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Cash Management

Cash management is concerned

with the managing of: cash flows into and out of the firm,

cash flows within the firm, and

cash balances held by the firm at a

point of time by financing deficit or

investing surplus cash

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FourFacets of Cash Management Cash planning

Managing the cash flows Optimum cash level

Investing surplus cash

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Optimum Cash Balance Optimum Cash Balance under Certainty:

Baumols Model, Beranek Model

Optimum Cash Balance under

Uncertainty: The MillerOrr Model

And Stone Model

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The Baumol Model

Assumptions: The firm is able to forecast its cash needs

with certainty.

The firms cash payments occur uniformlyover a period of time.

The opportunity cost of holding cash is

known and it does not change over time. The firm will incur the same transaction cost

whenever it converts securities to cash.

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The Baumol Model

The firm incurs a holding cost for keeping the cash balance. It is anopportunity cost; that is, the return foregone on the marketablesecurities. If the opportunity cost is k, then the firms holding cost formaintaining an average cash balance is as follows:

The firm incurs a transaction cost whenever it converts its marketablesecurities to cash. Total number of transactions during the year will betotal funds requirement, T, divided by the cash balance, C, i.e., T/C. The

per transaction cost is assumed to be constant. If per transaction cost isc, then the total transaction cost will be:

The total annual cost of the demand for cash will be:

The optimum cash balance, C*, is obtained when the total cost isminimum. The formula for the optimum cash balance is as follows:

Holding cost = ( / 2)k C

Transaction cost = ( / )c T C

* 2cTC

k!

Total cost = ( / 2) ( / )k C c T C

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IllustrationBaumol Model

Advani hemical Limited estimates its total cash requirement as Rs 2 crore next year. The companys opportunity

cost of funds is 15% per annum. The company will have to incur Rs 150 per transaction when it converts its short-termsecurities to cash. Determine the optimum cash balance. How much is the total annual cost of the demand for the

optimum cash balance? How many deposits will have to be made during the year?

T!

000,200Rs15.0

)000,000,20)(150(2C* !!

The annual cost will be:

3=+=+=

/+/=co total

During the year, the company will have to make 100 deposits, i.e. converting marketable securities to cash.

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The Beranek Model

This Model assume that the cash inflowsare steady but the outflows are periodic

This is the mirror image of the time patternof cash flows in Baumol model, whereinflows are periodic and outflows aresteady

Cash would be collected continuously at ata uniform rate, but would be disbursedover a short period of time

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In this pattern of cash flows, the challenge

is to profitably invest the funds between

the time of their receipts and the when a

group of cheques are presented to the bank

for the payment.

The trade off between interest income andtransaction cost and strategies employed

are parallel to those of Baumol Model

The Beranek Model

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The formula for optimum number of

transaction is same as that for the Baumol

Model

However, the cash is accumulated

gradually (rather than disbursed gradually),

so the transaction pattern would involve a

series of cash investment followed by one

disinvestment at the end of the period.

The Beranek Model

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The MillerOrr Model

The MO model provides for two control limitstheupper control limit and the lower control limit as wellas a return point.

If the firms cash flows fluctuate randomly and hit theupper limit, then it buys sufficient marketablesecurities to come back to a normal level of cashbalance (the return point).

Similarly, when the firms cash flows wander and hitthe lower limit, it sells sufficient marketablesecurities to bring the cash balance back to the normallevel (the return point).

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The Miller-Orr Model

The difference between the upper limit and the lower

limit depends on the following factors: the transaction cost (c)

the interest rate, (i)

the standard deviation (W) of net cash flows.

The formula for determining the distance between upper

and lower control limits (called Z) is as follows:1/ 3(Upper Limit Lower Limit) (3/ 4 Transaction ost ash Flow Variance/ Interest Rate)

Upper Limit Lo wer Limit + 3

Return Point Lo wer Limit +

The net effect is that the firms hold the average the cash balance equal to:

verage

Z

Z

ash alance Lower Limit + 4/3Z

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3bW 2

RP = 3 +LL

4I

UL = 3RP2LL

where: RP = return point

b = fixed cost per order for converting

marketable securities into cash.

I = daily interest rate earned on marketable securities

W2 = variance of daily changes in the expected cash balance

LL = the lower control limit

UL = the upper control limit

The Miller-Orr Model

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aja td. provide the following information

Annual yield: 12%, daily: 12/360= 0.0333%

Transaction cost: s. 1600

Change in daily cash balance, S.D., s.5000 Minimum Cash balance: s. 50000

Illustration: Miller-Orr Model

3bW 2 3*(1600)*(5000) 2

RP = 3 +LL = 3 +50000

4I 4 * (0.00033)

UL = 3RP2LL

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This model is based on the argument that the average

bank balance is determined by banks requirement of

maintaining compensatory bank balance in current

account when an overdraft is taken. (This practice isno more in India)

Minimizing transaction cost subject to the constraints

of matching average balance with target balance

se control limits similar to Miller and Orr Model

Except

Two sets of limits : outer limit and inner limit

The Stone Model

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When the balance reaches the outer limit, the finance

manager does not trigger securities purchase, as in

the case of Miller, but checks with the forecast for

the next pre-determined days. If he finds that the

forecasted cash flow is expected to move within the

inner limits, i.e. the balance is closer to target

balance, he does not order any securities transactions

and hence save on transaction cost. If forecast is out side the inner limits, he orders

buying or selling securities to reach the target

balance

The Stone Model

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A company has following forecast of cash flow during the next14 days ( s. in akh)

Illustration: The Stone Model

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14Cash

Forecast 8 4 -5 -4 5 -1 2 0 1 -16 7 -5 2 -5Cash

Actual8 3 -6 -3 6 -2 5 -4 0 -18 6 -6 -3 4

The finance Manager has set up upper outer limit of s. 40 lakh

and the lower outer limit of s. 23 lakh. Inner limit fixed at s.2lakh minus or plus respectivly from the outer limits. i.e. 40-2=38and 23 2 = 25 lakh

ook out time is 3 days

Day opened at target cash balance of s. 30 lakh

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Time Pattern ofCash flow

Baumol Model Beranek Model

All cash flows are certain All cash flows are certain

Cash inflows are periodic

and instantaneous

Cash outflows are periodic

and instantaneous

Cash outflows occur at a

constant rate

Cash inflows occur at a

constant rate

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Time Pattern ofCash flow

Miller-Orr Model Stone Model

Firm has minimum required

cash balance

Firm has minimum required

cash balanceCash flows are normally

distributed and standard

deviation does not change

Firm has some knowledge

of future cash flows

The Expected cash flow is

zero

Although this knowledge

contain error component

There is no autocorrelation

in cash flows

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ReceivableManagement

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Heuristic Approach to

Establishing Credit imit Heuristic approach is based on companys

actual experience

The formula or procedure here has the

weightage of managerial experience and

intuition behind it and therefore it is heuristic

in nature To establish a credit limit and granting credit,

following factors need to be considered

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Contributing

Factor

Rating Credit limit

%of net worth

Applicants Credit

Requirements

(C)

C

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Contributing

Factor

Rating Credit limit

%of net worth

Profit Margin

(M)

M

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Sequential Decision Analysis In this analysis, investigation is carried out

further stage only if the benefit of such

analysis outweighs its cost

Required to prepare decision tree

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Discriminant analysis is a statistical tool helpful for classificationpurposes.

To convey a basic understanding of discriminant analysis, we shallemploy the following assumptions:

There are two discrete groups (group 1 and group 2).

Two variables combined in a linear manner would be used for

discriminating between the two discrete groups (This meansthat the discriminant function will be Zi= aXi+ bYi).

These two variables arise from multivariate normalpopulations. While the means of the two variables in eachgroup are different, their variance/covariance matrix isidentical for each group.

Discriminant analysis and

customer classification

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1. Estimation of the discriminant function

2. Choice of the cutoff point for the discriminant

function

3. Examination of the predictive ability of the

discriminant functionContd.,

Steps involved in Discriminant

analysis

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In n n n num ntsthe et een

up sum fsquares fZiscoresandthedenom natorrepresentsthe

thin roupsum ofsquaresoftheZi scores.For maximising the ratio, given in quation, e set its partial

derivatives ith respect to a and (the t o parameters of thediscriminant function) equal to 0. doing this, e get the follo ing

normalequations:

a . 2x b. xy x

a . xy b

2y y

here 2x varianceof X

xy =covarianceofXand

2y=varianceofYx=difference et eenthe meanvaluesofXforthet ogroupsy=difference et eenthe meanvaluesofY forthet ogroups.

Contd.,

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Solving the above normal e uations, we get

2y. dx - xy. dy

a =

2x

. 2y - xy. xy

2x. dy - xy. dx

b =

2x. 2y - xy. xy

Contd.,

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The cutoff value which is supposed to separate the two groups, should be chosen in such a

way that it minimises the probability of misclassification. In theory, the cutoff value isrepresented by the point Z* because it results in minimal misclassification.

Discriminant functionZ1 Z* Z2

Group 1 Group 2

Contd.,

ProbabilityDistributions and Cut-off Level

Choice of the cut-off point for the

discriminant function

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In practice, the cut-off point is chosen in such a way that it

minimises misclassification in the estimation sample. Todefine this cut-off value, we proceed as follows:

(i) Calculate the Zi value for the observations and arrange

them in an ascending order.

(ii) Consider the mid-points of adjacently ranked observations,

in the area where the observations from the two groups

overlap, as possible cut-off levels.

(iii) Choose that cut-off point which minimises the total number

of misclassifications.

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Hence , it is desirable t examine the redictive abilit f the

discriminant f ncti n with reference t a new samp le which may be referred t as a va lidati n r holdout samp le . This invo lve s comparing

the classification of observa tions based on their discriminant function

scores with their actual classification. or this purpose the following

classificationma trix (confusionma trix) is prepared:

Actu l l ssification

Group 1 Group

Pre icte Group 1 11 12

lassification Group 2 21 22

If the discriminant mode l correctly predicts the group to whicheachobserva tionbelongs, all observa tions will be on the ma indiagonal

of the ma trix , i.e . in the C11and C22elements. The percentage of correct

predictions is:

C11 + C22

C11 + C22 + C21 + C22

Examination of the predictive ability of the

discriminant model