PM: Decision-making

Answer: B. Relevant costs are future, incremental cash flows that differ between decision alternatives. The original cost of machinery (B) is a sunk cost — it was paid in the past and cannot be recovered regardless of the decision. Sunk costs are always irrelevant. Additional materials (A) are relevant — they are a future incremental cost. Contribution forgone (C) is relevant — it is an opportunity cost (the benefit sacrificed). Overtime wages (D) are relevant — they are additional future costs that arise only if the order is accepted.

Answer: C. For material that is in regular use, using it on the order means the company must buy more to replace it for ongoing production. The relevant cost is therefore the replacement cost: 500kg × £11/kg = £5,500. Option A (£4,000 = 500 × £8) uses the original purchase price, but that is a sunk historical cost and is irrelevant. Option B (£1,500 = 500 × £3) is the scrap value, which would only be relevant if the material had no other use and would otherwise be sold for scrap — here it is in regular use, so scrap value does not apply. Option D (£2,500) has no sound basis. The key test: material in regular use is valued at replacement cost; material with no alternative use is valued at the higher of its scrap/resale value or its value in any alternative use.

Answer: D. Opportunity cost is the value of the best alternative foregone. If the factory switches to the special order, it forfeits the £40,000 contribution from Product J — this is the opportunity cost and must be included as a relevant cost in pricing the special order. Option A confuses full utilisation with zero opportunity cost — it is precisely because capacity is fully used that an opportunity cost exists. Variable costs (B) are direct costs of the special order, not the opportunity cost. Fixed costs (C) continue regardless and are generally irrelevant to the special order decision.

Answer: A. Contribution per unit = £75 − £45 = £30. BEP = Fixed costs ÷ Contribution/unit = £180,000 ÷ £30 = 6,000 units. Margin of safety = Budgeted sales − BEP = 8,000 − 6,000 = 2,000 units. MOS as % of budget = 2,000 ÷ 8,000 × 100 = 25%. The MOS means sales can fall 25% below budget before a loss is made. The examiner (SD25) warned that candidates often calculate the MOS correctly but fail to explain its implications — the explanation is what earns the full marks in Section C. Option B has wrong BEP. Option C has wrong MOS. Option D has wrong BEP.

Answer: B. The examiner (SD25) warned against averaging the individual C/S ratios — the weighted average must be built from total contribution over total revenue. Total revenue = A (3,000 × £60 = £180,000) + B (3,000 × £40 = £120,000) = £300,000. Total contribution = A (3,000 × £24 = £72,000) + B (3,000 × £20 = £60,000) = £132,000. Weighted average C/S ratio = £132,000 ÷ £300,000 = 0.44. Multi-product breakeven revenue = fixed costs ÷ C/S ratio = £100,000 ÷ 0.44 = £227,273. Option A (0.50) uses Product B's C/S ratio alone. Option C (0.40) uses Product A's C/S ratio alone. Option D has the correct C/S ratio but divides into the wrong figure for BEP. Breakeven revenue assumes the budgeted sales mix is maintained.

Answer: A. With one limiting factor, rank by contribution per machine hour and satisfy demand in that order. D = £36 ÷ 3 = £12/hr; E = £20 ÷ 2 = £10/hr; F = £45 ÷ 5 = £9/hr. Priority: D, then E, then F. Make D to maximum demand: 600 × 3 = 1,800 hrs (3,000 left). Make E to maximum demand: 800 × 2 = 1,600 hrs (1,400 left). Use the remaining 1,400 hrs on F: 1,400 ÷ 5 = 280 units. Total contribution = D (600 × £36 = £21,600) + E (800 × £20 = £16,000) + F (280 × £45 = £12,600) = £50,200, using all 4,800 hours. Option B ranks by contribution per unit (F highest at £45), which misuses the scarce hours. Option C makes F to its full 400 units, which needs 5,400 hours — more than available. Option D also mis-ranks. Always rank by contribution per unit of the limiting factor, never by contribution per unit of product.

Answer: D. The objective function maximises total contribution: 50X + 60Y (£50 per X unit plus £60 per Y unit). Machine constraints are inequalities (≤) — available hours cannot be exceeded: M1: 2X + 1Y ≤ 1,000; M2: 1X + 3Y ≤ 1,200. Non-negativity: X,Y ≥ 0 (cannot produce negative quantities). Option A transposes X and Y coefficients in the objective function. Option B uses minimisation and ≥ constraints — appropriate for a cost-minimisation problem, not profit maximisation. Option C uses equalities — the constraints should be inequalities as not all capacity need be used.

Answer: A. The shadow price (dual price) represents the increase in the optimal objective function value (total contribution) for each additional unit of the binding resource. Here, each additional machine hour increases total contribution by £18. This means the company should be willing to pay up to £18 per hour above the current rate to obtain more hours — the premium paid is worthwhile as long as it is less than £18. At exactly £18 extra, the company is indifferent. Above £18 extra cost per hour, additional hours destroy value. Option B misunderstands the direction. Option C describes contribution per hour for a specific product, not the shadow price. Option D is wrong — shadow prices are essential for capacity expansion decisions.

Answer: B. Total Revenue = PQ = (200−4Q)Q = 200Q − 4Q². Marginal Revenue = dTR/dQ = 200 − 8Q. Marginal Cost = Variable cost = £24 (constant). Set MR = MC: 200 − 8Q = 24 → 8Q = 176 → Q = 22. Price: P = 200 − 4(22) = 200 − 88 = £112. Profit check: Revenue = 22×£112 = £2,464; Variable costs = 22×£24 = £528; Fixed costs = £5,000; Profit = £2,464 − £528 − £5,000 = −£3,064. Still a loss at these volumes — the question tests whether students can apply MR=MC correctly, not whether the business is profitable overall. Option A sets P=MC (competitive market outcome). Option C uses wrong Q. Option D is close but uses Q=20: MR at Q=20=200-160=40≠24.

Answer: C. PED = % change in quantity demanded ÷ % change in price = −15% ÷ +10% = −1.5. The negative sign reflects the inverse relationship between price and quantity for a normal good. Because |PED| > 1, demand is elastic: a 1% price rise causes a more-than-1% fall in quantity, so total revenue falls. Check: old revenue = 5,000 × £40 = £200,000; new revenue = 4,250 × £44 = £187,000 — revenue has indeed fallen, confirming option C. Option A wrongly shows a positive PED (ignoring the inverse relationship) and mislabels demand as inelastic. Option B inverts the ratio (10% ÷ 15% = −0.67) and would suggest revenue rising. Option D calculates the PED correctly as −1.5 but misclassifies it as inelastic — any |PED| above 1 is elastic.

Answer: D. Market skimming involves setting a high initial price, targeting customers who will pay a premium (early adopters, status-seekers), then reducing the price as the market broadens and competition intensifies. It is appropriate when the product is innovative, demand from early adopters is inelastic, and the company wants to recover R&D costs quickly. Penetration pricing (A) uses a low initial price to build market share rapidly. Cost-plus (B) is based on costs, not market positioning. Complementary product pricing (C) relates to products used together — not the scenario described.

Answer: A. The examiner (SD25, Example 3) specifically identified this: cost-plus pricing is commonly used by retailers due to its simplicity — a standard percentage mark-up applied consistently across a wide product range. It does NOT guarantee profit maximisation (B) — profit maximisation requires MR=MC, which cost-plus ignores; the examiner explicitly flagged this as a candidate error. Cost-plus is actually inappropriate when demand is highly elastic (C) — the price it produces may not reflect market conditions. Option D describes penetration pricing, not cost-plus.

Answer: B. Relevant analysis (only include avoidable costs): Revenue £480,000 − Variable costs £320,000 = Contribution £160,000. Specific avoidable fixed costs £90,000. Divisional contribution after avoidable costs = £160,000 − £90,000 = £70,000. If the division closes, this £70,000 is lost — the company is worse off by £70,000 as head office costs (£120,000) continue regardless. The reported net loss of £50,000 (£480k−£320k−£90k−£120k) is misleading because it includes unavoidable allocated costs. The division should remain open. Option A uses the misleading net loss. Option C incorrectly uses allocated costs. Option D overstates the position — profitability depends on which costs are included.

Answer: C. Relevant make costs only include future incremental costs: Direct materials £8 + Labour £5 + Variable overhead £3 = £16/unit. Fixed overhead: the general fixed overhead (£2/unit absorbed) continues regardless — irrelevant. The machinery depreciation (£4/unit) is a sunk cost (non-cash) — irrelevant even though 'specific.' Total relevant make cost = £16/unit. Buy cost = £18/unit. Since £16 < £18, making is cheaper — the company should continue to make. Option A uses total absorbed cost (£22) which includes irrelevant fixed overhead. Option B is wrong — the relevant make cost is £16, not £18, so make is cheaper rather than equal to buy. Option D makes an unsupported assumption about capacity redeployment.

Answer: D. Expected value = Σ(outcome × probability). EV = (£200,000×0.3) + (£80,000×0.5) + (−£60,000×0.2) = £60,000 + £40,000 − £12,000 = £88,000. Check: probabilities sum to 1 (0.3+0.5+0.2=1.0 ✓). The EV of £88,000 represents the average outcome if the decision were repeated many times. However, EV has limitations — it ignores risk attitude and does not reflect what will actually happen on any single occasion. Option A divides by 3 (simple average). Option B adds incorrectly. Option C ignores the loss scenario.

Answer: A. Maximin (maximum of the minimums) identifies the worst-case outcome for each option, then selects the option with the highest (least bad) worst-case: Option 1 worst = −£20,000; Option 2 worst = +£5,000; Option 3 worst = −£40,000. Maximin selects Option 2 (worst case £5,000 is the best worst case). This criterion suits a risk-averse decision-maker who wants to protect against the worst outcome. Maximax (B) selects highest best-case, suiting optimists. Option 3 has the best maximax outcome (£200,000). Options C and D misdefine the criterion.

Answer: B. EV of investing = (£120,000 × 0.6) + (£20,000 × 0.4) − £50,000 investment cost = £72,000 + £8,000 − £50,000 = £30,000. EV of not investing = £0. Since the EV of investing (£30,000) exceeds the EV of not investing (£0), the investment is recommended on an expected value basis. Option A applies a risk-aversion judgement that goes beyond EV analysis. Option C uses only the best case. Option D compares the machine cost with the minimum profit, which is not an expected value comparison. Note that the gross EV of £80,000 overstates the benefit unless the £50,000 cost is deducted.

Answer: C. The examiner (SD25) specifically asked about CVP limitations and noted candidates needed more than just identification — they needed to discuss the limitation. Key CVP assumptions that create limitations: constant selling price (breaks down with volume discounts), constant variable cost per unit (breaks down with learning curves or economies of scale), constant sales mix in multi-product situations, and linear cost and revenue functions. CVP can be applied to multi-product situations (A) using weighted average C/S ratios. It is specifically used for planning (B — it uses projected not actual costs). CVP applies to services as well as manufacturing (D).

Answer: D. When a single resource is the binding constraint, products should be ranked by contribution per unit of the limiting resource — here, contribution per skilled labour hour. This ensures the scarce resource is allocated to the use that generates the most contribution per hour used. Ranking by total contribution per unit (A) ignores how much of the scarce resource each unit consumes — a product with high total contribution but very high resource usage may be less efficient than one with lower total contribution but minimal resource use. Selling price (B) and variable cost (C) alone are insufficient measures when a constraint applies.

Answer: A. Calculate profit at each volume: 100 units: Revenue £5,000 − VC £1,800 − FC £2,000 = £1,200. 200 units: Revenue £9,000 − VC £3,600 − FC £2,000 = £3,400. 300 units: Revenue £11,400 − VC £5,400 − FC £2,000 = £4,000. 400 units: Revenue £12,000 − VC £7,200 − FC £2,000 = £2,800. Maximum profit = £4,000 at 300 units × £38, which is option A. Confirm with the marginal revenue approach: MR from 100→200 = (£9,000−£5,000)÷100=£40/unit > MC £18 ✓. MR from 200→300 = (£11,400−£9,000)÷100=£24/unit > MC £18 ✓. MR from 300→400 = (£12,000−£11,400)÷100=£6/unit < MC £18 ✗. Stop at 300 units.

Answer: B. Sensitivity analysis calculates how much a key variable (volume, price, cost) must change to make the NPV zero — the margin of safety for that variable. An 18% margin on volume means the project remains viable unless volume falls more than 18%. The critical limitation is that sensitivity tests one variable at a time and does not indicate the probability of the adverse change occurring. Management must then judge how likely an 18% volume fall is. Option A applies a probability judgement without basis. Option C draws an unwarranted conclusion. Option D confuses sensitivity with a risk-adjusted discount rate.

Answer: C. Make-or-buy decisions require both financial and qualitative analysis. Key qualitative factors for outsourcing IT: loss of internal knowledge and capability that may be hard to rebuild if needed; reduced control over service quality and response times; data security — a third party with access to company systems creates security and confidentiality risks; and strategic importance — if IT is a core competency or competitive differentiator, outsourcing it may undermine competitive position. Staff preferences (A), provider tax location (B), and equipment age (D) are peripheral considerations at best.

Answer: D. Slack is the difference between the available and used amount of a non-binding constraint. Machine B has 1,500−900=600 hours of slack — it has 600 unused hours. A non-binding constraint has a shadow price of zero — paying for additional capacity on a non-binding constraint adds no value. Machine A (fully utilised, zero slack) is the binding constraint with a positive shadow price. Option A incorrectly identifies Machine B as the binding constraint. Option B misinterprets slack — it does not indicate that production should be reduced. Option C is wrong — slack implies a shadow price of zero, not positive.

Answer: A. Full cost-plus: Selling price = Total cost per unit × (1 + mark-up %) = £80 × 1.25 = £100. Note: 'total cost' in full cost-plus includes production and non-production costs (administration, selling). The mark-up of 25% is applied to the full cost of £80 to give a selling price of £100. Option B applies the mark-up to production cost only (£60×1.25=£75). Option C uses a mark-up of 20% on total cost (£80×1.20=£96). Option D is just the total cost before mark-up.

Answer: B. Since the workforce is at full capacity, the extra 300 hours must be worked as overtime. Overtime rate = £15 × 1.5 = £22.50/hour. Relevant labour cost = 300 × £22.50 = £6,750. The regular rate (£15) is the sunk cost of the existing workforce — workers are paid regardless. Only the incremental cost of overtime (the 50% premium) is relevant to the decision. However, the full overtime rate (£22.50) is the relevant cost because these specific hours would not be worked if the order were not accepted. Option A is 300 × £15 (basic rate — irrelevant base). Option C is the overtime premium only. Option D uses 500 hours.

Answer: D. Treat the 3:2 mix as a 'bundle' of 5 units. Contribution per bundle = (3 × £25) + (2 × £40) = £75 + £80 = £155. Total contribution required = fixed costs + target profit = £42,000 + £20,000 = £62,000. Number of bundles = £62,000 ÷ £155 = 400. So M = 400 × 3 = 1,200 units and N = 400 × 2 = 800 units. Check: 1,200 × £25 + 800 × £40 = £30,000 + £32,000 = £62,000 = fixed costs + target profit. The other options keep the 3:2 ratio but use the wrong number of bundles: option A (300 bundles) only reaches £46,500 contribution, option C (360 bundles) reaches £55,800, and option B (500 bundles) overshoots at £77,500. Always work in whole bundles of the fixed mix, then split back into individual products.

Answer: B. First, the decision without information. EV(Project A) = 0.6 × £50,000 + 0.4 × £20,000 = £30,000 + £8,000 = £38,000. EV(Project B) = 0.6 × £30,000 + 0.4 × £40,000 = £18,000 + £16,000 = £34,000. So without information the company chooses Project A, expected value £38,000. With perfect information, the company picks the best project for each known state: Good → Project A (£50,000); Poor → Project B (£40,000). Expected value with perfect information = 0.6 × £50,000 + 0.4 × £40,000 = £30,000 + £16,000 = £46,000. Value of perfect information = £46,000 − £38,000 = £8,000. Option A (£30,000) confuses the EV-without-information with the value of information. Option C (£20,000) is just the Poor-state improvement (£40,000 − £20,000), not the expected (probability-weighted) gain. Option D (£12,000) measures the gain over Project B rather than over the option actually chosen without information.

Answer: B. Joint cost decision: the joint cost (£80,000) is a sunk cost — irrelevant to the further processing decision. The decision is purely whether to further process X: Incremental revenue = £95,000 − £60,000 = £35,000. Incremental cost = £25,000. Net benefit of further processing = £35,000 − £25,000 = £10,000. Yes, further process. Option A incorrectly includes the sunk joint cost. Option C is an unsupported generalisation. Option D incorrectly treats the joint cost as relevant. Joint cost allocation methods are used for inventory valuation but are never relevant to further processing decisions.

Answer: A. Complementary product (or captive product) pricing involves pricing the core product low (or even at a loss) to build a customer base, then making profit on the complementary products or consumables that customers must also buy. Classic examples: printers (cheap) with expensive ink cartridges; razors (cheap) with expensive blades. Here, the basic software attracts users who then purchase high-margin add-ons. Market skimming (B) applies to a single product priced high initially. Penetration pricing (C) involves low prices across the product to gain share — but the premium add-ons are priced high. Cost-plus (D) derives price from cost, not strategic market positioning.

Answer: A. The shadow price of £25 means each additional hour of skilled labour increases total contribution by £25. The company should be willing to pay up to £25 more per hour (above the current rate) for additional hours, since each additional hour generates £25 more contribution. Maximum total premium for 50 hours = 50 × £25 = £1,250. This is the maximum additional cost that keeps the investment in additional capacity worthwhile. At exactly £25 extra per hour, the company breaks even on the additional hours; below £25 extra, it generates net benefit. Option B confuses total price with premium. Options C and D misapply or dismiss the concept.

Answer: A. Regret table (best outcome in each state minus each strategy's outcome): State 1 best=C(100): A regret=20, B regret=40, C regret=0. State 2 best=B(120): A regret=30, B regret=0, C regret=50. State 3 best=A(70): A regret=0, B regret=20, C regret=10. Maximum regret: A=max(20,30,0)=30; B=max(40,0,20)=40; C=max(0,50,10)=50. Minimax regret selects the strategy with the MINIMUM maximum regret = Strategy A (£30k maximum regret). This criterion suits decision-makers who want to minimise the worst-case 'missed opportunity', so Strategy A (option A) is selected.

Answer: B. On a breakeven chart: the total cost line starts at the fixed cost level (y-axis intercept) and slopes upward. The total revenue line starts at zero. Where they cross = breakeven point. At any volume to the RIGHT of breakeven, the gap between the revenue line (higher) and cost line (lower) = profit. At volumes to the LEFT, cost exceeds revenue = loss. The contribution is not directly visible as a gap on a standard breakeven chart (A). Fixed costs are shown as the y-intercept of the total cost line, not a vertical distance. The margin of safety is a horizontal distance (units) or percentage, not a vertical gap.

Answer: A. Current: 400 units × (£50−£30) = 400 × £20 = £8,000 contribution. With discount: price = £50 × 0.90 = £45. Contribution per unit = £45−£30 = £15. Total contribution = 600 × £15 = £9,000. Volume discounting is profitable here — contribution increases by £1,000. General test: does the additional contribution from extra units exceed the revenue lost from discounting existing units? Incremental contribution from 200 extra units = 200×£15=£3,000. Revenue lost on original 400 units = 400×£5=£2,000. Net benefit = £1,000 ✓. Option B is wrong — this discount increases contribution. Option C is wrong — not always beneficial (depends on numbers). Option D is wrong — £45 is well above VC of £30.

Answer: A. Book value (£50,000) and original cost (£120,000) are sunk costs — irrelevant to the decision. The relevant cost of using the machine is the net opportunity cost: if NOT used, sell immediately for £25,000. If USED, sell at end for £18,000. Relevant cost = £25,000 − £18,000 = £7,000 (the net value sacrificed by using the machine). This reflects what is genuinely given up by proceeding with the project. Option C uses only the current resale value without deducting what the machine fetches at project end. Option D is the sunk original cost — completely irrelevant.

Answer: A. Two points: (Q=1,000, P=£80) and (Q=1,200, P=£60). Slope (b) = change in P ÷ change in Q = (£80−£60) ÷ (1,000−1,200) = £20 ÷ (−200) = −£0.1 per unit. So b = 0.1. Intercept: P = a − bQ → £80 = a − 0.1(1,000) → £80 = a − £100 → a = £180. Demand equation: P = 180 − 0.1Q. Verify: at Q=1,200: P = 180 − 0.1(1,200) = 180 − 120 = £60 ✓. Option A correct. Option B uses wrong slope. Option C has wrong intercept. Option D has wrong intercept.

Answer: D. Financial savings from outsourcing must be weighed against qualitative risks: Supplier reliability (late deliveries can disrupt production); Quality control (external supplier may not meet internal standards consistently); Loss of expertise (knowledge and capability may be irreplaceable if insourcing is required in future); Strategic dependency (heavy reliance on a single external supplier creates vulnerability). Personal preferences (A) are not relevant business factors. Public listing status (B) is a weak proxy for reliability — many excellent private suppliers exist. The feasibility study cost (C) is a sunk cost — irrelevant to the going-forward decision.