Question

As the chief financial officer for ABC Company, you have to deal with unpredictable and large receipts and disbursements. Your company has adopted the use of the Miller-Orr model for management of checking balances. The variance of daily net cash flows is $14,392,000. The cost of making a purchase or sale of marketable securities is $170, and the rate you earn on marketable securities is 8%. Your company wishes to maintain a minimum balance in the checking account of $11,000.

a. Calculate the return point given by the Miller-Orr model.

b. Calculate the average balance in the checking account if the Miller-Orr model is used.

c. State the action that would be taken if the checking balance is $9,027 at the end of the day. Give a precise description including the dollar amount of any transfer.

Answer 1

Solution =

Variance of daily net cash flows = $14,392,000

Cost of transaction per sale = $170

Daily Rate on marketable securities =( 8% / 365) = 0.00022

Lower limit = $11000

a)  Return point = lower limit + (1/3 * spread)

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

=3* [(3 * 170* 14392000) / (4* 0.00022)]^1/3

⁼ 3 * (7339920000 / 0.00088)^1/3

^{= 3 * (20280.074)}

^{=$ 60840.222 or $ 60840}

Return point = $ 11000 + $( 60840/ 3) = $11000 + $ 20280

= $ 31280

b.) Average balance = ( optimal cash balance + upper limit) / 3

Optimal cash balance = $20280 ( from spread calculations)

Upper limit = lower limit + spread

= $ 11000 + $ 60840 = $ 71840

Average balance = ( 20280 + 71840 ) / 3 = $ 30706.67

c)  If the balance reaches outside the desired limit i. e, upper and lower limit , Miller orr model suggest to transfer the money in and out of account to return the balance to the normal or desired limit.

In the question, the checking balance reached below lower limit so the securities will be sold to bring the optimal cash balance . The securities amounted for selling should be of $ 11253 ( $20280 - $ 9027).