How do I use a decision tree to value a staged capital project?

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AcadiFi · Accepted Answer

Decision trees are essential when projects have sequential decisions and information arrives in stages. They capture the option to abandon or expand at each node, which standard DCF misses. For Helixvale's drug: Phase 1 costs $15M with 65% success probability. If successful, Phase 2 costs $40M with 45% success probability. Phase 3 costs $120M with 55% success probability. Successful launch yields PV of $900M; failure at any stage yields zero. Solve by backward induction starting from Phase 3: - EV at Phase 3 = 0.55 * 900 - 120 = $375M. Since $375M > 0, proceed. - EV at Phase 2 decision = 0.45 * 375 - 40 = $128.75M. Proceed. - EV at Phase 1 decision = 0.65 * 128.75 - 15 = $68.7M. The project is worth $68.7M at inception. Traditional DCF would compute -15 - 40/(1.x)^t - 120/(1.x)^t + 900*p_total/(1.x)^t, forcing you to incur future stage costs unconditionally. That understates value by $30-50M. ```mermaid flowchart LR A[Phase 1
$15M] -->|65%| B[Phase 2
$40M] A -->|35%| F[Fail
$0] B -->|45%| C[Phase 3
$120M] B -->|55%| G[Fail] C -->|55%| D[Launch
$900M PV] C -->|45%| H[Fail] ``` AcadiFi Level II candidates: be careful with discount rates. Strictly, probabilities in a decision tree are objective, and discount rates should reflect the project's risk after conditioning. In practice, a single risk-adjusted WACC is often applied throughout; real options theory offers more rigorous alternatives.

How do I use a decision tree to value a staged capital project?

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