13
Cash and Liquidity
Management
McGrawMcGraw-Hill/Irwin
Copyright © 2008 by The McGrawMcGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
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Reasons for Holding Cash
Understanding Float
Cash Collection and Concentration
Managing Cash Disbursements
Investing Idle Cash
Appendix
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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
13-1
Reasons for Holding Cash
ƒ Speculative motive – hold cash to take
advantage of unexpected opportunities
ƒ Precautionary motive – hold cash in
case of emergencies
ƒ Transaction motive – hold cash to pay
the day-to-day bills
ƒ Trade-off between opportunity cost of
holding cash relative to the transaction
cost of converting marketable securities
to cash for transactions
13-2
Understanding Float
ƒ Float – difference between cash balance
recorded in the cash account and the cash
balance recorded at the bank
ƒ Disbursement float
ƒ Generated when a firm writes checks
ƒ Available balance at bank – book balance > 0
ƒ Collection float
ƒ Checks received increase book balance before
the bank credits the account
ƒ Available balance at bank – book balance < 0
ƒ Net float = disbursement float - collection float
13-3
Example: Types of Float
ƒ You have $3,000 in your checking
account. You just deposited $2,000
and wrote a check for $2,500.
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What is the disbursement float?
What is the collection float?
What is the net float?
What is your book balance?
What is your available balance?
13-4
Example: Measuring Float
ƒ Size of float depends on the dollar amount and
the time delay
ƒ Delay = mailing time + processing delay +
availability delay
ƒ Suppose you mail a check for $1,000 and it
takes 3 days to reach its destination, 1 day to
process, and 1 day before the bank makes the
cash available
ƒ What is the average daily float (assuming 30day months)?
ƒ Method 1: (3+1+1)(1,000)/30 = 166.67
ƒ Method 2: (5/30)(1,000) + (25/30)(0) = 166.67
13-5
Example: Cost of Float
ƒ Cost of float – opportunity cost of not being
able to use the money
ƒ Suppose the average daily float is $3 million
with a weighted average delay of 5 days.
ƒ What is the total amount unavailable to earn
interest?
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5*3 million = 15 million
ƒ What is the NPV of a project that could reduce the
delay by 3 days if the cost is $8 million?
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Immediate cash inflow = 3*3 million = 9 million
NPV = 9 – 8 = $1 million
13-6
Cash Collection
Payment
Mailed
Payment
Received
Mailing Time
Payment
Deposited
Processing Delay
Cash
Available
Availability Delay
Collection Delay
One of the goals of float management is to try to reduce the
collection delay. There are several techniques that can reduce
various parts of the delay.
13-7
Example: Accelerating Collections
– Part I
ƒ Your company does business nationally and
currently all checks are sent to the headquarters in
Tampa, FL. You are considering a lock-box system
that will have checks processed in Phoenix, St. Louis
and Philadelphia. The Tampa office will continue to
process the checks it receives in house.
ƒ Collection time will be reduced by 2 days on average
ƒ Daily interest rate on T-bills = .01%
ƒ Average number of daily payments to each lockbox is
5,000
ƒ Average size of payment is $500
ƒ The processing fee is $.10 per check plus $10 to wire
funds to a centralized bank at the end of each day.
13-8
Example: Accelerating Collections
– Part II
ƒ Benefits
ƒ Average daily collections = (5,000)(500) = 2,500,000
ƒ Increased bank balance = 2(2,500,000) = 5,000,000
ƒ Costs
ƒ Daily cost = .1(5,000) + 10 = 510
ƒ Present value of daily cost = 510/.0001 = 5,100,000
ƒ NPV = 5,000,000 – 5,100,000 = -100,000
ƒ The company should not accept this lock-box
proposal
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Cash Disbursements
ƒ Slowing down payments can
increase disbursement float – but it
may not be ethical or optimal to do
this
ƒ Controlling disbursements
ƒ Zero-balance account
ƒ Controlled disbursement account
13-10
Investing Cash
ƒ Money market – financial instruments
with an original maturity of one year or
less
ƒ Temporary Cash Surpluses
ƒ Seasonal or cyclical activities – buy
marketable securities with seasonal
surpluses, convert securities back to cash
when deficits occur
ƒ Planned or possible expenditures –
accumulate marketable securities in
anticipation of upcoming expenses
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Figure 20.6
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Characteristics of Short-Term
Securities
ƒ Maturity – firms often limit the maturity of
short-term investments to 90 days to
avoid loss of principal due to changing
interest rates
ƒ Default risk – avoid investing in
marketable securities with significant
default risk
ƒ Marketability – ease of converting to cash
ƒ Taxability – consider different tax
characteristics when making a decision 13-13
Comprehensive Problem
ƒ A proposed single lockbox system will
reduce collection time 2 days on average
ƒ Daily interest rate on T-bills = .008%
ƒ Average number of daily payments to the
lockbox is 3,000
ƒ Average size of payment is $500
ƒ The processing fee is $.08 per check plus
$10 to wire funds each day.
ƒ What is the maximum investment that would
make this lockbox system acceptable?
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Target Cash Balances
ƒ Target cash balance – desired cash level
determined by trade-off between carrying
costs and shortage costs
ƒ Flexible policy - if a firm maintains a
marketable securities account, the
primary shortage cost is the trading cost
from buying and selling securities
ƒ Restrictive policy – generally borrow
short-term, so the shortage costs will be
the fees and interest associated with
arranging a loan
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Figure 20A.1
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BAT Model
ƒ Assumptions
ƒ Cash is spent at the same rate every day
ƒ Cash expenditures are known with certainty
ƒ Optimal cash balance is where opportunity
cost of holding cash = trading cost
ƒ Opportunity cost = (C/2)*R
ƒ Trading cost = (T/C)*F
ƒ Total cost = (C/2)*R + (T/C)*F
C* =
2 TF
R
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Example: BAT Model
ƒ 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.
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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?
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Miller-Orr Model
ƒ Model for cash inflows and outflows
that fluctuate randomly
ƒ Define an upper limit, a lower limit,
and a target balance
ƒ Management sets lower limit, L
(target
ƒ C* = L + [(3/4)Fσ2/R]1/3
balance)
ƒ U* = 3C* - 2L (upper limit)
ƒ Average cash balance = (4C* - L)/3
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Figure 20A.3
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Example: Miller-Orr Model
ƒ 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.
ƒ What is the target cash balance?
ƒ What is the upper limit?
ƒ What is the average cash balance?
13-21
Conclusions
ƒ The greater the interest rate, the lower
the target cash balance
ƒ The greater the fixed order cost, the
higher the target cash balance
ƒ It is generally more expensive to borrow
needed funds than it is to sell marketable
securities
ƒ Trading costs are usually very small
relative to opportunity costs for large
firms
13-22