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 7%, 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 7% return from holding additional government bonds. The benefit of each reduction is therefore $140 (0.07 * $2,000) per year. Each additional step should only be taken if this benefit of $140 per year exceeds the additional cost. Since the cost of a making a midday deposit is an extra $80 per year in lost production, this step should be taken. Similarly, the additional cost of increasing the frequent of pick-ups is $120 per year, which is also less than the benefit of $140 per year. However, the cost of employing a computerized cash management service is $180, so the additional benefit is smaller than the extra cost. Therefore, this additional step should not be taken, and the money holding should be reduced by $4,000 to $6,000.

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