Chapter 5 Solution - CF2 PDF

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1 Questions and ExercisesCHAPTER 5CASH MANAGEMENTBASIC1. Calculating Float In a typical month, the Warren Corporation receives 140 check totaling $113,500. These are delayed four days on average. What is the average daily float? ANSWER: the average daily float= total float/total days = 113500/30 x4 ...

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Questions and Exercises

CHAPTER 5 CASH MANAGEMENT BASIC 1. Calculating Float In a typical month, the Warren Corporation receives 140 check totaling $113,500. These are delayed four days on average. What is the average daily float? ANSWER: the average daily float= total float/total days = 113500/30 x4 = $15133 2. Calculating Net Float Each business day, on average, a company writes checks totaling $14,400 to pay its suppliers. The usual clearing time for the checks is four days. Meanwhile, the company is receiving payments from its customers each day, in the form of checks, totaling $25,300. The cash from the payments is available to the firm after two days. a. Calculate the company’s disbursement float, collection float, and net float. b. How would your answer to part (a) change if the collected funds were available in one day instead of two? Each business day companies writing checks to suppliers of $13,600 and such checks takes 4 days time to clear . ANSWER: Disbursement Float = Average amount of check* time to clear = 14400*4 = 57600$ Collection Float =(-25300*2) = -50600$ Net Float = Disbursement Float + collection Float = 57600$ - 50600$ = 7000 (b) Each business day companies writing checks to suppliers of $14,400 and such checks takes 4 days time to clear . Disbursement Float = Average amount of check* time to clear = 14400*4 = 57600$ Collection Float =(-25300*1)

Corporate Finance 11th edition by Ross, Westerfield, Jaffe, and Jordan

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= -25300$ Net Float = Disbursement Float + collection Float = 57600-25300= 32300$ 3. Costs of Float Purple Feet Wine, Inc., receives an average of $13,800 in checks per day. The delay in clearing is typically three days. The current interest rate is .018 percent per day. a. What is the company’s float? b. What is the most the company should be willing to pay today to eliminate its float entirely? c. What is the highest daily fee the company should be willing to pay to eliminate its float entirely? ANSWER: a. Float= $13,800x3= $41,400 b. Maximum Payment = $41,400 c. Maximum daily Charge = Float x Interest Rate= $41,400 x 0.018%= $7.452 4. Float and Weighted Average Delay Your neighbor goes to the post office once a month and picks up two checks, one for $9,700 and one for $2,600. The larger check takes four days to clear after it is deposited; the smaller one takes five days. a. What is the total float for the month? b. What is the average daily float? c. What are the average daily receipts and weighted average delay? ANSWER: a. the total float for the month= $9,700x4 + $2,600x5= 51800 b. the average daily float= 51800/30=1726.67 c. the average daily receipts= ($9,700 + $2,600)/30 =11300/30= 410 weighted average delay= 9700/($9,700 + $2,600) x 4 + 2600/($9,700 + $2,600) x5 = 4.21 5. NPV and Collection Time Your firm has an average receipt size of $119. A bank has approached you concerning a lockbox service that will decrease your total collection time by two days. You typically receive 5,650 checks per day. The daily interest rate is .015 percent. If the bank charges a fee of $160 per day, should the lockbox project be accepted? What would the net annual savings be if the service were adopted? ANSWER The average daily collections =average receipt × checks received per day= $119x 5650= $672350 Savings of the lockbox service = average collection * time saved= $672350x2= $1344700 PV of cost = Lock box fee /interest= 160/0.015%=1066666.667 The NPV = Savings - PV of cost NPV = $1344700 - 1066666.67=278033.33 > 0

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Questions and Exercises

the lockbox project should be accepted Annual savings = Savings × (1+i)^365 - Savings Annual savings = $1344700 (1+0.015%)^365 - $1344700 = $75669.19 Annual cost= $160(FVIFA365,.015%) = 160x[(1+i)^n -1]/i =160x[(1+0.015%)^365 -1]/0.015%= $64142.95 Annual savings = annual saving - annual cost = $75669.19 - $64142.95= $12282.37 6. Using Weighted Average Delay A mail-order firm processes 5,450 checks per month. Of these, 70 percent are for $55 and 30 percent are for $80. The $55 checks are delayed two days on average; the $80 checks are delayed three days on average. a. What is the average daily collection float? How do you interpret your answer? b. What is the weighted average delay? Use the result to calculate the average daily float. c. How much should the firm be willing to pay to eliminate the float? d. If the interest rate is 7 percent per year, calculate the daily cost of the float. e. How much should the firm be willing to pay to reduce the weighted average float by 1.5 days? ANSWER Amount: Time delays Item 1: $55x70%x5450= $209,825 2 Item 2: $80x30%x5450= $130,800 3 Total: $340,625

Total float $419,650 $392,400 $812,050

a. the average daily collection float= Total float/total days= $812,050/30= $27,068.33 b. the weighted average delay= 209,825/340,625 x 2 + 130,800/340,625 x 3=2.384 the average daily receipt= 340,625/30= 11,354.17 the average daily float= the average daily receipt x the weighted average delay = 11,354.17x 2.384 = $27,068.34 c. Maximum Payment = $27,068.33 d. the daily cost of the float= $27,068.33 x 7% = $1,894.78 e. the weighted average float by 1.5 days the average daily float= 11354.17x ( 2.384 -1.5)= 10037.086 Maximum Payment =$10037.086 7. Value of Lockboxes Paper Submarine Manufacturing is investigating a lockbox system to reduce its collection time. It has determined the following:

Corporate Finance 11th edition by Ross, Westerfield, Jaffe, and Jordan

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The total collection time will be reduced by three days if the lockbox system is adopted. a. What is the PV of adopting the system? b. What is the NPV of adopting the system? c. What is the net cash flow per day from adopting? Per check? ANSWER a. Average daily collections = $865 x 410 = $354650 The PV of the lockbox service = the daily payments x the number of days the collection is reduced PV = $354650* 3= 1063950 b. The PV of the cost = the daily cost / the daily interest rate Daily cost = $0.5*410 =$205 PV of cost =$205/0.02% = 1025000  NPV = PV of the service - costs= $1063950 - $1025000 = 38950 > 0 c. The net cash flows= the PV of the daily collections x the daily interest rate - the transaction cost / day, so: Net cash flow per day = 1063950x0.02% – $205= 7.79 Net cash flow per check = 7.79/410= $0.019 INTERMEDIATE 8. NPV and Reducing Float No More Books Corporation has an agreement with Floyd Bank, whereby the bank handles $2.9 million in collections a day and requires a $350,000 compensating balance. No More Books 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 $1.45 million of collections a day, and each requires a compensating balance of $190,000. No More Books’ financial management expects that collections will be accelerated by one day if the eastern region is divided. Should the company proceed with the new system? What will be the annual net savings? Assume that the T-bill rate is 5 percent annually. ANSWER

9. Lockboxes and Collection Time Bird’s Eye Treehouses, Inc., 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. The bank has estimated that use of the system will reduce collection time by two days. Based on the following information,

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Questions and Exercises

should the lockbox system be adopted? How would your answer change if there were a fixed charge of $5,000 per year in addition to the variable charge? (pay attention to the daily interest rate, affect daily

How would your answer change if there were a fixed charge of $5,000 per year in addition to the variable charge? (pay attention to the daily interest rate, affect daily) ANSWER a. Average daily collections = $865 x 630 = $544950 -

The PV of the lockbox service = the daily payments x the number of days the collection is reduced

PV = $544950* 2= 1089900 -

The PV of the cost = the daily cost / the daily interest rate

Daily interest rate = (1+7%)^1/365 -1 = 1.85x10^-4 Daily cost = $0.22*850 =$187 PV of cost =$187/(1.85x10^-4) = 1010810.81 NPV without fixed fee = PV of the service - costs= $1089900 - $1010810.81= $79089.19 > 0  the lockbox system should be adopted b. If there were a fixed charge of $5,000 per year in addition to the variable charge. PV of fixed fee = $5000/7%= $71428.57 NPV with fixed fee = $79089.19 - $71428.57 = $7660.62 > 0  the lockbox system should be adopted 10. Lockboxes and Collections It takes Cookie Cutter Modular Homes, Inc., about five days to receive and deposit checks from customers. Cookie Cutter’s management is considering a lockbox system to reduce the firm’s collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are $126,500, and the required rate of return is 9 percent per year. a. What is the reduction in outstanding cash balance as a result of implementing the lockbox system? b. What is the dollar return that could be earned on these savings? c. What is the maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the end of the month? What if the payment is due at the beginning of the month?

Corporate Finance 11th edition by Ross, Westerfield, Jaffe, and Jordan

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ANSWER a) Outstanding cash balance reduction = Average daily collections * Number of days = $126,500* 2 = $. b) Effective daily rate=(1 + rate of return)^(1/365) - 1 Daily dollar return = Outstanding cash balance reduction * ((1 + rate of return)^(1/365)-1) = $379,500* ((1 + 9%)^(1/365)-1) = $89.61 c-1) if the payment is due at the end of the month Payment = PV * Effective monthly rate = $379,500* ((1 + 9%)^(1/12) -1) = $2735.18 Maximum monthly charge = $2735.18 c-2) if the payment is due at the beginning of the month Maximum monthly charge = $2735.18 / [1+ ((1 + 9%)^(1/12) -1)]= $2715.6 11. Using the BAT Model Given the following information, calculate the target cash balance using the BAT model: Annual interest rate: 7%; Fixed order cost: $10; Total cash needed: $5,000. How do you interpret your answer? ANSWER the target cash balance when the opportunity cost = the trading cost  C/2 x R = T/C x F

12. Using Miller–Orr SlapShot plc has a fixed cost associated with buying and selling marketable securities of £100. The interest rate is currently 0.021 per cent per day, and the firm has estimated that the standard deviation of its daily net cash flows is £75. Management has set a lower limit of £1,100 on cash holdings. Calculate the target cash balance and upper limit using the Miller–Orr model. Describe how the system will work. ANSWER

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Questions and Exercises

13. Using Miller–Orr The variance of the daily cash flows for the Pele Bicycle Shop is $960,000. The opportunity cost to the firm of holding cash is 7 per cent per year. What should be the target cash level and the upper limit if the tolerable lower limit has been established as $150,000? The fixed cost of buying and selling securities is $500 per transaction. ANSWER R= 7% => Daily interest rate = (1+7%)^1/365 -1 = 1.85x10^-4 L= 150,000, F= 500

CHALLENGE 14. Costs and the BAT Model D&C Accountants needs a total of £4,000 in cash during the year for transactions and other purposes. Whenever cash runs low, the firm sells off £300 in securities and transfers the cash in. The interest rate is 6 per cent per year, and selling off securities costs £25 per sale. a. What is the opportunity cost under the current policy? The trading cost? With no additional calculations, would you say that D&C keeps too much or too little cash? Explain. b. What is the target cash balance derived using the BAT model? ANSWER T= £4,000 R=6% C= £300 a. The opportunity cost under the current policy= C/2 x R = £300/2 x 6% = 9 Trading cost= T/C x F = £4,000/£300 x 25 = 333.33 b. The target cash balance derived using the BAT model

15. Determining Optimal Cash Balances The Tommy Byrne Company is currently holding $700,000 in cash. It projects that over the next year its cash outflows will exceed cash inflows by $360,000 per month. How much of the current cash holding should be retained, and how much should be used to increase the company’s holdings of marketable securities? Each time these securities are bought or sold through a broker, the company pays a fee of $500. The annual interest rate on money market securities is 6.5 per cent. After the initial investment of excess cash, how many times during the next 12 months will securities be sold?

Corporate Finance 11th edition by Ross, Westerfield, Jaffe, and Jordan

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C= $700,000 T= $360,000x12= 4320000 F= 500 R= 6.5% The current cash holding should be retained:

Cash should be used to increase the company’s holdings of marketable securities = C- C* =700,000 257801.35 =442,198.65 After the initial investment of excess cash, times during the next 12 months will securities be sold: T/C* = $4320000/257801.35=16.76 16. Opportunity versus Trading Costs White Whale Corporation has an average daily cash balance of $1,300. Total cash needed for the year is $43,000. The interest rate is 5 percent, and replenishing the cash costs $8 each time. What are the opportunity cost of holding cash, the trading cost, and the total cost? What do you think of White Whale’s strategy? ANSWER The opportunity cost of holding cash= C/2 x R= $1,300/2 x 5% = $32.5 The trading cost= T/C x F = 43000/1300 x 8 = $264.62 The total cost = The opportunity cost of holding cash + The trading cost = $32.5+ $264.62=$297.12

 White Whale should increase daily cash balance from $1300 to 3709.45 (appox) 17. Using BAT All Night Corporation has determined that its target cash balance if it uses the BAT model is $2,700. The total cash needed for the year is $28,000, and the order cost is $10. What interest rate must All Night be using? ANSWER...