Quantitative Finance & Capital Budgeting Lab

Monte Carlo DCF & Project Risk Lab

Run 5,000 Monte Carlo simulation trials to model probabilistic DCF, expected NPV, loss probability, Value at Risk, and capital budgeting risk distributions.

Simulation Engine NPV Distribution Curve Percentile Matrix Risk Theory FAQ

Project Risk Presets

Load calibrated risk profiles.

Step 1: Set Triangular Probability Distributions (Min / Mode / Max)

Project Cash Flow & Risk Parameters

Min
Mode
Max
Upfront capital expenditure range.
Min
Mode
Max
Gross annual revenue receipts.
Min
Mode
Max
Direct operating expenses and maintenance.
Asset useful operating life.
Cost of capital hurdle rate.
Random pseudo-sampling cycles.
Expected Mean NPV
$364,250
Std Dev (Volatility): $142,500
Probability of Loss
6.2%
Low project risk profile
Value at Risk (P5 Downside)
-$32,400
5th percentile downside risk
P95 Upside Potential
$612,800
95th percentile upside potential

Empirical Probability Density

Simulated Net Present Value (NPV) Distribution

Negative NPV (Loss) Value Accretive (Profit)

Percentile Risk Distribution Table

Risk Percentile Net Present Value (NPV) Executive Interpretation

Quantitative Risk Engineering

Principles of Monte Carlo DCF

Why point estimates lead to capital allocation errors:

  • The Flaw of Averages: When plans rely on average conditions, they fail because average outcomes ignore volatility, asymmetric downside risks, and compounding cash deficits.
  • Triangular Sampling: By defining Minimum, Mode, and Maximum, engineers capture realistic positive or negative skew without needing complex parametric curves.
  • Value at Risk (P5 VaR): Represents the worst-case boundary where there is only a 5% chance of performing worse, providing a key downside metric for board approvals.
  • Hurdle Rate Calibration: Quantifies the exact probability that a project will exceed the company's cost of capital.

Calculate cost of capital in the WACC & Hurdle Rate Lab.

Mathematical Formulation

Monte Carlo DCF formulas

Triangular CDF: c = (Mode - Min) / (Max - Min)

Trial NPV = Sum_{t=1}^n [ (Rev_t - Cost_t) / (1 + r)^t ] - Capex

Expected NPV = (1 / N) * Sum_{i=1}^N NPV_i

P(Loss) = Count(NPV_i < 0) / N * 100%

Standard Deviation = Sqrt[ (1 / N) * Sum (NPV_i - Mean)^2 ]

Measure portfolio risk in the Value at Risk (VaR) Lab.

FAQ

Monte Carlo simulation questions

What is a Monte Carlo simulation in capital budgeting?

A Monte Carlo simulation is a mathematical technique that models project risk by repeatedly generating thousands of possible cash flow outcomes based on probability distributions (such as triangular min/mode/max ranges), producing a full distribution of Net Present Value (NPV) results instead of a single static number.

Why is Monte Carlo DCF superior to a single point-estimate NPV?

Static DCF models often suffer from the 'Flaw of Averages' by using single base-case values. Monte Carlo reveals the full distribution curve, standard deviation volatility, worst-case downside (P5 VaR), and exact probability of financial loss (P(NPV < 0)).

How is the Triangular Distribution used in project finance?

The triangular distribution models uncertainty when exact historical standard deviations are unavailable. It requires only three intuitive engineering estimates: Minimum (worst-case), Mode (most likely base-case), and Maximum (best-case).

What is the Probability of Loss metric?

Probability of Loss is the percentage of simulated Monte Carlo trials where the Net Present Value is negative (NPV < 0), meaning the project fails to return its required hurdle rate / cost of capital.

How many trials are recommended for Monte Carlo analysis?

5,000 to 10,000 iterations are standard in corporate finance and risk management. This provides high statistical precision with standard error of the mean below 1%.

Can I export the simulation results to CSV?

Yes. You can export complete summary percentiles (P5, P25, Median, P75, P95), expected mean, standard deviation, and histogram frequency bins as a UTF-8 CSV spreadsheet with formula defense.

Continue Exploring Risk & Valuation Tools

Explore our Risk & Resilience Hub, calculate enterprise hurdle rates in the WACC & Cost of Capital Lab, model parametric exposure in Value at Risk (VaR) Lab, stress test business resilience in Business Resilience Lab, or evaluate recovery time objectives in Business Continuity Lab.