Stochastic Forecasting vs. Deterministic Models for Middle Market Valuations

A deterministic DCF model produces one number: the valuation. Change any input assumption and you get a different number. Run a sensitivity table and you get a grid of numbers. But a grid is not a probability distribution, and a point estimate is not a risk assessment.

Monte Carlo simulation replaces each uncertain input — revenue growth, margin expansion, exit multiple, discount rate — with a probability distribution and samples from all of them simultaneously across 10,000 trials. The output is a distribution of valuations, not a point estimate.

Why It Matters

A deterministic model might say: "at a 10x exit multiple and 12% EBITDA margin, the valuation is $47M." A stochastic model says: "there is a 15% probability the valuation exceeds $60M, a 50% probability it exceeds $38M, and a 20% probability it falls below $22M." These are fundamentally different statements. The second is actionable for structuring debt tranches, setting earn-out thresholds, and underwriting downside scenarios.

Python Implementation Sketch

import numpy as np

def monte_carlo_valuation(n=10_000):
    revenue_growth = np.random.normal(0.08, 0.04, n)   # mean 8%, std 4%
    ebitda_margin  = np.random.normal(0.14, 0.03, n)   # mean 14%, std 3%
    exit_multiple  = np.random.normal(9.5,  1.5,  n)   # mean 9.5x, std 1.5x
    discount_rate  = np.random.normal(0.12, 0.02, n)   # mean 12%, std 2%

    base_revenue = 10  # $10M
    projected_ebitda = base_revenue * (1 + revenue_growth)**5 * ebitda_margin
    terminal_value = projected_ebitda * exit_multiple
    npv = terminal_value / (1 + discount_rate)**5

    return npv

valuations = monte_carlo_valuation()
print(f"Median valuation:  ${np.median(valuations):.1f}M")
print(f"5th percentile:    ${np.percentile(valuations, 5):.1f}M")
print(f"95th percentile:   ${np.percentile(valuations, 95):.1f}M")

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