The term cash is a surprisingly vague concept . The economic
definition of cash includes currency
savings account deposits in banks , and not deposited the
checks . However , financial managers often use
term cash to include short-term marketable securities .
Short-term marketable securities are often
called cash equivalents and include treasury bills,
certificates of deposit and repurchase agreements .
There are two main reasons for holding cash . First, money
is needed to meet the transactions
pattern. Needs related to the transaction from collection
activities of the firm disbursement normal.
The cash payment includes the payment of wages and salaries
, trade debts , taxes and dividends.
The cash is collected from sales from operations , asset
sales and new financing. Cash inflows
( Collections) and outflows (disbursements ) are not
perfectly synchronized , and a certain level of cash
which is needed as a buffer. If the company maintains a cash
balance is too low , it may run out of cash . If this is the case,
he must sell the securities or borrow . Sale of marketable
securities and loans include transaction costs.
Another reason is to hold cash balances compensation. Cash
balances are held at
banks to compensate for banking services provided to the
company. The cash balance for most
businesses can be considered as consisting of balances and
transactions clearing balances .
However, it would be wrong for a company to add the amount
of cash required to meet its
transaction is the amount of money needed to meet their
compensating balances
produce a cash balance of the target.
The Baumol model
William Baumol was the first to provide a formal model of
cash management incorporating
opportunity costs and trade costs.1 The model can be used to
determine the cash balance of the target.
Suppose Socks gold plc started the week 0 with a cash
balance of C = 1.2 million pounds, and
outflows exceed inflows by £ 600,000 per week . Its cash
balance will be reduced to zero at the end
week 2 , and the average cash balance will be the C / 2 =
1.2 million pounds / 2 = € 600,000 on
period of two weeks. At the end of the week or two socks to
replace the cash either by selling
securities or by borrowing.
If C has been set higher , say £ 2.4 million in cash would
last four weeks before the company would need to sell marketable securities,
but average cash balance of the company would amount to 1.2 million pounds
(from € 600,000 ) . If C has been set at € 600,000 , the cash would be
exhausted in a week
and the company would need to replenish with more frequently
, but the average cash balance would be his
fall from £ 600,000 to £ 300,000.
Because transaction costs are incurred once the cash is
restored ( eg,
brokerage fees for the sale of securities ) , developing
important initial cash balances
reduce transaction costs related to cash management.
However, the higher the average
cash balance , plus the opportunity cost (the return that
could be earned on
securities ) .
Limitations The Baumol model is a significant contribution
to the management of cash .
The limitations of the model are:
1 The model assumes that the company has a constant rate of
disbursement. In practice , payments may
be only partially successful because of different maturity
dates, and costs can not be predicted with
certainty.
2 The model assumes that there is no cash flow during the
projected period. In fact, most companies
experience of both inputs and outputs daily cash .
3 No safety stock is allowed. Companies will probably need
to keep a safety stock of cash designed
to reduce the possibility of a shortage of cash or cash-out
. However, since companies
may sell securities or to borrow a few hours, the need for
safety stock is
minimal.
The Baumol model is probably the simplest and most
stripped-down , sensitive to
determining the optimal cash position . Its main weakness is
that it assumes discrete , some
Cash flows . We then discuss a model designed to cope with
uncertainty.
The Miller- Orr model
Merton Miller and Daniel Orr has developed a model of
balance of cash to meet the cash flow and
outputs fluctuate randomly from day to day.2 In the Miller-
Orr model both cash inflows
and outflows are included. The model assumes that the
distribution of net cash daily
flow ( negative cash flow cash outflows ) is normally
distributed . Each day , the net cash flow
could be the expected value or a higher or lower value . We
assume that the expected
net cash flow is zero.
The model works in terms of high
(U) and lower ( L) control and a cash balance of the target
( Z). The company enables its cash balance
to wander aimlessly through the upper and lower limits . As
the cash balance is between
U and L , the firm makes no transaction. When the cash
balance reaches U, as developed
X , the company buys U - Z units ( eg, euros or pounds ) of
securities.
This action will reduce the cash balance to Z. Similarly ,
when cash balances fall
L as the point Y ( the lower limit ) , the company should
sell Z - The securities and increase
cash to Z. In both cases the cash balances back to Z.
management defines Lowest
limit , L, according to the degree of risk of a cash deficit
of the company is willing to tolerate.
As Baumol model , Miller -Orr model depends on trade costs
and opportunities
costs. The cost per transaction of purchase and sale of
marketable securities , F, is assumed to be
fixed . The opportunity cost percentage holding period cash
, R, is the daily interest rate
on marketable securities . Unlike the Baumol model , the
number of transactions per period
is a random variable which varies from one period to the
next , depending on the model of cash
inputs and outputs .
As a result, transaction costs per period depends on the
expected number of operations
in marketable securities during the period. Similarly, the
opportunity costs of holding cash
are based on the expected cash balance per period.
Given L, which is set by the company, the Miller- Orr model
solves for the cash balance of the target,
Z , and the upper limit , U. expected total cost of the
return policy of the balance of cash (Z , U) are
equal to the sum of transaction costs and expected the
expected opportunity costs. Values
Z ( point cash back ) and U (the upper limit ) that minimize
the expected total cost are
was determined by Miller and Orr :
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