Question

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

Required

1. Using ABC, 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: $766.59

Total cost per unit for model 212: $445.12

Step-by-step solution

Calculation of overhead cost per unit

Computation of overhead cost per unit for model 145

$\begin{array}{rcl}\mathbf{\text{TotalComponentcostperunit}}& \mathbf{=}& \mathbf{\text{Changeovercostperunit}}\mathbf{+}\mathbf{\text{Machiningcostperunit}}\mathbf{+}\mathbf{\text{Setupcostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{400}}{\mathbf{800}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{279}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{800}}{\mathbf{6}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{225}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{60}}{\mathbf{120}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{166}\mathbf{.}\mathbf{67}\mathbf{+}\mathbf{\$}\mathbf{55}\mathbf{.}\mathbf{8}\mathbf{+}\mathbf{\$}\mathbf{75}\\ & \mathbf{=}& \mathbf{\$}\mathbf{298}\mathbf{.}\mathbf{47}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Totalfinishingcostperunit}}& \mathbf{=}& \mathbf{\text{Weildingcostperunit}}\mathbf{+}\mathbf{\text{Inspecting}}\mathbf{}\mathbf{\text{costperunit}}\mathbf{+}\mathbf{\text{Reworkcostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{180}\mathbf{,}\mathbf{300}\mathbf{)}\mathbf{\times }\mathbf{800}}{\mathbf{3000}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{210}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{400}}{\mathbf{700}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{75}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{160}}{\mathbf{300}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{05}\mathbf{+}\mathbf{\$}\mathbf{80}\mathbf{+}\mathbf{\$}\mathbf{26}\mathbf{.}\mathbf{67}\\ & \mathbf{=}& \mathbf{\$}\mathbf{138}\mathbf{.}\mathbf{72}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Totalsupportcostperunit}}& \mathbf{=}& \mathbf{\text{Purchasingcostperunit}}\mathbf{+}\mathbf{\text{Providing}}\mathbf{}\mathbf{\text{costperunit+Providingutilitiescostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{135}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{300}}{\mathbf{450}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}{\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}{\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{60}\mathbf{+}\mathbf{\$}\mathbf{6}\mathbf{.}\mathbf{4}\mathbf{+}\mathbf{\$}\mathbf{13}\\ & \mathbf{=}& \mathbf{\$}\mathbf{79}\mathbf{.}\mathbf{4}\end{array}$

$\begin{array}{rcl}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{m}\mathit{p}\mathit{o}\mathit{n}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{F}\mathit{i}\mathit{n}\mathit{i}\mathit{s}\mathit{h}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{s}\mathit{u}\mathit{p}\mathit{p}\mathit{o}\mathit{r}\mathit{t}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{298}\mathbf{.}\mathbf{47}\mathbf{+}\mathbf{\$}\mathbf{138}\mathbf{.}\mathbf{72}\mathbf{+}\mathbf{\$}\mathbf{79}\mathbf{.}\mathbf{4}\\ & \mathbf{=}& \mathbf{\$}\mathbf{516}\mathbf{.}\mathbf{59}\end{array}$

Computation of overhead cost per unit for model 212

$\begin{array}{rcl}\mathbf{\text{TotalComponentcostperunit}}& \mathbf{=}& \mathbf{\text{Changeovercostperunit}}\mathbf{+}\mathbf{\text{Machiningcostperunit}}\mathbf{+}\mathbf{\text{Setupcostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{400}}{\mathbf{800}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{279}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{4}\mathbf{,}\mathbf{200}}{\mathbf{6}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{225}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{60}}{\mathbf{120}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{71}\mathbf{.}\mathbf{43}\mathbf{+}\mathbf{\$}\mathbf{55}\mathbf{.}\mathbf{8}\mathbf{+}\mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{14}\\ & \mathbf{=}& \mathbf{\$}\mathbf{159}\mathbf{.}\mathbf{37}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Totalfinishingcostperunit}}& \mathbf{=}& \mathbf{\text{Weildingcostperunit}}\mathbf{+}\mathbf{\text{Inspecting}}\mathbf{}\mathbf{\text{costperunit}}\mathbf{+}\mathbf{\text{Reworkcostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{180}\mathbf{,}\mathbf{300}\mathbf{)}\mathbf{\times }\mathbf{2}\mathbf{,}\mathbf{200}}{\mathbf{3000}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{210}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{300}}{\mathbf{700}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{75}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{140}}{\mathbf{300}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{37}\mathbf{.}\mathbf{78}\mathbf{+}\mathbf{\$}\mathbf{25}\mathbf{.}\mathbf{71}\mathbf{+}\mathbf{\$}\mathbf{10}\\ & \mathbf{=}& \mathbf{\$}\mathbf{73}\mathbf{.}\mathbf{49}\end{array}$

$\begin{array}{rcl}\mathbf{\text{Totalsupportcostperunit}}& \mathbf{=}& \mathbf{\text{Purchasingcostperunit}}\mathbf{+}\mathbf{\text{Providing}}\mathbf{}\mathbf{\text{costperunit+Providingutilitiescostperunit}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{\$}\mathbf{135}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{150}}{\mathbf{450}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}{\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\mathbf{+}\frac{\mathbf{(}\mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}{\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{,}\mathbf{500}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{12}\mathbf{.}\mathbf{86}\mathbf{+}\mathbf{\$}\mathbf{6}\mathbf{.}\mathbf{4}\mathbf{+}\mathbf{\$}\mathbf{13}\\ & \mathbf{=}& \mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{26}\end{array}$

$\begin{array}{rcl}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathit{h}\mathit{e}\mathit{a}\mathit{d}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{m}\mathit{p}\mathit{o}\mathit{n}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{F}\mathit{i}\mathit{n}\mathit{i}\mathit{s}\mathit{h}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{+}\mathit{s}\mathit{u}\mathit{p}\mathit{p}\mathit{o}\mathit{r}\mathit{t}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{159}\mathbf{.}\mathbf{37}\mathbf{+}\mathbf{\$}\mathbf{73}\mathbf{.}\mathbf{49}\mathbf{+}\mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{26}\\ & \mathbf{=}& \mathbf{\$}\mathbf{265}\mathbf{.}\mathbf{12}\end{array}$

Calculation of total cost per unit

$\begin{array}{rcl}\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{}\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{516}\mathbf{.}\mathbf{59}\\ & \mathbf{=}& \mathbf{\$}\mathbf{766}\mathbf{.}\mathbf{59}\\ \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{}\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{265}\mathbf{.}\mathbf{12}\\ & \mathbf{=}& \mathbf{\$}\mathbf{445}\mathbf{.}\mathbf{12}\end{array}$

Calculation of profit or loss per unit

$\begin{array}{rcl}\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{/}\mathit{L}\mathit{o}\mathit{s}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{145}& \mathbf{=}& \mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{-}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{820}\mathbf{-}\mathbf{\$}\mathbf{766}\mathbf{.}\mathbf{59}\\ & \mathbf{=}& \mathbf{\$}\mathbf{53}\mathbf{.}\mathbf{41}\\ \mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{/}\mathit{L}\mathit{o}\mathit{s}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}\mathbf{}\mathbf{212}& \mathbf{=}& \mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{-}\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathbf{cos}\mathit{t}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{480}\mathbf{-}\mathbf{\$}\mathbf{445}\mathbf{.}\mathbf{12}\\ & \mathbf{=}& \mathbf{\$}\mathbf{34}\mathbf{.}\mathbf{88}\end{array}$

Under ABC method both the products are generating profit. The reason for this is that the overheads has been allocated accurately based on the activity level by both the products.