Question

2. Assume short-term securities yield 5% and it costs $20 for buying and selling securities. The variance of the firm's daily net cash balances is $20,000. Management keeps at least $1,000 in cash balances. What is the maximum amount the firm will let accumulate in its cash account before investing in marketable securities? How much will the firm invest?

Answer 1

a]	Per the Miller-Orr Model, Optimal cash return point is given by:
	Return Point = Lower Limit + 1/3 × Spread
	Spread = 3*(3/4 x Transaction cost x Cashflow variance / interest rate)^(1/3)
	Substituting values:
	Spread = 3*(0.75 *20*20000/(0.05/365))^(1/3) =	$            3,896
	Optimal return point = 1000+3896/3 =	$            2,299
b]	Upper cash balance = lower limit+Spread = 1000+3896 =	$            4,896
c]	When the cash balance, which fluctuates randomly, touches
	the upper limit, the firm sells enough marketable securities
	to take the cash balance down to the optimal return point.
	Instead, if the cash balance touches the lower limit, enough
	marketable securities would be sold to raise the cash
	balance to the optimal return point.
	Till the cash balance raaches the upper limit or lower limit,
	it fluctuates randomly, with no action taken.
	The lower limit is set by the firm and would be based on its
	requirement for safety stock of cash in hand. Here, it is $1,000.
	ANSWERS:
1]	Maximum amount that will be accumulated before investing in marketable securities is the upper control limit of $4,896.
2]	The firm will invest till the return point is reached. So it will
	invest $4,896-$2299 = $2,597