19A.1 From the BAT model, we know that the target cash balance is: C* 5 √(2T 3 F )yR 5 √(2 3 $240,000 3 100)y.12 5 √$400,000,000 5 $20,000 The average cash balance will be C*y2 5 $20,000y2 5 $10,000. The opportunity cost of holding $10,000 when the going rate is 12 percent is $10,000 3 .12 5 $1,200. There will be $240,000y20,000 5 12 orders during the year, so the order cost, or trading cost, is also 12 3 $100 5 $1,200. The total cost is thus $2,400. If $15,000 is held, the average balance is $7,500. Verify that the opportunity, trading, and total costs in this case are $900, $1,600, and $2,500, respectively. If $25,000 is held, these numbers are $1,500, $960, and $2,460, respectively.
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