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Cash Management Chapter 27 Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 27A-1 Costs of Holding Cash Opportunity Costs Trading costs Total cost of holding cash C* Costs in dollars of holding cash Size of cash balance The investment income foregone when holding cash. Trading costs increase when the firm must sell securities to meet cash needs. 27A-2 The BAT Model F = The fixed cost of selling securities to raise cash T = The total amount of new cash needed R = The opportunity cost of holding cash, i.e., the interest rate. Time C 1 2 3 C 2 If we start with $C, spend at a constant rate each period and replace our cash with $C when we run out of cash, our average cash balance will be C 2 The opportunity cost of holding is C 2 C 2 R 27A-3 The BAT Model Time C As we transfer $C each period we incur a trading cost of F. 1 2 3 C 2 The trading cost is F T C T C If we need $T in total over the planning period we will pay $F times. 27A-4 The BAT Model C* Size of cash balance FTRC C2c os t T ot a l Opportunity Costs R C 2 FT C Trading costs FRTC 2* 27A-5 The BAT Model Opportunity Costs = Trading Costs FCTRC 2 The optimal cash balance is found where the opportunity costs equals the trading costs. R TFC 2* Multiply both sides by C FTRC 2 2 R FTC 22 27A-6 The Miller-Orr Model The firm allows its cash balance to wander randomly between upper and lower control limits. $ Time U C L When the cash balance reaches the upper control limit U, cash is invested elsewhere to get us to the target cash balance C. When the cash balance reaches the lower control limit, L, investments are sold to raise cash to get us up to the target cash balance. 27A-7 The Miller-Orr Model Math Given L, which is set by the firm, the Miller- Orr model solves for C* and U L R F C 3 2* 4 3 LCU 23 * where s2 is the variance of net daily cash flows. The average cash balance in the Miller-Orr model is: 3 4b a l a n c ec a s h A v e r a g e * LC 27A-8 Implications of the Miller-Orr Model To use the Miller-Orr model, the manager must do four things: 1. Set the lower control limit for the cash balance. 2. Estimate the standard deviation of daily cash flows. 3. Determine the interest rate. 4. Estimate the trading costs of buying and selling securities. 27A-9 Implications of the Miller-Orr Model The model clarifies the issues of cash management: The optimal cash position, C*, is positively related to trading costs, F, and negatively related to the interest rate R. C* and the average cash balance are positively related to the variability of cash flows. 27A-10 Other Factors Influencing the Target Cash Balance Borrowing Borrowing is likely to be more expensive than selling marketable securities. The need to borrow will depend on managements desire to hold low cash balances.
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