P1: Short-term decision making

Answer: C. Contribution per unit = selling price − variable cost = £25 − £17 = £8. Breakeven point = fixed costs ÷ contribution per unit = £90,000 ÷ £8 = 11,250 units. The figure 3,600 divides fixed costs by the selling price (£90,000 ÷ £25) — a common error that ignores variable costs. The 5,294 figure divides by the variable cost. Breakeven is reached when total contribution (units × £8) exactly covers fixed costs, which is why contribution, not selling price, is the correct divisor. 10,000 units does not follow from the figures.

Answer: D. Contribution per unit = £40 − £24 = £16. C/S ratio = contribution ÷ selling price = £16 ÷ £40 = 40%. The 60% figure is the variable cost to sales ratio (£24 ÷ £40), the complement of the C/S ratio. The 67% figure uses the wrong denominator (£16 ÷ £24 = 67%). The C/S ratio is useful for finding breakeven revenue (fixed costs ÷ C/S ratio) and for multi-product CVP analysis without having to work in units. 150% divides variable cost by contribution (£24 ÷ £16).

Answer: A. The £50,000 has already been spent and cannot be recovered regardless of whether the launch proceeds. It is a sunk cost and therefore irrelevant to the decision. Only future, incremental cash flows that differ between the available choices should be included in the analysis. Including sunk costs in decisions leads to a form of irrational thinking known as the sunk cost fallacy — committing to a course of action because of past expenditure rather than future expected value.

Answer: B. When a resource is scarce, the correct ranking criterion is contribution per unit of the limiting factor. Product Q earns £30 ÷ 3 = £10 per machine hour; Product P earns £20 ÷ 4 = £5 per machine hour. Product Q generates twice as much contribution from each scarce machine hour, so it should be prioritised. Ranking by contribution per unit (which would favour Q here anyway) is coincidental — it is the contribution per unit of the limiting factor that always gives the correct production priority.

Answer: C. With spare capacity and unavoidable fixed costs, the only relevant cost of making is the variable cost of £14 per unit. Comparing this with the £19 external price, making is £5 per unit cheaper. Fixed costs are irrelevant because they will be incurred whether or not the component is made internally. On purely financial grounds, the company should make the component. Non-financial factors (such as quality, reliability of supply and strategic considerations) may also be relevant but are not asked for here.

Answer: D. An opportunity cost is the benefit forgone from the next best alternative use of a resource. By diverting the machine to the special order, the company sacrifices £8,000 of contribution from Product X — this forgone benefit is a genuine economic cost of the decision and must be included as a relevant cost when assessing the minimum acceptable price for the special order. Sunk costs relate to past spending, not forgone future benefits. Opportunity costs involve no cash outflow but are nonetheless real economic costs.

Answer: A. A mark-up is added to cost, so selling price = cost × (1 + mark-up) = £45 × 1.30 = £58.50. The £64.29 figure is the classic mark-up versus margin error: if the target were a 30% margin on selling price, the selling price would be £45 ÷ (1 − 0.30) = £45 ÷ 0.70 = £64.29. A mark-up percentage is based on cost; a margin percentage is based on selling price. This distinction is tested frequently because candidates confuse the two. £54.00 applies a 20% mark-up, and £75.00 divides cost by 0.60.

Answer: A. Margin of safety in units = budgeted sales − breakeven sales = 12,000 − 8,400 = 3,600 units. Margin of safety as a percentage of budgeted sales = 3,600 ÷ 12,000 × 100 = 30%. This means sales could fall by 30% from budget before the company makes a loss. The 70% figure is the breakeven point as a percentage of budgeted sales (8,400 ÷ 12,000), not the margin of safety. A higher margin of safety indicates lower risk. 42% and 70,000 units do not follow from the figures; the margin of safety in units is 3,600.

Answer: B. Units required to achieve target profit = (fixed costs + target profit) ÷ contribution per unit = (£120,000 + £30,000) ÷ £15 = £150,000 ÷ £15 = 10,000 units. The 8,000 unit figure covers only the fixed costs (£120,000 ÷ £15) — that is the breakeven point. The 2,000 unit figure covers only the target profit (£30,000 ÷ £15). Both the fixed costs and the target profit must be covered by total contribution before the target profit is earned. 9,000 units does not follow from the figures.

Answer: C. With spare capacity, fixed overhead costs that will be incurred regardless are not relevant. The minimum price must cover the variable cost (£18) plus any avoidable fixed costs specific to this order (£4,000 ÷ 2,000 = £2 per unit). Minimum price = £18 + £2 = £20. The £18 figure ignores the specific additional fixed costs of the order. Any price above £20 per unit generates a positive contribution and improves overall profitability. £22.00 adds £4 a unit, misreading the £4,000 order cost as a per-unit figure, and £24.00 does not follow from the figures.

Answer: D. The shutdown decision is based on relevant (avoidable) costs. If the division closes, the company saves the avoidable fixed costs of £60,000 but loses the contribution of £50,000. Since avoidable fixed costs (£60,000) exceed contribution (£50,000), the company is better off by £10,000 if it closes the division. The head office costs of £70,000 are not avoidable and are irrelevant to the decision. The overall loss of £80,000 includes unavoidable fixed costs that do not affect the closure decision. The head office costs are indeed unavoidable, but that is a reason to leave them out, not a reason to keep the division. A positive contribution is not enough when the division's own avoidable fixed costs exceed it.

Answer: A. PED = percentage change in quantity demanded ÷ percentage change in price. Percentage change in quantity = (4,000 − 5,000) ÷ 5,000 × 100 = −20%. Percentage change in price = (£10 − £8) ÷ £8 × 100 = +25%. PED = −20% ÷ +25% = −0.80. A PED of −0.80 means demand is price inelastic (absolute value less than 1) — a 25% price rise causes only a 20% fall in demand, so total revenue rises. The common error is to use the new price as the base for the percentage price change. −1.25 inverts the ratio (25% ÷ 20%), and −2.00 does not follow from the figures.

Answer: B. Market skimming sets a high initial price to capture the maximum willingness to pay from early adopters before gradually reducing the price to attract more price-sensitive segments. It is suitable where the product has unique features, demand is inelastic initially, and there is no immediate competition. Penetration pricing would set a low price to build market share quickly, suitable where there is existing competition or where scale economies are available. Cost-plus and marginal cost pricing are cost-based methods that do not consider market conditions.

Answer: C. Weighted benefit scoring is used when a decision involves multiple criteria that vary in importance — for example, when choosing between suppliers or projects where cost, quality, reliability and strategic fit all matter but at different weights. Each criterion is assigned a weight reflecting its importance, options are scored against each, and the weighted total determines the preferred option. It is particularly useful when purely financial analysis would miss important qualitative factors or when decision makers need a structured way to balance trade-offs.

Answer: D. Breakeven revenue = fixed costs ÷ C/S ratio = £150,000 ÷ 0.40 = £375,000. At this revenue level, total contribution (40% × £375,000 = £150,000) exactly covers fixed costs. £250,000 divides by the 60% variable cost ratio instead of the 40% contribution ratio. £60,000 multiplies fixed costs by 0.40 instead of dividing, and £210,000 adds 40% to fixed costs. This approach is particularly useful when products are measured in revenue terms rather than units, or when the product mix is fixed.

Answer: A. Rank by contribution per machine hour: B = £30 ÷ 3 = £10/mh; A = £36 ÷ 4 = £9/mh. Produce all of B first: 300 × 3 = 900 hours used, 300 hours remaining. Produce A with remaining hours: 300 ÷ 4 = 75 units. Maximum contribution = (300 × £30) + (75 × £36) = £9,000 + £2,700 = £11,700. The £11,190 figure arises from the common error of ranking by contribution per unit (A first at £36 > £30): making all 200 A uses 800 hours; remaining 400 hours give 133 units B at £30 = £3,990; total £7,200 + £3,990 = £11,190, which is inferior. The £16,200 ignores the capacity constraint entirely.

Answer: B. The 500 kg already in stock has no relevant cost because it has no alternative use and cannot be resold — whatever happens, this cost has already been sunk and no future cash flow depends on what is decided about using it. The original purchase price (£1,500) is a sunk cost and irrelevant. The current purchase price (£5/kg) is only relevant for the additional 300 kg that must be bought. The relevant cost of the 800 kg total = £0 (for 500 kg in stock) + 300 kg × £5 = £1,500.

Answer: C. The workers are on permanent contracts and are currently idle — their wages will be paid regardless of whether the special order is accepted. There is no additional (incremental) cash outflow for labour if the order uses the idle time (150 hours available). The relevant cost is therefore zero. The £1,800 figure (150 hours × £12) is the total wage cost, but this is not incremental — it will be paid anyway. Relevant costs are future, incremental cash flows; payments already committed are not relevant. £2,400 values all 200 idle hours, and £600 values the 50 hours left over; neither is incremental.

Answer: D. When PED is −1.5 (elastic, absolute value > 1), a 10% price reduction leads to a 15% increase in quantity demanded (10% × 1.5). Revenue = price × quantity. Price falls by 10%, quantity rises by 15%, so revenue rises. Total revenue always increases when a price reduction is made for an elastic product (PED > 1 in absolute terms). Revenue remains unchanged at unit elasticity (PED = −1), and falls for inelastic products (PED < 1 in absolute terms).

Answer: A. Pricing at marginal cost means the price equals variable cost, so contribution is zero — no profit is made and none of the fixed costs are recovered through this product. Marginal cost pricing may be used in the short run to utilise spare capacity (where fixed costs are already covered by other products) or in competitive bidding, but it cannot be sustained long-run as it does not recover fixed costs. The company does not maximise profit at this price and does not always win contracts, as competitors may price below marginal cost.

Answer: B. A profitable special order might still be rejected on non-financial grounds — for example, if supplying a competitor could undermine the company's market position, expose its cost base, or assist a rival to compete more effectively. Using spare capacity (a financial argument) and positive contribution (also financial) support acceptance. Reduced fixed cost per unit is a financial benefit. Non-financial considerations include strategic implications, customer relationships, quality concerns, capacity strain for existing customers, and reputational effects.

Answer: C. Profit is maximised where marginal cost (MC) = marginal revenue (MR). MR is derived from the demand function: TR = PQ = (100 − 0.5Q)Q = 100Q − 0.5Q². MR = dTR/dQ = 100 − Q. Setting MC = MR: £20 = 100 − Q → Q = 80. Price = £100 − 0.5(80) = £100 − £40 = £60. This confirms the correct answer of £60. Pricing at variable cost gives zero contribution; the demand curve midpoint (£50) is not the profit-maximising point unless by coincidence.

Answer: C. With full capacity, making the component has an opportunity cost — the contribution forgone from Product Z. Relevant cost of making = variable cost + opportunity cost = £15 + £8 = £23. Comparing with the external price of £20: buying externally (£20) is cheaper than making (£23), so the company should buy. This differs from the spare-capacity case (where the relevant cost of making is just £15). Opportunity costs are the critical additional element when resources are scarce.

Answer: D. The relevant cost is the economic sacrifice of using the machine — its opportunity cost, which is the cash the company could receive if it sold the machine instead of using it for the order: £18,000. The original cost (£50,000) is sunk; the carrying amount (£30,000) is an accounting figure, not a cash flow; and zero is incorrect because the company forgoes £18,000 of resale proceeds. If the machine has no resale value and no other use, then the relevant cost would be zero. The opportunity cost is the correct relevant cost here.

Answer: A. Contribution: A = £40 − £28 = £12; B = £60 − £30 = £30. In a 2:1 bundle: revenue = (2 × £40) + £60 = £140; contribution = (2 × £12) + £30 = £54. Breakeven in bundles = £54,000 ÷ £54 = 1,000 bundles. Breakeven revenue = 1,000 × £140 = £140,000. The £180,000 figure uses only Product A's C/S ratio (£12/£40 = 30%), giving £54,000 ÷ 0.30 = £180,000. Multi-product CVP requires a weighted C/S ratio based on the actual product mix. £108,000 uses only Product B's C/S ratio (50%), and £162,000 does not follow from the figures.

Answer: B. Full cost per unit = direct cost + fixed overhead = £60 + £20 = £80. A 25% margin means cost is 75% of selling price: selling price = £80 ÷ 0.75 = £106.67. The £100.00 figure uses a 20% margin (£80 ÷ 0.80). The £112.50 figure does not follow from either a margin or a mark-up on the £80 full cost, and £80.00 is the full cost with no profit added. Note: margin is based on selling price (divide cost by 1 − margin); mark-up is based on cost (multiply cost by 1 + mark-up). The question specifies margin.

Answer: C. In a commodity market with homogeneous products, individual companies have little or no pricing power — they are price takers who must accept the prevailing market price. Setting a price significantly above the market rate would result in losing all sales to competitors. Cost-plus pricing is internally focused and ignores market realities, market skimming requires product differentiation, and price discrimination requires identifiable segments with different willingness to pay. Accepting the market price and focusing on cost efficiency is the rational approach.

Answer: D. The P/V chart plots profit (or contribution) on the vertical axis against volume (or revenue) on the horizontal axis. The line starts at the fixed cost loss (where volume is zero) and rises as volume increases. Its gradient represents the contribution earned per additional unit sold — or the C/S ratio if the horizontal axis is revenue. The line crosses the horizontal axis at the breakeven point. The slope directly shows how much each additional unit improves the profit position, which is why the C/S ratio and contribution per unit are key insights from the chart.

Answer: A. CVP analysis assumes that costs are either purely fixed or variable (linearly related to volume), that selling price is constant (linear revenue), and that in a multi-product setting the product mix remains fixed. In reality, costs often have stepped fixed and semi-variable elements, prices may change with volume (discounts), and the product mix may shift. The relevant range limits where the linear assumptions hold. Despite these limitations, CVP is a valuable tool for quick profitability analysis if its assumptions are understood.

Answer: B. The £15,000 already spent is a sunk cost — irrelevant to the make-or-buy decision going forward. The only relevant cost of completing internally is the future incremental cost of £8,000. Comparing £8,000 (make) with £10,000 (buy), completing internally is £2,000 cheaper on a relevant cost basis. Including the sunk £15,000 would incorrectly suggest that making is more expensive than buying. Relevant cost analysis focuses exclusively on future, incremental cash flows that differ between the options.

Answer: C. Price discrimination involves charging different prices to different market segments for the same (or similar) product when those segments have different price elasticities of demand — for example, business vs leisure train fares, or time-based pricing. It is profitable when segments can be separated, arbitrage prevented, and the segments have different willingness to pay. Charging uniform prices, cost-plus pricing, and price matching are all different approaches that do not involve discriminating between customer segments.

Answer: D. Minimum price must cover variable cost plus the opportunity cost of displaced contribution. Opportunity cost per unit = £10 (contribution forgone from regular sales). Minimum price = variable cost + opportunity cost = £20 + £10 = £30. At this price the special order neither improves nor worsens profitability — it just covers the relevant costs. Any price above £30 increases overall profit. The offered price of £35 exceeds this minimum, so the order is profitable. Opportunity costs are only relevant when capacity is fully utilised. £25 adds only half of the lost contribution.

Answer: A. Breakeven units = £90,000 ÷ £8 = 11,250 units. Margin of safety in units = 16,000 − 11,250 = 4,750 units. Margin of safety % = 4,750 ÷ 16,000 × 100 = 29.7%. 70.3% is the breakeven point as a percentage of budgeted sales (11,250 ÷ 16,000 × 100), not the margin of safety. 56.25% and 43.75% do not follow from the figures. The margin of safety shows how much sales could fall from budget before the company breaks even, making it a measure of business risk.

Answer: B. Absorption costing spreads fixed overhead across all units produced; as volume falls, fewer units absorb the fixed cost, raising the overhead per unit and therefore the full cost. If the company mechanically applies a mark-up to this rising full cost, it will increase prices at precisely the time demand is weakest — a potentially self-defeating strategy. Marginal cost pricing separates the variable cost from fixed overhead, allowing more flexible pricing that covers at least the variable cost while maintaining contribution. Fixed costs are not ignored by absorption pricing — quite the opposite, they drive the problem.

Answer: C. Contribution per labour hour: P = £24 ÷ 4 = £6/hr; Q = £15 ÷ 2 = £7.50/hr. Rank Q first. Make all Q: 200 × 2 = 400 hours; 400 hours remaining. Make all P: 100 × 4 = 400 hours. Both products' full demand fits in 800 hours. Maximum contribution = (200 × £15) + (100 × £24) = £3,000 + £2,400 = £5,400. £2,400 is Product P's contribution alone, and Q alone at full demand gives £3,000 (200 × £15). £4,500 and £6,900 do not follow from making both products to full demand. With exactly enough hours for full demand of both, no prioritisation decision is needed here — the ranking exercise would be needed only if capacity were tighter.

Answer: D. Contribution = revenue − variable costs = £200,000 − £150,000 = £50,000. Avoidable fixed costs = £40,000. Net benefit of keeping open = contribution − avoidable fixed costs = £50,000 − £40,000 = £10,000. The segment should be kept open. Head office costs of £25,000 are unavoidable (they will be reallocated elsewhere if the segment closes) and are irrelevant to the decision. The overall reported loss (£200,000 − £150,000 − £40,000 − £25,000 = −£15,000) includes allocated unavoidable costs and is misleading for this decision.

Answer: A. Maximising market share through penetration pricing — setting a low initial price to gain customers quickly, accepting short-term losses — is a legitimate and commonly used pricing objective in competitive markets where scale or network effects matter. Rigidly applying a cost-plus formula ignores market realities, attempting to extract maximum payments from all customers regardless of willingness to pay is unsustainable and ethically questionable, and never changing prices would prevent responding to cost or market changes.

Answer: C. The relevant labour cost = the direct cost of the labour + the opportunity cost of lost contribution. Direct cost = £15/hour (the contract workers must be paid for hours worked on the special order). Opportunity cost = £6/hour (the contribution forgone from the displaced work). Total relevant cost = £15 + £6 = £21/hour. At full capacity, using labour for the special order forgoes other profitable work, making the opportunity cost a genuine relevant cost. With spare capacity, the opportunity cost would be zero and the relevant cost would be just £15/hour. £9 deducts the lost contribution instead of adding it.

Answer: D. Profit is earned when revenue exceeds total cost, so the profit zone on a breakeven chart is the area to the right of the breakeven point where the revenue line sits above the total cost line. To the left of the breakeven point, costs exceed revenue and the area represents a loss. Fixed costs remain constant (a horizontal line), and the question of whether they exceed variable costs depends on the output level, not the profit zone. The vertical gap between the revenue and total cost lines represents the profit or loss at each level of output.

Answer: A. Current revenue = 2,000 × £50 = £100,000. New revenue = 1,700 × £55 = £93,500. Revenue falls by £6,500. PED check: % change in Q = (1,700 − 2,000)/2,000 = −15%; % change in P = (£55 − £50)/£50 = +10%; PED = −15/10 = −1.5. Since PED is elastic (absolute value > 1), a price rise reduces total revenue — consistent with the calculated fall. When demand is elastic, the proportional volume decline outweighs the price increase. A revenue rise would occur only if demand were inelastic.

Answer: B. Contribution per machine hour: X = £18/3 = £6/hr; Y = £20/5 = £4/hr. Rank X first. Make all X: 200 × 3 = 600 hours; 400 hours remaining. Make Y: 400/5 = 80 units of Y. Maximum contribution = (200 × £18) + (80 × £20) = £3,600 + £1,600 = £5,200. The £3,600 figure produces only product X (all 200 units), ignoring the remaining 400 hours that could produce Y. The £2,000 figure represents only Y at full demand (100 × £20). Ranking by contribution per unit would favour Y first (£20 > £18), giving a worse total: 100Y (500 hrs) + 166X (498 hrs) = (100×£20) + (166×£18) = £2,000 + £2,988 = £4,988 — inferior. £3,200 does not follow from the figures.

Answer: C. Supplier A weighted score = (8 × 0.50) + (5 × 0.30) + (7 × 0.20) = 4.00 + 1.50 + 1.40 = 6.90. Supplier B weighted score = (6 × 0.50) + (9 × 0.30) + (8 × 0.20) = 3.00 + 2.70 + 1.60 = 7.30. Supplier B has the higher weighted score (7.30 vs 6.90). Despite Supplier A's price advantage (the highest-weighted criterion), Supplier B's superior quality score is sufficient to give it an overall higher weighted score. Weighted benefit scoring makes trade-offs between criteria explicit and forces a structured comparison. 6.9 is Supplier A's correct score but it is the lower of the two, and 7.1 does not follow for either supplier.

Answer: D. Material relevant cost = scrap value foregone = £300 (this is the opportunity cost — the company could sell the material for scrap, so using it for the order forgoes £300 of cash). Labour relevant cost = £0 (idle workers are already being paid; no incremental cash flow from using them). Total relevant cost = £300 + £0 = £300. The book value (£1,000) is a sunk cost. The standard labour cost (200 × £10 = £2,000) is not incremental because idle workers are paid regardless. Any price above £300 for the special order covers relevant costs and improves profit. £3,000 uses the book value and the standard labour cost (£1,000 + £2,000), and £2,300 adds the £2,000 labour cost to the scrap value.

Answer: A. When actual production (8,000 units) is below budgeted production (10,000 units), the fixed overhead per unit rises: £100,000 ÷ 8,000 = £12.50 vs the budgeted £10.00. If the company sticks with the budgeted full cost (£10/unit absorbed), the price set will not fully recover actual fixed overhead — under-recovery means the company is in effect pricing below actual full cost. The correct full cost pricing would use the higher actual overhead rate, but that may price the company out of the market, illustrating a fundamental limitation of cost-plus pricing.

Answer: B. Beyond financial analysis, a make-or-buy decision should consider whether an external supplier can deliver consistent quality and reliable supply, whether the company would become dependent on a single source, and whether strategic know-how might be lost by outsourcing. Standard cost, OAR and fixed cost per unit are all financial factors already captured (or appropriately excluded) in the relevant cost analysis. Supplier reliability and quality are genuine non-financial considerations that could make buying inadvisable even when financially attractive.