Urban Elite Cosmetics has used a traditional cost accounting system to apply quality$-$control costs uniformly to all products at a rate of $16$ percent of direct$-$labor cost. Monthly direct$-$labor cost for Satin Sheen makeup is $$109,000.$ In an attempt to more equitably distribute quality$-$control costs, management is considering activity$-$based costing. The monthly data shown in the following chart have been gathered for Satin Sheen makeup.

Activity Cost Pool Cost Driver Pool Rates Quantity of Driver for Satin Sheen

Incoming material inspection Type of material $ $22\mathrm{.}00$ per type $24$ types

In$-$process inspection Number of units $0\mathrm{.}28$ per unit $44,000$ units

Product certification Per order $149\mathrm{.}00$ per order $60$ orders

Required:

Calculate the monthly quality$-$control cost to be assigned to the Satin Sheen product line under each of the following product$-$costing systems.

Traditional system, which assigns overhead on the basis of direct$-$labor cost.

Activity$-$based costing.

Does the traditional product$-$costing system overcost or undercost the Satin Sheen product line with respect to quality$-$control costs? By what amount?