Chapter 6, Problem 6.17P

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 using the traditional costing system.

Answer to Problem 6.17P

The product margin for the X and P is $220,000 and $1,400,000, respectively.

Explanation of Solution

Calculate the product margin using the traditional costing system:

Traditional Costing System
Product Margin
Particulars	X	P	Total
Sales (1)	$2,800,000	$7,920,000	$10,720,000
Less: Costs
Direct materials	$1,440,000	$4,240,000	$5,680,000
Direct labor	$480,000	$960,000	$1,440,000
Manufacturing overhead (2)	$660,000	$1,320,000	$1,980,000
Product Margin	$220,000	$1,400,000	$1,620,000

Table: (1)

Thus, the product margin for the X and P is $220,000 and $1,400,000, respectively.

Working note 1:

Calculate the sales:

Particulars	X	P
Units sold	20,000	80,000
Sales price per unit	$140	$99
Total sales	$2,800,000	$7,920,000

Table: (2)

Working note 2:

Calculate the manufacturing overhead:

X:

  $\begin{array}{c}\text{Manufacturing overhead = }\frac{\text{Xtreme direct labor hour}}{\text{Total direct labor hour}}\text{ × Total manufacturing overhead}\\ \text{= }\frac{\text{40,000}}{\text{120,000}}\text{ ×}\text{ \$1,980,000}\\ \text{= \$660,000}\end{array}$

P:

  $\begin{array}{c}\text{Manufacturing overhead = }\frac{\text{Pathfinder direct labor hours}}{\text{Total direct labor hours}}\text{ × Total manufacturing overhead}\\ \text{= }\frac{\text{80,000}}{\text{120,000}}\text{ ×}\text{ \$1,980,000}\\ \text{= \$1,320,000}\end{array}$

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 6.17P

The product margin for X and P is ($12,400) and $1,731,400, respectively.

Explanation of Solution

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

Activity-based Costing System
Product Margin
Particulars	X	P	Total
Sales	$2,800,000	$7,920,000	$10,720,000
Less: Costs
Direct materials	$1,440,000	$4,240,000	$5,680,000
Direct labor	$480,000	$960,000	$1,440,000
Manufacturing overhead (3)	$892,400	$988,600	$1,881,000
Product Margin	($12,400)	$1,731,400	$1,719,000

Table: (3)

Thus, the product margin for X and P is ($12,400) and $1,731,400, respectively.

Working note 3:

Calculate the manufacturing overhead:

Particulars	ManufacturingOverhead(a)	Activity			Total cost
		X (b)	P (c)	Total(d)	X   $\left(\frac{\text{a}}{\text{d}}\times \text{ b}\right)$	P   $\left(\frac{\text{a}}{\text{d}}\times \text{ c}\right)$
Supporting direct labor	$783,600	40,000	80,000	120,000	$261,200	$522,400
Batch setups	$495,000	200	100	300	$330,000	$165,000
Product-sustaining	$602,400	1	1	2	$301,200	$301,200
Total manufacturing overhead cost					$892,400	$988,600

Table: (4)

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 6.17P

Traditional Cost System
Particulars	X (a)	% (a/c)	P (b)	% (b/c)	Total (c)
Direct materials	$1,440,000	25.35%	$4,240,000	74.65%	$5,680,000
Direct labor	$480,000	33.33%	$960,000	66.67%	$1,440,000
Manufacturing overhead	$660,000	33.33%	$988,600	66.67%	$1,980,000
Total cost	$2,580,000	28.35%	$6,520,000	71.65%	$9,100,000
Activity-based costing system
Direct materials	$1,440,000	25.35%	$4,240,000	74.65%	$5,680,000
Direct labor	$480,000	33.33%	$960,000	66.67%	$1,440,000
Supporting direct labor	$261,200	33.33%	$522,400	66.67%	$783,600
Batch setups	$330,000	66.67%	$165,000	33.33%	$495,000
Product-sustaining	$301,200	50.00%	$301,200	50.00%	$602,400
Total product cost	$2,812,400	31.25%	$6,188,600	68.75%	$9,001,000
Others					$99,000
Total cost					$9,100,000

Table: (5)

• 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	X (a)	% (a/c)	P (b)	% (b/c)	Total (c)
Direct materials	$1,440,000	25.35%	$4,240,000	74.65%	$5,680,000
Direct labor	$480,000	33.33%	$960,000	66.67%	$1,440,000
Manufacturing overhead	$660,000	33.33%	$988,600	66.67%	$1,980,000
Total cost	$2,580,000	28.35%	$6,520,000	71.65%	$9,100,000
Activity-based costing system
Direct materials	$1,440,000	25.35%	$4,240,000	74.65%	$5,680,000
Direct labor	$480,000	33.33%	$960,000	66.67%	$1,440,000
Supporting direct labor	$261,200	33.33%	$522,400	66.67%	$783,600
Batch setups	$330,000	66.67%	$165,000	33.33%	$495,000
Product-sustaining	$301,200	50.00%	$301,200	50.00%	$602,400
Total product cost	$2,812,400	31.25%	$6,188,600	68.75%	$9,001,000
Others					$99,000
Total cost					$9,100,000

Table: (6)

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

The product margin for X and P is $220,000 and $1,400,000 under the traditional costing system. The product margin for X and P is ($12,400) and $1,731,400 under activity-based costing system. The reason behind the change in the allocation of the manufacturing overhead. The overheads are allocated on the basis of the direct labor hours in the 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.