Worked example 1

Component Co manufactures two components, C1 and C2. The company is considering adopting an Activity Based Costing system. The following data is available:

	C1	C2
Production units	2,000	5,000
---	---	---
Direct material cost per unit	$25	$30
Direct labour cost per unit	$15	$10

Total production overheads are $188,000, which are analysed as follows:

Activity Cost Pool	Cost ($)	Cost Driver
Machining	80,000	Machine hours
---	---	---
Set-ups	48,000	Number of production runs
Material handling	60,000	Number of material requisitions

The activities for each component are:

	C1	C2
Machine hours per unit	2.0	1.2
---	---	---
Number of production runs	40	80
Number of material requisitions	60	90

Required: Calculate the full cost per unit for components C1 and C2 using Activity Based Costing.

Show solution outline

Step 1: Calculate Total Activity for Each Cost Driver

Total Machine Hours:
- C1: 2,000 units × 2.0 hours/unit = 4,000 hours
- C2: 5,000 units × 1.2 hours/unit = 6,000 hours
- Total: 4,000 + 6,000 = 10,000 machine hours
Total Production Runs: 40 + 80 = 120 runs
Total Material Requisitions: 60 + 90 = 150 requisitions

Step 2: Calculate Cost Driver Rates

Machining Rate: $\frac{\text{\textdollar}80,000}{10,000 \text{ machine hours}} = \text{\textdollar}8.00 \text{ per machine hour}$
Set-up Rate: $\frac{\text{\textdollar}48,000}{120 \text{ production runs}} = \text{\textdollar}400 \text{ per run}$
Material Handling Rate: $\frac{\text{\textdollar}60,000}{150 \text{ requisitions}} = \text{\textdollar}400 \text{ per requisition}$

Step 3: Allocate Overhead Costs to Products

For Component C1:

Machining: 4,000 hours × $8.00/hour = $32,000
Set-ups: 40 runs × $400/run = $16,000
Material Handling: 60 requisitions × $400/requisition = $24,000
Total Overhead for C1: $32,000 + $16,000 + $24,000 = $72,000

For Component C2:

Machining: 6,000 hours × $8.00/hour = $48,000
Set-ups: 80 runs × $400/run = $32,000
Material Handling: 90 requisitions × $400/requisition = $36,000
Total Overhead for C2: $48,000 + $32,000 + $36,000 = $116,000 (Check: $72,000 + $116,000 = $188,000, which matches total overheads)

Step 4: Calculate Full Cost Per Unit

For Component C1:

Direct Costs per unit: $25 (material) + $15 (labour) = $40.00
Overhead per unit: $\frac{\text{\textdollar}72,000}{2,000 \text{ units}} = \text{\textdollar}36.00$
Full Cost per unit (C1): $40.00 + $36.00 = $76.00

For Component C2:

Direct Costs per unit: $30 (material) + $10 (labour) = $40.00
Overhead per unit: $\frac{\text{\textdollar}116,000}{5,000 \text{ units}} = \text{\textdollar}23.20$
Full Cost per unit (C2): $40.00 + $23.20 = $63.20

Worked example 2

Deluxe Gadgets Ltd produces two products: a Standard model and a Premium model. Total overheads are $150,000. The company currently uses direct labour hours to absorb overheads. Total direct labour hours are 10,000.

Product Data:

	Standard	Premium
Annual Production (units)	8,000	2,000
---	---	---
Direct Cost per unit	$30	$50
Direct Labour Hours per unit	1.0	1.0

Management is considering ABC. Overheads have been analysed:

Activity	Cost ($)	Cost Driver	Standard	Premium
Machining	80,000	Machine Hours	4,000	2,000
---	---	---	---	---
Quality Control	70,000	No. of Inspections	150	200

Required: (a) Calculate the overhead cost per unit for each product using the traditional method (direct labour hours). (b) Calculate the full cost per unit for each product using ABC. (c) Comment on the difference in the unit costs.

Show solution outline

(a) Traditional Absorption Costing

Step 1: Calculate Overhead Absorption Rate (OAR)

Total Direct Labour Hours = (8,000 units × 1.0 hr) + (2,000 units × 1.0 hr) = 10,000 hours
OAR = $\frac{\text{Total Overheads}}{\text{Total Direct Labour Hours}} = \frac{\text{\textdollar}150,000}{10,000 \text{ hours}} = \text{\textdollar}15 \text{ per direct labour hour}$

Step 2: Calculate Overhead Cost per Unit

Standard: 1.0 DLH/unit × $15/DLH = $15.00
Premium: 1.0 DLH/unit × $15/DLH = $15.00

(b) Activity Based Costing

Step 1: Calculate Cost Driver Rates

Total Machine Hours = 4,000 + 2,000 = 6,000 hours
Total Inspections = 150 + 200 = 350 inspections
Machining Rate: $\frac{\text{\textdollar}80,000}{6,000 \text{ hours}} = \text{\textdollar}13.33 \text{ per machine hour}$
Quality Control Rate: $\frac{\text{\textdollar}70,000}{350 \text{ inspections}} = \text{\textdollar}200 \text{ per inspection}$

Step 2: Allocate Overheads and Calculate Full Unit Cost For Standard Model (8,000 units):

Machining: 4,000 MH × $13.33/MH = $53,320
Quality Control: 150 inspections × $200/inspection = $30,000
Total Overhead = $53,320 + $30,000 = $83,320
Overhead per unit = $\frac{\text{\textdollar}83,320}{8,000 \text{ units}} = \text{\textdollar}10.42$
Full Cost per unit: $30 (Direct) + $10.42 (Overhead) = $40.42

For Premium Model (2,000 units):

Machining: 2,000 MH × $13.33/MH = $26,660
Quality Control: 200 inspections × $200/inspection = $40,000
Total Overhead = $26,660 + $40,000 = $66,660
Overhead per unit = $\frac{\text{\textdollar}66,660}{2,000 \text{ units}} = \text{\textdollar}33.33$
Full Cost per unit: $50 (Direct) + $33.33 (Overhead) = $83.33 (Note: Total ABC overheads = $83,320 + $66,660 = $149,980. The small difference from $150,000 is due to rounding the machining rate.)

(c) Commentary

The traditional method allocated an equal overhead cost ($15.00) to both products because they use the same number of direct labour hours. This under-costs the complex Premium model and over-costs the simpler Standard model.

ABC reveals that the Premium model is significantly more expensive to produce ($83.33 vs. traditional full cost of $65). This is because it consumes a disproportionately high amount of the expensive quality control activity (200 of 350 inspections for only 20% of the units). Pricing based on the traditional cost would likely lead to the Premium model being sold at a loss or a very low margin.

Activity Based Costing — practice questions