## [solution]: 19A.1 From the BAT model, we know that the target cash balance is: C * 5 √ (2 T 3 F ) y R 5...

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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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