Question

Hollow Inc. produces blue widgets and gray widgets. Blue widgets are in much greater demand in the market and the firm sells 120,000 blue widgets a year. Hollow. sells 6,000 gray widgets per year in small boutiques. Things have a short shelf life. They must be distributed, sold, and consumed within two months of manufactureing

Both things use the identical production process and production facilities. Direct labor is $0.50 per thing and direct material is $0.50 per thing. Things are produced in batches. Blue widgetd are produced in batches of 600 units and gray widgets in batches of 30. Each batch of wigets goes through the process, which is the machine that converts raw inputs into wigets. Each batch requires engineers to reset the machine for the next batch, calibrate settings, and test the first 10 things for product quality and conformity to standards. Even if sequential batches of the same wigets are made, setups must be performed for each new batch. All the overhead costs are incurred in setups. Indirect labor, indirect materials, and supplies consumed during setup cost $360,000 per year. The only costs of producing things are direct labor, direct materials, and the overhead of setups. The company is currently allocating setup costs to things based on direct labor cost.

The firm has been selling blue widgets for $4 per unit and gray things for $6 per unit. But foreign competition for blue things is starting to put pressure on the $4 price. Some competitors are selling blue widgets for as low as $3 per unit. Management is considering putting more emphasis on selling gray widgets, whose margins are higher. On the other hand, management worries that the current system for allocating overhead costs is misrepresenting the costs of the two products because direct labor costs are not representative of the time spent by each product.

Assuming overheads are allocated on the basis of number of batches, the unit product cost of gray widgets is:

• A. $6.90
• B. $3.857
• C. $31.00
• D. None of these are correct

Answer 1

Option C: $31
Explanation:
Step 1: Overhead allocation
Product	units	Units per batch	No of batches
Blue widgets	1,20,000	600	200
Gray widgets	6,000	30	200
Total			400
Overhead cost per batch = Total overhead / Total batches
= $360,000 / 400
= $900 per batch
overhead allocated to Gray widgets = number of batches × cost per batch
=200 × $900
= $180,000
Overhead per unit for Gray widgets = aloocated overhead / number of units
= $180,000 / 6,000
= $30 per unit
Step 2: Product cost per unit calculations (Gray widgets)
Direct materials	$.50
Direct labor	$.50
Overhead	$30
Total product cost	$31 per unit