Probabilistic DCF
Monte Carlo Simulation
From Point Estimate to Probability-Weighted Value Distribution
Chapter 28 is the DCF system's probabilistic capstone. Where Chapters 26 and 27 identify and rank assumption risks, Chapter 28 quantifies them in full — running 10,000+ complete DCF re-computations with randomly drawn inputs to produce a probability-weighted Enterprise Value distribution, complete with P10 through P90 confidence intervals and a full histogram. This is the analytical tool that transforms a single-point valuation into a defensible, statistically grounded range.
Why Probabilistic DCF Matters
A standard DCF produces a single Enterprise Value from a single set of assumptions. But every assumption carries uncertainty — WACC could be 11% or 13%, terminal growth could be 2% or 3%, margins could converge to 18% or 22%. The standard model presents one answer and asks the reader to trust it. Probabilistic DCF replaces that single answer with a full distribution: the range and shape of all possible values given realistic uncertainty across all key inputs.
Monte Carlo Simulation — named for the Monaco casino district — is the most widely used probabilistic technique in quantitative finance. It works by treating key DCF inputs not as fixed numbers but as random variables drawn from probability distributions. Each simulation run draws a fresh WACC, a fresh growth rate, and a fresh terminal assumption and computes a full DCF. Repeat 10,000 times. The resulting 10,000 Enterprise Values, when sorted and binned, form a frequency distribution that reveals the most likely value range, the upside potential, and the downside risk — each with an associated probability.
For professional valuations, this output is uniquely valuable: it allows the appraiser to state not just a concluded value, but a confidence interval. "We conclude Enterprise Value is in the range of $18M–$24M, with a median of $21M and a 90% probability that true value lies between $14M and $28M" is a fundamentally more defensible and informative conclusion than "$21M."
The Probabilistic DCF Architecture
The Output Distribution
10,000+ iterations produce a frequency distribution. The P10–P90 interval is the reported confidence range. Indicative example.
How Equitest Implements Chapter 28 Probabilistic DCF
Chapter 28 is a complete probabilistic simulation engine built directly on the DCF model from Chapters 20–24. Every run is a full model re-computation — not an approximation or a lookup table.
Top Tornado Drivers Pre-Loaded as Stochastic Inputs
Chapter 28 opens with the top-ranked variables from the Chapter 27 Tornado Chart pre-selected as the simulation inputs — typically WACC, terminal growth rate, and the exit multiple or revenue CAGR depending on their ranking. This creates a coherent analytical chain across Chapters 26–28: identify sensitive variables (sensitivity analysis), rank them by impact (Tornado), then simulate their joint uncertainty (Monte Carlo). The analyst can add or substitute any DCF input variable.
Normal and Triangular Distributions Per Variable
For each stochastic variable, the analyst specifies the distribution type and parameters. WACC and exit multiple use normal distributions (mean = Chapter 21 WACC or Chapter 17 median multiple; σ = analyst-specified, with guidance on typical σ values by variable type). Revenue growth and terminal growth rate use triangular distributions (min, most likely, max) — reflecting their naturally bounded, non-symmetric uncertainty profiles. All distribution parameters are disclosed in the report.
10,000+ Full DCF Re-Computations in Seconds
Each of the 10,000+ iterations is a complete, independent DCF: fresh draws for all stochastic variables, full revenue-to-FCF waterfall recomputed, terminal value derived under both Gordon Growth and exit multiple approaches, cash flows discounted at the drawn WACC, Enterprise Value computed. Three independently drawn random variables produce 30,000+ random draws per simulation run. All iterations complete in seconds; the full run history is stored and reusable within the report session.
Full Histogram + P10 / P25 / P50 / P75 / P90
The 10,000+ Enterprise Value outcomes are sorted and binned into a frequency histogram with 20 buckets, rendered in the report with a diverging color scale (tails shaded lighter than the core distribution). Summary statistics presented: mean, median (P50), standard deviation, skewness, P10, P25, P75, P90. The P10–P90 interval is the primary reported confidence range. Distribution shape and skewness are interpreted in the auto-generated narrative: right-skewed suggests upside optionality; left-skewed signals asymmetric downside risk.
Probability of Value Exceeding Any Threshold
Beyond percentile statistics, Chapter 28 lets the analyst enter any target Enterprise Value and computes the probability — from the simulation distribution — that true value exceeds that threshold. For example: "What is the probability that Enterprise Value exceeds the proposed acquisition price of $25M?" or "What is the probability that value exceeds the outstanding debt of $12M?" These probability statements are directly reportable to boards, investors, and courts.
P10–P90 Range Feeds the Football Field Chart
The P10–P90 confidence interval from Chapter 28 automatically populates the Football Field Chart in Chapter 35 as a dedicated "Probabilistic DCF" bar — sitting alongside the point-estimate DCF range, market multiple ranges, and comparable transaction ranges. When the Monte Carlo range aligns with the market-method ranges, it reinforces the analytical conclusion. When it diverges, the divergence is analytically meaningful and is documented in the Chapter 35 reconciliation narrative.
Running Chapter 28 — Step by Step
Review the Pre-Selected Variables
Chapter 28 opens with the top two or three variables from the Chapter 27 Tornado Chart pre-loaded. Review the pre-selection and confirm or adjust — substituting or adding any variable whose uncertainty you want to model probabilistically. Typically three variables are sufficient; adding more beyond four rarely changes the distribution meaningfully while adding simulation complexity.
Set the Distribution Parameters
For each variable, choose the distribution type and set the parameters. For WACC: the Chapter 21 value is pre-loaded as the mean; set σ based on your confidence in the WACC estimate (typically 50–100 bps for well-supported WACCs). For growth rates: set min, most likely, and max based on the Chapter 26 sensitivity ranges. Equitest provides guidance ranges for each variable type.
Run the Simulation
Click Run. Equitest executes 10,000+ iterations in seconds, drawing fresh variable combinations for each and running the full DCF computation. A progress indicator shows the simulation status. Results are available immediately when the run completes; re-running with different distribution parameters takes another few seconds.
Interpret the Distribution and Confidence Intervals
Review the histogram shape, the P10–P90 interval, and the auto-generated narrative. A narrow distribution (P10 to P90 spanning less than 30% of median) indicates low assumption sensitivity; a wide distribution signals high uncertainty and warrants additional sensitivity disclosure. Note any skewness — a right-skewed distribution suggests upside optionality that may justify a valuation premium in negotiation contexts.
Use Probability Threshold Statements if Relevant
If the engagement involves a specific valuation threshold — an acquisition price, a debt covenant trigger, a fairness threshold, or a regulatory minimum — enter it as a target value. Equitest computes and reports the probability that the true Enterprise Value exceeds (or falls below) that threshold, providing a direct, probabilistically grounded answer to the specific question the engagement is designed to answer.
