6.2 Overhead Absorption Rates: Per Unit, Per Labour Hour and Per Machine Hour

6.2 Overhead Absorption Rates: Per Unit, Per Labour Hour and Per Machine Hour

Key Concept: Overhead absorption (or overhead recovery) is the mechanism by which indirect production overheads accumulated in production cost centres are charged into individual cost units. To avoid the delays and distortions of historical actual figures, management accountants establish Predetermined Overhead Absorption Rates (OARs) at the start of the budget period based on budgeted expenditure and budgeted activity.

Fundamentals and Rationale of Overhead Absorption

Once each production cost centre has a budgeted overhead total (Section 6.1 explains where it comes from; in PCTN tasks it is given to you), the final stage is Overhead Absorption. A standard textbook definition of overhead absorption is:

"The charging of overheads to cost units by means of rates calculated in relation to suitable bases."

Why Absorption Costing is Essential

1. Financial Reporting Compliance (IAS 2 / FRS 102): Under UK and International accounting standards, the valuation of inventory (closing work-in-progress and finished goods) on the Statement of Financial Position must include not only prime costs (direct materials and direct labour) but also a systematic allocation of fixed and variable production overheads incurred in converting materials into finished goods.
2. Determining Comprehensive Cost of Production: To establish whether a product line is profitable, management must understand its total cost. Ignoring indirect overheads risks pricing goods below full cost, leading to unintended operational losses.
3. Guiding Pricing Decisions: In industries using cost-plus contracts (such as bespoke engineering, construction, and government defence procurement), commercial selling prices are established by adding a target profit mark-up to full absorption cost.

---

Why Use Predetermined Rates Instead of Actual Rates?

A foundational question in cost accounting is: Why do businesses calculate predetermined overhead absorption rates at the beginning of the year using estimates, rather than calculating actual rates at the end of the year using historical figures?

Waiting until the end of the financial year to establish actual overhead rates creates severe commercial and operational problems:

1. Lack of Timeliness for Day-to-Day Operations: A business cannot wait until the financial year ends on 31 December to quote a selling price to a customer in February, or to invoice a completed bespoke fabrication in May. Managers need immediate cost figures every single day.
2. Erratic Seasonal Fluctuations in Expenditure: Actual overhead expenditures do not occur smoothly across the year. Factory heating and lighting bills are substantially higher in January than in July; machinery maintenance overhauls often take place during the annual August factory shutdown; quarterly rent and annual insurance premiums fall due at irregular intervals. If actual monthly overheads were absorbed into monthly output, identical products manufactured in January would carry significantly higher unit overhead costs than those made in July.
3. Distortions Caused by Monthly Volume Fluctuations: Fixed overhead costs (such as factory rent, rates, and depreciation) remain constant regardless of short-term output. If output drops in December due to Christmas holidays, dividing fixed overheads by fewer units would cause the calculated actual unit overhead rate to skyrocket, paradoxically making products seem most expensive to produce when factory activity is at its lowest.
4. Providing a Fixed Cost Benchmark: Predetermined rates establish standard targets against which actual performance can be benchmarked, enabling variance analysis and managerial cost control.

---

The Predetermined Overhead Absorption Rate Formula

The universal mathematical formula for calculating a Predetermined Overhead Absorption Rate (OAR) is:

$\text{Predetermined OAR} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Activity Level (Absorption Base)}}$

Where:

• Budgeted Production Overhead: The projected indirect manufacturing expenses for the department for the upcoming budget period (derived from Stage 1 and Stage 2 budget schedules).
• Budgeted Activity Level: The anticipated volume of activity (expressed in labour hours, machine hours, or units) planned for that department during the same period.

---

Selecting the Appropriate Absorption Base

The choice of absorption base is critical. The base should reflect the primary operational driver that causes overheads to be incurred in that specific production department.

1. Direct Labour Hour Rate

$\text{OAR per Direct Labour Hour} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Direct Labour Hours}}$

• Best Environment: Labour-intensive production cost centres where skilled or semi-skilled operatives manually manufacture, assemble, or finish products using hand tools.
• Operational Justification: Overheads such as factory supervision, canteen, lighting, and general factory operating costs correlate directly with the human labour hours worked.

2. Machine Hour Rate

$\text{OAR per Machine Hour} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Machine Hours}}$

• Best Environment: Capital-intensive, automated, or mechanized production cost centres (such as CNC machining bays, automated bottling plants, or chemical process lines).
• Operational Justification: The predominant overheads in automated bays—machinery depreciation, electric power, machinery insurance, cutting tooling, and technical maintenance—are driven by running the machines, not by manual labour.

3. Unit of Output Rate

$\text{OAR per Unit} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Units of Output}}$

• Best Environment: Continuous manufacturing facilities producing a single, homogeneous, standardized product (e.g. brickworks, cement plants, sugar refineries).
• Operational Justification: When every unit produced is identical and consumes exactly the same resources and processing time, overheads can be divided equally across units. It is totally unsuitable for factories making diverse or bespoke products.

4. Percentage of Direct Labour Cost

$\text{OAR (\% of Direct Labour Cost)} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Direct Labour Cost}} \times 100\%$

• Limitations: Distorts product costs if workers are paid different hourly rates for reasons unrelated to overhead usage. For example, a senior master craftsman earning £25/hour using a basic manual bench would attract 2.5 times more overhead than an apprentice earning £10/hour, even though both consume identical factory overhead resources.

5. Percentage of Direct Material Cost

$\text{OAR (\% of Direct Material Cost)} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Direct Material Cost}} \times 100\%$

• Limitations: Highly problematic because commodity material prices fluctuate independently of factory overheads. A product made from expensive titanium would absorb ten times more factory rent and lighting overhead than an identical product made from carbon steel, which is completely irrational.

6. Percentage of Prime Cost

$\text{OAR (\% of Prime Cost)} = \frac{\text{Budgeted Production Overhead}}{\text{Budgeted Prime Cost (Direct Materials + Direct Labour)}} \times 100\%$

• Limitations: Combines the distortions of both material cost and labour cost methods.

---

Comparison of Overhead Absorption Bases

The following table summarizes the primary absorption bases:

---

PCTN-Style Task: Comparing the Three Bases

PCTN names three absorption bases: per unit, per labour hour and per machine hour. The percentage-of-cost bases above appear in some textbooks, but the PCTN specification does not list them. A typical task gives you one set of budgeted figures and asks for all three rates.

Dales Kitchenware Ltd makes two products, a pan (A) and a casserole dish (B), in one production department. Its budget shows:

Absorption rates:

• Per unit: £96,000 ÷ 12,000 units = £8.00 per unit
• Per labour hour: £96,000 ÷ 8,000 hours = £12.00 per labour hour
• Per machine hour: £96,000 ÷ 4,800 hours = £20.00 per machine hour

Overhead absorbed per unit of each product:

Every basis absorbs the full £96,000 at budgeted activity. For example, on the labour hour basis, 8,000 × £6.00 plus 4,000 × £12.00 comes to £96,000. But the per-unit basis charges both products the same £8.00, even though B takes twice as long to make and uses twice the machine time. A per-unit rate is only fair when all units are identical. When products differ, a time-based rate charges each product for the resources it actually uses.

If Product B uses £14.00 of direct materials and 1 labour hour at £15.00 per hour, its unit cost on the labour hour basis is £14.00 + £15.00 + £12.00 = £41.00.

---

Blanket (Plant-Wide) Rates versus Departmental Rates

• Blanket (Plant-Wide) Rate: A single overhead absorption rate calculated for the entire factory (Total Factory Budgeted Overhead ÷ Total Factory Budgeted Activity). While computationally fast, blanket rates are only accurate if all products spend roughly identical time in all departments, or if the departments have similar cost structures. In practice, blanket rates cause massive cost cross-subsidization.
• Departmental Absorption Rates: Separate, tailored OARs calculated for each individual production department (e.g. machine hour rate for Machining, labour hour rate for Assembly). This ensures products that spend 10 hours in Machining and 1 hour in Assembly absorb overheads reflecting the actual facilities consumed.

---

Comprehensive Worked Example: Calculating OARs and Absorbing Overheads

To see how predetermined rates work in practice, examine Ribble Valley Manufacturing Ltd, an engineering firm in Preston with two production cost centres: Machining (capital-intensive CNC milling) and Assembly (labour-intensive manual assembly).

1. Annual Departmental Budgets

For the upcoming financial year, the management accountant prepares the following departmental budgets:

2. Establishing Predetermined OARs

• Machining Department: Because Machining is automated and capital-intensive, machine hours represent the primary cost driver. $\text{Machining OAR} = \frac{£180,000}{20,000 \text{ machine hours}} = £9.00 \text{ per machine hour}$
• Assembly Department: Because Assembly is manual and labour-intensive, direct labour hours represent the primary cost driver. $\text{Assembly OAR} = \frac{£120,000}{15,000 \text{ direct labour hours}} = £8.00 \text{ per direct labour hour}$

---

3. Absorbing Overheads into a Specific Cost Unit: Job 604

The company receives an order for Job 604, a bespoke specialist conveyor drive unit. The job cost sheet records the following direct expenditures and operating times:

• Direct Materials: 40 kg specialized alloy steel @ £8.50/kg (£340.00) plus pre-machined internal gears (£160.00) = £500.00
• Direct Labour:
  • Machining: 3.0 direct labour hours @ £18.00/hour = £54.00
  • Assembly: 8.0 direct labour hours @ £15.00/hour = £120.00
  • Total Direct Labour: £174.00
• Prime Cost: £500.00 + £174.00 = £674.00

Calculating Production Overhead Absorption:

• Machining Department Overhead Absorbed: Job 604 required 6.0 machine hours on the CNC milling centres. $\text{Absorbed Machining Overhead} = 6.0 \text{ machine hours} \times £9.00 = £54.00$
• Assembly Department Overhead Absorbed: Job 604 required 8.0 direct labour hours in the assembly shop. $\text{Absorbed Assembly Overhead} = 8.0 \text{ direct labour hours} \times £8.00 = £64.00$
• Total Production Overhead Absorbed: £54.00 + £64.00 = £118.00

Full Product Cost Build-Up and Pricing:

This calculation highlights the power of predetermined absorption rates: the company was able to quote an accurate, profitable commercial price of £1,138.50 immediately upon receiving the specification, fully covering all manufacturing and administrative overheads.

---

Common Exam Pitfalls and Practical Traps

• Trap 1: Using Actual Hours to Calculate the Predetermined OAR. A predetermined rate is set before the financial period starts. You must always divide Budgeted Overhead by Budgeted Activity. Actual figures are only used later during the period to calculate the overhead absorbed.
• Trap 2: Mismatching Departmental Bases. In an automated machine shop, never absorb overheads using labour hours. In a manual assembly shop, never absorb overheads using machine hours. Match the base to the department's operational nature.
• Trap 3: Forgetting to Multiply Actual Activity by the OAR. To calculate overhead absorbed into a job, multiply the actual hours consumed by that job by the predetermined hourly rate. Do not use the budgeted hours of the job.