📚 Year 9 CIE Accounting Formula & Theorem Quick Reference Guide | 九年级CIE会计公式定理速查手册
This guide collates all the essential accounting equations, theorems, and formulas you will meet in Year 9 of the CIE curriculum. Use it as a one‑stop revision card to quickly check definitions, plug numbers, and master the logic behind double‑entry bookkeeping, financial statements, and basic ratio analysis.
本手册汇总了九年级CIE会计课程中你必须掌握的所有核心等式、定理与公式。把它当作速查卡片——可以随时核对定义、代入数字，快速掌握复式记账、财务报表编制以及基础比率分析背后的逻辑。
1. The Fundamental Accounting Equation | 基本会计等式
The accounting equation is the bedrock of the subject. It must always balance. Every transaction affects at least two elements, keeping the equation intact.
会计等式是这门学科的基石，它必须始终保持平衡。每一笔经济业务都至少影响两个要素，从而维持等式的成立。
Assets = Liabilities + Equity
资产 = 负债 + 所有者权益
A deeper form, useful for understanding profit, is:
理解利润含义时，可将其展开为：
Assets = Liabilities + Capital + (Revenue − Expenses)
资产 = 负债 + 资本 + (收入 − 费用)
2. Double‑Entry Rules | 复式记账规则
Every transaction has two sides: a debit (Dr) and a credit (Cr). The total Dr must always equal the total Cr. This is not a formula you move numbers into; it is a theorem of balance.
每一笔交易都有借方(Dr)和贷方(Cr)两个方面，且借方总额必须始终等于贷方总额。这不是需要代入数字的公式，而是一条关于平衡的定理。
| Element | Increase | Decrease |
|---|---|---|
| Assets / 资产 | Dr | Cr |
| Liabilities / 负债 | Cr | Dr |
| Capital / 资本 | Cr | Dr |
| Revenue / 收入 | Cr | Dr |
| Expenses / 费用 | Dr | Cr |
Remember the mnemonic ‘DEAD CLIC’: Debit Expenses, Assets, Drawings; Credit Liabilities, Income, Capital.
记住缩写词“DEAD CLIC”：借方记费用、资产、提款；贷方记负债、收入、资本。
3. The Trial Balance Theorem | 试算平衡定理
A trial balance lists all ledger balances. The total of debit balances must equal the total of credit balances. If it does not, an error has occurred.
试算表列示所有分类账余额。借方余额合计必须等于贷方余额合计；若不相等，则意味着存在差错。
Σ Debit balances = Σ Credit balances
借方余额合计 = 贷方余额合计
A balanced trial balance does not prove accuracy; it only proves the arithmetic equality of double entries. Errors of omission, commission, principle, original entry, compensating errors, and complete reversal are not revealed.
试算表平衡并不证明完全正确，它只证明复式记账的算术平衡。遗漏错误、记账错误、原则错误、原始分录错误、抵销错误和完全颠倒错误都无法通过试算平衡发现。
4. Income Statement Formulae | 利润表公式
The income statement calculates profit over a period. It is built step‑by‑step from sales to net profit.
利润表计算一定时期内的利润，它从销售额出发，逐层计算至净利润。
Cost of Sales / 销货成本:
Cost of Sales = Opening Inventory + Purchases − Closing Inventory
销货成本 = 期初存货 + 购货 − 期末存货
If carriage inwards is given, it is added to purchases before calculating cost of sales.
若给出购货运费，应将其加至购货中，再计算销货成本。
Gross Profit / 毛利润:
Gross Profit = Sales Revenue − Cost of Sales
毛利润 = 销售收入 − 销货成本
Net Profit / 净利润:
Net Profit = Gross Profit + Other Income − Operating Expenses
净利润 = 毛利润 + 其他收入 − 营业费用
5. Statement of Financial Position (Balance Sheet) | 财务状况表(资产负债表)公式
The statement of financial position shows assets, liabilities and equity at a point in time. It follows directly from the accounting equation but is presented in a standard layout.
财务状况表反映企业在某一时点的资产、负债和所有者权益。它直接源于会计等式，但需按标准格式列示。
Total Assets = Total Liabilities + Total Equity
总资产 = 总负债 + 所有者权益合计
Equity = Capital + Retained Earnings (Net Profit − Drawings).
所有者权益 = 资本 + 留存收益(净利润 − 提款)。
Working Capital = Current Assets − Current Liabilities. This shows the liquid buffer available for day‑to‑day operations.
营运资本 = 流动资产 − 流动负债。它显示了日常经营中可用的流动性缓冲。
6. Gross Profit Margin and Mark‑up | 毛利率与成本加成率
These two ratios connect gross profit to selling price or cost. They are used to check pricing strategies and to estimate missing figures.
这两个比率将毛利润与售价或成本联系起来，可用于检验定价策略，也可用于推算缺失数据。
Gross Profit Margin = (Gross Profit ÷ Sales Revenue) × 100%
毛利率 = (毛利润 ÷ 销售收入) × 100%
Mark‑up = (Gross Profit ÷ Cost of Sales) × 100%
成本加成率 = (毛利润 ÷ 销货成本) × 100%
The relationship: If mark‑up is m%, then gross profit margin ≈ m / (100+m) × 100%. For example, a 25% mark‑up gives a 20% gross profit margin.
两者关系：若成本加成率为 m%，则毛利率 ≈ m / (100+m) × 100%。例如，25% 的成本加成率意味着约 20% 的毛利率。
7. Net Profit Margin and Expense Ratios | 净利润率与费用比率
These show the proportion of sales kept as net profit or consumed by a particular expense. They are vital for control and benchmarking.
这些比率显示销售收入中有多大比例转化为净利润，或有多大比例被某项费用消耗，对于成本控制和行业对标非常重要。
Net Profit Margin = (Net Profit ÷ Sales Revenue) × 100%
净利润率 = (净利润 ÷ 销售收入) × 100%
Expense Ratio = (Specific Expense ÷ Sales Revenue) × 100%
费用比率 = (某项费用 ÷ 销售收入) × 100%
8. Inventory Valuation Methods | 存货估值方法
Inventories must be valued at the lower of cost and net realisable value (NRV). Two common cost‑flow assumptions appear in the syllabus.
存货必须按成本与可变现净值(NRV)孰低原则估值。大纲中涉及两种常见的成本流转假设。
FIFO (First‑In, First‑Out): The oldest units are assumed sold first. Closing inventory consists of the most recent purchases.
先进先出法(FIFO)：假定最先购入的存货最先售出，期末存货由最近购入的批次构成。
AVCO (Weighted Average Cost): A new average cost is recalculated after each purchase.
加权平均成本法(AVCO)：每次购货后重新计算平均成本。
Weighted Average Cost per unit = Total Cost of Goods Available ÷ Total Units Available
单位加权平均成本 = 可供销售商品总成本 ÷ 可供销售商品总数量
9. Depreciation Methods | 折旧方法
Depreciation spreads the cost of a non‑current asset over its useful life. Two main methods are examined at Year 9 level.
折旧是将非流动资产的成本在其使用寿命内进行分摊。九年级阶段主要考查两种方法。
Straight‑Line Method / 直线法:
Annual Depreciation = (Cost − Residual Value) ÷ Useful Life
年折旧额 = (原值 − 残值) ÷ 使用年限
Reducing (Diminishing) Balance Method / 余额递减法:
Annual Depreciation = Net Book Value × Depreciation Rate
年折旧额 = 账面净值 × 折旧率
Net Book Value = Cost − Accumulated Depreciation. The depreciation charge falls each year.
账面净值 = 原值 − 累计折旧。每年的折旧费用逐年递减。
10. Provision for Doubtful Debts | 呆账准备
The prudence concept requires that expected losses from trade receivables be estimated and charged as an expense.
谨慎性原则要求对预计无法收回的应收账款进行估计，并将其确认为费用。
Provision for Doubtful Debts = Trade Receivables × Estimated Percentage
呆账准备 = 应收账款 × 估计百分比
The increase or decrease in provision compared with the previous period is recorded in the income statement.
与上期相比，呆账准备的增减额应计入利润表。
11. Liquidity Ratios | 流动性比率
Liquidity ratios measure a business’s ability to meet short‑term obligations. Two ratios are essential.
流动性比率衡量企业偿还短期债务的能力。以下两个比率至关重要。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
A ratio above 1.5:1 is generally considered safe, though this depends on the industry.
一般认为高于 1.5:1 较为安全，但也取决于行业特征。
Quick (Acid‑Test) Ratio = (Current Assets − Inventory) ÷ Current Liabilities
速动比率(酸性测试比率) = (流动资产 − 存货) ÷ 流动负债
A quick ratio near 1:1 indicates the business can pay its current liabilities without selling inventory.
速动比率接近 1:1，意味着企业无需出售存货即可偿还流动负债。
12. Bank Reconciliation Statement | 银行调节表
This statement explains the difference between the cash book balance and the bank statement balance. The adjusted cash book balance is used in financial statements.
银行调节表说明现金账簿余额与银行对账单余额之间的差异。调整后的现金账簿余额用于编制财务报表。
Adjusted Cash Book Balance = Original Cash Book Balance + Unrecorded Credits − Unrecorded Debits
调整后现金账簿余额 = 原现金账簿余额 + 未记录的贷项 − 未记录的借项
Bank Statement Balance + Unpresented Cheques − Uncredited Deposits = Adjusted Cash Book Balance
银行对账单余额 + 未兑现支票 − 未入账存款 = 调整后现金账簿余额
Timing differences such as unpresented cheques and uncredited deposits must be listed in the reconciliation.
未兑现支票、未入账存款等时间性差异必须在调节表中逐一列示。
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