Monte Carlo simulations on a DCF

Scenario analysis gives you three points (bull, base, bear) and their probabilities. Monte Carlo simulation goes further: instead of three discrete outcomes, you assign a probability distribution to each input—revenue growth, margins, capex intensity, WACC—and run thousands of simulations. Each iteration draws random values from those distributions, calculates a DCF valuation, and records it. After 10,000 runs, you have a full distribution of possible valuations. You can see not just the expected value, but the 25th and 75th percentiles, the chance of valuation exceeding $100 billion, and the probability the stock is cheap at current prices. For many investors, Monte Carlo is overkill; for those managing large portfolios or making binary decisions (acquire or not), it's invaluable.

Quick definition

Monte Carlo simulation in DCF modeling assigns probability distributions (not point estimates) to key inputs—like "revenue growth is normally distributed around 10% with standard deviation of 3%"—then runs the DCF thousands of times with randomly drawn values. The result is a probability distribution of enterprise values, not a single point estimate or three scenarios.

Key takeaways

• Monte Carlo is useful when you need to quantify tail risks or when model uncertainty is the dominant driver of decision risk.
• Assign probability distributions (normal, log-normal, triangular, uniform) to 3–5 key inputs; the model becomes intractable with too many uncertain inputs.
• Run 5,000–10,000 simulations; each generates one valuation. The distribution of outcomes is your answer.
• Interpret results: mean valuation, median (50th percentile), 25th and 75th percentiles, and the probability of landing in attractive valuation ranges.
• Monte Carlo is most valuable for highly uncertain businesses or when you're making a large capital allocation decision; for routine stock picking, sensitivity and scenario analysis are often sufficient.

Why Monte Carlo beats three scenarios

Scenario analysis captures three outcomes (bull, base, bear) and forces you to assign discrete probabilities. Monte Carlo recognizes that reality is continuous: revenue growth could be 8%, 10.5%, or 12%, not just 5%, 10%, or 15%. By assigning a distribution (e.g., normal distribution centered at 10% with a standard deviation of 3%), you model the realistic range of uncertainty.

Monte Carlo also surfaces tail risks and opportunities that discrete scenarios may miss. If you run 10,000 simulations, you might discover a 5% chance the company is worth $150 billion (far above your base case) or a 10% chance it's worth $30 billion (far below). These tail outcomes matter if you're sizing a large bet or deciding whether to acquire the company.

Assigning probability distributions

For each uncertain input, choose a distribution type:

Normal distribution: Revenue growth centered at 12% with standard deviation 2% means most outcomes cluster around 12%, with a 68% chance of 10–14% and a 95% chance of 8–16%. Use this for relatively predictable variables like revenue growth in a stable market.

Log-normal distribution: Used for variables that can't go below zero but can grow unboundedly, like enterprise value or stock price. Revenue growth is better modeled log-normally than normally because you can't have negative revenue.

Triangular distribution: You specify three points—minimum, most likely (mode), maximum—and the distribution is triangular between them. Example: perpetuity growth has a minimum of 1%, most likely of 2.5%, and maximum of 4%. This is useful when you have directional intuition but limited historical data.

Uniform distribution: All values between a minimum and maximum are equally likely. Example: WACC between 7% and 9%. Use this for inputs where you have genuine uncertainty.

Setting up a Monte Carlo model

1. Choose your key uncertain inputs. Typically: revenue growth, operating margin, capex intensity, terminal growth rate, WACC, and tax rate. Limit to 5–7 variables; more becomes unwieldy.

2. Assign distributions. For each input, research historical values, management guidance, and consensus forecasts. Fit a distribution. Example:

   • Revenue growth (years 1–5): Normal, mean 12%, std dev 2.5%
   • Terminal EBITDA margin: Triangular, min 12%, mode 16%, max 20%
   • Terminal growth rate: Triangular, min 1.5%, mode 2.5%, max 3.5%
   • WACC: Normal, mean 9%, std dev 1%

3. Correlate related variables (optional). If you assume high revenue growth, margins may compress (negative correlation) or expand (positive correlation). Monte Carlo software can model correlations, but for simplicity, many analysts ignore correlation and run simulations with independent draws. Independence is conservative (creates wider ranges).

4. Run the simulation. Generate 10,000 random draws from each distribution. For each draw set, calculate enterprise value using your DCF model. Record the result.

5. Analyze the output distribution. Calculate mean, median, 25th percentile, 75th percentile, 1st and 99th percentiles. Visualize as a histogram or cumulative distribution.

Example: software company Monte Carlo

Imagine you're valuing a SaaS business and define:

• Revenue growth, years 1–5: Normal, mean 20%, std dev 4%
• Operating margin, year 10: Triangular, min 20%, mode 25%, max 30%
• Terminal growth: Triangular, min 2%, mode 2.5%, max 3%
• WACC: Normal, mean 9%, std dev 0.8%
• Terminal revenue multiple: Triangular, min 8x, mode 12x, max 16x

You run 10,000 simulations. The results:

• Mean valuation: $95B
• Median valuation: $92B
• 25th percentile: $75B
• 75th percentile: $115B
• 1st percentile: $40B
• 99th percentile: $160B

This tells you: the company's likely fair value is in the $75–$115 billion range; there's a 1% chance it's below $40B and a 1% chance it's above $160B. If the stock trades at $80B market cap, it's slightly expensive (below your median of $92B) but within the plausible range.

Interpreting the output distribution

Mean vs median: The mean is the average valuation; the median is the 50th percentile. For skewed distributions, they diverge. If the distribution is right-skewed (tail extends upward), the mean is higher than the median, suggesting upside outliers are larger than downside outliers. If left-skewed, the opposite. Right skew is common in early-stage companies (limited downside at zero, unlimited upside in principle); left skew is common in mature companies (limited upside, downside if business deteriorates).

Percentiles and ranges: The 25th–75th percentile range captures 50% of outcomes. This is your "likely outcome" range. The 10th–90th percentile range captures 80% of outcomes. Use these ranges for decision-making: if fair value is likely between $75B and $115B, and the stock trades at $70B, it's an attractive entry point with 2 out of 3 chance of outperforming the valuation.

Tail risks: The 1st and 99th percentiles represent 1-in-100 scenarios. A 1% chance the company is worth less than $40B is a real downside risk if the business faces disruption or a severe recession. Conversely, a 1% chance of $160B valuation represents upside if the company takes significant market share or enters high-margin adjacent markets.

Probability of attractiveness

Monte Carlo lets you answer: "What's the probability this stock is attractive at the current price?" If fair value distribution has a median of $92B and the stock trades at $80B, calculate the probability that fair value exceeds $80B. (Roughly 70–80%, depending on the distribution shape.) This is more realistic than "the stock is cheap or expensive" because it acknowledges uncertainty.

Similarly, calculate the probability that fair value exceeds $100B (upside case) or falls below $60B (downside case). These probabilities inform position sizing: if there's only a 30% chance of upside, you size the position smaller than if there's a 60% chance.

Real-world example: streaming company Monte Carlo

Imagine you're valuing a streaming video platform and building a Monte Carlo because subscriber growth and churn are highly uncertain.

Distributions:

• Subscriber growth years 1–5: Normal, mean 15%, std dev 6% (wider range than typical due to churn uncertainty)
• Terminal margin: Triangular, min 12%, mode 18%, max 24%
• Terminal growth: Triangular, min 1.5%, mode 2.5%, max 3.5%
• WACC: Normal, mean 10%, std dev 1.2%
• Terminal revenue multiple: Triangular, min 6x, mode 9x, max 12x (reflects optionality around advertising upside)

Results from 10,000 simulations:

• Mean: $85B
• Median: $75B
• 25th percentile: $45B
• 75th percentile: $110B
• Probability fair value > $80B: 55%
• Probability fair value < $50B: 20%
• Probability fair value > $120B: 10%

Interpretation: The wide range ($45B–$110B for the interquartile) reflects high uncertainty around subscriber and margin trajectory. The stock trades at $70B market cap. The probability it's attractive (fair value > $70B) is ~60%, but downside risk of valuation below $50B is material (20% probability). You'd want a position size commensurate with that 20% tail risk.

Common Monte Carlo mistakes

Mistake one: too many variables. If you assign distributions to 15 inputs, the simulation becomes a black box and the output distribution becomes so wide it's useless. Stick to the 3–5 variables that drive 80% of valuation variance.

Mistake two: distributions that don't match the business reality. Normal distributions assume symmetrical outcomes, but revenue growth in a young, high-growth company is often log-normally distributed (bounded below at zero, unbounded above). Use a distribution that matches the underlying dynamics.

Mistake three: ignoring correlation. If you model revenue growth and operating margin as independent, but they're actually correlated (high growth companies often have lower margins as they scale), your simulation overstates precision. Add correlation coefficients for related variables.

Mistake four: misinterpreting the results. A median valuation of $80B does not mean the stock is fairly valued at $80B. It means that's the 50th percentile outcome given your distribution assumptions. If the stock trades at $80B and your model is correct, you have a 50% chance of outperforming. If you demand 25% upside before buying (at $60B), you're implicitly betting on outcomes in the 60th–70th percentile range.

Mistake five: false precision. Monte Carlo can seduce you into thinking your valuation is more precise than it really is. The simulation is only as good as your distribution assumptions. Garbage in, garbage out.

When to use Monte Carlo

Use Monte Carlo when:

• You're managing a large, concentrated position. Monte Carlo helps you understand downside risk precisely, informing position sizing.
• The business has binary outcomes. A clinical-stage biotech, a company in a high-disruption risk industry, or a turnaround situation benefits from seeing the full distribution of outcomes, not just three scenarios.
• Uncertainty is the dominant driver of returns. If two-thirds of your valuation variance comes from one or two key drivers, Monte Carlo helps you model that directly.
• You're evaluating an acquisition. The acquiring company needs to understand the full range of possible returns from the target, including tail risks.

Don't use Monte Carlo when:

• Your models are sensitive to correlations you can't quantify. If multiple variables move together but you don't know the correlation strengths, simulations overstate precision.
• The business is simple and predictable. For a stable utility or a cash-cowing mature business, scenario analysis is sufficient.
• You lack data to calibrate distributions. If you're guessing at distribution parameters, the simulation is more art than science.

FAQ

Q: How many simulations should I run?
A: 10,000 is standard. 5,000 is acceptable; 1,000 is risky (output distribution may be choppy due to sampling variance). Running 100,000 gives incrementally better precision but rarely changes conclusions materially.

Q: Should I model correlation between inputs?
A: If possible, yes. Revenue growth and operating margin often correlate. Use historical data or management commentary to calibrate correlations. But if you can't quantify them, running independent simulations is conservative (produces wider distributions).

Q: What's the difference between Monte Carlo and scenario analysis?
A: Scenario analysis builds three discrete outcomes (bull, base, bear) with assigned probabilities. Monte Carlo assigns continuous distributions to inputs and runs thousands of iterations. Monte Carlo captures more nuance but requires more parameter calibration. For most investors, scenario analysis is sufficient; Monte Carlo is for higher-conviction or capital-intensive decisions.

Q: Can I use Monte Carlo to generate a required return on the stock?
A: Not directly. Monte Carlo generates a distribution of intrinsic values. Compare the current market price to that distribution to infer required returns. If fair value distribution has mean $80B and the stock trades at $60B, expected return is approximately (80–60)/60 = 33%. But this ignores the tail risk of being wrong; account for that in your return target.

Q: How do I communicate Monte Carlo results to non-technical investors?
A: Use simple language and visuals. "We modeled the company's fair value across 10,000 scenarios. The likely range is $70–$100B (where 50% of outcomes fall). There's a 20% chance of downside below $50B and a 30% chance of upside above $110B." Show a histogram or percentile chart.

Q: What if my Monte Carlo distribution is bimodal (two distinct peaks)?
A: That's a signal the business has two possible futures that don't blend smoothly (e.g., disruption happens or doesn't). Either build two explicit scenarios and weight them probabilistically, or re-examine your distribution assumptions. Bimodality often signals you should use scenario analysis instead of continuous distributions.

Related concepts

• Scenario analysis — discrete outcomes with probabilities; Monte Carlo is the continuous extension.
• Sensitivity analysis — changing one or two variables at a time; Monte Carlo changes many together.
• Probability distributions — foundation of Monte Carlo; choose distributions matching business dynamics.
• Tail risks — Monte Carlo surfaces 1%–5% tail outcomes that scenario analysis may miss.
• Position sizing — use Monte Carlo output to determine appropriate position sizing based on risk/reward.

Summary

Monte Carlo simulation assigns probability distributions to DCF inputs and runs thousands of iterations to generate a distribution of valuations. This is more realistic than discrete scenarios when uncertainty is continuous and you need to quantify tail risks. Run 10,000 simulations, interpret the mean and percentiles, and calculate the probability fair value exceeds the current stock price. Monte Carlo is most valuable for uncertain businesses, large capital allocation decisions, or scenarios with significant tail risks. For simple, stable businesses or routine stock picking, scenario analysis is often sufficient.

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