Profitability ratios (`ratios.profitability`)¶

Answers the question "does the company earn enough on what it uses?". Returns ROE, ROI, ROA, ROS, the EBITDA and EBIT margins, the capital turnover and the decomposition of ROE in three factors and in the leverage form, each with its formula and the numbers substituted in the audit trail. A ratio that cannot be computed is reported as not defined with the reason, and the other ratios are still computed.

Formula¶

\[ \text{ROE} = \frac{\text{net income}}{\text{equity}} \qquad \text{ROI} = \frac{\text{EBIT}}{\text{operating return base}} \qquad \text{ROS} = \frac{\text{EBIT}}{\text{revenue}} \]

\[ \text{capital turnover} = \frac{\text{revenue}}{\text{operating return base}} \qquad \text{ROI} = \text{ROS} \times \text{capital turnover} \]

\[ \text{EBITDA margin} = \frac{\text{EBITDA}}{\text{revenue}} \qquad \text{EBIT margin} = \frac{\text{EBIT}}{\text{revenue}} \]

The three-factor (DuPont) decomposition:

\[ \text{ROE} = \underbrace{\frac{\text{net income}}{\text{revenue}}}_{\text{net margin}} \times \underbrace{\frac{\text{revenue}}{\text{total assets}}}_{\text{asset turnover}} \times \underbrace{\frac{\text{total assets}}{\text{equity}}}_{\text{equity multiplier}} \]

\[ \text{ROA} = \frac{\text{EBIT}}{\text{total assets}} \]

The leverage form, computed when the leverage inputs are given:

\[ \text{ROE} = \left[\text{ROI} + (\text{ROI} - i)\,\frac{D}{E}\right](1 - t) \qquad i = \frac{\text{financial charges}}{D} \qquad t = \frac{\text{taxes}}{\text{pre-tax income}} \]

where \(D\) is the gross financial debt or the net financial position, as chosen in leverage.debt_basis, \(E\) the equity and \(t\) the effective tax rate. \((\text{ROI} - i) \times D/E\) is the leverage effect. The form equals ROE when the operating return base is the invested capital and the invested capital equals \(E + D\); otherwise the difference shows the effect of non-operating items.

The operating return base is the operating invested capital or the total assets, as chosen in operating_return_base. Balance-sheet amounts are closing balances, or the average of opening and closing balances, as chosen in balances.

Example¶

from decimal import Decimal

import fairmark as fm

r = fm.ratios.profitability(
    balances="closing",
    operating_return_base="invested_capital",
    ebitda_definition="reported EBITDA, no adjustments",
    income_statement={"revenue": 5000, "ebitda": 800, "ebit": 500, "net_income": 260},
    closing={"equity": 2000, "total_assets": 6000, "invested_capital": 4000},
)
assert r.roe["value"] == Decimal("0.13")  # 260 / 2000
assert r.roi["value"] == Decimal("0.125")  # 500 / 4000
assert r.capital_turnover["value"] == Decimal("1.25")  # 5000 / 4000

# Negative equity: ROE is not defined, the other ratios are computed.
n = fm.ratios.profitability(
    balances="closing",
    operating_return_base="total_assets",
    ebitda_definition="reported EBITDA, no adjustments",
    income_statement={"revenue": 5000, "ebitda": 800, "ebit": 500, "net_income": 260},
    closing={"equity": -100, "total_assets": 6000},
)
assert n.roe["value"] is None
print(n.roe["not_defined"])  # equity is negative (-100)

# Leverage form, D on the net financial position: equals ROE when capital = E + D.
lev = fm.ratios.profitability(
    balances="closing",
    operating_return_base="invested_capital",
    ebitda_definition="reported EBITDA, no adjustments",
    income_statement={"revenue": 5000, "ebitda": 800, "ebit": 500, "net_income": 260},
    closing={"equity": 2000, "total_assets": 6000, "invested_capital": 4000, "debt": 2000},
    leverage={
        "debt_basis": "net_financial_position",
        "financial_charges": 100,
        "taxes": 140,
        "pre_tax_income": 400,
    },
)
assert lev.roe_leverage["cost_of_debt"]["value"] == Decimal("0.05")  # 100 / 2000
assert lev.roe_leverage["leverage_effect"]["value"] == Decimal("0.075")  # (0.125 − 0.05) × 1
assert lev.roe_leverage["roe"]["value"] == Decimal("0.13")  # 0.2 × (1 − 0.35)

Inputs¶

Field	Meaning	Default
`balances`	`closing`, or `average` of the opening and closing balance sheets	required
`operating_return_base`	`invested_capital` or `total_assets`: the capital of ROI and of the capital turnover	required
`ebitda_definition`	How EBITDA was measured, in words, not empty; echoed in the conventions	required
`income_statement`	`revenue`, `ebitda`, `ebit`, `net_income` of the period, currency units	required
`closing`	`equity`, `total_assets`; with an invested capital base, `invested_capital`; with `leverage`, `debt` (D on the chosen basis); currency units	required
`opening`	Same fields at the start of the period	required with average balances, not used otherwise
`leverage`	`debt_basis` (`gross_financial_debt` or `net_financial_position`, no default), `financial_charges`, `taxes`, `pre_tax_income` of the period, currency units	optional: without it the leverage form is not defined

Outputs¶

Every ratio is an object {"value": ..., "not_defined": ...}: value is null when the ratio is not defined, and not_defined then gives the reason.

Field	Meaning
`roe`	Net income / equity, decimal fraction
`roi`	EBIT / operating return base, decimal fraction
`roa`	EBIT / total assets, decimal fraction
`ros`	EBIT / revenue, decimal fraction
`ebitda_margin`	EBITDA / revenue, decimal fraction
`ebit_margin`	EBIT / revenue, decimal fraction
`capital_turnover`	Revenue / operating return base, times per period
`roe_three_factor`	`net_margin`, `asset_turnover`, `equity_multiplier` and their product `roe`
`roe_leverage`	`roi`, `cost_of_debt` (i), `debt_to_equity` (D/E), `leverage_effect`, `pre_tax_roe`, `tax_rate` (t) and `roe`

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

Convention	Options	Default
Balances	closing, average of opening and closing	required
Operating return base	invested capital, total assets; an invested capital given with a total-assets base is reported as not used	required
EBITDA definition	as given by the analyst, non-empty	required
ROS	EBIT / revenue, equal to the EBIT margin	fixed
ROA	EBIT / total assets	fixed
Leverage form	D on `debt_basis`; i = financial charges / D; t = taxes / pre-tax income (effective); ROI on the operating return base; `debt` given without `leverage` is reported as not used	`debt_basis` required when `leverage` is given
Three-factor ROE	on total assets (asset turnover and equity multiplier), whatever the operating return base	fixed
Balances	applied to every balance-sheet amount, numerator or denominator, D included	fixed
Not defined	zero denominator; equity zero or negative for ROE, the equity multiplier and D/E; invested capital zero or negative for ROI on an invested capital base; no `leverage` inputs for the leverage form	fixed

ROS is EBIT over revenue, so it equals the EBIT margin; both are returned so that the chain ROI = ROS × capital turnover reads directly.

Errors¶

Code	When
`FM-E001`	Average balances without `opening`; `invested_capital` missing with an invested capital base; `debt` missing or `debt_basis` missing with `leverage`; an empty or blank `ebitda_definition`; a field is missing or unknown
`FM-E008`	Arithmetic overflow (inputs far outside a realistic range)

Accuracy¶

Each ratio is one decimal division, exact up to the 28 significant digits of the decimal type. The three-factor ROE is the product of the three rounded factors and can differ from the direct ROE in the 28^th digit.

Verified against¶

Golden cases in tests/golden/ratios.profitability/ (closing and average balances on both operating return bases, negative equity, negative invested capital, zero revenue, the leverage form on both bases of D and with zero pre-tax income), whose expected values come from scripts/reference_ratios.py (Python decimal at 50 digits), with the closed form written in each file.

Profitability ratios (ratios.profitability)¶