A firm manufactures padded shipping bags. One hundred bags are packed in a cardboard carton. At present,

Question:

A firm manufactures padded shipping bags. One hundred bags are packed in a cardboard carton. At present, machine operators fill the cardboard cartons by eye: that is, when the cardboard carton looks full, it is assumed to contain 100 shipping bags. Actual inspection reveals that the cardboard carton may contain anywhere from 98 to 123 bags with an average quantity of 105.5 bags.
The management has never received complaints from its customers about cartons containing fewer than 100 bags. Nevertheless, management realizes that they are giving away 51/2% of their output by overfilling the cartons. One solution would be to count the shipping bags to ensure that 100 are packed in each carton. Another solution would be to weigh each filled shipping carton. Underweight cartons would have additional shipping bags added, and overweight cartons would have some shipping bags removed. This would not be a perfect solution because the actual weight of the shipping bags varies slightly. If the weighing is done, it is believed that the average quantity of bags per carton could be reduced to 102, with almost no cartons containing fewer than 100 bags.
The weighing equipment would cost $18,600. The equipment would be depreciated by straight-line depreciation using a l0-year depreciable life and a $3600 at the end of 10 years. The $18,600 worth of equipment qualifies for a 10% investment tax credit. One person, hired at a cost of $16,000 per year, would be required to operate the weighing equipment and to add or remove padded bags from the cardboard cartons. 200,000 cartons will be ,checked on the weighing equipment each year, with an average removal of 3.5 padded bags per carton with a manufacturing cost of 3 cents per bag. This large profitable has a 50% combined federal-plus-state incremental tax rate. Assume a 10-year study period for the analysis and an after-tax of 20%.
Compute:
(a) The after-tax present worth of this investment.
(b) The after-tax of this investment.
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