Question

Way Cool produces two different models of air conditioners. The company produces the mechanical systems in their components department. The mechanical systems are combined with the housing assembly in its finishing department. The activities, costs, and drivers associated with these two manufacturing processes and the production support process follow.

Process Activity Overhead Cost Driver Quantity

Components Changeover \( 500,000 Number of batches 800

Machining 279,000 Machine hours 6,000

Setups 225,000 Number of setups 120

\)1,004,000

Finishing Welding \( 180,300 Welding hours 3,000

Inspecting 210,000 Number of inspections 700

Rework 75,000 Rework orders 300

\) 465,300

Support Purchasing \( 135,000 Purchase orders 450

Providing space 32,000 Number of units 5,000

Providing utilities 65,000 Number of units 5,000

\) 232,000

Additional production information concerning its two product lines follows.

Model 145 Model 212

Units produced …………………………… 1,500 3,500

Welding hours …………………………….. 800 2,200

Batches …………………………………….. 400 400

Number of inspections ………………….. 400 300

Machine hours ……………………………. 1,800 4,200

Setups ……………………………………… 60 60

Rework orders ……………………………. 160 140

Purchase orders ………………………….. 300 150

Required

1. Using a plantwide overhead rate based on machine hours, compute the overhead cost per unit for each product line.

2. Determine the total cost per unit for each product line if the direct labor and direct materials costs per unit are \(250 for Model 145 and \)180 for Model 212.

3. If the market price for Model 145 is \(820 and the market price for Model 212 is \)480, determine the profit or loss per unit for each model. Comment on the results.

Short answer

Total cost per unit for model 145: $590.26

Total cost per unit for model 212: $520.26

Step-by-step solution

Calculation of overhead cost per unit

$\begin{array}{rcl}\mathrm{Total}\mathrm{overhead}\mathrm{cost}& =& \mathrm{Components}\mathrm{cost}+\mathrm{Finishing}\mathrm{cost}+\mathrm{Support}\mathrm{cost}\\ & =& \$1,004,000+\$465,300+\$232,000\\ & =& \$1,701,300\end{array}$

$\begin{array}{rcl}\mathrm{Plantwide}\mathrm{overhead}\mathrm{rate}\mathrm{for}\mathrm{each}\mathrm{product}\mathrm{line}& =& \frac{\mathrm{Total}\mathrm{overhead}\mathrm{cost}}{\mathrm{Total}\mathrm{machine}\mathrm{hour}}\\ & =& \frac{\$1,701,300}{1,800+4,200}\\ & =& \$283.55\end{array}$

Calculation of total cost per unit

$\begin{array}{rcl}\mathrm{Total}\mathrm{cost}\mathrm{per}\mathrm{unit}\mathrm{for}\mathrm{Model}145& =& \frac{\mathrm{Direct}\mathrm{material}\mathrm{and}\mathrm{direct}\mathrm{labor}\mathrm{cost}+\mathrm{Overhead}\mathrm{cost}\mathrm{based}\mathrm{on}\mathrm{Plantwide}\mathrm{rate}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{units}}\\ & =& \frac{\left(\$250\times 1,500\right)+\left(\$283.55\times 1,800\right)}{1,500}\\ & =& \frac{\$375,000+\$510,390}{1,500}\\ & =& \$590.26\end{array}$

$\begin{array}{rcl}\mathrm{Total}\mathrm{cost}\mathrm{for}\mathrm{Model}212& =& \frac{\mathrm{Direct}\mathrm{material}\mathrm{and}\mathrm{direct}\mathrm{labor}\mathrm{cost}+\mathrm{Overhead}\mathrm{cost}\mathrm{based}\mathrm{on}\mathrm{plantwide}\mathrm{rate}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{products}}\\ & =& \frac{\left(\$180\times 3,500\right)+\left(\$283.55\times 4,200\right)}{3,500}\\ & =& \frac{\$630,000+\$1,190,910}{3,500}\\ & =& \$520.26\end{array}$

Calculation of profit per unit

$\begin{array}{rcl}\mathrm{Profit}\mathrm{per}\mathrm{unit}\mathrm{for}\mathrm{model}145& =& \mathrm{Market}\mathrm{price}\mathrm{per}\mathrm{unit}-\mathrm{Total}\mathrm{cost}\mathrm{per}\mathrm{unit}\\ & =& \$820-\$590.26\\ & =& \$229.74\end{array}$

$\begin{array}{rcl}\mathrm{Profit}\mathrm{per}\mathrm{unit}\mathrm{for}\mathrm{model}212& =& \mathrm{Market}\mathrm{price}\mathrm{per}\mathrm{unit}-\mathrm{Total}\mathrm{cost}\mathrm{per}\mathrm{unit}\\ & =& \$480-\$520.26\\ & =& -\$40.26\end{array}$

As per the plant-wide overhead rate model, 145 is profitable due to lower machine hours and lower overhead allocation, and model 212 is not profitable due to higher machine hours and higher overhead allocation.