Collection time = (2.3 ´ 0.5) + 1 + 2.1 = 4.25 days
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-1
Section: 19.3
Topic: Collection time
68. You are considering implementing a lockbox system for your firm. The system is expected to reduce the average collection time by 1.2 days. On an average day, your firm receives 320 checks with an average value of $99 each. The daily interest rate on Treasury bills is 0.014 percent. What is the anticipated amount of the daily savings if this system is implemented?
A. $2.61
B. $3.29
C. $4.45
D. $5.32
E. $5.78
Daily savings = 320 ´ $99 ´ 1.2 ´ 0.00014 = $5.32
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox daily savings
69. Roger's Distributors receives an average of 216 checks a day. The average amount per check is $629. The firm is considering a lockbox system which it anticipates will reduce the average collection time by 1.5 days. The daily interest rate on Treasury bills is 0.011 percent. What is the amount of the expected daily savings of the lockbox system?
A. $2.04
B. $6.92
C. $14.95
D. $18.10
E. $22.42
Daily savings = 216 ´ $629 ´ 1.5 ´ 0.00011 = $22.42
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox daily savings
70. Hand Tools, Inc. receives an average of 611 checks a day. The average amount per check is $425. The firm is considering a lockbox system which it anticipates will reduce the average collection time by 1 day. The bank charges $0.275 a check for this service. The daily interest rate on Treasury bills is 0.013 percent. What is the average daily cost of the lockbox system?
A. $31.16
B. $54.19
C. $168.03
D. $180.11
E. $199.19
Daily cost = 611 ´ $0.275 = $168.03
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox daily cost
71. You are considering implementing a lockbox system for your firm. The system is expected to reduce the average collection time by 1.3 days. On an average day, your firm receives 136 checks with an average value of $219 each. The daily interest rate on Treasury bills is 0.021 percent. The bank charge per check is $0.22. What is the anticipated daily cost of the lockbox system?
A. $3.48
B. $6.25
C. $12.60
D. $29.92
E. $36.17
Daily cost = 136 ´ $0.22 = $29.92
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox daily cost
72. You are considering implementing a lockbox system for your firm. The system is expected to reduce the average collection time by 2.8 days. On an average day, your firm receives 2,419 checks with an average value of $1,287 each. The daily interest rate on Treasury bills is 0.016 percent. The bank charge per check is $0.30. What is the net present value of this lockbox arrangement?
A. -$4,535,625
B. -$2,611,575
C. $187,419
D. $4,181,483
E. $13,252,733
Net present value = [2,419 ´ $1,287 ´ 2.8] - [(2,419 ´ $0.30)/.00016] = $4,181,483
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox net present value
73. Rosewell International receives an average of 268 checks a day with an average amount per check of $820. The firm is considering a lockbox system which it anticipates will reduce the average collection time by 1.4 days. The bank charges $0.21 a check for this service. The daily interest rate on Treasury bills is 0.02 percent. What is the net present value of this lockbox arrangement?
A. -$61,640
B. -$26,264,
C. $26,264
D. $30,820
E. $61,640
Net present value = [268 ´ $820 ´ 1.4] - [(268 ´ $0.21)/.0002] = $26,264
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox net present value
74. The Eliot Co. needs $185,000 a week to pay bills. The standard deviation of the weekly disbursements is $17,600. The firm has established a lower cash balance limit of $75,000. The applicable interest rate is 5.5 percent and the fixed cost of transferring funds is $47. Based on the BAT model, what is the optimal initial cash balance?
A. $90,668
B. $97,515
C. $104,141
D. $128,224
E. $136,509
Optimal initial cash balance = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
75. Theo's Bar & Grill needs $147,000 a week to pay bills. The standard deviation of the weekly disbursements is $9,600. The firm has established a lower cash balance limit of $40,000. The applicable interest rate is 3.5 percent and the fixed cost of transferring funds is $45. Based on the BAT model, what is the optimal average cash balance?
A. $36,199
B. $49,568
C. $70,100
D. $99,136
E. $112,400
Optimal average cash balance = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
76. Parkway Express needs $318,000 a week to pay bills. The standard deviation of the weekly disbursements is $31,000. The firm has established a lower cash balance limit of $60,000. The applicable interest rate is 4.5 percent and the fixed cost of transferring funds is $65. Based on the BAT model, what is the opportunity cost of holding cash?
A. $3,873
B. $4,918
C. $5,207
D. $109,283
E. $110,440
Opportunity cost = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
77. Penco Supply spends $428,000 a week to pay bills and maintains a lower cash balance limit of $75,000. The standard deviation of its disbursements is $18,900. The applicable interest rate is 5 percent and the fixed cost of transferring funds is $65. What is the firm's optimal initial cash balance based on the BAT model?
A. $150,600
B. $158,929
C. $170,096
D. $221,506
E. $240,553
Optimal initial cash balance = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
78. Your firm spends $54,000 a week to pay bills and maintains a lower cash balance limit of $45,000. The standard deviation of your disbursements is $12,100. The applicable interest rate is 4.5 percent and the fixed cost of transferring funds is $55. What is your opportunity cost of holding cash based on the BAT model?
A. $1,318
B. $1,864
C. $2,204
D. $2,311
E. $3,709
Opportunity cost = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
79. Rosie O'Grady's spends $98,000 a week to pay bills and maintains a lower cash balance limit of $95,000. The standard deviation of the disbursements is $14,600. The applicable interest rate is 4.8 percent and the fixed cost of transferring funds is $50. What is this firm's total cost of holding cash based on the BAT model?
A. $1,431
B. $2,862
C. $3,034
D. $4,912
E. $4,946
Optimal initial cash balance = 
Opportunity cost = 
Trading cost = [52/($103,037.21/$98,000)] ´ $50 = $2,472.893
Total cost = $2,472.893 + $2,472.893 = $4,946
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
80. Your firm spends $346,000 a week to pay bills and maintains a lower cash balance limit of $150,000. The standard deviation of your disbursements is $28,700. The applicable interest rate is 5 percent and the fixed cost of transferring funds is $60. What is your optimal average cash balance based on the BAT model?
A. $103,900
B. $146,500
C. $182,200
D. $207,800
E. $249,900
Optimal average cash balance = 
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: BAT model
81. The Cow Pie Spreader Co. spends $214,000 a week to pay bills and maintains a lower cash balance limit of $175,000. The standard deviation of the disbursements is $16,000. The applicable weekly interest rate is 0.025 percent and the fixed cost of transferring funds is $49. What is the firm's cash balance target based on the Miller-Orr model?
A. $208,511
B. $247,560
C. $251,006
D. $254,545
E. $258,878
Cash balance target = $175,000 + [0.75 ´ $49 ´ ($16,0002/.00025)]1/3 = $208,511
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
82. The Blue Moon Hotel and Spa spends $359,000 a week to pay bills and maintains a lower cash balance limit of $250,000. The standard deviation of the disbursements is $46,800. The applicable weekly interest rate is 0.045 percent and the fixed cost of transferring funds is $60. What is the hotel's optimal upper cash limit based on the Miller-Orr model?
A. $430,836
B. $447,905
C. $528,700
D. $739,459
E. $861,672
Cash balance target = $250,000 + [0.75 ´ $60 ´ ($46,8002/.00045)]1/3 = $310,278.70
Upper cash limit = 3 ´ $310,278.70 - (2 ´ $250,000) = $430,836
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
83. Donaldson, Inc. spends $94,000 a week to pay bills and maintains a lower cash balance limit of $50,000. The standard deviation of the disbursements is $13,000. The applicable weekly interest rate is 0.045 percent and the fixed cost of transferring funds is $52. What is your optimal average cash balance based on the Miller-Orr model?
A. $78,778
B. $82,623
C. $231,969
D. $236,334
E. $247,868
Cash balance target = $50,000 + [0.75 ´ $52 ´ ($13,0002/.00045)]1/3 = $74,466.94
Average cash balance = [(4 ´ $74,466.94) - $50,000]/3 = $82,623
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
84. The Burger Stop spends $52,000 a week to pay bills and maintains a lower cash balance limit of $60,000. The standard deviation of the disbursements is $7,500. The applicable weekly interest rate is 0.04 percent and the fixed cost of transferring funds is $50. What is your optimal average cash balance based on the Miller-Orr model?
A. $79,116
B. $83,208
C. $110,315
D. $237,348
E. $249,624
Cash balance target = $60,000 + [0.75 ´ $50 ´ ($7,5002/.0004)]1/3 = $77,405.96
Average cash balance = [(4 ´ $77,405.96) - $60,000]/3 = $83,208
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
85. Your firm spends $48,000 a week to pay bills and maintains a lower cash balance limit of $50,000. The standard deviation of the disbursements is $8,600. The applicable weekly interest rate is 0.054 percent and the fixed cost of transferring funds is $65. What is your cash balance target based on the Miller-Orr model?
A. $48,156
B. $49,990
C. $54,884
D. $68,830
E. $75,726
Cash balance target = $50,000 + [.75 ´ $65 ´ ($8,6002/.00054)]1/3 = $68,830
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
86. Travel Inn Express spends $109,000 a week to pay bills and maintains a lower cash balance limit of $125,000. The standard deviation of the disbursements is $14,400. The applicable weekly interest rate is 0.039 percent and the fixed cost of transferring funds is $58. What is the inn's cash balance target based on the Miller-Orr model?
A. $28,492
B. $31,359
C. $153,492
D. $156,359
E. $225,417
Cash balance target = $125,000 + [0.75 ´ $58 ´ ($14,4002/.00039)]1/3 = $153,492
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
Learning Objective: 19-3
Section: 19.A
Topic: Miller-Orr model
Essay Questions
87. Explain how a lockbox system operates and why a firm might consider implementing such a system.
A lockbox system entails opening post office boxes in various geographic locations. These locations are selected such that they are close to the firm's key customers. At each of those sites, a representative from a local bank collects the incoming checks and deposits them into the firm's account. The information on the deposits is forwarded to the firm so customer accounts can be credited for the payments. The firm transfers funds from these remote bank accounts into one or more centralized bank accounts on a routine basis. A lockbox system reduces mailing and processing times, and creates a one-time cash inflow for the firm.
Feedback: Refer to section 19.3
AACSB: Reflective thinking
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox systems
88. Explain how the Check Clearing Act for the 21st Century affects both collection and disbursement float.
Check 21 eliminated the need to present an original check to the check writer's bank to receive payment. Now, the bank receiving the check as a deposit can electronically transmit a copy of the check to the check writer's bank and receive immediate payment. This reduces both collection and disbursement float times.
Feedback: Refer to section 19.2
AACSB: Reflective thinking
Bloom's: Comprehension
Difficulty: Basic
Learning Objective: 19-1
Section: 19.2
Topic: Check Clearing Act for the 21st Century
89. Explain how the unethical use of uncollected funds has been impacted by the growth of on-line retailing and banking.
Whenever cash is moved electronically, both collection and disbursement float disappears. Reducing float limits the ability of a firm to earn income by investing uncollected cash.
Feedback: Refer to section 19.2
AACSB: Reflective thinking and Ethics
Bloom's: Comprehension
Difficulty: Basic
Learning Objective: 19-1
Section: 19.2
Topic: Internet banking
90. Float management systems may provide only minimal benefits to a firm. Given that most firms have other projects with higher positive net present values, why should a firm's managers spend time implementing a float management system?
Students should explain that any project with a positive net present value adds value to the overall firm and should be implemented. Generally speaking, the majority of employee or management time required by a float management system is spent on the implementation of the system. Once the system is in place, management and employee time required for float management tends to be rather minimal.
Feedback: Refer to section 19.2
AACSB: Reflective thinking
Bloom's: Application
Difficulty: Basic
Learning Objective: 19-1
Section: 19.2
Topic: NPV of float management
91. Explain what a zero-balance account is, how it is used, and how it affects cash management.
A zero-balance account is a checking account which is frequently used either for payroll or accounts payable purposes. Funds are transferred from a master account into the zero-balance account only as needed to cover checks presented for payment. All excess funds are held in the master account. By concentrating the firm's safety stock of cash in one account, the firm can better utilize its funds.
Feedback: Refer to section 19.4
AACSB: Reflective thinking
Bloom's: Comprehension
Difficulty: Basic
Learning Objective: 19-2
Section: 19.4
Topic: Zero-balance accounts
Multiple Choice Questions
92. Each business day, on average, a company writes checks totaling $26,000 to pay its suppliers. The usual clearing time for the checks is 5 days. Meanwhile, the company is receiving payments from its customers each day, in the form of checks, totaling $40,000. The cash from the payments is available to the firm after 2 days. What is the amount of the firm's average net float?
A. $30,00
B. $50,000
C. $80,000
D. $110,000
E. $130,000
Net float = 5($26,000) - 2($40,000) = $50,000
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-2
Learning Objective: 19-1
Section: 19.2
Topic: Net float
93. Purple Feet Wine, Inc. receives an average of $6,000 in checks per day. The delay in clearing is typically 3 days. The current interest rate is 0.025 percent per day. Assume 30 days per month. What is the highest daily fee the company should be willing to pay to eliminate its float entirely?
A. $1.50
B. $3.00
C. $3.75
D. $4.50
E. $6.00
Maximum daily fee = ($6,000 ´ 3) ´ 0.00025 = $4.50
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-3
Learning Objective: 19-1
Section: 19.2
Topic: Cost of float
94. Your neighbor goes to the post office once a month and picks up two checks, one for $18,000 and one for $4,000. The larger check takes 4 days to clear after it is deposited; the smaller one takes 6 days. Assume 30 days per month. What is the weighted average delay?
A. 4.21 days
B. 4.36 days
C. 4.78 days
D. 5.00 days
E. 6.00 days
Total monthly receipts = $18,000 + $4,000 = $22,000
Weighted average delay = [($18,000/$22,000) ´ 4] + [($4,000/$22,000) ´ 6] = 4.36 days
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-4
Learning Objective: 19-1
Section: 19.2
Topic: Weighted average delay
95. Your firm has an average receipt size of $60. A bank has approached you concerning a lockbox service that will decrease your total collection time by 1 day. You typically receive 28,000 checks per day. The daily interest rate is 0.016 percent. What is the NPV of the lockbox project if the bank charges a fee of $210 per day?
A. $367,500
B. $427,500
C. $903,350
D. $1,412,500
E. $1,680,000
NPV of service = $60(28,000) - ($210/0.00016) = $367,500
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-5
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox NPV
96. A mail-order firm processes 5,000 checks per month. Of these, 55 percent are for $55 and 45 percent are for $65. The $55 checks are delayed 2 days on average; the $65 checks are delayed 5 days on average. Assume each month has 30 days. The interest rate is 6 percent per year. How much should the firm be willing to pay to reduce the weighted average float by 1.4 days?
A. $4,165
B. $13,883
C. $41,650
D. $138,883
E. $416,500
Maximum payment = Average daily float = 1.4{[(0.55 ´ 5,000 ´ $55) + (0.45 ´ 5,000 ´ $65)]/30} = $13,883
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-6
Learning Objective: 19-1
Section: 19.2
Topic: Average daily float
97. Paper Submarine Manufacturing is investigating a lockbox system to reduce its collection time. It has determined the following:
The total collection time will be reduced by 2 days if the lockbox system is adopted. What is the NPV of adopting the lockbox system?
A. $600,000
B. $775,000
C. $975,000
D. $1,200,000
E. $1,425,000
NPV = (2 ´ 300 ´ $4,000) - [($0.65 ´ 300)/0.0002] = $1,425,000
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-7
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox NPV
98. Home Roasted Turkeys disburses checks every 4 weeks that average $70,000 and take 5 days to clear. How much interest can the company earn if it delays transfer of funds from an interest-bearing account that pays 0.02 percent per day for these 5 days? Ignore the effects of compound interest. Assume 52 weeks in a year.
A. $36
B. $91
C. $182
D. $364
E. $910
Interest = $70,000 (5) (52/4) (0.0002) = $910
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-9
Learning Objective: 19-2
Section: 19.3
Topic: Value of delay
99. Never Again Enterprises has an agreement with The Worth Bank whereby the bank handles $3.12 million in collections a day and requires a $1,000,000 compensating balance. Never Again is contemplating canceling the agreement and dividing its eastern region so that two other banks will handle its business. Banks A and B will each handle $1.56 million of collections a day, and each requires a compensating balance of $1,550,000. Never Again's financial management expects that collections will be accelerated by one day if the eastern region is divided. The T-bill rate is 5 percent annually. What is the amount of the annual net savings if this plan is adopted?
A. $10,200
B. $51,000
C. $76,500
D. $102,000
E. $125,000
NPV = $3,120,000 - [2($1,550,000) - $1,000,000] = $1,020,000
Net savings = 0.05($1,020,000) = $51,000
AACSB: Analytic
Bloom's: Application
Difficulty: Basic
EOC #: 19-10
Learning Objective: 19-2
Section: 19.3
Topic: NPV of float reduction
100. Mountaintop Inns, a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system offered by a bank located in Pittsburgh, Pennsylvania. The bank has estimated that use of the system will reduce collection time by one day. In addition to the variable charge shown below, there is also a fixed charge of $4,320 per year for the lockbox system. Assume a year has 365 days. What is the NPV of the lockbox system given the following information?
A. -$156,727
B. -$131,301
C. -$74,208
D. $11,507
E. $26,433
NPV = (1 ´ 750 ´ $1,800) - [($0.30 ´ 750)/(1.061/365 - 1)] - [$4,320/0.06] = -$131,301
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
EOC #: 19-11
Learning Objective: 19-2
Section: 19.3
Topic: Lockbox NPV
101. Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia-area bank will provide this service for an annual fee of $25,000 plus 10 cents per transaction. The estimated reduction in collection and processing time is one day. The average customer payment in this region is $8,200. Treasury bills are currently yielding 5 percent per year. Assume a year has 365 days. Approximately how many customers each day, on average, are needed to make the system profitable for Cow Chips, Inc.?
A. 56
B. 67
C. 74
D. 83
E. 89
NPV = 0 = ($8,200 ´ 1 ´ N) - ($0.10 ´ N)/0.000134 - $25,000/0.05
N = 67 customers per day
AACSB: Analytic
Bloom's: Analysis
Difficulty: Intermediate
EOC #: 19-12
Learning Objective: 19-2
Section: 19.3
Topic: Transactions required
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