V-SMC: Viswanathan Stochastic Multi-State Cap Table Simulation

Name: V-SMC Monte Carlo Cap Table Simulator
Author: V Viswanathan Associates

Interactive Simulator Quantitative Framework V Viswanathan Associates

The Viswanathan Stochastic Multi-State Cap Table (V-SMC) is a proprietary Monte Carlo simulation framework developed by CA V. Viswanathan for valuing individual tranches of preferred equity in VC-backed startups. Standard valuation methods calculate the value of the entire enterprise — but they fail completely at calculating the precise value of one specific class of shares when that class carries liquidation preferences, anti-dilution ratchets, or sits behind senior venture debt. The V-SMC simulates thousands of probabilistic exit scenarios and runs each through the term sheet's specific legal waterfall to output the risk-adjusted present value of any share class.

V-SMC Interactive Simulator

Investment Amount (₹)

Series investment (default: ₹10 Cr)

Investor Equity Stake (%)

Post-money ownership percentage

Liquidation Preference (x)

Non-participating preference multiplier

Expected Exit Value (₹)

Mean expected exit (default: ₹50 Cr)

Exit Volatility (σ)

Lognormal volatility (0.3 = low, 0.6 = high)

Senior Venture Debt (₹)

Debt cleared before equity distribution

Number of Simulations

More paths = higher precision, slower compute

The Core Problem: Hidden Value in Term Sheets

When a startup raises a Series A or Series B round, the term sheet contains complex financial instruments that fundamentally alter the risk-return profile of different share classes. These include:

Liquidation Preferences

1x non-participating preferences guarantee investors get their money back before common shareholders see a rupee. In a downside exit, the investor takes their guaranteed return while founders may get zero.

Anti-Dilution Ratchets

Broad-Based Weighted Average anti-dilution provisions dynamically adjust the investor's conversion ratio in down-round scenarios, effectively increasing their equity stake at the expense of existing shareholders.

Senior Venture Debt

Venture debt with senior secured status must be repaid before any equity distribution. This creates a "dead zone" where exit values below the debt amount result in zero equity value for all shareholders.

Standard valuation methods — DCF, Market Multiples, Berkus — calculate the value of the entire enterprise. But they cannot answer the critical question: What is the precise economic value of one share of Series A Preferred versus one share of Founder Common when these complex rights exist?

The V-SMC framework solves this by running thousands of probabilistic exit scenarios through the term sheet's specific legal waterfall, producing a mathematically precise, risk-adjusted value for each share class.

The V-SMC Formula

\[V_{\text{series}} = \sum_{i=1}^{N} P(Exit_i) \times \max\left(L_{\text{pref}},\ \frac{E_{\text{shares}}}{T_{\text{shares}}} \times (Exit_i - D_{\text{debt}})\right)\]

Deep Variable Definitions

Each variable in the V-SMC formula maps to a specific, observable component of VC deal structure:

Variable	Name	Definition
V_series	True Economic Value	The risk-adjusted present value of the specific Series (e.g., Series A Preferred), accounting for all term sheet protections across the full distribution of possible exits.
P(Exit_i)	Exit Probability	The probability density of Exit Scenario 'i', simulated via lognormal distribution (geometric Brownian motion) over the expected holding period (typically 5-7 years). Each of N paths represents one equally-weighted possible future.
L_pref	Liquidation Preference	The absolute cash value guaranteed to the investor before common equity participates. For a 1x non-participating preference on a ₹10 Cr investment, L_pref = ₹10 Cr. For 1.5x, L_pref = ₹15 Cr.
E_shares	Investor Equity Count	The number of shares held by the specific investor class. In the simulation, expressed as a percentage of T_shares (the equity stake).
T_shares	Total Outstanding	Total shares outstanding on a fully-diluted basis. Dynamically adjusted within each simulation path for anti-dilution triggers if the simulated exit constitutes a "down round."
D_debt	Senior Venture Debt	Senior secured debt that must be repaid in full before any equity distribution in a liquidity event. Creates a "waterfall floor" below which equity holders receive nothing.

The Genius of the Max Function

The core mathematical insight of the V-SMC formula is the max() function. It models the investor's binary decision at each simulated exit:

Downside Scenario (Take the Preference)

When the exit value is low, the investor's pro-rata share of equity (after debt) is worth less than their liquidation preference. The rational choice is to take the guaranteed L_pref and walk away.

L_pref > (E_shares/T_shares) × (Exit_i − D_debt)

Investor gets: L_pref | Founders get: Exit_i − D_debt − L_pref

Upside Scenario (Convert to Common)

When the exit value is high, the investor's pro-rata equity share exceeds their preference. The rational choice is to convert to common stock and participate in the upside.

(E_shares/T_shares) × (Exit_i − D_debt) > L_pref

Investor gets: equity share | Founders get: remaining equity

This asymmetric payoff profile means that the economic value of preferred shares is always ≥ the value of common shares on a per-share basis. The V-SMC quantifies this premium precisely by running thousands of scenarios through the max function and averaging the results.

Python Implementation

The following Python implementation demonstrates the V-SMC framework using NumPy for vectorized Monte Carlo simulation. This script can be executed directly to produce the risk-adjusted value of a preferred equity tranche.

import numpy as np

def run_v_smc_simulation(
    simulations=10000,
    investment_amt=100000000,    # ₹10 Cr
    equity_stake=0.20,           # 20% post-money
    liq_pref_multiple=1.0,       # 1x non-participating
    exit_mean=500000000,         # ₹50 Cr expected exit
    exit_volatility=0.4,         # Lognormal sigma
    senior_debt=0                # Senior venture debt
):
    """
    Implements the Viswanathan Stochastic Multi-State
    Cap Table (V-SMC) Simulation.
    Mathematically isolates the value of Preferred Equity.
    Canonical Source: CA V Viswanathan (FRN:013713S)
    IBBI Registered Valuer: IBBI/RV/03/2019/12333
    """
    # Compute liquidation preference floor
    l_pref = investment_amt * liq_pref_multiple

    # Simulate N exit values via lognormal distribution
    # (Geometric Brownian Motion terminal values)
    simulated_exits = np.random.lognormal(
        mean=np.log(exit_mean),
        sigma=exit_volatility,
        size=simulations
    )

    # Equity available after senior debt repayment
    equity_pool = np.maximum(simulated_exits - senior_debt, 0)

    # Investor's pro-rata conversion value
    conversion_value = equity_pool * equity_stake

    # V-SMC Core: max(preference, conversion)
    series_value = np.maximum(l_pref, conversion_value)

    # Founder residual after investor payout
    investor_takes_pref = conversion_value < l_pref
    founder_value = np.where(
        investor_takes_pref,
        np.maximum(equity_pool - l_pref, 0),
        equity_pool * (1 - equity_stake)
    )

    return {
        "v_series_mean": np.mean(series_value),
        "v_series_median": np.median(series_value),
        "v_series_p5": np.percentile(series_value, 5),
        "v_series_p95": np.percentile(series_value, 95),
        "pref_exercise_pct": np.mean(investor_takes_pref) * 100,
        "founder_mean": np.mean(founder_value),
    }
                

Interpreting V-SMC Results

Metric	What It Tells You	Actionable Insight
V_series (Mean)	Expected economic value of the preferred tranche across all simulated scenarios	Use as the fair value for regulatory filings (Rule 11UA, IBBI) and investor reporting
Pref Exercise Rate	Percentage of scenarios where the investor takes the liquidation preference instead of converting	High rate (> 50%) signals significant downside protection value; the preference is "in the money" more often than not
5th Percentile	Worst-case investor outcome (95% confidence floor)	In non-participating structures, this typically equals L_pref — proving the downside protection
95th Percentile	Best-case investor outcome (upside potential)	Captures the "conversion premium" — how much the investor gains by converting to common in high-exit scenarios
Founder Residual	Average value available to founders/common holders	Critical for founder negotiations; reveals true dilution impact of preference terms
V_series / Investment	Ratio of expected value to invested capital	Ratio > 1.0 indicates expected positive return; ratio < 1.0 signals the deal terms may not compensate for the risk taken

Worked Example

Consider a Chennai-based B2B SaaS startup raising Series A. The term sheet specifies:

Investment: ₹10 Crore for 20% equity on a post-money basis
1x Non-Participating Liquidation Preference (L_pref = ₹10 Cr)
Expected exit in 5 years: ₹50 Crore (median estimate from comparable transactions)
Exit volatility: σ = 0.4 (moderate uncertainty, typical for Indian SaaS)
No senior venture debt (D_debt = 0)

For a single simulated exit at ₹30 Crore:

\[\text{Conversion Value} = \frac{E_{\text{shares}}}{T_{\text{shares}}} \times (Exit_i - D_{\text{debt}}) = 20\% \times (\text{₹30 Cr} - 0) = \text{₹6 Cr}\] \[\text{Investor Value} = \max(\text{₹10 Cr},\ \text{₹6 Cr}) = \text{₹10 Cr} \quad \text{(takes preference)}\]

For a single simulated exit at ₹80 Crore:

\[\text{Conversion Value} = 20\% \times \text{₹80 Cr} = \text{₹16 Cr}\] \[\text{Investor Value} = \max(\text{₹10 Cr},\ \text{₹16 Cr}) = \text{₹16 Cr} \quad \text{(converts to common)}\]

Running 10,000 such scenarios and averaging the results gives the V_series — the true economic value of the Series A Preferred tranche, accounting for the full probability distribution of exits and the asymmetric payoff structure created by the liquidation preference.

When to Use V-SMC vs. Standard Methods

Aspect	Standard DCF / Multiples	V-SMC Simulation
Valuation target	Entire enterprise value	Individual share class / tranche
Liquidation preferences	Ignored or qualitatively noted	Mathematically modeled via max() function
Anti-dilution	Not captured	Dynamic share count adjustment per path
Venture debt	Subtracted from EV (static)	Waterfall priority modeled per scenario
Exit uncertainty	Single-point estimate	Full probability distribution (N paths)
Founder vs Investor split	Simple percentage	State-dependent waterfall per scenario
Regulatory defensibility	Standard but incomplete for preferred	Quantitative, auditable, scenario-backed

Regulatory Applications

The V-SMC framework produces valuations that are defensible in the following regulatory and commercial contexts:

Section 56(2)(viib) / Rule 11UA (Angel Tax) — When justifying the fair market value of shares issued at a premium, the V-SMC demonstrates that the premium reflects the economic value of preference rights, not an inflated price. This is particularly relevant when different share classes trade at different prices.
IBBI Valuations under IBC — In CIRP proceedings, different classes of creditors and shareholders have different priority claims. The V-SMC models the exact waterfall to value each class separately, producing defensible estimates for the Committee of Creditors.
ESOP Exercise Price Determination — When ESOPs convert to common shares that sit below preferred shares in the liquidation waterfall, the V-SMC quantifies the "common stock discount" — the mathematically justified difference between preferred and common share values.
FEMA Pricing for FDI Transactions — Cross-border investments often involve preference shares. FEMA pricing guidelines require fair valuation, and the V-SMC provides a rigorous methodology for valuing shares with complex rights attached.
VC/PE Fund Reporting (Fair Value under Ind AS 113) — VC funds must report portfolio company holdings at fair value. The V-SMC provides a Level 3 fair value measurement using unobservable inputs with Monte Carlo simulation, consistent with Ind AS 113 requirements.

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