ACCA FM · Chapter 9
Risk and uncertainty in investment appraisal MCQs with Answers
8 multiple-choice questions on Risk and uncertainty in investment appraisal for ACCA FM Financial Management. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
In sensitivity analysis, what does the maximum cost of capital at which a project remains acceptable equal?
- A) The risk-free rate of interest
- B) The project's internal rate of return
- C) The company's current weighted average cost of capital
- D) The rate that gives the shortest discounted payback period
Show answer & explanation
Answer: B) The project's internal rate of return
The NPV of a conventional project falls as the discount rate rises and becomes zero at the IRR. The sensitivity of the project to the cost of capital is therefore measured by comparing the IRR with the current cost of capital: the difference is the margin of safety.
Question 2
A project has an NPV of $42,000. The present value of sales revenue is $600,000, the present value of contribution is $280,000 and the present value of variable costs is $320,000. By what percentage could the selling price fall before the project's NPV becomes zero?
- A) 7.0%
- B) 13.1%
- C) 15.0%
- D) 46.7%
Show answer & explanation
Answer: A) 7.0%
Sensitivity = NPV / PV of the cash flow affected. A change in selling price affects sales revenue only, so sensitivity = 42,000 / 600,000 = 7.0%. 15.0% is the sensitivity to sales volume, which changes contribution, and 13.1% is the sensitivity to variable costs.
Question 3
A project has the following possible NPVs: -$20,000 with probability 0.3, $40,000 with probability 0.5 and $90,000 with probability 0.2. What is the expected NPV?
- A) $32,000
- B) $36,667
- C) $40,000
- D) $44,000
Show answer & explanation
Answer: A) $32,000
Expected NPV = (-20,000 x 0.3) + (40,000 x 0.5) + (90,000 x 0.2) = -6,000 + 20,000 + 18,000 = $32,000. The simple average of the three outcomes ($36,667) ignores the probabilities, and treating the loss as positive gives $44,000.
Question 4
Which of the following correctly distinguishes risk from uncertainty in investment appraisal?
- A) Risk exists where outcomes are certain; uncertainty exists where they are not
- B) Uncertainty can be measured using expected values, but risk cannot
- C) Risk exists where probabilities can be assigned to possible outcomes; uncertainty exists where they cannot
- D) Risk relates only to future cash inflows, while uncertainty relates only to the initial investment
Show answer & explanation
Answer: C) Risk exists where probabilities can be assigned to possible outcomes; uncertainty exists where they cannot
Risk describes a situation where there are several possible outcomes and probabilities can be estimated, for example from past experience. Uncertainty describes a situation where outcomes cannot be predicted or assigned probabilities with confidence. Probability-based techniques such as expected values therefore apply to risk.
Question 5
Which of the following is a limitation of sensitivity analysis?
- A) It cannot identify which variables are most critical to the project
- B) It can only be applied to projects with a negative NPV
- C) It requires probabilities to be estimated for each variable
- D) It considers the effect of changing only one variable at a time and does not indicate how likely that change is
Show answer & explanation
Answer: D) It considers the effect of changing only one variable at a time and does not indicate how likely that change is
Sensitivity analysis identifies the critical variables by calculating how much each could change before the NPV becomes zero. However, it assumes the other variables remain at their expected values, while in practice variables may change together, and it does not use probabilities, so it says nothing about the likelihood of the change.
Question 6
A project costs $70,000 now. The year 1 cash inflow will be $50,000 (probability 0.6) or $30,000 (probability 0.4). Independently, the year 2 cash inflow will be $60,000 (probability 0.7) or $40,000 (probability 0.3). The discount rate is 10% (DFs 0.909 and 0.826). What is the probability that the project will have a negative NPV?
- A) 12%
- B) 28%
- C) 30%
- D) 40%
Show answer & explanation
Answer: A) 12%
NPVs of the four combinations: (50,000; 60,000) +25,010; (50,000; 40,000) +8,490; (30,000; 60,000) +6,830; (30,000; 40,000) -9,690. Only the last combination is negative, with joint probability 0.4 x 0.3 = 0.12, i.e. 12%. The other options use single-period probabilities or the wrong combination.
Question 7
A project has an initial investment of $250,000 and an NPV of $30,000. By what percentage could the initial investment increase before the project ceased to be worthwhile?
- A) 6.0%
- B) 8.3%
- C) 10.7%
- D) 12.0%
Show answer & explanation
Answer: D) 12.0%
The initial investment occurs at time 0, so its present value equals its cost. Sensitivity = NPV / PV of investment = 30,000 / 250,000 = 12.0%. Dividing by the PV of inflows (280,000) gives 10.7%, which is the sensitivity of the inflows, not the investment.
Question 8
Which of the following is a limitation of using expected NPV to decide whether to accept a one-off project?
- A) The expected value may not correspond to any outcome that can actually occur, and it ignores the spread of possible outcomes
- B) Expected values cannot be calculated when there are more than two possible outcomes
- C) Expected NPV always understates the true return of a project
- D) Expected values do not use probabilities
Show answer & explanation
Answer: A) The expected value may not correspond to any outcome that can actually occur, and it ignores the spread of possible outcomes
An expected value is a long-run average, which is most meaningful when a decision is repeated many times. For a one-off project the actual outcome will be one of the possible results, not the average, and the expected value conceals the risk of a large loss. It also relies on subjective probability estimates.