Question

CVP Analysis, Impact of Activity-Based Costing

Salem Electronics currently produces two products: a programmable calculator and a tape recorder. A recent marketing study indicated that consumers would react favorably to a radio with the Salem brand name. Owner Kenneth Booth was interested in the possibility. Before any commitment was made, however, Kenneth wanted to know what the incremental fixed costs would be and how many radios must be sold to cover these costs.

In response, Betty Johnson, the marketing manager, gathered data for the current products to help in projecting overhead costs for the new product. The overhead costs based on 30,000 direct labor hours follow. (The high-low method using direct labor hours as the independent variable was used to determine the fixed and variable costs.)

		Fixed		Variable
Materials handling		$         —		$18,000
Power		—		22,000
Engineering		100,000		—
Machine costs		30,000*		80,000
Inspection		40,000		—
Setups		60,000		—
*All depreciation.

The following activity data were also gathered:

		Calculators		Recorders
Units produced		20,000		20,000
Direct labor hours		10,000		20,000
Machine hours		10,000		10,000
Material moves		120		120
Kilowatt-hours		1,000		1,000
Engineering hours		4,000		1,000
Hours of inspection		700		1,400
Number of setups		20		40

Betty was told that a plantwide overhead rate was used to assign overhead costs based on direct labor hours. She was also informed by engineering that if 20,000 radios were produced and sold (her projection based on her marketing study), they would have the same activity data as the recorders (use the same direct labor hours, machine hours, setups, and so on).

Engineering also provided the following additional estimates for the proposed product line:

Prime costs per unit	$18
Depreciation on new equipment	18,000

Upon receiving these estimates, Betty did some quick calculations and became quite excited. With a selling price of $26 and just $18,000 of additional fixed costs, only 4,500 units had to be sold to break even. Since Betty was confident that 20,000 units could be sold, she was prepared to strongly recommend the new product line.

Required:

1. Reproduce Betty's break-even calculation using conventional cost assignments.
Variable overhead rate: $ per direct labor hour
Unit variable cost: $
Break-even:  units

How much additional profit would be expected under this scenario, assuming that 20,000 radios are sold?
$

2. Use an activity-based costing approach, and calculate the break-even point and the incremental profit that would be earned on sales of 20,000 units. In your computation for break-even point, round amounts to the nearest cent and round your final answer to the nearest whole unit. In your analysis assume that the expected engineering hours, inspection hours, and setups are realized and that depreciation is a fixed cost.

Break-even point		units
Incremental profit (loss)	$	Loss

Answer 1

Required:
1. Reproduce Betty's break-even calculation using conventional cost assignments.
Variable overhead rate: = ($18,000 + $22,000 + $80,000)/30,000	$            4.00	per direct labor hour
Unit variable cost = Unit prime cost + Unit variable overhead
Unit variable cost = $18 + $4 x (1 direct labor hour per unit)	$          22.00
Break-even:  = Fixed Cost/(SP - VC)
Break-even units = $18,000/($26 –$22) =	4,500.00
2) How much additional profit would be expected under this scenario, assuming that 20,000 radios are sold?
Additional profit= Contribution margin × (Unit sales –Break-even sales)
Additional profit= $4 × (20,000 –4,500) =	$   62,000.00
2. Use an activity-based costing approach, and calculate the break-even point and the incremental profit that would be earned on sales of 20,000 units. In your computation for break-even point, round amounts to the nearest cent and round your final answer to the nearest whole unit. In your analysis assume that the expected engineering hours, inspection hours, and setups are realized and that depreciation is a fixed cost.
Unit-based variable costs:
Materials handling	$   18,000.00
Power	$   22,000.00
Machine costs	$   80,000.00
Total	$ 120,000.00
Machine hours (10000 + 10000)	20000
Pool Rate	$            6.00
Overhead ($6 × 10,000/20,000)	$            3.00
Prime cost	$          18.00
Total unit variable cost	$          21.00
Product-level:Engineering (X2) = $100,000/5,000 =	$          20.00	Per Engineering Hour
Batch-level:Inspection (X3) = $40,000/2,100 =	$          19.05	Per inspection Hour
Setups (X4) = $60,000/60 =	$     1,000.00	Per setup
Break-even units (where X1equals units):
$26X1= $18,000 + $21X1+ $20X2+ $19.05 X3+ $1,000 X4
X1= ($18,000 + $20X2+ $19.05X3+ $1,000X4)/5
X1= [$18,000 + ($20 ×1,000) + ($19.05 ×$1,400) + ($1,000 × $40)]/5
Break even units X1 =	20,933.33	units
Sales = 20,000 x $26	$ 520,000.00
Less: Variable Cost (21 x 20000)	$ 420,000.00
Contribution Margin	$ 100,000.00
Less: Fixed Cost	$   18,000.00
Incremental profit	$   82,000.00