Monte Carlo distribution of intrinsic value; margin of safety as a probability

"""M06 · Monte Carlo distribution of intrinsic value; margin of safety as a probability.

Exercise stubs. See notes.md §6.7.

Model: the two-stage DCF of m06_dcf.dcf_value with uncertain inputs
    fcf0 ~ N(mu, sd), growth ~ N(mu, sd), wacc ~ N(mu, sd), terminal_g ~ N(mu, sd),
independent, truncated to the region wacc - terminal_g >= min_spread (rejection sampling).
"""

from __future__ import annotations

import numpy as np


def dcf_value_vec(fcf0, growth, wacc, terminal_g, years: int = 5) -> np.ndarray:
    """Vectorised two-stage DCF value (same convention as m06_dcf.dcf_value, value only).

    Inputs are scalars or 1-D arrays that broadcast to a common shape (k,). Return shape (k,)
    (a scalar input returns shape (1,)). No loops over draws: use numpy broadcasting with
    t = 1..years along a second axis.
    """
    raise NotImplementedError


def simulate_intrinsic_values(n: int, seed: int, fcf0=(100.0, 0.0), growth=(0.15, 0.0),
                              wacc=(0.12, 0.0), terminal_g=(0.05, 0.0), years: int = 5,
                              min_spread: float = 0.01) -> np.ndarray:
    """Return exactly n simulated intrinsic values (np.ndarray, shape (n,)).

    Each input argument is a (mean, sd) pair for an independent normal. Use
    np.random.default_rng(seed). Reject draws with wacc - terminal_g < min_spread and draw
    again until n accepted values exist. With all sd = 0 every value equals the point DCF.
    """
    raise NotImplementedError


def prob_value_exceeds_price(values: np.ndarray, price: float) -> float:
    """Monte Carlo estimate of P(V > price) as a float."""
    raise NotImplementedError


def value_quantile(values: np.ndarray, q: float) -> float:
    """q-quantile of the simulated values."""
    raise NotImplementedError


def margin_of_safety(value_estimate: float, price: float) -> float:
    """Graham margin of safety (V - P)/V."""
    raise NotImplementedError