   $139,675             $0    $116,925        $0
   Fixed Cost           $350          $500        $350           $250         500      $250

   Total Cost                      $117,775                   $140,275              $117,675



3-Bank Solution:
                   Combination           1
    Group    Bank A    Bank B                       Bank C

         1                 $28,055
         2                 $46,027
         3                 $42,842
Total VC           $0     $116,925                       $0
Fixed Cost       $350         $500                     $250

                                                  $118,025

Minimum Cost Solution =                           $117,425 Select the one-bank system, B

				
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