Determining Optimum Cash

8/14/2019 Determining Optimum Cash

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DETERMINING THE OPTIMUM

LEVELS OF CASH BALANCE


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IN ORDER TO INVEST EXCESSFUNDS,THEFINANCIAL MANAGER MUST KNOW

MINIMUM AMOUNT THAT MUST BE KEPT IN FORM

OF THE CASH .SEASONAL FACTORS AND CYCLICAL

REQUIRENENTS MAKE IT DIFFICULT TO ASCERTAIN

THESE AMOUNT ACCURATELY.A RANGE OF CASHMANAGEMENT MODELS WHICH MAY BE USED BY

THE FINANCE MANAGER HELP HIM TO MAINTAIN

APPROX. ENOUGH CASH IN THE CO. TO COVER

TRANSACTIONS PRECAUTIONARY ANDSPECULATIVE BALANCE . THESE MODELS ARE

DISCUSSED BELOW.


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BAUMOL MODEL

IN THIS MODEL FIRM IS ASSUMSD TORECEIVE CASH PERIODICALLY BUT TOPAY OUT CASH CONTINUOUSLY AT THE

STEADY RATE.I.E THE FIRMS INFLOWSARE LUMPY BUT ITS OUTFLOWS ARE

NOT.WHEN THE CASH INFLOWS IS

RECEIVED THE FIRM PUTS ENOUGH

CASHINITS DISBURSEMENT A/C TOCOVER OUTFLOWS UNTIL THE NEXT

INFLOW IS RECEIVED.


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THERE ARE SEVERAL TYPES OF BUSINESS

THAT EXPERIENCETIME PATTERN OF CASHFLOW SIMILAR TO THIS.FOR EXAMPLE

FOR FIRM THAT MANAGE RENTAL PROPERTY

RENTS ARE OFTEN RECEIVED OVER ASHORTPERIOD EARLY IN THE MONTH BUT OTHER

EXPENSES CONTINUE EVENLY THROUGH OUT

THE MONTH


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ASSUMPTIONS OF THIS MODEL

ARE;


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IT ASSUMES THAT INVESTMENT YIELD

AFIXED RATE OF RETURN PER PERIOD

REGARDLESS OF THE LENGTH OF THEINVESTMENT

THE TRANSACTION COST OF INVESTING AND

DIS INVESTINGIS A FIXED COST I.E INDEPENDENT OF THE

INVESTMENT THESE TRANSACTION COST

CONSIST

OF ALL THE OUT OF POCKET COST OF

MAKING OR SELLING THE INVESTMENT


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COMMISSIONS, POSTAGE TELEPHONE

CHARGES,OPPORTUNITY COST OFDIVERTED MANAGERIAL EFFORTS AND

SO FORTH


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STRATEGIES


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1. TWO TRANSACTION

STRATEGY


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WHEN THE CASH INFLOW IS RECEIVED

INVEST ONE HALF OF THE TOTAL INFLOW PUT

THE REMAINING ONE HALF IN DISBURSEMENT

A/C.

DURING THE FIRST HALF OF THE PERIOD PAY

DISBURSEMENT FROM THE DISBURSEMENT

A/C .THIS A/CWILL BE DRAINED ONE HALF OF THE WAY

THROUGH THE PERIOD. AT THAT TIME SELL

THE INV. AND PLACE THE RESULTING FUNDS

IN THE DISBURSEMENT A/C.


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USE THESE FUNDS TO PAY

DISBURSEMENTS DURING THE

REMAINDER OF THE PERIOD


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TO SEE THE NET GAIN FROM THIS

STRATEGY LET Y BE THE AMOUNT OF

THE CASH INFLOW AND i BE THEINTEREST RATE PER PERIOD.SINCE IN

THIS STRATEGY ONE HALF THE INFLOW

IS INVESTED FOR ONE HALF THE

PERIOD,THE INTEREST INCOME IS

INVESTMENT INCOME=(1/2)(1/2)iy=(1/4)iy


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BUT THERE ARE TWO TRANSACTION IN THIS

SRTATEGY: ONE INVESTMENT AND ONEDISINVESTMENT.IF THE COST PER

TRANSACTION IS a,THE TRANSACTION COST

OF THIS STRATEGY IS 2l,AND THE PROFIT IS

PROFIT=(1/4)iy 2a


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2).THREE TRANSACTION

STRATEGY


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1). WHEN THE CASH FLOW IS RECEIVED,

INITIALLY INVEST TWO-THIRD OF IT.PLACE

THE REMAINING ONE THIRD IN THEDISBURSEMENT A/C.

2). ONE THIRD OF THE WAY THROUGH THE

PERIOD, THE DISBURSEMENT A/C WILL BEEXHAUSTED.AT THE TIME, DISINVEST ONE

HALF OF THE FUNDS IN THE INV. A/C.


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THIS STRATEGY INVOLVES ONE INV.

TRANSACTION AND TWO DISINVESTMENTTRANSACTION.THIS STRATEGY CAPTURE A

GREATER

PORTION OF THE INITIAL CASH INFLOW IN

THE INV. A/C

INTERESTINCOME=(2/3)(1/3)iy+(1/3)(1/3)iy=(1/3)iy

AND PROFIT= (1/3)iy 3a


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3). OPTIMAL STRATEGY

THIS STRATEGY IS BASED UPON THE

OPTIMAL NO. OF TRANSACTIONS FORA FIRM WITH PERIODIC INFLOW AND

STEADY OUTFLOWS. IN GENERAL THE

INTEREST INCOME FROM INV.

STRATEGIES IN THIS SITUATIONIS:


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INTEREST INCOME=[n-1/2n]

where n= no. of transaction

profit =[(n-1)/ 2n] iy - na

as the no. of transaction inc., the int. income

inc. but so does the total transaction costs .

For some level of n,the profit is at a max.


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To find this we take first derivative of the

profit function,and solve for the optimal n.

n*=(iy/2a)1/2

where n* = optimal no. of transaction


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For ex.: a firm runs an apartment complex cash

comes in the beginning of the month and is

disbursed uniformly through out the followingmonths. For the up coming month,

the firm expects to have cash expenses of

rs.2,50,000. by investing in a money mkt. a/c. it can

earn 0.5 % per month. Transaction cost areestimated at rs. 50 per transaction .what is the firm


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To formulate this strategy, the optimal no. of

transactions is first computed:

n*=(iy /2a)1/2

= [(0.005) (2,50,000)/2(50)]1/2

= 5.o


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Profit=[(n-1)/2n] iy na

=(5-1)/2(5)(0.005)(2,50,000)-5(50)

= 500 250 = rs. 250


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THE BERANEK MODEL

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Determining Optimum Cash