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, but would cost an extra $80 per year in lost production. Jan’s can reduce cash holdings to $6,000 if it hires an armored car service to pick up cash more frequently for a fee of $120 per year. Employing a computerized cash management service for an annual fee of $180 would reduce cash holdings to $4,000. Jan’s plans on purchasing government bonds paying a 5% interest rate with any cash holding reductions. What is Jan’s optimal money holding?

$4,000

Explanation:

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

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