P2: Capital investment

Answer: D. Relevant cash flows are those that are incremental — occurring only if the project proceeds — and are actual future cash flows. Incremental annual operating costs meet both criteria and are therefore included. Sunk costs such as past market research spending are irrecoverable regardless of the decision and are excluded. Depreciation is a non-cash accounting charge, not a cash flow, so it is excluded from DCF analysis (though the tax effect of capital allowances may be included separately). Apportioned shares of overhead that do not change in total are not incremental and are therefore irrelevant to the investment decision.

Answer: A. Tax on operating cash flows = £200,000 × 25% = £50,000. Because tax is payable one year in arrears, the tax relating to year 1 operating cash flows is paid in year 2 — not year 1. A common error is to assume tax is paid in the same year as the cash flow (giving year 1), or to net off tax within year 1, or to apply the wrong rate. Another error is calculating tax on the net cash flow after an incorrect adjustment. The full cash flow is £200,000; the after-tax position emerges by including the year 2 outflow of £50,000 as a separate cash flow item.

Answer: B. Consistency between cash flows and discount rate is essential: a nominal (money) discount rate must be applied to nominal (money) cash flows — i.e. cash flows expressed in the prices of the year they arise — not to real (current-price) cash flows. So either the real cash flows must be inflated to money terms for discounting at the nominal rate, or the nominal rate must be converted to a real rate (using the Fisher formula) and applied to the real cash flows. Mixing real cash flows with a nominal rate would understate the NPV by applying a rate that implicitly includes an inflation component not reflected in the cash flows.

Answer: C. Working capital outflow at time 0: −£30,000 (already in present value terms). Working capital recovery at end of year 3: +£30,000 × 0.751 = +£22,530. Net PV impact = −£30,000 + £22,530 = −£7,470. The net cost reflects the time value of money — the recovery is worth less than the initial outlay because it occurs later. A common error is to assume working capital nets to zero (ignoring discounting), or to forget that the recovery occurs at project end. The outflow at time 0 requires no discounting since it is already at present value.

Answer: D. When mutually exclusive projects have different lives and can be repeated, their NPVs cover different time periods and therefore represent incomparable quantities. Project A's NPV covers 3 years of cash flows while Project B's covers 5 years; comparing them directly is like comparing the value of 3 years of one investment against 5 years of another. Adjusting for unequal lives — using equivalent annual annuity or the lowest common multiple approach — puts them on a comparable basis. The discount rate accounts for time value but not for the difference in the number of periods covered, and neither a shorter nor longer life is inherently superior.

Answer: A. Equivalent annual annuity = NPV ÷ annuity factor = £18,000 ÷ 2.487 = £7,238 (rounded to the nearest pound). This converts the total NPV into an equivalent constant annual value, enabling fair comparison with projects of different durations. A common error is to divide the NPV by the number of years (£18,000 ÷ 3 = £6,000), which ignores the time value of money captured by the annuity factor. Multiplying rather than dividing (£18,000 × 2.487 = £44,766) reverses the calculation. The EAA itself is not simply the total NPV restated.

Answer: B. The option to expand is a real option — it gives the company the right (but not the obligation) to make a further investment if conditions prove favourable, which is intrinsically valuable since the company only needs to exercise it if doing so is beneficial. This optionality adds value to the project beyond what the base-case DCF NPV captures, particularly where future uncertainty is high. It is not a sunk cost (which relates to past expenditure) and should not be treated as a certain future cash outflow, since whether it is exercised depends on future conditions. Real options are a recognised source of value in strategic investment decisions.

Answer: C. Profitability index (PI) = NPV ÷ initial investment. Project X: £40,000 ÷ £100,000 = 0.40. Project Y: £30,000 ÷ £60,000 = 0.50. Project Z: £25,000 ÷ £80,000 = 0.3125. Project Y has the highest PI at 0.50, meaning it generates the most NPV per pound of capital invested, making it the priority under capital rationing. Despite Project X having the largest absolute NPV, its PI is lower than Project Y's, so in a capital-constrained environment Project Y should be funded first. PI ranking ensures the available capital generates the maximum total NPV.

Answer: D. A fundamental limitation of ARR is that it is based on accounting profit — which includes non-cash items such as depreciation — rather than actual cash flows, and it takes no account of the time value of money, treating a profit earned in year 5 as equivalent in value to one earned in year 1. In contrast, NPV explicitly discounts future cash flows to present value, reflecting their true worth today. ARR does not consider time value of money at all, which can lead to different and potentially inferior investment decisions compared with NPV, and it does not always rank projects correctly under capital rationing.

Answer: A. The IRR decision rule states that a project should be accepted if its IRR exceeds the organisation's required rate of return (cost of capital). Here, an IRR of 14% exceeds the 10% cost of capital, so the project should be accepted. Rejecting when IRR exceeds cost of capital would invert the rule. The rule does not require the IRR to equal the cost of capital — equality would give a zero NPV and borderline acceptance. The IRR decision rule does provide a clear basis for an accept or reject recommendation, though it has known limitations (particularly with unconventional cash flows or mutually exclusive projects).

Answer: B. For mutually exclusive projects, NPV is the superior decision criterion because it directly measures the absolute increase in shareholder wealth in today's money. A higher IRR indicates a better return per pound invested but does not maximise total wealth creation if the NPV is lower. IRR and NPV can conflict when projects differ in scale, timing or life — exactly the kind of situation that mutually exclusive comparisons often present. Maximising IRR is not equivalent to maximising NPV or shareholder wealth when choices involve different investment scales; a smaller investment at a higher rate may produce less absolute value than a larger investment at a lower rate.

Answer: C. Setting a deliberately low initial price to build market share rapidly, with the intention of raising prices later, is the defining feature of penetration pricing. Price skimming is the opposite approach — setting a high initial price to exploit early adopters' willingness to pay and gradually reducing it as competitors enter. Premium pricing maintains a consistently high price to signal quality and exclusivity, with no intention of reducing it as volume grows. Loss-leader pricing sells a specific item below cost to drive traffic that generates profit elsewhere, which is different from penetration pricing's market-share-building rationale.

Answer: D. Loss-leader pricing involves deliberately pricing one product below cost (or at a very slim margin) with the explicit aim of attracting customers who will then generate profitable purchases elsewhere — exactly the supermarket own-brand scenario described. Price skimming involves a high initial price, not a below-cost price. Penetration pricing sets a low initial price to build long-term market share for that specific product, rather than using its sacrifice to drive traffic to other products. Premium pricing sets a consistently high price to signal quality, which is the opposite of what is described.

Answer: A. Year 1 writing-down allowance = £80,000 × 25% = £20,000. Tax saved = £20,000 × 25% = £5,000. Since tax is paid one year in arrears, the tax saving arising from the year 1 capital allowance is received (i.e. reduces the tax payment) in year 2, not year 1. A common error is to report the WDA itself (£20,000) rather than the tax saving it generates (£5,000). Another error is to assume the saving is received in year 1 when tax is on an arrears basis.

Answer: B. Two fundamental limitations of payback are that it ignores all cash flows occurring after the payback cut-off date (which may be the most profitable period of the project) and that it makes no adjustment for the time value of money — a cash inflow in year 3 is treated identically to one received in year 1. Payback measures the speed of cost recovery, not the total return over a project's life — making it a poor substitute for NPV or IRR when total value creation matters. Discounted payback addresses the time-value limitation but standard payback does not discount cash flows at all.

Answer: C. Standard IRR implicitly assumes that intermediate cash flows can be reinvested at the IRR rate — an unrealistic assumption when the IRR is high, since few organisations can routinely find investments at that rate. MIRR instead assumes reinvestment at the cost of capital, which is more realistic and typically more conservative. This is the specific limitation MIRR addresses. Both MIRR and IRR involve discounting; MIRR does not eliminate it. And MIRR will not always exceed standard IRR — the relative magnitude depends on the specific cash flow profile and reinvestment assumption used.

Answer: D. The £45,000 represents the proceeds the company would forgo if it uses the machine for the project instead of selling it — this is an opportunity cost and should be included as a relevant cost (cash outflow equivalent) of the project. It is not a sunk cost, since the sunk cost would be the machine's original purchase price, not the current realisable value. Treating it as a project benefit would incorrectly double-count the machine's value. The fact that no additional cash is spent on the machine does not make the opportunity cost irrelevant — the forgone sale proceeds are a genuine economic sacrifice.

Answer: A. PV year 1: £35,000 × 0.909 = £31,815. PV year 2: £40,000 × 0.826 = £33,040. PV year 3: £30,000 × 0.751 = £22,530. Total PV of inflows = £31,815 + £33,040 + £22,530 = £87,385. NPV = £87,385 − £80,000 = £7,385. A common error is to add undiscounted cash flows (£35,000 + £40,000 + £30,000 = £105,000, giving a false NPV of £25,000). Another is to net only some years, or to apply discount factors to the wrong periods. Every year's cash flow must be discounted individually before summing. £5,000 does not follow from the figures.

Answer: B. Under capital rationing with divisible projects, rank by PI (highest first) and invest accordingly. PI: Q = 0.45, P = 0.40. Fund Q in full: outlay £80,000, NPV £36,000; budget remaining £70,000. Fund 70% of P (£70,000 ÷ £100,000): NPV £40,000 × 0.70 = £28,000. Total NPV = £36,000 + £28,000 = £64,000. Funding both fully would require £180,000, exceeding the £150,000 budget. Funding only P gives £40,000 and only Q gives £36,000 — the combined strategy yields the most value per pound of capital constrained.

Answer: C. Sensitivity margin = NPV ÷ PV of the variable = £5,000 ÷ £30,000 = 16.67%, rounded to 16.7%. This means that if labour costs increase by 16.7% (i.e. the PV of labour costs rises by £5,000), the NPV falls exactly to zero — any larger increase would make the project unacceptable. The variable with the smallest sensitivity margin is the most sensitive, since it takes the smallest adverse change to destroy project value. The 83.3% figure is the complement (1 − 16.7%) and does not have the stated meaning; the 5.0% and direction-reversed interpretations are also incorrect.

Answer: D. Premium pricing relies on high price as a signal of quality and exclusivity, so reducing price — even when facing weak demand — can damage the brand's perceived status and make the product less desirable to its target customers, who may equate lower price with lower quality. This is a key strategic risk of deviating from premium pricing for aspirational goods. Price reductions do not always improve long-term profitability; for premium brands, the value of exclusivity can outweigh the short-term revenue benefit of lower prices. There is no general legal prohibition on price changes, and price clearly does affect perceptions of quality and exclusivity.

Answer: A. Working capital tied up in a project represents a real cash outflow when it is first invested, and is typically recovered (returned) as a cash inflow at the end of the project when stocks are run down and receivables collected. Both the initial outflow and the terminal recovery must be included in the DCF analysis. Unlike depreciation, working capital movements are actual cash flows and therefore must be included, not excluded. Working capital is not a revenue item — it is a current asset tied up in the business — and it is normally recovered at project end rather than being a permanent loss.

Answer: B. IRR by interpolation = lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (higher rate − lower rate). = 10% + [4,000 ÷ (4,000 − (−2,000))] × (15% − 10%). = 10% + [4,000 ÷ 6,000] × 5%. = 10% + 0.6667 × 5% = 10% + 3.333% = 13.3%. 12.5% is simply the midpoint of 10% and 15%, which ignores the relative sizes of the two NPVs. 11.0% and 14.0% do not follow from the interpolation. The denominator must be the total spread: NPV at lower rate minus NPV at higher rate = 4,000 − (−2,000) = 6,000.

Answer: C. With an 80% learning curve, each time cumulative output doubles, the cumulative average time per unit falls to 80% of the previous average. First unit: 160 hours (cumulative average = 160 hours). After 2 units: cumulative average = 160 × 0.80 = 128 hours; total = 2 × 128 = 256 hours. After 4 units: cumulative average = 128 × 0.80 = 102.4 hours; total = 4 × 102.4 = 409.6 hours. A common error is to apply the 80% reduction to the first-unit time rather than the cumulative average (160 × 0.80 × 4 = 512 hours). The 384 figure might arise from applying 80% only once to 4 × 160. The 640 figure is simply 4 × 160 with no learning applied.

Answer: D. Fisher formula: (1 + real rate) = (1 + nominal rate) ÷ (1 + inflation rate) = 1.15 ÷ 1.05 = 1.0952. Real rate = 0.0952 = 9.52%. A common error is to simply subtract inflation from the nominal rate: 15% − 5% = 10%, which is an approximation that overestimates the real rate slightly. The Fisher formula correctly accounts for the compounding interaction between inflation and the nominal rate. Adding rates (15% + 5% = 20%) would give the nominal rate if a real rate and inflation were given, but in reverse — it is not the correct answer here. 10.48% does not follow from the Fisher formula.

Answer: A. PV of annuity = £60,000 × 3.791 = £227,460. NPV = PV of inflows − initial investment = £227,460 − £200,000 = £27,460. The positive NPV indicates the project earns more than the required 10% return and should be accepted. A common error is to simply multiply the annual cash flow by the number of years (£60,000 × 5 = £300,000, overstating PV by ignoring discounting). The negative NPV figure (−£27,460) would arise from reversing the calculation — subtracting the PV from the investment rather than vice versa. That error gives the £100,000 option (£300,000 − £200,000).

Answer: B. Year 1 TWDV: £120,000 − (£120,000 × 25%) = £120,000 − £30,000 = £90,000. Year 2 WDA: £90,000 × 25% = £22,500. Tax saving: £22,500 × 25% = £5,625. Since tax is payable one year in arrears, the saving from the year 2 allowance reduces the year 3 tax bill — i.e., it is received in year 3. A common error is to report the WDA itself (£22,500) rather than the tax saving on it. Another is to assume the saving is received in the same year (year 2). The time-lag is critical in getting the correct year of cash benefit. £7,500 is the saving on the year 1 allowance (£30,000 × 25%), which would itself be received in year 3, not year 2.

Answer: C. The £15,000 market study cost has already been incurred and cannot be recovered regardless of whether the project proceeds or not — it is a sunk cost, which is irrelevant to the forward-looking investment decision. DCF analysis is based on future, incremental cash flows, not past expenditure. Including sunk costs in an appraisal would lead to keeping bad investments simply because money has already been spent on them. The relevant cost principle requires including only costs that will actually change as a result of the decision — sunk costs, by definition, will not change.

Answer: D. NPV is theoretically superior because it uses cash flows (not accounting profits), considers all cash flows across the full project life (not just up to a cut-off date), applies discounting to reflect the time value of money, and directly measures the expected increase in shareholder wealth in present-value terms. ARR uses accounting profit rather than cash flows and ignores the time value of money — both significant limitations. Payback ignores all cash flows after the cut-off date and similarly makes no time-value adjustment. NPV and ARR can and do give different decisions, which is precisely why the choice of technique matters.

Answer: A. A real option such as the right to abandon can add value precisely because it limits downside risk — if year 1 results are poor, the company can cut losses by abandoning rather than continuing. If the value of this option (the potential losses avoided) exceeds the negative base-case NPV, the overall project value may be positive. Negative base-case NPVs do not automatically make a project unacceptable once optionality is factored in. The option to abandon does have value if it genuinely reduces potential downside, and real options can add value regardless of whether the base NPV is positive or negative.

Answer: B. Bundling at a price below the combined standalone prices captures customers whose combined willingness to pay for both products exceeds the bundle price, even if they wouldn't purchase each product separately at full price — this expands the addressable market for the combined offering and increases overall revenue from that customer segment. Bundling does not automatically reduce total revenue; when designed correctly, it increases it by converting previously non-purchasing customers. The bundle price does not have to equal the sum of standalone prices — the discount is the economic mechanism that makes bundling work. Bundling is widely used in software and services, not limited to physical products.

Answer: C. The profitability index method works cleanly for divisible projects because it allows partial investment — simply follow the PI ranking and invest whatever fraction of capital remains. When projects are indivisible, following the PI ranking may not result in a feasible whole-project combination that best uses the available budget; a lower-ranked combination might actually generate a higher total NPV by filling the budget more completely. The correct approach is to enumerate all feasible combinations of whole projects within the budget and select the one with the highest total NPV. Indivisibility makes the PI method unreliable, not more reliable, and it does not make capital rationing analysis impossible.

Answer: D. The factory manager's salary will not change in total regardless of whether the project proceeds — it is a committed fixed cost. Since there is no incremental cash flow arising from this decision, the salary is not a relevant cost. An opportunity cost arises only if using the manager's time on the project means they cannot perform some other activity that has economic value — if they have spare time or the project fills otherwise idle time, there is no opportunity cost. The relevant cost principle excludes costs that do not change as a result of the decision, regardless of whether they are fixed or variable.

Answer: A. Discounted payback improves on simple payback by applying a discount rate to the cash flows before calculating the payback period, which accounts for the time value of money — a cash inflow in year 3 is worth less than one in year 1, and discounted payback reflects this, whereas simple payback treats them as identical. However, discounted payback still shares one key limitation with simple payback: it ignores cash flows occurring after the payback cut-off date. It does not eliminate uncertainty from the appraisal — the cash flows are still estimates, just now discounted ones.

Answer: B. When an asset is disposed of at the end of the project, the remaining tax written-down value (£50,000) minus the disposal proceeds (nil) gives the balancing allowance = £50,000. Tax saving = £50,000 × 25% = £12,500. Because tax is paid one year in arrears, this saving arises in year 4 (one year after the year 3 disposal). A common error is to take the full TWDV of £50,000 as the cash flow rather than the tax saving on it. Another error is to place the saving in year 3 (the year of disposal) rather than year 4.

Answer: C. Using the 80% learning curve: cumulative average time per unit after 2 units = 160 × 0.80 = 128 hours; after 4 units = 128 × 0.80 = 102.4 hours. Total time for 4 units = 4 × 102.4 = 409.6 hours. Total labour cost = 409.6 × £20 = £8,192. A common error is to multiply the first unit time by 4 with no learning applied: 160 × 4 × £20 = £12,800. £5,120 is the total for the first two units only (2 × 128 hours × £20), and £6,400 doubles the first unit's time (2 × 160 hours × £20); neither covers four units on the curve.

Answer: D. With spare capacity, using the machine for the project incurs only the incremental variable cost: 100 hours × £8 = £800. There is no opportunity cost because the spare capacity has no alternative use. The fixed overhead absorption rate (£15 per hour) represents a charge for overheads that will be incurred regardless of this project — they are not incremental, so they are irrelevant. The full absorption cost (£23 per hour) incorrectly includes this non-incremental fixed cost. The relevant cost is not zero — the variable cost of running the machine does change as a result of the decision.

Answer: A. For a special order that does not affect existing business, only incremental costs matter. Contribution = £30 − £22 = £8 per unit. Fixed overhead (£8) is not incremental — it is incurred regardless — so the total absorbed cost (£30) is misleading. The order generates £8 × 500 = £4,000 incremental profit and should be accepted. Rejecting because absorbed cost equals price is a common error that treats non-incremental fixed costs as though they change with the decision.

Answer: B. Launching at a high price to capture early adopters and then reducing as competition grows is price skimming. Penetration pricing is the opposite — deliberately low initial pricing to build volume. Cost-plus sets price from cost up, unrelated to staged reductions. Premium pricing maintains permanently high pricing rather than reducing price over time.

Answer: C. A higher IRR rate does not mean more absolute value — it depends on scale. Project A earns a high percentage on £10,000; Project B earns a lower percentage on £500,000. The absolute NPV of B is almost certainly much larger, creating more total shareholder value. This is precisely why NPV is preferred over IRR — it measures absolute value, not just the percentage return.

Answer: D. In a nominal DCF, each cash flow is inflated at its own specific rate to produce money-term figures, then discounted at the nominal rate. Material costs inflate at 6%, so that specific rate applies — using the general 4% rate would understate material costs in later years. General inflation is used to build the nominal rate (via Fisher formula), not to inflate individual cash flow lines. Expressing costs in real terms and then discounting at a nominal rate mixes two different bases.

Answer: A. The decision uses only incremental amounts from the split-off point. Incremental revenue = £36,000 − £25,000 = £11,000. Incremental cost = £8,000. Net benefit = £3,000 positive, so further processing should occur. The joint cost of £40,000 is irrelevant — already incurred and allocated regardless of this decision. Each product's further-processing decision is made independently. Each further-processing decision stands alone, so the other product's value is irrelevant, and processing further is worthwhile only when incremental revenue exceeds incremental cost, not always.

Answer: B. Setting a low price for high access is penetration-style pricing motivated by humanitarian rather than commercial goals. A profit-maximiser might charge a premium price given the drug's life-critical nature and limited substitutes — precisely the ethical tension pharmaceutical pricing debates involve. Premium pricing charges the maximum the market bears; loss-leader uses one product to drive others' profits; skimming starts high and comes down.

Answer: C. MIRR = (TV ÷ initial investment)^(1/n) − 1 = (400,000 ÷ 200,000)^(1/5) − 1 = 2^0.20 − 1. 2^0.20 = 1.1487, so MIRR ≈ 14.87%. The 100% figure mistakes the gain (£200,000) as the rate. The 12% is the reinvestment rate input, not the MIRR itself. The 20% arises from dividing 100% by 5 years, ignoring compounding.

Answer: D. LCM of 2 and 3 = 6 years. Over 6 years, P repeats three times and Q twice, giving a common end-point for a fair comparison. Using 2 or 3 years leaves one project mid-cycle, making comparison meaningless. The horizon is the mathematical LCM of the specific lives, not a fixed number like 10 years.

Answer: D. Sensitivity = NPV ÷ PV of the variable = £12,000 ÷ £80,000 = 0.15 = 15%. The initial investment can rise by 15% before NPV reaches zero. A common error divides investment by NPV (£80,000 ÷ £12,000 = 6.7), which has no useful sensitivity interpretation. The variable with the smallest sensitivity margin is the most sensitive, since it takes the smallest adverse change to eliminate project value. 12% reads the £12,000 NPV as a percentage, and 8% does not follow from the figures.

Answer: A. At full capacity, 200 hours used on the new contract displaces existing production, sacrificing £15 × 200 = £3,000 contribution. This is the opportunity cost — a real economic sacrifice included as a relevant cost. It is not sunk; the forgone contribution is a future cash flow. Fixed overhead absorption is non-incremental and not the correct measure here.

Answer: B. Adding a contribution margin to variable cost is marginal (contribution) cost-plus pricing. Full cost-plus uses total absorbed cost (variable + fixed) as the base. Market-based works backwards from market price. Penetration pricing is a strategic choice unrelated to cost-plus methodology. Full cost-plus instead uses total absorbed cost (variable plus fixed) as the starting point. Penetration is a market-entry strategy, not a cost-based formula.

Answer: C. Real cash flows (today's prices) must be discounted at the real rate; money cash flows (inflated to each future year's prices) must be discounted at the nominal rate. Applying a real rate to money flows produces a systematically incorrect NPV. Specific inflation adjustments inflate flows further away from real terms, not towards them.

Answer: D. Average investment = £200,000 ÷ 2 = £100,000. ARR = £30,000 ÷ £100,000 = 30%. Using full initial investment as denominator gives 15% — a common error. Dividing £200,000 ÷ £30,000 gives 6.7, not a meaningful ARR figure. This halving convention (average investment = initial ÷ 2 when there is no residual value) is the standard ARR formula for the average investment basis. 3% does not follow from the figures.

Answer: A. Deferral lets the company learn more before committing — if conditions worsen, it can walk away; if they improve, it proceeds. This asymmetric payoff gives the option positive value even when current NPV is already marginally positive. Deferring does not always worsen NPV; the information value can outweigh delay cost.

Answer: B. Cumulative after year 1: £30,000. After year 2: £80,000. Remaining: £120,000 − £80,000 = £40,000. Year 3 recovers £40,000 ÷ £60,000 = 0.667 years = 8 months. Payback = 2 years 8 months. A common error assumes payback occurs at exactly year 3 without interpolating within it. Always interpolate within the final year using the fraction: remaining balance ÷ that year's cash inflow × 12 months. 1 year 6 months does not follow from the cumulative cash flows; only £30,000 has been recovered after year 1.