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Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lock-box system. She forecasts that 300 payments a day will be made to lock boxes, with an average payment size of $1,500. The bank's charge for operating the lock boxes is either $.40 a check or compensating balances of $800,000.
a. If the interest rate is 9 percent, which method of payment is cheaper?
b. What reduction in the time to collect and process each check is needed to justify use
of the lock-box system?

Book for guidance : Operations Management for Competitive Advantage by Chase, Jacobs, & Aquilano

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The solution explains how to evaluate a lock box system.

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a. We need to compare the cost of the two systems.

The total yearly cost of the lock box system is 300 X 365 X 0.4 = $43,800. (Total checks per day are 300 X 365 days in year X 0.40 the charge per check)
If the bank does not charge for the check but ...

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