ACCA Applied Skills · Performance Management

Pricing decisions: formula sheet

Full chapter guide

Key formulas

Price elasticity of demand: PED = % change in quantity demanded ÷ % change in price; Use the absolute value. Above 1 is elastic, below 1 is inelastic, equal to 1 is unitary.
Demand line: P = a − bQ; a is the price where demand is zero. It is the intercept on the price axis.
Gradient b: b = change in price ÷ change in quantity; If price falls $1 for every 50 extra units, b = 1 ÷ 50 = 0.02.
Finding a: a = P + bQ; Use any known price and quantity point on the line.
Marginal revenue: MR = a − 2bQ; The slope is twice that of the demand line. It holds for a straight-line demand curve.
Profit-maximising output: MR = MC, so Q = (a − MC) ÷ 2b; Substitute Q back into P = a − bQ to get the price. This assumes MC is constant.
Point elasticity on a straight line: PED = (1 ÷ b) × (P ÷ Q); Elasticity changes along the line. It is higher at higher prices.
Revenue effect: Elastic: raise price, revenue falls. Inelastic: raise price, revenue rises.; Reverse the effect for a price cut.
Demand function: P = a − bQ; P is price, Q is quantity demanded. This is a straight-line demand curve.
Slope of demand curve (b): b = change in price ÷ change in quantity; Use the price change for a given change in demand. For example, a $5 price change that moves demand by 500 units gives b = 5 ÷ 500 = 0.01.
Intercept of demand curve (a): a = current price + (b × current quantity); This is the price at which demand would be zero. It is the same as the price at Q = 0.
Marginal revenue function: MR = a − 2bQ; Same intercept as the demand function, twice the slope. Derived from total revenue PQ = aQ − bQ² by differentiating.
Profit-maximising condition: MR = MC; MC is usually the constant variable cost per unit.
Profit-maximising quantity: Q = (a − MC) ÷ 2b; Comes from solving a − 2bQ = MC.
Profit-maximising price: P = a − bQ; Substitute the optimal Q into the demand function. Do not use the MR equation.
Maximum profit: Profit = (P − MC) × Q − fixed costs; This holds where MC is the constant variable cost per unit.
Full cost: Full cost per unit = variable cost per unit + fixed overhead absorbed per unit; Fixed overhead per unit = budgeted fixed overhead ÷ budgeted activity level.
Price with mark-up on cost: Selling price = cost × (1 + mark-up %); Use full cost for full cost-plus and variable cost for marginal cost-plus.
Mark-up on cost: Mark-up % = (selling price − cost) ÷ cost × 100; Use this to find the mark-up a current price implies.
Margin on selling price: Margin % = (selling price − cost) ÷ selling price × 100; Margin % = mark-up % ÷ (1 + mark-up %).
Required mark-up for a target return: Mark-up % = required profit ÷ total cost base × 100; Used when a target profit is set and the cost base is known.
Skimming: when it suits: Inelastic demand at launch + unique or protected product + high development costs + short life cycle; These are conditions, not a calculation. Check each against the scenario. Not all need to hold.
Penetration: when it suits: Elastic demand + economies of scale + easy entry for rivals + long life cycle or need for early share; Again, these are indicators. Use the facts given and say which matter most.
Price elasticity of demand: PED = % change in quantity demanded ÷ % change in price; Ignore the sign when comparing. PED above 1 is elastic, so a price cut raises revenue. PED below 1 is inelastic.
Profit at a given price: Profit = (Price − Variable cost per unit) × Volume − Fixed costs; Use this to compare the two strategies over the period in the question.
Conditions for price discrimination: Separable markets + different price elasticities of demand; Both are needed. Charge more in the less elastic (less price-sensitive) market.
Bundle price test: Bundle price < sum of individual prices, and bundle contribution > contribution lost from discounts; Compare total contribution with and without the bundle, not just revenue.
Loss leader test: Contribution from extra sales of other products > loss on the leader; The strategy only pays if customers buy the profitable items as well.
Volume discount contribution: Contribution per unit at discounted price × volume − contribution at normal price × volume; Use contribution (selling price less variable cost) to judge if a discount increases profit.
Minimum price of a special order: Minimum price = Relevant cost of the order (incremental cash costs + opportunity costs); Any price above this increases profit. Add a margin if the question asks for a target profit.
Relevant cost of materials: Already held and no other use: scrap/resale value (₹0 if none). Held and used elsewhere: replacement cost. Not held: current purchase cost.; Use the cost of the benefit given up. Check whether the material is regularly used.
Relevant cost of labour: Spare capacity: ₹0 extra if paid anyway. Fully used: pay + lost contribution (after pay) from the diverted work.; Count labour once only. Pay plus contribution after pay equals contribution before labour cost. Use one of these routes, never both.
Opportunity cost with scarce resource: Opportunity cost = contribution per unit of resource × units of resource diverted; Add this to the cash cost of the order. The opportunity cost is the contribution forgone. Count the cost of the resource once only: either add the resource cost to contribution calculated after it, or use contribution before it and add nothing more.
Make-or-buy with no scarcity: Make if relevant variable cost of making < buying price; Include avoidable fixed costs. Ignore unavoidable fixed costs.

Quick revision

Price elasticity of demand = % change in quantity demanded ÷ % change in price.
If demand is elastic (absolute value above 1), a price cut raises revenue.
If demand is inelastic (absolute value below 1), a price rise raises revenue.
Profit is maximised where marginal revenue = marginal cost.
With a straight-line demand curve P = a − bQ, MR = a − 2bQ.
Find the quantity from MR = MC, then put it into the demand function to get the price.
Full cost-plus: price = full cost per unit + mark-up.
Cost-plus is simple but ignores demand and competitors.
Market skimming: high initial price, then lower; suits novel products with less price-sensitive buyers.
Market penetration: low initial price to win share quickly; suits price-sensitive markets and scale economies.
Special order price should at least cover relevant costs, including any opportunity cost.
Make-or-buy: compare the relevant cost of making with the buying price, and consider capacity and quality.

Common mistakes

Working out the % change using the new figure as the base. Fix: Always divide the change by the original (starting) figure.
Using b as the quantity change per $1 price change, instead of price change per unit. Fix: Invert it. b = $1 ÷ 50 units = 0.02. Check by seeing that P falls as Q rises.
Using MR = a − bQ instead of a − 2bQ. Fix: Always write the demand equation first, then double the b term in MR. Keep a unchanged.
Calculating b upside down, as quantity change ÷ price change. Fix: b is price per unit of quantity: price change ÷ quantity change. Check that b is a small number such as 0.01.
Mixing up mark-up on cost with margin on selling price. Fix: Check the base. Mark-up uses cost: cost × (1 + m). Margin uses price: cost ÷ (1 − m).
Using the wrong activity level to absorb fixed overhead. Fix: Use the activity level given for absorption, usually budgeted production, unless told otherwise.
Reversing the two strategies, such as saying skimming means a low price. Fix: Remember that skimming takes the cream off the top, so the price is high. Penetration pushes into the market, so the price is low.
Listing advantages and disadvantages without linking them to the scenario. Fix: Pick the points that match the case facts and quote them. Say which advantage applies and why.
Confusing loss leader with captive product pricing. Fix: Ask whether the customer is locked in. Captive means the add-on only works with the main product. Loss leader just draws customers in.
Saying price discrimination works whenever prices differ. Fix: Always state the two conditions: separable markets and different elasticities. Also note that the product must be the same, not a different version.

Exam tips

Show the demand line, the MR line and the MR = MC step on separate lines. Marks are given for method even if the final number is wrong.
In objective test questions, you only get marks for the right answer. Do a quick check: substitute your optimal Q back into the demand line.
For written Section C parts, always tie the factor to the scenario (for example, many substitutes means elastic). Generic lists score poorly.
Do not forget to state the elastic or inelastic conclusion and what it means for the pricing decision.
When fixed costs appear in a question, say they are irrelevant to the optimal price, then ignore them.
In Section C, show the demand equation, the MR equation and the MR = MC line separately. Marks are given for each step, even if the final figure is wrong.
In objective test questions there are no part marks, so check b and a with the original data before you choose an answer. Plugging your Q back into the demand equation takes seconds.
Read the cost data carefully. Use the variable cost per unit as MC, and bring in fixed costs only when asked for profit. Watch for MC that changes at a given volume, which you should state and test.