Cash and Liquidity Management
Reasons for Holding Cash
•
•
•
•
Speculative motive—the need to hold cash to take advantage
of additional investment opportunities, such as bargain
purchases.
Precautionary motive—the need to hold cash as a safety
margin to act as a financial reserve.
Transaction motive—the need to hold cash to satisfy normal
disbursement and collection activities associated with a firm’s
ongoing operations.
Compensating balance requirements—cash balances kept at
commercial banks to compensate for banking services the
firm receives.
Target Cash Balance
Key issues:
• What is the trade-off between carrying a large cash
balance versus a small cash balance?
carrying costs versus shortage costs.
That is,
• What is the proper management of the cash
balance? BAT model versus Miller–Orr model.
The BAT Model
Starting cash
C=$2 000 000
Average cash
$500 000=C/4
0
4
8
Weeks
The 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 ([C/2]*R) = trading cost ([T/C]*F):

C 
2T  F /R
F = fixed cost of making a securities trade to replenish cash
T = total amount of new cash needed for transactions purposes over
the relevant planning period
R = the opportunity cost of holding cash (the interest rate on
marketable securities)
Miller–Orr Model
•
Assumes that, if left unmanaged, a company’s cash balance
would follow a random walk with zero drift.
•
Cash balance is allowed to wander freely between an upper
limit (U*) and a lower limit (L).
•
If cash holdings reach U*, management intervenes by
withdrawing U* – C* dollars to return the cash balance to the
target level C*.
•
If cash balance reaches L, management intervenes by
injecting C* – L dollars to return the cash balance to the
target level C*.
Miller–Orr Model
Cash
U*
C*
L
Time
X
Y
U* is the upper control limit. L is the lower control limit. The target
cash balance is C*. As long as cash is between L and U*, no
transaction is made.
Miller–Orr Model
L  set by the firm
2
3

σ
C L F

R
4

U   3 C  2  L




Avg. cash balance  4  C  L / 3
1
3
Example—Miller–Orr Model
Assume L = $0, F = $10, i = 0.5 per cent per month and
the standard deviation of monthly cash flows is $2000.
3

C  $0    $10  $2000

0.005
4

 $1 817

U   3  $1 817   2  $0 
 $5451
Avg. cash balance  4  $1 817  $0 /3
 $2423
2
1
3
Miller–Orr Model Implications
• Considers the effect of uncertainty (through 2 in
net cash flows).
–
–
The higher the 2, the greater the difference between C*
and L.
The higher the 2, the higher is the upper limit and the
average cash balance.
• All things being equal:
–
–
the greater the interest rate, the lower is the C*
the greater the order costs, the higher is the C*.
Miller–Orr Model With Overdraft
•
Yield on short-term investments < cost of bank overdraft <
yield on long-term investments.
•
A dollar invested in short-term assets earns less than the
costs saved by applying that dollar to reduce overdraft usage.
•
The company invests nothing in short-term assets and as
much as possible in long-term assets, while meeting its
liquidity needs through using the overdraft facility.
Miller–Orr Model With Overdraft
U 0
 3

2
C    F    / R  d 

 4


L  3 C
Target overdrawn level  2  C 
Where:
d = cost of bank overdraft
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3