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Break-Even Analysis

盈亏平衡分析

Overview

概述

Break-even analysis finds the point where total revenue equals total costs — zero profit, zero loss. It separates costs into fixed and variable, then calculates the volume (units or revenue) needed to cover fixed costs through contribution margin.
盈亏平衡分析用于找到总收入等于总成本的临界点——此时利润为零，也无亏损。它将成本划分为固定成本和可变成本，随后通过边际贡献计算覆盖固定成本所需的产量（单位数量或收入金额）。

Framework

框架

IRON LAW: Fixed vs Variable Classification Must Be Rigorous

Fixed costs do NOT change with volume (rent, salaries, insurance).
Variable costs change PROPORTIONALLY with volume (materials, shipping per unit, commissions).

"Salaries" is NOT always fixed — a sales commission is variable.
"Rent" is NOT always fixed — a percentage-rent lease is variable.
Misclassification directly corrupts the break-even calculation.
IRON LAW: Fixed vs Variable Classification Must Be Rigorous

Fixed costs do NOT change with volume (rent, salaries, insurance).
Variable costs change PROPORTIONALLY with volume (materials, shipping per unit, commissions).

"Salaries" is NOT always fixed — a sales commission is variable.
"Rent" is NOT always fixed — a percentage-rent lease is variable.
Misclassification directly corrupts the break-even calculation.

Core Formulas

核心公式

Contribution Margin per Unit = Selling Price - Variable Cost per Unit
Break-Even Units = Fixed Costs / Contribution Margin per Unit
Break-Even Revenue = Fixed Costs / Contribution Margin Ratio
Contribution Margin Ratio = Contribution Margin per Unit / Selling Price
Margin of Safety = (Actual Sales - Break-Even Sales) / Actual Sales
Degree of Operating Leverage (DOL) = Contribution Margin / Net Income
Contribution Margin per Unit = Selling Price - Variable Cost per Unit
Break-Even Units = Fixed Costs / Contribution Margin per Unit
Break-Even Revenue = Fixed Costs / Contribution Margin Ratio
Contribution Margin Ratio = Contribution Margin per Unit / Selling Price
Margin of Safety = (Actual Sales - Break-Even Sales) / Actual Sales
Degree of Operating Leverage (DOL) = Contribution Margin / Net Income

Step 1: Classify All Costs

第一步：对所有成本进行分类

Separate every cost line into fixed or variable. For semi-variable costs (e.g., electricity with a base charge + usage), split into fixed and variable portions.
将每一项成本划分为固定成本或可变成本。对于半可变成本（如包含基础费用+使用费用的电费），需拆分为固定部分和可变部分。

Step 2: Calculate Break-Even Point

第二步：计算盈亏平衡点

  • Single product: BEP units = Fixed Costs / CM per unit
  • Multiple products: Use weighted-average CM based on product mix, then BEP = Fixed / Weighted CM
  • 单一产品：盈亏平衡产量（BEP units）= 固定成本 / 单位边际贡献（CM per unit）
  • 多种产品：基于产品组合使用加权平均边际贡献，随后盈亏平衡点=固定成本/加权平均边际贡献

Step 3: Assess Margin of Safety

第三步：评估安全边际

How far above break-even are current sales? Higher margin of safety = more resilience to downturns.
当前销售额比盈亏平衡点高出多少？安全边际越高，应对市场低迷的韧性越强。

Step 4: Scenario Analysis

第四步：情景分析

Test: What happens if price drops 10%? If volume drops 20%? If fixed costs increase? Build a scenario table.
测试以下情景：降价10%会怎样？销量下降20%会怎样？固定成本增加会怎样？制作情景分析表。

Output Format

输出格式

markdown
undefined
markdown
undefined

Break-Even Analysis: {Product/Business}

Break-Even Analysis: {Product/Business}

Cost Structure

Cost Structure

CategoryAmountFixed/Variable
{item}${X}F/V
CategoryAmountFixed/Variable
{item}${X}F/V

Break-Even Calculation

Break-Even Calculation

  • Fixed Costs: ${X}/period
  • Variable Cost per Unit: ${X}
  • Selling Price per Unit: ${X}
  • Contribution Margin: ${X} ({X%})
  • Break-Even: {N} units / ${X} revenue
  • Margin of Safety: {X%}
  • Fixed Costs: ${X}/period
  • Variable Cost per Unit: ${X}
  • Selling Price per Unit: ${X}
  • Contribution Margin: ${X} ({X%})
  • Break-Even: {N} units / ${X} revenue
  • Margin of Safety: {X%}

Scenario Analysis

Scenario Analysis

ScenarioBEP UnitsMargin of Safety
Base case{N}{X%}
Price -10%{N}{X%}
Volume -20%N/A{X%}
Fixed costs +15%{N}{X%}
undefined
ScenarioBEP UnitsMargin of Safety
Base case{N}{X%}
Price -10%{N}{X%}
Volume -20%N/A{X%}
Fixed costs +15%{N}{X%}
undefined

Examples

示例

Correct Application

正确应用示例

Scenario: Break-even for a Taiwanese bubble tea shop
  • Fixed costs: NT$150,000/month (rent NT$60K, staff NT$70K, utilities NT$20K)
  • Variable cost: NT$25/cup (ingredients NT$15, cup/straw NT$5, packaging NT$5)
  • Price: NT$55/cup
  • CM = NT$30/cup (54.5%)
  • BEP = 150,000 / 30 = 5,000 cups/month ≈ 167 cups/day ✓
场景：某台湾奶茶店的盈亏平衡分析
  • 固定成本：150,000新台币/月（租金6万新台币、员工薪资7万新台币、水电费2万新台币）
  • 可变成本：25新台币/杯（原材料15新台币、杯具/吸管5新台币、包装5新台币）
  • 售价：55新台币/杯
  • 边际贡献（CM）：30新台币/杯（54.5%）
  • 盈亏平衡产量（BEP）= 150000 / 30 = 5000杯/月 ≈ 167杯/天 ✓

Incorrect Application

错误应用示例

  • Classified staff wages as variable cost → For a shop with fixed staff (not per-cup labor), wages are fixed. This understates BEP. Violates Iron Law.
  • 将员工薪资归类为可变成本→对于拥有固定员工（非按杯计薪）的店铺，薪资属于固定成本。这种分类会低估盈亏平衡产量，违反了铁律。

Gotchas

注意事项

  • Step-fixed costs: Rent is fixed until you need a second location. Staff is fixed until you need another shift. These "step" at certain volume thresholds — model them as fixed within their relevant range.
  • Multi-product businesses: Most real businesses sell multiple products. Use weighted-average CM or calculate BEP in revenue (not units).
  • Break-even ignores time value: BEP tells you the volume, not when you'll reach it. A business that breaks even at 10,000 units but takes 3 years to get there may run out of cash.
  • Contribution margin is not gross margin: Gross margin uses COGS (which may include fixed manufacturing overhead). CM uses only variable costs.
  • 阶梯式固定成本：租金在需要开设第二家门店前是固定成本。员工薪资在需要增加班次前是固定成本。这些成本在特定产量阈值处呈“阶梯式”增长——在其适用范围内按固定成本建模。
  • 多产品业务：大多数实际运营的企业销售多种产品。使用加权平均边际贡献，或是以收入（而非产量）为单位计算盈亏平衡点。
  • 盈亏平衡分析忽略货币的时间价值：盈亏平衡点只告诉你所需的产量，却不告诉你何时能达到该产量。一家需要卖出10000单位产品才能盈亏平衡，但需要3年才能达到该销量的企业可能会耗尽资金。
  • 边际贡献不等于毛利率：毛利率使用销货成本（COGS，可能包含固定制造费用），而边际贡献仅使用可变成本。

Scripts

脚本工具

ScriptDescriptionUsage
scripts/breakeven.py
Compute break-even quantity, revenue, and contribution margin
python scripts/breakeven.py --help
Run 
python scripts/breakeven.py --verify
to execute built-in sanity tests.
脚本描述使用方法
scripts/breakeven.py
计算盈亏平衡产量、收入及边际贡献
python scripts/breakeven.py --help
运行
python scripts/breakeven.py --verify
以执行内置的合理性测试。

References

参考资料

  • For multi-product break-even methodology, see 
    references/multi-product-bep.md
  • 关于多产品盈亏平衡分析方法，请参阅
    references/multi-product-bep.md