Question

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 used to purchase government bonds earning 5 percent, then how much money should Jan's hold? a. 10,000 b.8,000 c. 6,000 d.4,000

Answer 1

In case holding is $10000,

Reduction in cash holding=(10000-10000)=0

Interest earned in government bonds=Reduction in holdings*5%=0*5%=0

Cost of deposits=0

Additional benefit=0-0=0

In case of making a mid day deposit,

Reduction in cash holding=(10000-8000)=$2000

Interest earned in government bonds=Reduction in holdings*5%=2000*5%=$100

Cost of deposits=$80

Additional benefit=100-80=$20

In case of using a armed car service

Reduction in cash holding=(10000-6000)=4000

Interest earned in government bonds=Reduction in holdings*5%=4000*5%=$200

Cost of deposits=$120

Additional benefit=200-120=$80

In case of using computerized cash management service

Reduction in cash holding=(10000-4000)=6000

Interest earned in government bonds=Reduction in holdings*5%=6000*5%=$300

Cost of deposits=$180

Additional benefit=300-180=$120

Additional benefit is maximized in case of computerized management service. So, Optimal cash holding is $4000

Correct option is

d) $4000