chap028 - Chapter 28: Cash Management 28.1 Firms need to...

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Unformatted text preview: Chapter 28: Cash Management 28.1 Firms need to hold cash to: a. Satisfy the transaction needs. For example, cash is collected from sales and new financing and disbursed as wages, salaries, trade debts, taxes and dividends. b. Maintain compensating balances. A minimum required compensating balance at banks providing credit service to the firm may impose a lower limit on the level of cash a firm holds. 28.2 a. Decrease. Examine the Baumol model. As the interest rate (k) increases, the optimal cash balance must also rise. b. Increase. Examine the Baumol model. As brokerage costs (F, the per transaction costs) rise, the optimal balance increases. c. Decrease. Clearly, if the bank lowers its compensating balance requirement, a firm will not be required to hold as much of its assets as cash. d. Decrease. If the cost of borrowing falls, a firm need not hold as much of its assets as cash because the cost of running short, i.e. the cost to borrow to fill cash needs, is lower. e. Increase. As a firm's credit rating falls, its cost to borrow increases. Thus, the firm cannot as easily afford to run short of cash and its cash balance must be higher. f. Decrease. Introduction of direct banking fees would increase the fixed costs associated with holding cash. As fixed costs rise, the optimal balance must also rise. 28.3 The average weekly cash balance is $20,750 [ ($24,000 + $34,000 + $10,000 +$15,000)/ 4]. With monthly compounding, the return that the firm can earn on its average balance is $20,750 [[( 1 + 0.12/12)12 - 1] = $2,631.62 Your answer may differ if you made different assumptions about the interest payments. 28.4 a. The total amount of cash that will be disbursed during the year is: $345,000 * 12 = $4,140,000 Using the optimal cash balance formula, 2FT 2($500)(4,140,000) C* = = = $243,193 K 0.07 $243,193 should be kept as cash. The balance, $556,807 (=$800,000-$243,193), should be invested in marketable securities. The number of times marketable securities will be sold during the next twelve months is $4,140,000 / $243,193 = 17 times b. 28.5 C* = T= 2FT K KC *2 7.5% (20mil) 2 7.5% 20 2 = = = $3,000(mil) 2F 2 5,000 0.01 3,000 Average weekly disbursement = = $57.69mil 52 28.6 Use the Miller-Orr formula. Answers to End-of-Chapter Problems B-225 The target cash balance = Z* = 3 3F 2 +L 4K The upper limit = H*=3Z*-2L The daily opportunity cost = K= 365 1.08 - 1 = 0.000211 Z* = 3 3($600)($1,440,00) + $20,000 = $34,536 4(0.000211) H* = $63,608 The average cash balance: 4Z * - L 4($34,536) - $20,000 C* = = = $39,381 3 3 28.7 a. H + 2L g g 200,000 + 2 100,000 = = $133,333 3 3 H + 2L s = 300,000 + 2 150,000 = $200,000 Z *= s s 3 3 Z *= g b. Gold Star: s = Z g * - L g 4K g / 3Fg 2 g ( ) 3 ( 133,333 - 100,000) 3 4 0.000261 6,444,251 = 3 2,000 Kg = 365 1.10 - 1 = 0.000261 Silver Star: s 2 = Z g * - L g 4K g / 3Fg = g Kg = 365 ( ) 3 ( 200,000 - 150,000) 3 4 0.000236 15,733,333 3 2,000 1.09 - 1 = 0.000236 So, Silver Star Co. has a more volatile daily cash flow. 28.8 Garden Groves float = 150 ($15,000) = $2,250,000 Increase in collected cash balance if a 3 day lockbox is installed = 3($2,250,000) = $6,750,000 Annual earnings from this amount = $6,750,000 x 0.075 = $506,250 The system should be installed if its cost is below this amount. Variable cost $ 0.5 x 150 x 365 = $27,375 Fixed cost = 80,000 Total cost =$107,375 The lockbox system should be installed. The net earnings from the use of the system are $398,875 (= $506,250 - $107,375) 28.9 To make the system profitable, the net earnings of installing the lockbox system must be non-negative. The lower limit for acceptability is zero profits. B-226 Answers to End-of-Chapter Problems Let N be the number of customers per day. Earnings = ($4,500) (N) (2) (0.06) = $540 x N Costs: Variable cost: N (365) ($0.25) = $91.25 x N Fixed cost: $15,000 Equate Earnings to total costs: N = 33.43 Salisbury Stakes needs at least 34 customers per day for the lockbox system to be profitable. 28.10 Disbursement float = $12,000 x 5 = $60,000 Collection float = -$15,000 x 3 = -$45,000 Net float = $60,000 - $45,000 = $15,000 If funds are collected in four days rather than three, disbursement float will not change. Collection float will change to -$60,000. This change makes the net float equal to zero. 28.11 a. b. c. Reduction in outstanding cash balances = $100,000 x 3 days = $300,000 Return on savings = $300,000 (0.12) = $360,000 Maximum monthly charge = $36,000 / 12 = $3,000 Note: The calculation in part b assumes annual compounding. The answer in part c does not account for the time value of money. With monthly compounding of the interest earned, the return on savings at the end of the year is $300,000 [(1.01)12 - 1] = $38,047.51 The present value of this amount is $38,047.51 / (1.01) 12 = $33,765.23 Compute the monthly payment as an annuity with a discount rate of 1% per period for twelve periods. That annuity factor is 11.2551. Thus, the payment is $33,765.23 = (Payment) (11.2551) Payment = $3,000 Notice, as long as the treatment of the cash flows is the same, the payment is the same. 28.12 The cash savings are the earnings from the interest bearing account. Assuming daily compounding, the three-day return to the delayed payment is ($200,000)[(1.0004)3-1] = $240.096 The interest rate for two weeks is 0.5615% (=(1.0004)14-1). Therefore, the present value of this annuity is 1 1 - 26 (1.005615) = $5,793.12 ($240.096) 0.005615 The Walter Company will save $5,793.12 per year. 28.13 If the Miller Company divides the eastern region, collections will be accelerated by one day freeing up $4 million per day. Compensating balances will be increased by $100,000 [=2($300,000)-$500,000]. The net effect is to have $3,900,000 to invest. If T-bills pay 7% per year, the annual net savings from the division of the eastern region is $3,900,000 x 0.07 = $273,000. 28.14 Lockbox: interest saved = 7,500 x 250 x 1.5 x0.0003 = $843.75 Annual saving (Annual charge) = 843.75 x 365 - 30,000 - 0.3 x 250 x 365 = $250,593.75 Annual saving (Concentration Banking) = 7,500 x 250 x1 x 0.0003 x 365 Answers to End-of-Chapter Problems B-227 = 562.5 x 365 = $205,312.5 So the lockbox system is recommended. 28.15 The important characteristics of short-term marketable securities are: i. maturity ii. default risk iii. marketability iv. taxability B-228 Answers to End-of-Chapter Problems ...
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