19a-1 cash and liquidity management - appendix chapter 19 - a copyright © 2013 by the mcgraw-hill...
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19A-1
Cash and Liquidity Management -
Appendix
Chapter 19 - A
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
19A-2
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A More
General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-3
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A
More General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-4
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.
19A-5
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A
More General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-6
The BAT Model
C
Time 1 2 3
C
2–
C -
19A-7
The BAT ModelIf 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 C is:
2
RC
2
19A-8
The BAT ModelF = The fixed cost of selling securities to
raise cashT = The total amount of new cash neededR = The opportunity cost of holding cash,
i.e., the interest rate
Time
C
1 2 3
C2–
19A-9
The BAT Model
Time
C
As we transfer $C each period we incur a trading cost of F.
1 2 3
C2–
The trading cost is× F
–TC
–TC
If we need $T in total over the planning period we will pay $F times.
19A-10
The BAT Model
C* Size of cash balance
FT
RC
C2
cost Total
Opportunity Costs
RC
2
FT
C
Trading costs
FR
TC
2*
19A-11
The BAT Model
Opportunity Costs = Trading Costs
FC
TR
C
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
19A-12
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A
More General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-13
The Miller-Orr ModelThe 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.
19A-14
The Miller-Orr ModelThe firm allows its cash balance to wander randomly between upper and lower control limits.
$
Time
U
C
L
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.
19A-15
The Miller-Orr Model Math
Given L, which is set by the firm, the Miller-Orr model solves for C* and U:
LR
FσC 3
2*
4
3LCU 23 **
where s2 is the variance of net daily cash flows.
3
4balancecash Average
* LC
The average cash balance in the Miller-Orr model is:
19A-16
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A
More General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-17
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.
19A-18
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.
19A-19
Chapter Outline(Appendix)
• The Basic Idea• The BAT Model• The Miller-Orr Model: A More
General Approach• Implications of the BAT and
Miller-Orr Models• Other Factors Influencing
the Target Cash Balance
19A-20
Other Factors Influencing the
Target Cash Balance
BorrowingBorrowing 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.
19A-21
Formulas
FT
RC
C2
cost Total
FR
TC
2*
The BAT Model
19A-22
Formulas
LR
FσC 3
2*
4
3 LCU 23 **
3
4balancecash Average
* LC
The Miller-Orr Model
19A-23
Questions?