Which model is cash management model?

Answer 1

Cash management modelsCash management models are aimed at minimising the total costs associated with movements between a company's current account (very liquid but not earning interest) and their short-term investments (less liquid but earning interest).

The models are devised to answer the questions:

• at what point should funds be moved?
• how much should be moved in one go?

The Baumol cash management model

Baumol noted that cash balances are very similar to inventory levels, and developed a model based on the economic order quantity(EOQ).Assumptions:

• cash use is steady and predictable
• cash inflows are known and regular
• day-to-day cash needs are funded from current account
• buffer cash is held in short-term investments.

The formula calculates the amount of funds to inject into the current account or to transfer into short-term investments at one time:

where:

CO = transaction costs (brokerage,commission, etc.)

D = demand for cash over the period

CH = cost of holding cash.

The model suggests that when interest rates are high, the cash balance held in non-interest-bearing current accounts should be low. However its weakness is the unrealistic nature of the assumptions on which it is based.

Example using the Baumol model

A company generates $10,000 per month excess cash, which it intends to invest in short-term securities. The interest rate it can expect to earn on its investment is 5% pa. The transaction costs associated with each separate investment of funds is constant at $50.

Required:

(a)What is the optimum amount of cash to be invested in each transaction?

(b)How many transactions will arise each year?

(c)What is the cost of making those transactions pa?

(d)What is the opportunity cost of holding cash pa?

Solution:

The Miller-Orr cash management model

The Miller-Orr model is used for setting the target cash balance for a company.

The diagram below shows how the model works over time.

• The model sets higher and lower control limits, H and L, respectively, and a target cash balance, Z.
• When the cash balance reaches H, then (H-Z) dollars are transferred from cash to marketable securities, i.e. the firm buys (H-Z) dollars of securities.
• Similarly when the cash balance hits L, then (Z-L) dollars are transferred from marketable securities to cash.

The lower limit, L is set by management depending upon how much risk of a cash shortfall the firm is willing to accept, and this, in turn, depends both on access to borrowings and on the consequences of a cash shortfall.

The formulae for the Miller-Orr model are:

Return point = Lower limit + (1/3 × spread)

Spread = 3 [ (3/4 × Transaction cost × Variance of cash flows) ÷ Interest rate ] 1/3

Note: variance and interest rates should be expressed in daily terms. Variance = standard deviation squared.

Example using the Miller-Orr model

The minimum cash balance of $20,000 is required at Miller-Orr Co,and transferring money to or from the bank costs $50 per transaction. Inspection of daily cash flows over the past year suggests that the standard deviation is $3,000 per day, and hence the variance (standard deviation squared) is $9 million. The interest rate is 0.03% per day.

Calculate:

(i)the spread between the upper and lower limits

(ii) the upper limit

(iii)the return point.

Solution:

(i)Spread = 3 (3/4 × 50× 9,000,000/0.0003)1/3 = $31,200

(ii) Upper limit = 20,000 + 31,200 = $51,200

(iii)Return point = 20,000 + 31,200/3 = $30,400