MI · Certificate Level

Decision-Making Techniques

Cost-volume-profit (CVP) analysis (breakeven point, margin of safety, contribution/sales ratio, target profit analysis, multi-product breakeven with weighted average C/S ratio), relevant costing (identifying relevant costs and revenues, sunk costs, opportunity costs, committed costs), limiting factor analysis (single constraint — contribution per limiting factor, multiple constraints — linear programming graphical method), make or buy decisions, closure and discontinuation decisions, pricing decisions (cost-plus pricing, target costing, market-based pricing), and further processing decisions at the split-off point.

45 min read

Learning Objectives

•Calculate the breakeven point in units and in revenue
•Calculate the margin of safety in units, revenue, and as a percentage
•Calculate the contribution/sales (C/S) ratio and use it for target profit and breakeven analysis
•Apply CVP analysis to multi-product scenarios using a weighted average C/S ratio
•Identify relevant costs and revenues for decision-making and distinguish them from sunk, committed, and non-relevant costs
•Apply limiting factor analysis to determine the optimal production plan when a single resource is scarce
•Solve simple linear programming problems graphically for two-product, two-constraint scenarios
•Apply relevant costing to make or buy, closure/discontinuation, and further processing decisions
•Describe and compare cost-plus, target costing, and market-based pricing approaches

Cost-Volume-Profit (CVP) Analysis

CVP analysis (also called breakeven analysis) examines the relationship between costs, volume of activity, and profit. It is based on marginal costing principles — separating costs into variable and fixed.

Key assumptions of CVP analysis:

Selling price per unit is constant (no volume discounts)
Variable cost per unit is constant
Total fixed costs are constant within the relevant range
All units produced are sold (no inventory changes) or the analysis is in terms of sales units
In multi-product analysis, the sales mix remains constant

Breakeven Point

The breakeven point (BEP) is the level of activity at which total revenue equals total costs — the entity makes neither a profit nor a loss. Contribution exactly covers fixed costs.

Breakeven in units:

BEP (units) = Total fixed costs ÷ Contribution per unit

Breakeven in revenue:

BEP (revenue) = Total fixed costs ÷ C/S ratio

Or: BEP (revenue) = BEP (units) × Selling price per unit

Margin of Safety

The margin of safety measures how far sales can fall below the budgeted or actual level before the entity reaches breakeven — the buffer between actual/expected sales and breakeven.

Margin of safety (units) = Budgeted sales units − Breakeven units

Margin of safety (revenue) = Budgeted revenue − Breakeven revenue

Margin of safety (%) = (Budgeted sales − Breakeven sales) ÷ Budgeted sales × 100

A higher margin of safety indicates lower risk — the entity can absorb a larger drop in sales before making a loss. A low margin of safety means the entity is operating close to breakeven — any sales decline could quickly turn the business unprofitable.

Contribution/Sales (C/S) Ratio

The C/S ratio (also called the profit-volume ratio or P/V ratio) expresses contribution as a percentage of selling price.

C/S ratio = Contribution per unit ÷ Selling price per unit

Or: C/S ratio = Total contribution ÷ Total revenue

The C/S ratio shows how much of each £1 of revenue is available to cover fixed costs and generate profit. A C/S ratio of 40% means 40p of every £1 of sales is contribution.

Uses:

Breakeven revenue = Fixed costs ÷ C/S ratio
Revenue needed for a target profit = (Fixed costs + Target profit) ÷ C/S ratio
Comparing the profitability of different products — a higher C/S ratio means each £1 of sales contributes more to covering fixed costs

Target Profit Analysis

To achieve a target profit, the entity needs to generate enough contribution to cover fixed costs AND the desired profit.

Units for target profit = (Fixed costs + Target profit) ÷ Contribution per unit

Revenue for target profit = (Fixed costs + Target profit) ÷ C/S ratio

Multi-Product CVP Analysis

When an entity sells multiple products, breakeven analysis requires a weighted average C/S ratio based on the sales mix.

Weighted average C/S ratio = Total contribution (all products) ÷ Total revenue (all products)

Then:

Breakeven revenue (total) = Fixed costs ÷ Weighted average C/S ratio

Assumption: The sales mix remains constant at all activity levels. If the mix changes, the breakeven point changes.

Relevant Costing

Relevant costs are costs that should be considered when making a specific decision. They are the costs (and revenues) that differ between alternatives. Only relevant costs and revenues should influence a decision — irrelevant costs should be ignored.

Characteristics of a relevant cost:

Future: The cost must arise in the future — past costs are irrelevant (they cannot be changed by the decision)
Incremental (differential): The cost must differ between the alternatives being considered
Cash flow: Relevant costs are cash flows, not accounting charges. Depreciation is not a relevant cost (it is a non-cash allocation of a past cost).

Types of irrelevant cost:

Type	Definition	Example
Sunk cost	A cost already incurred that cannot be recovered regardless of the decision. It is a past cost.	Research expenditure already spent, money already paid for a machine. The decision now is whether to continue, not whether to have started.
Committed cost	A future cost that the entity is contractually obliged to incur regardless of the decision.	A non-cancellable lease payment, a fixed-term employment contract with no termination clause.
Non-cash cost	An accounting charge that does not involve a cash flow.	Depreciation, amortisation, notional rent, allocated head office overheads.
General fixed overhead	Fixed overhead that will be incurred regardless of the decision.	Factory rent, general management salaries — these continue whether or not a particular product is made.

Opportunity cost:

The benefit foregone by choosing one alternative over the next best alternative. Opportunity costs are always relevant — they represent the sacrifice of the best rejected option. Example: if a machine can be used for Project A or Project B but not both, the opportunity cost of choosing A is the contribution that would have been earned from B.

Relevant cost of materials already in inventory:

If the material is in regular use (and will be replaced): relevant cost = replacement cost
If the material is not in regular use: relevant cost = the higher of (a) net realisable value (what it could be sold for) and (b) value in best alternative use. If it has no alternative use and no resale value, the relevant cost is nil (it is a sunk cost).

Limiting Factor Analysis

When a single resource is scarce (a limiting factor or bottleneck), the entity cannot produce enough of all products to meet demand. It must decide which products to prioritise. The rule is to maximise total contribution by prioritising products that generate the highest contribution per unit of the scarce resource.

Steps for single limiting factor analysis:

Identify the limiting factor (the resource in short supply — machine hours, labour hours, kg of material, etc.)
Calculate the contribution per unit of the limiting factor for each product
Rank products in order of contribution per limiting factor unit (highest first)
Allocate the scarce resource to products in rank order until all the resource is used up
Calculate total contribution and profit from the optimal production plan

Key insight: The product with the highest contribution per unit of product is not necessarily the most profitable when a resource is scarce. It is the contribution per unit of the scarce resource that matters.

Multiple Constraints — Linear Programming (Graphical Method)

When there are two or more limiting factors simultaneously, the optimal solution cannot be found by simple ranking. Linear programming (LP) is used. At the Certificate Level exam, only the graphical method is required (for problems with two decision variables).

Steps for the graphical method:

Define the decision variables: Let x = units of Product A, y = units of Product B
Formulate the objective function: Maximise total contribution C = (contribution per A × x) + (contribution per B × y)
Formulate the constraints: Each limiting factor gives a linear inequality (e.g., 2x + 3y ≤ 1,200 for machine hours). Also: non-negativity constraints (x ≥ 0, y ≥ 0) and demand constraints (x ≤ max demand for A, y ≤ max demand for B).
Graph the constraints: Plot each constraint line on a graph with x and y axes. The feasible region is the area satisfying all constraints simultaneously.
Identify the optimal solution: The optimal solution is always at a corner point (vertex) of the feasible region. Either: (a) test all corner points by substituting into the objective function and selecting the one giving the highest contribution, or (b) use the iso-contribution line method — draw a line representing the objective function and slide it outward until it touches the last corner of the feasible region.

Shadow price (dual price): The increase in the optimal value of the objective function (total contribution) for each additional unit of a binding constraint. It represents the maximum premium the entity should pay above the normal cost for one extra unit of the scarce resource.

Make or Buy Decisions

A make or buy decision involves choosing whether to manufacture a component in-house or purchase it from an external supplier.

Decision rule (no limiting factor): Compare the relevant cost of making (incremental production costs — variable costs + any avoidable fixed costs) with the purchase price. Choose the cheaper option.

Decision rule (with a limiting factor): If in-house capacity is constrained, buying externally frees up capacity for other uses. Consider the opportunity cost of using capacity for in-house production. The relevant cost of making = incremental cost + opportunity cost (contribution lost from the next best use of the freed capacity).

Non-financial considerations: Quality control (can you ensure the external supplier meets quality standards?), reliability of supply, dependency on a single supplier, confidentiality of proprietary processes, employee morale and job losses, strategic importance of the capability, flexibility to respond to changes in demand.

Closure and Discontinuation Decisions

Should a product, service line, department, or segment be discontinued? The decision depends on whether the entity would be better off financially without it.

Decision rule: A product/segment should be discontinued only if the revenues and avoidable costs saved result in a net improvement. If the segment makes a positive contribution (revenue > variable costs + directly avoidable fixed costs), it should generally be retained — even if it shows an accounting loss after allocated fixed overheads.

Why an accounting loss does not necessarily mean discontinuation is correct:

Allocated fixed overheads (head office, rent apportionment, shared services) are often unavoidable — they will not disappear if the segment is closed. They will simply be reallocated to the remaining segments, reducing their profits.
Only costs that are directly avoidable (i.e., they genuinely cease if the segment closes) are relevant. Common fixed costs that continue regardless are irrelevant to the decision.
The relevant question is: does closing the segment increase or decrease total company profit?

Additional considerations: Impact on remaining products (complementary sales, customer perception), redundancy costs (one-off), lease break costs, reputational effects, long-term strategy (is the segment growing?).

Pricing Decisions

Approach	Method	Advantages	Disadvantages
Cost-plus pricing	Calculate the full cost of the product (or marginal cost), then add a mark-up to achieve the desired profit margin. `Price = Cost + (Cost × Mark-up %)` The cost base may be: full production cost, total cost (including selling/admin), or marginal cost (then the mark-up must cover fixed costs AND profit).	Simple, easy to calculate, ensures all costs are covered (full cost basis), provides a consistent basis for pricing, useful when cost information is reliable	Ignores demand and competition, circular logic (volume determines cost, but price determines volume), may overprice or underprice relative to the market, does not reflect customers' willingness to pay
Target costing	Start with the market price (what customers are willing to pay), deduct the required profit margin, and derive the target cost. Then design the product to meet the target cost. `Target cost = Market price − Required profit`	Market-focused (starts with what customers will pay), encourages cost reduction and efficiency, used during product design (where 80%+ of costs are determined), promotes continuous improvement	Requires accurate market research, may not be achievable if current costs exceed the target significantly, can put excessive pressure on cost reduction (quality risk), may not suit unique/innovative products with no market benchmark
Market-based pricing	Price is set based on market conditions — competitor prices, customer demand, perceived value, and market positioning. Includes: penetration pricing (low initial price to gain market share), skimming (high initial price for innovative products), competitive pricing (matching competitor prices).	Reflects market reality, responsive to competition and demand, maximises revenue if demand is well understood	May not cover costs (if market price is below full cost), requires market research and competitive intelligence, may lead to price wars in competitive markets

Further Processing Decisions

In joint process costing, two or more products emerge from a common process up to a split-off point. After split-off, each product can be: (a) sold immediately at the split-off point, or (b) processed further into a higher-value product.

Decision rule: Process further only if the incremental revenue from further processing exceeds the incremental cost of further processing.

Incremental revenue = Revenue after further processing − Revenue at split-off

Incremental cost = Cost of further processing (additional materials, labour, overheads)

If incremental revenue > incremental cost → process further.

If incremental revenue < incremental cost → sell at split-off.

Important: The joint process costs (costs incurred before split-off) are irrelevant to the further processing decision. These costs are sunk at the split-off point — they have already been incurred regardless of whether the product is sold at split-off or processed further. Only the incremental costs and revenues beyond split-off are relevant.

Examiner Focus

CVP analysis is tested in almost every MI sitting. You MUST know: BEP = Fixed costs ÷ CPU; MoS = Budgeted − BEP; C/S ratio = CPU ÷ SP; Target profit units = (FC + TP) ÷ CPU. These formulas must be instant recall. Multi-product BEP uses the weighted average C/S ratio.

Common Pitfall

In limiting factor analysis, the product with the highest contribution per UNIT is NOT necessarily the most profitable when a resource is scarce. You must rank by contribution per unit of the SCARCE RESOURCE. This is the most common error — and the examiner specifically tests it.

Study Tip

For relevant costing decisions, ask three questions: (1) Is it FUTURE? (past costs are sunk — ignore them), (2) Does it DIFFER between alternatives? (if the same regardless, ignore it), (3) Is it a CASH FLOW? (depreciation and allocated overheads are not cash — ignore them). Only costs that pass all three tests are relevant.

Examiner Focus

Closure/discontinuation: a product showing an accounting LOSS may still make a positive CONTRIBUTION. If so, it is covering some fixed costs and should usually be RETAINED. Closing it would make the remaining products absorb more fixed costs, reducing total profit. Only close if avoidable costs saved > revenue lost.

Watch Out

Further processing decisions: JOINT COSTS ARE SUNK. They are incurred before the split-off point regardless of whether the product is sold or processed further. ONLY the incremental costs and revenues beyond split-off are relevant. Students who include joint costs in further processing analysis always get the wrong answer.

Study Tip

For make or buy with a limiting factor: the relevant cost of making includes the OPPORTUNITY COST of using scarce capacity. If making in-house uses capacity that could earn contribution from other products, that lost contribution is a relevant cost of making.

Key Definitions

Breakeven point

The level of activity where total revenue equals total costs — zero profit. BEP (units) = Fixed costs ÷ Contribution per unit.

Margin of safety

The amount by which budgeted or actual sales exceed the breakeven point. Measures the buffer before a loss is incurred. Higher = lower risk.

Contribution/sales (C/S) ratio

Contribution per unit ÷ Selling price per unit. Shows how much of each £1 of revenue contributes to covering fixed costs and profit.

Relevant cost

A cost that is future, incremental (differs between alternatives), and a cash flow. Only relevant costs should influence a decision.

Sunk cost

A cost already incurred that cannot be recovered regardless of the decision. Past and irrelevant. Must be ignored in decision-making.

Opportunity cost

The benefit foregone by choosing one alternative over the next best option. Always relevant — represents the sacrifice of the rejected alternative.

Committed cost

A future cost the entity is contractually obliged to incur regardless of the decision. Irrelevant because it cannot be avoided.

Limiting factor (bottleneck)

A scarce resource that constrains the entity's ability to produce. When one factor is scarce, maximise contribution per unit of the limiting factor.

Shadow price (dual price)

The increase in total contribution for each additional unit of a binding constraint. The maximum premium worth paying for one extra unit of the scarce resource.

Cost-plus pricing

Setting the price by adding a mark-up to the cost (full cost or marginal cost). Simple but ignores demand and competition.

Target costing

Starting from the market price, deducting the required profit, and deriving a target cost. The product is designed to meet this cost. Market-driven, not cost-driven.

Split-off point

The point in a joint process where individual products become separately identifiable. Joint costs before this point are sunk for the further processing decision.

Key Formulas

Worked Examples

Practice Questions

Question 1 of 8

A product sells for £25, variable cost is £15, fixed costs are £50,000. The breakeven point in units is:

Question 2 of 8

Budgeted sales are 8,000 units and breakeven is 6,000 units. The margin of safety percentage is:

Question 3 of 8

Which of the following is a relevant cost for decision-making?

Question 4 of 8

Product A contributes £12/unit using 3 labour hours. Product B contributes £20/unit using 4 labour hours. Labour is the scarce resource. Which product should be prioritised?

Question 5 of 8

Product X contributes £18/unit using 2 machine hours. Product Y contributes £30/unit using 5 machine hours. Machine hours are scarce. Which product should be prioritised?

Question 6 of 8

A product currently generates revenue of £200,000, variable costs of £120,000, directly avoidable fixed costs of £50,000, and allocated head office costs of £40,000. It shows an accounting loss. The product should be:

Question 7 of 8

In target costing, the target cost is calculated as:

Question 8 of 8

At the split-off point, Product P can be sold for £8,000 or processed further at an additional cost of £3,000 and sold for £12,000. The company should:

Source and Version

Syllabus: ICAEW ACA Certificate Level 2026 · Reviewed: 2026-05-04

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