Optimum Cash Balance

CASH MANAGEMENT
NATURE OF CASH

In cash management the term cash has been used in two
senses:-

Narrow Sense: Under this cash covers currency and
generally accepted equivalents of cash, viz., cheques,
demand drafts and banks demand deposits.

Broad Sense: Here, cash includes not only the above
stated but also near cash assets. There are Bank’s time
deposits and marketable securities.
MOTIVES FOR HOLDING CASH
J M Keynes identified three possible motives for holding
cash :
• Transaction motive
• Precautionary motive
• Speculative motive
Objectives of Cash Management
• To meet Cash Payments
To quote Bollen,”Cash is an oil to lubricate the
ever turning wheels of business: without it , the
process grinds to a stop”.
• To maintain Minimum Cash Balance (Reserve)
Features of Cash Management
• Cash Planning (estimate Cash Surplus/ Deficit through
Cash Budget)
• Cash Flows Management (Cash Inflows & Cash
Outflows)
• Determination of Optimum Cash Balance (cost of
excess cash and danger of cash deficiency will match)
• Investment of Surplus Cash (properly invested in
marketable securities, to earn profits)
CASH MANAGEMENT MODELS
Several cash management models have addressed this issue
of split between marketable securities and cash holdings.
Two such models are :
• Baumol model
• Miller and Orr model
BAUMOL MODEL
• Provides for Cost efficient transactional balances
• Assumes that the demand for cash can be predicted with
certainty
• determines the optimal conversion size/lot
• focus of the model is to minimise the total cost
• associated with cash management
• comprising total conversion costs (that is, costs incurred each
time marketable securities are converted into cash)
and
the opportunity cost of keeping idle cash balances which
otherwise could have been invested in marketable securities
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
C*
Size of cash balance
BAUMOL MODEL
2CF
ECL=
O
where:
ECL = Economic Conversion lot or Optimum Cash Balance
C = Cost per conversion
F = Projected cash requirements during the planning period
O= interest rate per planning period on investment in marketable securities
BAUMOL MODEL-Example
• V ltd.’s estimated cash need for the year are Rs. 20
Lakhs. Cost of transaction is Rs.2000/lot & the
opportunity cost is 20%. Calculate Economic
Conversion Lot?
Here, C= Rs.2000, F= Rs.20 Lakhs & O= 20% or 0.20
EOL=
2 x 2000 x 20 lakhs = Rs. 2 Lakhs
0.20
MILLER & ORR MODEL
• Provides for cost-efficient transactional
balances
• assumes uncertain cash flows
• determines an upper limit and return point
for cash balances.
• Objective of Model is to determine the
optimum cash balance level which minimises
the cost of cash management
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.
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 Z.
U
When the cash balance
reaches the lower
control limit, L,
investments are sold to
Z raise cash to get us up
to the target cash
L balance.
Time
MILLER AND ORR MODEL
3b 2
RP =
3
+ LL
4I
UL = 3RP – 2LL
where: RP = return point
b = fixed cost per order for converting marketable securities into cash.
I = daily interest rate earned on marketable securities
 2 = variance of daily changes in the expected cash balance
LL = the lower control limit
UL = the upper control limit
MILLER AND ORR MODEL- Example
• X Ltd. has a policy of maintaining a minimum cash balance
of Rs. 500,000. The standard deviation of the company’s
daily cash flows is Rs.200,000 & the annual interest rate is
14%. The transaction cost of buying or selling securities is Rs.
150 per transaction. Calculate X Ltd.’s return point & upper
control limit?
Return point = 3 3 x 150 x 200,000 x 200,000 + 500,000
4 x 0.14
365
= Rs. 727,227
Upper Control Limit = 3 RP – 2LL= 3 x727,227 – 2 x 500,000
= Rs. 16,81,681
FLOAT
• The cash balance shown by a firm on its books is called
the book, or ledger, balance whereas the balance shown
in its bank account is called the available, or collected,
balance. The difference between the available balance
and the ledger balance is referred to as float.
• There are two kinds of float :-
disbursement float - cheque issued but not debited in the
customer’s A/c
payment float- cheque deposited but not credited in the
customer’s A/c
Accelerating Collections
Customer
mails
payment
Company
receives
payment
Company
deposits
payment
Cash
received
time
Mail
delay
Processing
delay
Clearing
delay
Mail
float
Processing
float
Clearing
float
Collection float
MONEY MARKET INSTRUMENTS OR MARKETABLE SECURITIES
• Mutual fund scheme
(Money market schemes)
• Treasury bills
• Commercial paper
• Certificates of deposit
• Inter-corporate deposits
(Call deposits, 3 months and 6 months deposits)
• Bill discounting