Terminal value, capitalised normalised income (`tv.normalised_income`)¶

Returns the terminal value at the horizon N as a normalised income capitalised at a rate i, as in the income-based reasoning of Italian practice: the income R that the business can earn on a sustainable basis after the horizon, divided by the capitalisation rate, with or without a perpetual growth. Estimating R and i is outside the method. The basis is a required input: enterprise for an operating income capitalised at a rate for all capital providers, equity for a net income capitalised at a cost of equity; there is no default.

Formula¶

\[ TV_N = \frac{R}{i} \qquad\text{or, with a growth } g < i,\qquad TV_N = \frac{R}{i - g} \]

Example¶

from decimal import Decimal

import fairmark as fm

r = fm.tv.normalised_income(120, "0.08", "equity")
assert r.terminal_value == Decimal("1500")
assert r.basis == "equity"
print(r.conventions[3])  # no growth: R / i (default)

grown = fm.tv.normalised_income(120, "0.09", "enterprise", growth="0.01", growth_cap="0.02")
assert grown.terminal_value == Decimal("1500")
assert grown.growth_cap["status"] == "respected"

Inputs¶

Field	Meaning	Default
`income`	Normalised income R of period N + 1, in currency units	required
`capitalisation_rate`	Capitalisation rate i, decimal fraction per period, above 0 and above the growth	required
`basis`	`enterprise` (operating income) or `equity` (net income)	required, no default
`growth`	Perpetual growth of the income, decimal fraction per period, above −1 and below i	none (R / i)
`growth_cap`	Upper bound for the growth, decimal fraction per period	none, reported as absent

Outputs¶

Field	Meaning
`terminal_value`	Terminal value at N, not discounted
`basis`	`enterprise` or `equity`, as declared
`growth_cap`	The growth (0 when not given) against the cap; `null` without a cap

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

Convention	Options	Default
Growth	none (R / i), or given (R / (i − g))	none, reported as default
Capitalisation rate	given	none: must be given
Basis	enterprise or equity	none: must be given
Growth cap	value or none	none, reported as absent

Errors¶

Code	When
`FM-E001`	The growth is −100% or lower, `basis` is missing or not `enterprise` or `equity`, or a field is missing or unknown
`FM-E004`	The growth is equal to or greater than the capitalisation rate
`FM-E018`	The capitalisation rate is zero or negative (checked first)
`FM-E008`	Arithmetic overflow (inputs far outside a realistic range)

Accuracy¶

One division (and one subtraction with growth): exact up to the 28 significant digits of the decimal type.

Verified against¶

Golden cases in tests/golden/tv.normalised_income/, from closed forms written in each file and an independent 50-digit computation (scripts/reference_tv.py).

Terminal value, capitalised normalised income (tv.normalised_income)¶