Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# 47 2160000 u 19078141 10 using the bat model and

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Unformatted text preview: t is the weighted average delay times the average checks received per day. Assuming a 30 day month, we get: Average daily float = 2.49(\$344,500/30 days) Average daily float = \$28,620 c. d. The most the firm should pay is the total amount of the average float, or \$28,620. The average daily interest rate is: 1.07 = (1 + R)365 R = .01854% per day The daily cost of float is the average daily float times the daily interest rate, so: Daily cost of the float = \$28,620(.0001854) Daily cost of the float = \$5.31 e. The most the firm should pay is still the average daily float. Under the reduced collection time assumption, we get: New average daily float = 1.5(\$344,500/30) New average daily float = \$17,225 7. a. The present value of adopting the system is the number of days collections are reduced times the average daily collections, so: PV = 3(385)(\$1,105) PV = \$1,276,275 b. The NPV of adopting the system is the present value of the savings minus the cost of adopting the system. The cost of adopting the system is the present value of the fee per transaction times the number of transactions. This is a perpetuity, so: NPV = \$1,276,275 – [\$0.50(385)/.0002] NPV = \$313,775 517 c. The net cash flows is the present value of the average daily collections times the daily interest rate, minus the transaction cost per day, so: Net cash flow per day = \$1,276,275(.0002) – \$0.50(385) Net cash flow per day = \$62.76 The net cash flow per check is the net cash flow per day divided by the number of checks received per day, or: Net cash flow per check = \$62.76/385 Net cash flow per check = \$0.16 Alternatively, we could find the net cash flow per check as the number of days the system reduces collection time times the average check amount times the daily interest rate, minus the transaction cost per check. Doing so, we confirm our previous answer as: Net cash flow per check = 3(\$1,105)(.0002) – \$0.50 Net cash flow per check = \$0.16 per check 8. a. The reduction in cash balance from adopting the lockbox is the number of days the system reduces collection time times the average daily collections, so: Cash balance reduction = 3(\$145,000) Cash balance reduction = \$435,000 b. The dollar return that can be earned is the average daily interest rate times the cash balance reduction. The average daily interest rate is: Average daily rate = 1.091/365 – 1 Average daily rate = .0236% per day The daily dollar return that can be earned from the reduction in days to clear the checks is: Daily dollar return = \$435,000(.000236) Daily dollar return = \$102.72 c. If the company takes the lockbox, it will receive three payments early, with the first payment occurring today. We can use the daily interest rate from part b, so the savings are: Savings = \$145,000 + \$145,000(PVIFA.0236%,2) Savings = \$434,897.32 If the lockbox payments occur at the end of the month, we need the effective monthly interest rate, which is: Monthly interest rate = 1.091/12 – 1 Monthly interest rate = 0.7207% 518 Assuming the lockbox payments occur at the end of the month, the lockbox payments, which are a perpetuity, will be: PV = C/R \$434,897.32 = C / .007207 C = \$3,134.35 It could also be assumed that the lockbox payments occur at the beginning of the month. If so, we would need to use the PV of a perpetuity due, which is: PV = C + C / R Solving for C: C = (PV × R) / (1 + R) C = (434,897.32 × .007207) / (1 + .007207) C = \$3,112.02 9. The interest that the company could earn will be the amount of the checks times the number of days it will delay payment times the number of weeks that checks will be disbursed times the daily interest rate, so: Interest = \$93,000(7)(52/2)(.00015) Interest = \$2,538.90 10. The benefit of the new arrangement is the \$4 million in accelerated collections since the new system will speed up collections by one day. The cost is the new compensating balance, but the company will recover the existing compensating balance, so: NPV = \$4,000,000 – (\$500,000 – 400,000) NPV = \$3,900,000 The company should proceed with the new system. The savings are the NPV times the annual interest rate, so: Net savings = \$3,900,000(.05) Net savings = \$195,000 Intermediate 11. To find the NPV of taking the lockbox, we first need to calculate the present value of the savings. The present value of the savings will be the reduction in collection time times the average daily collections, so: PV = 2(750)(\$980) PV = \$1,470,000 And the daily interest rate is: Daily interest rate = 1.0701/365 – 1 Daily interest rate = .00019 or .019% per day 519 The transaction costs are a perpetuity. The cost per day is the cost per transaction times the number of transactions per day, so the NPV of taking the lockbox is: NPV = \$1,470,000 – [\$0.35(750)/.00019] NPV = \$54,015.17 Without the fee, the lockbox system should be accepted. To calculate the NPV of the lockbox with the annual fee, we can simply use the NPV of the lockbox without the annual fee and subtract the addition cost. The annual fee is a perpetuity, so, with...
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