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

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 ov~ht 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 lO-year depreciable
life and a $3600 salvage value 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 corporation has a 50% combined federal-plus-state
incremental tax rate. Assume a lO-year study period for the analysis and an
after-tax MARR of 20%. Compute:

 (a) The after-tax present worth of this investment.

 (b) The after-tax internal rate of return of this

 (c) The after-tax simple payback period of this investment.

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