variance-analysis

Anthropic ｜ 金融與投資 ｜ 原文 ｜ Apache-2.0

把預算與實際的財務差異拆成驅動因素，並寫成說明和 waterfall

---
name: variance-analysis
description: 把財務差異拆解成各項驅動因素，附上敘述說明和 waterfall 分析。分析預算對實際、期間對期間的變化、營收或費用差異，或替管理層準備差異說明時使用。
argument-hint: "<項目> <期間> vs <比較基準>"
---

# 差異分析

**重要**：這個 skill 協助差異分析的工作流程，但不提供財務建議。所有分析在用於報告之前，都應該由合格的財務專業人員審閱。

差異拆解的技巧、重大性門檻、敘述產生、waterfall 圖的方法，以及預算 vs 實際 vs 預測的比較。

## 差異拆解技巧

### 價格 / 數量拆解

最基本的差異拆解。用於營收、銷貨成本，以及任何能表示成 價格 x 數量 的指標。

**公式：**
```
Total Variance = Actual - Budget (or Prior)

Volume Effect  = (Actual Volume - Budget Volume) x Budget Price
Price Effect   = (Actual Price - Budget Price) x Actual Volume
Mix Effect     = Residual (interaction term), or allocated proportionally

Verification:  Volume Effect + Price Effect = Total Variance
               (when mix is embedded in the price/volume terms)
```

**三向拆解（把 mix 分開）：**
```
Volume Effect = (Actual Volume - Budget Volume) x Budget Price x Budget Mix
Price Effect  = (Actual Price - Budget Price) x Budget Volume x Actual Mix
Mix Effect    = Budget Price x Budget Volume x (Actual Mix - Budget Mix)
```

**範例：營收差異**
- 預算：10,000 單位，每單位 $50 = $500,000
- 實際：11,000 單位，每單位 $48 = $528,000
- 總差異：+$28,000 有利
  - 數量效應：+1,000 單位 x $50 = +$50,000（有利，賣出更多單位）
  - 價格效應：-$2 x 11,000 單位 = -$22,000（不利，ASP 較低）
  - 淨額：+$28,000

### 費率 / Mix 拆解

用於分析各分群單位經濟效益不同的混合費率。

**公式：**
```
Rate Effect = Sum of (Actual Volume_i x (Actual Rate_i - Budget Rate_i))
Mix Effect  = Sum of (Budget Rate_i x (Actual Volume_i - Expected Volume_i at Budget Mix))
```

**範例：毛利差異**
- 產品 A：毛利率 60%，產品 B：毛利率 40%
- 預算 mix：50% A、50% B → 混合毛利率 50%
- 實際 mix：40% A、60% B → 混合毛利率 48%
- Mix 效應解釋了 2 個百分點的毛利壓縮

### 人數 / 薪酬拆解

用於分析薪資和人事成本差異。

```
Total Comp Variance = Actual Compensation - Budget Compensation

Decompose into:
1. Headcount variance    = (Actual HC - Budget HC) x Budget Avg Comp
2. Rate variance         = (Actual Avg Comp - Budget Avg Comp) x Budget HC
3. Mix variance          = Difference due to level/department mix shift
4. Timing variance       = Hiring earlier/later than planned (partial-period effect)
5. Attrition impact      = Savings from unplanned departures (partially offset by backfill costs)
```

### 支出類別拆解

用於價格/數量不適用時的營運費用分析。

```
Total OpEx Variance = Actual OpEx - Budget OpEx

Decompose by:
1. Headcount-driven costs    (salaries, benefits, payroll taxes, recruiting)
2. Volume-driven costs       (hosting, transaction fees, commissions, shipping)
3. Discretionary spend       (travel, events, professional services, marketing programs)
4. Contractual/fixed costs   (rent, insurance, software licenses, subscriptions)
5. One-time / non-recurring  (severance, legal settlements, write-offs, project costs)
6. Timing / phasing          (spend shifted between periods vs plan)
```

## 重大性門檻與調查觸發條件

### 設定門檻

重大性門檻決定哪些差異需要調查和敘述說明。門檻的設定依據：

1. **財務報表重大性：** 通常是某個關鍵基準（營收、總資產、淨利）的 1-5%
2. **項目大小：** 金額較大的項目適用較低的百分比門檻
3. **波動性：** 波動較大的項目可能需要較高的門檻，避免雜訊
4. **管理層關注：** 多大的差異會改變決策？

### 建議的門檻框架

| 比較類型 | 金額門檻 | 百分比門檻 | 觸發條件 |
|----------------|-----------------|---------------------|---------|
| 實際 vs 預算 | 依組織而定 | 10% | 任一超過 |
| 實際 vs 前期 | 依組織而定 | 15% | 任一超過 |
| 實際 vs 預測 | 依組織而定 | 5% | 任一超過 |
| 連續期間（MoM） | 依組織而定 | 20% | 任一超過 |

*金額門檻依你的組織規模設定。常見做法：損益表項目取營收的 0.5%-1%。*

### 調查的優先順序

當多項差異都超過門檻時，依下列順序決定調查優先順序：

1. **絕對金額差異最大的**：對損益影響最大
2. **百分比差異最大的**：可能表示流程問題或錯誤
3. **方向出乎意料的**：差異與趨勢或預期相反
4. **新出現的差異**：原本照計畫走、現在偏離的項目
5. **累積/趨勢性差異**：每一期都在擴大

## 差異說明的敘述產生

### 每則差異敘述的結構

```
[Line Item]: [Favorable/Unfavorable] variance of $[amount] ([percentage]%)
vs [comparison basis] for [period]

Driver: [Primary driver description]
[2-3 sentences explaining the business reason for the variance, with specific
quantification of contributing factors]

Outlook: [One-time / Expected to continue / Improving / Deteriorating]
Action: [None required / Monitor / Investigate further / Update forecast]
```

### 敘述品質檢查清單

好的差異敘述應該：

- [ ] **具體：** 寫出實際的驅動因素，不是只說「比預期高」
- [ ] **量化：** 包含每個驅動因素的金額和百分比影響
- [ ] **有因果：** 解釋為什麼會發生，不只是發生了什麼
- [ ] **有前瞻性：** 說明這個差異預期會不會持續
- [ ] **可行動：** 指出需要的後續動作或決策
- [ ] **簡潔：** 2-4 句，不是一整段廢話

### 要避免的常見敘述反模式

- 「營收比預算高，是因為營收比較高」（循環論證，沒有實際解釋）
- 「這一期的費用偏高」（模糊，哪些費用？為什麼？）
- 只寫「時間差」，卻沒說明什麼提早或延後、何時會恢復正常
- 只寫「一次性」，卻沒解釋那個項目是什麼
- 對重大差異只寫「各種小項目」（必須再進一步拆解）
- 只聚焦在最大的驅動因素，忽略互相抵銷的項目

## Waterfall 圖的方法

### 概念

waterfall（或 bridge）圖顯示如何透過一連串正向和負向的貢獻項目，從一個值走到另一個值。用來視覺化差異拆解。

### 資料結構

```
Starting value:  [Base/Budget/Prior period amount]
Drivers:         [List of contributing factors with signed amounts]
Ending value:    [Actual/Current period amount]

Verification:    Starting value + Sum of all drivers = Ending value
```

### 純文字 Waterfall 格式

沒有圖表工具時，以純文字 waterfall 呈現：

```
WATERFALL: Revenue — Q4 Actual vs Q4 Budget

Q4 Budget Revenue                                    $10,000K
  |
  |--[+] Volume growth (new customers)               +$800K
  |--[+] Expansion revenue (existing customers)      +$400K
  |--[-] Price reductions / discounting               -$200K
  |--[-] Churn / contraction                          -$350K
  |--[+] FX tailwind                                  +$50K
  |--[-] Timing (deals slipped to Q1)                 -$150K
  |
Q4 Actual Revenue                                    $10,550K

Net Variance: +$550K (+5.5% favorable)
```

### Bridge 調節表

用調節表來補充 waterfall：

| 驅動因素 | 金額 | 佔差異 % | 累計 |
|--------|--------|---------------|------------|
| Volume growth | +$800K | 145% | +$800K |
| Expansion revenue | +$400K | 73% | +$1,200K |
| Price reductions | -$200K | -36% | +$1,000K |
| Churn / contraction | -$350K | -64% | +$650K |
| FX tailwind | +$50K | 9% | +$700K |
| Timing (deal slippage) | -$150K | -27% | +$550K |
| **Total variance** | **+$550K** | **100%** | |

*注意：當有互相抵銷的項目時，個別驅動因素的百分比可以超過 100%。*

### Waterfall 最佳實務

1. 驅動因素從最大的正向排到最大的負向（或依合乎邏輯的業務順序）
2. 最多保留 5-8 個驅動因素，較小的項目併成「Other」
3. 驗證 waterfall 有對平（起點 + 驅動因素 = 終點）
4. 用顏色標示：有利用綠色、不利用紅色（視覺化圖表中）
5. 每根長條都標上金額和簡短說明
6. 加上一根「Total Variance」的總結長條

## 預算 vs 實際 vs 預測的比較

### 三向比較框架

| 指標 | 預算 | 預測 | 實際 | 預算差異 ($) | 預算差異 (%) | 預測差異 ($) | 預測差異 (%) |
|--------|--------|----------|--------|-------------|-------------|---------------|---------------|
| Revenue | $X | $X | $X | $X | X% | $X | X% |
| COGS | $X | $X | $X | $X | X% | $X | X% |
| Gross Profit | $X | $X | $X | $X | X% | $X | X% |

### 什麼時候用哪一種比較

- **實際 vs 預算：** 年度績效衡量、薪酬決策、董事會報告。預算在年初設定，通常不會更動。
- **實際 vs 預測：** 營運管理、找出浮現中的問題。預測會定期（每月或每季）更新，反映目前的預期。
- **預測 vs 預算：** 了解自規劃以來預期如何改變。適合用來找出規劃準確度的問題。
- **實際 vs 前期：** 趨勢分析、連續期間績效。預算沒有意義時很有用（新業務線、收購後）。
- **實際 vs 去年同期：** 年增長分析、排除季節性的比較。

### 預測準確度分析

追蹤預測隨時間的準確度，以改善規劃：

```
Forecast Accuracy = 1 - |Actual - Forecast| / |Actual|

MAPE (Mean Absolute Percentage Error) = Average of |Actual - Forecast| / |Actual| across periods
```

| 期間 | 預測 | 實際 | 差異 | 準確度 |
|--------|----------|--------|----------|----------|
| Jan    | $X       | $X     | $X (X%)  | XX%      |
| Feb    | $X       | $X     | $X (X%)  | XX%      |
| ...    | ...      | ...    | ...      | ...      |
| **Avg**|          |        | **MAPE** | **XX%**  |

### 差異趨勢

追蹤差異在一年中如何演變，找出系統性偏差：

- **持續有利：** 預算可能太保守（藏私）
- **持續不利：** 預算可能太積極，或是執行有問題
- **不利持續擴大：** 績效惡化或目標不切實際
- **差異縮小：** 預測準確度隨年度進行而改善（正常的模式）
- **波動大：** 業務難以預測，或預測方法有問題

---
name: variance-analysis
description: Decompose financial variances into drivers with narrative explanations and waterfall analysis. Use when analyzing budget vs. actual, period-over-period changes, revenue or expense variances, or preparing variance commentary for leadership.
argument-hint: "<line item> <period> vs <comparison>"
---

# Variance Analysis

**Important**: This skill assists with variance analysis workflows but does not provide financial advice. All analyses should be reviewed by qualified financial professionals before use in reporting.

Techniques for decomposing variances, materiality thresholds, narrative generation, waterfall chart methodology, and budget vs actual vs forecast comparisons.

## Variance Decomposition Techniques

### Price / Volume Decomposition

The most fundamental variance decomposition. Used for revenue, cost of goods, and any metric that can be expressed as Price x Volume.

**Formula:**
```
Total Variance = Actual - Budget (or Prior)

Volume Effect  = (Actual Volume - Budget Volume) x Budget Price
Price Effect   = (Actual Price - Budget Price) x Actual Volume
Mix Effect     = Residual (interaction term), or allocated proportionally

Verification:  Volume Effect + Price Effect = Total Variance
               (when mix is embedded in the price/volume terms)
```

**Three-way decomposition (separating mix):**
```
Volume Effect = (Actual Volume - Budget Volume) x Budget Price x Budget Mix
Price Effect  = (Actual Price - Budget Price) x Budget Volume x Actual Mix
Mix Effect    = Budget Price x Budget Volume x (Actual Mix - Budget Mix)
```

**Example — Revenue variance:**
- Budget: 10,000 units at $50 = $500,000
- Actual: 11,000 units at $48 = $528,000
- Total variance: +$28,000 favorable
  - Volume effect: +1,000 units x $50 = +$50,000 (favorable — sold more units)
  - Price effect: -$2 x 11,000 units = -$22,000 (unfavorable — lower ASP)
  - Net: +$28,000

### Rate / Mix Decomposition

Used when analyzing blended rates across segments with different unit economics.

**Formula:**
```
Rate Effect = Sum of (Actual Volume_i x (Actual Rate_i - Budget Rate_i))
Mix Effect  = Sum of (Budget Rate_i x (Actual Volume_i - Expected Volume_i at Budget Mix))
```

**Example — Gross margin variance:**
- Product A: 60% margin, Product B: 40% margin
- Budget mix: 50% A, 50% B → Blended margin 50%
- Actual mix: 40% A, 60% B → Blended margin 48%
- Mix effect explains 2pp of margin compression

### Headcount / Compensation Decomposition

Used for analyzing payroll and people-cost variances.

```
Total Comp Variance = Actual Compensation - Budget Compensation

Decompose into:
1. Headcount variance    = (Actual HC - Budget HC) x Budget Avg Comp
2. Rate variance         = (Actual Avg Comp - Budget Avg Comp) x Budget HC
3. Mix variance          = Difference due to level/department mix shift
4. Timing variance       = Hiring earlier/later than planned (partial-period effect)
5. Attrition impact      = Savings from unplanned departures (partially offset by backfill costs)
```

### Spend Category Decomposition

Used for operating expense analysis when price/volume is not applicable.

```
Total OpEx Variance = Actual OpEx - Budget OpEx

Decompose by:
1. Headcount-driven costs    (salaries, benefits, payroll taxes, recruiting)
2. Volume-driven costs       (hosting, transaction fees, commissions, shipping)
3. Discretionary spend       (travel, events, professional services, marketing programs)
4. Contractual/fixed costs   (rent, insurance, software licenses, subscriptions)
5. One-time / non-recurring  (severance, legal settlements, write-offs, project costs)
6. Timing / phasing          (spend shifted between periods vs plan)
```

## Materiality Thresholds and Investigation Triggers

### Setting Thresholds

Materiality thresholds determine which variances require investigation and narrative explanation. Set thresholds based on:

1. **Financial statement materiality:** Typically 1-5% of a key benchmark (revenue, total assets, net income)
2. **Line item size:** Larger line items warrant lower percentage thresholds
3. **Volatility:** More volatile line items may need higher thresholds to avoid noise
4. **Management attention:** What level of variance would change a decision?

### Recommended Threshold Framework

| Comparison Type | Dollar Threshold | Percentage Threshold | Trigger |
|----------------|-----------------|---------------------|---------|
| Actual vs Budget | Organization-specific | 10% | Either exceeded |
| Actual vs Prior Period | Organization-specific | 15% | Either exceeded |
| Actual vs Forecast | Organization-specific | 5% | Either exceeded |
| Sequential (MoM) | Organization-specific | 20% | Either exceeded |

*Set dollar thresholds based on your organization's size. Common practice: 0.5%-1% of revenue for income statement items.*

### Investigation Priority

When multiple variances exceed thresholds, prioritize investigation by:

1. **Largest absolute dollar variance** — biggest P&L impact
2. **Largest percentage variance** — may indicate process issue or error
3. **Unexpected direction** — variance opposite to trend or expectation
4. **New variance** — item that was on track and is now off
5. **Cumulative/trending variance** — growing each period

## Narrative Generation for Variance Explanations

### Structure for Each Variance Narrative

```
[Line Item]: [Favorable/Unfavorable] variance of $[amount] ([percentage]%)
vs [comparison basis] for [period]

Driver: [Primary driver description]
[2-3 sentences explaining the business reason for the variance, with specific
quantification of contributing factors]

Outlook: [One-time / Expected to continue / Improving / Deteriorating]
Action: [None required / Monitor / Investigate further / Update forecast]
```

### Narrative Quality Checklist

Good variance narratives should be:

- [ ] **Specific:** Names the actual driver, not just "higher than expected"
- [ ] **Quantified:** Includes dollar and percentage impact of each driver
- [ ] **Causal:** Explains WHY it happened, not just WHAT happened
- [ ] **Forward-looking:** States whether the variance is expected to continue
- [ ] **Actionable:** Identifies any required follow-up or decision
- [ ] **Concise:** 2-4 sentences, not a paragraph of filler

### Common Narrative Anti-Patterns to Avoid

- "Revenue was higher than budget due to higher revenue" (circular — no actual explanation)
- "Expenses were elevated this period" (vague — which expenses? why?)
- "Timing" without specifying what was early/late and when it will normalize
- "One-time" without explaining what the item was
- "Various small items" for a material variance (must decompose further)
- Focusing only on the largest driver and ignoring offsetting items

## Waterfall Chart Methodology

### Concept

A waterfall (or bridge) chart shows how you get from one value to another through a series of positive and negative contributors. Used to visualize variance decomposition.

### Data Structure

```
Starting value:  [Base/Budget/Prior period amount]
Drivers:         [List of contributing factors with signed amounts]
Ending value:    [Actual/Current period amount]

Verification:    Starting value + Sum of all drivers = Ending value
```

### Text-Based Waterfall Format

When a charting tool is not available, present as a text waterfall:

```
WATERFALL: Revenue — Q4 Actual vs Q4 Budget

Q4 Budget Revenue                                    $10,000K
  |
  |--[+] Volume growth (new customers)               +$800K
  |--[+] Expansion revenue (existing customers)      +$400K
  |--[-] Price reductions / discounting               -$200K
  |--[-] Churn / contraction                          -$350K
  |--[+] FX tailwind                                  +$50K
  |--[-] Timing (deals slipped to Q1)                 -$150K
  |
Q4 Actual Revenue                                    $10,550K

Net Variance: +$550K (+5.5% favorable)
```

### Bridge Reconciliation Table

Complement the waterfall with a reconciliation table:

| Driver | Amount | % of Variance | Cumulative |
|--------|--------|---------------|------------|
| Volume growth | +$800K | 145% | +$800K |
| Expansion revenue | +$400K | 73% | +$1,200K |
| Price reductions | -$200K | -36% | +$1,000K |
| Churn / contraction | -$350K | -64% | +$650K |
| FX tailwind | +$50K | 9% | +$700K |
| Timing (deal slippage) | -$150K | -27% | +$550K |
| **Total variance** | **+$550K** | **100%** | |

*Note: Percentages can exceed 100% for individual drivers when there are offsetting items.*

### Waterfall Best Practices

1. Order drivers from largest positive to largest negative (or in logical business sequence)
2. Keep to 5-8 drivers maximum — aggregate smaller items into "Other"
3. Verify the waterfall reconciles (start + drivers = end)
4. Color-code: green for favorable, red for unfavorable (in visual charts)
5. Label each bar with both the amount and a brief description
6. Include a "Total Variance" summary bar

## Budget vs Actual vs Forecast Comparisons

### Three-Way Comparison Framework

| Metric | Budget | Forecast | Actual | Bud Var ($) | Bud Var (%) | Fcast Var ($) | Fcast Var (%) |
|--------|--------|----------|--------|-------------|-------------|---------------|---------------|
| Revenue | $X | $X | $X | $X | X% | $X | X% |
| COGS | $X | $X | $X | $X | X% | $X | X% |
| Gross Profit | $X | $X | $X | $X | X% | $X | X% |

### When to Use Each Comparison

- **Actual vs Budget:** Annual performance measurement, compensation decisions, board reporting. Budget is set at the beginning of the year and typically not changed.
- **Actual vs Forecast:** Operational management, identifying emerging issues. Forecast is updated periodically (monthly or quarterly) to reflect current expectations.
- **Forecast vs Budget:** Understanding how expectations have changed since planning. Useful for identifying planning accuracy issues.
- **Actual vs Prior Period:** Trend analysis, sequential performance. Useful when budget is not meaningful (new business lines, post-acquisition).
- **Actual vs Prior Year:** Year-over-year growth analysis, seasonality-adjusted comparison.

### Forecast Accuracy Analysis

Track how accurate forecasts are over time to improve planning:

```
Forecast Accuracy = 1 - |Actual - Forecast| / |Actual|

MAPE (Mean Absolute Percentage Error) = Average of |Actual - Forecast| / |Actual| across periods
```

| Period | Forecast | Actual | Variance | Accuracy |
|--------|----------|--------|----------|----------|
| Jan    | $X       | $X     | $X (X%)  | XX%      |
| Feb    | $X       | $X     | $X (X%)  | XX%      |
| ...    | ...      | ...    | ...      | ...      |
| **Avg**|          |        | **MAPE** | **XX%**  |

### Variance Trending

Track how variances evolve over the year to identify systematic bias:

- **Consistently favorable:** Budget may be too conservative (sandbagging)
- **Consistently unfavorable:** Budget may be too aggressive or execution issues
- **Growing unfavorable:** Deteriorating performance or unrealistic targets
- **Shrinking variance:** Forecast accuracy improving through the year (normal pattern)
- **Volatile:** Unpredictable business or poor forecasting methodology