IB Business Management HLTopic 6 — The Business Management ToolkitPapers 1, 2 & 3Quantitative tool~11 min read
Using Decision Trees
Two options, both risky, different price tags. A decision tree puts a single number on each one so they can be compared fairly. The maths is easy. The marks are lost by forgetting to take the cost off, or by treating the answer as a prediction.
📘 What you need to know
Squares are decision points. The business chooses which branch to take.
Circles are chance nodes. The business does not choose; probability decides.
Probabilities on the branches from one circle must add up to 1.
Expected value = (payoff × probability) added up for every branch, then take off the cost.
Losses go in as negative numbers, and brackets in the diagram usually mean a loss.
The expected value is never the amount you will actually get. It is only a fair way to compare options.
Reading the diagram
Harbour Sail Tours has to pick one branch out of square A. Everything to the right of a circle is outside its control.
The calculation
Expected value of an option
(payoff × probability) + (payoff × probability) − cost
Work left to right in the diagram but right to left in the maths: start at the payoffs, multiply each by its probability, add them, then subtract the cost written on the branch. Do it once per option and compare the two answers.
The single most common lost mark is forgetting the cost. If the question gives you revenue figures, the cost has not been taken off yet. If it gives you profit or loss figures, it usually has. Check the column heading before you start.
Worked examples
WORKED EXAMPLE
Use the tree above to calculate the expected value of refitting the two boats. [2 marks]
Step 1: success branch$700,000 × 0.6 = $420,000Step 2: failure branch$150,000 × 0.4 = $60,000Step 3: add them$420,000 + $60,000 = $480,000Step 4: take off the cost$480,000 − $260,000Expected value = $220,000show every line — method marks are given even if the arithmetic slips
WORKED EXAMPLE
Calculate the expected value of buying a third boat, and recommend an option on financial grounds. [4 marks]
Step 1: success branch$1,200,000 × 0.5 = $600,000Step 2: failure branch$250,000 × 0.5 = $125,000Step 3: add, then subtract the cost$725,000 − $480,000 = $245,000Step 4: compare and decide$245,000 beats $220,000 by $25,000, so on financial grounds Harbour Sail should buy the third boat.Buy the third boat: EV $245,000the gap is small — say so, because that is where judgement marks live
A close result is a finding, not a problem. When two expected values are only $25,000 apart, the honest conclusion is that the tree cannot separate them, so the decision should turn on other things: cash available, staff, and how much loss the owners could survive.
What the tree does not tell you
Strength of the tool
Weakness of the tool
Turns two very different options into one comparable number
Probabilities are estimates, often little better than an informed guess
Forces managers to think about risk before committing money
Only the outcomes someone thought of appear on the tree
Can reveal options that had not been discussed
Ignores qualitative issues such as staff morale and reputation
Makes the reasoning visible, so others can challenge it
Takes time and research, and figures go stale before the decision is made
Handles several stages of a decision, not just one
An expected value assumes the choice is repeated many times, which it is not
🧩 The method, every time
Check the column heading. Revenue or profit? That decides whether you subtract the cost.
Check the probabilities add to 1 at each circle.
Multiply each payoff by its probability.
Add the results for that option.
Subtract the cost shown on the option branch.
Compare, decide, then question it. Name one non-financial factor before you finish.
💡 Exam tips
Write the units. “$245,000”, not “245”.
Keep negative payoffs negative all the way through. A loss of $30,000 enters the sum as −$30,000.
If the question says “on financial grounds”, give the numbers and pick the higher one — nothing else.
If it says “recommend”, add the non-financial side: cash flow, skills, staff, brand.
Say plainly that the expected value is not a forecast of what the business will earn. That is a quick, reliable evaluation point.
Time lag matters. A tree built six months before the decision may already be wrong.
⚠ Common mix-ups
Forgetting to subtract the cost when the diagram shows revenue.
Adding the probabilities to the payoffs instead of multiplying.
Treating the expected value as the profit the business will make.
Mixing up squares and circles. Squares are choices; circles are chance.
Ignoring a negative sign, which usually makes the risky option look far better than it is.
Stopping at the number. Top marks need a judgement about the quality of the estimates.
Up next: Working With Descriptive Statistics — every probability and payoff on that tree came from data. Now learn how to summarise data properly.
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