biz-breakeven

asgard-ai-platform ｜ 商業與營運 ｜ 原文 ｜ MIT

做損益兩平分析，算出要賣多少才不虧

---
name: "biz-breakeven"
description: "進行損益兩平分析，算出涵蓋所有成本所需的銷售量或營收。當使用者需要計算損益兩平點、評估安全邊際、評估營運槓桿、或決定價格與銷量的取捨時使用，即使他們說的是「我們要賣幾個才夠」、「什麼時候會開始賺錢」或「如果降價會怎樣」也一樣。"
metadata:
  category: "WP-15 商學院—財務"
  tags: ["finance", "breakeven", "cost-analysis"]
---

# 損益兩平分析（Break-Even Analysis）

## 概述

損益兩平分析找出總營收等於總成本的那個點，也就是不賺也不賠。它把成本分成固定和變動，再算出需要多少銷量（單位數或營收），才能透過邊際貢獻（contribution margin）涵蓋固定成本。

## 框架

```
鐵律：固定與變動的分類必須嚴謹

固定成本「不會」隨銷量變動（租金、薪資、保險）。
變動成本會隨銷量「按比例」變動（原料、每單位運費、佣金）。

「薪資」不一定是固定的，業務佣金就是變動的。
「租金」不一定是固定的，抽成式租約就是變動的。
分類錯誤會直接破壞損益兩平的計算。
```

### 核心公式

```
每單位邊際貢獻 = 售價 - 每單位變動成本
損益兩平單位數 = 固定成本 / 每單位邊際貢獻
損益兩平營收 = 固定成本 / 邊際貢獻率
邊際貢獻率 = 每單位邊際貢獻 / 售價
安全邊際 = (實際銷售額 - 損益兩平銷售額) / 實際銷售額
營運槓桿度（DOL）= 邊際貢獻 / 淨利
```

### 步驟 1：分類所有成本

把每一項成本分成固定或變動。對於半變動成本（例如電費有基本費加用量費），要拆成固定和變動兩部分。

### 步驟 2：計算損益兩平點

- **單一產品**：BEP 單位數 = 固定成本 / 每單位 CM
- **多個產品**：依產品組合用加權平均 CM，然後 BEP = 固定成本 / 加權 CM

### 步驟 3：評估安全邊際

目前的銷售高出損益兩平多少？安全邊際越高 = 對景氣下滑的抗壓性越強。

### 步驟 4：情境分析

測試：價格降 10% 會怎樣？銷量降 20% 呢？固定成本增加呢？建立一張情境表。

## 輸出格式

```markdown
# 損益兩平分析：{產品/事業}

## 成本結構
| 類別 | 金額 | 固定/變動 |
|----------|--------|---------------|
| {項目} | ${X} | F/V |

## 損益兩平計算
- 固定成本：${X}/期
- 每單位變動成本：${X}
- 每單位售價：${X}
- 邊際貢獻：${X}（{X%}）
- **損益兩平：{N} 單位 / ${X} 營收**
- 安全邊際：{X%}

## 情境分析
| 情境 | BEP 單位數 | 安全邊際 |
|----------|-----------|-----------------|
| 基準情境 | {N} | {X%} |
| 價格 -10% | {N} | {X%} |
| 銷量 -20% | N/A | {X%} |
| 固定成本 +15% | {N} | {X%} |
```

## 範例

### 正確的應用
**情境：** 台灣一家珍珠奶茶店的損益兩平
- 固定成本：NT$150,000/月（租金 NT$60K、人事 NT$70K、水電 NT$20K）
- 變動成本：NT$25/杯（原料 NT$15、杯子／吸管 NT$5、包材 NT$5）
- 價格：NT$55/杯
- CM = NT$30/杯（54.5%）
- **BEP = 150,000 / 30 = 5,000 杯/月 ≈ 167 杯/天** ✓

### 錯誤的應用
- 把員工薪資分類為變動成本 → 對一家員工是固定配置（不是按杯計酬）的店來說，薪資是固定的。這樣會低估 BEP。違反鐵律。

## 常見陷阱

- **階梯式固定成本**：租金在你需要第二個據點之前是固定的。人事在你需要多一個班次之前是固定的。這些成本會在某些銷量門檻「跳階」，要把它們建模成在各自相關範圍內的固定成本。
- **多產品的事業**：大多數真實的事業都賣多種產品。要用加權平均 CM，或用營收（而不是單位數）來算 BEP。
- **損益兩平忽略貨幣的時間價值**：BEP 告訴你銷量，不會告訴你什麼時候能達到。一個在 10,000 單位損益兩平、但要花 3 年才到得了的事業，現金可能會先燒完。
- **邊際貢獻不是毛利**：毛利用的是銷貨成本（COGS，可能包含固定的製造費用）。CM 只用變動成本。

## 腳本

| 腳本 | 說明 | 用法 |
|--------|-------------|-------|
| `scripts/breakeven.py` | 計算損益兩平數量、營收和邊際貢獻 | `python scripts/breakeven.py --help` |

執行 `python scripts/breakeven.py --verify` 可以跑內建的健全性測試。

## 參考資料

- 多產品損益兩平的方法，見 `references/multi-product-bep.md`

---
name: "biz-breakeven"
description: "Perform break-even analysis to determine the sales volume or revenue needed to cover all costs. Use this skill when the user needs to calculate break-even point, assess margin of safety, evaluate operating leverage, or decide pricing and volume trade-offs — even if they say 'how many units do we need to sell', 'when will we be profitable', or 'what happens if we lower the price'."
metadata:
  category: "WP-15 商學院—財務"
  tags: ["finance", "breakeven", "cost-analysis"]
---

# Break-Even Analysis

## Overview

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.

## Framework

```
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

```
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

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.

### Step 2: Calculate Break-Even Point

- **Single product**: BEP units = Fixed Costs / CM per unit
- **Multiple products**: Use weighted-average CM based on product mix, then BEP = Fixed / Weighted CM

### Step 3: Assess Margin of Safety

How far above break-even are current sales? Higher margin of safety = more resilience to downturns.

### Step 4: Scenario Analysis

Test: What happens if price drops 10%? If volume drops 20%? If fixed costs increase? Build a scenario table.

## Output Format

```markdown
# Break-Even Analysis: {Product/Business}

## Cost Structure
| Category | Amount | Fixed/Variable |
|----------|--------|---------------|
| {item} | ${X} | F/V |

## 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%}

## Scenario Analysis
| Scenario | BEP Units | Margin of Safety |
|----------|-----------|-----------------|
| Base case | {N} | {X%} |
| Price -10% | {N} | {X%} |
| Volume -20% | N/A | {X%} |
| Fixed costs +15% | {N} | {X%} |
```

## Examples

### Correct Application
**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** ✓

### Incorrect Application
- 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.

## Gotchas

- **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.

## Scripts

| Script | Description | Usage |
|--------|-------------|-------|
| `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.

## References

- For multi-product break-even methodology, see `references/multi-product-bep.md`