Terminal value, comparison of techniques (`tv.compare`)¶

Runs several terminal value techniques on one consistent set of inputs and returns each terminal value at the horizon N with its implied assumptions, side by side. The conclusion of a valuation often depends more on the technique than on any single input; this method shows by how much. Consistency is by construction: the rate of the terminal phase, the growth cap and the basis (enterprise or equity) are given once and apply to every technique.

How it works¶

Each technique is written as {"<method id>": {terms}}, where the terms are the inputs of that method without rate and growth_cap:

Technique	Terms	Shared inputs used
`tv.gordon`	`growth`, `next_flow` or `last_flow`	rate, growth cap
`tv.value_driver`	`nopat_next`, `growth`, `ronic`	rate, growth cap
`tv.h_model`	`last_flow`, `short_term_growth`, `long_term_growth`, `half_life`	rate, growth cap
`tv.exit_multiple`	`multiple`, `metric`, `metric_value`, optional `next_flow`	rate and growth cap when `next_flow` is given; the metric must be on the declared basis
`tv.limited_horizon`	`flow`, `periods`, optional `growth`, `residual_value`	rate, growth cap
`tv.normalised_income`	`income`, `capitalisation_rate`, `basis`, optional `growth`	growth cap; the capitalisation rate stays its own; `basis` must match the declared basis
`tv.liquidation`	`assets`, `liabilities`, `liquidation_costs`, `tax_on_gains`, `basis`	none; `basis` must match the declared basis

Each technique is computed by its own method, so a row of the comparison equals the result of that method run alone. Steps and conventions of each technique appear in explain, prefixed with its position and id, for example [1] tv.gordon: Terminal value at N. The first technique that fails returns its error; there are no partial results. A technique entry must have exactly one key, the method id; an entry with several keys is refused with a message that lists them.

Each row records method_version, the version of the technique that produced it. A numerical change in any tv.* method therefore requires a new version of tv.compare as well; a test pins the technique versions together with the version of tv.compare.

tv.normalised_income and tv.liquidation declare their own basis, checked against the basis of the comparison like the exit multiples (FM-E019 when they differ). Inside the comparison, tv.normalised_income keeps its own capitalisation rate, which is not the shared discount rate; explain.conventions states it. An exit multiple without next_flow has no implied growth, so it is not checked against the growth cap; explain.conventions states it when it applies.

Example¶

from decimal import Decimal

import fairmark as fm

r = fm.tv.compare(
    "0.10",
    "enterprise",
    [
        {"tv.gordon": {"growth": "0.02", "last_flow": 100}},
        {"tv.value_driver": {"nopat_next": 150, "growth": "0.02", "ronic": "0.12"}},
        {"tv.exit_multiple": {"multiple": "7.5", "metric": "ebitda", "metric_value": 180,
                              "next_flow": 95}},
    ],
    growth_cap="0.03",
)
values = [row["terminal_value"] for row in r.results]
assert r.results[0]["method_version"] == "1"
assert values[0] == Decimal("1275")
assert values[2] == Decimal("1350")
assert round(r.results[2]["output"]["implied_growth"], 6) == Decimal("0.029630")

try:  # P/E is an equity measure: never mixed into an enterprise comparison
    fm.tv.compare("0.10", "enterprise", [
        {"tv.exit_multiple": {"multiple": 12, "metric": "earnings", "metric_value": 50}},
    ])
except fm.FairmarkError as err:
    assert err.code == "FM-E019"

Inputs¶

Field	Meaning	Default
`rate`	Discount rate of the terminal phase, decimal fraction per period, shared	required
`basis`	`enterprise` or `equity`, shared by every terminal value compared	required
`growth_cap`	Upper bound for the perpetual growth, decimal fraction per period, shared	none, reported as absent
`techniques`	List of `{"<method id>": {terms}}`, at least one; a technique may appear more than once	required

Outputs¶

Field	Meaning
`basis`	The declared basis
`results`	One row per technique, in the order requested: `method`, `method_version`, `terminal_value` and `output`, the technique's own output with its implied assumptions

Conventions (explicit, reported in `explain.conventions`)¶

Convention	Options	Default
Basis	enterprise or equity, declared once	none: must be given
Rate	one rate for every technique that discounts; the capitalisation rate of `tv.normalised_income` is its own	none: must be given
Growth cap	one value for every growth-based technique, or none	none, reported as absent

Errors¶

Code	When
`FM-E001`	The list of techniques is empty, an entry has more than one key, a technique id is unknown, or a field is missing or unknown
`FM-E019`	An exit multiple, a normalised income or a liquidation is on the other basis than the one declared
Any code of a technique	The first technique that fails returns its own error (for example `FM-E004`, `FM-E018`)

Accuracy¶

Each row has the accuracy of its method; the comparison adds no arithmetic.

Verified against¶

tests/golden/tv.compare/: seven techniques on one rate, basis and cap, each expected value computed on its own by an independent 50-digit script (scripts/reference_tv.py).
A Python test checks that each row equals the method run alone.

Terminal value, comparison of techniques (tv.compare)¶