ACCA PM · Chapter 9
Dealing with risk and uncertainty MCQs with Answers
11 multiple-choice questions on Dealing with risk and uncertainty for ACCA PM Performance Management. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
A bakery must decide the size of a daily order: small, medium or large. Daily demand may be low (probability 0.3), medium (probability 0.5) or high (probability 0.2). Profits ($) for each combination are: Small order: low 40, medium 40, high 40 Medium order: low 20, medium 60, high 60 Large order: low -10, medium 45, high 100 Which order size would be chosen using the maximax criterion?
- A) Large
- B) Small
- C) Medium
- D) Medium or large equally
Show answer & explanation
Answer: A) Large
Maximax selects the option with the highest possible payoff. The best outcomes are: small $40, medium $60, large $100. The large order offers the highest maximum, so an optimistic decision-maker would choose it.
Question 2
A bakery must decide the size of a daily order: small, medium or large. Daily demand may be low (probability 0.3), medium (probability 0.5) or high (probability 0.2). Profits ($) for each combination are: Small order: low 40, medium 40, high 40 Medium order: low 20, medium 60, high 60 Large order: low -10, medium 45, high 100 Which order size would be chosen using expected values, and what is its expected profit?
- A) Large, with expected profit of $39.50
- B) Medium, with expected profit of $48
- C) Small, with expected profit of $40
- D) Large, with expected profit of $45.00
Show answer & explanation
Answer: B) Medium, with expected profit of $48
EV small = $40. EV medium = (0.3 x 20) + (0.5 x 60) + (0.2 x 60) = $48. EV large = (0.3 x -10) + (0.5 x 45) + (0.2 x 100) = $39.50. The medium order has the highest EV.
Question 3
A bakery must decide the size of a daily order: small, medium or large. Daily demand may be low (probability 0.3), medium (probability 0.5) or high (probability 0.2). Profits ($) for each combination are: Small order: low 40, medium 40, high 40 Medium order: low 20, medium 60, high 60 Large order: low -10, medium 45, high 100 Which order size would be chosen using the maximin criterion?
- A) Small
- B) Medium
- C) Large
- D) Small or medium equally
Show answer & explanation
Answer: A) Small
Maximin selects the option whose worst outcome is the best. Worst outcomes: small $40, medium $20, large -$10. The small order has the highest minimum, so a pessimistic or risk-averse decision-maker would choose it.
Question 4
A bakery must decide the size of a daily order: small, medium or large. Daily demand may be low (probability 0.3), medium (probability 0.5) or high (probability 0.2). Profits ($) for each combination are: Small order: low 40, medium 40, high 40 Medium order: low 20, medium 60, high 60 Large order: low -10, medium 45, high 100 Which order size would be chosen using the minimax regret criterion?
- A) Small
- B) Large
- C) Small or large equally
- D) Medium
Show answer & explanation
Answer: D) Medium
Best payoff for each demand level: low 40, medium 60, high 100. Regrets: small 0, 20, 60 (maximum 60); medium 20, 0, 40 (maximum 40); large 50, 15, 0 (maximum 50). The lowest maximum regret is 40, for the medium order.
Question 5
A bakery must decide the size of a daily order: small, medium or large. Daily demand may be low (probability 0.3), medium (probability 0.5) or high (probability 0.2). Profits ($) for each combination are: Small order: low 40, medium 40, high 40 Medium order: low 20, medium 60, high 60 Large order: low -10, medium 45, high 100 What is the expected value of perfect information about daily demand?
- A) $62
- B) $52
- C) $14
- D) $8.50
Show answer & explanation
Answer: C) $14
With perfect information the bakery would choose the best order for each demand level: EV = (0.3 x 40) + (0.5 x 60) + (0.2 x 100) = $62. Without information the best EV is $48. EVPI = $62 - $48 = $14, the maximum worth paying for a perfect demand forecast.
Question 6
A manager always chooses the option with the best worst-case outcome. Which attitude to risk and decision criterion does this indicate?
- A) Risk-seeking, using the maximax criterion
- B) Risk-neutral, using expected values
- C) Risk-seeking, using the minimax regret criterion
- D) Risk-averse, using the maximin criterion
Show answer & explanation
Answer: D) Risk-averse, using the maximin criterion
Choosing the option whose worst outcome is least bad reflects a pessimistic, risk-averse attitude and is the maximin rule. Maximax suits a risk-seeker, and expected values suit a risk-neutral decision-maker.
Question 7
Which of the following is a limitation of using expected values for decision-making?
- A) The expected value may not correspond to any actual outcome, so it is less reliable for one-off decisions
- B) It cannot be used when probabilities are known
- C) It takes too much account of the decision-maker's attitude to risk
- D) It considers only the worst possible outcome of each option
Show answer & explanation
Answer: A) The expected value may not correspond to any actual outcome, so it is less reliable for one-off decisions
An expected value is a long-run average; it is most meaningful for decisions repeated many times. For a one-off decision the actual result will be one of the possible outcomes, not the EV. It also ignores the decision-maker's attitude to risk and depends on reliable probability estimates.
Question 8
A company is deciding whether to launch a product at a cost of $100,000. There is a 0.6 probability of success, giving a return of $300,000. If the launch fails (probability 0.4), the company can either abandon the product and sell the equipment for $50,000, or spend $30,000 modifying it, in which case there is a 0.5 probability of a return of $200,000 and a 0.5 probability of a return of $20,000. All values are in present value terms. What is the expected value of launching the product, assuming the best choice is made at each decision point?
- A) $100,000
- B) $124,000
- C) $112,000
- D) $212,000
Show answer & explanation
Answer: C) $112,000
Roll back from the right. If the launch fails: modifying gives (0.5 x $200,000) + (0.5 x $20,000) - $30,000 = $80,000, which exceeds the $50,000 from abandoning, so modify. EV of launch = (0.6 x $300,000) + (0.4 x $80,000) - $100,000 = $112,000.
Question 9
A project has a net present value of $50,000. The present value of sales revenue is $400,000. By what percentage could the selling price fall before the project's NPV becomes zero (the sensitivity of the project to selling price)?
- A) 8.0%
- B) 12.5%
- C) 87.5%
- D) 14.3%
Show answer & explanation
Answer: B) 12.5%
Sensitivity = NPV / PV of the cash flow concerned = $50,000 / $400,000 = 12.5%. If selling prices fell by more than 12.5%, the NPV would become negative, assuming all other variables are unchanged.
Question 10
Option A gives a certain profit of $50,000. Option B gives a profit of $120,000 if demand is strong and a loss of $20,000 if demand is weak. Above what probability of strong demand would Option B have the higher expected value?
- A) 0.42
- B) 0.58
- C) 0.50
- D) 0.60
Show answer & explanation
Answer: C) 0.50
Let p be the probability of strong demand. EV of B = 120,000p - 20,000(1 - p) = 140,000p - 20,000. Setting this equal to 50,000 gives 140,000p = 70,000, so p = 0.50. Above this probability, B's expected value exceeds the certain $50,000.
Question 11
Which of the following statements about the expected value of perfect information is correct?
- A) It is the maximum amount that should be paid for information that predicts the outcome with certainty
- B) It is always equal to the expected value of the best decision without information
- C) It can be negative if the information leads to a different decision
- D) It equals the value of imperfect information in all cases
Show answer & explanation
Answer: A) It is the maximum amount that should be paid for information that predicts the outcome with certainty
EVPI = EV with perfect information - EV without information. It sets a ceiling on what a decision-maker should pay for a forecast, since no information can be worth more than perfect information. It cannot be negative, and imperfect information is normally worth less.