Chapter 17, Problem 1PSB

To determine

Activity Based Costing (ABC) Method:

Activity based costing (ABC) is a method of costing that determines the tasks that the company executes and allocates the cost of each task to all products and services.

Plant Wide Overhead Rate:

Plantwide overhead rate is a sole overhead rate that a company uses to assign all of its manufacturing overhead costs to its products.

Activity Rates:

Activity rates used to assign overhead cost to products and customers. Activity rate can be computed by dividing the cost assigned to the activity by the total activity

Overhead Costs:

Overhead costs also referred as manufacturing overhead is the sum total of costs incurred in producing a product other than the variable costs such as direct material and direct labor

1.

To compute:Manufacturing cost per unit and gross profit per unit.

Explanation of Solution

Given below is the table for the calculation of plantwide overhead rate:

Plantwide overhead rate
Particulars	($)
Indirect manufacturing costs
Engineering support costs	56,250
Electricity costs	112,500
Setup costs	41,250
Total indirect manufacturing costs$\left[A\right]$	210,000
Budgeted machine hours:
Standard $\left(40,000\text{ units}\times \text{3 machine hours per unit}\right)$	120,000 hours
Deluxe $\left(10,000\text{ units}\times \text{3 machine hours per unit}\right)$	30,000 hours
Total budgeted machine hours$\left[B\right]$	150,000 hours
Plantwide overhead rate $\left[\frac{\left(A\right)}{\left(B\right)}\right]$	$1.40

Table(1)

Plantwide overhead rate is $1.40 per machine hour.

Given below is the computation of manufacturing cost per unit:

Cost per unit
Particulars	Standard ($)	Deluxe B ($)
Direct materials	4.00	8.00
Direct labor$\left(\text{Direct labor hours per unit}\times \text{Direct labor rate}\right)$	80.00	100.00
Indirect manufacturing overhead cost$\left(\text{Machine hours per unit}\times \text{Plantwide overhead rate}\right)$	4.20	4.20
Manufacturing cost per unit	88.20	112.20

Table(2)

Calculation of gross profit per unit:

Gross profit per unit
Particulars	Standard ($)	Deluxe B ($)
Market price	92.00	125.00
Cost	(88.20)	(112.20)
Gross profit per unit	3.80	12.80

Table(3)

Hence,manufacturing cost per unit for Standard is $88.20 per unit and for Deluxe is $112.20 per unit. Gross profit per unit for standard is $3.80per unit and for Deluxe is $12.80 per unit.

2.

To determine

To compute: Gross profit generated by each customer of Standard and Deluxe using plant wide overhead rate.

Explanation of Solution

Given below is the computation of manufacturing cost using plant wide overhead rate using ABC method:

Calculation of gross profit generated by each customer:

Profit generated by each customer
Particulars	Standard	Deluxe
Gross profit per unit $\left(\text{A}\right)$	$3.80	$12.80
Number of units	40,000	10,000
Number of customers	1,000	1,000
Units purchased by customers $\left(\text{B}\right)$	40	10
Gross profit generated by each customer $$\left[\frac{\left(\text{A}\right)}{\left(\text{B}\right)}\right]$$	$152.00	$128.00

Table(4)

Gross profit generated by each customer of Standard is $152 and Deluxe is $128.

Given below is the cost of providing service to each customer:

Given,
Customer service cost is $250,000.
Number of customers is 2,000 $\left(1,000\text{ Standard}+1,000\text{ Deluxe}\right)$ .

Formula for calculating cost of providing service to each customer:

   $\text{cost of providing service to each customer}=\frac{\text{Customer service costs}}{\text{Number of customers}}$

Substitute $250,000 for the value of customer service costs and 2,000 for the value of number of customers.

   $\begin{array}{c}\text{cost of providing service to each customer}=\frac{\text{\$250,000}}{2,000}\\ =\$125\text{ per customer}\end{array}$

The cost of providing service to each customer is $125 per customer.

Given below is the calculation of profit/loss per customer:

Profit/loss per customer
	Standard ($)	Deluxe ($)
Gross profit per customer	152	128
Cost of providing service to each customer	(125)	(125)
Profit/loss per customer	27	3

Table(5)

• From the above calculation it can be interpreted that gross profit per customer of Standard and Deluxe are sufficient to meet the cost of providing service to each customer.
• The comparison between gross profit per customer and cost of providing service to each customer helps to understand whether Company is earning sufficient gross profit to meet the cost of providing service to each customer.

Hence, gross profit generated by each customer of Standard is $152 and Deluxe is $128. Cost of providing service to each customer is $125.

3.

To determine

To compute: Manufacturing cost of each product using ABC method.

Explanation of Solution

Activity $\left(\text{A}\right)$	Cost ($) $\left(\text{B}\right)$	Driver	Quantity $\left(\text{C}\right)$ $\left(\text{Standard}+\text{Deluxe}\right)$	Cost per driver ($) $\frac{\left(\text{B}\right)}{\left(\text{C}\right)}$
Engineering support costs	56,250	Engineering modifications	75	750
Electricity costs	112,500	Machine hours	150,000	0.75
Setup costs	41,250	Batches	250	165

Table(6)

Given below is the computation of total manufacturing cost per unit:

Total cost per unit
Activity	Quantity per driver		Overhead costs	Standard ($)	Deluxe ($)
	Standard ($)	Deluxe ($)	Cost per driver ($)
Engineering support	50	25	750	37,500	18,750
Electricity	120,000	30,000	0.75	90,000	22,500
Setup cost	175	75	165	28,875	12,375
Total Overhead cost$$\left(\text{A}\right)$$				156,375	53,625
Number of units $\left(\text{B}\right)$				40,000	10,000
Overhead cost per unit $\left[\frac{\left(A\right)}{\left(B\right)}\right]$				3.91	5.36
Direct materials per unit				4.00	8.00
Direct labor per unit				80.00	100.00
Total				87.91	113.36

Table(7)

Given below is the calculation of gross profit:

Gross profit per unit
Particulars	Standard ($)	Deluxe B ($)
Market price	92.00	125.00
Less: Manufacturing cost per unit	(87.91)	(113.36)
Gross profit per unit	4.09	11.64

Table(8)

Working note:

Calculation of machine hours:

   $\begin{array}{c}\text{Machine hours}=\left(\begin{array}{l}\left(\text{Units of Standard}\times \text{Machine hour per unit of Standard}\right)\\ +\left(\text{Units of Deluxe}\times \text{Machine hour per unit of Deluxe}\right)\end{array}\right)\\ =\left(40,000\text{ units}\times 3\right)+\left(10,000\text{ units}\times 3\right)\\ =120,000\text{ units}+30,000\text{ units}\\ =150,000\text{ units}\end{array}$

Hence,manufacturing cost of Standard is $87.91 and Deluxe is $113.36.Gross profit per unit for Standard is $4.09 and Deluxe is $11.64 per unit.

4.

To determine

To compute: Profit generated by each customer.

Explanation of Solution

Given below is the computation of profit generated by each customer:

Particulars	Standard ($)	Deluxe B ($)
Gross profit per unit$\left(\text{A}\right)$	$4.09	$11.64
Number of units	40,000 units	10,000 units
Number of customers	1,000	1,000
Units purchased by customers$\left(\text{B}\right)$	40	10
Gross profit per customer$$\left(\text{A}\right)\times \left(\text{B}\right)$$	$163.60	$116.40

Table(9)

The cost of providing service to each customer is $125 per customer.

Given below is the calculation of profit/loss per customer:

Profit/loss per customer
	Standard ($)	Deluxe ($)
Gross profit per customer	163.60	116.40
Cost of providing service to each customer	125	125
Profit/loss per customer	$38.60	($8.60)

Table(10)

• From the above calculation it can be interpreted that gross profit per customer of Standard is sufficient to meet the cost of providing service to each customeras it earns a profit of $38.60 Whereas gross profit per customer of Deluxeis not sufficient to meet the cost of providing service to each customer as Deluxe incurs a loss of $8.60.
• The comparison between gross profit per customer and cost of providing service to each customer helps to understand whether Company is earning sufficient gross profit to meet the cost of providing service to each customer.

Hence,gross profit generated by each customer of standard is $163.60 and Deluxe is $116.40.

5.

To determine

To identify: Activity based costing gives better information to the managers.

Explanation of Solution

• Activity based costing method is more preferable than plant wide overhead rate method. Activity based costing method allocates the cost of each task to all products and services. Whereas in plant wide overhead rate method, costs are allocated on the basis of volume.
• Plant wide overhead is only feasible for companies which manufactures only single product or provides only single service.
• It is preferable to use activity based costing in companies where more than one product is manufactured or more than one servicesare provided, for more accurate results.

Hence, activity based costing gives better information to the managers.