Chapter 20
Appendix
•Cash and Liquidity
Management - Appendix
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Target Cash Balances
• Target cash balance – desired cash level
determined by trade-off between carrying
costs and shortage costs
• Flexible policy - if a firm maintains a
marketable securities account, the primary
shortage cost is the trading cost from
buying and selling securities
• Restrictive policy – generally borrow shortterm, so the shortage costs will be the fees
and interest associated with arranging a
loan
20A-1
Figure 20A.1
20A-2
BAT Model
• Assumptions
• Cash is spent at the same rate every day
• Cash expenditures are known with certainty
• Optimal cash balance is where opportunity cost of
holding cash = trading cost
• Opportunity cost = (C/2)*R
• Trading cost = (T/C)*F
• Total cost = (C/2)*R + (T/C)*F
C* 
2TF
R
20A-3
Example: BAT Model
• Your firm will have $5 million in cash
expenditures over the next year. The
interest rate is 4% and the fixed trading
cost is $25 per transaction.
•
•
•
•
•
What is the optimal cash balance?
What is the average cash balance?
What is the opportunity cost?
What is the shortage cost?
What is the total cost?
20A-4
Miller-Orr Model
• Model for cash inflows and outflows that
fluctuate randomly
• Define an upper limit, a lower limit and a
target balance
•
•
•
•
Management sets lower limit, L
C* = L + [(3/4)F2/R]1/3 (target balance)
U* = 3C* - 2L
(upper limit)
Average cash balance = (4C* - L)/3
20A-5
Figure 20A.3
20A-6
Example: Miller-Orr Model
• Suppose that we wish to maintain a
minimum cash balance of $50,000. Our
fixed trading cost is $250 per trade, the
interest rate is .5% per month and the
standard deviation of monthly cash flows is
$10,000.
• What is the target cash balance?
• What is the upper limit?
• What is the average cash balance?
20A-7
Conclusions
• The greater the interest rate, the lower the
target cash balance
• The greater the fixed order cost, the higher
the target cash balance
• It is generally more expensive to borrow
needed funds than it is to sell marketable
securities
• Trading costs are usually very small
relative to opportunity costs for large firms
20A-8
Chapter 20
Appendix
•End of Chapter
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.