🔢 How to calculate expected value
The Formula: Expected value (EV) = Σ (outcome × probability)
Add up all (outcome × probability) for each possible result at a chance node.
Worked example
Option A: success ($100 000, probability 0.6) and failure ($20 000, probability 0.4).
- EV = ($100 000 × 0.6) + ($20 000 × 0.4)
- EV = $60 000 + $8 000 = $68 000
Always check that probabilities at each chance node add up to 1.0. If they don't, something is wrong! ✅
💵 Net expected value
The Formula: Net expected value = Expected value − Cost of the option
- If Option A costs $50 000 and EV = $68 000
- Net EV = $68 000 − $50 000 = $18 000
- This is the expected NET gain from choosing Option A
Compare net EVs to choose between options. But remember — the highest net EV isn't always best if it's also the riskiest!
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Drawing a decision tree
- Step 1: Start with a decision node (square) on the left
- Step 2: Draw branches for each option
- Step 3: Add chance nodes (circle) where outcomes are uncertain
- Step 4: Draw branches for each outcome with probabilities
- Step 5: Write the financial value at the end of each branch
- Step 6: Calculate expected values working RIGHT to LEFT
- Step 7: Mark REJECTED options with two diagonal lines on the branch to show which option was not chosen
Work backwards! Calculate from the right side first (outcomes), then move left to compare options at the decision node.
Exam tip: Always show rejected alternatives by drawing two diagonal lines across the branch you did NOT choose. The Nov 2024 markscheme awarded marks for this. It shows the examiner you understand the decision process.
⚖️ Evaluating the results
- The option with the highest net EV is mathematically the best
- BUT consider: How reliable are the probability estimates?
- How much can the business afford to lose if it goes wrong?
- What about stakeholder impact, ethics, reputation?
- A risk-averse business may prefer lower EV with more certainty
In 10-mark questions, use the decision tree calculation PLUS qualitative evaluation for top marks.