How do I set up a Monte Carlo simulation for a capital project?

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AcadiFi · Accepted Answer

Monte Carlo simulation draws input variables from assumed distributions, recomputes NPV thousands of times, and delivers a full output distribution — mean, percentiles, probability of loss. Steps for Wintergate: (1) Identify 5-8 key stochastic inputs (volume, price, unit cost, capex, terminal growth, WACC). (2) Assign distributions calibrated to data: volume Normal(mu, sigma) from historical demand, commodity input costs lognormal from futures vol, WACC triangular. (3) Specify correlations — volume and price often negatively correlated via elasticity; input costs positively correlated with each other. (4) Draw 10,000 or 50,000 scenarios; compute NPV each time. (5) Summarize: mean NPV, 5th percentile, probability NPV < 0. ```mermaid flowchart TD A[Define
Distributions] --> B[Specify
Correlations] B --> C[Draw Random
Samples] C --> D[Compute NPV
Each Path] D --> E[Analyze
Distribution] ``` Suppose base-case deterministic NPV is $22M. Simulation might yield E[NPV] = $19.4M, 5th percentile = -$8M, P(NPV < 0) = 18%. This probabilistic output transforms the discussion: 'we have an 18% chance of losing money' is far more decision-useful than 'NPV is positive'. Pitfalls AcadiFi candidates must avoid: (1) Ignoring correlations produces falsely narrow NPV distributions. (2) Using Normal distributions for heavy-tailed inputs underestimates tail risk — use lognormal or Student-t where appropriate. (3) Simulation output is only as good as the input distributions; garbage in, garbage out. Always run sensitivity on the distributional assumptions themselves.

How do I set up a Monte Carlo simulation for a capital project?

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