In: Accounting
Approximately Relevant ABC
Reducir, Inc., produces two different types of hydraulic cylinders. Reducir produces a major subassembly for the cylinders in the Cutting and Welding Department. Other parts and the subassembly are then assembled in the Assembly Department. The activities, expected costs, and drivers associated with these two manufacturing processes are given below.
Process | Activity | Cost | Activity Driver | Expected Quantity |
Cutting and Welding | Welding | $ 776,000 | Welding hours | 4,000 |
Machining | 450,000 | Machine hours | 10,000 | |
Inspecting | 448,250 | No. of inspections | 1,000 | |
Materials handling | 300,000 | No. of batches | 12,000 | |
Setups | 240,000 | No. of setups | 100 | |
$2,214,250 | ||||
Assembly | Changeover | $ 180,000 | Changeover hours | 1,000 |
Rework | 61,750 | Rework orders | 50 | |
Testing | 300,000 | No. of tests | 750 | |
Materials handling | 380,000 | No. of parts | 50,000 | |
Engineering support | 130,000 | Engineering hours | 2,000 | |
$1,051,750 |
Other overhead activities, their costs, and drivers are listed below.
Activity | Cost | Activity Driver | Quantity |
Purchasing | $ 135,000 | Purchase requisitions | 500 |
Receiving | 274,000 | Receiving orders | 2,000 |
Paying suppliers | 225,000 | No. of invoices | 1,000 |
Providing space and utilities | 100,000 | Machine hours | 10,000 |
Total | $ 734,000 |
Other production information concerning the two hydraulic cylinders is also provided:
Cylinder A | Cylinder B | ||||
Units produced | 1,500 | 3,000 | |||
Welding hours | 1,600 | 2,400 | |||
Machine hours | 3,000 | 7,000 | |||
Inspections | 500 | 500 | |||
Moves | 7,200 | 4,800 | |||
Batches | 45 | 55 | |||
Changeover hours | 540 | 460 | |||
Rework orders | 5 | 45 | |||
No. of tests | 500 | 250 | |||
Parts | 40,000 | 10,000 | |||
Engineering hours | 1,500 | 500 | |||
Requisitions | 425 | 75 | |||
Receiving orders | 1,800 | 200 | |||
Invoices | 650 | 350 |
Process | Activity | Cost |
Cutting and Welding | Welding | $ 2,000,000 |
Machining | 1,000,000 | |
Inspecting | 50,000 | |
Materials handling | 72,000 | |
Setups | 400,000 | |
$3,522,000 | ||
Assembly | Changeover | $ 28,000 |
Rework | 50,000 | |
Testing | 40,000 | |
Materials handling | 60,000 | |
Engineering support | 70,000 | |
$248,000 |
Other overhead activities:.
Activity | Cost |
Purchasing | $ 50,000 |
Receiving | 70,000 |
Paying suppliers | 80,000 |
Providing space and utilities | 30,000 |
$230,000 |
The per unit overhead cost using the 14 activity-based drivers is $1,108 and $779 for Cylinder A and Cylinder B, respectively.
Required:
1. Determine the percentage of total costs represented by the three most expensive activities.
85%
2. If required, round your interim calculations
and final answers to the nearest dollar.
Allocate the costs of all other activities to the three activities
identified in Requirement 1 in proportion to their individual
activity costs.
Allocation | |
Welding | $352,941 |
Machining | $176,471 |
Setups | $70,588 |
Calculate the total activity costs of all the three activities.
Cost pools | |
Welding | $2,352,941 |
Machining | $1,176,471 |
Setups | $470,588 |
Activity Rates | ||
Welding | $588 | per welding hour |
Machining | $118 | per machine hour |
Setups | $4706 | per batch |
Now assign these total costs to the products using the drivers of the three chosen activities.
Cylinder A | Cylinder B | |||
Rate 1 (welding) | $ | $ | ||
Rate 2 (machining) | $ | $ | ||
Rate 3 (setups) | $ | $ | ||
Total overhead costs | $ | $ | ||
Unit overhead costs | $ | $ |
3. Using the costs assigned in Requirement 2, calculate the percentage error using the ABC costs as a benchmark. Round your answers to one decimal place. If an item is negative, use a minus (-) sign to indicate.
Percentage error | |
Cylinder A | % |
Cylinder B | % |
SOLUTION
1. Plantwide rate = ($2,214,250 + $1,051,750 + $734,000)/10,000
= $400 per machine hour
Cylinder A: Unit cost = $400 × 3,000 = $1,200,000
Unit overhead cost = $1,200,000/1,500 = $800.00
Cylinder B: $400 × 7,000 = $2,800,000
Unit overhead cost = $2,800,000/3,000 = $933.33
2. Rates:
Welding
Rate 1: $776,000/4,000 = $194.00 per welding hour
Machining
Rate 2: $450,000/10,000 = $45.00 per machine hour
Inspecting
Rate 3: $448,250/1,000 = $448.25 per inspection
Materials Handling
Rate 4: $300,000/12,000 = $25.00 per move
Setups
Rate 5: $240,000/100 = $2,400.00 per batch
Changeover
Rate 6: $180,000/1,000 = $180.00 per changeover hour
Rework
Rate 7: $61,750/50 = $1,235.00 per rework order
Testing
Rate 8: $300,000/750 = $400.00 per test
Materials Handling
Rate 9: $380,000/50,000 = $7.60 per part
Engineering Support
Rate 10: $130,000/2,000 = $65.00 per engineering hour
Purchasing
Rate 11: $135,000/500 = $270.00 per requisition
Receiving
Rate 12: $274,000/2,000 = $137.00 per receiving order
Paying Suppliers
Rate 13: $225,000/1,000 = $225.00 per invoice
Providing Space and Utilities
Rate 14: $100,000/10,000 = $10.00 per machine hour
Overhead assignment:
Cylinder A Cylinder B
Rate 1:
$194 × 1,600 welding hours $ 310,400
$194 × 2,400 welding hours $ 465,600
Rate 2:
$45 × 3,000 machine hours 135,000
$45 × 7,000 machine hours 315,000
Rate 3:
$448.25 × 500 inspections 224,125
$448.25 × 500 inspections 224,125
Rate 4:
$25 × 7,200 moves 180,000
$25 × 4,800 moves 120,000
Rate 5:
$2,400 × 45 batches 108,000
$2,400 × 55 batches 132,000
Rate 6:
$180 × 540 changeover hours 97,200
$180 × 460 changeover hours 82,800
Rate 7:
$1,235 × 5 rework orders 6,175
$1,235 × 45 rework orders 55,575
Rate 8:
$400 × 500 tests 200,000
$400 × 250 tests 100,000
Rate 9:
$7.60 × 40,000 parts 304,000
$7.60 × 10,000 parts 76,000
Rate 10:
$65 × 1,500 engineering hours 97,500
$65 × 500 engineering hours 32,500
Rate 11:
$270 × 425 requisitions 114,750
$270 × 75 requisitions 20,250
Rate 12:
$137 × 1,800 receiving orders 246,600
$137 × 200 receiving orders 27,400
Rate 13:
$225 × 650 invoices 146,250
$225 × 350 invoices 78,750
Rate 14:
$10 × 3,000 machine hours 30,000
$10 × 7,000 machine hours 70,000
Total overhead costs $2,200,000 $1,800,000
Units produced ÷ 1,500 ÷ 3,000
Overhead per unit $ 1,467 $ 600
Using plantwide rate assignments, Cylinder A is undercosted, and Cylinder B is overcosted. The activity assignments capture the cause-and-effect relationships and thus reflect the overhead consumption patterns better than the machine hour pattern of the plantwide rate.
3. Global consumption ratios:
Cylinder A: $2,200,000/$4,000,000 = 0.55
Cylinder B: $1,800,000/$4,000,000 = 0.45
4. Welding: (1,600/4,000, 2,400/4,000) = (0.40, 0.60)
Materials handling (parts): (40,000/50,000, 10,000/50,000) = (0.80, 0.20)
Set up two equations (the w’s represent the allocation rates):
0.40w1 + 0.80w2 = 0.55
0.60w1 + 0.20w2 = 0.45
Solving (multiply the second equation by –4 and add to the first):
–2w1 = –1.25
w1 = 0.625
and thus,
w2 = 0.375
Cost pools:
Welding: 0.625 × $4,000,000 = $2,500,000
Materials handling: 0.375 × $4,000,000 = $1,500,000
Activity rates:
Rate 1: Welding: $2,500,000/4,000 = $625 per welding hour
Rate 2: Materials handling (assembly): $1,500,000/50,000 = $30.00 per part
Overhead assignment:
Cylinder A Cylinder B
Rate 1:
$625 × 1,600 welding hours $ 1,000,000
$625 × 2,400 welding hours $ 1,500,000
Rate 2:
$30.00 × 40,000 parts 1,200,000
$30.00 × 10,000 parts 300,000
Total overhead costs $ 2,200,000 $ 1,800,000
Units produced ÷ 1,500 ÷ 3,000
Overhead per unit $ 1,466.67* $ 600.00
*Rounded to the nearest cent.
We are able to take a 14-driver system and reduce it to a 2-driver system and achieve exactly the same overhead cost assignments as the more complex system. This after-the-fact simplification has two major advantages: (1) it allows nonfinancial managers to more readily read, understand, and interpret product cost reports; and (2) the actual values only need to be collected for two drivers instead of 14, producing considerable cost savings.
5. Inspection: (500/1,000, 500/1,000) = (0.50, 0.50)
Engineering: (1,500/2,000, 500/2,000) = (0.75, 0.25)
Set up two equations (the w’s represent the allocation rates):
0.50w1 + 0.75w2 = 0.55
0.50w1 + 0.25w2 = 0.45
Solving (subtract the second equation from the first):
0.50w2 = 0.10
w2 = 0.20
and thus,
w1 = 0.80
Cost pools:
Inspection: 0.80 × $4,000,000 = $3,200,000
Engineering: 0.20 × $4,000,000 = $800,000
Activity rates:
Rate 1: Inspection: $3,200,000/1,000 = $3,200 per inspection
Rate 2: Engineering: $800,000/2,000 = $400 per hour
Overhead assignment:
Cylinder A Cylinder B
Rate 1:
$3,200 × 500 inspections $1,600,000
$3,200 × 500 inspections $1,600,000
Rate 2:
$400 × 1,500 engineering hours 600,000
$400 × 500 engineering hours 200,000
Total overhead costs $2,200,000 $1,800,000
Units produced ÷ 1,500 ÷ 3,000
Overhead per unit $ 1,467.67* $ 600.00
*Rounded to the nearest cent.