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Decision trees and expected values

Edexcel IAL Business · WBS13 Business decisions and strategy

A decision tree sets out the options facing a business, the possible outcomes of each, how likely they are and what each is worth. Calculating expected values lets managers compare risky options on the same basis.

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Drawing a decision tree

A square is a decision node: a point where managers choose between options. Each branch from it is an option, labelled with its cost.
A circle is a chance node: a point where the outcome is uncertain. Each branch is an outcome with its probability; the probabilities from one chance node add up to 1.
At the end of each branch is the financial outcome (payoff).

Trees are drawn left to right and worked out right to left.

Expected value

Expected value (EV) at a chance node = sum of (probability x outcome).

Net expected value of an option = EV - cost of the option.

Example: Option A, launch a new product, costs $2m: success (0.6) earns $5m, failure (0.4) earns $1m. EV = 0.6 x 5 + 0.4 x 1 = $3.4m; net = 3.4 - 2 = $1.4m.

Option B, modify an existing product, costs $0.5m: success (0.7) earns $2m, failure (0.3) $0.8m. EV = 0.7 x 2 + 0.3 x 0.8 = $1.64m; net = 1.64 - 0.5 = $1.14m.

On financial grounds choose A; the rejected option is crossed out with two short lines (a 'gate') on the decision tree.

Real exam examples

January 2020 WBS13, Q2 (car maker): expanding the dealer network gave 0.4 x $7m + 0.6 x -$1m = $2.2m; a premium relaunch gave 0.2 x $15m + 0.8 x -$2m = $1.4m. The tree favoured the dealer network, but the mark scheme also credited the time needed to expand dealerships and the state of the Indian economy as factors that could change the decision.
October 2024 WBS13, Q2 (holiday villages): a new village gave (0.8 x EUR780m) - (0.2 x EUR120m) - EUR520m = EUR80m; a takeover gave (0.7 x EUR220m) - (0.3 x EUR70m) - EUR100m = EUR33m.

Both were 20-mark questions: the calculation supports the argument, but the marks come from judging it.

Strengths and limitations

Strengths: makes managers set out options, risks and outcomes logically; puts a value on risk; easy to compare options; useful for presenting a case.

Limitations:

Probabilities and payoffs are estimates and may be biased or based on little data.
Expected value is an average over many repeats; a one-off decision will produce one actual outcome, not the EV.
Ignores the business's attitude to risk: a firm that cannot survive a large loss may reject the higher-EV option.
Ignores qualitative factors (staff, brand, ethics, strategy) and the time value of money.
The external environment can change after the decision.

Worked example

A firm can spend $250,000 on a marketing campaign. Outcomes: high sales (0.5) $900,000, medium (0.3) $400,000, low (0.2) a loss of $200,000. Calculate the net expected value.

EV = 0.5 x 900,000 + 0.3 x 400,000 + 0.2 x (-200,000) = 450,000 + 120,000 - 40,000 = $530,000.
Net EV = 530,000 - 250,000 = $280,000.
Check: probabilities 0.5 + 0.3 + 0.2 = 1.

Answer: Net expected value $280,000.

Key idea: Squares are decisions, circles are chance nodes. EV = sum of probability x outcome; net EV = EV - cost. Probabilities at a node sum to 1. Estimates, averages and attitude to risk limit the method.

Check yourself

Option A costs $2m. Success (probability 0.6) earns $5m; failure (0.4) earns $1m. Calculate the net expected value.
Show answer
$1.40 m. EV = 0.6 x 5 + 0.4 x 1 = 3.4; net = 3.4 - 2 = $1.4m.
Option B costs $0.5m. Success (0.7) earns $2m; failure (0.3) earns $0.8m. Calculate the net expected value.
Show answer
$1.14 m. EV = 0.7 x 2 + 0.3 x 0.8 = 1.64; net = 1.64 - 0.5 = $1.14m.
October 2024 WBS13: a new holiday village costs EUR520m. Success (0.8) is worth EUR780m; failure (0.2) is a loss of EUR120m. Calculate the expected monetary value of the option.
Show answer
EUR80 m. (0.8 x 780) - (0.2 x 120) - 520 = 624 - 24 - 520 = EUR80m.
January 2020 WBS13: a premium relaunch has a 0.2 chance of $15m and a 0.8 chance of -$2m. Calculate the expected value.
Show answer
$1.4 m. 0.2 x 15 + 0.8 x (-2) = 3 - 1.6 = $1.4m.
At a chance node the probability of high demand is 0.45 and of medium demand is 0.35. The only other outcome is low demand. What is its probability?
Show answer
0.20. Probabilities sum to 1: 1 - 0.45 - 0.35 = 0.20.
On a decision tree, what does a circle represent?
- A decision node, where managers choose
- The final payoff
- A chance node, where the outcome is uncertain
- The cost of an option
Show answer
A chance node, where the outcome is uncertain. Circles show uncertain outcomes; squares show decisions.
Why might a business reject the option with the highest expected value?
- The option carries a risk of a loss that the business could not survive
- Expected values are always wrong
- The highest EV option always has the lowest cost
- Decision trees cannot compare more than two options
Show answer
The option carries a risk of a loss that the business could not survive. EV is an average; attitude to risk matters for one-off decisions.
Explain one limitation of decision trees.
Show answer
The probabilities and financial outcomes are only estimates, which may be inaccurate or biased, so the expected values and the decision based on them may be wrong.. Say what is estimated and the consequence.

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Last updated 8 November 2026. Spotted a mistake? Tell us.