Equity valuation is often implemented as a deterministic pipeline: select point inputs, compute a discounted cash flow (DCF) number, and compare it to market price. This design hides uncertainty, makes model risk difficult to quantify, and encourages overconfident decisions under regime shifts. The point estimate is the problem; the distribution is the deliverable. This working paper specifies an alternative from first principles: a valuation pipeline that produces \emph{probability distributions} over enterprise value and connects those distributions to \emph{explicit decision policies}. Cash flows are modeled as strictly positive stochastic processes on their natural support, the perpetuity constraint $r>g_{\mathrm{term}}$ is enforced without distorting the dependence structure, growth and discount-rate components are coupled through a heavy-tailed copula, and a two-level Monte Carlo design separates path-level variability from parameter (model) risk. The evaluation target is neither a single accuracy number nor the unobservable intrinsic value itself: a \emph{convergence model} maps the valuation gap to realized excess returns, and the framework is falsified if the estimated convergence speed is indistinguishable from zero.

This paper is implemented live on the site as the Probabilistic Equity Valuator — a Monte Carlo DCF that returns a distribution over intrinsic value instead of a single number, exactly as the paper argues for.

How it's implemented. Each simulation runs a discounted cash flow on stochastically sampled inputs, and the two levels of randomness the paper distinguishes are kept separate. Parameter (model) risk: growth, terminal growth and the discount rate are drawn jointly through a heavy-tailed t-copula (default \( \nu = 4 \), with growth and the discount rate negatively correlated), so the dependence structure is preserved rather than assuming independence. Path-level variability: each year's free cash flow follows a log-increment process \( CF_i = CF_0\,\exp\!\left(\sum_k \ell_k\right),\ \ell_k \sim \mathcal{N}(\log(1+g_k),\,\sigma^2) \), which keeps cash flows strictly positive on their natural support and uses a data-driven \( \sigma \) estimated from historical FCF volatility. The perpetuity constraint \( r > g_{\mathrm{term}} \) is enforced by rejection sampling with a minimum spread so the Gordon denominator never collapses, and variance reduction (Latin-Hypercube sampling + antithetic variates) plus a market-sentiment growth prior round out the engine.

Why. A single DCF number hides model risk and invites overconfidence under regime shifts — the paper's thesis that "the point estimate is the problem; the distribution is the deliverable." The page therefore reports the full picture: percentiles (p10–p90), median and mean fair value, and decision-relevant probabilities — P(undervalued), P(>50% upside), P(>20% downside), and expected/worst-case downside — alongside block-bootstrap convergence diagnostics (standard errors on the percentiles and a converged flag) so the distribution itself can be trusted.

Scope note. The paper's convergence model — mapping the valuation gap to realized excess returns, with the framework falsified if convergence speed is indistinguishable from zero — is currently represented by the forward-looking Monte Carlo convergence diagnostics, not yet by a historical backtest that verifies the gap predicts ex-post returns. That falsification step remains future work.