BAUMOL'S MODEL OF OPTIMUM CASH BALANCE UNDER CERTAINTY

• BAUMOL’S MODEL
  OPTIMUM CASH BALANCE UNDER CERTAINTY
  CASH MANAGEMENT
  WORKING CAPITAL MANAGEMENT
• FINANCIAL MANAGEMENT
• OPTIMUM CASH BALANCE

1. MAIN RESPONSIBILITY OF THE FINANCIAL MANAGER IS TO MAINTAIN A SOUND LIQUIDITY POSITION OF THE FIRM SO THAT DUES ARE SETTLED IN TIME. THE FIRM NEEDS CASH TO PURCHASE RAW MATERIALS AND PAY WAGES AND OTHER EXPENSES.
2. A FIRM MAINTAINS THE OPERATING CASH BALANCE FOR TRANSACTION PURPOSE. IT MY CARRY ADDITIONAL CASH AS BUFFER STOCK.
3. THE FIRM SHOULD MAINTAIN OPTIMUM JUST ENOUGH NEITHER TOO MUCH NOR TOO LESS CASH BALANCE

• TWO MODELS:

1. OPTIMUM CASH BALANCE UNDER CERTAINTY BAUMOL’S MODEL
2. OPTIMUM CASH BALANCE UNDER UN- CERTAINTY THE MILLER –ORR MODEL

• CASH MGMT MODELS
• WILLIAM J BAUMOL MODEL

1. DEVELOPED A MODEL ( THE TRANSACTION DEMAND FOR CASH: AN INVENTORY THEORETIC APPROACH) USED IN INVENTORY MGMT BUT HAS APPLICATION IN DETERMINING THE OPTIMAL CASH BALANCE ALSO. THE OPTIMAL CASH BALANCE IS REACHED AT A POINT WHERE THE TOTAL COST IS THE MINIMUM.
2. FORMAL APPROACH FOR DETERMINING A FIRM’S OPTIMUM CASH BALANCE UNDER CERTAINTY
3. CONSIDERS CASH MANAGEMENT SIMILAR TO THE INVENTORY MANAGEMENT
4. FIRM ATTEMPT TO MINIMIZE THE SUM COST OF HOLDING CASH INVENTORY ( INVENTORY OF  CASH) AND COST OF CONVERTING MARKETABLE SECURITIES TO CASH

• ASSUMPTIONS

1. THE FIRM IS ABLE TO FORECAST ITS CASH NEEDS WITH CERTAINTY
2. THE FIRM’S CASH PAYMENTS OCCUR UNIFORMLY OVER A PERIOD OF TIME
3. THE OPPORTUNITY COST OF HOLDING CASH IS KNOWN AS AND IT DOE NOT CHANGE OVER TIME
4. THE FIRM WILL INCUR THE SAME TRANSACTION COST WHENEVER IT CONVERTS SECURITIES TO CASH

• EXAMPLE
• ASSUMING THE FIRM REQUIRE CASH BALANCE OF C AND IT SELLS MARKETABLE SECURITIES AND REALIZE C AND ITS CASH BALANCE DECREASES AND REACHES TO ZERO ,AGAIN FIRM SELL SECURITIES AND HAVE C BALANCE  AND SO . THIS PATTERN CONTINUES OVER TIME. AS THE CASH BALANCE REDUCES EVENLY THE AVERAGE CASH BALANCE WILL BE C/2

• HOLDING COST FOR KEEPING THE CASH BALANCE. OPPORTUNITY COST THAT IS THE RETURN FOREGONE ON THE MARKETABLE SECURITIES. OPPORTUNITY COST IS K,THEN THE FIRM ‘S HOLDING COST FOR MAINTAINING AN AVERAGE CASH BALANCE
• HOLDING COST=k(C/2)
• INCURS A TRANSACTION COST FOR CONVERSION OF MARKETABLE SECURITIES TO CASH. TOTAL NUMBER OF TRANSACTIONS DURING THE YEAR WILL BE TOTAL T AND IT IS DIVIDED BY C SO TRANSACTION COST=T/C
• IF THE TRANSACTION COST PER TRANSACTION IS c AND THEN TRANSACTION COST=c(T/C)
• TOTAL COST= k(C/2)+c(T/C)
• HOLDING COST INCREASE AS DEMAND FOR CASH INCREASES BUT TRANSACTION COST REDUCE BECAUSE WITH INCREASING C THE NUMBER OF TRANSACTION WILL BE LESS.TRADE OFF BETWEEN HOLDING AND TRANSACTION COST

• T
• OPTIMAL CASH BALANCE
• 
  
• FORMULAE

1. C=√(2CT/K) WHERE:-
2. C = OPTIMUM BALANCE
3. T=TOTAL CASH NEEDED DURING THE YEAR
4. c = PER TRANSACTION COST
5. K = OPPORTUNITY COST OF HOLDING CASH