IB Business Management SLTopic 8 — The Pre-Released StatementPaper 1Toolkit~10 min read
Bringing Decision Trees Into Your Answers
A decision tree puts numbers on a choice. You estimate what each outcome is worth, how likely it is, and what the option costs, then compare. The maths takes a minute. The mistake that costs most marks is forgetting to subtract the cost at the end.
What you need to know
A decision tree is a quantitative tool for tracing the possible outcomes of a choice.
Squares are decisions you control. Circles are chance events you do not.
Expected monetary value (EMV) = each outcome multiplied by its probability, added together.
Net gain = EMV minus the cost of taking that option. This is the figure you compare.
Probabilities on any set of branches must add up to 1.
The numbers are estimates, so a decision tree supports judgement rather than replacing it.
The two formulas
Expected monetary value
EMV = (probability × outcome) + (probability × outcome)
Net gain
Net gain = EMV − cost of the option
If a question gives you a cost and you never use it, you have almost certainly missed the last mark. Cross the cost off the paper once you have subtracted it.
A worked tree for ABC
Suppose ABC has $50m of finance available and two ways to use it. Here are the estimates its managers have come up with.
Option A looks better until you take the $50m off. This is the single most common slip in decision tree questions.
WORKED EXAMPLE
Using the estimates above, recommend which option ABC should choose. Justify your answer. [4]
Step 1: EMV of Option A(0.55 × $110m) + (0.45 × $30m)= $60.5m + $13.5m = $74m [1]Step 2: EMV of Option B(0.70 × $70m) + (0.30 × $40m)= $49m + $12m = $61m [1]Step 3: take off the cost of eachA: $74m − $50m = $24m net gainB: $61m − $30m = $31m net gain [1]Step 4: recommendChoose B: upgrading the concrete plants [1]Say why: B has the higher net gain ($31m against $24m) and the lower cost, so it is also the safer use of the finance.
Where ABC could actually use one
Expanding e-waste processing. High potential profits from recovered gold, set against the risk of falling metal prices or not collecting enough material.
Investing in concrete efficiency. The cost of new equipment, weighed against long-term savings on energy.
Entering a new geographic market. Profit from a growing economy, against the risk of political instability or weak construction demand.
The evaluation writes itself. Every one of ABC’s decisions depends on a number nobody can know: the future gold price, how much e-waste gets collected, whether a recession arrives. That is exactly the limitation of a decision tree, and it is a strong closing point in a discuss answer.
Strengths and limitations
Why managers use them
Why they should not rely on them
Drawing the tree can reveal options that nobody had thought about.
The probabilities are forecasts. If ABC guesses the chance of strong gold prices wrongly, every number after it is wrong too.
Managers are forced to put a figure on risk instead of talking vaguely about it.
External shocks such as a recession or a new emissions law are hard to build into a probability.
It gives a clear financial comparison between very different options, like recycling and concrete.
Qualitative factors are left out entirely. Reputation, employee morale and CSR do not appear anywhere in the maths.
The research needed to produce the estimates is useful in itself.
Time lag. By the time ABC builds the plant, the conditions the tree assumed may have changed.
WORKED EXAMPLE
Explain one limitation of using a decision tree to choose between these two options. [2]
Step 1: the point
A decision tree only includes outcomes that can be given a money value, so qualitative factors are ignored [1]
Step 2: apply itExpanding e-waste recycling would improve ABC’s reputation and CSR profile with governments and investors, but none of that appears in the $24m figure, so the tree understates the value of Option A [1]2 marksA limitation question is not an invitation to say “the numbers might be wrong” and stop. Say which number, and why it matters here.
Exam tip
Always subtract the cost. Compare net gains, not expected values.
Check the probabilities add to 1. If they do not, you have misread the question.
Show every line of working. Method marks are awarded even when the arithmetic slips.
Write the currency and the m. “$61m” not “61”.
Give a recommendation, not just a number. Calculate questions want the figure; recommend questions want a decision.
Have one qualitative limitation ready. Reputation and CSR are the obvious ones for ABC.
Label the shapes if you draw one. Square for decision, circle for chance.
Common mix-up
Comparing EMVs and ignoring cost. This alone flips the answer in the example above.
Adding the probabilities to the outcomes instead of multiplying.
Treating the result as certain. EMV is an average of outcomes, and ABC will get one outcome, not the average.
Confusing the shapes. A decision is a square because ABC chooses it; chance is a circle because it does not.
Saying “the estimates may be wrong” with no example. Name the estimate you doubt.
Forgetting the time lag. Gold prices can move between planning the plant and opening it.
Up next: Bringing Circular Business Models Into Your Answers — the idea that ties ABC’s two businesses into one story.
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