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Unformatted text preview: the fee, the NPV of taking the lockbox is: NPV = $54,015.17 – [$5,000/.07] NPV = –$17,413.40 With the fee, the lockbox system should not be accepted. 12. To find the minimum number of payments per day needed to make the lockbox system feasible is the number of checks that makes the NPV of the decision equal to zero. The average daily interest rate is: Daily interest rate = 1.051/365 – 1 Daily interest rate = .0134% per day The present value of the savings is the average payment amount times the days the collection period is reduced times the number of customers. The costs are the transaction fee and the annual fee. Both are perpetuities. The total transaction costs are the transaction costs per check times the number of checks. The equation for the NPV of the project, where N is the number of checks transacted per day, is: NPV = 0 = ($5,300)(1)N – $0.10(N)/.000134 – $20,000/.05 $400,000 = $5,300N – $748.05N $4,551.95N = $400,000 N = 87.87 ≈ 88 customers per day 520 APPENDIX 27A
1. a. b. c. d. e. f. Decrease. This will lower the trading costs, which will cause a decrease in the target cash balance. Decrease. This will increase the holding cost, which will cause a decrease in the target cash balance. Increase. This will increase the amount of cash that the firm has to hold in non-interest bearing accounts, so they will have to raise the target cash balance to meet this requirement. Decrease. If the credit rating improves, then the firm can borrow more easily, allowing it to lower the target cash balance and borrow if a cash shortfall occurs. Increase. If the cost of borrowing increases, the firm will need to hold more cash to protect against cash shortfalls as its borrowing costs become more prohibitive. Either. This depends somewhat on what the fees apply to, but if direct fees are established, then the compensating balance may be lowered, thus lowering the target cash balance. If, on the other hand, fees are charged on the number of transactions, then the firm may wish to hold a higher cash balance so they are not transferring money into the account as often. 2. The target cash balance using the BAT model is: C* = [(2T × F)/R]1/2 C* = [2($8,500)($25)/.06]1/2 C* = $2,661.45 The initial balance should be $2,661.45, and whenever the balance drops to $0, another $2,661.45 should be transferred in. 3. The holding cost is the average daily cash balance times the interest rate, so: Holding cost = ($1,300)(.05) Holding cost = $65.00 The trading costs are the total cash needed times the replenishing costs, divided by the average daily balance times two, so: Trading cost = [($43,000)($8)]/[($1,300)(2)] Trading cost = $132.31 The total cost is the sum of the holding cost and the trading cost, so: Total cost = $65.00 + 132.31 Total cost = $197.31 521 The target cash balance using the BAT model is: C* = [(2T × F)/R]1/2 C* = [2($43,000)($8)/.05]1/2 C* = $3,709.45 They should increase their average daily cash balance to: New average cash balance = $3,709.45/2 New average cash balance = $1,854.72 This would minimize the costs. The new total cost would be: New total cost = ($1,845.72)(.05) + [($43,000)($8)]/[2($1,854.72)] New total cost = $185.47 4. a. The opportunity costs are the amount transferred times the interest rate, divided by two, so: Opportunity cost = ($1,500)(.05)/2 Opportunity cost = $37.50 The trading costs are the total cash balance times the trading cost per transaction, divided by the amount transferred, so: Trading cost = ($16,000)($25)/$1,500 Trading cost = $266.67 The firm keeps too little in cash because the trading costs are much higher than the opportunity costs. b. The target cash balance using the BAT model is: C* = [(2T × F)/R]1/2 C* = [2($16,000)($25)/.05]1/2 C* = $4,000 5. The total cash needed is the cash shortage per month times twelve months, so: Total cash = 12($140,000) Total cash = $1,680,000 The target cash balance using the BAT model is: C* = [(2T × F)/R]1/2 C* = [2($1,680,000)($500)/.057]1/2 C* = $171,679.02 522 The company should invest: Invest = $690,000 – 171,679.02 Invest = $518,320.98 of its current cash holdings in marketable securities to bring the cash balance down to the optimal level. Over the rest of the year, sell securities: Sell securities = $1,680,000/$171,679.02 Sell securities = 9.79 ≈ 10 times. 6. The lower limit is the minimum balance allowed in the account, and the upper limit is the maximum balance allowed in the account. When the account balance drops to the lower limit: Securities sold = $80,000 – 43,000 Securities sold = $37,000 in marketable securities will be sold, and the proceeds deposited in the account. This moves the account balance back to the target cash level. When the account balance rises to the upper limit, then: Securities purchased = $125,000 – 80,000 Securities purchased = $45,000 of marketable securities will be purchased. This expenditure brings the cash level back down to the target balance of $80,000. 7. The target cash balance using the Miller-Orr model is: C* = L + (3/4 × F × σ 2 / R]1/3 C* = $1,50...
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