Finance Discussion Topic #4
jandreg
chap027a.pptMcGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Cash Management
Appendix 27A
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27A-*
Key Concepts and Skills
- Be able to use the BAT and Miller-Orr models
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27A-*
Chapter Outline
27A.1 The Basic Idea
27A.2 The BAT Model
27A.3 The Miller-Orr Model: A More General Approach
27A.4 Implications of the BAT and Miller-Orr Models
27A.5 Other Factors Influencing the Target Cash Balance
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Costs 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.
Opportunity Costs
Trading costs
Total cost of holding cash
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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
1 2 3
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
C
2
–
C
2
–
C
2
–
C
2
–
The opportunity cost of holding is
×R
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The BAT Model
Time
As we transfer $C each period we incur a trading cost of F.
1 2 3
C
C
2
–
–
T
C
The trading cost is × F
–
T
C
If we need $T in total over the planning period we will pay $F times.
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The BAT Model
C*
Size of cash balance
Opportunity Costs
Trading costs
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Multiply both sides by 2C, divide by K.
Take a square root.
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The BAT Model
Opportunity Costs = Trading Costs
The optimal cash balance is found where the opportunity costs equals the trading costs.
Multiply both sides by C
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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 = .1
C* = $9,552.49
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The Miller-Orr Model
- The firm allows its cash balance to wander randomly between upper and lower control limits.
$
Time
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.
U
C
L
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The Miller-Orr Model Math
- Given L, which is set by the firm, the Miller-Orr model solves for C* and U
where s2 is the variance of net daily cash flows.
- The average cash balance in the Miller-Orr model is:
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L (Z) is a lower (upper) limit on the amount of cash to be held, while C* is the optimal cash balance.
Example: Suppose F = $25, R = 1% per month, and the variance of monthly cash flows is $25,000,000 per month. Assume a minimum cash balance of $10,000.
C* = 10,000 + ( ¾ (25)(25,000,000)/.01)1/3 = $13,605.62
U* = 3(13,605.62) – 2(10,000) = $20,816.86
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Implications of the Miller-Orr Model
- To use the Miller-Orr model, the manager must do four things:
Set the lower control limit for the cash balance.
Estimate the standard deviation of daily cash flows.
Determine the interest rate.
Estimate the trading costs of buying and selling securities.
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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.
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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 management’s desire to hold low cash balances.
F
R
T
C
2
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F
T
C
R
C
2
F
T
R
C
C2
cost Total
F
C
T
R
C
2
R
TF
C
2
*
FTR
C
2
2
R
FT
C
2
2
L
R
Fσ
C
3
2
*
4
3
LCU 23
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3
4
balancecash Average
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LC
