Chapter 4, Problem 36P

Reducir, Inc., produces two different types of hydraulic cylinders. Reducir produces a major subassembly for the cylinders in the Cutting and Welding Department. Other parts and the subassembly are then assembled in the Assembly Department. The activities, expected costs, and drivers associated with these two manufacturing processes are given below.

Note: In the assembly process, the materials-handling activity is a function of product characteristics rather than batch activity.

Other overhead activities, their costs, and drivers are listed below.

Other production information concerning the two hydraulic cylinders is also provided:

Required:

1. 1. Using a plantwide rate based on machine hours, calculate the total overhead cost assigned to each product and the unit overhead cost.
2. 2. Using activity rates, calculate the total overhead cost assigned to each product and the unit overhead cost. Comment on the accuracy of the plantwide rate.
3. 3. Calculate the global consumption ratios.
4. 4. Calculate the consumption ratios for welding and materials handling (Assembly) and show that two drivers, welding hours and number of parts, can be used to achieve the same ABC product costs calculated in Requirement 2. Explain the value of this simplification.
5. 5. Calculate the consumption ratios for inspection and engineering, and show that the drivers for these two activities also duplicate the ABC product costs calculated in Requirement 2.

To determine

Compute the total overhead cost assigned to each product and the unit overhead cost using a plantwide rate based on machine hours for incorporation R.

Explanation of Solution

Plantwide overhead rate: Plantwide overhead rate is the rate a company uses to allocate its manufacturing overhead costs to products and cost centres.

Step 1: Calculate plantwide overhead rate based on machine hours.

$\begin{array}{c}\text{Plantwide rate = }\frac{\text{Total overhead activity costs}}{\text{Total machine hours}}\\ =\frac{\left(\$2,214,250\text{}+\$1,051,750+\$734,000\right)}{10,000\text{machine hours}}\\ =\frac{\$4,000,000}{10,000\text{machine hours}}\\ =\$400\text{per machine hour}\end{array}$

Step 2: Determine the total overhead cost assigned to each product and the unit overhead cost.

For cylinder A,

$\begin{array}{c}\text{Total overhead cost assigned =}\text{Plantwide rate }\times \text{machine hours}\\ \text{=\$400}\times \text{3,000}\text{hours}\\ \text{=\$1,200,000}\end{array}$

$\begin{array}{c}\text{Unit overhead cost = }\frac{\text{Total overhead cost assigned}}{\text{Units produced}}\\ =\frac{\$1,200,000}{1,500\text{units}}\\ =\$800\end{array}$

Therefore, the total overhead cost assigned and unit overhead cost for cylinder A is $1,200,000 and $800 respectively.

For cylinder B,

$\begin{array}{c}\text{Total overhead cost assigned =}\text{Plantwide rate }\times \text{machine hours}\\ \text{=\$400}\times 7\text{,000}\text{hours}\\ \text{=\$2,800,000}\end{array}$

$\begin{array}{c}\text{Unit overhead cost = }\frac{\text{Total overhead cost assigned}}{\text{Units produced}}\\ =\frac{\$2,800,000}{3,000\text{units}}\\ =\$933.33\end{array}$

Therefore, the total overhead cost assigned and unit overhead cost for cylinder B is $2,800,000 and $933.33 respectively.

To determine

Determine the total overhead cost assigned to each product and the unit overhead cost using an activity rate for incorporation R and provide comment on the accuracy of the plantwide rate.

Explanation of Solution

Activity rates: Activity rates are calculated by dividing the budgeted activity costs by the amount of activity output as measured by the activity driver.

Step 1: Calculate activity rates.

Particulars
Cost of welding	$ 776,000
Divide: Welding hours	4,000 hours
Activity rate	$194.00 per welding hour
Cost of machining	$ 450,000
Divide: Machine hours	10,000 hours
Activity rate	$45.00 per machine hour
Cost of inspecting	$ 448,250
Divide: Number of inspections	1,000 inspections
Activity rate	$448.25 per inspection
Cost of materials handling	$ 300,000
Divide: Number of batches	12,000
Activity rate	$25.00 per move
Cost of setups	$ 240,000
Divide: Number of setups	100
Activity rate	$2,400.00 per batch
Cost of changeover	$ 180,000
Divide: change over hours	1,000 change over hours
Activity rate	$180.00 per changeover hour
Cost of rework	$ 61,750
Divide: Rework orders	50 rework orders
Activity rate	$1,235.00 per rework order
Cost of testing	$ 300,000
Divide: Number of tests	750 tests
Activity rate	$400.00 per test
Cost of materials handling	$ 380,000
Divide: Number of parts	50,000 parts
Activity rate	$7.60 per part
Cost of engineering support	$ 130,000
Divide: Engineering hours	2,000 hours
Activity rate	$65.00 per engineering hour
Cost of purchasing	$ 135,000
Divide: Purchase requisitions	500 requisitions
Activity rate	$270.00 per requisition
Cost of receiving	$ 274,000
Divide: Receiving orders	2,000 receiving orders
Activity rate	$137.00 per receiving order
Cost of paying suppliers	$ 225,000
Divide: Number of invoices	1,000 invoices
Activity rate	$225.00 per invoice
Cost of providing space and utilities	$ 100,000
Divide: Machine hours	10,000 machine hours
Activity rate	$10.00 per machine hour

Table (1)

Step 2: calculate the total overhead cost assigned to each product.

Particulars	Cylinder A ($)	Cylinder B ($)
Welding
Activity rate ×  welding hours
$194  ×  1,600 welding hours	$ 310,400
$194  ×  2,400 welding hours		$ 465,600
Machining
Activity rate ×  machine hours
$45 × 3,000 machine hours	$ 135,000
$45 * 7,000 machine hours		$ 315,000
Inspecting
Activity rate ×  number of inspections
$448.25 ×   500 inspections	$ 224,125
$448.25 ×  500 inspections		$ 224,125
Materials handling
Activity rate × number of moves
$25 × 7,200 moves	$ 180,000
$25 × 4,800 moves		$ 120,000
Setups
Activity rate × number of batches
$2,400  × 45 batches	$ 108,000
$2,400 × 55 batches		$ 132,000
Change over
Activity rate × change over hours
$180 × 540 change over hours	$ 97,200
$180 × 460 change over hours		$ 82,800
Rework
Activity rate × rework orders
$1,235 × 5 rework orders	$ 6,175
$1,235 × 45 rework orders		$ 55,575
Testing
Activity rate × number of tests
$400 ×  500 tests	$2,00,000
$400 ×  250 tests		$1,00,000
Materials handling
Activity rate × number of tests
$7.60 × 40,000 parts	$ 304,000
$7.60 × 10,000 parts		$ 76,000
Engineering support
Activity rate × Engineering hours
$65 × 1,500 engineering hours	$ 97,500
$65 × 500 engineering hours		$ 32,500
Purchasing
Activity rate × number of purchase requisitions
$270 × 425 requisitions	$ 114,750
$270 × 75 requisitions		$ 20,250
Receiving
Activity rate × number of receiving orders
$137 × 1,800 receiving orders	$ 246,600
$137 × 200 receiving orders		$ 27,400
Paying suppliers
Activity rate × number of invoices
$225 ×  650 invoices	$ 146,250
$225 ×  350 invoices		$ 78,750
Providing space and utilities
Activity rate × machine hours
$10  ×  3,000 machine hours	$ 30,000
$10  ×  7,000 machine hours		$ 70,000
Total overhead costs	$ 2,200,000	$ 1,800,000
Divide: Units produced	1,500 units	3,000 units
Overhead per unit	$ 1,467	$ 600

Table (2)

Thus, the overhead per unit for cylinder A and cylinder B is $1,467 and $600 respectively.

The overhead consumption patterns better than the machine hour pattern of the plantwide rate because, Cylinder B is overcosted, and Cylinder A is undercosted. The activity assignments obtain the cause-and-effect relationships.

To determine

Compute global consumption ratio.

Explanation of Solution

Global consumption ratio: The global consumption ratio is the proportion of the total activity costs absorbed by a provided product or cost object.

Calculate global consumption ratio:

For Cylinder A:

$\begin{array}{c}\text{Global consumption ratio = }\frac{\text{Assigned total overhead cost}}{\text{Budgeted total overhead cost}}\\ =\frac{\$2,200,000}{\left(\$2,214,250+\$1,051,750+\$734,000\right)}\\ =\frac{\$2,200,000}{\$4,000,000}\\ =0.55\end{array}$

For Cylinder B:

$\begin{array}{c}\text{Global consumption ratio = }\frac{\text{Assigned total overhead cost}}{\text{Budgeted total overhead cost}}\\ =\frac{\$1,800,000}{\left(\$2,214,250+\$1,051,750+\$734,000\right)}\\ =\frac{\$1,800,000}{\$4,000,000}\\ =0.45\end{array}$

Therefore, the global consumption ratio for Cylinder A and Cylinder B is 0.55 and 0.45 respectively.

To determine

Determine the consumption ratios for materials handling (Assembly) and welding and justify that two drivers, welding hours and several parts, can be used to achieve the same ABC product costs. Explain the value of this simplification.

Explanation of Solution

Overhead consumption ratio: The overhead consumption ratios simply estimate the proportion of each activity used by individual products. The overhead consumption ratio is mainly suitable to allocate the costs of a shared resource.

Compute the consumption ratios for materials handling (Assembly) and welding:

For Welding:

$\begin{array}{c}\text{Consumption ratio = }\left(\frac{\text{welding hours for cylinder A}}{\text{Expected quantity}},\frac{\text{welding hours for cylinder B}}{\text{Expected quantity}}\right)\\ =\left(\frac{1,600}{4,000},\frac{2,400}{4,000}\right)\\ =\left(0.40,0.60\right)\end{array}$

For Material handling (parts):

$\begin{array}{c}\text{Consumption ratio = }\left(\frac{\text{Parts for cylinder A}}{\text{Expected quantity}},\frac{\text{Parts for cylinder B}}{\text{Expected quantity}}\right)\\ =\left(\frac{40,000}{50,000},\frac{10,000}{50,000}\right)\\ =\left(0.80,0.20\right)\end{array}$

Set up two equations, where W’s represent the allocation rates:

$\begin{array}{l}0.40{\text{w}}_1+0.80{\text{w}}_2=0.55\left(\text{Equation 1}\right)\\ 0.60{\text{w}}_1+0.20{\text{w}}_2=0.45\left(\text{Equation 2}\right)\end{array}$

Multiply second equation by -4:

$\begin{array}{l}\left(0.60\times -4\right){\text{w}}_1+\left(0.20\times -4\right){\text{w}}_2=\left(0.45\times -4\right)\\ -2.4{\text{w}}_1+-0.8{\text{w}}_2=-1.8\end{array}$

By solving:

$\begin{array}{l}-2{\text{w}}_1=-1.25\\ {\text{w}}_1=0.625\end{array}$

And thus,

${\text{w}}_2=0.375$

Cost pools:

$\begin{array}{c}{\text{Welding = w}}_1\times \text{Total overhead cost}\\ \text{=0}\text{.625}\times \text{\$4,000,000}\\ \text{=\$2,500,000}\end{array}$

$\begin{array}{c}{\text{Materials handling = w}}_2\times \text{Total overhead cost}\\ \text{=0}\text{.375}\times \text{\$4,000,000}\\ \text{=\$1,500,000}\end{array}$

Activity rates:

$\begin{array}{c}\text{Welding}\text{=}\frac{\text{Cost pool for welding}}{\text{Welding hours}}\\ =\frac{\$2,500,000}{4,000}\\ =\$625\text{welding hour}\end{array}$

$\begin{array}{c}\text{Materials handling}\left(\text{assembly}\right)\text{ = }\frac{\text{Cost pools for material handling}}{\text{Number of parts}}\\ =\frac{\$1,500,000}{50,000}\\ =\$30\text{per part}\end{array}$

Assign overhead for the two products:

Particulars	Cylinder A	Cylinder B
Welding
Activity rate × welding hours
$625  × 1,600 welding hours	$ 1,000,000
$625  × 2,400 welding hours		$ 1,500,000
Material handling
Activity rate × Number of parts
$30 × 40,000 parts	$ 1,200,000
$30 × 10,000 parts		$ 300,000
Total overhead costs	$ 2,200,000	$ 1,800,000
Divide: Units produced	1,500 units	3,000 units
Overhead per unit	$1,467 (rounded)	$ 600

Table (3)

We can take a 14-driver system and decrease it to a two-driver system and obtain the same overhead cost assignments as the more complex system. This After-the-fact simplification has two major benefits:

(1) It assists nonfinancial managers to more easily read, understands, and interpret product cost reports

(2) The actual values only need to be obtained for two drivers instead of 14, producing considerable cost savings.

To determine

Ascertain the consumption ratios for inspection and engineering, and prove that the drivers for these two activities also duplicate the ABC product costs.

Explanation of Solution

Compute the consumption ratios for inspection and engineering:

$\begin{array}{c}\text{For inspection =}\left(\frac{\text{Number of inspection for cylinder A}}{\text{Total number of inspections}},\frac{\text{Number of inspection for cylinder B}}{\text{Total number of inspections}}\right)\\ =\left(\frac{500}{1,000},\frac{500}{1,000}\right)\\ =\left(0.50,0.50\right)\end{array}$

$\begin{array}{c}\text{For engineering = }\left(\frac{\text{Engineering hours for A}}{\text{Total engineering hours}},\frac{\text{Engineering hours for B}}{\text{Total engineering hours}}\right)\\ =\left(\frac{1,500}{2,000},\frac{500}{2,000}\right)\\ =\left(0.75,0.25\right)\end{array}$

Construct two equations (w’s represent the allocation rates):

$\begin{array}{l}0.50{\text{w}}_1+0.75{\text{w}}_2=0.55\\ 0.50{\text{w}}_1+0.25{\text{w}}_2=0.45\end{array}$

Subtract the second equation from the first:

$\begin{array}{c}0.5{\text{w}}_2=0.10\\ {\text{w}}_2=0.20\end{array}$

And thus,

${\text{w}}_1=0.80$

Cost pools:

$\begin{array}{c}{\text{Inspection = w}}_1\times \text{Total overhead cost}\\ \text{=0}\text{.80}\times \text{\$4,000,000}\\ \text{=\$3,200,000}\end{array}$

$\begin{array}{c}{\text{Engineering = w}}_2\times \text{Total overhead cost}\\ \text{=0}\text{.20}\times \text{\$4,000,000}\\ =\$800,000\end{array}$

Calculate the activity rates:

$\begin{array}{c}\text{Inspection =}\frac{\text{Cost pools for inspection}}{\text{Number of inspections}}\\ =\frac{\$3,200,000}{1,000}\\ =3,200\text{per inspection}\end{array}$

$\begin{array}{c}\text{Engineering =}\frac{\text{Cost pools for engineering}}{\text{Engineering hours}}\\ =\frac{\$800,000}{2,000}\\ =400\text{per hour}\end{array}$

Therefore, the activity rate for inspection and engineering is $3,200 per inspection and $400 per hour respectively.

Assign the overhead for cylinder A and cylinder B:

Particulars	Cylinder A	Cylinder B
Inspection
Activity rate × Number of inspections
$3,200  × 500 inspections	$ 1,600,000
$3,200  × 500inspections		$ 1,600,000
Engineering
Activity rate × Engineering hours
$400 × 1,500 engineering hours	$ 600,000
$400 × 500 engineering hours		$ 200,000
Total overhead costs	$ 2,200,000	$ 1,800,000
Divide: Units produced	1,500 units	3,000 units
Overhead per unit	$1,467.67 (rounded)	$ 600.00

Thus, the overhead per unit for Cylinder A and Cylinder B is $1,467.67 and $600 respectively.