# Cash Management using Baumol Model

1) Company A is using the Baumol model to find cash balances. Recently the model called for an average balance (C*/2) of $500 and the rate on marketable securities was 4%. A rapid increase in interest rates has driven the interest rate up to 9% What is the appropriate average cash balance now?

2) Company A receives $2 million in payments of which $500,000 is needed for cash payments made during the next year. Each time the company deposits money in its account, a charge of $2.00 is assessed to cover certain admin costs. If the company can hold marketable securities which yield 5% and then convert these securities to cash at a cost of only the $2 deposit charge, what is the total cost for one year of holding the minumum cost cash balance based on the Baumol model?

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1) Company A is using the Baumol model to find cash balances. Recently the model called for an average balance (C*/2) of $500 and the rate on marketable securities was 4%. A rapid increase in interest rates has driven the interest rate up to 9% What is the appropriate average cash balance now?

The Baumol Model

C = square root of ( 2 x Total Demand during the period x Fixed Transaction Cost)/ Interest rate

1000 = square root of ( 2 x Total Demand during the period x Fixed Transaction Cost)/ 4%

Or (Total Demand during the period x Fixed Transaction Cost) = (1000^2 x4% )/2= 20,000

^2 stands for square

You can use (Total Demand during the period x Fixed Transaction Cost) directly in the calculation without finding Fixed Transaction Cost separately

When interest rate becomes 9%

C = square root of 2 x (Total Demand during the period x Fixed Transaction Cost)/ Interest rate

= square root of ( 2 x 20,000)/ 9%

as (Total Demand during the period x Fixed Transaction Cost) = 20,000 (Calculated above)

or C = square root of ( 2 x 20,000)/ 9% = 666.67

or average balance (C*/2) = 666.67 /2 = $ 333.33

2) Company A receives $2 million in payments of which $500,000 is needed for cash payments made during the next year. Each time the company deposits money in its account, a charge of $2.00 is assessed to cover certain admin costs. If the company can hold marketable securities which yield 5% and then convert these securities to cash at a cost of only the $2 deposit charge, what is the total cost for one year of holding the minimum cost cash balance based on the Baumol model?

C = square root of ( 2 x Total Demand during the period x Fixed Transaction Cost)/ Interest rate

C = square root of ( 2 x 500,000 x $2 )/ 5% = $6324.55

Opportunity cost = Average cash balance x Interest rate; (C/2 x i) = (6324.55/2) x 5%=$158.11

Trading cost = Total disbursements during period/ Initial Cash balance x given fixed cost; (T/C) x F = ($500,000/$6324.55)x $ 2 = $158.11

Total Cost = Opportunity cost + Trading cost = $ 158.11 + $ 158.11 = $ 316.22

Answer: the total cost for one year of holding the minimum cost cash balance based on the Baumol model = $ 316.22