CMA Final · Strategic Cost Management

Pricing Decisions and Strategies: formula sheet

Full chapter guide

Key formulas

Profit: Profit = (Selling price per unit − Variable cost per unit) × Units sold − Fixed costs; Use this to test any proposed price and volume.
Contribution per unit: Contribution per unit = Selling price − Variable cost per unit; The minimum price in a short-run decision must at least cover variable cost.
Target price from return on capital: Price per unit = (Total cost + Required return on capital employed) ÷ Units; Required return = Capital employed × Target return %.
Price elasticity of demand: Elasticity = % change in quantity demanded ÷ % change in price; Ignore the sign when reading it. Above 1 means elastic, below 1 means inelastic.
Profit-maximising rule (economic theory): Marginal revenue = Marginal cost; Profit is highest at the output where this holds, subject to MC rising faster than MR.
Full cost per unit: Full cost = Variable cost per unit + Fixed cost ÷ Budgeted units; Use the volume the question states. Include selling and distribution cost if the question asks for full cost of sales.
Cost-plus price (markup on cost): Selling price = Cost × (1 + Markup %); Cost may be full cost or variable cost, depending on the method.
Price from margin on sales: Selling price = Cost ÷ (1 − Margin % on sales); Use when profit is given as a percentage of selling price.
Required profit under ROCE: Required profit = Target ROCE % × Capital employed; Capital employed may include fixed assets and working capital, as the question states.
Markup % for ROCE pricing: Markup % on cost = Required profit ÷ Total cost × 100; Total cost here means the cost base the markup is applied to, for the same volume.
Markup on variable cost: Markup on variable cost = Fixed cost + Required profit; Divide by variable cost to get a markup percentage.
Target cost: Target cost = Target selling price − Target profit; Target profit may be given as an amount per unit, a percentage of sales, or a return on investment.
Target profit on sales: Target profit = Target price × Profit margin % on sales; If profit is a markup on cost, then profit = Target cost × markup %, so Target cost = Price ÷ (1 + markup %).
Target profit on investment: Target profit = Capital employed × Required return %; Divide by units to get profit per unit when the return is on total investment.
Cost gap: Cost gap = Current (estimated) cost − Target cost; A positive gap means cost must be reduced. A negative gap means the product already meets the target.
Cost-plus price (for contrast): Price = Cost + Markup; Target costing reverses this: Cost = Price − Profit.
Price elasticity of demand: Ed = (% change in quantity) ÷ (% change in price); Normally negative. Use the absolute value |Ed| to classify: above 1 elastic, below 1 inelastic, equal to 1 unit elastic.
Point elasticity: Ed = (dQ ÷ dP) × (P ÷ Q); For a demand equation Q = a − bP, dQ ÷ dP = −b. Use P and Q at the point asked.
Linear demand (price form): P = a − bQ; a is the price at which quantity is zero. b is the price fall per extra unit.
Total and marginal revenue: TR = P × Q = aQ − bQ²; MR = d(TR) ÷ dQ = a − 2bQ; For a straight-line demand curve, MR has the same intercept as demand but twice the slope.
MR and elasticity: MR = P × (1 − 1 ÷ |Ed|); MR is positive only when |Ed| is above 1. A profit-maximiser with positive MC therefore prices where demand is elastic.
Profit-maximising condition: MR = MC; Also check that MR cuts MC from above, so the point is a maximum. Price is then read from the demand curve.
Markup rule (constant elasticity): P = MC × |Ed| ÷ (|Ed| − 1); Valid only for |Ed| above 1. It follows from MR = MC and the MR–elasticity link.
Bundle price benefit: Bundle price < Σ individual prices; Bundle contribution = Bundle price − Σ variable costs of items; Accept the bundle only if its contribution beats the contribution lost or gained from separate sales.
Loss leader test: Net gain = Contribution from extra sales of other products − Loss on leader item; Strategy is justified only if net gain is positive.
Skimming vs penetration check: Compare total contribution = (Price − Variable cost per unit) × Volume, for each strategy over the planning period; Include fixed costs and the time period; skimming has high margin and low volume, penetration the reverse.
Predatory pricing indicator: Price < Average variable cost (or relevant cost); A rule of thumb for identification, not a legal test in every case.
Minimum transfer price (seller): Minimum price = Variable cost per unit + Opportunity cost per unit; Opportunity cost is zero with spare capacity. At full capacity it is the contribution lost on external sales.
Minimum price at full capacity: Minimum price = Variable cost + (External price − Variable cost) = External price; Adjust for any selling or distribution cost saved on internal transfers.
Maximum transfer price (buyer): Maximum price = Lower of (External purchase price, Net marginal revenue of the buyer); Net marginal revenue = Final selling price − buyer's further processing cost, per unit.
Acceptable range: Minimum price ≤ Transfer price ≤ Maximum price; A transfer is worthwhile for the company only if the minimum is not above the maximum.
Cost-plus transfer price: Transfer price = Cost per unit + Mark-up % × Cost per unit; State whether cost is variable or full cost. Mark-up is on cost, not on price, unless told otherwise.
Minimum price for a special order: Minimum price = Incremental cost + Opportunity cost of capacity used; Use only relevant costs. Ignore sunk costs and fixed costs that do not change.
Joint product apportionment (NRV method): NRV at split-off = Final sales value − Further processing cost − Selling cost after split-off; Joint costs are shared in the ratio of NRV. Joint cost allocation does not affect the decision to process further.

Quick revision

Price depends on cost, customers, competitors, law and company objectives.
Cost-plus price = cost base + mark-up; always check whether the base is full or variable cost.
Mark-up on cost and margin on selling price are different; convert carefully.
Target cost = target selling price − target profit.
Cost gap = current estimated cost − target cost; close it through design and process changes.
Target costing starts from the market price; cost-plus starts from the cost.
Price elasticity = % change in quantity demanded ÷ % change in price.
Demand is elastic when the elasticity magnitude is above 1; a price cut then raises revenue.
Skimming suits distinctive new products; penetration suits price-sensitive markets seeking share.
Minimum transfer price = marginal cost + opportunity cost of the transferring division.
Special orders are judged on relevant costs and contribution, considering spare capacity.
Always end a numerical answer with a clear recommendation.

Common mistakes

Listing factors generically without using the case facts. Fix: Quote a fact from the case against each factor and state whether it pushes the price up or down.
Classifying a factor in the wrong group, such as treating competitors' prices as internal. Fix: Ask if the firm can change it. If yes, internal. If no, external.
Applying the markup to the wrong cost base, for example full cost markup percentage on variable cost. Fix: Write the cost base next to the markup. A markup computed on full cost applies only to full cost.
Confusing markup on cost with margin on sales. Fix: Use Cost × (1 + markup) for markup on cost, and Cost ÷ (1 − margin) for margin on sales.
Treating profit margin on sales as markup on cost. Fix: Read the base. For margin on sales, profit = % × price. For markup on cost, target cost = price ÷ (1 + markup).
Adding profit to cost to get the target price. Fix: In target costing the price is given by the market. Always subtract profit from price.
Setting price equal to marginal cost, or treating MR as equal to price. Fix: Always derive MR from TR. For P = a − bQ, MR = a − 2bQ, not a − bQ.
Substituting the optimal quantity into the MR equation to get price. Fix: Find Q from MR = MC. Then put Q into the demand equation. Price comes only from demand.
Treating loss leader and predatory pricing as the same thing. Fix: Loss leader aims to raise total profit through other sales. Predatory aims to eliminate rivals and later raise prices. State the objective.
Recommending skimming for any new product. Fix: Check for uniqueness, protection from entry and low price sensitivity. Otherwise penetration may fit.

Exam tips

Always start with the pricing objective. Examiners reward answers that link factors to it.
Tie each factor to a fact in the case. A bare list earns few marks.
Split factors clearly into internal and external. Use short headed bullets.
For numbers, show contribution and total profit at each option before you recommend.
End with a firm recommendation and one risk.
Write the cost base and volume at the top of your working. Examiners give marks for a clear structure even if one figure slips.
Show required profit separately in ROCE questions. It is usually a marked step.
Read whether the markup is on cost or on sales before you start.