Financial Management
CASH MANAGEMENT
Part A: Discussion of basic theories and various formulas pertaining to the management of cash of a business enterprise in the most effective and efficient manner
Part B: 2 Illustrations with solutions
Part A:
Cash includes near cash
assets such as marketable securities and time deposits in banks. The reason why
these near cash assets are included in cash is that they can readily be
converted into cash. Usually, excess cash is invested in marketable securities
as it contributes to profitability.
Cash is one of the most important components of
current assets. Every firm should have adequate cash, neither more nor less.
Inadequate cash will lead to production interruptions, while excessive cash
remains idle and will impair profitability. Hence, there is a need for cash
management.
The strategies for cash
management are discussed in detail in the following lines:
1. Projection of cash flows and planning:
The cash planning and the
projection of cash flows are determined with the help of Cash Budget. The Cash
Budget is the most important tool in cash management. It is a device to help a
firm to plan and control the use of cash. It is a statement showing the estimated
cash inflows and cash outflows over the firm’s planning horizon. In other words
the net cash position i.e., surplus or deficiency of a firm is highlighted by
the cash budget from one budgeting period to another period. (We have discussed
Cash Budget in the Chapter: Budgets and Budgetary Control System).
2. Determining optimal level of cash holding by the
company:
The optimal level of cash
holding by a company can be determined with the help of the following three models:
(a) Inventory
model (also known as Baumol Model),
(b) Stochastic
model (also known as Miller-Orr Model), and
(c) Probability
model.
The Baumol Model
Most firms try to minimise the sum of the cost
of holding cash and the cost of
converting marketable securities into cash. William J. Baumol
developed a cash management model for determining a firm’s optimum cash balance
under certainty which is normally used in inventory management. As per the
model, cash and inventory management problems are one and the same. There are certain
assumptions
that are made in the model. They are as follows:
1.
The firm is able to forecast its cash requirements with certainty and
receive a specific amount at regular intervals.
2.
The firm’s cash payments occur uniformly over a period of time i.e. a steady
rate of cash outflows.
3.
The opportunity cost of holding cash is known and does not change over
time. Cash holdings incur an opportunity cost in the form of opportunity
foregone.
4. The firm will incur the same transaction cost whenever it converts securities
to cash. Each transaction incurs a fixed and variable cost.
For example, let us assume that the firm sells securities and starts with a cash balance of C rupees. [Here, C = Conversion Amount] When the firm spends cash, its cash balance starts decreasing and reaches zero. The firm again gets back its money by selling marketable securities. As the cash balance decreases gradually, the average cash balance will be: C/2.
The firm incurs a cost known as holding cost
for maintaining the cash balance. It is the opportunity cost in terms of the
return inevitable on the marketable securities. If the opportunity cost of
holding Rs 1 per annum is H, then the firm’s total holding cost per annum for
maintaining an average cash balance of C/2 is as follows:
Total Holding Cost (THC) = H x (C/2)
Whenever the firm converts its marketable securities to cash, it incurs a cost known as transaction cost. Total number of transactions in a particular year will be total annual funds required (A) divided by the cash balance (C) i.e. A/C. The assumption here is that the cost per transaction is constant. If the cost per transaction is T, then the total transaction cost will be:
Total Transaction Cost (TTC) = T x (A/C)
Therefore, the total annual cost of maintaining the cash balances =
Total of Holding and Transaction Cost (THTC) = THC + TTC
= [H x (C/2)] + [T x (A/C)]
Optimum Conversion Amount (OCA)
Optimum Conversion Amount (also called Optimum
Transaction Size) implies optimum amount of marketable
securities required to be converted into cash per transaction. It is the
trade-off between the cost of holding cash (i.e. opportunity cost of holding
cash) and the cost of transaction (i.e. cost of converting marketable
securities into cash). As the cash balance increases within the existing annual
cash needs of the firm, the total annual holding cost will also increase and
the total annual transaction cost will decrease because of a decline in the
number of transactions. Hence, it can be said that there is a relationship
between the holding cost and the transaction cost. OCA is reached at a point
where the two opposing costs are equal and where the total of holding and
transaction costs is the minimum.
Optimum Conversion Amount (OCA)
OCA = √
(2AT/H)
|
Where, T = |
The cost per transaction |
|
A = |
The total cash needed during the year |
|
H = |
The opportunity cost of holding Rs 1 per annum |
When there is
increase in the cost per transaction and in the total annual cash required, the
OCA will also increase. However, when there is increase in the opportunity cost
of holding Rs 1 per annum, the OCA will decrease.
Average Cash Balance = C/2
If cash balance is Optimum Conversion Amount (OCA),
Average Cash Balance = (OCA)/2
Limitations of the Baumol model
1. It does not allow cash flows to fluctuate.
2. Overdraft is not considered.
3. There are uncertainties in the pattern of future cash flows.
The Miller-Orr Model
The objective of cash management, according to Miller-Orr Model, is to
determine the optimum cash balance level which minimises the cost of cash
management. The Miller-Orr Model is, in fact, an attempt to make the Baumol
Model more realistic as regards the pattern of cash flows. As against the
assumption of uniform and certain levels of cash balances in the Baumol Model,
the Miller-Orr Model assumes that cash balances randomly fluctuate between an upper
limit (U) and a lower limit (L). When the cash
balances hit the upper limit, the firm has too much cash and should buy enough
marketable securities to bring the cash balances back to the optimum
level. When the cash balances hit the lower limit, the financial
manager should sell enough marketable securities to return to the optimum
level again. Optimum level of
cash balance (i.e. Normal level of cash balance) is, therefore, also known as
‘Return Point’.
According to the Miller-Orr Model, as in the Baumol Model, the optimum cash balance can be expressed symbolically as follows:
|
Where, Z = |
(3br2/4i) 1/3 |
|
b = |
Transaction cost per transaction |
|
r = |
Standard deviation of the daily changes in cash balances |
|
i = |
Rate of interest per rupee per day |
|
L = |
Lower limit of cash balance |
If the lower limit of cash balance is zero (i.e. L =
0),
Optimum level of cash balance = Z = (3br2/4i)
1/3
The Miller-Orr Model also specifies the relationship
among the upper limit of cash balance, the lower limit of cash balance and the
optimum level of cash balance as follows:
U = L + 3Z
Where, U = Upper limit of cash balance
If the lower limit of cash balance is zero (i.e. L =
0), U = 3Z
Most firms don’t use their cash flows uniformly and also cannot predict their daily cash inflows and outflows. Mille-Orr Model helps them by allowing daily cash flow variation. Under this model, the firm allows the cash balance to fluctuate between the upper limit and the lower limit, making a purchase and sale of marketable securities only when one of these limits is reached. The assumption made here is that the net cash flows are normally distributed with a zero value of mean and a standard deviation. This model provides two limits – the upper limit and the lower limit as well as a return point (i.e. Optimum level of cash balance). When the firm’s cash limit fluctuates at random and touches the upper limit, the firm buys sufficient marketable securities to come back to a normal level of cash balance i.e. the return point. Similarly, when the firm’s cash flows wander and touch the lower limit, it sells sufficient marketable securities to bring the cash balance back to the normal level of cash balance i.e. the return point.
The lower limit is set by the firm based on its desired minimum “safety stock” of cash in hand. The firm should also determine the following factors:
1. An interest rate per rupee per day for marketable securities: (i),
2. A fixed transaction cost per transaction of buying and selling marketable securities: (b), and
3. The standard deviation of the daily changes in cash balances: (r).
The upper limit and the return point are than calculated by the Miller-Orr Model as follows:
Return point (i.e.
optimum level of cash balance) = L + Z
|
Where, L = |
Lower limit of cash balance |
|
Z = |
(3br2/4i) 1/3 |
|
b = |
Transaction cost per transaction |
|
r = |
Standard deviation of the daily changes in cash
balances |
|
i = |
Rate of interest per rupee per day |
If the transaction cost is higher or cash flows show greater
fluctuations, the upper limit and lower limit will be far off from each other.
As the interest rate increases, the limits will come closer. There is an
inverse relationship between Z and the interest rate.
The Miller-Orr Model is more realistic as it allows variation in cash
balance within the lower and upper limits. The lower limit can be set according
to the firm’s liquidity requirement. To determine the standard deviation of net
cash flows the pasty data of the net cash flow behaviour can be used.
Managerial attention is needed only if the cash balance deviates from the
limits.
Probability Model
According to this model, a Finance Manager has to
estimate probabilistic out comes for net cash flows on the basis of his prior
knowledge and experience. He has to determine what is the operating cash
balance for a given period, what is the expected net cash flow at the end of
the period and what is the probability of occurrence of this expected closing
net cash flows.
The optimum cash balance at the beginning of the
planning period is determined with the help of the probability distribution of
net cash flows. Cost of cash shortages, opportunity cost of holding cash
balances and the transaction cost.
Assumptions:
1. Cash is invested in marketable
securities at the end of the planning period say a week or a month.
2. Cash inflows take place
continuously throughout the planning period.
3. Cash inflows are of different
sizes.
4. Cash inflows are not fully
controllable by the management of firm.
5. Sale of marketable securities
and other short term investments will be affected at the end of the planning
period.
The probability model
prescribed the decision rule for the Finance Manager that he should go on
investing in marketable securities from the opening cash balance until the
expectation that the ending cash balance will be below the optimum cash
balance, where the ratio of the incremental net return per rupee of investment
is equal to the incremental shortage cost per rupee.
Part B
Illustration 1
United Industries Ltd. projects that cash outlays of
Rs 37, 50,000 will occur uniformly throughout the coming year. United
Industries plans to meet its cash requirements by periodically selling
marketable securities from its portfolio. The firm’s marketable securities are
invested to earn a return on investment of 12% and the cost per transaction of
converting securities into cash is Rs 40.
Using the Baumol Model determine -
(a). The optimal transaction size of
marketable securities to cash;
(b). The average cash balance of the
company;
(c). Number of transactions of
marketable securities to cash required per year; and
(d). The total annual cost of
maintaining cash balances of the company.
Illustration 2
The Cyberglobe Company has experienced a stochastic demand
for its product resulting in cash balances that fluctuate randomly. The
standard deviation of daily net cash flows is Rs 1,000. The company wants to
impose upper and lower control limits of cash balances for conversion of cash
into marketable securities and vice-versa. The current interest rate on
marketable securities is 6%. The fixed cost associated with each transfer is Rs
1,000 and minimum cash balance to be maintained is Rs 10,000.
Compute –
(a). The Optimum
Level of Cash Balance, and
(b).
The Upper Limit of Cash Balance.
Solution: 2
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