📚 Cambridge IGCSE Accounting Formula & Theorem Quick Reference Handbook | 剑桥IGCSE会计公式定理速查手册
This handbook brings together every essential formula, theorem and relationship you must master for the Cambridge IGCSE Accounting examination. Each entry is presented with a clear definition, its mathematical expression using standard Unicode symbols, and a practical explanation of how it is applied to business transactions and financial statements.
本手册汇集了剑桥IGCSE会计考试必须掌握的每一项核心公式、定理和关系。每个条目都配有清晰的定义、使用标准Unicode符号的数学表达式，以及如何应用于企业交易和财务报表的实用说明。
1. The Accounting Equation | 会计等式
The accounting equation is the foundation of the double-entry system. It states that every business transaction has a dual effect that keeps the equation in balance at all times.
会计等式是复式记账系统的基石。它表明每笔企业交易都具有双重影响，使该等式始终保持平衡。
Assets = Capital + Liabilities
资产 = 资本 + 负债
Assets are the resources owned or controlled by the business, such as cash, inventory and property. Capital represents the owner’s stake (original investment plus retained profits), while liabilities are the amounts owed to external parties. Every transaction can be analysed to show how this equality is maintained.
资产是企业拥有或控制的资源，例如现金、存货和房地产。资本代表所有者的权益（原始投资加留存利润），而负债是欠外部各方的金额。每一笔交易都可以分析，以显示这一相等关系如何维持。
2. Expanded Accounting Equation | 扩展会计等式
When income, expenses and drawings are introduced, the basic equation expands to reflect the changes in capital throughout an accounting period.
当引入收入、费用和提款时，基本等式会扩展以反映整个会计期间资本的变化。
Assets = Liabilities + Capital + (Revenue – Expenses) – Drawings
资产 = 负债 + 资本 + (收入 – 费用) – 提款
Revenue increases profit and therefore increases capital, while expenses and drawings reduce capital. The term (Revenue – Expenses) represents the profit or loss for the period before drawings. This expanded form helps students understand how the income statement links directly to the statement of financial position through closing capital.
收入增加利润，从而增加资本，而费用和提款减少资本。(收入 – 费用) 表示扣除提款前的当期利润或亏损。这种扩展形式有助于学生理解利润表如何通过期末资本直接与财务状况表联系起来。
3. Calculation of Profit | 利润计算
Profit is measured at two key levels: gross profit from trading activities and profit for the year (net profit) after all other income and expenses.
利润在两个关键层面衡量：来自经营活动的毛利，以及扣除所有其他收入和费用后的年度利润（净利润）。
Gross Profit = Sales – Cost of Sales
毛利 = 销售收入 – 销售成本
Cost of sales is calculated as: Opening Inventory + Purchases – Closing Inventory. This represents the direct cost of goods sold during the period.
销售成本计算如下：期初存货 + 采购 – 期末存货。这代表了在该期间售出商品的直接成本。
Cost of Sales = Opening Inventory + Purchases – Closing Inventory
销售成本 = 期初存货 + 采购 – 期末存货
Profit for the Year = Gross Profit + Other Income – Expenses
年度利润 = 毛利 + 其他收入 – 费用
Other income includes discounts received, rent received or commission earned. Expenses cover all operating costs such as wages, rent, depreciation and general administrative costs.
其他收入包括收到的折扣、收到的租金或赚取的佣金。费用涵盖所有运营成本，如工资、租金、折旧和一般行政费用。
4. Profitability Ratios | 盈利能力比率
Profitability ratios evaluate how effectively a business converts sales into profit and uses its capital to generate returns. Each ratio is expressed as a percentage.
盈利能力比率评估企业将销售转化为利润以及利用资本产生回报的效率。每个比率以百分比表示。
Gross Profit Margin = (Gross Profit ÷ Sales) × 100%
毛利率 = (毛利 ÷ 销售收入) × 100%
A higher gross margin suggests efficient control of production or purchasing costs relative to selling price. The ratio should be monitored over time and compared with industry averages.
较高的毛利率表明对生产成本或采购成本相对于售价的有效控制。该比率应随着时间推移进行监控，并与行业平均水平进行比较。
Net Profit Margin = (Profit for the Year ÷ Sales) × 100%
净利率 = (年度利润 ÷ 销售收入) × 100%
This shows the percentage of each sales dollar that remains after all expenses are covered. It is a key indicator of overall expense management.
这显示了在覆盖所有费用后，每单位销售收入所剩余的百分比。它是衡量总体费用管理的关键指标。
Expense Ratio = (Specific Expense ÷ Sales) × 100%
费用比率 = (特定费用 ÷ 销售收入) × 100%
Managers calculate individual expense ratios (e.g. rent/sales × 100%) to identify areas where costs are rising faster than revenue.
管理层计算各个费用比率（例如租金/销售收入 × 100%），以确定成本增长快于收入的领域。
Return on Capital Employed (ROCE) = (Profit for the Year ÷ Capital Employed) × 100%
已动用资本回报率 = (年度利润 ÷ 已动用资本) × 100%
Capital employed is typically calculated as Total Assets – Current Liabilities, or equivalently as Owner’s Equity + Non-current Liabilities. ROCE measures the return generated on the long-term funds invested in the business.
已动用资本通常计算为总资产 – 流动负债，或等价地计算为所有者权益 + 非流动负债。ROCE 衡量投入企业的长期资金所产生的回报。
5. Liquidity Ratios | 流动性比率
Liquidity ratios assess the ability of a business to meet its short-term obligations as they fall due. Two standard measures are examined at IGCSE level.
流动性比率评估企业在到期时履行其短期义务的能力。IGCSE 考试涉及两项标准指标。
Current Ratio = Current Assets ÷ Current Liabilities
流动比率 = 流动资产 ÷ 流动负债
A current ratio of between 1.5:1 and 2:1 is generally considered healthy, though the ideal level varies by industry. A ratio below 1 may indicate liquidity problems.
流动比率在 1.5:1 至 2:1 之间通常被认为是健康的，尽管理想水平因行业而异。比率低于 1 可能表明存在流动性问题。
Quick Ratio (Acid Test) = (Current Assets – Inventory) ÷ Current Liabilities
速动比率（酸性测试）= (流动资产 – 存货) ÷ 流动负债
Inventory is excluded because it is not always readily convertible to cash. A quick ratio of around 1:1 is often viewed as acceptable, showing the business can pay immediate debts without selling inventory.
存货被排除在外，因为它并不总是能快速转换为现金。速动比率约为 1:1 通常被认为是可接受的，表明企业无需出售存货就能偿还即时债务。
6. Efficiency Ratios | 效率比率
Efficiency ratios measure how well a business manages its inventory, collects cash from credit customers and pays its own suppliers. Average balances are used to smooth seasonal fluctuations.
效率比率衡量企业管理存货、向赊销客户收回现金以及向供应商付款的效率。使用平均余额来平滑季节性波动。
Average Inventory = (Opening Inventory + Closing Inventory) ÷ 2
平均存货 = (期初存货 + 期末存货) ÷ 2
Inventory Turnover (times) = Cost of Sales ÷ Average Inventory
存货周转率（次数）= 销售成本 ÷ 平均存货
This ratio shows how many times the average inventory is sold and replaced during the year. A higher turnover may indicate efficient stock management, but could also mean the business risks running out of stock.
该比率显示平均存货在一年内被销售和替换的次数。较高的周转率可能表明存货管理效率高，但也可能意味着企业面临缺货风险。
Inventory Turnover in Days = (Average Inventory ÷ Cost of Sales) × 365
存货周转天数 = (平均存货 ÷ 销售成本) × 365
This expresses turnover as the average number of days it takes to sell the stock on hand. A shorter period is generally preferred.
这将周转率表示为售出现有存货所需的平均天数。通常较短的周期更为理想。
Trade Receivables Collection Period = (Average Trade Receivables ÷ Credit Sales) × 365
应收账款周转天数 = (平均应收账款 ÷ 赊销收入) × 365
This indicates the average time taken by credit customers to settle their accounts. If the period is longer than the credit terms offered, the business may need to tighten credit control.
这表明赊销客户结清账款所需的平均时间。如果该周期长于提供的信用期限，企业可能需要加强信用控制。
Trade Payables Payment Period = (Average Trade Payables ÷ Credit Purchases) × 365
应付账款周转天数 = (平均应付账款 ÷ 赊购金额) × 365
This shows how long, on average, a business takes to pay its suppliers. While delaying payment helps cash flow, paying too slowly may damage supplier relationships.
这显示企业平均需要多长时间向供应商付款。虽然延迟付款有助于现金流，但付款过慢可能损害供应商关系。
7. Depreciation of Non-current Assets | 非流动资产折旧
Depreciation is the systematic allocation of a non-current asset’s cost over its useful life. Two methods are examinable: the straight-line method and the reducing balance method.
折旧是将非流动资产成本在其使用寿命内进行系统性分配。两种方法需考试掌握：直线法和余额递减法。
Straight-line Depreciation per Year = (Cost – Residual Value) ÷ Useful Life (years)
年直线折旧额 = (成本 – 残值) ÷ 使用年限（年）
An equal amount of depreciation is charged each year. The net book value (NBV) at the end of any year is Cost – Accumulated Depreciation.
每年计提相等金额的折旧。任何年末的账面净值 (NBV) 为成本 – 累计折旧。
Reducing Balance Depreciation = Net Book Value at Start of Year × Depreciation Rate (%)
余额递减折旧 = 年初账面净值 × 折旧率 (%)
A fixed percentage is applied to the diminishing net book value each year. This results in a higher depreciation charge in the early years. The residual value is not subtracted in the formula, but the rate is chosen so that the asset is never fully written down below its scrap value.
每年以固定百分比应用于递减的账面净值。这导致早期折旧费用较高。公式中不减去残值，但选择的折旧率应确保资产不会被减记至低于其废料价值。
8. Trial Balance and Error Correction | 试算平衡与错误纠正
The trial balance is a list of all ledger account balances at a particular date. If total debits equal total credits, the books are arithmetically correct, but errors may still exist.
试算平衡表是特定日期所有分类账户余额的列表。如果借方总额等于贷方总额，则账簿在算术上是正确的，但错误仍可能存在。
Total Debit Balances = Total Credit Balances
借方余额总额 = 贷方余额总额
Errors that do not affect the balancing of the trial balance include: error of omission (transaction not recorded), error of commission (posted to wrong account of same class), error of principle (capital expenditure treated as revenue or vice versa), error of original entry (incorrect amount in day book), compensating error (two errors that cancel each other) and complete reversal of entries (debit and credit reversed).
不影响试算平衡表平衡的错误包括：遗漏错误（未记录交易）、入账错误（记入同类的错误账户）、原则性错误（资本性支出作为收益性支出处理或反之）、原值错误（日记账中的错误金额）、抵销错误（两个相互抵消的错误）和完全颠倒分录（借贷方颠倒）。
When a trial balance difference exists, a suspense account is opened to make the totals agree. The difference is temporarily placed in the suspense account until the error(s) are located and corrected through journal entries. The suspense account must be cleared to zero by the time final accounts are prepared.
当试算平衡表存在差额时，会开设一个暂记账户使总额相等。差额暂时记入暂记账户，直到通过日记账分录找到并更正错误。在编制最终财务报表时，暂记账户必须清零。
9. Bank Reconciliation | 银行对账
A bank reconciliation statement explains the difference between the cash book balance and the bank statement balance at a particular date. The aim is not to alter the cash book directly, but to identify items causing the difference and bring the records into agreement.
银行对账单解释了特定日期现金账簿余额与银行对账单余额之间的差异。目的不是直接修改现金账，而是确定导致差异的项目，并使记录一致。
The updated cash book balance is calculated first: start with the unadjusted cash book balance, add amounts not yet recorded (e.g. bank interest received, direct credits) and deduct unpresented cheques? No, unpresented cheques are already recorded in the cash book but not yet on the bank statement, so they are adjusted in the reconciliation, not in the cash book. The correct procedure: update the cash book for items discovered on the bank statement that have not yet been entered in the cash book (bank charges, standing orders, direct debits, credit transfers). The adjusted cash book balance is then compared to the bank statement balance, and the reconciling items are unpresented cheques (deducted from bank statement balance) and outstanding lodgements (added to bank statement balance) to arrive at the adjusted cash book balance.
首先计算更新后的现金账余额：从尚未调整的现金账余额开始，加上尚未记录的金额（如收到的银行利息、直接贷记）并减去未经记录的支款？不，未兑现支票已在现金账中记录但未反映在银行对账单上，因此它们在对账中调整，而不是在现金账中。正确的程序：针对银行对账单上发现但尚未记入现金账的项目（银行手续费、定期付款指令、直接借记、贷项转账）更新现金账。然后将调整后的现金账余额与银行对账单余额进行比较，调节项目为未兑现支票（从银行对账单余额中扣除）和未记入贷项（加至银行对账单余额），从而得出调整后的现金账余额。
Adjusted Cash Book Balance = Unadjusted Cash Book Balance + Direct Credits – Direct Debits/Bank Charges
调整后现金账余额 = 未调整现金账余额 + 直接贷记 – 直接借记/银行手续费
Adjusted Cash Book Balance = Bank Statement Balance – Unpresented Cheques + Outstanding Lodgements
调整后现金账余额 = 银行对账单余额 – 未兑现支票 + 未记入贷项
The final adjusted cash book balance is the figure that appears in the statement of financial position.
最终调整后的现金账余额即为出现在财务状况表中的数字。
10. Control Accounts and Suspense Accounts | 控制账户与暂记账户
Control accounts are part of the double-entry system and act as summary accounts for the sales ledger and purchases ledger. They provide an independent check on the accuracy of individual customer and supplier accounts.
控制账户是复式记账系统的一部分，充当销售分类账和采购分类账的汇总账户。它们为个别客户和供应商账户的准确性提供独立检查。
The sales ledger control account typically records: opening debit balance (trade receivables), plus credit sales, less receipts from credit customers, less returns inwards, less discounts allowed and less bad debts written off. The closing debit balance should equal the total of individual customer accounts in the sales ledger.
销售分类账控制账户通常记录：期初借方余额（应收账款），加上赊销，减去从赊销客户收到的款项，减去销售退回，减去允许的折扣和冲销的坏账。期末借方余额应等于销售分类账中个别客户账户的总和。
The purchases ledger control account records: opening credit balance (trade payables), plus credit purchases, less payments to credit suppliers, less returns outwards and less discounts received. The closing credit balance matches the total of individual supplier accounts.
采购分类账控制账户记录：期初贷方余额（应付账款），加上赊购，减去支付给赊购供应商的款项，减去采购退回和收到的折扣。期末贷方余额与个别供应商账户的总和一致。
A suspense account is used temporarily when a trial balance fails to agree. The difference is placed in a suspense account, and journal entries are then passed to correct the errors and eliminate the suspense balance. Typical corrections include adjusting incorrect postings, recording omitted items and reversing entries that were completely reversed.
当试算平衡表不一致时，临时使用暂记账户。差额记入暂记账户，然后通过日记账分录更正错误并消除暂记账户余额。典型的更正包括调整错误过账、记录遗漏项目和冲销完全颠倒的分录。
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