Library/Fundamental Analysis and Valuation/Statement Ratios/Interest-Coverage Ratio

D18-F01-A04 / Complete engineering topic

Interest-Coverage Ratio

Calculate times-interest-earned without netting interest income or importing a universal distress threshold.

Interest-Coverage Ratio turns aligned statement facts into an auditable diagnostic with visible definition boundariesD18 / D18-F01

Calculate times-interest-earned without netting interest income or importing a universal distress threshold.

The decision this tutorial makes visible

Interest coverage provides a compact earnings-versus-financing-cost diagnostic, but capitalization, netting, and EBITDA variants can change it materially.

The precise question is: How many times does period EBIT cover positive gross interest expense under the selected convention?

An analyst needs to see what changed in the business; a builder needs every source fact, clock, unit, sign, average, adjustment, and reason code needed to reproduce the diagnostic.

Intuition before notation

The numerator is the operating earnings pool selected for the period; the denominator is a positive financing cost. A zero denominator is not infinite strength—it is outside this ratio's useful state.

This package selects one explicit statement-ratio convention and compares material alternatives. It does not label issuer-defined measures as universal or hide non-meaningful denominator states.

Scope and nearby methods

Canonical times-interest-earned = period EBIT / positive gross interest expense. EBITDA coverage, net-interest coverage, and fixed-charge coverage are separate variants.

VariantDefinitionBest useMain limitation
EBIT/gross interest packageTimes-interest-earnedDepreciation-aware operating coverageCapitalized interest and noncash items may matter
EBITDA/interestAdd D&A before divisionCovenant or supplementary analysisIgnores replacement capital needs
Fixed-charge coverageExpand denominator beyond interestLease and fixed-commitment analysisNot interchangeable with ICR

What is sourced, selected, synthetic, and derived

RoleMaterial claimEvidenceBoundary
Sourced factThe paper computes interest coverage as EBIT divided by interest expense and distinguishes the arithmetic from vulnerability thresholds used in that study.S1 and supporting sourcesStudy thresholds, samples, and macroprudential use are not universal company-level decision rules.
Implementation choiceCanonical times-interest-earned = period EBIT / positive gross interest expense. EBITDA coverage, net-interest coverage, and fixed-charge coverage are separate variants.Frozen package definition contractNearby variants remain named and separate.
Synthetic teaching inputAll company amounts, periods, scenarios, and calculated teaching paths are repository-authored synthetic data.datasets/canonical-input.json and scenario-results.jsonNo value is represented as a live provider observation or filed issuer fact.
Author-derived calculationSynthetic EBIT 150 divided by positive gross interest expense 50 gives 3.0× coverage and zero arithmetic shortfall.Formula, shared fixture, independent arithmetic, and Python/TypeScript parityArithmetic fidelity does not prove an analytical or investment conclusion.
Scope boundaryThe output does not establish investment quality, solvency, valuation, peer superiority, forecast accuracy, profitability, covenant compliance, or investment advice.No empirical or advisory claim is testedUse the result as one documented diagnostic.

Primary regulator, accounting-body, institution, paper, and filed-entity sources establish reporting and definition boundaries. The fixtures, calculations, scenarios, and conclusions about those fixtures are repository-authored and synthetic.

Formula, symbols, and numerical policy

Plain text
Interest Coverage = EBIT / Gross Interest Expense
SymbolMeaningUnitPolicy
EBITEarnings before interest and taxcurrency/periodDeclared package subtotal
IGross interest expensecurrency/periodPositive magnitude
ICRInterest coveragetimesEBIT/I
  • Use one currency and scale for every amount in a calculation; ratios are dimensionless and days use the declared period day count.
  • Do not round inputs or intermediate averages; round displayed percentages, days, and multiples only after calculation.
  • Return a diagnostic null for structurally valid but economically uninterpretable denominators; reject malformed schemas and non-finite numbers.
  • Preserve filed signs in common-size statements and normalize expense/debt signs explicitly for ratios that require positive denominators.

Read the formula in the same order as the algorithm. Validate identity, ordering, units, and supported state first. Apply the selected denominator, equality, and mapping rules second. Calculate with unrounded numeric values. Round only at the declared presentation boundary, and preserve null as a diagnostic rather than coercing it to zero.

Build the algorithm

  1. Map period EBIT and gross interest expense under one convention.
  2. Reject malformed facts and diagnose nonpositive interest.
  3. Divide EBIT by interest without rounding.
  4. Classify the exact 1× arithmetic boundary without assigning a universal credit judgment.

Production-minded operational checklist

  1. Map gross interest
  2. Freeze EBIT bridge
  3. Check capitalization and leases
  4. Do not import a universal threshold

A precise ratio is unsafe when its framework, period, unit, source fact, numerator, denominator, average, sign, or adjustment policy is ambiguous. Stop and map the evidence before calculating.

Worked synthetic example

The canonical fixture is synthetic teaching data, not a filed issuer statement or provider observation. Its primary author-derived output, interest_coverage_ratio, is 3.0. The complete input and output are in datasets/canonical-input.json and datasets/expected-output.json.

Synthetic EBIT 150 divided by positive gross interest expense 50 gives 3.0× coverage and zero arithmetic shortfall.

Counterfactual checkpoint

Same debt, higher interest. Hold EBIT constant while gross interest expense rises. The output changes because The ratio measures a period flow relationship, not debt principal directly.

The structured result retains state and diagnostics in addition to the primary number. That makes the calculation independently reviewable and prevents a partial, null, rejected, or definition-bounded outcome from being mistaken for an unqualified value.

Boundary and counterexample workbook

The playground computes every scenario at 61 deterministic parameter states. The table uses the declared focus step and states whether that focus reproduces the canonical fixture. The full state ledger and compressed transition segments are in datasets/scenario-results.json.

ScenarioReview focusPurposeStatePrimary outputDiagnosticDecision segments
Canonical EBIT sweepStep 30 · canonical fixtureMove EBIT through the canonical 3× value.covered3.00×covered · ebit-divided-by-gross-interest-expense1
Exact 1× boundaryStep 30 · comparison focusCross EBIT equal to interest.covered1.00×covered · ebit-divided-by-gross-interest-expense2
Negative EBITStep 30 · comparison focusObserve signed coverage and shortfall.not-covered-0.80×not-covered · ebit-divided-by-gross-interest-expense1
Interest-cost sensitivityStep 30 · comparison focusIncrease gross interest while EBIT stays fixed.covered2.14×covered · ebit-divided-by-gross-interest-expense1
Zero-interest boundaryStep 30 · comparison focusApproach the not-meaningful denominator state.covered6.00×covered · ebit-divided-by-gross-interest-expense2
Low coverage rangeStep 30 · comparison focusInspect states below 1× without a universal rating label.not-covered0.60×not-covered · ebit-divided-by-gross-interest-expense2
High coverage rangeStep 30 · comparison focusInspect large ratios without calling them infinite safety.covered7.50×covered · ebit-divided-by-gross-interest-expense1

These rows are not backtest observations. They are controlled counterexamples that expose how one driver changes the state, output, or reason code while the rest of the contract stays fixed.

Visualize the boundary

Interest-Coverage Ratio annotated teaching map

Open this SVG at full size, or use the guided playground to compare the seven topic-specific canonical, boundary, policy, and failure scenarios.

The Mermaid flow answers where the selected calculation sits in the processing sequence. The SVG keeps the formula, output, decision boundary, and invariant visible together. The lab lets the reader step through the same structured states without changing the underlying definition.

Five coordinated teaching views

Interest-Coverage Ratio learning promise

The hero fixes the practitioner question and the builder contract before any ratio is interpreted.

Interest-Coverage Ratio formula anatomy

The formula view keeps units, policies, and the material denominator boundary beside the symbols.

Interest-Coverage Ratio independently auditable worked example

The worked-example view separates synthetic input, author-derived output, invariant, and counterfactual.

Interest-Coverage Ratio variant comparison

The comparison view prevents same-label measures from being treated as interchangeable.

Interest-Coverage Ratio evidence lineage

The lineage view shows where entity, period, framework, unit, sign, and definition decisions enter.

AssetLearning purposeStatic fallback
Article heroQuestion and learning contractEmbedded SVG text
Formula anatomyUnits, policies, denominator gateSymbol table
Worked exampleIndependent arithmetic and invariantFixture JSON
Definition comparisonVariant selectionComparison table
Evidence lineageSource-to-output audit pathClaim ledger
Guided playgroundCanonical, boundary, comparison, and failure statesScenario ledger

Implementation walkthrough

The Python and TypeScript references validate the same JSON contract, retain components and reason codes, calculate at full precision, and are compared against shared expected output plus 427 scenario states.

The main implementation branches are:

  • gross interest <= 0 — Return not-meaningful, because This denominator cannot answer the coverage question.
  • coverage = 1 — Classify arithmetic covered, because EBIT exactly equals gross interest.
  • coverage < 1 — Expose currency shortfall, because EBIT is below period interest under this convention.

Neither reference silently fetches data, mutates caller-owned inputs outside the declared engine behavior, guesses hidden state, or substitutes a provider default. Shared JSON fixtures make value, null, state, and reason-code drift visible across languages.

Testing and validation

Definition tests compare every canonical field, reject malformed state, and exercise the material boundary. Family validation recomputes every playground state from the reference function. Independent arithmetic is recorded beside the fixture rather than inferred only from implementation output.

The audit must preserve these invariants:

  • At exactly EBIT = interest, coverage is 1× and the arithmetic shortfall is zero.
  • Netting interest income is a different denominator convention.
  • A zero interest denominator returns not-meaningful rather than infinity.
  • The output retains components, state, and a reason code rather than publishing an unexplained scalar.

Passing definition and parity checks proves that the implementation matches the selected contract. It does not prove production performance, universal applicability, or a later market outcome.

Failure modes and misuse

  • A correct ratio can still be distorted by acquisitions, disposals, seasonality, inflation, foreign exchange, restatements, or classification choices.
  • Cross-company comparison requires the same framework, consolidation scope, period length, mapping, and analytical definition.
  • Ratios summarize reported accounting amounts; they do not measure market value, forecast cash flows, or establish investment merit.

Debugging order

When a result looks surprising, inspect the state in this order:

  1. Confirm entity, period, framework, currency, and scale
  2. Trace every source fact and sign
  3. Recompute averages and bridges independently
  4. Check denominator state and selected variant
  5. Compare unrounded Python and TypeScript output

Evidence and historical boundary

Historical decision: not useful. A named issuer is not useful for the canonical arithmetic because filings mix company-specific labels, fiscal calendars, tax effects, lease policies, segments, and non-GAAP reconciliations. Primary filings are used to prove definition variability; controlled synthetic statements isolate the mechanism without implying a company judgment.

The primary sources are IMF corporate balance-sheet stress testing, SEC financial-statement guide, SEC EDGAR XBRL APIs. They support the source roles listed in the research ledger. They do not supply a redistributable filed/provider observation or support investment quality, solvency, valuation, peer superiority, forecast accuracy, profitability, covenant compliance, or investment advice.

Practical questions and review answers

What exactly does this package calculate?

Canonical times-interest-earned = period EBIT / positive gross interest expense. EBITDA coverage, net-interest coverage, and fixed-charge coverage are separate variants. The structured output includes components, state, and a reason code; the headline ratio is never the whole audit record.

Why can a filing platform, data vendor, spreadsheet, or company presentation disagree?

They may map different statement rows, fiscal periods, signs, tax or lease policies, cash definitions, balance averages, or non-GAAP adjustments. Compare the definition and evidence ledger before comparing numbers.

Can quarterly, trailing-twelve-month, and annual facts be mixed?

No. A flow numerator and every flow denominator must cover the declared period, while balance-sheet stocks must come from the matching boundary dates. Annualization is a separate, declared analytical transformation.

When should the output be null rather than zero or infinity?

At the material boundary: EBIT equals gross interest at exactly 1×. Null means the package cannot answer its stated question under that denominator state; it is not a missing cosmetic value.

Does a negative, high, or improving result automatically mean good or bad?

No. Interpretation depends on sector, business model, accounting framework, period, definition, and the components that moved. The ratio can describe a state without establishing its cause or desirability.

Does passing the code and parity checks prove investment value?

No. It proves that Python, TypeScript, fixtures, visuals, and the playground implement the frozen definition. It does not establish forecasting ability, solvency, covenant compliance, valuation, peer superiority, or investment suitability.

Where can I inspect every scenario rather than one example?

Open the guided 427-state playground and the full scenario-results.json.

Summary and next topic

You can now carry the result from Interest-Coverage Ratio into Net-Debt/EBITDA only after carrying forward the fact-mapping ledger and resetting method-specific numerator and denominator choices. The learning flow is: Cash Conversion Cycle → Interest-Coverage Ratio → Net-Debt/EBITDA. Carry the result forward only with its scope, clock, state, and evidence label.

Interest-Coverage Ratio calculation flow

This flow identifies the selected calculation stages and the structured output.

Rendering system map…

Takeaway: One times is an arithmetic equality, not a universal rating threshold; EBITDA, net-interest, and fixed-charge variants answer different questions.

ReferencesPrimary sources and evidence notes

Expand the source trail, evidence role, and limitations behind the engineering choices.

S1 — Stress Testing Corporate Balance Sheets

  • Organization or authors: International Monetary Fund staff
  • Source type: Official institution working paper
  • Publication or effective date: 2015-11
  • Version: IMF Working Paper WP/15/216
  • URL or DOI: https://www.imf.org/external/pubs/ft/wp/2015/wp15216.pdf
  • Accessed: 2026-08-04
  • Jurisdiction: Cross-country corporate-sector analysis
  • Supports: The paper computes interest coverage as EBIT divided by interest expense and distinguishes the arithmetic from vulnerability thresholds used in that study.
  • Limitations: Study thresholds, samples, and macroprudential use are not universal company-level decision rules.

S2 — Beginners' Guide to Financial Statements

  • Organization or authors: U.S. Securities and Exchange Commission
  • Source type: Official regulator investor publication
  • Publication or effective date: 2007-02-05
  • Version: Current SEC web publication
  • URL or DOI: https://www.sec.gov/about/reports-publications/investor-publications/beginners-guide-financial-statements
  • Accessed: 2026-08-04
  • Jurisdiction: United States public-company reporting
  • Supports: Balance sheets describe a point in time, while income and cash-flow statements describe a period; notes are part of interpreting the reported amounts.
  • Limitations: It does not prescribe the package ratios, XBRL mapping, normalization choices, or cross-company conclusions.

S3 — EDGAR Application Programming Interfaces

  • Organization or authors: U.S. Securities and Exchange Commission
  • Source type: Official regulator technical documentation
  • Publication or effective date: 2025-04-08
  • Version: Company Facts, Company Concept, and Frames API documentation
  • URL or DOI: https://www.sec.gov/search-filings/edgar-application-programming-interfaces
  • Accessed: 2026-08-04
  • Jurisdiction: United States public filings
  • Supports: EDGAR exposes filed XBRL facts with taxonomy, unit, form, period, and filing context; company extensions and fiscal-calendar differences require explicit mapping.
  • Limitations: A matching tag does not by itself prove semantic comparability, adjustment policy, or the correct ratio denominator.

Evidence boundary

The sources establish the exact rule, interface, protocol, or research context named above. They do not verify the repository-authored synthetic fixture, thresholds, empirical usefulness, execution probability, or profitability. Package-selected choices remain labeled as implementation choices wherever they are used.

statement-ratios.ts
/** Deterministic TypeScript reference calculations for D18-F01. */

type Inputs = Record<string, unknown>;
type Output = Record<string, unknown>;

function numberValue(name: string, value: unknown): number {
  if (typeof value !== "number" || !Number.isFinite(value)) throw new RangeError(`${name} must be a finite number`);
  return value;
}

function positive(name: string, value: unknown): number {
  const parsed = numberValue(name, value);
  if (parsed <= 0) throw new RangeError(`${name} must be positive`);
  return parsed;
}

function booleanValue(name: string, value: unknown): boolean {
  if (typeof value !== "boolean") throw new RangeError(`${name} must be boolean`);
  return value;
}

const average = (beginning: number, ending: number): number => (beginning + ending) / 2;
const clean = (value: number): number => {
  const rounded = Math.round((value + Number.EPSILON) * 1e12) / 1e12;
  return Object.is(rounded, -0) ? 0 : rounded;
};

export function dupontDecomposition(input: Inputs): Output {
  const income = numberValue("net_income", input.net_income);
  const revenue = numberValue("revenue", input.revenue);
  const averageAssets = average(numberValue("beginning_assets", input.beginning_assets), numberValue("ending_assets", input.ending_assets));
  const averageEquity = average(numberValue("beginning_equity", input.beginning_equity), numberValue("ending_equity", input.ending_equity));
  if (revenue === 0 || averageAssets <= 0 || averageEquity <= 0) {
    const reasons: string[] = [];
    if (revenue === 0) reasons.push("zero-revenue");
    if (averageAssets <= 0) reasons.push("nonpositive-average-assets");
    if (averageEquity <= 0) reasons.push("nonpositive-average-equity");
    return { net_profit_margin: null, asset_turnover: null, equity_multiplier: null, dupont_roe: null, direct_roe: null, identity_gap: null,
      average_assets: clean(averageAssets), average_equity: clean(averageEquity), state: "not-meaningful", reason: reasons.join("+") };
  }
  const margin = income / revenue;
  const turnover = revenue / averageAssets;
  const multiplier = averageAssets / averageEquity;
  const dupontRoe = margin * turnover * multiplier;
  const directRoe = income / averageEquity;
  return { net_profit_margin: clean(margin), asset_turnover: clean(turnover), equity_multiplier: clean(multiplier), dupont_roe: clean(dupontRoe),
    direct_roe: clean(directRoe), identity_gap: clean(dupontRoe - directRoe), average_assets: clean(averageAssets), average_equity: clean(averageEquity),
    state: income < 0 ? "loss" : "calculated", reason: "three-factor-identity-reconciles" };
}

export function roicCalculation(input: Inputs): Output {
  const profit = numberValue("operating_profit", input.operating_profit);
  const taxRate = numberValue("normalized_tax_rate", input.normalized_tax_rate);
  if (taxRate < 0 || taxRate > 1) throw new RangeError("normalized_tax_rate must be between 0 and 1");
  const capitalBegin = numberValue("beginning_operating_assets", input.beginning_operating_assets) - numberValue("beginning_operating_liabilities", input.beginning_operating_liabilities);
  const capitalEnd = numberValue("ending_operating_assets", input.ending_operating_assets) - numberValue("ending_operating_liabilities", input.ending_operating_liabilities);
  const averageCapital = average(capitalBegin, capitalEnd);
  const nopat = profit * (1 - taxRate);
  if (averageCapital <= 0) return { nopat: clean(nopat), beginning_invested_capital: clean(capitalBegin), ending_invested_capital: clean(capitalEnd),
    average_invested_capital: clean(averageCapital), roic: null, state: "not-meaningful", reason: "nonpositive-average-invested-capital" };
  return { nopat: clean(nopat), beginning_invested_capital: clean(capitalBegin), ending_invested_capital: clean(capitalEnd),
    average_invested_capital: clean(averageCapital), roic: clean(nopat / averageCapital), state: nopat < 0 ? "loss" : "calculated",
    reason: "package-operating-capital-definition" };
}

export function cashConversionCycle(input: Inputs): Output {
  const revenue = numberValue("revenue", input.revenue);
  const cogs = numberValue("cost_of_goods_sold", input.cost_of_goods_sold);
  const days = positive("day_count", input.day_count);
  const receivablesBegin = numberValue("beginning_receivables", input.beginning_receivables);
  const receivablesEnd = numberValue("ending_receivables", input.ending_receivables);
  const inventoryBegin = numberValue("beginning_inventory", input.beginning_inventory);
  const inventoryEnd = numberValue("ending_inventory", input.ending_inventory);
  const payablesBegin = numberValue("beginning_trade_payables", input.beginning_trade_payables);
  const payablesEnd = numberValue("ending_trade_payables", input.ending_trade_payables);
  if (Math.min(receivablesBegin, receivablesEnd, inventoryBegin, inventoryEnd, payablesBegin, payablesEnd) < 0) throw new RangeError("working-capital balances must be nonnegative");
  const receivables = average(receivablesBegin, receivablesEnd);
  const inventory = average(inventoryBegin, inventoryEnd);
  const payables = average(payablesBegin, payablesEnd);
  if (revenue <= 0 || cogs <= 0) return { average_receivables: clean(receivables), average_inventory: clean(inventory), average_trade_payables: clean(payables),
    days_sales_outstanding: null, days_inventory_outstanding: null, days_payables_outstanding: null, cash_conversion_cycle_days: null,
    state: "not-meaningful", reason: revenue <= 0 ? "nonpositive-revenue" : "nonpositive-cogs" };
  const dso = receivables / revenue * days;
  const dio = inventory / cogs * days;
  const dpo = payables / cogs * days;
  const ccc = dio + dso - dpo;
  return { average_receivables: clean(receivables), average_inventory: clean(inventory), average_trade_payables: clean(payables),
    days_sales_outstanding: clean(dso), days_inventory_outstanding: clean(dio), days_payables_outstanding: clean(dpo),
    cash_conversion_cycle_days: clean(ccc), state: ccc < 0 ? "negative-cycle" : "calculated", reason: "dio-plus-dso-minus-dpo" };
}

export function interestCoverageRatio(input: Inputs): Output {
  const ebit = numberValue("ebit", input.ebit);
  const interest = numberValue("gross_interest_expense", input.gross_interest_expense);
  if (interest <= 0) return { ebit: clean(ebit), gross_interest_expense: clean(interest), interest_coverage_ratio: null,
    coverage_shortfall: null, state: "not-meaningful", reason: "nonpositive-gross-interest-expense" };
  const ratio = ebit / interest;
  return { ebit: clean(ebit), gross_interest_expense: clean(interest), interest_coverage_ratio: clean(ratio),
    coverage_shortfall: clean(Math.max(0, interest - ebit)), state: ratio >= 1 ? "covered" : "not-covered",
    reason: "ebit-divided-by-gross-interest-expense" };
}

export function netDebtToEbitda(input: Inputs): Output {
  const income = numberValue("net_income", input.net_income);
  const interest = numberValue("interest_expense", input.interest_expense);
  const tax = numberValue("income_tax_expense", input.income_tax_expense);
  const da = numberValue("depreciation_and_amortization", input.depreciation_and_amortization);
  const currentDebt = numberValue("current_borrowings", input.current_borrowings);
  const noncurrentDebt = numberValue("noncurrent_borrowings", input.noncurrent_borrowings);
  const leases = numberValue("lease_liabilities", input.lease_liabilities);
  const cash = numberValue("cash_and_cash_equivalents", input.cash_and_cash_equivalents);
  const includeLeases = booleanValue("include_lease_liabilities", input.include_lease_liabilities);
  if (Math.min(interest, da, currentDebt, noncurrentDebt, leases, cash) < 0) throw new RangeError("debt, cash, interest, and D&A inputs must be nonnegative");
  const ebitda = income + interest + tax + da;
  const grossDebt = currentDebt + noncurrentDebt + (includeLeases ? leases : 0);
  const netDebt = grossDebt - cash;
  if (ebitda <= 0) return { ebitda: clean(ebitda), gross_debt: clean(grossDebt), net_debt: clean(netDebt), net_debt_to_ebitda: null,
    lease_policy: includeLeases ? "included" : "excluded", state: "not-meaningful", reason: "nonpositive-ebitda" };
  return { ebitda: clean(ebitda), gross_debt: clean(grossDebt), net_debt: clean(netDebt), net_debt_to_ebitda: clean(netDebt / ebitda),
    lease_policy: includeLeases ? "included" : "excluded", state: netDebt < 0 ? "net-cash" : "net-debt", reason: "net-debt-divided-by-ebitda" };
}

interface Item { label: string; value: number }
interface Period { period: string; items: Item[] }

export function commonSizeStatements(input: Inputs): Output {
  const statementType = input.statement_type;
  if (statementType !== "income" && statementType !== "balance") throw new RangeError("statement_type must be 'income' or 'balance'");
  const baseLabel = input.base_label;
  const focusLabel = input.focus_label;
  if (typeof baseLabel !== "string" || !baseLabel.trim()) throw new RangeError("base_label must be a nonempty string");
  if (typeof focusLabel !== "string" || !focusLabel.trim()) throw new RangeError("focus_label must be a nonempty string");
  if (!Array.isArray(input.periods) || input.periods.length < 2) throw new RangeError("periods must contain at least two period objects");
  let expectedLabels: string[] | null = null;
  let previousFocus: number | null = null;
  const normalizedPeriods = (input.periods as unknown[]).map((rawPeriod, periodIndex) => {
    if (!rawPeriod || typeof rawPeriod !== "object") throw new RangeError(`periods[${periodIndex}] must be an object`);
    const period = rawPeriod as Record<string, unknown>;
    if (typeof period.period !== "string" || !period.period.trim()) throw new RangeError(`periods[${periodIndex}].period must be a nonempty string`);
    if (!Array.isArray(period.items) || period.items.length < 4) throw new RangeError(`periods[${periodIndex}].items must contain at least four rows`);
    const seen = new Set<string>();
    const parsed = (period.items as unknown[]).map((rawItem, itemIndex): Item => {
      if (!rawItem || typeof rawItem !== "object") throw new RangeError(`periods[${periodIndex}].items[${itemIndex}] must be an object`);
      const item = rawItem as Record<string, unknown>;
      if (typeof item.label !== "string" || !item.label.trim() || seen.has(item.label)) throw new RangeError("statement item labels must be nonempty and unique within a period");
      seen.add(item.label);
      return { label: item.label, value: numberValue(`${period.period}.${item.label}`, item.value) };
    });
    const labels = parsed.map((item) => item.label);
    if (expectedLabels === null) expectedLabels = labels;
    else if (labels.join("\u0000") !== expectedLabels.join("\u0000")) throw new RangeError("every period must use the same ordered line-item labels");
    const values = Object.fromEntries(parsed.map((item) => [item.label, item.value]));
    if (!(baseLabel in values) || !(focusLabel in values)) throw new RangeError("base_label and focus_label must exist in every period");
    const base = values[baseLabel];
    if (base === 0 || (statementType === "balance" && base < 0)) throw new RangeError("the common-size base must be nonzero and positive for balance sheets");
    const focusPercentage = values[focusLabel] / base * 100;
    const result = { period: (period.period as string).trim(), base_value: clean(base), focus_percentage: clean(focusPercentage),
      focus_change_pp: previousFocus === null ? null : clean(focusPercentage - previousFocus),
      items: parsed.map((item) => ({ label: item.label, value: clean(item.value), common_size_pct: clean(item.value / base * 100) })) };
    previousFocus = focusPercentage;
    return result;
  });
  const latest = normalizedPeriods[normalizedPeriods.length - 1];
  return { statement_type: statementType, base_label: baseLabel, focus_label: focusLabel, period_count: normalizedPeriods.length,
    line_item_count: normalizedPeriods[0].items.length, focus_percentage: latest.focus_percentage, focus_change_pp: latest.focus_change_pp,
    periods: normalizedPeriods, state: "calculated", reason: "signed-line-items-divided-by-period-base" };
}

export function calculate(topicId: string, input: Inputs): Output {
  if (!input || typeof input !== "object" || Array.isArray(input)) throw new RangeError("inputs must be an object");
  switch (topicId) {
    case "D18-F01-A01": return dupontDecomposition(input);
    case "D18-F01-A02": return roicCalculation(input);
    case "D18-F01-A03": return cashConversionCycle(input);
    case "D18-F01-A04": return interestCoverageRatio(input);
    case "D18-F01-A05": return netDebtToEbitda(input);
    case "D18-F01-A06": return commonSizeStatements(input);
    default: throw new RangeError(`unsupported topic_id: ${topicId}`);
  }
}
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