Relevant Costs for Specific Decisions: Materials, Labour, Equipment and Overheads

A company is asked to quote for a one-off contract. The finance team prices it from the standard cost card: materials at the cost recorded in stock, labour at the standard rate, overhead at the full absorption rate. The price looks fair.

But the stock was bought at last year’s prices and will cost more to replace, the labour is on a fixed wage and is idle half the week. The overhead rate includes costs that will be paid whether the contract is won or not. The standard cost card answers a different question.

The question for a quote is: what is the lowest price at which the contract adds to the company’s cash? This topic shows how to find the relevant cost of materials, labour, equipment and overheads for a decision, using the tests from the previous topic, and how to turn them into a minimum price. It builds on the relevant costs and opportunity cost topic.

The next topic starts cost-volume-profit analysis with break-even and margin of safety.

Materials, labour and equipment

Materials

The relevant cost of materials is the additional cash that will be paid, or the benefit lost, by using them for the purpose in question. The historical cost of stock is a sunk cost and is never the relevant cost. The rules are:

• Not held in stock: the relevant cost is the purchase cost.
• Held in stock and in regular use: if used for the contract, the stock must be replaced for other work, so the relevant cost is the replacement cost.
• Held in stock and not in regular use: the relevant cost is the benefit that would be lost by using them: either the net disposal (scrap) value, or the benefit of any alternative use, such as the purchase cost avoided by using them as a substitute. Use the higher.

These are the deprival value of the materials: what the company would lose if it were deprived of them. If only part of the quantity is in stock, apply the rule to the part in stock and add the purchase cost of the rest.

Labour

The relevant cost of labour is the additional cash spent, or saved, as a direct result of the decision.

• Variable cost, not in short supply (for example part-time staff paid by the hour): the relevant cost is the pay.
• Fixed cost with spare capacity: the relevant cost is zero. Idle time would be paid for anyway.
• In limited supply: the relevant cost is the pay plus the contribution lost by moving the labour from its next best use. If the work could instead be done by paying overtime, use the lower of the two alternatives.

Equipment

The book value of equipment is irrelevant. If a machine would be sold if it were not used for the project, the relevant cost is its sale value now less its sale value after the project. If it would be kept in any case, the relevant cost is the fall in its resale value, plus any extra running or repair cost.

Overheads, and turning relevant costs into a price

Overheads follow the same rule: only future cash that the decision changes is relevant.

• Fixed overhead absorption rate: not relevant. Absorption is not spending, and the cash will be spent whether or not the contract is taken.
• Variable overhead rate: usually relevant, because it estimates the cash spent on each extra hour worked.
• Extra fixed costs: relevant if they are extra cash spending caused by the decision (for example supervisor overtime or hire of a machine), or cash saved.

Adding the relevant costs of materials, labour, equipment and overheads gives the minimum price at which the contract does not reduce the company’s cash. The company will usually quote above this, to earn a contribution. The difference between the price and the relevant cost is the cash benefit of the contract.

Points to watch

• The question may not say whether materials are in regular use. If the stock was bought for the contract, or arises from a decision no longer to use them, treat them as not in regular use. If the company regularly buys them, treat them as in regular use.
• When labour has spare capacity only for part of the time, apply the zero rule to that part and the scarce rule to the rest.
• Compare two ways of finding extra labour (overtime or diverting) and choose the cheaper, then say which you chose.
• Say why each excluded item is excluded: that is where marks are earned.

Layouts

1. Materials in regular use: quantity × current replacement price.
2. Materials not in regular use: stock quantity × scrap value per unit (or best alternative) + extra quantity × purchase price.
3. Scarce labour: hours × (pay per hour + contribution lost per hour) compared with hours × overtime rate; choose the lower.
4. Spare labour: hours × zero.
5. Equipment: sale value now − sale value after use.
6. Variable overhead: hours × variable rate. Extra fixed cash costs: as given.
7. Minimum price = total of relevant costs.

Money is in naira and answers are exact.

Worked examples

1. Material A.
   Regular use, so replacement cost: 3,000 × 380 = ₦1,140,000.
   The ₦350 stock cost is sunk.
2. Material B in stock. Not in regular use, so the scrap value forgone: ₦120,000. The cost of ₦210,000 is sunk.
3. Material B to be bought.
   1,200 − 800 = 400 kg × 260 = ₦104,000.
   Material B total 120,000 + 104,000 = ₦224,000.
4. Total relevant cost of materials.
   1,140,000 + 224,000 = ₦1,364,000.

1. Department 1. Spare capacity: relevant cost zero.
2. Department 2.
   Overtime: 260 × 150% = ₦390 an hour.
   Diverting: 260 + 90 = ₦350 an hour.
   Divert, as it is cheaper: 80 × 350 = ₦28,000.
3. Department 3.
   Contribution lost per hour 300 ÷ 2.5 = ₦120.
   Relevant cost per hour 240 + 120 = ₦360.
   200 × 360 = ₦72,000.
4. Total relevant cost of labour.
   0 + 28,000 + 72,000 = ₦100,000.

1. Machine.
   21,000 − 12,000 = ₦9,000.
   The cost of ₦180,000 and the book value are ignored.
2. Variable overhead.
   500 × 45 = ₦22,500, a cash cost per hour.
3. Fixed overhead absorbed.
   500 × 60 = ₦30,000.
   Not relevant.
4. Supervision overtime. ₦8,000 extra cash, relevant.

Expect variants: a contract priced for a minimum quote, labour partly spare, materials that can be used as a substitute for something else, and a question that asks you to compare the relevant cost with the offered price.

Items that often appear in decision questions

Machine. Depreciation is not a cash flow and is irrelevant. If using the machine lowers its resale value, the fall in resale value is the relevant cost: resale value ₦90,000, falling ₦200 for each 1,000 units; 30,000 units cost 30 × 200 = ₦6,000. Materials with no other use that would otherwise be thrown away at a cost: using them avoids the disposal cost, which is a benefit (20,000 kg, disposal ₦400 per 5,000 kg, avoids ₦1,600); the original cost is sunk.

Materials with an alternative use are charged at what they would save elsewhere (the price of the item they would replace), not at original or replacement cost. Labour already paid and redeployed costs nothing extra, but contract labour or overtime for extra output is relevant.

Salaries and redundancy: a manager’s salary and redundancy pay are relevant if shutting down avoids the salary or causes the redundancy cost; general fixed overheads and apportioned non-production costs are not relevant.

A minimum quotation schedule, and why relevant costing is not enough in the long term

Example. A contract needs 800 kg of Material Y (300 kg in stock bought at ₦400; regular use; replacement cost ₦450; resale value ₦250), 300 hours of workers on a guaranteed wage with spare capacity, 60 hours of engineers, a machine for 7 weeks, a specially developed component and 400 kg of another material costing ₦400,000. The engineers are at full capacity: overtime costs ₦4,000 an hour, or they could leave a product that earns ₦90,000 per 20 hours.

The machine hire already paid has 3 weeks left; another block of 10 weeks costs ₦900,000, or a machine can be bought for ₦9m and sold for ₦8m. The component cost ₦2m to make and its use means missing an exhibition (fee for non-attendance ₦100,000) but the sales it would have won can still be made.

• Material Y:
  in regular use, so valued at replacement cost: 800 × 450 = ₦360,000 (the original cost is sunk; resale value is irrelevant).
• Workers: paid anyway: nil.
• Engineers:
  overtime 60 × 4,000 = ₦240,000, against lost contribution 3 units × 90,000 = ₦270,000: take the lower, ₦240,000.
• Machine: rent block ₦900,000, against buy and sell ₦1,000,000: take ₦900,000 (the first payment is sunk).
• Component: cost is sunk; the relevant cost is the fee ₦100,000; the chief executive’s salary and time are not relevant.
• Other material: ₦400,000.
• Excluded: hospitality already spent (sunk), absorbed fixed overhead and the normal mark-up.

Minimum price = 360,000 + 240,000 + 900,000 + 100,000 + 400,000 = ₦2,000,000. This price gives no profit and no contribution to fixed costs, so it is not sustainable in the long term, when the business needs to cover all costs, earn the return that investors expect and consider market conditions. It is suited to a one-off order to enter a market.

Mutually exclusive contracts, and why relevant-cost and routine job-cost results differ

For two contracts of which only one can be done, list for each the incremental revenue and savings (including the sale or alternative use of materials released and the penalty for cancelling the other) and the incremental costs, and choose the higher net figure. Example (₦m). Delta: price 9.0; Echo: price 10.0. Choosing Delta releases Echo’s materials (held 0.8, contracted 1.4), which could replace material normally costing 20% less on another job: saving 80% × 2.2 = 1.76.

Choosing Echo lets Delta’s stock be sold for 1.2. Materials already contracted for must be paid whichever is chosen, so are not incremental. Delta: materials to buy 1.5, labour 3.0, penalty for cancelling Echo 0.5. Echo: materials to buy 1.0, labour 2.4, penalty for cancelling Delta 0.9. Delta: 9.0 + 1.76 − (1.5 + 3.0 + 0.5) = 5.76. Echo: 10.0 + 1.2 − (1.0 + 2.4 + 0.9) = 6.90. Take Echo, by 1.14m. Fixed salaries, head office costs and notional interest are left out.

Also consider: the reliability of the estimates (the difference is small, so test sensitivity), whether the alternative use of materials will really arise, goodwill and future contracts, and whether the constraints that make the contracts exclusive can be overcome.

Relevant-cost profit against routine job-cost profit. A job-costing report shows a different result because it charges:

• labour that is paid anyway (idle time) that is not incremental
• materials at book value, not replacement cost or realisable value
• a share of fixed overhead that would be incurred anyway (and at a recalculated absorption rate)
• it ignores contribution lost on other products and fixed costs avoided

A contract can show a loss in the job-cost report yet add to profit on a relevant-cost basis, so the decision should use relevant costs.

More items from a contract estimate

Material in stock with no alternative use (book value ₦50,000, replacement price ₦90,000, scrap value ₦30,000): the relevant cost is the scrap value forgone, ₦30,000. Material bought in bulk when only 70% will be used and the rest has no use: the relevant cost is the whole bulk price (₦80,000), not 70% of it.

Skilled labour in short supply working at weekends: the premium (30% above the normal rate) is incremental, and the normal-rate cost is relevant if the hours must be bought or other work given up. Idle unskilled labour: only the incremental pay is relevant (for instance, time off in lieu for weekend hours). Equipment rented out when not used: the relevant cost is the contribution lost, not the rent.

Non-monetary factors before accepting: publicity and goodwill, future work from the client, effect on existing customers and capacity, staff morale from overtime, and the standing of a public-sector client.

Hire or buy a machine, recruit or replace labour, and why reported profit differs

Machine. Compare hiring with buying and then renting out the idle time. Hire: 10 weeks × ₦40,000 = ₦400,000. Buy: cost ₦2.5m less resale ₦1.5m = ₦1.0m, less rental income 30 weeks × ₦25,000 = ₦0.75m, net ₦250,000: take the lower, ₦250,000. Running costs of the weeks used are relevant; depreciation is not. Skilled labour. Recruiting costs ₦120 an hour; transferring existing staff costs nothing extra in pay (they are paid anyway) but their replacement on the old work costs ₦110: take the lower, ₦110.

Supervisor: salary and unpaid overtime are not incremental; a bonus paid only if the project goes ahead is relevant. Material part in stock: the stock is charged at resale value (5,000 × ₦20 = ₦100,000) and the remainder at current purchase price (5,000 × ₦50 = ₦250,000).

Why the year-end profit report differs from the profit built into the quotation: it includes depreciation and absorbed overheads, charges materials at inventory valuation rather than relevant cost, and charges staff for their time on the project. Why contribution is the basis: decisions change activity, and the relevant items are those that change with it.

Opportunity cost matters because resources are scarce, so each use must be compared with the best alternative forgone, especially when several resources are scarce at once.

Common mistakes

• Using the stock record cost. It is sunk. Use replacement or scrap value.
• Charging spare fixed labour. It costs nothing extra.
• Forgetting lost contribution when labour is scarce.
• Adding the absorbed fixed overhead. It is not cash caused by the decision.
• Using book value for the machine. Use the sale values.
• Not choosing the cheaper way to find labour. Compare overtime with diversion.

Quick revision

• Materials: not in stock, purchase; in stock regular, replacement; in stock not regular, scrap or alternative use.
• Labour: spare, zero; scarce, pay plus lost contribution or overtime if cheaper.
• Equipment: sale value now less sale value after use.
• Overhead: fixed absorption not relevant; variable rate relevant; extra fixed cash relevant.
• Minimum price = sum of relevant costs.

How the marks are earned

• Calculate: a mark for each resource, with the right rule and the figure.
• Explain exclusions: a mark for each item left out, with the reason.
• Advise: compare the price with the relevant cost and state the decision.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

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