12.2 Relevant Costs of Materials, Labour, and Overheads

Determining the relevant cost of operational resources requires applying specific decision logic to each cost element: direct materials, direct labour, and production overheads. Rather than relying on standard rates or historical ledger entries, the management accountant must examine the current availability, operational deployment, and alternative uses of each resource.

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1. Direct Materials Decision Framework

When a specific contract or operational decision requires raw materials, the relevant cost depends entirely on whether the material is currently held in inventory and, if so, whether it is in regular ongoing use.

Case 1: Material Not in Stock

If the material is not currently held in inventory, the business must purchase it on the open market. The relevant cost is the current purchase (replacement) price paid to suppliers, including any necessary delivery or inward freight charges.

Case 2: Material Held in Stock and in Regular Ongoing Use

If the material is already held in warehouse inventory and is continuously consumed by the company's regular product lines, taking units from stock for a special project depletes the inventory. To maintain normal operations, the company must purchase replacement units from the supplier. Therefore, the relevant cost is the current replacement price, NOT the original historical cost paid when the material was bought.

Case 3: Material Held in Stock with No Regular Use (Surplus or Obsolete)

If the material was purchased for a prior discontinued contract and has no ongoing use in normal production, using it for the proposed project does not trigger a replacement purchase. Instead, the relevant cost is the opportunity cost of what the business gives up by consuming it:

1. Scrap Sale: The net realizable value (NRV) obtained by selling the material to a scrap dealer.
2. Alternative Substitution: The net cost savings achieved by modifying the material to replace another standard raw material in another department.
3. Decision Rule: The relevant cost is the higher of the Net Realizable Scrap Value and the Net Value in Alternative Use (the best forgone economic alternative).

Case 4: Obsolete Material Incurring Disposal Costs

Occasionally, surplus chemical or hazardous materials incur legal environmental disposal fees if discarded. If utilizing the material in a new contract safely neutralizes or consumes it, the company avoids paying the disposal fee. This avoided cash outflow is treated as a negative relevant cost (a cash saving / benefit) that reduces the total cost of the contract.

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2. Direct Labour Decision Framework

Direct labour is not automatically a variable cost. In modern business, employment contracts, union agreements, and labor regulations often mean that the basic workforce is paid a fixed salary regardless of actual production output. The relevant cost of labour depends strictly on spare capacity and operational constraints.

Condition 1: Casual or Temporary Labour

If the company hires casual workers, freelancers, or subcontractors specifically for the contract, the entire wage payment is an incremental cash outflow. The relevant cost is the gross wage rate paid.

Condition 2: Permanent Workforce with Spare (Idle) Capacity

If permanent employees are under-utilized and have sufficient idle time to complete the work during normal paid hours, their basic wages will be paid regardless of whether the project is accepted. No additional cash leaves the company bank account. Therefore, the relevant cost of utilizing idle permanent labour is $0 (nil).

Condition 3: Permanent Workforce at Full Capacity with Overtime Permitted

If permanent employees are fully occupied but management can schedule overtime shifts to complete the project, the incremental cash outflow is the overtime wage rate (basic wage plus overtime premium):

$$\text{Relevant Cost per Hour} = \text{Overtime Hourly Wage Rate}$$

Condition 4: Permanent Workforce at Full Capacity with Overtime NOT Permitted (Diverted Labour)

If the workforce is working at 100% capacity and overtime cannot be worked (due to factory operating limits, union rules, or safety legislation), the only way to perform the project is to divert workers away from producing another profitable product (Product X).

Diverting labour causes the business to lose the sales revenue of Product X while saving Product X's direct materials and variable overheads. The net cash lost is Product X's contribution forgone:

$$\text{Contribution Forgone per Hour} = \frac{\text{Selling Price of Product X} - \text{Variable Costs of Product X}}{\text{Direct Labour Hours Required per Unit of Product X}}$$

When evaluating the project, the relevant cost per direct labour hour is:

$$\text{Relevant Cost per Diverted Hour} = \text{Direct Wages Paid on Project} + \text{Contribution Forgone per Hour}$$

Alternatively, if the company continues paying normal wages to the diverted workers, the incremental cash effect on the company as a whole is: $\text{Direct Wages Paid} + \text{Lost Contribution} - \text{Normal Wages Paid} = \text{Lost Contribution of Diverted Production}$. When preparing a full contract cost build-up where the contract is charged for labour wages, the candidate must add the opportunity cost (lost contribution) to the labor charge.

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3. Relevant Costs of Overheads

Overheads represent indirect production expenditures and are divided into variable and fixed categories:

Variable Production Overheads

Variable overheads (machine power, cutting lubricants, consumables) vary directly with production activity. If undertaking the project requires operating machines for 100 hours at a variable overhead rate of $4 per hour, the $400 expenditure represents an incremental cash outflow and is 100% relevant.

Fixed Production Overheads

1. General Factory / Corporate Fixed Overheads: Building rent, property rates, factory insurance, and departmental management salaries that are absorbed into production using standard rates are non-relevant. Total fixed spending does not change.
2. Directly Attributable Incremental Fixed Overheads: Fixed expenditures incurred specifically and exclusively for the contract—such as renting a specialized testing rig for $2,500 or hiring an external site safety supervisor for $1,800—are relevant.

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4. Comprehensive Master Numerical Scenario: "Apex Engineering - Contract Titan"

Apex Engineering has received an invitation to submit a competitive tender for Contract Titan. The contract requires the following resources:

1. Direct Materials

• Material Alpha: 800 kg required. Apex has 1,200 kg in inventory, purchased six months ago for $14 per kg. Material Alpha is used continuously in regular production. The current supplier replacement price is $18 per kg. Its scrap value is $9 per kg.
• Material Beta: 400 units required. Apex holds 400 units in inventory from an aborted job. Original cost was $25 per unit. It has no ongoing use in normal production. It could be sold to a scrap merchant for $8 per unit. Alternatively, it could be modified using $3 per unit of labour to substitute for Material Gamma, which currently costs $16 per unit.
• Material Delta: 250 litres required. None in stock. Must be purchased from an overseas supplier at $30 per litre plus $500 total freight for the batch.
• Material Epsilon: 60 drums required. Apex has 60 drums in stock of an obsolete toxic solvent. Under environmental regulations, Apex must pay a hazardous waste contractor $10 per drum to dispose of it. Using it in Contract Titan safely consumes it without disposal fees.

2. Direct Labour

• Department 1 (Unskilled): 500 hours required. The workforce consists of permanent employees paid $16 per hour. Due to a seasonal lull, Department 1 currently has 700 hours of idle time available.
• Department 2 (Semi-Skilled): 300 hours required. The department operates at full capacity. Overtime is permitted and is paid at time-and-a-half ($\text{\textdollar}20 \times 1.5 = \text{\textdollar}30$ per hour).
• Department 3 (Skilled Technicians): 200 hours required. Technicians are paid $24 per hour and operate at 100% capacity. Overtime is strictly prohibited. The only way to fulfill Contract Titan is to divert technicians from producing standard Product Z. Product Z sells for $110, incurs direct materials of $40, variable overhead of $10, and requires 2 hours of Department 3 labour. Product Z's contribution after charging its labour is $110 − $40 − $10 − (2 × $24) = $12 per unit, or $6 per technician hour.

3. Overheads

• Variable overhead is incurred at $5 per direct labour hour worked.
• General factory fixed overhead is absorbed at a standard rate of $12 per direct labour hour.
• Specialized diagnostic machinery must be hired specifically for Contract Titan at a cost of $3,200.

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Step-by-Step Evaluation and Solution

Direct Materials Analysis:

1. Material Alpha: In regular use $\rightarrow$ Relevant cost is current replacement price: $800 \text{ kg} \times \text{\textdollar}18 = \text{\textdollar}14,400$.
2. Material Beta: Obsolete stock. Compare scrap sale versus modification:
   • Scrap value: $400 \times \text{\textdollar}8 = \text{\textdollar}3,200$.
   • Net substitution value: $400 \times (\text{\textdollar}16 \text{ saved} - \text{\textdollar}3 \text{ labour}) = 400 \times \text{\textdollar}13 = \text{\textdollar}5,200$.
   • Higher alternative is substitution: Relevant cost is $5,200.
3. Material Delta: Not in stock $\rightarrow$ Current purchase price + freight: $(250 \text{ litres} \times \text{\textdollar}30) + \text{\textdollar}500 = \text{\textdollar}7,500 + \text{\textdollar}500 = \text{\textdollar}8,000$.
4. Material Epsilon: Hazardous waste avoided $\rightarrow$ Benefit / negative cost: $60 \text{ drums} \times -\text{\textdollar}10 = -\text{\textdollar}600$.

• Total Relevant Direct Material Cost: $\text{\textdollar}14,400 + \text{\textdollar}5,200 + \text{\textdollar}8,000 - \text{\textdollar}600 = \text{\textdollar}27,000$.

Direct Labour Analysis:

1. Department 1: Idle permanent workforce $\rightarrow$ Relevant cost is $0.
2. Department 2: Full capacity with overtime permitted $\rightarrow 300 \text{ hours} \times \text{\textdollar}30 = \text{\textdollar}9,000$.
3. Department 3: Full capacity with labour diverted from Product Z:
   • Direct wages paid: $200 \text{ hours} \times \text{\textdollar}24 = \text{\textdollar}4,800$.
   • Lost contribution from Product Z:

$$\text{Units of Z lost} = \frac{200 \text{ hours}}{2 \text{ hours/unit}} = 100 \text{ units}$$ $$\text{Contribution per unit of Z} = \text{Selling Price} - \text{Variable Costs} = \text{\textdollar}110 - \text{\textdollar}40 - \text{\textdollar}10 - (2 \times \text{\textdollar}24) = \text{\textdollar}12$$ $$\text{Total Lost Contribution} = 100 \text{ units} \times \text{\textdollar}12 = \text{\textdollar}1,200$$

• Total relevant cost of Dept 3: $\text{\textdollar}4,800 \text{ wages} + \text{\textdollar}1,200 \text{ opportunity cost} = \text{\textdollar}6,000$.
• Total Relevant Direct Labour Cost: $\text{\textdollar}0 + \text{\textdollar}9,000 + \text{\textdollar}6,000 = \text{\textdollar}15,000$.

Overheads Analysis:

1. Variable Overheads: Incurred on incremental hours worked:
   • Dept 1 hours worked on contract: 500 hours
   • Dept 2 hours worked on contract: 300 hours
   • Dept 3 hours worked on contract: 200 hours
   • Total hours = $500 + 300 + 200 = 1,000 \text{ hours} \times \text{\textdollar}5 = \text{\textdollar}5,000$. (Product Z's own variable overhead is already reflected in the $12 contribution forgone, so the contract is charged the variable overhead on all 1,000 hours it actually uses.)
2. General Absorbed Fixed Overhead: Standard rate of $12/hour is non-relevant: $0.
3. Specific Diagnostic Machine Hire: Directly attributable incremental fixed cost: $3,200.

• Total Relevant Overheads: $\text{\textdollar}5,000 + \text{\textdollar}3,200 = \text{\textdollar}8,200$.

Total Relevant Cost of Contract Titan:

$$\text{Total Relevant Cost} = \text{\textdollar}27,000 \text{ (Materials)} + \text{\textdollar}15,000 \text{ (Labour)} + \text{\textdollar}8,200 \text{ (Overheads)} = \text{\textdollar}50,200$$