Chapter 4, Problem 8CE

Patterson Company produces wafers for integrated circuits. Data for the most recent year are provided:

^aCalculated using number of dies as the single unit-level driver.

^bCalculated by multiplying the consumption ratio of each product by the cost of each activity.

Required:

1. 1. Using the five most expensive activities, calculate the overhead cost assigned to each product. Assume that the costs of the other activities are assigned in proportion to the cost of the five activities.
2. 2. Calculate the error relative to the fully specified ABC product cost and comment on the outcome.
3. 3. What if activities 1, 2, 5, and 8 each had a cost of $650,000 and the remaining activities had a cost of $50,000? Calculate the cost assigned to Wafer A by a fully specified ABC system and then by an approximately relevant ABC approach. Comment on the implications for the approximately relevant approach.

To determine

Compute the overheads assigned to each product of P Company using the five most expensive activities assuming the cost of other activities are assigned in proportion to the cost of the five activities.

Explanation of Solution

Overhead consumption ratio: An overhead consumption ratio is a measurement tool used to calculate the proportion of the overhead activity that is consumed by a particular product.

Approximately relevant activity based costing: Approximately relevant activity based costing

Compute the overhead cost to be assigned to both products of P Company using the five most expensive activities.

Activity	Budgeted cost ($)	Expected consumption ratio
		Wafer A	Wafer B
Testing products	720,000 (1)	60 %	40 %
Handling water lots	360,000 (2)	45 %	55 %
Inserting dies	840,000 (3)	70 %	30 %
Purchasing materials	480,000 (4)	20 %	80 %
Moving materials	600,000 (5)	50 %	50 %
Total activity cost	3,000,000

Table (1)

Working notes:

(1) Calculate the budgeted cost for the activity of testing hours of P Company.

$\begin{array}{c}\text{Budgeted cost = Original costs + }\left[\left(\frac{\text{Original cost}}{\text{Total cost of expensive activities }}\right)\times \text{Total cost of inexpensive activities}\right]\\ =\$600,000+\left[\left(\frac{\$600,000}{\$2,500,000}\right)\times \$500,000\right]\\ =\$600,000+\left[.24\times \$500,000\right]\\ =\$600,000+\$120,000\\ =\$720,000\end{array}$

(2) Calculate the budgeted cost for the activity of handling water lots of P Company.

$\begin{array}{c}\text{Budgeted cost = Original costs + }\left[\left(\frac{\text{Original cost}}{\text{Total cost of expensive activities }}\right)\times \text{Total cost of inexpensive activities}\right]\\ =\$300,000+\left[\left(\frac{\$300,000}{\$2,500,000}\right)\times \$500,000\right]\\ =\$300,000+\left[.12\times \$500,000\right]\\ =\$300,000+\$60,000\\ =\$360,000\end{array}$

(3) Calculate the budgeted cost for the activity of testing hours of P Company.

$\begin{array}{c}\text{Budgeted cost = Original costs + }\left[\left(\frac{\text{Original cost}}{\text{Total cost of expensive activities }}\right)\times \text{Total cost of inexpensive activities}\right]\\ =\$700,000+\left[\left(\frac{\$700,000}{\$2,500,000}\right)\times \$500,000\right]\\ =\$700,000+\left[.28\times \$500,000\right]\\ =\$700,000+\$140,000\\ =\$840,000\end{array}$

(4) Calculate the budgeted cost for the activity of purchasing materials of P Company.

$\begin{array}{c}\text{Budgeted cost = Original costs + }\left[\left(\frac{\text{Original cost}}{\text{Total cost of expensive activities }}\right)\times \text{Total cost of inexpensive activities}\right]\\ =\$400,000+\left[\left(\frac{\$400,000}{\$2,500,000}\right)\times \$500,000\right]\\ =\$400,000+\left[.16\times \$500,000\right]\\ =\$400,000+\$80,000\\ =\$480,000\end{array}$

(5) Calculate the budgeted cost for the activity of purchasing materials of P Company.

$\begin{array}{c}\text{Budgeted cost = Original costs + }\left[\left(\frac{\text{Original cost}}{\text{Total cost of expensive activities }}\right)\times \text{Total cost of inexpensive activities}\right]\\ =\$500,000+\left[\left(\frac{\$500,000}{\$2,500,000}\right)\times \$500,000\right]\\ =\$500,000+\left[.2\times \$500,000\right]\\ =\$500,000+\$100,000\\ =\$600,000\end{array}$

Compute the total approximately relevant activity based cost for all activities by using consumption ratios.

Wafer A:

Activity	Consumption ratio (%)	Budgeted activity cost ($)	Reduced ABC system ($)
	(a)	(b)	$\left(a\right)\times \left(b\right)$
Testing products	60 %	720,000	432,000
Handling water lots	45 %	360,000	162,000
Inserting dies	70 %	840,000	588,000
Purchasing materials	20 %	480,000	96,000
Moving materials	50 %	600,000	300,000
Total activity cost			1,578,000

Table (2)

Wafer B:

Activity	Consumption ratio (%)	Budgeted activity cost ($)	Reduced ABC system ($)
	(a)	(b)	$\left(a\right)\times \left(b\right)$
Testing products	40 %	720,000	288,000
Handling water lots	55 %	360,000	198,000
Inserting dies	30 %	840,000	252,000
Purchasing materials	80 %	480,000	384,000
Moving materials	50 %	600,000	300,000
Total activity cost			1,422,000

Table (3)

To determine

Compute the relative error for both products with respect to fully specified activity based costing and provide information on the result.

Explanation of Solution

Calculate the relative error for both products with respect to fully specified activity based costing and provide information on the result. 

Wafer A:

$\begin{array}{c}\text{Relative error =}\frac{\left(\text{Reduced Activity based cost}-\text{Total activity cost assigned}\right)}{\text{Total activity cost assigned}}\\ =\frac{\left(\$1,578,000-\$1,500,000\right)}{\$1,500,000}\\ =0.052\\ =5.2\%\end{array}$

Wafer B:

$\begin{array}{c}\text{Relative error =}\frac{\left(\text{Reduced Activity based cost}-\text{Total activity cost assigned}\right)}{\text{Total activity cost assigned}}\\ =\frac{\left(\$1,422,000-\$1,500,000\right)}{\$1,500,000}\\ =\left(-0.052\right)\\ =\left(-5.2\%\right)\end{array}$

From the above calculated result, the maximum error is 5.2 percent with respect to activity based cost assignments that indicates a positive result indicated better accuracy.

To determine

Calculate the cost assigned to Wafer A by a fully specified activity based costing system and activity based costing system. Activities of developing test program, making probe cards, engineering designs, and purchasing materials costs $650,000 each and the remaining activities costs $50,000. Provide information on the implications for the relevant approach.

Explanation of Solution

Wafer A:

$\begin{array}{c}\text{Activity based cost }\text{=}\left[\begin{array}{l}\text{Activity cost}\times \\ \left(\text{Total consumption ratios}\right)\end{array}\right]+\left[\begin{array}{l}\text{Activity cost of remaining activities}\times \\ \left(\text{Total consumption ratios}\right)\end{array}\right]\\ =\left[\$650,000\times \left(\begin{array}{l}25\%+10\%15\%+\\ 20\%\end{array}\right)\right]+\left[\$50,000\times \left(\begin{array}{l}60\%+55\%+45\%70\%+\\ 35\%+65\%+50\%+30\%\end{array}\right)\right]\\ =\left[\$650,000\times \left(\begin{array}{l}.25+.10+.15+\\ .20\end{array}\right)\right]+\left[\$50,000\times \left(\begin{array}{l}.60+.55+.45+.7+\\ .35+.65+.5+.3\end{array}\right)\right]\\ =\left[\$650,000\times 0.7\right]+\left[\$50,000\times 4.1\right]\\ =\$455,000+\$205,000\\ =\$660,000\end{array}$

Compute the approximately relevant cost for the activities 1, 2, 5, and 8 of P Company.

$\begin{array}{c}\text{Reassigned cost}\text{=}\text{Activity based cost}\text{+}\text{Engineering hours}\times \text{Purchasing materials}\\ =\$650,000+.25\times \$400,000\\ =\$750,000\end{array}$

Compute the approximately relevant cost for Wafer A.

$\begin{array}{c}\text{Approximately relevant cost =}\text{Reassigned cost}\times \left(\text{Expected consumption ratios of Wafer A}\right)\\ =\$750,000\left(25\%+10\%+15\%+20\%\right)\\ =\$750,000\left(.25+.10+.15+.20\right)\\ =\$525,000\end{array}$

Compute the error term of P Company with respect to the costing techniques used.

$\begin{array}{c}\text{Difference in costing=Activity based cost}-\text{Approximately relevanet cost}\\ =\$660,000-\$525,000\\ =\$135,000\end{array}$

Compute the relative error between the costing techniques used by P Company.

$\begin{array}{c}\text{Relative error}\text{=}\frac{\left(\text{Approximately relevant cost}-\text{Activity based cost}\right)}{\text{Activity based cost}}\\ =\frac{\left(\$525,000-\$660,000\right)}{\$660,000}\\ =\frac{-\left(\$165,000\right)}{\$660,000}\\ =-20.5\%\end{array}$