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Unformatted text preview: leave capital structure unchanged. 12. It is unethical because you have essentially tricked the grocery store into making you an interestfree loan, and the grocery store is harmed because it could have earned interest on the money instead of loaning it to you. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. The average daily float is the average amount of checks received per day times the average number of days delay, divided by the number of days in a month. Assuming 30 days in a month, the average daily float is: Average daily float = 4($156,000)/30 Average daily float = $20,800 2. a. The disbursement float is the average monthly checks written times the average number of days for the checks to clear, so: Disbursement float = 4($14,000) Disbursement float = $56,000 The collection float is the average monthly checks received times the average number of days for the checks to clear, so: Collection float = 2(–$26,000) Collection float = –$52,000 The net float is the disbursement float plus the collection float, so: Net float = $56,000 – 52,000 Net float = $4,000 514 b. The new collection float will be: Collection float = 1(–$26,000) Collection float = –$26,000 And the new net float will be: Net float = $56,000 – 26,000 Net float = $30,000 3. a. The collection float is the average daily checks received times the average number of days for the checks to clear, so: Collection float = 3($19,000) Collection float = $57,000 b. c. The firm should pay no more than the amount of the float, or $57,000, to eliminate the float. The maximum daily charge the firm should be willing to pay is the collection float times the daily interest rate, so: Maximum daily charge = $57,000(.00019) Maximum daily charge = $10.83 4. a. Total float = 4($17,000) + 5($6,000) Total float = $98,000 b. The average daily float is the total float divided by the number of days in a month. Assuming 30 days in a month, the average daily float is: Average daily float = $98,000/30 Average daily float = $3,266.67 c. The average daily receipts are the average daily checks received divided by the number of days in a month. Assuming a 30 day month: Average daily receipts = ($17,000 + 6,000)/30 Average daily receipts = $766.67 The weighted average delay is the sum of the days to clear a check, times the amount of the check divided by the average daily receipts, so: Weighted average delay = 4($17,000/$23,000) + 5($6,000/$23,000) Weighted average delay = 4.26 days 515 5. The average daily collections are the number of checks received times the average value of a check, so: Average daily collections = $108(8,500) Average daily collections = $918,000 The present value of the lockbox service is the average daily receipts times the number of days the collection is reduced, so: PV = (2 day reduction)($918,000) PV = $1,836,000 The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily interest rate. So: PV of cost = $225/.00016 PV of cost = $1,406,250 The firm should take the lockbox service. The NPV of the lockbox is the cost plus the present value of the reduction in collection time, so: NPV = –$1,406,250 + 1,836,000 NPV = $429,750 The annual savings excluding the cost would be the future value of the savings minus the costs, so: Annual savings = $1,836,000(1.00016)365 – 1,836,000 Annual savings = $110,406.05 And the annual cost would be the future value of the daily cost, which is an annuity, so: Annual cost = $225(FVIFA365,.016%) Annual cost = $84,563.46 So, the annual net savings would be: Annual net savings = $110,406.05 – 84,563.46 Annual net savings = $25,842.59 6. a. The average daily float is the sum of the percentage each check amount is of the total checks received times the number of checks received times the amount of the check times the number of days until the check clears, divided by the number of days in a month. Assuming a 30 day month, we get: Average daily float = [.60(5,300)($55)(2) + .40(5,300)($80)(3)]/30 Average daily float = $28,620 On average, there is $28,620 that is uncollected and not available to the firm. 516 b. The total collections are the sum of the percentage of each check amount received times the total checks received times the amount of the check, so: Total collections = .60(5,300)($55) + .40(5,300)($80) Total collections = $344,500 The weighted average delay is the sum of the average number of days a check of a specific amount is delayed, times the percentage that check amount makes up of the total checks received, so: Weighted average delay = 2[.60(5,300)($55)/$344,500] + 3[.40(5,300)($80) /$344,500] Weighted average delay = 2.49 days The average daily floa...
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 Spring '10
 eshmalwi
 Finance, Corporate Finance

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