Jan's Dry Cleaning holds $10,000 on a typical day, although only $2,000 is essential for carrying out business. Making a midday deposit is estimated to reduce cash holdings to $8,000 and cost an extra $80 per year in lost production. If, in addition, an armored car service is engaged to pick up cash more frequently for a fee of $120 per year, cash holdings will be further reduced to $6,000 per day. Employing a computerized cash management service for an annual fee of $180 would reduce cash holdings further to $4,000. If any reduction in cash holdings will be invested in government bonds earning 3%, then how much money should Jan's hold?

Question

Quizplus · Accepted Answer

Note that each additional step reduces the average money holding by $2,000, and that the benefit of each reduction is the 3% return from holding additional government bonds. The benefit of each reduction is therefore $60 (0.03 * $2,000) per year. Each additional step should only be taken if this benefit of $60 per year exceeds the additional cost. Since the cost of a making a midday deposit is an extra $80 per year in lost production, the additional benefit is smaller than the extra cost. Therefore, this additional step should not be taken, and the money holding should not be reduced at all but remain $10,000.

Jan's Dry Cleaning Holds $10,000 on a Typical Day, Although