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Part 2 · Section C

Decision Analysis

Cost-volume-profit analysis, relevant costs for short-term decisions, and pricing. At 25% this is the heaviest section of the whole CMA exam, and nearly every question involves a calculation built on one idea: contribution margin.

Begin topic 1 Decision tools

About 25 of the 100 multiple-choice questions, and a frequent essay topic. Estimated study time: 34 hours.

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Your learning path

Three topics. CVP and marginal analysis carry most of the marks; master contribution margin first.

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Topic 1 of 3

Cost-volume-profit

How volume, price, variable cost and fixed cost combine to produce profit, and how to solve for the volume that hits a target.

Contribution margin and breakevenThe core CVP equation

Contribution margin (CM) is sales less all variable costs (manufacturing and selling). It first covers fixed costs; anything left is profit. The breakeven point is where total CM equals fixed costs.

Profit equation
$$\text{Operating income} = Q(P - V) - F$$

Q units, P price, V variable cost per unit, F total fixed costs. CM ratio = (P − V) ÷ P.

Breakeven
$$Q_{BE} = \frac{F}{P - V} \qquad S_{BE} = \frac{F}{CM\%}$$
Target profit
$$Q = \frac{F + \text{Target pre-tax}}{P - V}$$ $$\text{Pre-tax} = \frac{\text{After-tax target}}{1 - t}$$
Exam trapVariable selling costs (commissions, shipping) reduce contribution margin. Using only variable manufacturing cost overstates CM and understates breakeven.
Exam trapNever add an after-tax target directly to fixed costs. Divide it by (1 − tax rate) first.
Multi-product CVPComposite units and weighted CM ratios

With several products, breakeven depends on the sales mix. Use a composite unit when the mix is given in units, or a weighted CM ratio when it is given in sales dollars. A shift toward lower-margin products raises breakeven.

Mix in units
$$\text{Packs}_{BE} = \frac{F}{\sum m_i (P_i - V_i)}$$

mi = units of product i in one composite pack. Units of i = packs × mi.

Mix in sales dollars
$$S_{BE} = \frac{F}{\sum s_i \cdot CM\%_i}$$

si = product i's share of total sales dollars.

Exam trapA mix given in units cannot be used as dollar weights (or vice versa). Check which one the question gives.
Margin of safety and operating leverageHow risky is the profit?
Margin of safety
$$MOS = S - S_{BE} \qquad MOS\% = \frac{S - S_{BE}}{S}$$
Degree of operating leverage
$$DOL = \frac{\text{Contribution margin}}{\text{Operating income}} = \frac{1}{MOS\%}$$ $$\%\Delta\,\text{Income} = DOL \times \%\Delta\,\text{Sales}$$

Cost structure: automating (higher fixed, lower variable cost) raises breakeven and DOL but gives more profit at high volume. Two structures cost the same at the indifference point.

Indifference point
$$Q^{*} = \frac{F_2 - F_1}{V_1 - V_2}$$

Above Q*, the structure with the lower variable cost (higher fixed cost) is cheaper.

Exam trapDOL is not constant: it is highest just above breakeven and falls as sales rise. A DOL computed at one volume applies only to changes from that volume.
CVP assumptions and sensitivityWhen the model breaks
  • Costs split cleanly into fixed and variable; behavior is linear within the relevant range.
  • Selling price per unit is constant (no volume discounts).
  • The sales mix is constant (for multi-product analysis).
  • Units produced equal units sold (no inventory change), so variable-costing income applies.

Sensitivity analysis recomputes profit or breakeven when one input changes: a price cut, a wage increase, a new fixed cost. Work each change through the CM per unit or the fixed costs, then re-solve.

Instructor noteAlmost every CVP question reduces to one equation: Q(P − V) − F = target. Write it out, substitute what you know and solve for the unknown, whether that is volume, price, variable cost or fixed cost.

Finished Cost-volume-profit?

Mark it complete when you can solve breakeven, after-tax targets, mixes and DOL without notes.

Topic 2 of 3

Marginal analysis

Short-term decisions turn on one question: which revenues and costs differ between the alternatives? Everything else is noise.

Relevant costsFuture, differential, and including opportunity cost

A cost or revenue is relevant only if it is in the future and differs between the alternatives.

Relevant and irrelevant items
Item Relevant? Reason
Sunk cost (book value of old equipment, past R&D) No Already incurred; no decision can change it
Allocated common fixed costs that continue either way No Same total under every alternative
Avoidable fixed costs (a supervisor who would be laid off) Yes Differs between alternatives
Opportunity cost (rent forgone, displaced sales) Yes Benefit given up by choosing an alternative
Variable costs that change with the decision Usually yes Unless identical under both alternatives
Disposal value of old assets Yes Future cash that depends on the decision

Always weigh qualitative factors too: quality, supplier reliability, employee morale, customer relationships, and long-run strategic effects.

Exam trapFixed overhead "per unit" in a cost sheet is usually an allocation of costs that will continue. Treat it as irrelevant unless the question says part of it is avoidable.
Special ordersIdle capacity vs full capacity
Special order
$$\Delta\text{Income} = Q_s(P_s - V_s) - \Delta F - \underbrace{Q_d (P - V)}_{\text{displaced CM}}$$ $$P_{\min} = V_s + \frac{\Delta F + \text{Displaced CM}}{Q_s}$$

Qd = regular units given up when the order exceeds idle capacity. Vs excludes variable costs not incurred on the order (e.g. commissions).

Exam trapAt full capacity, the lost contribution on displaced regular sales is a relevant cost. Check whether the order fits in idle capacity before deciding.
Make or buyAvoidable costs and the use of freed capacity
Make or buy
$$\text{Relevant cost to make} = Q \cdot V + F_{\text{avoidable}} + \text{Opportunity cost of capacity}$$

Buy if the purchase price × Q is lower. Maximum price worth paying = relevant cost to make ÷ Q.

Exam trapThe "full cost per unit" includes unavoidable fixed overhead. Compare the purchase price only with the costs that would disappear, plus any opportunity income from the freed capacity.
Sell or process further, and dropping a segmentIncremental revenue and avoidable cost
  • Sell or process further: process if incremental revenue after split-off exceeds the separable (further-processing) cost. Joint costs are sunk.
  • Drop a segment: drop only if the contribution lost is less than the fixed costs avoided (plus any income from using the freed resources). Allocated common costs remain and are reallocated to the other segments.
Drop a segment
$$\Delta\text{Income} = -\,\text{Segment CM} + F_{\text{avoidable}} + \text{Opportunity income}$$
Scarce resourcesContribution per unit of the constraint
Scarce resource
$$\text{Rank by } \frac{P - V}{\text{Constraint units per product}}$$

Fill demand for the highest-ranked product first, then the next, until the constraint is used up.

Exam trapRanking by CM per unit or by CM ratio is wrong when a resource is scarce. With no constraint (ample capacity), make every product with a positive CM up to demand.
Instructor noteLay out every relevant-cost answer as a two-column comparison (alternative A vs B, or a single "incremental" column). It forces you to ask, line by line, whether each item changes, which is how the exam's distractors are built.

Finished Marginal analysis?

Mark it complete when you can solve a special order with displacement and a make-or-buy with opportunity cost.

Topic 3 of 3

Pricing

Prices built up from cost, worked back from the market, shaped by demand elasticity and market structure, and limited by law.

Cost-based pricingMarkups on different cost bases

Cost-plus pricing adds a markup to a cost base. The smaller the base (variable cost vs full manufacturing cost vs full life-cycle cost), the larger the markup must be, because it has to cover everything outside the base plus profit.

Cost-plus price
$$P = \text{Cost base} \times (1 + m)$$
Required markup
$$m = \frac{\text{Target profit} + \text{Costs outside the base}}{\text{Costs in the base}}$$
Exam trapCost-plus prices are circular: unit fixed cost depends on volume, and volume depends on price. A lower volume raises unit cost, which raises the cost-plus price, which lowers volume again.
Exam trapA markup on cost is not a margin on price. A 25% markup on a $80 cost gives a $100 price, which is a 20% margin on price. Converting: margin = markup ÷ (1 + markup); markup = margin ÷ (1 − margin).
Target costing and market-based pricingStart from the price customers will pay
Target cost
$$\text{Target cost} = \text{Target price} - \text{Desired profit}$$

If the estimated cost exceeds the target cost, close the gap through value engineering before launch, or do not launch.

  • Target costing is market-driven and applied at the design stage, where most costs are locked in, with cross-functional teams and suppliers.
  • Value engineering removes cost without removing features customers value; it separates value-added from non-value-added cost.
  • Value-based pricing sets price from the customer's perceived value, not cost.
Price elasticity of demandHow quantity responds to price
Price elasticity of demand (midpoint)
$$E_d = \frac{(Q_2 - Q_1) \,/\, \tfrac{Q_1 + Q_2}{2}}{(P_2 - P_1) \,/\, \tfrac{P_1 + P_2}{2}}$$

|E| > 1 elastic: a price rise lowers total revenue. |E| < 1 inelastic: a price rise raises revenue. |E| = 1 unitary. The exam uses the midpoint (arc) method unless told otherwise.

Exam trapElasticity predicts the effect on revenue, not on profit. For profit, compare contribution margin at each price.
Exam trapElasticity of demand is negative for normal goods, because price and quantity move in opposite directions. Classify it by its absolute value: −1.22 is elastic (|E| > 1), even though −1.22 is "less than 1".
Market structures, life-cycle pricing and the lawHow much pricing power a firm has
Market structures
Structure Sellers and product Pricing power
Perfect competition Many sellers, identical product, free entry None: price taker; P = MR = MC in the long run
Monopolistic competition Many sellers, differentiated products Some, through branding and differentiation
Oligopoly Few large interdependent sellers, high entry barriers Significant; prices tend to be sticky (kinked demand curve)
Monopoly One seller, no close substitutes Greatest: sets output where MR = MC and charges what demand allows
  • Profit is maximized where marginal revenue = marginal cost, in every structure.
  • Life-cycle pricing: price skimming (high introductory price for innovators, with little competition and inelastic early demand) vs penetration pricing (low price to win share quickly where demand is elastic and scale economies exist). Prices usually fall in maturity and decline.
  • Legal limits (US): the Robinson-Patman Act bans price discrimination between business customers that harms competition unless justified by cost differences or meeting competition; the Sherman Act bans price fixing and collusion; predatory pricing (below cost to drive out rivals) and dumping (selling abroad below cost or home price) are illegal.
Exam trapIn short-run decisions with idle capacity, fixed costs that will not change are irrelevant, so any price above variable cost adds profit. Do not add allocated fixed cost per unit to a short-run price floor; for long-run or regular pricing, fixed costs and a return must be covered.
Instructor noteIn the short run, any price above variable cost adds contribution; in the long run, prices must cover all costs, including fixed costs and a return on investment. Many pricing questions test exactly that distinction.

Finished Pricing?

Mark it complete when you can compute a markup, a target cost and an elasticity, and match a market to its pricing power.

Calculators

Interactive tools

Each tool is pre-filled with an example from the lessons. Change any input; the results show the method, your numbers and what they mean.

Interactive CVP graph (multi-product)

Enter up to four products with their price, variable cost and sales mix in units. The tool finds the composite breakeven, the units of each product, the target-profit volume (before or after tax), margin of safety and operating leverage, and draws the breakeven chart.

Products, costs and targets

Make-vs-buy analyzer

Separates relevant from irrelevant costs: only variable costs, avoidable fixed costs and the opportunity cost of the freed capacity count.

Part costs and offer

Special-order analyzer

Tests a one-time order against idle capacity: displaced regular sales are a relevant cost; allocated fixed overhead is not.

Order and capacity

Print-ready

Formula sheet

Every formula in Decision Analysis on one sheet. Print it from here: the sidebar is hidden and the sheet prints black on white.

Spaced repetition

Flashcards

Recall first, then flip. Your grade schedules the next review (SM-2-lite).

Exam-style questions

Practice MCQs

Practice mode gives instant feedback; timed mode allows 1.8 minutes per question, like the exam. Filter by topic, difficulty, or questions you missed.

Essay section

Written-response practice

Write your answer first (aim for about 30 minutes per case), then compare it with the model answer and score yourself against the rubric. Show your calculations: the exam awards marks for method.

Key terms

Glossary

Search the section's vocabulary. Underlined terms in the lessons show these definitions on hover or keyboard focus.