Chapter 4, Problem 11E

1.

To determine

Overhead cost per unit for each product line.

Explanation of Solution

Table showing total departmental overhead cost of model 145 and model 212:

Activity	Overhead rate ($)	Value of activity driver of model 145	Value of activity driver for model 212	Overhead cost of model 145 ($) $$\left(\text{Rate}\times \text{Value}\right)$$	Overhead cost of model 212 ($) $$\left(\text{Rate}\times \text{Value}\right)$$
Changeover	625.0	400	400	250,000	250,000
Machining	46.5	1,800	4,200	83,700	195,300
Setups	1,875.0	60	60	112,500	112,500
Welding	60.0	800	2,200	48,080	132,220
Inspecting	300.0	400	300	120,000	90,000
Reworks	250.0	160	140	40,000	35,000
Purchasing	300.0	300	150	90,000	45,000
Space	6.4	1,500	3,500	9,600	22,400
Utilities	13.0	1,500	3,500	19,500	45,500
Total overhead cost	773,380	927,920

Table(1)

Formula to compute overhead cost per unit is,

   $\text{Overhead}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{overhead}\text{cost}}{\text{Total}\text{units}\text{produced}}$

Model 145

Given,
Total units produced are 1,500.

Substitute 1,500 units for produced units and $773,380 for total overhead cost in the formula.

   $\begin{array}{c}\text{Overhead}\text{cost}\text{per}\text{unit}=\frac{\$773,380}{\text{1,500 units}}\\ =\text{\$515}\text{.59}\end{array}$

Model 212

Given,
Totalunits produced are 3,500.

Substitute 3,500 units for produced units and $927,920 for total overhead cost in the formula.

   $\begin{array}{c}\text{Overhead}\text{cost}\text{per}\text{unit}=\frac{\$927,920}{\text{3,500 units}}\\ =\text{\$265}\text{.12}\end{array}$

Hence, overhead cost per unit for product 145 is $515.59 and for product 212 is $265.12.

Working notes:

Formula to calculate departmental overhead rate is,

   $\text{Departmental}\text{overhead}\text{rate}=\frac{\text{Budgeted}\text{overhead}\text{cost}}{\text{Budgeted}\text{activity}\text{level}}$

Calculation of overhead rate for changeover activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$5,00,000}{800}\\ =\$625.0\end{array}$

Calculation of overhead rate for machining activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$279,000}{6,000}\\ =\$46.5\end{array}$

Calculation of overhead rate for setups activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$225,000}{120}\\ =\$1,875.0\end{array}$

Calculation of overhead rate for welding activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$180,300}{3000}\\ =\$60.1\end{array}$

Calculation of overhead rate for inspecting activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$210,000}{700}\\ =\$300.0\end{array}$

Calculation of overhead rate for rework activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$75,000}{300}\\ =\$250.0\end{array}$

Calculation of overhead rate for purchasing activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$135,000}{450}\\ =\$300.0\end{array}$

Calculation of overhead rate for providing space activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$32,000}{5,000}\\ =\$6.4\end{array}$

Calculation of overhead rate for providing utility activity,

   $\begin{array}{c}\text{Overhead}\text{rate}=\frac{\$65,000}{5,000}\\ =\$13.0\end{array}$

2.

To determine

Total cost per unit for each product line.

Explanation of Solution

Formula to compute total cost per unit is,

   $\text{Per}\text{unit}\text{cost}=\text{Direct}\text{material}\text{and}\text{labour}\text{cost}\text{per}\text{unit}+\text{Overhead}\text{cost}\text{per}\text{unit}$

Model 145

Given,
Direct labor and material cost per unit is $250.
Overhead cost per unit is $515.59.

Substitute $250 for direct labor and material cost per unit and $515.59 for overhead cost per unit in the formula.

   $\begin{array}{c}\text{Total}\text{per}\text{unit}\text{cost}=\$250+\$515.59\\ =\$765.59\end{array}$

Model 212

Given,
Direct labor and material cost per unit is $180.
Overhead cost per unit is $265.12.

Substitute $180 for direct labor and material cost per unit and $265.12 for overhead cost per unit in the formula.

   $\begin{array}{c}\text{Total}\text{per}\text{unit}\text{cost}=\$180+\$265.12\\ =\$445.12\end{array}$

Hence, total cost per unit for product 145 is $765.59 and for product 212 is $445.12.

3.

To determine

Profit or loss per unit for each model.

Explanation of Solution

Formula to compute profit or loss per unit is,

   $\text{Profit}\text{or}\text{loss}\text{per}\text{unit}=\text{Market}\text{price}-\text{Total}\text{cost}$

Model 145

Given,
Market price per unit is $820.
Total cost per unit is $765.59.

Substitute $820 for market price per unit and $765.59 for total cost per unit in the formula.

   $\begin{array}{c}\text{Profit}\text{or}\text{loss}\text{per}\text{unit}=\$820-\$765.59\\ =\$54.41\end{array}$

Model 212

Given,
Market price per unit is $480.
Total cost per unit is $445.12.

Substitute $480 for market price per unit and $445.12 for total cost per unit in the formula.

   $\begin{array}{c}\text{Profit}\text{or}\text{loss}\text{per}\text{unit}=\$480-\$445.12\\ =\$34.88\end{array}$

Hence, profit per unit for product 145 is $54.41 andfor product 212 is $34.88.