BA2: Decision making

Answer: A. Expected value = Σ(probability × outcome) = (0.3 × £20,000) + (0.5 × £10,000) + (0.2 × −£5,000) = £6,000 + £5,000 − £1,000 = £10,000. The £12,000 figure adds the loss instead of subtracting it; £11,000 mishandles the loss probability; and £8,333 is the simple unweighted average of the three outcomes, ignoring the probabilities. Expected value weights each outcome by its probability and treats losses as negative.

Answer: C. Coefficient of variation = standard deviation ÷ mean = £60 ÷ £400 = 0.15, i.e. 15%. It measures relative risk per unit of return and allows comparison between projects of different size. The 667% figure inverts the ratio (mean ÷ standard deviation); 0.15% fails to convert the decimal to a percentage correctly; and 24% is unsupported by the figures.

Answer: B. Contribution per unit = £25 − £15 = £10. Breakeven point = fixed costs ÷ contribution per unit = £40,000 ÷ £10 = 4,000 units. Margin of safety = budgeted sales − breakeven sales = 6,000 − 4,000 = 2,000 units. It shows by how much sales can fall before a loss arises. The 4,000-unit figure is the breakeven point itself, not the margin of safety; 6,000 units is budgeted sales; and 1,600 units is unsupported.

Answer: C. When one resource is scarce, products are ranked by contribution per unit of the limiting factor, not per unit of product. Product X earns £30 ÷ 3 = £10 per machine hour; Product Y earns £24 ÷ 2 = £12 per machine hour. Product Y therefore generates more contribution from each scarce machine hour and should be prioritised. Ranking by contribution per unit (which would point to Product X) is the classic error; choosing on resource use alone ignores contribution; and the answer naming Product X on a per-machine-hour basis states the right rule but the wrong product.

Answer: D. Cumulative cash flow is £30,000 after year 1 and £70,000 after year 2, leaving £30,000 of the £100,000 still to be recovered. Year 3 generates £50,000, so the remaining £30,000 is recovered in £30,000 ÷ £50,000 = 0.6 of year 3. Payback = 2.6 years. The 2-year and 3-year figures round to whole years and ignore the within-year timing, and 2.4 years uses the wrong fraction. The method assumes inflows accrue evenly within the year.

Answer: A. Risk describes situations where the possible outcomes and their probabilities are known or can be estimated, allowing tools such as expected values to be used. Uncertainty describes situations where probabilities cannot meaningfully be assigned. The two are not synonyms, risk is not confined to financial decisions, and uncertainty cannot always be eliminated by more data. The availability of probabilities is the key dividing line.

Answer: B. Expected value = (0.5 × £30,000) + (0.3 × £10,000) + (0.2 × −£20,000) = £15,000 + £3,000 − £4,000 = £14,000. The £18,000 figure adds the loss instead of subtracting it. The £6,667 figure is the unweighted average of the three outcomes, ignoring the probabilities. Expected value weights each outcome by its probability and treats the loss as a negative amount.

Answer: C. For projects with the same expected return, the one with the higher standard deviation of returns has the greater spread of possible outcomes and is therefore the riskier. Standard deviation measures dispersion, not the level of expected profit, the payback period, or any tax effect. Where expected returns differ, the coefficient of variation (standard deviation relative to the mean) gives a better risk comparison.

Answer: D. Contribution per unit = £40 − £24 = £16. Breakeven point = fixed costs ÷ contribution per unit = £96,000 ÷ £16 = 6,000 units. The 2,400-unit figure divides fixed costs by the selling price rather than by contribution, and 4,000 divides by the variable cost. Breakeven is reached when total contribution exactly covers fixed costs, which is why contribution per unit is the correct divisor. 3,840 does not follow from the price, cost and fixed-cost figures given.

Answer: A. Units required = (fixed costs + target profit) ÷ contribution per unit = (£150,000 + £50,000) ÷ £20 = £200,000 ÷ £20 = 10,000 units. The 7,500-unit figure covers only the fixed costs, omitting the target profit, and 2,500 covers only the profit. To reach a target profit, total contribution must cover both the fixed costs and the desired profit, so both are included in the numerator. 5,000 deducts the target profit from fixed costs ((£150,000 − £50,000) ÷ £20) instead of adding it.

Answer: B. Contribution per unit = £50 − £30 = £20. The contribution to sales ratio = contribution ÷ selling price = £20 ÷ £50 = 0.40, or 40%. The 60% figure is the variable cost to sales ratio (£30 ÷ £50). The C/S ratio is useful for finding the breakeven revenue (fixed costs ÷ C/S ratio) and for products measured in revenue rather than units. It expresses contribution as a proportion of selling price. 167% divides selling price by variable cost (£50 ÷ £30), which is not a contribution measure.

Answer: C. With spare capacity and no incremental fixed costs, the relevant comparison is the marginal cost to make (£18) against the price to buy (£16). Buying is £2 per unit cheaper, so on purely financial grounds the company should buy. Making would cost more, so there is no £2 saving from making, and the options are not equal. Non-financial factors such as employment or supply reliability may matter too, but the question asks on financial grounds only.

Answer: D. Year 1: £9,000 × 0.909 = £8,181. Year 2: £9,000 × 0.826 = £7,434. Present value of inflows = £15,615. NPV = £15,615 − £15,000 = £615. The positive NPV indicates the project is worthwhile. The £3,000 figure is the undiscounted net cash flow (£18,000 − £15,000), ignoring the time value of money, and £15,615 omits the initial investment. Discounting each inflow and deducting the outlay gives the NPV.

Answer: A. With constant annual inflows, payback period = initial investment ÷ annual inflow = £24,000 ÷ £8,000 = 3 years. Payback measures how quickly the original outlay is recovered in cash terms and ignores both the time value of money and any cash received after the payback point. The other figures do not match £24,000 recovered at £8,000 a year. A shorter payback is generally regarded as less risky.

Answer: A. For independent events, the probability that both occur is the product of their individual probabilities: 0.3 × 0.4 = 0.12. The 0.70 figure adds the probabilities, which would (loosely) relate to the chance of one or the other, not both. Multiplying probabilities gives the joint probability of independent events occurring together; adding them is appropriate only for mutually exclusive outcomes. 0.35 averages the two probabilities and 0.10 is their difference; neither is a joint probability.

Answer: B. Coefficient of variation = standard deviation ÷ mean = £40 ÷ £200 = 0.20, or 20%. It expresses risk relative to the expected return, which allows a fair comparison of risk between projects of different sizes. The 500% figure inverts the ratio (mean ÷ standard deviation), and 5% misplaces the decimal. A lower coefficient of variation means less risk per unit of return.

Answer: C. For a normal distribution, about 95% of observations fall within two standard deviations of the mean, while roughly 68% fall within one standard deviation and about 99.7% within three. The 50% figure would be the proportion below the mean. These benchmark percentages of the normal curve are widely used to assess how likely a value within a given range is.

Answer: D. Margin of safety in units = 10,000 − 7,500 = 2,500 units. As a percentage of budgeted sales = 2,500 ÷ 10,000 = 25%. This shows sales could fall by a quarter before the company makes a loss. The 75% figure expresses the breakeven point as a proportion of budgeted sales, not the margin of safety, and 33% wrongly uses breakeven as the denominator. The margin of safety is measured relative to budgeted sales.

Answer: A. Breakeven revenue = fixed costs ÷ contribution to sales ratio = £120,000 ÷ 0.40 = £300,000. At this level of revenue, total contribution (40% of £300,000 = £120,000) exactly covers the fixed costs. The £48,000 figure multiplies fixed costs by the ratio instead of dividing, and £200,000 uses an incorrect ratio. The C/S ratio lets breakeven be expressed in revenue terms without needing a unit selling price. £480,000 multiplies fixed costs by 4 instead of dividing by 0.40.

Answer: B. When one resource is scarce, products are ranked by contribution per unit of that resource. Product P earns £40 ÷ 4 = £10 per labour hour; product Q earns £36 ÷ 3 = £12 per labour hour. Product Q has the higher contribution per scarce labour hour (£12) and should be made first. The £40 and £36 figures are the contributions per unit, not per labour hour, and ranking by those would give the wrong priority.

Answer: C. A relevant cost is a future incremental cash flow caused by the decision. A share of existing fixed overheads that will be incurred whether or not the order is accepted is not relevant — it does not change with the decision. The additional materials, extra labour and additional variable overheads are all incremental costs caused by the order and so are relevant. Apportioned, unavoidable fixed costs should be excluded from special-order decisions.

Answer: D. Compound interest applies the rate to the growing balance: £10,000 × (1.06)² = £10,000 × 1.1236 = £11,236. The £11,200 figure is simple interest (£10,000 + 2 × £600). The small excess of £11,236 over £11,200 is the interest earned in year two on year one's interest. The £10,600 figure applies only one year's interest. Compounding earns interest on accumulated interest as well as on the principal. £11,000 does not follow from a 6% rate, simple or compound.

Answer: A. Present value = future cash flow × discount factor = £12,000 × 0.794 = £9,528. The discount factor of less than 1 reduces the future sum to its value today, reflecting the time value of money. The £15,120 figure divides by the factor instead of multiplying, which compounds rather than discounts, and £12,000 ignores discounting altogether. Multiplying by the appropriate discount factor converts a future amount to present value. £11,040 deducts 8% once (£12,000 × 0.92) instead of applying the three-year factor.

Answer: B. The IRR is the discount rate that makes a project's net present value exactly zero — the rate at which the present value of inflows equals the present value of outflows. A project is generally acceptable if its IRR exceeds the cost of capital. The IRR is not about minimising payback, maximising accounting profit, or the accounting rate of return; it is defined entirely in terms of discounted cash flows and a zero NPV.

Answer: C. Better information has value because it can lead to better decisions; in principle its worth is the increase in expected value (the improvement in the expected outcome) that acting on it allows, which sets a ceiling on what should be paid for it. It is not the total project cost, the dispersion of outcomes, or the payback period. Information is worth paying for only up to the additional expected benefit it brings.

Answer: D. The mean = sum of values ÷ number of values = (90 + 110 + 100 + 120) ÷ 4 = 420 ÷ 4 = 105 units. The 420 figure is the total before dividing by the four days. The 100 and 110 figures are individual observations, not the average. The arithmetic mean divides the total by the number of observations and is the most widely used measure of central tendency.

Answer: A. Contribution per unit = £25 − £15 = £10, so breakeven volume = £80,000 ÷ £10 = 8,000 units. Breakeven revenue = 8,000 × £25 = £200,000 (equivalently, fixed costs ÷ C/S ratio = £80,000 ÷ 0.40 = £200,000). The £133,333 figure uses an incorrect ratio, and £80,000 is the fixed cost, not the breakeven revenue. Breakeven revenue is the sales value at which total contribution equals fixed costs. £320,000 does not follow from the figures given.

Answer: B. Contribution per unit of limiting factor = contribution per unit ÷ quantity of the scarce resource used = £45 ÷ 5 kg = £9 per kg. This is the figure used to rank products when material is scarce — the higher the contribution per kg, the higher the priority. The £45 figure is contribution per unit, not per kg, and £225 multiplies rather than divides. Ranking by the resource that is scarce, not by contribution per unit, maximises total contribution.

Answer: C. Because the £8 fixed overhead is unavoidable (it will be incurred whether the component is made or bought), it is not relevant to the decision. The relevant cost of making is the £14 variable cost, which is compared with the £18 buy-in price. Making is therefore £4 per unit cheaper. Comparing the full £22 with £18 would wrongly include the unavoidable fixed overhead. Only avoidable, incremental costs are relevant in a make-or-buy decision. Adding the £8 fixed overhead to the buy price (£26) is equally wrong, because an unavoidable cost is incurred under both options. The costs are not equal: making saves £4 a unit.

Answer: D. The time value of money holds that a sum received today is worth more than the same sum received later, because money in hand can be invested to earn a return (and because of risk and inflation). It does not mean money loses all value or that inflation is irrelevant. Discounting future cash flows to present value is the practical application of this principle, not something to be avoided.

Answer: B. Present value of inflows = £7,000 × 3.605 = £25,235. NPV = £25,235 − £25,000 = £235. The small positive NPV suggests the project is marginally worthwhile at a 12% cost of capital. The £10,000 figure is the undiscounted net cash flow (£35,000 − £25,000), ignoring discounting, and £25,235 omits the initial investment. The annuity factor discounts the five equal annual receipts in a single calculation.

Answer: C. A project is financially acceptable when its internal rate of return exceeds the cost of capital, because this means it earns a return greater than the cost of the funds used. Here the IRR of 15% is above the 10% cost of capital, so the project should be accepted; equivalently, its NPV at 10% would be positive. A higher IRR relative to the cost of capital is favourable, not a reason to reject or defer.

Answer: D. Focusing only on the best possible payoff and disregarding the risk of poor outcomes reflects a risk-seeking, optimistic attitude. A risk-averse decision maker would weigh the downside heavily and prefer safer options, while a risk-neutral one would judge purely on expected values. The attitude to risk shapes which decision rule a manager favours when probabilities are uncertain.

Answer: D. A risk-neutral decision maker judges options purely on expected value and is indifferent to the spread of outcomes, so they would choose project Y for its higher expected value of £45,000. A risk-averse decision maker might prefer the lower-risk project X despite its lower expected value. Risk attitude determines how the standard deviation is weighed; risk neutrality ignores it and focuses on the expected outcome alone.

Answer: A. The mean = sum of values ÷ number of values = (22 + 25 + 28 + 30 + 25) ÷ 5 = 130 ÷ 5 = 26 units. The figure 130 is the total before dividing, and 25 is the mode (the most frequent value), not the mean. The arithmetic mean uses every observation and divides by the count, which is what distinguishes it from the mode or the median.

Answer: B. Contribution per unit = £60 − £36 = £24. Breakeven point = fixed costs ÷ contribution per unit = £144,000 ÷ £24 = 6,000 units. The 2,400-unit figure divides fixed costs by the selling price, and 4,000 divides by the variable cost. Breakeven is the volume at which total contribution exactly covers fixed costs, so contribution per unit is always the correct divisor.

Answer: C. Margin of safety = budgeted sales − breakeven sales = 8,000 − 6,000 = 2,000 units. It shows by how much sales can fall before the company moves into a loss. The 6,000-unit figure is the breakeven point itself, 8,000 is budgeted sales, and 14,000 wrongly adds the two together. The margin of safety is the cushion between expected sales and the breakeven level.

Answer: D. When labour is the scarce resource, products are ranked by contribution per labour hour. Product A earns £20 ÷ 2 = £10 per hour; product B earns £33 ÷ 3 = £11 per hour. Product B generates more contribution from each scarce labour hour and should be made first. Ranking by contribution per unit would wrongly favour product B for a different reason, and product B does not use fewer hours per unit — it is the contribution per scarce hour that matters.

Answer: A. Cost to make = (4,000 × £25) + £20,000 specific fixed = £100,000 + £20,000 = £120,000. Cost to buy = 4,000 × £32 = £128,000. Making is £8,000 cheaper, so the company should make. The specific fixed cost is included because it is avoidable — it would disappear if the component were bought. Buying is not cheaper here, and the costs are not equal. Only avoidable costs enter the make-or-buy comparison. A saving of £28,000 ignores the £20,000 specific fixed cost, which is avoidable and therefore relevant.

Answer: B. Present value of inflows = £12,000 × (0.909 + 0.826 + 0.751) = £12,000 × 2.486 = £29,832. NPV = £29,832 − £30,000 = −£168. The slightly negative NPV suggests the project just fails to cover its cost of capital. The £6,000 figure is the undiscounted net cash flow (£36,000 − £30,000), ignoring discounting, and £29,832 omits the initial investment. Discounting each inflow and deducting the outlay gives the NPV.

Answer: C. Present value = £3,000 × 3.312 = £9,936. The annuity factor discounts the four equal annual receipts in a single calculation. The £12,000 figure is the undiscounted total of the four receipts, ignoring the time value of money. The annuity factor is the sum of the individual discount factors for years 1 to 4, so it is applied once to the annual amount to give the present value of the whole stream. £9,000 is three years' receipts undiscounted, and £2,400 deducts 20% from a single receipt; neither applies the annuity factor.

Answer: D. Cumulative cash flow reaches £40,000 after two years, leaving £10,000 of the £50,000 still to recover. Year 3 generates £20,000, so the remaining £10,000 is recovered in £10,000 ÷ £20,000 = 0.5 of that year. Payback = 2.5 years. The 2-year and 3-year figures round to whole years and ignore the within-year timing. Payback assumes inflows accrue evenly through each year. 2.4 years does not follow from the figures.

Answer: A. A normal distribution is symmetrical and bell-shaped, so its mean, median and mode all coincide at the centre. They are not different from one another, nor are they necessarily zero — the mean can take any value. The symmetry of the normal curve is what makes the three measures of central tendency equal, a property used when applying the distribution to probability questions.

Answer: A. Expected value = (0.25 × £80,000) + (0.5 × £40,000) + (0.25 × £10,000) = £20,000 + £20,000 + £2,500 = £42,500. The £43,333 figure is the simple unweighted average of the three outcomes, ignoring the probabilities, and £130,000 is the sum of the outcomes. Expected value weights each outcome by its probability, giving more influence to the more likely £40,000 result.

Answer: B. Units required = (fixed costs + target profit) ÷ contribution per unit = (£200,000 + £75,000) ÷ £25 = £275,000 ÷ £25 = 11,000 units. The 8,000-unit figure covers only the fixed costs, omitting the target profit, and 3,000 covers only the profit. To reach a target profit, total contribution must cover both fixed costs and the desired profit, so both are included in the numerator. 13,750 divides by £20 instead of the £25 contribution per unit.

Answer: C. Contribution per unit = £80 − £52 = £28. C/S ratio = contribution ÷ selling price = £28 ÷ £80 = 0.35, or 35%. The 65% figure is the variable cost to sales ratio (£52 ÷ £80), and 28% mistakes the contribution in pounds for a percentage. The C/S ratio expresses contribution as a proportion of selling price and is used to find breakeven revenue and to compare products. 53% does not follow from the price and cost figures.

Answer: D. Breakeven revenue = fixed costs ÷ C/S ratio = £105,000 ÷ 0.30 = £350,000. At this revenue, total contribution (30% of £350,000 = £105,000) exactly covers the fixed costs. The £31,500 figure multiplies fixed costs by the ratio instead of dividing. The C/S ratio lets breakeven be calculated directly in revenue terms, which is useful when a single unit selling price is not available. £315,000 deducts 10% from the correct figure, and £150,000 divides by 0.70 (the variable cost ratio) instead of the 30% contribution ratio.

Answer: A. Contribution per machine hour = contribution per unit ÷ machine hours per unit = £60 ÷ 4 = £15. This figure is used to rank products when machine hours are the limiting factor — the higher the contribution per scarce hour, the higher the priority. The £60 figure is contribution per unit, not per hour, and £240 multiplies instead of dividing. Maximising contribution per unit of the scarce resource maximises total contribution.

Answer: B. The relevant cost of making is the marginal (variable) cost plus any fixed costs that would be avoided if the component were bought in; this is what should be compared with the buy-in price. The full absorption cost includes unavoidable fixed overheads that do not change with the decision and so overstates the make cost. The product's selling price and the sunk machinery cost are irrelevant to the choice. Only avoidable, incremental costs count.

Answer: C. Present value of inflows = £18,000 × (0.909 + 0.826 + 0.751) = £18,000 × 2.486 = £44,748. NPV = £44,748 − £40,000 = £4,748. The positive NPV indicates the project is worthwhile at this cost of capital. The £14,000 figure is the undiscounted net cash flow (£54,000 − £40,000), ignoring the time value of money, and £44,748 omits the initial investment. Discounting the inflows and deducting the outlay gives the NPV.

Answer: D. Compound interest applies the rate to the growing balance: £6,000 × (1.05)³ = £6,000 × 1.157625 = £6,946 (to the nearest £). The £6,900 figure is simple interest (£6,000 + 3 × £300), which applies the rate only to the original principal. The £46 difference is the interest earned on accumulated interest. Compounding earns interest on previous interest as well as on the principal. £7,000 and £6,315 do not follow from three years at 5%, simple or compound.

Answer: A. Present value = future cash flow × discount factor = £20,000 × 0.621 = £12,420. The discount factor of less than 1 reduces the future sum to its value today, reflecting the time value of money. The £32,206 figure divides by the factor instead of multiplying, which compounds rather than discounts, and £20,000 ignores discounting altogether. Multiplying the future amount by the discount factor gives its present value. £18,000 deducts 10% from the future sum instead of applying the five-year factor.

Answer: B. Expected value is a long-run average, so for a single, one-off decision the calculated figure may not match any outcome that can actually occur, and it also takes no account of the decision maker's attitude to risk. It is straightforward to calculate, it explicitly uses the probabilities of outcomes, and it applies to financial data. The mismatch between a long-run average and a single real outcome is the key limitation for one-off decisions.