Question

Crowell Ltd. is considering using the Miller-Orr model to manage its cash flows. The minimum cash balance would be KES 4,000,000. Other information is as follows:

• Interest rate per annum = 14.4%
• Transaction cost per sale = KES 25,000
• Standard deviation of daily cash flows = KES 50,000
• A year has 360 days.

Required:

Calculate the Miller-Orr model upper limit and return point, and explain how these would be used to manage the cash balances of Crowell Ltd.

Answer 1

Upper limit = Lower limit + Spread

Lower limit = minimum cash balance = KES 4000000

Spread = 3[3/4 X (transaction cost*variance of cash flows)/interest rate]^1/3

transaction cost = KES25000

standard deviation of cash flows = KES 50000 hence variance = (standard deviation)^2 = 50000 ^2

Annual interest rate =14.4%, number of days = 360 , daily interest rate = .144/360 = 0.04%

Spread = 3[3/4 X (25000 x 50000^2)/0.0004]^1/3

= 1468075.37

Upper Limit = Lower limit + Spread = 4000000 + 1468075.37 = KES 5468075.37

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Return point = lower limit + spread/3

= 4000000 + 1468075.37/3 =KES 4489358.46

The moment the actual cash balance touches the lower point i.e. 4000000 the company will have to replenish funds by selling investments in marketable securities  and if actual cash balance touches 5468075 it will have to buy marketable securities to pull down the cash balance to the return point cash balance.