ACCA Applied Skills · Performance Management

Make-or-buy and other short-term decisions: formula sheet

Full chapter guide

Key formulas

Relevant cost test: Relevant cost = future + incremental + cash flow (including opportunity costs); If a cost fails any one of these tests, leave it out.
Opportunity cost: Opportunity cost = benefit lost from the best alternative use of the resource; Use the higher of the alternatives that actually apply, such as resale value or the cost of replacement.
Material already in stock, regularly used: Relevant cost = current replacement cost; Using it means it must be replaced.
Material in stock, not needed again: Relevant cost = higher of resale value and cost of using it in another job (net of any disposal cost); If it would otherwise be disposed of at a cost, avoiding that cost is a benefit.
Labour: spare capacity: Relevant cost = extra payment only (often nil for fixed-wage staff); Paying idle workers anyway means no incremental cost.
Labour: no spare capacity: Relevant cost = wages + lost contribution after labour cost (which equals the lost contribution before labour cost on its own); Add the wage to the contribution measured after labour cost. If the contribution is measured before labour cost, it already includes the wage, so use it on its own and do not add the wage again.
Overheads: Relevant cost = extra overhead spending only; Absorbed overhead rates are not relevant unless spending changes.
Basic make-or-buy rule: Make if relevant cost of making < purchase price; buy if purchase price < relevant cost of making; Relevant cost of making = variable costs + avoidable fixed costs + any opportunity costs. Compare per unit or in total.
Relevant cost of making: Direct materials + direct labour + variable overhead + avoidable fixed costs; Exclude unavoidable fixed overheads and sunk costs. Add opportunity cost if resources have another use.
Limiting factor ranking: Extra cost of buying per unit of scarce resource = (buy price − variable cost of making) ÷ scarce resource units per unit; Buy the component with the lowest figure first. Make the ones with the highest.
Saving or extra cost: Total saving = (relevant cost of making − buy price) × units; A positive answer means buying saves money, before non-financial factors.
Contribution per unit: Contribution per unit = selling price per unit − variable cost per unit; Use only variable costs. Exclude fixed overheads and absorbed fixed costs.
Contribution per unit of limiting factor: Contribution per limiting factor unit = contribution per unit ÷ units of scarce resource used per unit of product; This is the ranking measure. Higher is better.
Resource needed for a product: Resource used = units produced × resource per unit; Use maximum demand for units when you allocate the resource in rank order.
Total contribution of the plan: Total contribution = Σ (units made × contribution per unit); Subtract fixed costs only if the question asks for profit.
Value of extra scarce resource: Maximum price worth paying per extra unit = normal price + contribution per unit of resource earned by the marginal product; The marginal product is the one that is only partly made. This links to shadow prices.
Objective function: Maximise C = (contribution per unit of X × X) + (contribution per unit of Y × Y); Use contribution per unit, not profit, because fixed costs do not change with the mix.
Resource constraint: (hours per unit of X × X) + (hours per unit of Y × Y) ≤ hours available; Write one for each scarce resource. Add non-negativity: X ≥ 0, Y ≥ 0.
Slack: Slack = resource available − resource used at the optimal solution; Slack is zero for a binding constraint. Slack means the constraint is not limiting output.
Shadow price: Shadow price = increase in optimal total contribution ÷ 1 extra unit of the resource; Valid only for a small change, while the same constraints stay binding. It is zero where there is slack.
Shadow prices by simultaneous equations: For each product: Σ (shadow price × resource used per unit) = contribution per unit; Use this for products that are made in the optimal plan. It gives all shadow prices in one go.
Shut-down rule: Close if avoidable fixed costs > contribution lost; Use the contribution of the unit, not its accounting profit. Include only fixed costs that really stop on closure.
Net effect of closure: Gain/(loss) from closing = avoidable fixed costs saved − contribution lost; Add any other cash effects, such as redundancy costs, sale proceeds of assets or lost contribution on linked products.
Contribution: Contribution = sales revenue − variable costs; Variable costs include direct materials, direct labour if truly variable, and variable overheads.
Special order acceptance: Accept if order revenue > relevant costs of the order; Equivalent: accept if the order adds positive incremental profit.
Relevant cost with full capacity: Relevant cost = variable cost of order + contribution forgone on displaced sales; With spare capacity the contribution forgone is zero.
Minimum acceptable price: Minimum price = relevant cost of the order; This gives a floor price. Any price above it adds profit, though other factors may matter.

Quick revision

Relevant costs are future, incremental cash flows.
Ignore sunk costs, depreciation and non-cash items.
Fixed overheads are relevant only if they change because of the decision.
Material already in stock: if it is regularly used and would be replaced, the relevant cost is its replacement cost. If it is not needed and would not be replaced, the relevant cost is the higher of its resale value and its value in the next best alternative use. If it has no other use and no resale value, the relevant cost is zero.
Labour with spare capacity costs nothing extra; labour at full capacity costs pay plus lost contribution.
Make-or-buy: compare relevant cost of making with the buy-in price.
Limiting factor: rank by contribution per unit of the scarce resource, not per product.
With one scarce resource, fill the best-ranked product first, up to its demand.
A shadow price is the extra contribution from one more unit of a scarce resource.
A resource with spare capacity has a shadow price of zero.
Shut-down: compare contribution lost with fixed costs avoided, then add non-financial factors.
Special order: accept if the extra revenue exceeds relevant costs, including any lost sales.

Common mistakes

Including the historical cost of materials already in stock. Fix: Ask what using the material actually costs now: replacement cost if it will be replaced, otherwise the higher of resale value and alternative use.
Treating all labour as relevant at the full wage rate. Fix: Check for spare capacity. If staff are paid anyway, the incremental cost is nil. If not, add the lost contribution from diverted work.
Using the full absorption cost of making. Fix: Remove fixed overheads that continue whether you make or buy. Use only variable and avoidable fixed costs.
Choosing the item with the largest total extra cost of buying to make, when capacity is limited. Fix: Divide the extra cost of buying by the scarce resource per unit. Rank on that figure.
Ranking by contribution per unit of product instead of per unit of scarce resource. Fix: Always divide by the resource used per unit before ranking. Write the ranking line in your table so you cannot skip it.
Ignoring maximum demand and making the top-ranked product until the resource runs out. Fix: Cap each product at maximum demand. Only the lowest-ranked product made should be limited by the resource rather than by demand.
Using profit instead of contribution in the objective function. Fix: Use selling price less variable costs only. Fixed costs are not affected by the mix.
Giving a shadow price for a resource with slack. Fix: Test every constraint at the optimum first. If some is left unused, the shadow price is zero.
Closing a unit because it shows an accounting loss. Fix: Look at contribution and avoidable fixed costs only. A unit with positive contribution after avoidable costs should usually stay.
Treating all fixed costs as avoidable. Fix: Ask of each fixed cost: does it stop if we close? Allocated head office costs usually do not.

Exam tips

Write a short line beside each item saying relevant or not, and why. Markers reward the reasoning in Section C.
Look for hidden words such as already purchased, committed, apportioned and depreciation. They usually signal irrelevant items.
Read the stock wording carefully: regularly used, no other use, or could be sold. Each gives a different rule.
OT questions are marked all or nothing, with no partial credit, so check you have excluded sunk and non-cash items before you answer.
State your recommendation and mention one or two qualitative factors when the question asks for advice.
Read the scenario for which fixed costs are avoidable. Examiners often hide this in one sentence.
Show the relevant cost of making as a clear list so you earn method marks even if a figure is wrong.
In limiting factor questions, show the extra cost of buying per scarce unit for every item. The ranking earns marks.