Monte Carlo Simulation Inside a DCF

A standard DCF hands you a single number — "this company is worth $4.2 billion" — with a confidence that the underlying assumptions never actually earned. Revenue growth, margins, and the discount rate are each genuinely uncertain, and the model quietly pretends they're known to the decimal point. A Monte Carlo DCF is the same cash-flow machinery, run not once but thousands of times, each time drawing a fresh, randomly sampled set of inputs from a realistic range — turning "the company is worth $4.2 billion" into "the company is most likely worth between $3.1 and $5.6 billion, with a median around $4.2 billion."

Think of forecasting a road trip's arrival time. You could say "we'll arrive at 3:47pm," treating traffic, weather, and rest stops as fixed. Or you could say "based on a thousand simulated trips with realistic variation in each factor, we'll most likely arrive between 3:15 and 4:45pm, with 3:47 the single most probable time." The second answer is more work but tells the truth about what you actually know.

The mechanics

For each of many trials $k = 1, \dots, K$, draw a fresh set of inputs from specified probability distributions, compute the DCF's implied value $V_k$, and after all $K$ trials look at the distribution of results:

$$g_k \sim \mathcal{N}(0.08, 0.02), \quad m_k \sim \mathcal{N}(0.22, 0.03), \quad r_k \sim \mathcal{N}(0.09, 0.01)$$

In words: instead of fixing revenue growth $g$ at exactly 8 percent, margin $m$ at exactly 22 percent, and the discount rate $r$ at exactly 9 percent, each is drawn randomly on every trial from a normal distribution centered on the analyst's best guess, with a spread reflecting genuine uncertainty. Each trial's draws feed through the ordinary DCF formula to produce one value $V_k$; repeating this thousands of times builds up a full distribution of $V_k$ rather than a single point.

Worked example: a tiny three-trial illustration

To see the mechanics stripped down, run just three trials of a simplified one-year model: value equals next year's free cash flow divided by (discount rate minus growth), a single-stage Gordon-growth shortcut.

Trial 1: $g = 0.07$, $r = 0.10$: $\text{FCF} = 100 \times 1.07 = 107$, value $= 107 / (0.10 - 0.07) = 3{,}567$. Trial 2: $g = 0.09$, $r = 0.08$: $\text{FCF} = 109$, value $= 109 / (0.08 - 0.09)$ — negative denominator, model breaks (growth exceeds the discount rate, an impossible perpetuity). A real simulation must constrain draws so $g < r$ on every trial, or such trials are discarded and flagged. Trial 3: $g = 0.05$, $r = 0.11$: $\text{FCF} = 105$, value $= 105 / (0.11 - 0.05) = 1{,}750$.

Even three trials show the value swinging from roughly 1,750 to 3,567 to an undefined blowup — a preview of how wide and how fragile the full distribution can be.

Worked example: reading percentiles from a full run

Running 10,000 trials of a full multi-year DCF for a real company produces enterprise values with a 10th percentile of $2.9 billion, a median of $4.2 billion, and a 90th percentile of $6.1 billion. An investor comparing this to a $5.5 billion market cap can now say something sharper than "the DCF says it's undervalued": specifically, the market price sits around the 80th percentile of the simulated distribution — the stock is priced for a fairly optimistic, though not extreme, scenario.

What this means in practice

Monte Carlo DCFs are standard in private equity and infrastructure valuation, where a handful of variables (commodity prices, occupancy rates, refinancing spreads) dominate the outcome and their uncertainty is large enough that a single-point answer would be actively misleading. The output — a distribution rather than a number — is also a better match for how investment committees actually think about risk: not "is it worth $4.2 billion" but "what's the chance we lose money at this price."

Key terms

• Trial — one full run of the DCF using one randomly drawn set of inputs.
• Input distribution — the assumed probability distribution (e.g., normal, triangular) each uncertain input is drawn from.
• Output distribution — the resulting spread of computed values across all trials.
• Correlated inputs — inputs that should be drawn jointly, not independently, when real-world scenarios move them together.