Decision Trees (DP IB Business Management)
Revision Note
Written by: Lisa Eades
Reviewed by: Steve Vorster
Decision Tree Diagrams
A decision tree is a quantitative method of tracing the outcomes of a decision so that the most profitable decision can be identified
Research-based estimates and probabilities are used to calculate likely outcomes
The net gain from a decision can be identified and used to consider whether an investment is worthwhile
Using decision trees provides several key advantages to the decision making process
Constructing a decision tree diagram may reveal options that haven't previously been considered
Managers are forced to consider the risks associated with their choice, ahead of implementation
The quantitative approach requires deep research to be carried out
Decision tree diagrams
The key elements in a decision tree diagram are
Decision points
Outcomes
Probabilities
Expected monetary values
Diagram: a simple decision tree diagram
Points where decisions need to be made are called Decision Points and are represented by squares
Square A represents the fact that a choice is required on opening a new store or expanding the website
Points where there are different outcomes are represented by circles called nodes
Circles B and C represent points at which the different options have a range of outcomes - success or failure
The probability or likelihood of each outcome is shown on the diagram
A certain outcome has a probability of 1
An impossible outcome has a probability of 0
Opening a new store has a 0.7 probability of success and a 0.3 probability of failure
Expanding the website has a 0.6 probability of success and a 0.4 probability of failure
The monetary value of each decision is based on the expected profit or loss of the outcome
If opening a new store is successful a £420,000 profit is expected
If opening a new store is unsuccessful a £24,000 loss is expected
If expanding the website is successful a £480,000 profit is expected
If expanding the website is unsuccessful a £32,000 loss is expected
Calculating expected monetary values
To compare the options, a business should take into account the expected values of each decision presented in the decision tree diagram
To calculate the expected monetary value of a decision, the following formula is used
(Expected value of success x Probability) + (Expected value of failure x Probability)
Using the example above the expected value of opening a new store is
(£420,000 x 0.7) + (-£24,000 x 0.3)
= £294,000 + -£7,200
= £286,800
Using the example above the expected value of expanding the website is
(£480,000 x 0.6) + (-£32,000 x 0.4)
= £288,000 + -£12,800
= £275,200
As the expected value of opening a new store is higher at £286,800, than that of expanding the website at £275,200, based purely on financial terms, the business should choose the option to open a new store
Variations in the decision tree diagram
In some cases, the decision tree diagram provides expected revenues rather than profit or loss for the range of outcomes
In these diagrams, the costs related to each outcome are also provided
To calculate the expected value of each outcome, costs must be deducted from expected revenues
Explanation
To calculate the expected monetary value of a decision, revenues and costs are included in the diagram
(Expected value of success x Probability) + ( Expected value of failure x Probability) - Cost
The expected value of launching a new product is
(£520,000 x 0.6) + (-£54,000 x 0.4) - £280,000
= £312,000 + -£21,600 - £280,000
= £290,400 - £280,000
= £ 10,400
The expected value of improving the existing product is
(£225,000 x 0.9) + (-£22,000 x 0.1) - £190,000
= £202,500 + -£2,200 - £190,000
= £200,300 - £190,000
= £ 10,300
As the expected value of launching a new product is marginally higher at £10,400 than that of improving the existing product at £10,300, the business should choose the option to launch a new product
In this case the decision tree has demonstrated that there is little between the two options and the business should look at other factors that may inform their decision
Worked Example
Caramelac is a lactose-free chocolate product manufactured by a large multinational confectionery business. In recent years increased competition from other well-known brands has started to impact on sales of the product and managers are determined to maintain Caramelac’s market share.
Market research has shown that the business has two options:
a) Redevelop the product
b) Create a new advertising campaign
The expected outcomes and the probabilities of success and failure are shown in the decision tree below
Calculate the expected values of each option and decide, on financial grounds, which option the Caramelac's brand managers should choose. (6 marks)
Answer:
Step 1 - Calculate the expected value of redeveloping the product
(£840,000 x 0.5) + (-£84,000 x 0.5)
= £420,000 + -£42,000
= £378,000 (2 marks)
Step 2 - Calculate the expected value of the advertising campaign
(£660,000 x 0.6) + (-£76,000 x 0.4)
= £396,000 + -£30,400
= £365,600 (2 marks)
Step 3 - Interpret the outcomes and make a decision
As the expected value of redeveloping the product is higher at £378,000 than that of the advertising campaign at £365,600 (1 mark), the business should choose the option to redevelop the product (1 mark).
Examiner Tips and Tricks
Expected values are not the same thing as profit or revenues generated by a choice. In the above example, launching a new product is expected to either generate a positive revenue figure of £520,000 or generate a negative revenue figure of £54,000. It is never forecast that a revenue figure of £200,300 will be achieved. This is purely a figure used in making the choice between this option and the alternative and does not represent the actual amount of revenue that is expected to be achieved.
Limitations of Using Decision Trees
Constructing decision trees that can support effective decision-making requires skill to avoid bias and takes significant amounts of time to gather reliable data
A decision tree is constructed using estimates which rarely take full account of external factors and cannot include all possible eventualities
Qualitative elements such as human resource impacts are not considered, which may affect the probability of success of a decision
The time lag between the construction of a decision tree diagram and the implementation of the decision is likely to further affect the reliability of the expected values
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