Appendix 19ADETERMINING THE TARGET CASH BALANCESLIDES19A.1Chapter 19 Appendix19A.2Costs of Holding Cash19A.3The BAT Model – I19A.4The BAT Model – II19A.5The BAT Model – III19A.6The BAT Model – IV19A.7The Miller-Orr Model19A.8The Miller-Orr Model: Math19A.9Implications of the Miller-Orr Model19A.10I mplications of the Miller-Orr Model (ctd.)19A.11O ther Factors Influencing the Target Cash Balance19A.12E nd of ChapterAPPENDIX ORGANIZATION19A.1 The Basic Idea19A.2 The BAT Model19A.3 The Miller-Orr Model: A More General Approach19A.4 Implications of the BAT and Miller-Orr Models19A.5 Other Factors Influencing the Target Cash BalanceANNOTATED APPENDIX OUTLINESlide 1: Chapter 19 AppendixTarget cash balance – the desired cash balance as determined bythe trade-off between carrying costs and storage costsAdjustment costs – costs associated with holding low levels ofcash; shortage costsWith a flexible working capital policy, the trade-off is between theopportunity cost of cash balances and the adjustment costs ofbuying, selling, and managing securities.19A.1The Basic IdeaSlide 2: Costs of Holding CashThere is an optimal cash level that minimizes the total costs ofholding cash.19A.2The BAT (Baumol-Allais-Tobin) ModelSlide 3: The BAT Model – ISlide 4: The BAT Model – IISlide 5: The BAT Model – IISlide 6: The BAT Model – IVDefine:C = optimal cash transfer amount (amount of marketable securities tosell to raise cash)F = fixed cost of selling securitiesT = cash needed for transactions over entire planning periodR = opportunity cost of cash (interest rate on marketable securities)Assume that cash is paid out at a constant rate through time.Opportunity cost = Average cash balance × Interest rate= (C ⁄ 2) × RT rading cost = # of transactions × Cost per transfer = (T ⁄ C) × FTotal cost = Oppor tunity cost + Trading cost = (C ⁄ 2)R + (T ⁄ C)FTo find the optimal transfer amount, take a first derivative of the costfunction relative to C and set it equal to zero. You can also find it bysetting opportunity cost = trading cost and solving for C.Method 1: Method 2: Example: Hermes Co. has cash outflows of $500 per day, the interest rate is 10% and the fixed transfer cost is $25. T = 365 × 500 = 182,500 F = 25 R = .119A.3The Miller-Orr Model: A More General ApproachSlide 7: The Miller-Orr ModelThe Miller-Orr model offers a general approach to handling uncertaincash flows.The basic idea:U * = upper limit on cash balanceL = lower limit on cash balanceC * = target cash balanceR FT C R FT C C FT R C FT R C TC 22202222====-+=∂∂R FT C R TF C F C T R C 2222===49.552,9$1.)500,182)(25(2==C CWhen cash reaches U*, the firm transfers cash (buys securities) in theamount of U*− C*. If cash falls below L, the firm sells C*− L worth ofsecurities to add to cash.Slide 8: The Miller-Orr Model: MathUsing the model:Given the variance (σ2) of cash flow (“cash flow” refers to both theamounts that go into and come out of the cash balance) per period, theinterest rate per period (period may be a day, week, or month as longas the two are consistent), and L, the target balance and upper limit,are given by:C* = L + ( ¾ × F ×σ2⁄ R)1/3U* = 3C*− 2LExample: Suppose F = $25, R = 1% per month, and the variance ofmonthly cash flows is $25,000,000 per month. Assume a minimumcash balance of $10,000.C* = 10,000 + ( ¾ (25)(25,000,000)/.01)1/3 = $13,605.62U* = 3(13,605.62) – 2(10,000) = $20,816.8619A.4Implications of the BAT and Miller-Orr ModelsSlide 9: Implications of the Miller-Orr ModelSlide 10: Implications of the Miller-Orr Model (ctd.)From both:-The higher the interest rate (opportunity cost), the lower the targetbalance.-The higher the transaction cost, the higher the target balance.From Miller-Orr:-The greater the variability of cash flows, the higher the target balance 19A.5Other Factors Influencing the Target Cash BalanceSlide 11: Other Factors Influencing the Target Cash Balance-Flexible versus restrictive short-term financing policy-Compensating balance requirements-The number and complexity of checking accountsSlide 12: End of Chapter。