Smithson, Inc. produces two types of gas grills a family model and a deluxe model. Smithson's controller has decided to use a plantwide overhead rate based on direct labor costs. The president of the company recently heard of activitybased costing and wants to see how the results would differ if this system were used. Two activity cost pools were developed: machining and machine setup. Presented below is information related to the company's operations:

$\backslash$table$[[,$Family Model,Deluxe Model$],[$Direct labor costs,$$75,000,$$$150,000,],[$Machine hours,$2,000,2,000,],[$Setup hours,$200,800,]]$

Total estimated overhead costs are $$450,000.$ Overhead cost allocated to the machining activity cost pool is $$270,000$ and $$180,000$ is allocated to the machine setup activity cost pool.

Instructions

$($a$)$ Compute the overhead rate using the traditional $($plantwide$)$ approach.

$($b$)$ Compute the overhead rates using the activity$-$based costing approach.

$($c$)$ Determine the difference in allocation between the two approaches.

$($d$)$ Smithson, Inc. decided to implement the activity$-$based costing approach and was quite successful in its use. However, the controller is wondering if instead of only two activity cost pools, they should expand to three activity cost pools based on the following:

$\backslash$table$[[,$Family Model,,Deluxe Model$],[$Direct labor costs,$$75,000,$$$150,000,],[$Machine hours,$2,000,2,000],[$Setup hours,$200,800,],[$Packaging hours,$50,75,]]$

The estimated overhead of $$450,000$ is allocated as follows: machining activity cost pool $$240,000,$ machine set up $$170,000$ and packaging $$40,000.$

$(1)$ Determine the overhead rates using the activity$-$based costing approach with three cost pools.

$(2)$ Determine the overhead allocation for the family model and the deluxe model using three activity cost pools. What is the difference in allocation between two activity cost pools and three activity cost pools? Is the difference in allocation worth using the third activity cost pool?