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A-Level · Decision Trees and Quantitative Decision-Making

BUS.AL2 Decision Trees and Quantitative Decision-Making

AQA 7132 · Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions in the spaces provided. Show working for every calculation. Where a question uses the Green Brew Ltd case, the necessary figures are given in that question's prompt.

Which one of the following best describes a 'decision tree' in a business decision context?

A) A table showing monthly cash flows
B) A diagram showing decision and chance nodes with outcomes and probabilities
C) A marketing plan that lists possible product names
D) A staff rota showing shift patterns

(Total for Question 1 is 1 mark)

Define the term 'expected value' as used when completing a decision tree in business decision-making.

(Total for Question 2 is 2 marks)

In a decision tree diagram for a business like Green Brew Ltd, label which node is a decision node and which is a chance node. Give one-word labels for each.

(Total for Question 3 is 1 mark)

Green Brew Ltd considers a low-cost marketing test costing 100 pounds that has a 0.5 probability of increasing sales by 300 pounds and a 0.5 probability of making no gain. Calculate the expected value of the test (not net gain). Show your working.

(Total for Question 4 is 2 marks)

Green Brew Ltd case: Green Brew Ltd will decide between two options to expand sales. Option A is to buy a coffee van for 3,000 pounds. If successful (probability 0.6) the extra revenue net of variable costs is 8,000 pounds; if unsuccessful (probability 0.4) the extra revenue net of variable costs is 2,000 pounds. Complete the decision tree for Option A and calculate the expected value at the chance node and the net gain for Option A (expected value minus the 3,000 pound cost). Show all steps.

(Total for Question 5 is 8 marks)

Using your results for Option A from question 5, state one reason, based on the numbers, why Option A might be attractive to Green Brew Ltd. Use the case in your explanation.

(Total for Question 6 is 1 mark)

Green Brew Ltd Option B: do nothing, keep current operations with no cost and no extra revenue. State the expected value and net gain for Option B.

(Total for Question 7 is 1 mark)

Green Brew Ltd considers a third option, Option C: rent a small kiosk for 500 pounds. The kiosk has a 0.7 probability of producing an extra net revenue of 1,500 pounds and a 0.3 probability of producing an extra net revenue of 200 pounds. Calculate the expected value at the chance node for Option C (not net gain). Show your working.

(Total for Question 8 is 1 mark)

Using your answer to question 8, calculate the net gain for Option C (expected value minus the 500 pound cost). Show your working.

(Total for Question 9 is 1 mark)

Which option gives the highest net gain for Green Brew Ltd, using the figures in this pack? Choose one option and give its net gain in pounds.

(Total for Question 10 is 1 mark)

State one non-numeric factor Green Brew Ltd should consider that a decision tree does not capture when choosing between Option A, B and C.

(Total for Question 11 is 1 mark)

Explain briefly why the accuracy of a decision tree's recommendation depends on the probabilities used. Use Green Brew Ltd as the context in your explanation.

(Total for Question 12 is 1 mark)

Green Brew Ltd might combine options, for example run the kiosk first and if that succeeds later buy the van. State one practical limit of using decision trees to model such sequential or combined strategies.

(Total for Question 13 is 1 mark)

Evaluate the limitations of decision-tree analysis as a tool for business decision-making, using examples and figures from the Green Brew Ltd case where relevant. You should consider both numeric and non-numeric limitations and reach a justified conclusion.

(Total for Question 14 is 12 marks)

Mark scheme · BUS.AL2 Decision Trees and Quantitative Decision-Making

Question 1

B1 B cao
Answer: B

Question 2

B1 a clear statement that expected value is the probability weighted average of outcomes
B1 or equivalent, e.g. sum of each outcome multiplied by its probability
Answer: Expected value is the sum of each possible outcome multiplied by its probability, the probability weighted average of outcomes.

Question 3

B1 Decision node = 'Decision', Chance node = 'Chance' or 'Probability' (either phrasing)
Answer: Decision node: Decision. Chance node: Chance.

Question 4

M1 0.5 x 300 + 0.5 x 0 seen
A1 150 pounds cao
Answer: 150 pounds.

Question 5

M1 multiplies 0.6 by 8,000 or shows 0.6 x 8000
A1 4,800 pounds cao for 0.6 x 8,000
M1 multiplies 0.4 by 2,000 or shows 0.4 x 2000
A1 800 pounds cao for 0.4 x 2,000
M1 adds the two products, 4,800 + 800
A1 5,600 pounds cao for the expected value at the chance node
M1 subtracts the cost 3,000 from the expected value or shows 5,600 - 3,000
A1 2,600 pounds cao for the net gain of Option A
Answer: Expected value = 5,600 pounds; Net gain = 2,600 pounds.

Question 6

B1 states that the net gain is positive, e.g. net gain of 2,600 pounds so expected returns exceed the cost
Answer: The net gain is positive: expected net gain is 2,600 pounds, so the expected returns exceed the 3,000 pound cost.

Question 7

B1 states EV = 0 and net gain = 0
Answer: Expected value = 0 pounds; Net gain = 0 pounds.

Question 8

M1 0.7 x 1,500 + 0.3 x 200 seen
A1 1,110 pounds cao
Answer: 1,110 pounds.

Question 9

M1 1,110 - 500 seen (ft from question 8)
A1 610 pounds cao
Answer: 610 pounds.

Question 10

B1 identifies Option A and gives 2,600 pounds, or identifies Option C and gives 610 pounds, or Option B with 0, but correct highest is Option A 2,600
Answer: Option A, net gain 2,600 pounds.

Question 11

B1 any valid non-numeric factor, e.g. effect on brand image, staff workload, customer convenience, regulatory issues, or long-term strategic fit
Answer: For example, effect on brand image: a coffee van may improve local presence but could distract from the core cafe brand.

Question 12

B1 explains that if probabilities are wrong the expected values will be wrong, e.g. if the 0.6 success probability for the van is overestimated then the EV and net gain will be too high and option choice may be wrong
Answer: If the 0.6 probability of van success is too high, the EV of 5,600 pounds is overstated and the net gain 2,600 pounds is misleading, so the recommended option could be wrong.

Question 13

B1 states a practical limit, e.g. trees become complex with many branches and changing probabilities, making them hard to draw and unreliable
Answer: Decision trees become complex and hard to manage for sequential or combined strategies, and probabilities for later stages may change, reducing reliability.

Question 14

Level 1 (1-4): Makes simple, undeveloped points about limitations of decision trees with little or no use of the case figures and no clear judgement.
Level 2 (5-8): Develops several points about limitations, uses some case figures or examples, and offers a partial judgement but does not fully balance strengths and weaknesses.
Level 3 (9-12): Provides a well developed evaluation of the limitations, applies case figures and examples (for example the 0.6 probability and the 3,000 pound cost for the van), analyses implications for Green Brew Ltd and reaches a balanced, justified conclusion.
Indicative content:
- Numeric limitations: decision trees depend on estimated probabilities and monetary outcomes; if the 0.6 success probability for the van is uncertain or biased, the EV of 5,600 pounds and net gain of 2,600 pounds are unreliable.
- Numeric limitations continued: decision trees usually ignore risk preferences and variance; two options with similar EVs may differ in risk, for example Option A has a wide outcome range 8,000 or 2,000, whereas Option C outcomes are smaller, so EV alone hides volatility.
- Practical limitations: complex or sequential decisions make trees large and impractical, and probabilities for later nodes may change after earlier decisions, reducing predictive value for strategies like 'test kiosk then buy van'.
- Qualitative factors: decision trees omit non-financial considerations such as brand impact, customer experience, staff capacity, or strategic fit, which might favour the van despite numbers or rule it out despite a positive net gain.
- Data availability and time: accurate probabilities and outcomes require good market research, which can be costly and time-consuming; small firms like Green Brew Ltd may lack reliable data, making estimates speculative.
- Behavioural limitations: managers may be overconfident about probabilities or influenced by bias, leading to inappropriate weighting of outcomes, so a numerically superior option in the tree might be rejected for intuitive reasons and vice versa.
- Counterbalance: decision trees are still useful as a structured, transparent way to compare options numerically; they force explicit assumptions and make it easier to test sensitivity by changing probabilities and figures.
- Conclusion guidance: a balanced conclusion might say decision trees are valuable as a decision aid but their output should not be followed blindly; for Green Brew Ltd the positive net gain for Option A is persuasive, but the firm should check the probability estimates, consider risk tolerance and qualitative factors before committing.

Decision Trees and Quantitative Decision-Making - Worksheets, Questions and Revision