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Float Management

Cash Management. Suppose that the rate of interest increases from 4 to 8 percent per year. Would firms` cash balances go up or down relative to sales? Explain.

23. Cash and Inventory Management. According to the economic order quantity inventory model and the Baumol model of cash management, what will happen to cash balances and inventory levels if the firm`s production and sales both double? What is the implication of your answer for percentage of sales financial planning models (see Section 18.2)?

24. Float Management. Some years ago, Merrill Lynch increased its float by mailing checks drawn on West Coast banks to customers in the East and checks drawn on East Coast banks to customers in the West. A subsequent class action suit against Merrill Lynch revealed that in 28 months from September 1976 Merrill Lynch disbursed $1.25 billion in 365,000 checks to New York State customers alone. The plaintiff `s lawyer calculated that by using a remote bank Merrill Lynch had increased its average float by 11вБД2 days.7

a. How much did Merrill Lynch disburse per day to New York State customers?

b. What was the total gain to Merrill Lynch over the 28 months, assuming an interest rate of 8 percent?

c. What was the present value of the increase in float if the benefits were expected to be permanent?

d. Suppose that the use of remote banks had involved Merrill Lynch in extra expenses. What was the maximum extra cost per check that Merrill Lynch would have been prepared to pay?

1 a. The ledger balance is $940 + $100 Ј $40 = $1,000.

b. Availability float is $100, since you do not yet have access to the funds you have deposited.

c. Payment float is $40, since the check that you wrote has not yet cleared.

d. The bank`s ledger balance is $940 + $100 = $1,040. The bank is aware of the check you deposited but is not aware of the check you wrote.

e. Ledger balance plus payment float = $1,000 + $40 = $1,040, which equals the bank`s ledger balance. Available balance + availability float = $940 + $100 = $1,040, also equal to the bank`s ledger balance.

2 The current market value of Ford is $57 billion. The 2-day reduction in float is worth $800 million. This increases the value of Ford to $57.8 billion. The new stock price will be 57.8/1.14 = $50.70 per share. Ford should be willing to pay up to $800 million for the system, since the present value of the savings is $800 million.

3 The benefit of the lock-box system, and the price the firm should be willing to pay for the system, is higher when:

a. Payment size is higher (since interest is earned on more funds).

b. Payments per day are higher (since interest is earned on more funds).

c. The interest rate is higher (since the cost of float is higher).

5 At an interest rate of 4 percent, the optimal initial cash balance is _2 1,260,000 20 = $35,496 .04

The average cash balance will be one-half this amount, or $17,748. The firm will need to sell securities 1,260,000/35,496 = 35.5 times per year. Therefore, annual trading costs will be 35.5 $20 = $710 per year. Because the interest rate is lower, the firm is willing to hold larger cash balances.

6 a. Higher interest rates will lead to lower cash balances.

b. Higher volatility will lead to higher cash balances.

c. Higher transaction costs will lead to higher cash balances.