Question 20A.1: The Vulcan Corporation has cash outflows of $100 per day, se...
The Vulcan Corporation has cash outflows of $100 per day, seven days a week. The interest rate is 5 percent, and the fixed cost of replenishing cash balances is $10 per transaction. What is the optimal initial cash balance? What is the total cost?
The total cash needed for the year is 365 days × $100 = $36,500. From the BAT model, we have that the optimal initial balance is:
C^{*}= \sqrt{(2T\times F)/R}
=\sqrt{(2\times \$36,500\times 10)/.05}
= \sqrt{\$14.6 million}
= \$3,821
The average cash balance is $3,821/2 = $1,911, so the opportunity cost is $1,911 × .05= $96. Because Vulcan needs $100 per day, the $3,821 balance will last $3,821/100 = 38.21 days. The firm needs to resupply the account 365/38.21 = 9.6 times per year, so the trading (order) cost is $96. The total cost is $192.