Question

North CO (NC), through its subsidiaries, engages in the generation, transmission, and distribution of electricity. It operates in four segments: Gas Distribution Operations, Gas Pipeline Investments, Wholesale Gas Services, and Gas Marketing Services. The company also constructs, acquires, owns, and manages power generation assets, including renewable energy facilities and sells electricity in the wholesale market; and distributes natural gas in Illinois, Georgia, Virginia, and Tennessee, as well as provides gas marketing services, wholesale gas services, and gas pipeline investments operations. Assume that it costs Southern $30 to convert marketable securities to cash and the firm’s marketable securities portfolio will earn an 8% annual return (use 365 day year). Also, assume that the standard deviation of Southern’s daily net cash flows is estimated to be $27,000. Assume the LCL is $1,000. The North CO uses the Miller Orr model.

a)      Calculate the spread.

b)      Calculate the target cash balance

c)      Calculate the upper control limit

d)      Calculate the average cash balance

Answer 1

a]	Spread = 3*(3/4 x Transaction cost x Cashflow variance / interest rate)^(1/3)
	Substituting values:
	Spread = 3*(0.75 *30*27000^2/(0.08/365))^(1/3) =	$        126,423
b]	Target cash balance is given by:
	Target cash balance = Lower Limit + 1/3 × Spread = 1000+126423/3 =	$           43,141
c]	Upper control limit = lower limit+Spread = 1000+126423 =	$        127,423
d]	Average cash balance = (4*Target cash balance-Lower limit)/3 = (4*43141-1000)/3 =	$           57,188