Chapter 5, Problem 5.16P

To determine

Concept introduction:

Profit margin:

The profit margin is the percentage charged by the seller on the sale of the goods. The difference between the sales price and the cost price of the product is known as the profit margin.

Requirement 1:

Calculate the product margin for product B300 and T500.

Answer to Problem 5.16P

The product margin for the B300 and T500 is $363,700 and $136,300, respectively.

Explanation of Solution

Calculate the product margin for product B300 and T500:

Traditional Costing System
Product Margin
Particulars	B300	T500	Total
Sales (1)	$1,400,000	$700,000	$2,100,000
Less: Costs
Direct materials	$436,300	$251,700	$688,000
Direct labor	$200,000	$104,000	$304,000
Manufacturing overhead (2)	$400,000	$208,000	$608,000
Product Margin	$363,700	$136,300	$500,000

Table: (1)

Thus, the product margin for B300 and T500 is $363,700 and $136,300, respectively.

Working note 1:

Calculate the sales:

Particulars	B300	T500
Units sold	70000	17500
Sales price per unit	$20	$40
Total sales	$1,400,000	$700,000

Table: (2)

Working note 2:

Calculate the manufacturing overhead:

B300:

  $\begin{array}{c}\text{Manufacturing overhead = }\frac{\text{B300 direct labor}}{\text{Total direct labor}}\times \text{ Total manufacturing overhead}\\ =\frac{\$200,000}{\$304,000}\times \text{ \$608,000}\\ \text{= \$400,000}\end{array}$

T500:

  $\begin{array}{c}\text{Manufacturing overhead = }\frac{\text{B300 direct labor}}{\text{Total direct labor}}\times \text{ Total manufacturing overhead}\\ =\frac{\$104,000}{\$304,000}\times \text{ \$608,000}\\ \text{= \$208,000}\end{array}$

To determine

Concept introduction:

Activity rate:

The activity rate is determined by dividing the net activity cost, with the total number of activities. The calculation of the activity rate is the second step in the implementation of activity-based costing. After establishing the relationship between the overheads and the activity, the management has to ascertain the activity rate for that specific activity.

Requirement 2:

Calculate the product margin using the activity-based costing system.

Answer to Problem 5.16P

The product margin for B300 and T500 is $496,200 and ($29,200), respectively.

Explanation of Solution

Calculate the product margin using the activity-based costing system:

Activity-based Costing System
Product Margin
Particulars	B300	T500	Total
Sales	$1,400,000	$700,000	$2,100,000
Less: Costs
Direct materials	$436,300	$251,700	$688,000
Direct labor	$200,000	$104,000	$304,000
Manufacturing overhead	$267,500	$373,500	$641,000
Product Margin	$496,200	($29,200)	$467,000

Table: (3)

Thus, the product margin for B300 and T500 is $496,200 and ($29,200) respectively.

Working note 3:

Calculate the manufacturing overhead:

Particulars	ManufacturingOverhead(a)	Activity			Total cost
		B300(b)	T500(c)	Total(d)	B300   $\left(\frac{\text{a}}{\text{d}}\times \text{ b}\right)$	T500   $\left(\frac{\text{a}}{\text{d}}\times \text{ c}\right)$
Machining	$213,500	$90,000	$62,500	$152,500	$126,000.00	$87,500.00
Setups	$157,500	75	300	375	$31,500.00	$126,000.00
Product-sustaining	$120,000	1	1	2	$60,000.00	$60,000.00
Selling and distribution expenses	$150,000				$50,000	$100,000
Total manufacturing overhead cost					$267,500.00	$373,500.00

Table: (3)

To determine

Concept introduction:

Activity-based costing (ABC):

Activity-based costing refers to the method of costing where the overhead cost is assigned to various products. This costing method identifies the relationship between the manufacturing overhead costs and the activities. After establishing the relationship, the indirect cost is allocated to the products.

Requirement 3:

Prepare a report stating the comparison of the traditional and activity-based cost assignments.

Answer to Problem 5.16P

Traditional Cost System
Particulars	B300 (a)	% (a/c)	T500 (b)	% (b/c)	Total (c)
Direct materials	$436,300	63.42%	$251,700	36.58%	$688,000
Direct labor	$200,000	65.79%	$104,000	34.21%	$304,000
Manufacturing overhead	$400,000	65.79%	$208,000	34.21%	$608,000
Total cost	$1,036,300	64.77%	$563,700	35.23%	$1,600,000
Activity based costing system
Direct materials	$436,300	63.42%	$251,700	36.58%	$688,000
Direct labor	$200,000	65.79%	$104,000	34.21%	$304,000
Machining	$126,000	59.02%	$87,500	40.98%	$213,500
Setups	$31,500	20.00%	$126,000	80.00%	$157,500
Product-sustaining	$60,000	50.00%	$60,000	50.00%	$120,000
Total cost	$853,800	57.57%	$629,200	42.43%	$1,483,000

Table: (4)

• The main reason behind the difference is the allocation of the manufacturing overheads in two different methods.

Explanation of Solution

Prepare a report stating the comparison of the traditional and activity-based cost assignments:

Traditional Cost System
Particulars	B300 (a)	% (a/c)	T500 (b)	% (b/c)	Total (c)
Direct materials	$436,300	63.42%	$251,700	36.58%	$688,000
Direct labor	$200,000	65.79%	$104,000	34.21%	$304,000
Manufacturing overhead	$400,000	65.79%	$208,000	34.21%	$608,000
Total cost	$1,036,300	64.77%	$563,700	35.23%	$1,600,000
Activity based costing system
Direct materials	$436,300	63.42%	$251,700	36.58%	$688,000
Direct labor	$200,000	65.79%	$104,000	34.21%	$304,000
Machining	$126,000	59.02%	$87,500	40.98%	$213,500
Setups	$31,500	20.00%	$126,000	80.00%	$157,500
Product-sustaining	$60,000	50.00%	$60,000	50.00%	$120,000
Total cost	$853,800	57.57%	$629,200	42.43%	$1,483,000

Table: (5)

Explain the reason behind the difference of traditional and activity-based cost assignments:

The product margin for B300 and T500 is $363,700 and $136,300 under traditional costing system. The product margin for B300 and T500 is $496,200 and ($29,200) under activity-based costing system. The reason behind the change is the allocation of the manufacturing overhead. The overheads are allocated on the basis of the direct labor in traditional costing system and they are allocated on the basis of different cost activity under activity-based costing system.

Therefore, the main reason behind the difference is the allocation of the manufacturing overheads in two different methods.