FM: Investment appraisal

Answer: A. Relevant cash flows are future, incremental and cash-based — they change as a direct result of accepting the project. Option B is a sunk cost, already incurred and therefore irrelevant. Option C is a non-cash accounting allocation and is excluded (though the tax effect of capital allowances is relevant). Option D is an apportionment of overheads that would be incurred regardless, so it is not incremental. Only option A satisfies all three tests of relevance.

Answer: C. Payback is the time taken to recover the initial outlay from cumulative net cash inflows. After two years, £200,000 has been recovered, leaving £50,000 of the £250,000 outlay outstanding. This is recovered part-way through year three: £50,000 ÷ £100,000 = 0.5 of a year, giving a payback of 2.5 years. Option A stops once £200,000 is recovered, option B rounds up to a whole third year, and option D understates the time. Payback is simple but ignores the time value of money and any cash flows arising after the payback point.

Answer: B. Payback's main weaknesses are that it ignores the time value of money — treating a pound received in year four as equal to a pound received in year one — and that it disregards all cash flows after payback is reached, so it can reject highly profitable longer-term projects. It is in fact simple to calculate (so option A is wrong), it tends to favour quick-payback projects (so option C is wrong), and it is easiest to compute with constant cash flows (so option D is wrong). Its strength is its focus on liquidity.

Answer: D. Discounted payback first discounts each cash flow to its present value at the cost of capital, then accumulates those present values to find when the initial outlay is recovered — correcting ordinary payback's main weakness by allowing for the time value of money. Because discounting reduces the value of later cash flows, discounted payback is always equal to or longer than ordinary payback, so option B is wrong. It still ignores cash flows arising beyond the payback point. Options A and C mischaracterise the method.

Answer: A. ARR (average investment basis) = average annual accounting profit ÷ average investment × 100. Average investment = (initial investment + residual value) ÷ 2 = (£200,000 + £0) ÷ 2 = £100,000. ARR = £30,000 ÷ £100,000 = 30%. Option B (15%) uses the full initial investment of £200,000 as the denominator (the initial-investment basis). Options C and D arise from other denominator errors. ARR is based on accounting profit rather than cash flows and ignores the time value of money.

Answer: B. NPV = present value of the inflows − the initial outlay. PV of the inflows = £30,000 × 3.791 (the five-year annuity factor) = £113,730. NPV = £113,730 − £100,000 = £13,730. Option A ignores discounting altogether (£150,000 − £100,000). Option C is the present value of the inflows before deducting the outlay. Option D is just one year's cash flow. A positive NPV of £13,730 means the project is expected to add that amount to shareholder wealth, so it should be accepted.

Answer: A. A positive NPV means the present value of the project's cash inflows exceeds the initial outlay when discounted at the cost of capital, so the project is expected to increase shareholder wealth and should be accepted; a negative NPV means it should be rejected. Among mutually exclusive projects, the one with the highest positive NPV is preferred. Options B, C and D are not the NPV rule and would tend to point towards rejecting or mis-ranking worthwhile projects.

Answer: C. IRR ≈ L + [NPV_L ÷ (NPV_L − NPV_H)] × (H − L), where L = 10% and H = 20%. = 10% + [13,730 ÷ (13,730 − (−10,270))] × 10% = 10% + (13,730 ÷ 24,000) × 10% = 10% + 5.7% = 15.7%. Option B (49.7%) is the common 'double negative' error — using 13,730 ÷ (13,730 − 10,270) and forgetting that subtracting a negative NPV enlarges the denominator. Options A and D are simply the two trial rates. The IRR is the discount rate at which the NPV equals zero.

Answer: D. The IRR is the discount rate at which a project's NPV is zero. A project is acceptable when its IRR is greater than the cost of capital, because that implies a positive NPV at the company's actual cost of capital. Here 15.7% exceeds 10%, so the project should be accepted. Option A misstates the decision rule, while options B and C misdescribe what the IRR represents. For independent projects, the IRR and NPV rules give the same accept/reject decision.

Answer: B. DCF methods discount future cash flows to present value, recognising that money received sooner is worth more than money received later, and they take into account all of a project's relevant cash flows over its whole life. Payback ignores both the time value of money and post-payback cash flows, while ARR uses accounting profit and also ignores discounting. Option A is untrue (DCF is more involved), option C is back-to-front (DCF uses cash, not profit), and option D is not an advantage.

Answer: A. NPV gives the absolute amount by which a project increases shareholder wealth and ranks mutually exclusive projects reliably. IRR, being a percentage, can rank such projects incorrectly (for instance favouring a small high-return project over a larger one that adds more total value), can produce multiple IRRs where cash flows are unconventional, and assumes reinvestment at the IRR itself. Option B overstates the case, option C is wrong (NPV does need the cost of capital), and option D reverses which measure is absolute and which is a percentage.

Answer: B. The Fisher equation links the rates as (1 + money rate) = (1 + real rate) × (1 + inflation rate). So (1 + real rate) = 1.155 ÷ 1.05 = 1.10, giving a real cost of capital of 10.0%. Option A simply adds the two rates and option C subtracts inflation from the money rate (15.5% − 5%), both of which ignore the compounding built into the Fisher relationship. Option D results from multiplying rather than dividing. The real rate is used to discount cash flows expressed in today's (current) prices.

Answer: D. A money (nominal) cash flow inflates the current-price amount by the specific inflation rate, compounded over the relevant number of years: £50,000 × (1.06)² = £50,000 × 1.1236 = £56,180. Option A applies only one year of inflation (£50,000 × 1.06), option B ignores inflation entirely, and option C applies three years of inflation instead of two. In the money method these inflated cash flows are discounted at the money cost of capital.

Answer: C. The first-year capital allowance = £400,000 × 25% = £100,000. The tax saving is the reduction in the tax bill that this allowance produces = £100,000 × 30% = £30,000. Option A is the allowance itself rather than the tax saving it generates, option B applies the 30% tax rate to the full cost, and option D confuses the two percentages. In nominal-terms DCF these tax savings are included as relevant cash inflows, often lagged by a year where tax is paid in arrears.

Answer: B. With tax paid one year in arrears, the tax on year-1 operating profit is paid in year 2, so although the operating cash flow is shown in year 1, the related tax outflow is placed in year 2. The tax savings from capital allowances are lagged in the same way. Options A, C and D misplace the timing. Correctly applying the one-year lag to both the tax charge and the capital-allowance tax savings is a recurring examiner concern.

Answer: C. Two approaches are consistent: discount money (nominal) cash flows at the money cost of capital, or discount real cash flows at the real cost of capital. Mixing the two — options A and B — gives the wrong answer, and option D applies an entirely inappropriate rate. The money method is usually preferred where cash flows inflate at different specific rates, or where tax (computed on nominal figures) is involved, because it handles those features naturally.

Answer: D. Tax on the operating inflow = £200,000 × 30% = £60,000, so the after-tax operating cash flow = £200,000 − £60,000 = £140,000. Option A ignores tax altogether, option B states the tax itself rather than the net flow, and option C adds the tax instead of deducting it. In a full appraisal, capital allowances would generate a separate tax saving that is treated as an additional cash inflow.

Answer: A. Risk exists where the range of possible outcomes and their probabilities can be estimated, usually from experience, so it can be quantified using tools such as expected values. Uncertainty exists where reliable probabilities cannot be assigned. Option B wrongly equates the two, while options C and D are untrue. The distinction matters because different techniques suit each: probability-based methods for risk, and sensitivity analysis for uncertainty.

Answer: B. Sensitivity analysis examines how much one input variable — selling price, sales volume, costs, the cost of capital and so on — can change before the NPV reaches zero and the decision would reverse. It identifies the variables to which the project is most sensitive: the smaller the percentage change required, the more sensitive and therefore riskier that variable. It does not assign probabilities (option A), calculate expected values (option C) or measure payback (option D).

Answer: C. Sensitivity = project NPV ÷ present value of the variable concerned × 100 = £20,000 ÷ £200,000 = 10%. So sales revenue could fall by 10% before the NPV reached zero and the project ceased to be worthwhile. The smaller this percentage, the more sensitive the project is to that variable, and the more attention management should give to forecasting it. Options A, B and D do not follow from dividing the NPV by the PV of revenue.

Answer: D. Expected value = Σ (probability × outcome) = (0.3 × £100,000) + (0.5 × £150,000) + (0.2 × £40,000) = £30,000 + £75,000 + £8,000 = £113,000. Option A takes only the most likely outcome, option C sums the outcomes ignoring the probabilities, and option B is a simple unweighted average. The expected value is a probability-weighted average; its weakness is that it may not match any actual possible outcome and ignores the decision-maker's attitude to risk.

Answer: A. An expected value is a probability-weighted average that is most meaningful when a decision is repeated many times; for a one-off project the actual result may differ greatly from the average, which itself may not even be a possible outcome. It also conceals the spread of outcomes and ignores the decision-maker's risk attitude. Option B is wrong (probabilities are exactly what the method needs), and options C and D are simply untrue.

Answer: B. The expected NPV summarises the average outcome but hides the spread. Knowing there is a 25% chance of a £60,000 loss reveals the downside risk, which a risk-averse decision-maker considers alongside the positive expected value before deciding. Option A ignores risk attitude, while options C and D treat a single statistic as decisive when it is the trade-off between expected return and risk that actually matters.

Answer: C. A risk-adjusted discount rate adds a risk premium to the cost of capital, so riskier projects are discounted at a higher rate and must clear a higher hurdle to return a positive NPV. Sensitivity analysis (option B) tests individual variables but does not itself adjust the rate, and payback (A) and ARR (D) are appraisal methods that build in no such premium. Certainty equivalents are an alternative approach that reduces the cash flows rather than raising the rate.

Answer: D. Lease-or-buy is a financing decision (the asset has already been chosen on investment grounds), so the question is simply the cheapest way to finance it. Because the cash flows are relatively certain and debt-like, they are discounted at the after-tax cost of borrowing rather than the WACC. Using the WACC (option A) would understate the value of the more certain financing flows. Options B and C are not the appropriate rate for this financing comparison.

Answer: A. Since both options finance the same chosen asset, the decision turns on which has the lower present value of net costs when discounted at the after-tax cost of borrowing. The cheaper financing option is selected. Options C and D ignore the analysis, and option B selects the more expensive choice. Relevant cash flows usually include the lease payments, the capital-allowance tax savings forgone by leasing rather than buying, and any residual value of the asset.

Answer: B. The equivalent annual cost method compares assets or replacement cycles of different lengths by converting the present value of each cycle's costs into an equivalent constant annual amount; the cycle with the lowest equivalent annual cost is optimal. It is the standard tool for asset-replacement decisions. Options A, C and D concern financing, share issues and dividends respectively, none of which the EAC method addresses.

Answer: C. Equivalent annual cost = present value of costs ÷ annuity factor for the cycle length = £50,000 ÷ 3.170 = £15,773. This converts the lump-sum present value into a constant annual cost so that cycles of different lengths can be compared on a like-for-like basis. Option A simply divides by four years and ignores discounting, option B restates the present value, and option D multiplies by the annuity factor instead of dividing by it.

Answer: D. Capital rationing exists where the funds available are not enough to finance every project with a positive NPV, forcing the company to select a subset. It may be 'hard' (imposed externally by the capital markets) or 'soft' (imposed internally by management). Under single-period rationing with divisible projects, projects are ranked by profitability index. Options A, B and C describe circumstances in which rationing does not arise.

Answer: A. Profitability index = present value of future cash inflows ÷ initial investment = £100,000 ÷ £80,000 = 1.25. Under single-period capital rationing with divisible projects, projects are ranked by profitability index (highest first) to maximise the NPV generated per pound of scarce capital. Option B inverts the ratio, option C states the NPV (£100,000 − £80,000) in pounds rather than the index, and option D does not follow. A profitability index above 1.0 indicates a positive NPV.