Break Even Analysis

---
name: break-even-analysis
description: "Compute break-even units, break-even revenue, contribution margin, and margin of safety with the deterministic break-even engine."
argument-hint: <fixed_costs> <selling_price> <variable_cost> <actual_revenue>
risk_level: LOW
rule_type: professional-standard
quality_tier: tested
allowed-tools: bash
capability:
  purpose: [financial_analysis, unit_economics_modelling]
  not_for: [certified_audit_opinion, public_offering_prospectus]
  requires: [<fixed_costs> <selling_price> <variable_cost> <actual_revenue>]
  produces: [bep_units, bep_revenue, contribution_margin, margin_of_safety]
  consumes: [context.scale, marketing.cac]
  deterministic: true
  cross_domain_relevance:
    strategy: high
    marketing: medium
    tax: medium
---

# Break-Even Analysis

Determines the sales level where revenue exactly covers fixed plus variable costs — the baseline for pricing and target setting.

## Formulas (engines/break-even.js)
* **Contribution Margin** = Price − Variable Cost per unit.
* **Contribution Margin Ratio** = CM ÷ Price.
* **Break-Even Units** = Fixed Costs ÷ CM.
* **Break-Even Revenue** = Units × Price.
* **Margin of Safety** = Actual Revenue − Break-Even Revenue.

## Multi-Product Note
For multi-product cases, use the weighted-average contribution margin (weights = sales mix composition); the result is an approximation — valid only if the mix stays constant.

## Scope & Safety
* **Use for**: minimum selling price, sales targets, evaluating fixed costs (rent, admin salaries).
* **Do not use for**: multi-period profit analysis (assumes constant price & costs), or production decisions with limited capacity without constraints.
* Main assumptions: constant price, linear variable costs, all units sold — state the assumptions when presenting.
* The engine throws when price ≤ variable cost (non-positive contribution margin) — that signals an infeasible model, not an error.

## Hybrid Execution Model
Pass `fixedCosts, pricePerUnit, variableCostPerUnit, actualRevenue` to `engines/break-even.js`; present the 5 outputs plus interpretation. Trust Envelope: risk LOW, `as_of` assumption date.

## Worked Example
Input: fixed 20 million/month, price 25.000, variable cost 15.000, actual revenue 60 million.
Output: CM = **10.000**; Ratio = **0.40**; BEP = 20 million ÷ 10.000 = **2,000 units** = **50 million**; Margin of Safety = 60 − 50 = **10 million** (16.7% above BEP — a thin margin; be cautious when revenue declines).