Monte Carlo NPV / Tornado — Engineering Fundamentals
Why probabilistic, triangular vs lognormal, tornado interpretation, and the pitfalls of un-correlated inputs.
1. Why probabilistic NPV
Deterministic NPV gives a single number that hides risk. Two projects with identical "base-case" NPVs can have wildly different downside exposure — one might have ±10 % spread on inputs, the other ±50 %. A Monte Carlo simulation propagates the uncertainty of each input through the cash-flow model and produces a distribution of NPV outcomes. From that distribution you can answer questions the deterministic case cannot:
- What is the probability the project loses money?
- What is the 10th-percentile outcome (downside scenario)?
- Which inputs drive the variance most?
For midstream/E&P projects with multi-decade cash flows and commodity-price exposure, MC is the industry standard for FID-stage economic analysis.
2. Distribution choice
| Distribution | Parameters | Best for |
|---|---|---|
| Triangular (used here) | min / mode / max | Engineering judgment; no historic data |
| Lognormal | μ, σ (of ln x) | Reservoir volumes, recovery factors, OOIP |
| Normal | μ, σ | Centered, symmetric variables (rare in E&P) |
| Beta (PERT) | min, mode, max, λ | Smoother than triangular; project schedules |
| Uniform | min, max | Pure ignorance; rare in practice |
Triangular is the default for engineering ranges because it captures asymmetry (upside vs downside skew) and is interpretable: min = "I am 95 % sure it won't be worse than this," mode = "most likely value," max = "95 % sure it won't be better than this." For commodity prices and reservoir recovery, lognormal is more appropriate — replace the triangular sampler in your modelling if you have historic data to fit.
3. Reading P10/P50/P90
The percentile output P10/P50/P90 is the industry standard reporting convention (SPE/PRMS):
- P50 (median) — the 50/50 outcome. NOT the same as the mean if the distribution is skewed.
- P90 (upside) — there is a 90 % chance the NPV is at or above this value. Note: some petroleum engineering literature uses "P90" to mean the 90 % probability of EXCEEDANCE (which is mathematically the 10th percentile). This calculator uses the standard "10 % of values fall below, 90 % above" convention for downside reporting. If your team uses the reverse convention, swap labels.
- P10 (downside) — 10 % chance NPV is at or below this.
- P(NPV > 0) — fraction of iterations that returned positive NPV. A common "go/no-go" threshold is 70–85 %.
4. The tornado chart
The tornado bar for each input shows how much NPV moves when that input alone is varied from its min to its max (others held at mode). Bars are sorted longest-to-shortest from the top — looking like a tornado funnel.
Use the tornado to:
- Prioritize de-risking. The top 2–3 bars deserve the most field/lab work to narrow their distributions. A wide CAPEX range may be the largest tornado driver — investing in detailed FEED engineering shrinks that range.
- Identify "no-regret" actions. If the discount rate's bar is small, you don't need to argue about WACC. If reservoir decline rate dominates, that's where your geology team should focus.
- Find sign-flips. A bar that crosses zero from positive to negative NPV indicates a critical threshold — that variable can sink the project alone if it hits its low end.
5. Pitfalls & correlation
Three common errors that bias MC results:
- Un-correlated inputs. CAPEX and project life are often positively correlated (bigger project takes longer to build and lasts longer). Revenue and OPEX may be correlated (gas-price shocks raise both). This calculator samples each variable independently — if your inputs are strongly correlated, the resulting distribution will be too wide.
- Optimism bias on the mode. Studies of CAPEX overruns show project teams systematically pick a mode value that turns out to be the 10th–30th percentile of actuals. Cross-check your mode against historical reference-class data (Flyvbjerg "reference class forecasting").
- Ignoring fat tails. Triangular distributions have no tails beyond max. Real commodity-price distributions have long upper tails (2008 oil, 2022 LNG) and lower tails (negative WTI in April 2020). If tail events matter, use lognormal with explicit thick-tail parameters or empirical bootstrapping.
6. References
- Newendorp, P.D.; Schuyler, J. (2000). Decision Analysis for Petroleum Exploration, 2nd ed. Planning Press.
- SPE 84218 — Monte Carlo Simulation in Oil & Gas Project Economics.
- Mun, J. (2010). Modeling Risk: Applying Monte Carlo Risk Analysis, Real Options Analysis, 2nd ed. Wiley.
- Murtha, J.A.; Ross, J. (2009). "Probabilistic forecasting in petroleum engineering." JPT 61(7), 24–25.
- SPE/PRMS (2018). Petroleum Resources Management System — P10/P50/P90 conventions.
- Flyvbjerg, B. (2006). "From Nobel Prize to project management: getting risks right." Project Management Journal 37(3), 5–15.