Terminal value, value driver (`tv.value_driver`)¶

Returns the terminal value at the horizon N when growth is earned by reinvestment: to grow at g, a business that earns a return on new invested capital (RONIC) must reinvest g / RONIC of its net operating profit after tax (NOPAT). The free cash flow is what remains. The method makes value creation explicit: growth adds value only when RONIC exceeds the rate, and when RONIC equals the rate the terminal value does not depend on g.

Formula¶

For \(-1 < g < r\) and \(RONIC > 0\):

\[ \text{reinvestment rate} = \frac{g}{RONIC}, \qquad TV_N = \frac{NOPAT_{N+1}\,\left(1 - \dfrac{g}{RONIC}\right)}{r - g} \]

When \(RONIC = r\) the formula reduces to \(TV_N = NOPAT_{N+1} / r\); the method computes it directly in that form, so the result is exactly independent of g. When RONIC is below g the reinvestment rate exceeds 100% and the free cash flow at N + 1 is negative; the method returns the value and states it in explain.conventions.

Example¶

The table "The Big Assumption" in Damodaran's valuation lectures values a NOPAT of 100 at a cost of capital of 10%; with growth 2% and a return on capital of 6% it shows 833:

from decimal import Decimal

import fairmark as fm

r = fm.tv.value_driver(100, "0.02", "0.06", "0.10")
assert round(r.terminal_value) == 833
assert r.value_of_growth == "destroys"

# RONIC equal to the rate: growth creates no value, TV = NOPAT / r for any g
flat = fm.tv.value_driver(100, "0.03", "0.10", "0.10")
assert flat.terminal_value == Decimal("1000")
assert flat.value_of_growth == "none"

# NOPAT 150, growth 2%, RONIC 12%: one sixth of NOPAT is reinvested
up = fm.tv.value_driver(150, "0.02", "0.12", "0.10")
assert round(up.reinvestment_rate, 6) == Decimal("0.166667")

Inputs¶

Field	Meaning	Default
`nopat_next`	NOPAT of period N + 1, in currency units	required
`growth`	Perpetual growth, decimal fraction per period, above −1 and below `rate`	required
`ronic`	Return on new invested capital, decimal fraction per period, above 0	required
`rate`	Discount rate of the terminal phase, decimal fraction per period	required
`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
`reinvestment_rate`	g / RONIC
`next_free_cash_flow`	NOPAT_{N+1} × (1 − g / RONIC)
`value_of_growth`	`creates` (RONIC above the rate), `none` (equal) or `destroys` (below)
`growth_cap`	`{growth, cap, status}`; `null` without a cap

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

Convention	Options	Default
Growth from reinvestment	reinvestment rate g / RONIC of NOPAT_{N+1}	fixed
Reinvestment rate above 100%	reported in `explain.conventions`, not refused	fixed
Rate of the terminal phase	given, may differ from the explicit phase	none: must be given
Growth cap	value or none	none, reported as absent

Errors¶

Code	When
`FM-E001`	The growth is −100% or lower, or a field is missing or unknown
`FM-E004`	The growth is equal to or greater than the rate
`FM-E018`	RONIC is zero or negative
`FM-E008`	Arithmetic overflow (inputs far outside a realistic range)

Accuracy¶

Rational operations only: exact up to the 28 significant digits of the decimal type. The reinvestment rate is rounded at the 28^th digit when it is not a finite decimal (such as ⅙).

Verified against¶

Four cells of the table "The Big Assumption" (Damodaran, NYU Stern valuation lecture slides: NOPAT 100 in year n+1, cost of capital 10%) match at their published precision, including the column where the return on capital equals the cost of capital and the value is 1,000 at every growth (tests/golden/tv.value_driver/).
An independent 50-digit computation (scripts/reference_tv.py).

Terminal value, value driver (tv.value_driver)¶