Question 19A.S-TP.1: The BAT Model Given the following information, calculate the...
The BAT Model Given the following information, calculate the target cash balance using the BAT model:
| Annual interest rate | 12% |
| Fixed order cost | $100 |
| Total cash needed | $240,000 |
What are the opportunity cost of holding cash, the trading cost, and the total cost? What would each of these costs be if $15,000 were held instead? If $25,000 were held?
From the BAT model, we know that the target cash balance is:
C^{*}=\sqrt{(2T\times F)/R}
=\sqrt{(2 \times \$ 240,000\times \$100)/.12}
=\sqrt{\$ 400,000,000}
= $20,000
The average cash balance will be C*/2 = $20,000/2 = $10,000. The opportunity cost of holding $10,000 when the going rate is 12 percent is $10,000 × .12 = $1,200. There will be $240,000/$20,000 = 12 orders during the year, so the order cost, or trading cost, is also 12 × $100 = $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.