CMA Final · Strategic Cost Management

Decisions involving Alternative Choices: formula sheet

Full chapter guide

Key formulas

Relevant cost rule: Relevant cost = future + cash (or cash-equivalent) + differs between alternatives; A cost must pass all three tests. Failing any one makes it irrelevant.
Relevant cost of a resource: Relevant cost = cash outlay + opportunity cost; Cash outlay is the extra spending caused by the decision. Opportunity cost is the contribution or value lost from the next best use.
Relevant cost of material in stock: Not needed again: higher of resale value and value in alternative use. Needed again: current replacement cost; The original purchase price is a sunk cost and is ignored.
Relevant cost of labour: Spare capacity (idle paid labour): nil. Fully used: wages + contribution lost per hour × hours; Contribution lost applies when labour is diverted from other work. For extra hours paid at a premium, use the premium rate.
Incremental analysis: Incremental profit = Incremental revenue − Incremental (relevant) cost; Choose the alternative with the higher incremental profit, or the lower relevant cost when revenue is the same.
Avoidable fixed cost test: Include a fixed cost only if it is saved or newly incurred by the decision; Allocated head-office or common costs that continue are irrelevant.
Relevant cost of making: Relevant cost of making = Variable cost + Avoidable fixed cost + Opportunity cost; Opportunity cost is zero if the capacity is idle. Exclude unavoidable fixed cost and sunk cost.
Relevant cost of buying: Relevant cost of buying = Purchase price + Other incremental buying costs − Any saleable value of released resources; Add freight, inspection and ordering cost. Subtract rent or sale proceeds from released capacity only if it is actually earned.
Decision rule: Make if relevant cost of making < relevant cost of buying; otherwise buy; Check qualitative factors before the final recommendation.
Limited capacity ranking: Extra cost of buying per unit of scarce resource = (Buy price − Relevant variable cost of making) ÷ Scarce resource units per unit of component; Make components with the highest ratio first, until the scarce resource runs out.
Opportunity cost of capacity: Opportunity cost = Contribution lost from the next best use of the capacity; Use contribution, not profit, because fixed costs continue either way.
Contribution per unit on the special order: Special price per unit − Relevant variable cost per unit; Use only costs that change because of the order. Ignore apportioned fixed costs that do not change.
Incremental profit with spare capacity: (Special price − Variable cost per unit) × Order units − Additional fixed costs of the order; Accept if the result is positive, subject to non-financial factors.
Incremental profit at full capacity: Incremental revenue − Incremental costs − Contribution lost on displaced regular sales; The lost contribution is an opportunity cost. Include it only for units of regular sales actually displaced.
Minimum acceptable price per unit: Relevant variable cost per unit + Additional fixed cost ÷ Order units + Opportunity cost per unit; This is the price at which the order just breaks even. Any price above it adds profit.
Contribution: Contribution = Sales − Variable cost; Variable cost includes variable selling and distribution cost, not just production cost.
Continue/shut rule: Continue if Contribution > Avoidable fixed costs; shut if Contribution < Avoidable fixed costs; If equal, the firm is indifferent on financial grounds; qualitative factors decide.
Net advantage of continuing: Advantage of continuing = Contribution − Avoidable fixed costs (+ contribution gained on other products − closure costs avoided, where relevant); Include only items that change because of the decision.
Alternative use of capacity: Shut only if Benefit of alternative use (or rent/sale proceeds) > Contribution − Avoidable fixed costs of the unit; Use this when freed space or capacity can earn income.
Short-run shutdown point: Operate while Selling price per unit ≥ Variable cost per unit (plus avoidable fixed cost per unit if it is to be saved by closing); Unavoidable fixed costs are paid in either case, so ignore them.
Contribution per unit: Contribution = Selling price − Variable cost per unit; Use only variable costs. Allocated fixed costs are irrelevant to the ranking.
Contribution per unit of limiting factor: Contribution per key factor unit = Contribution per unit ÷ Units of limiting factor used per unit of product; Rank products on this figure, highest first. Valid for a single binding constraint.
Production plan under one constraint: Units of a product = Lower of (maximum demand, remaining resource ÷ resource per unit); Allot in rank order until the resource is exhausted.
Profit: Profit = Total contribution − Fixed costs; Fixed costs are deducted once, after the mix is decided.
LP objective function: Maximise Z = c1x1 + c2x2 + …, where c = contribution per unit; Use contribution, not selling price, as the coefficient.
LP constraints: a1x1 + a2x2 + … ≤ b (for each resource); x1, x2 ≥ 0; Add demand limits as extra constraints such as x1 ≤ maximum demand.
Shadow price of a resource: Shadow price = Increase in total contribution from one extra unit of a binding resource; It is the most you would pay above the normal price for extra units of that resource. It is zero for a non-binding resource, and it holds only within a limited range.
Incremental revenue: Incremental revenue = Sales value after further processing − Sales value at split-off point; Use the same quantity in both. If there is processing loss, use the final saleable quantity for the after-processing value.
Incremental profit: Incremental profit = Incremental revenue − Further processing cost; Include only avoidable costs: variable costs and any specific fixed cost caused by the decision.
Decision rule: Process further if incremental revenue > incremental cost; sell at split-off if incremental revenue < incremental cost; If both are equal, you are indifferent on financial grounds. Non-financial factors can then decide.
Joint cost treatment: Joint cost allocated to a product = irrelevant; The allocation method (physical units, net realisable value) changes reported product profit, not the decision.
Relevant cost of an asset or material: Relevant cost = Cash outflow avoided or incurred in future + Opportunity cost; Use the higher of resale value and value in alternative use as the opportunity cost. Ignore book value.
Incremental profit of an option: Incremental profit = Incremental revenue − Incremental cost; Compare options on this basis. Pick the higher figure.
Minimum price for a special order: Minimum price = Incremental cost + Opportunity cost (contribution lost on displaced work); With idle capacity, the opportunity cost is zero.
Replacement decision (undiscounted): Net benefit of replacing = Total running-cost saving over the period + Scrap value of new asset at end − (Cost of new asset − Resale value of old asset today) − Scrap value of old asset at end; Use present values if the problem gives a discount rate. A positive result favours replacement.
Cost-plus price: Price = Cost per unit + Mark-up % × Cost per unit; Use this for long-term pricing. Check that the cost base is stated: full or variable.

Quick revision

Relevant cost is a future cash flow that differs between alternatives.
Sunk costs and committed costs are never relevant.
Opportunity cost is the benefit given up by choosing an option, and it is relevant.
Make or buy: compare avoidable cost of making with the purchase price, then check for use of freed capacity.
Special order: accept if incremental revenue exceeds incremental cost, after allowing for any lost sales or displaced contribution.
Shutdown: compare contribution lost with avoidable fixed costs saved.
Only avoidable fixed costs affect a shutdown or make-or-buy decision.
Limiting factor: rank by contribution per unit of the scarce resource.
With more than one constraint, use a linear programming style approach rather than simple ranking.
Joint costs are irrelevant to sell or process further; compare extra revenue with extra processing cost.
Replacement decisions use relevant cash flows; book value of the old asset is sunk, but its sale value is relevant.
Always end with a recommendation and qualitative factors.

Common mistakes

Including depreciation or the original cost of stock material in the relevant cost. Fix: Depreciation is non-cash and past-based. Stock material is valued at replacement cost or best alternative use, never at its purchase price.
Ignoring opportunity cost because no cash is paid. Fix: Whenever a resource has another use, such as hiring out, resale, or use on another product, add that lost benefit as a cost of the chosen option.
Comparing the buy price with the full absorption cost of making. Fix: Remove fixed overhead that continues even if you buy. Keep only avoidable costs.
Ignoring opportunity cost when capacity is fully used. Fix: Read the capacity statement first. If it is full, add the contribution lost from the next best use.
Rejecting the order because the price is below full cost per unit. Fix: Compare the price with the relevant variable cost. Fixed costs that do not change are ignored.
Ignoring the opportunity cost when capacity is full. Fix: Always check spare capacity first. If regular sales are displaced, deduct their lost contribution.
Closing a unit because it shows a net loss Fix: Rebuild the statement from contribution. Deduct only avoidable fixed costs.
Treating all fixed costs as avoidable Fix: Read the wording. Allocated head office cost, depreciation of unsaleable assets and common rent usually continue.
Ranking products by contribution per unit instead of per unit of the limiting factor. Fix: Always divide by the units of scarce resource used and rank on that figure.
Ignoring the maximum demand for the top-ranked product. Fix: Cap each product at its demand, then pass the leftover resource to the next-ranked product.

Exam tips

In case-based MCQs, read the data line by line and cross out sunk, committed and non-cash items before you calculate.
In written answers, show a short working note for each relevant cost, with a reason for items you exclude. Markers give credit for the reasoning.
Watch for hidden opportunity costs: spare machine hire, scarce material, labour diverted from other work, and stock material with a scrap or resale value.
Always end with a recommendation and one qualitative factor. A calculation without a decision loses marks.
Check the wording on fixed cost: if the question says the cost is avoidable, specific, or will be incurred, treat it as relevant.
Read the capacity sentence first. It decides whether opportunity cost is zero or a lost contribution.
Show the split of fixed cost into avoidable and unavoidable. Examiners award marks for this classification.
In limited-capacity questions, show the ratio per scarce resource hour for each component, then the ranking table.