CIMA BA2 · Chapter 9
Risk and uncertainty in decision making MCQs with Answers
11 multiple-choice questions on Risk and uncertainty in decision making for CIMA BA2 Fundamentals of Management Accounting. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
What is the difference between RISK and UNCERTAINTY in decision making?
- A) Under risk, probabilities can be assigned to possible outcomes; under uncertainty, they cannot be reliably estimated
- B) Risk relates only to losses, whereas uncertainty relates only to gains
- C) Risk applies to long-term decisions and uncertainty to short-term decisions
- D) There is no difference; the terms are interchangeable
Show answer & explanation
Answer: A) Under risk, probabilities can be assigned to possible outcomes; under uncertainty, they cannot be reliably estimated
Risk exists when there are several possible outcomes and their likelihood can be quantified, for example from past data. Uncertainty exists when outcomes, or their likelihood, cannot be reliably predicted. Techniques such as expected values require probabilities and therefore apply to risk.
Question 2
A project could produce a profit of $40,000 (probability 0.3), a profit of $25,000 (probability 0.5) or a loss of $10,000 (probability 0.2). What is the expected value of the project's profit?
- A) $18,333
- B) $26,500
- C) $25,000
- D) $22,500
Show answer & explanation
Answer: D) $22,500
Expected value = sum of (outcome x probability) = ($40,000 x 0.3) + ($25,000 x 0.5) + (-$10,000 x 0.2) = $12,000 + $12,500 - $2,000 = $22,500.
Question 3
A risk-neutral manager must choose between two mutually exclusive projects: Project X: profit $60,000 (probability 0.4) or $20,000 (probability 0.6) Project Y: profit $90,000 (probability 0.3), $10,000 (probability 0.5) or a loss of $5,000 (probability 0.2) Which project should be chosen and what is its expected profit?
- A) Project Y, with an expected profit of $31,000
- B) Project Y, with an expected profit of $90,000
- C) Project X, with an expected profit of $36,000
- D) Project X, with an expected profit of $40,000
Show answer & explanation
Answer: C) Project X, with an expected profit of $36,000
EV of X = ($60,000 x 0.4) + ($20,000 x 0.6) = $24,000 + $12,000 = $36,000. EV of Y = ($90,000 x 0.3) + ($10,000 x 0.5) - ($5,000 x 0.2) = $27,000 + $5,000 - $1,000 = $31,000. A risk-neutral manager chooses the higher expected value, so Project X.
Question 4
Which of the following is a limitation of using EXPECTED VALUES to make decisions?
- A) Expected values cannot be calculated when there are more than two outcomes
- B) The expected value is a long-run average and may not be a possible outcome of a one-off decision
- C) Expected values take full account of the decision maker's attitude to risk
- D) Expected values ignore the probabilities of the outcomes
Show answer & explanation
Answer: B) The expected value is a long-run average and may not be a possible outcome of a one-off decision
An expected value is the average result if a decision were repeated many times. For a one-off decision the actual outcome will be one of the individual outcomes, not the average. Expected values also ignore the decision maker's attitude to risk and the spread of outcomes, and they depend on the accuracy of the probabilities.
Question 5
A manager prefers an investment with a certain return of $50,000 to an alternative offering an equal chance of $0 or $110,000. What is the manager's attitude to risk most likely to be?
- A) Risk averse
- B) Risk seeking
- C) Risk neutral
- D) Indifferent to all outcomes
Show answer & explanation
Answer: A) Risk averse
The alternative has an expected value of 0.5 x $110,000 = $55,000, which is higher than the certain $50,000. Choosing the lower but certain amount shows a willingness to give up expected return to avoid risk, which is risk aversion. A risk-neutral manager would choose the higher expected value.
Question 6
The weekly demand for a product is normally distributed with a mean of 500 units and a standard deviation of 40 units. What is the probability that demand in a week will exceed 560 units? (The area under the normal curve between the mean and z = 1.5 is 0.4332.)
- A) 0.4332
- B) 0.9332
- C) 0.1336
- D) 0.0668
Show answer & explanation
Answer: D) 0.0668
z = (560 - 500) / 40 = 1.5. The area between the mean and z = 1.5 is 0.4332. Half the distribution lies above the mean, so the probability of exceeding 560 = 0.5000 - 0.4332 = 0.0668.
Question 7
The weekly demand for a product is normally distributed with a mean of 500 units and a standard deviation of 40 units. What is the probability that demand in a week will be between 440 and 580 units? (Areas between the mean and z: z = 1.5 is 0.4332; z = 2.0 is 0.4772.)
- A) 0.0440
- B) 0.0896
- C) 0.9772
- D) 0.9104
Show answer & explanation
Answer: D) 0.9104
For 440 units, z = (440 - 500) / 40 = -1.5, area to the mean 0.4332. For 580 units, z = (580 - 500) / 40 = 2.0, area to the mean 0.4772. Because the values lie on opposite sides of the mean, the areas are added: 0.4332 + 0.4772 = 0.9104.
Question 8
Two machines operate independently. The probability that machine 1 breaks down in a week is 0.10 and the probability that machine 2 breaks down is 0.15. What is the probability that AT LEAST ONE machine breaks down in a week?
- A) 0.250
- B) 0.015
- C) 0.765
- D) 0.235
Show answer & explanation
Answer: D) 0.235
The probability that neither breaks down = (1 - 0.10) x (1 - 0.15) = 0.90 x 0.85 = 0.765. The probability that at least one breaks down = 1 - 0.765 = 0.235. Simply adding 0.10 and 0.15 double-counts the case where both break down (0.10 x 0.15 = 0.015).
Question 9
A company budgets to sell 20,000 units at $15 each. Variable cost is $9 per unit and fixed costs are $84,000. By what percentage could the SELLING PRICE fall before the company would make neither a profit nor a loss, assuming all other estimates are unchanged?
- A) 12%
- B) 20%
- C) 30%
- D) 42.9%
Show answer & explanation
Answer: A) 12%
Budgeted profit = (20,000 x $15) - (20,000 x $9) - $84,000 = $300,000 - $180,000 - $84,000 = $36,000. A fall in price reduces revenue directly, so revenue can fall by $36,000 before profit is eliminated. Sensitivity = $36,000 / $300,000 = 12%.
Question 10
Which of the following is a limitation of SENSITIVITY ANALYSIS?
- A) It normally changes only one variable at a time, whereas in practice several variables may change together
- B) It cannot identify which estimates are most critical to a decision
- C) It requires the probability of each outcome to be known
- D) It can only be used for decisions with a single possible outcome
Show answer & explanation
Answer: A) It normally changes only one variable at a time, whereas in practice several variables may change together
Sensitivity analysis measures how far a single estimate can change before the decision changes, which helps identify critical variables. Its main limitation is that it usually varies one factor at a time while holding others constant. It does not require probabilities, which is why it does not show how likely a change is.
Question 11
For a normal distribution, approximately what proportion of values lie within ONE standard deviation either side of the mean?
- A) 50%
- B) 95%
- C) 68%
- D) 99.7%
Show answer & explanation
Answer: C) 68%
For any normal distribution, about 68% of values lie within one standard deviation of the mean, about 95% within two standard deviations and about 99.7% within three. 50% of values lie on each side of the mean.