Relevant Cost Analysis: formula sheet

Key formulas

Relevant cost of a decision

Relevant cost = Future incremental cash cost + Opportunity cost

Use only costs that change because of the decision.

Opportunity cost of a resource

Opportunity cost = Contribution or benefit lost from the best alternative use

Applies when the resource is scarce or already in use. If it is in surplus with no other use, it is nil.

Relevant cost of material

Material in regular use: current replacement cost. Material in stock, not needed again: higher of resale value and cost of alternative use (else nil). Material in stock needed again: replacement cost.

Historical cost is never relevant by itself.

Relevant cost of labour

Spare capacity: nil extra cost if wages are fixed. Fully utilised: wages paid + contribution lost elsewhere

Extra labour hired is charged at its additional pay.

Incremental analysis

Incremental profit = Incremental revenue − Incremental (relevant) cost

Accept the alternative with positive and higher incremental profit.

Relevant cost of making (per unit)

Variable cost + avoidable fixed cost per unit + opportunity cost per unit

Use only costs that disappear or arise because of the decision. Unavoidable fixed cost is excluded.

Decision rule (spare capacity)

Make if relevant cost of making < purchase price; buy if purchase price < relevant cost of making

If the two are equal, decide on qualitative factors.

Opportunity cost of capacity

Contribution forgone from the best alternative use of the capacity released or used

Applies when capacity is limited. If buying frees capacity, the contribution earned from it is a benefit of buying.

Extra cost of buying per scarce hour (limited capacity)

(Purchase price − variable cost of making) ÷ scarce resource units per unit of component

Rank components by this figure. Buy those with the lowest extra cost per scarce unit first.

Net advantage of buying

Relevant cost of making − purchase price

Positive means buying saves money. Multiply by volume for the total.

Incremental profit

Incremental profit = Incremental revenue − Incremental (relevant) costs

Accept if the result is positive, subject to qualitative factors.

Relevant cost of the order

Relevant cost = Variable cost of the order + Additional fixed or specific costs + Opportunity cost

Opportunity cost is the contribution lost on regular sales displaced. It is zero with idle capacity.

Minimum acceptable price per unit

Minimum price = Relevant cost of the order ÷ Units in the order

With idle capacity and no extra fixed cost, this is the variable cost per unit. At this price profit is zero.

Opportunity cost at full capacity

Opportunity cost = Units displaced × Contribution per unit on regular sales

Use contribution, not profit, because fixed costs stay the same.

Material relevant cost

Stock material: replacement cost if it will be replaced; otherwise higher of resale value and use elsewhere. Material with no other use: disposal value or nil

Use current figures, not historical cost.

Contribution

Contribution = Sales − Variable costs

Variable costs include variable selling and distribution costs that stop on closure.

Net advantage of continuing

Advantage of continuing = Contribution − Avoidable fixed costs

If positive, continue. If negative, drop (before other factors).

Decision rule

Drop if Avoidable fixed costs saved > Contribution lost

Ignore unavoidable fixed costs and sunk costs; they are the same under both options.

With alternative use of capacity

Drop only if Avoidable fixed costs saved + Benefit from alternative use > Contribution lost

Add net cash gain from renting out or redeploying freed resources. Deduct one-time closure costs where relevant.

Shutdown point (short run)

Continue if Sales ≥ Variable costs + Avoidable fixed costs

Same rule stated as a break-even for closure.

Incremental revenue

Incremental revenue = Sales value after further processing − Sales value at split-off

Use total value for the quantity actually sold, after allowing for any loss or yield change in further processing.

Incremental profit from further processing

Incremental profit = Incremental revenue − Additional (avoidable) processing cost

Include only costs that change: extra materials, labour, variable overhead, avoidable fixed cost, extra packing or selling cost.

Decision rule

Process further if incremental profit > 0; otherwise sell at split-off

If it equals zero, you are indifferent, so qualitative factors decide.

Joint cost

Joint cost = irrelevant (same under both options)

Never allocate or deduct it when comparing the two options.

Indifference price

Break-even final price per output unit = (Split-off price per input unit + Relevant further processing cost per input unit) ÷ Output units per input unit

Use it when the question asks for the minimum final selling price that justifies further processing. Here, an input unit means one unit of split-off output that is put into further processing. Example (Kaveri Foods data): split-off price ₹90 per kg, relevant processing cost ₹80,000 ÷ 10,000 kg = ₹8 per kg, yield 90%. So (90 + 8) ÷ 0.9 = ₹108.89.

Contribution per unit

Contribution per unit = Selling price per unit − Variable cost per unit

Use only variable costs. Ignore fixed costs, apportioned overheads and sunk costs.

Contribution per unit of limiting factor

Contribution per limiting factor unit = Contribution per unit ÷ Units of scarce resource used per unit of product

Rank products from highest to lowest on this figure. Use it only when one resource is the single binding constraint.

Resource requirement

Resource needed = Units produced × Resource per unit

Compare total need at full demand with availability to confirm that the constraint actually binds.

Total contribution and profit

Profit = Σ (Units × Contribution per unit) − Fixed costs

Fixed costs are deducted once, after choosing the mix.

Opportunity cost of the scarce resource (one constraint)

Value of one extra unit of resource = Contribution per unit of resource of the marginal (last-ranked, partly produced) product

Valid for one constraint. Maximum price for extra resource = normal price per unit of resource + this opportunity value.

Two-constraint LP model

Maximise Z = c₁x₁ + c₂x₂ subject to a₁x₁ + a₂x₂ ≤ A, b₁x₁ + b₂x₂ ≤ B, x₁, x₂ ≥ 0

Check every corner point of the feasible region. The best one gives the optimal mix.

Relevant cost of material to be bought

Current purchase (replacement) price × quantity needed

Include carriage inward if it changes with the decision.

Relevant cost of stock material in regular use

Replacement cost × quantity used

Using it forces a future purchase.

Relevant cost of stock material not needed again

Higher of (resale value − selling cost) and (value in alternative use)

If neither exists, the cost is nil. Original cost is ignored.

Relevant cost of labour at full capacity

Wages paid for the job + contribution lost after deducting the labour wages

This equals the contribution lost before labour cost. Use one version only: if you add wages separately, the lost contribution must be after labour wages, otherwise the wages are counted twice.

Relevant cost of labour with spare capacity

Nil (if wages are fixed and idle time is paid anyway)

Add any extra cost such as overtime premium or hiring.

Replacement decision (incremental cash)

Relevant cost of keeping = future cash costs − resale value at the end; of replacing = new cost + future cash costs − resale value at the end − old machine sale value now

Book value and depreciation are excluded. Discount if the timings differ.

Quick revision

• A relevant cost is a future cost that differs between alternatives.
• Sunk costs are never relevant, whatever their size.
• Opportunity cost is the benefit lost from the next best use of a resource, and it is relevant.
• Make or buy: compare avoidable cost of making with the purchase price, not full absorption cost.
• If fixed costs are unavoidable, they do not affect make or buy.
• Special order: with spare capacity, relevant cost is the incremental cost; at full capacity, add lost contribution.
• Drop a product only if its contribution is less than the avoidable fixed costs saved, after effects on other products.
• Joint costs are irrelevant to the sell or process further decision.
• Process further if incremental revenue exceeds incremental processing cost.
• With one limiting factor, rank products by contribution per unit of the scarce resource.
• Material already in stock: use replacement cost if it will be replaced, otherwise the higher of resale value and use elsewhere.
• Labour: relevant cost is the wage paid extra plus any contribution lost if labour is diverted from other work.

Common mistakes

• Using the book value or historical cost of stock materials as the relevant cost. Fix: Ask what the firm will actually give up or pay now: replacement cost, resale value or alternative use value.
• Treating allocated fixed overheads as relevant. Fix: Include fixed cost only if it will actually increase or be avoided because of the decision.
• Comparing the buy price with the full absorbed cost per unit. Fix: Remove fixed overhead that continues after buying. Include only avoidable fixed cost.
• Ignoring the opportunity cost when capacity is limited. Fix: Ask what the plant would do with the freed capacity. Add that contribution to the cost of making.
• Rejecting the order because the price is below full cost per unit. Fix: Compare the price with relevant cost only. Fixed costs that stay the same are ignored when capacity is idle.
• Ignoring opportunity cost when capacity is full. Fix: Check the capacity line first. If regular sales are displaced, add their lost contribution to the relevant cost.
• Dropping a product because the segment profit statement shows a loss. Fix: Rebuild the figure as contribution less avoidable fixed costs only.
• Treating all fixed costs as avoidable. Fix: Check the wording. Deduct only costs that stop on closure. Allocated head-office cost and shared depreciation stay.
• Deducting allocated joint cost from each product's final value before comparing. Fix: Compare only incremental revenue and incremental cost. Joint cost is the same in both options, so leave it out.
• Comparing final selling price with further processing cost only, ignoring the split-off value. Fix: Always subtract the split-off value. It is the opportunity cost of processing further.

Exam tips

• In MCQs, scan for the trap: sunk cost, committed cost, absorbed fixed overhead or depreciation. The correct option usually excludes it.
• In written answers, show a short table of items included and excluded with a one-word reason. This earns method marks even if a figure is wrong.
• For materials, read carefully whether the stock will be replaced. The answer changes between replacement cost, resale value and nil.
• For labour, check whether workers are on fixed pay with idle time or fully occupied. Opportunity cost applies only in the second case.
• Close every answer with a clear recommendation and one or two qualitative factors.
• Read the capacity statement first. It decides whether opportunity cost is nil or must be added.
• Label every fixed cost as avoidable or unavoidable before computing. Examiners award marks for this classification.
• In limited capacity questions, show the extra cost per scarce hour for each part. That table earns the method marks.