Question

Refer to the information in Exercise 17-7 to answer the following requirements.

Required

1. Determine departmental overhead rates and compute the overhead cost per unit for each product line. Base your overhead assignment for the components department on machine hours. Use welding hours to assign overhead costs to the finishing department. Assign costs to the support department based on number of purchase orders.

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: $636.63

Total cost per unit for model 145: $500.38

Step-by-step solution

Calculation of overhead cost per unit

$\begin{array}{rcl}Overead\cos tperunitforcomponentsdepartment& =& \frac{TotalOverhead\cos t}{Totalmacjinehour}\\ & =& \frac{\$1,004,000}{6,000}\\ & =& \$167.33\end{array}$

$\begin{array}{rcl}Overhead\cos tperunitforfinishingdeparment& =& \frac{TotalOverhead\cos t}{Totalweldinghour}\\ & =& \frac{\$465,300}{3,000}\\ & =& \$155.1\end{array}$

$\begin{array}{rcl}Overhead\cos tperunitforsupportdeparment& =& \frac{TotalOverhead\cos t}{Totalnumberofpurchaseorder}\\ & =& \frac{\$232,000}{450}\\ & =& \$515.55\end{array}$

role="math" localid="1656266062682" $\begin{array}{rcl}\mathit{O}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{145}& \mathbf{=}& \frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{e}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{s}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{+}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{i}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{+}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{S}\mathbf{u}\mathbf{p}\mathbf{p}\mathbf{o}\mathbf{r}\mathbf{t}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{u}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{s}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{o}\mathbf{d}\mathbf{u}\mathbf{c}\mathbf{e}\mathbf{d}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{167}\mathbf{.}\mathbf{33}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{800}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{155}\mathbf{.}\mathbf{1}\mathbf{\times }\mathbf{800}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{515}\mathbf{.}\mathbf{55}\mathbf{\times }\mathbf{300}\mathbf{)}}{\mathbf{1}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{301}\mathbf{,}\mathbf{194}\mathbf{+}\mathbf{\$}\mathbf{124}\mathbf{,}\mathbf{080}\mathbf{+}\mathbf{\$}\mathbf{154}\mathbf{,}\mathbf{665}}{\mathbf{1}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{386}\mathbf{.}\mathbf{626}\end{array}$

$\begin{array}{rcl}\mathit{O}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{212}& \mathbf{=}& \frac{\mathbf{Total}\mathbf{}\mathbf{componenets}\mathbf{}\mathbf{cost}\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{finishing}\mathbf{}\mathbf{cost}\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{Support}\mathbf{}\mathbf{cost}}{\mathbf{Total}\mathbf{}\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{units}\mathbf{}\mathbf{produced}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{167}\mathbf{.}\mathbf{33}\mathbf{\times }\mathbf{4}\mathbf{,}\mathbf{200}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{155}\mathbf{.}\mathbf{1}\mathbf{\times }\mathbf{2}\mathbf{,}\mathbf{200}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{515}\mathbf{.}\mathbf{55}\mathbf{\times }\mathbf{150}\mathbf{)}}{\mathbf{3}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{702}\mathbf{,}\mathbf{786}\mathbf{+}\mathbf{\$}\mathbf{341}\mathbf{,}\mathbf{220}\mathbf{+}\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{332}\mathbf{.}\mathbf{5}}{\mathbf{3}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{320}\mathbf{.}\mathbf{38}\end{array}$

Calculation of total cost per unit

$\begin{array}{rcl}\mathit{T}\mathit{h}\mathit{e}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{145}& \mathbf{=}& \mathit{D}\mathit{i}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{e}\mathit{r}\mathit{i}\mathit{a}\mathit{l}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{d}\mathit{i}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathbf{}\mathit{l}\mathit{a}\mathit{b}\mathit{o}\mathit{r}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{250}\mathbf{+}\mathbf{\$}\mathbf{386}\mathbf{.}\mathbf{63}\\ & \mathbf{=}& \mathbf{\$}\mathbf{636}\mathbf{.}\mathbf{63}\end{array}$

$\begin{array}{rcl}\mathit{T}\mathit{h}\mathit{e}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{212}& \mathbf{=}& \mathit{D}\mathit{i}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{e}\mathit{r}\mathit{i}\mathit{a}\mathit{l}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{d}\mathit{i}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathbf{}\mathit{l}\mathit{a}\mathit{b}\mathit{o}\mathit{r}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{180}\mathbf{+}\mathbf{\$}\mathbf{320}\mathbf{.}\mathbf{38}\\ & \mathbf{=}& \mathbf{\$}\mathbf{500}\mathbf{.}\mathbf{38}\end{array}$

Calculation of profit per unit

$\begin{array}{rcl}\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{/}\mathit{l}\mathit{o}\mathit{s}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{145}& \mathbf{=}& \mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{-}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{820}\mathbf{-}\mathbf{\$}\mathbf{636}\mathbf{.}\mathbf{63}\\ & \mathbf{=}& \mathbf{\$}\mathbf{183}\mathbf{.}\mathbf{37}\end{array}$

$\begin{array}{rcl}\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{/}\mathit{l}\mathit{o}\mathit{s}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{212}& \mathbf{=}& \mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{-}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{480}\mathbf{-}\mathbf{\$}\mathbf{500}\mathbf{.}\mathbf{38}\\ & \mathbf{=}& \mathbf{-}\mathbf{\$}\mathbf{20}\mathbf{.}\mathbf{38}\end{array}$

There is a loss on model 212 and profit on model 145. Model 212 is having losses due to higher welding hours and machine hours constituting higher overhead cost.