Transcript Chap019 App.pptx

Chapter
19 - A
Cash and Liquidity
Management - Appendix
19A-1
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-2
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-3
Costs of Holding Cash
Costs in dollars
of holding cash
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
19A-4
C*
Size of cash balance
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-5
The BAT Model
C -
–
C
2C
1
19A-6
2
3
Time
The BAT Model
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 C is:
2
19A-7
C
R
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
C
C
–2
19A-8
1
2
3
Time
The BAT Model
As we transfer $C each
period we incur a trading
cost of F.
C
If we need $T in total
over the planning period
we will pay $F T times.
–C2
–
C
1
19A-9
2
3 Time
The trading cost is
T ×F
–C
The BAT Model
C
T
Total cost   R   F
2
C
Opportunity C
R
Costs
2
T
Trading costs  F
C
C*
2T
C 
F
R
*
19A-10
Size of cash balance
The BAT Model
The optimal cash balance is found where the
opportunity costs equals the trading costs.
Opportunity Costs = Trading Costs
C
T
R  F
2
C
Multiply both sides by C
C2
R T F
2
19A-11
T F
C  2
R
2
2TF
C 
R
*
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-12
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 U, cash is invested elsewhere to get us to the
target cash balance C.
U
C
L
19A-13
Time
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 lower control
limit, L, investments are sold to raise cash to get us
up to the target cash balance.
U
C
L
19A-14
Time
The Miller-Orr Model Math
Given L, which is set by the firm, the Miller-Orr
model solves for C* and U:
2
3Fσ
C 
L
4R
*
3
U  3C  2 L
*
*
where s2 is the variance of net daily cash flows.
The average cash balance in the
Miller-Orr model is:
19A-15
4C *  L
Average cash balance 
3
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-16
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
19A-17
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.
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-18
Chapter Outline
(Appendix)
• The Basic Idea
• The BAT Model
• The Miller-Orr Model: A More
General Approach
• Implications of the BAT and MillerOrr Models
• Other Factors Influencing the Target
Cash Balance
19A-19
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.
19A-20
Formulas
The BAT Model
C
T
Total cost   R   F
2
C
2T
C 
F
R
*
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Formulas
The Miller-Orr Model
2
3
Fσ
C 3
L
4R
*
U  3C  2 L
*
*
4C *  L
Average cash balance 
3
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19A-23