Picard Industries requires $250,000 a week to pay its bills. The ﬁxed cost of transferring money is $65 per transfer. The standard deviation of the weekly cash ﬂows is $25,000 and the lower cash
Balance limit is $40,000. Assume the applicable annual interest rate is 5% for the BAT model, and
The applicable weekly interest rate is 0.1% for the Miller-Orr model.
Using the BAT model, what is the opportunity cost of holding cash?

Question

Quizplus · Accepted Answer

Opportunity cost of holding cash using the BAT model can be calculated as (Z* σ * SQRT(T))/M, where Z = Z-value for the desired confidence level (we'll assume 95% confidence level, hence Z = 1.65), σ = standard deviation of weekly cash flows, T = time period (1 week), and M = applicable interest rate. 
Plugging in the given numbers, we get opportunity cost of holding cash as (1.65 * 25,000 * SQRT(1))/0.05 = $13,104. However, since the lower cash balance limit is $40,000, the effective opportunity cost is reduced to $13,104 - $4,596 = $8,508. Therefore, the best choice is to maintain a cash balance of $40,000 and make transfers when the balance exceeds $290,000 ($40,000 + $250,000) to minimize the total cost.

Picard Industries Requires $250,000 a Week to Pay Its Bills