Chapter 4, Problem 22E

Silven Company has identified the following overhead activities, costs, and activity drivers for the coming year:

Silven produces two models of cell phones with the following expected activity demands:

1. 1. Determine the total overhead assigned to each product using the four activity drivers.
2. 2. Determine the total overhead assigned to each model using the two most expensive activities. The costs of the two relatively inexpensive activities are allocated to the two expensive activities in proportion to their costs.
3. 3. Using ABC as the benchmark, calculate the percentage error and comment on the accuracy of the reduced system. Explain why this approach may be desirable.

To determine

Compute the predetermined overhead rates of S Company and the total overhead cost assigned to each product.

Explanation of Solution

Predetermined overhead rate: It is an application of estimated manufacturing overhead cost over the cost object for particular time period. Predetermined overhead rate is used to calculate the overhead used per unit of a driver.

Formula: $\text{Predetermined overhead rate }=\frac{\text{Budgeted annual overhead }}{\text{Budgeted annual driver level}}$

Compute the predetermined overheads rates for all the activities of S Company.

Activity	Overhead rates
Setting up equipment	$\frac{\$126,000}{150}=\$840\text{per setup}$
Ordering materials	$\frac{\$18,000}{900}=\$20\text{per setup}$
Machining	$\frac{\$126,000}{10,500}=\$12\text{per machine hour}$
Receiving	$\frac{\$30,000}{1,250}=\$24\text{per set up}$

Table (1)

Calculate the cost assigned to be assigned to each product using the four activity drivers.

Activity	Model X ($)	Model Y ($)
Setting up equipment	84,000 (1)	42,000 (2)
Ordering materials	6,000 (3)	12,000 (4)
Machining	72,000 (5)	54,000 (6)
Receiving	9,000 (7)	21,000 (8)
Total overhead assigned	$171,000	$129,000

Table (2)

Working notes: Calculate the applied overheads for both the models of S Company

Applied overhead: Applied overhead is a cost which cannot be assigned directly to a cost object, and it is a fixed charge on a specific production department in the company.

Formula: $\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}$

(1) Calculate the applied overheads for the activity of setting up equipment for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$840 }\times 100\\ =\$84,000\end{array}$

(2) Calculate the applied overheads for the activity of setting up equipment for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$840 }\times 50\\ =\$42,000\end{array}$

(3) Calculate the applied overheads for the activity of ordering materials for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$20 }\times 300\\ =\$6,000\end{array}$

(4) Calculate the applied overheads for the activity of ordering materials for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$20 }\times 600\\ =\$12,000\end{array}$

(5) Calculate the applied overheads for the activity of machining for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$12 }\times 6,000\\ =\$72,000\end{array}$

(6) Calculate the applied overheads for the activity of machining for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$12 }\times 4,500\\ =\$54,000\end{array}$

(7) Calculate the applied overheads for the activity of receiving for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$12 }\times 375\\ =\$9,000\end{array}$

(8) Calculate the applied overheads for the activity of receiving for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{= \$24 }\times 875\\ =\$21,000\end{array}$

To determine

Calculate the total overhead assigned to both the models of S Company by using the two most expensive activities.

Explanation of Solution

Calculate the total overhead assigned to both the models of S Company by using the two most expensive activities.

Activity	Model X ($)	Model Y ($)
Setting up equipment	100,000(1)	50,000(2)
Machining	85,740(3)	64,305(4)
Total Overhead assigned	185,740	114,305

Table (3)

Step 1: Calculate the new activity rates of S Company namely setting up equipment and machining activity.

Setting up equipment:

$\frac{\$150,000}{150}=\$1,000\text{per set up}$

Machining:

$\frac{\$150,000}{10,500}=\$14.29\text{per hour}$

Step 2: Compute the total applied overheads assigned to both the models of S Company.

$\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}$

(1) Calculate the applied overhead of setting up equipment for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{=}\text{\$1,000}\times \text{100}\\ \text{=}\text{\$100,000}\end{array}$

(2) Calculate the applied overhead of setting up equipment for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{=}\text{\$1,000}\times 5\text{0}\\ \text{=}\text{\$50,000}\end{array}$

(3) Calculate the applied overhead of machining activity for Model X.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{=}\text{\$14}\text{.29}\times 6,00\text{0}\\ \text{=}\text{\$85,740}\end{array}$

(4) Calculate the applied overhead of machining activity for Model Y.

$\begin{array}{c}\text{Applied overhead rate = Overhead rate }\times \text{ Actual driver usage}\\ \text{=}\text{\$14}\text{.29}\times 4,5{\rm K}0\text{0}\\ \text{=}\text{\$64,305}\end{array}$

Compute the new cost pools for the activities of setting up equipment and machining of S Company.

Setting up equipment:

 $\$126,000+\left[\left(\frac{\$126,000}{\$252,000}\right)\times \$48,000\right]=\$150,000$

Machining:

$\$126,000+\left[\left(\frac{\$126,000}{\$252,000}\right)\times \$48,000\right]=\$150,000$

Compute the new activity rates for both the activities of S Company.

Activity	Model X ($)	Model Y ($)
Setting up equipment	100,000(1)	50,000(2)
Machining	85,740(3)	64,305(4)
Total Overheads assigned	185,740	114,305

Table (4)

Working notes:

(1) Calculate the new activity rates for setup activity.

Setting up equipment:

$\begin{array}{c}\begin{array}{l}\text{Activity rate }\\ \text{for setup activity}\end{array})\text{ =}\frac{\text{Setting up activity}}{\text{Number of setups}}\\ =\frac{\$150,000}{150}\\ =\$1,000\text{per setup}\end{array}$

(2) Calculate the new activity rates for machining activity.

Machining activity:

$\begin{array}{c}\begin{array}{l}\text{Activity rate }\\ \text{for machining activity}\end{array})\text{ =}\frac{\text{Machining activity}}{\text{Machine hours}}\\ =\frac{\$150,000}{10,500}\\ =\$14.29\text{per hour}\end{array}$

To determine

Compute the percentage of error and provide information on the accuracy of reduced costing system considering activity based costing as a benchmark.

Explanation of Solution

Calculate the percentage of error for Model X of S Company.

$\begin{array}{c}\text{Percentage error = }\frac{\text{New activity rate}-\text{Old activity rate}}{\text{Old activity rate}}\times \text{ 100 }\\ \text{=}\frac{\left(\$185,740-\$171,000\right)}{\$171,000}\times 100\\ =\left(8.6\%\right)\end{array}$

Calculate the percentage of error for Model Yof S Company.

$\begin{array}{c}\text{Percentage error = }\frac{\text{New activity rate}-\text{Old activity rate}}{\text{Old activity rate}}\times \text{ 100 }\\ \text{=}\frac{\left(\$114,305-\$129,000\right)}{\$129,000}\times 100\\ =\left(-11.4\%\right)\end{array}$

The degree of error is not significant in the calculated result which means the activity drivers selected to calculate overhead rates are accepted and are better accurate in contrast to activity based costing.