Product Costing: Plantwide Overhead versus Activity$-$Based Costing

Sterling Industries produces machine parts as a contract provider for a large manufacturing company. Sterling produces two particular parts, shafts and

gears. The competition is keen among contract producers, and Sterling's top management realizes how vulnerable its market is to cost$-$cutting

competitors. Hence, having a very accurate understanding of costs is important to Sterling's survival.

Sterling's president, Sheila Hudson, has observed that the company's current cost to produce shafts is $$37\mathrm{.}36,$ and the current cost to produce gears

is $$22\mathrm{.}88.$ She indicated to the controller that she suspects some problems with the cost system because Sterling is suddenly experiencing extraordinary

competition on shafts, but it seems to have a virtual corner on the gears market. She is even considering dropping the shaft line and converting the

company to a one$-$product manufacturer of gears. She asked the controller, George Coleman, to conduct a thorough cost study and to consider whether

changes in the cost system are necessary. The controller collected the following data about the company's costs and various manufacturing activities for

the most recent month:

The controller was able to summarize the company's total manufacturing overhead into the following pools:

Required

a$.$ Calculate Sterling's current plantwide overhead rate based on direct labor hours.

$

per direct labor hour

b$.$ Verify Sterling's calculation of overhead cost per unit of $$20\mathrm{.}00$ for shafts and $$10\mathrm{.}00$ for gears.

Shafts:

$

$/$

units $=$$$20\mathrm{.}00$ per unit

Gears:

$$1$

$0$

units $=$$$10\mathrm{.}00$ per unit

c$.$ Calculate the manufacturing overhead cost in total and per unit for shafts and gears using activity$-$based costing, assuming each of the five cost pools

represents a separate activity pool. Use the most appropriate activity driver for assigning activity costs to the two products.

Note: Round your answers to two decimal places.

d$.$ Comment on Sterling's current cost system and the reason the company is facing fierce competition for shafts but little competition for gears.

Sterling is

costs to shafts.

Sterling is

costs to gears.

Please answer all parts of the question.