Ross7eCh27Cash Management(公司理财,罗斯,第七版)

C ´K Opportunity Costs 2
Trading costs T F C* Size of cash balance The optimal cash balance is found where the opportunity costs equals the trading costs
Trading costs increase when the firm must sell securities to meet cash needs.
Total cost of holding cash Opportunity Costs The investment income foregone when holding cash. Trading costs
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27.2 Determining the Target Cash Balance
The Baumol Model The Miller-Orr Model Other Factors Influencing the Target Cash Balance
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Time
The opportunity cost C is C of holding – × – 2 2K
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The Baumol Model
C T Total cost K F 2 C
The model clarifies the issues of cash management:
The best return point, Z, is positively related to trading costs, F, and negatively related to the interest rate K. Z and the average cash balance are positively related to the variability of cash flows.
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Other Factors Influencing the Target Cash Balance
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C
C*
2T ´F K
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The Baumol Model
The optimal cash balance is found where the opportunity costs equals the trading costs Opportunity Costs = Trading Costs
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The Baumol Model
F = The fixed cost of selling securities to raise cash T = The total amount of new cash needed K = The opportunity cost of holding cash, a.k.a. the interest rate. C C – 2
Compensating Balance
Firms have cash in the bank as a compensation for banking services. Large corporations have thousands of accounts with several dozen banks—sometimes it makes more sense to leave cash alone than to manage each account on a daily basis.
Time
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The Miller-Orr Model Math
Given L, which is set by the firm, the Miller-Orr model solves for Z and H
is invested elsewhere to get us to the target cash balance Z.
H
When the cash balance reaches the lower control limit, L, investments are sold Z to raise cash to get us up to the target cash balance. L
C T ´K ´F 2 C
Multiply both sides by C
C ´ K T ´ F 2
2
T ´F C 2 ´ K
2
2TF C K
*
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CHAPTER
27
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Cash Management
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Chapter Outline
27.1 Reasons for Holding Cash 27.2 Determining the Target Cash Balance 27.3 Managing the Collection and Disbursement of Cash 27.4 Investing Idle Cash 27.5 Summary & Conclቤተ መጻሕፍቲ ባይዱsions
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H 3Z 2L 3 F σ Z* 3 L 4K where s2 is the variance of net daily cash flows. • The average cash balance in the Miller-Orr model is 4Z * L Averagecash balance 3
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The Miller-Orr Model
The firm allows its cash balance to wander randomly between upper and lower control limits. $ When the cash balance reaches the upper control limit H cash
As we transfer $C each period we incur a trading cost of F each period.
If we need $T in total over the planning period we will T pay $F times. – C T Time The trading cost is – × F C
Borrowing
Borrowing is likely to be more expensive than selling marketable securities. The need to borrow will depend on management’s desire to hold low cash balances.
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
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Costs of Holding Cash
Costs in dollars of holding cash
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