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Monte Carlo DCF

For informational and educational purposes only • Not investment advice.

Apple

iPhone, services, devices

Median Fair Value

$182.29

Stock price: $333.69

Low probability above stock price

The model runs many DCF valuations using different assumptions. The Median Fair Value represents the 50th percentile of the simulated results. Select Run New Simulation to generate a new set of random outcomes.

Distribution of Simulated Fair Values

Each bar shows how many Monte Carlo simulations produced a fair value within that price range. Taller bars indicate fair values that occurred more frequently across all simulations. Together, the bars form the probability distribution of all simulated intrinsic values.

1148657290$128.03$156.17$184.30$212.43$240.57$268.70P10$153.60Median$182.29P90$221.78Number of simulationsSimulated fair value per share

Key Valuation Metrics

Each click performs 1,000 complete DCF valuations using newly generated random assumptions to create a new distribution of possible Fair Values.

Time Horizon
Simulations
Equity Risk Premium
%
Range: 2–10%

Monte Carlo DCF Formulas

The following formulas are applied within each Monte Carlo simulation to calculate one possible Fair Value per Share.

Present Value of Enterprise Value
Enterprise Value=∑t=1nFCFt(1+WACC)t+TV(1+WACC)n \text{Enterprise Value} = \sum_{t=1}^{n} \frac{FCF_t}{(1+WACC)^t} + \frac{TV}{(1+WACC)^n}
Terminal Value
Terminal Value=FCFn+1WACC−g \text{Terminal Value} = \frac{FCF_{n+1}} {WACC-g}
Fair Value per Share
Fair Value Per Share=Enterprise Value−Net DebtShares Outstanding \text{Fair Value Per Share} = \frac{ \text{Enterprise Value} - \text{Net Debt} }{ \text{Shares Outstanding} }
Monte Carlo Simulation
FVi=DCF(gi,  WACCi,  TGi) FV_i = DCF (g_i,\;WACC_i,\;TG_i)
Median Fair Value
Median Fair Value=Median⁡(FV1,…,FVN) \text{Median Fair Value} = \operatorname{Median} (FV_1,\ldots,FV_N)

What is the Monte Carlo DCF Model?

The Monte Carlo DCF Model estimates a company's intrinsic value by running many complete Discounted Cash Flow (DCF) valuations instead of relying on a single forecast.

Each valuation uses slightly different assumptions for Revenue Growth, WACC and Terminal Growth. This creates many possible future scenarios and shows how the estimated Fair Value changes when these assumptions vary.

Instead of producing one exact valuation, the model generates a distribution of possible Fair Values. This shows the central valuation, the range of possible outcomes and how sensitive the valuation is to changes in the underlying assumptions.

How the Monte Carlo DCF Model Calculates Fair Value

Monte Carlo DCF starts with a standard DCF framework, randomly varies key assumptions such as Revenue Growth, WACC and Terminal Growth, runs many complete DCF valuations, and summarizes the resulting distribution of possible Fair Values.

Set Base Assumptions
→
Randomize Key Inputs
→
Run One DCF
→
Repeat Many Simulations
→
Build Value Distribution
→
Calculate Percentiles
→
Interpret Probability

Key Model Assumptions

• Revenue and Free Cash Flow are projected over the selected forecast period.
• Revenue Growth gradually moves toward the Terminal Growth Rate.
• The Free Cash Flow Margin gradually moves toward a normalized target based on the median of up to the five most recent valid historical Free Cash Flow Margins.
• Revenue Growth, WACC and Terminal Growth vary across simulations within model-defined ranges around their Base assumptions.
• The Risk-Free Rate is based on the U.S. 10-Year Treasury yield published by the Federal Reserve Board.
• Each simulation performs one complete DCF valuation.
• Enterprise Value is adjusted for Net Debt or Net Cash to estimate Equity Value.
• The resulting Fair Values form the Simulation Distribution.

Step 1 — Generate Random Simulation Assumptions

Each simulation randomly selects:
Revenue Growth
Base: 13.1%
Random Draw: Between 9.2% and 17.1%
WACC
Base: 10.4%
Random Draw: Between 9.4% and 11.4%
Terminal Growth
Base: 2.5%
Random Draw: Between 1.5% and 3.5%

Unlike the Standard DCF and Scenario DCF, Monte Carlo DCF evaluates many randomly generated combinations of assumptions rather than relying on one or a few predefined cases. Every simulation randomly samples one value, with every value in the range equally likely, for Revenue Growth, WACC and Terminal Growth. These random assumptions represent one possible future for Apple.

Step 2 — Run One Complete DCF

Random Revenue Growth
Random WACC
Random Terminal Growth
↓
Run Full DCF
↓
Fair Value Per Share


Example Simulation:
Revenue Growth = 14.7%
WACC = 10.7%
Terminal Growth = 2.7%
Fair Value = $189.76

Each simulation performs one complete DCF valuation using randomly generated assumptions. The example above shows one actual simulation from the current Monte Carlo run. The underlying DCF calculation follows the same general process as the Standard DCF and Scenario DCF models. The key difference is that Monte Carlo DCF uses a new combination of assumptions in every simulation.

The results of the simulations are summarized in the Monte Carlo Simulation Summary.

Step 3 — Repeat the DCF Simulation

Simulation 1 → Fair Value
Simulation 2 → Fair Value
Simulation 3 → Fair Value
...
Simulation 1,000 → Fair Value

Rather than relying on one valuation, the model repeats the complete DCF calculation 1,000 times.

Every simulation uses a different combination of Revenue Growth, WACC and Terminal Growth assumptions, producing one Fair Value per Share.

The resulting collection of simulated Fair Values is used to build the valuation distribution shown in the Monte Carlo Simulation Summary.

Step 4 — Build the Valuation Distribution

All Simulated Fair Values
↓
Sort from Lowest to Highest
↓
P10 • Median (P50) • P90

After every simulation has produced one Fair Value per Share, the model collects all 1,000 results.

The simulated Fair Values are sorted from lowest to highest. Together, these values form the Simulation Distribution.

This distribution shows the range and frequency of possible intrinsic values rather than one fixed valuation estimate.

The P10, Median (P50) and P90 values identified from the ordered results are summarized in the Monte Carlo Simulation Summary.

Step 5 — Calculate Valuation Statistics

Median Fair Value = 50th Percentile (P50)

P10 = 10% of Simulated Fair Values Are At or Below

P50 = 50% Lower • 50% Higher

P90 = 90% of Simulated Fair Values Are At or Below

Probability Fair Value Exceeds Current Price = Simulations Above Stock Price / Total Simulations

The Median Fair Value represents the 50th percentile of the simulated Fair Values, with half of the results below it and half above it.

P10 and P90 describe the lower and upper parts of the simulated valuation range, while the probability above the Current Price shows how often the simulated Fair Value exceeds today's stock price.

These statistics can be found in the Monte Carlo Simulation Summary.

Step 6 — Interpret the Results

P10 → Lower Valuation Outcome

Median (P50) → Central Valuation Estimate

P90 → Upper Valuation Outcome

Wider P10–P90 Range → Greater Valuation Uncertainty

Higher Probability Above Current Price → More Simulations Produce Fair Values Above the Current Stock Price

The Monte Carlo DCF does not attempt to predict one exact intrinsic value. Instead, it estimates a range of possible Fair Values by evaluating many simulated outcomes. The Median represents the central estimate, while the P10–P90 range illustrates valuation uncertainty and the probability above the Current Price shows how often the simulated Fair Value exceeds the current stock price.

Monte Carlo Simulation Summary

The table summarizes the distribution of all simulated DCF valuations.

StatisticDescriptionValue
SimulationsCompleted DCF valuations1,000
LowestLowest simulated fair value$128.03
P1010th percentile$153.60
P2525th percentile$165.59
MeanAverage simulated fair value$184.89
Median50th percentile$182.29
P7575th percentile$202.48
P9090th percentile$221.78
HighestHighest simulated fair value$268.70
Current PriceCurrent market price$333.69
Probability Fair Value Exceeds Current PriceSimulations above today's price0.0%
Valuation UncertaintyOverall spread of outcomesLow