📚 Year 9 WJEC Business: Quick Reference Formula & Theorem Handbook | 九年级 WJEC 商务：公式定理速查手册
This handbook gathers the essential formulas, principles and short-cut rules that every Year 9 WJEC Business student needs at their fingertips. It is designed as a rapid revision tool, linking each calculation or economic law to a simple example so you can apply them confidently in exam-style questions.
本手册汇集了每位九年级 WJEC 商务学生都需烂熟于心的核心公式、原则与速查要点。它被设计成快速复习利器，每个计算或经济定律都配以简单实例，帮助你在考试类题目中自信应用。
1. Total Revenue Formula | 总收入公式
Total revenue (TR) is the money a business receives from selling its goods or services before any costs are deducted. It is often called turnover or sales revenue and is the starting point for all profit calculations.
总收入是指企业在扣除任何成本之前，通过销售商品或服务获得的资金。它常被称为营业额或销售收入，是所有利润计算的起点。
Total Revenue = Selling Price per Unit × Quantity Sold
For example, if a bakery sells 500 loaves of bread at £1.20 each, total revenue = £1.20 × 500 = £600.
例如，一家面包店以每条 1.20 英镑的价格售出 500 条面包，总收入 = 1.20 英镑 × 500 = 600 英镑。
Firms can increase total revenue by raising the price, selling more units, or doing both. However, a price rise may reduce the quantity demanded, so the overall effect on revenue depends on price elasticity.
企业可以通过提高价格、销售更多产品或两者兼施来增加总收入。但提价可能减少需求量，因此对收入的总体影响取决于价格弹性。
Total revenue is vital for calculating break-even and profit margins. Without tracking revenue, a business cannot know if it is covering its costs.
总收入对于计算盈亏平衡和利润率至关重要。不追踪收入，企业就无法知晓是否覆盖了成本。
2. Total Costs: Fixed and Variable | 总成本：固定与变动
Total costs (TC) are all the expenses a business incurs in producing and selling its output. They are split into fixed costs and variable costs to help managers understand cost behaviour.
总成本是企业在生产和销售其产出时发生的全部开支。它们分为固定成本和变动成本，以帮助管理者理解成本行为。
Total Costs = Fixed Costs + Variable Costs
Fixed costs do not change with output in the short run – examples include rent, insurance and salaries. Variable costs change directly with output – examples include raw materials, packaging and piece-rate labour.
固定成本在短期内不随产出变化——例如租金、保险费和薪金。变动成本直接随产出变化——例如原材料、包装和计件工资。
If a firm pays £2,000 per month in rent (fixed) and each unit made costs £3 in materials (variable), producing 800 units gives total costs = £2,000 + (£3 × 800) = £4,400.
如果一家企业每月支付 2,000 英镑租金（固定），每件产品材料成本为 3 英镑（变动），生产 800 件的总成本 = 2,000 + (3 × 800) = 4,400 英镑。
Understanding the split helps when making decisions about scaling production: as output grows, fixed costs are spread over more units, lowering average fixed cost.
理解这种划分有助于决策产量规模：随着产出增加，固定成本被分摊到更多产品上，从而降低平均固定成本。
3. Profit Calculation | 利润计算
Profit is the financial reward a business earns when total revenue exceeds total costs. It is the fundamental motive for most private-sector enterprises and a key indicator of financial health.
利润是当总收入超过总成本时企业获得的财务回报。它是大多数私营企业最基本的动机，也是衡量财务状况的关键指标。
Profit = Total Revenue − Total Costs
If the bakery mentioned earlier had total costs of £480 for the 500 loaves, its profit would be £600 − £480 = £120. This is often called net profit or operating profit at a basic level.
如果前面提到的面包店为 500 条面包付出了 480 英镑的总成本，其利润为 600 − 480 = 120 英镑。在基础层面这通常被称为净利润或营业利润。
A negative result means a loss. Managers must monitor profit regularly; sustained losses can lead to business failure.
负值表示亏损。管理者必须定期监控利润；持续亏损可能导致企业倒闭。
Profit can be reinvested in the business (retained profit) or distributed to owners. The formula is simple but depends on accurate revenue and cost data.
利润可再投资于企业（留存利润）或分配给所有者。公式虽简单，但依赖于准确的收入和成本数据。
4. Break-even Analysis | 盈亏平衡分析
Break-even is the point at which total revenue equals total costs and the business makes neither profit nor loss. It is a critical planning tool for start-ups and for launching new products.
盈亏平衡点是指总收入等于总成本、企业既不盈利也不亏损的时点。它是初创企业和推出新产品时的重要规划工具。
Break-even Output (units) = Fixed Costs ÷ (Selling Price − Variable Cost per Unit)
The bottom part of the formula, (Selling Price – Variable Cost per Unit), is called the contribution per unit. It shows how much each sale contributes towards fixed costs once variable costs are covered.
公式的下半部分（售价 − 单位变动成本）被称为单位贡献毛利。它表明在覆盖变动成本后，每笔销售能为固定成本做出多大贡献。
For instance, if fixed costs are £10,000, selling price is £25 and variable cost per unit is £15, contribution per unit = £10. Break-even output = £10,000 ÷ £10 = 1,000 units.
例如，若固定成本为 10,000 英镑，售价为 25 英镑，单位变动成本为 15 英镑，则单位贡献毛利 = 10 英镑。盈亏平衡产量 = 10,000 ÷ 10 = 1,000 件。
ak-even point in sales value by multiplying break-even units by the selling price: 1,000 × £25 = £25,000.
你也可将盈亏平衡产量乘以售价得出盈亏平衡销售额：1,000 × 25 英镑 = 25,000 英镑。
Break-even charts visually show the output level where total revenue and total cost lines cross. Below this output the business makes a loss; above it, a profit.
盈亏平衡图直观地展示总收入线与总成本线交叉的产出水平。低于此产出则亏损，高于则盈利。
5. Margin of Safety | 安全边际
Margin of safety measures how much sales can fall before the business reaches its break-even point. It is a cushion against uncertainty and risk.
安全边际衡量在销售跌至盈亏平衡点之前，企业尚可承受的下降空间。它是对抗不确定性和风险的安全垫。
Margin of Safety = Actual Sales − Break-even Sales
It can be expressed in units, sales value, or as a percentage of actual sales. A higher margin of safety means the business is more resilient to downturns.
它可用件数、销售额或实际销售百分比表示。安全边际越高，企业抵御低迷的能力越强。
margin of safety is 1,500 − 1,000 = 500 units. As a percentage: (500 ÷ 1,500) × 100 = 33.3%.
沿用上例，若实际销量为 1,500 件，盈亏平衡点为 1,000 件，则安全边际为 1,500 − 1,000 = 500 件。百分比：(500 ÷ 1,500) × 100 = 33.3%。
Businesses aim to widen their margin of safety by cutting fixed costs, raising the contribution per unit or boosting sales volume.
企业通过削减固定成本、提高单位贡献毛利或扩大销量来扩大安全边际。
6. Gross Profit Margin | 毛利率
Gross profit is the difference between revenue and the direct costs of making the product (cost of sales). The gross profit margin expresses this as a percentage, revealing how efficiently a business turns materials into money.
毛利是收入与制造产品的直接成本（销售成本）之差。毛利率将其用百分比表示，揭示企业将原料转化为金钱的效率。
Gross Profit = Total Revenue − Cost of Sales
Gross Profit Margin (%) = (Gross Profit ÷ Total Revenue) × 100
If a clothing retailer generates £50,000 in revenue and the clothes cost £30,000 to buy (cost of sales), gross profit is £20,000. The gross profit margin = (£20,000 ÷ £50,000) × 100 = 40%.
若一家服装零售商的收入为 50,000 英镑，服装采购成本（销售成本）为 30,000 英镑，则毛利为 20,000 英镑。毛利率 = (20,000 ÷ 50,000) × 100 = 40%。
A 40% gross margin means 40 pence from each £1 of sales stays in the business to cover other expenses and generate profit. A declining margin may signal rising material costs or discounting, requiring investigation.
40% 的毛利率意味着每 1 英镑销售中有 40 便士留在企业，用于覆盖其他开支并产生利润。毛利率下滑可能预示材料成本上升或打折促销，需引起重视。
7. Net Profit Margin | 净利润率
Net profit takes all business expenses – including operating costs, interest and tax – away from revenue. The net profit margin shows the percentage of sales that ends up as final profit.
净利润从收入中扣除了所有业务开支——包括营业成本、利息和税收。净利润率则显示最终转化为利润的销售百分比。
Net Profit = Total Revenue − Total Costs (all expenses)
Net Profit Margin (%) = (Net Profit ÷ Total Revenue) × 100
Suppose the same retailer has additional overheads of £15,000 (rent, wages, marketing). Net profit = £50,000 revenue − £30,000 cost of sales − £15,000 overheads = £5,000. Net margin = (£5,000 ÷ £50,000) × 100 = 10%.
假设同一零售商另有 15,000 英镑的间接费用（租金、工资、营销）。净利润 = 50,000 收入 − 30,000 销售成本 − 15,000 间接费用 = 5,000 英镑。净利润率 = (5,000 ÷ 50,000) × 100 = 10%。
A 10% net margin means 10 pence of every sales pound is profit. Comparing net margins over time or against competitors helps assess cost control and pricing power.
10% 的净利润率意味着每 1 英镑销售中有 10 便士为利润。比较不同时期的净利润率或与竞争对手对比，有助于评估成本控制能力和定价权。
8. Law of Demand | 需求定律
The law of demand states that, all other factors being equal, as the price of a product increases, the quantity demanded decreases, and vice versa. This inverse relationship is one of the most fundamental principles in business and economics.
需求定律指出，在其他因素不变的情况下，产品价格上升，需求量下降；反之亦然。这种反向关系是商务和经济学中最基本的原理之一。
It rests on two effects: the substitution effect (consumers switch to cheaper alternatives) and the income effect (a price rise reduces the purchasing power of a fixed income).
它基于两个效应：替代效应（消费者转向更便宜的替代品）和收入效应（价格上涨降低了固定收入的购买力）。
For example, if a cinema raises ticket prices from £8 to £12, some customers may choose to stream films at home, reducing quantity demanded. Businesses must consider this when pricing products.
例如，如果一家电影院将票价从 8 英镑上调至 12 英镑，一些顾客可能选择在家流媒体观影，导致需求量下降。企业定价时必须考虑这一点。
Demand can be shown on a downward-sloping demand curve. Shifts in the curve happen when non-price factors such as income, tastes or the price of related goods change.
需求可用一条向下倾斜的需求曲线表示。当收入、偏好或相关商品价格等非价格因素变化时，需求曲线会发生平移。
9. Law of Supply | 供给定律
The law of supply says that as the market price of a product rises, the quantity supplied typically increases, ceteris paribus (all else equal). Producers are motivated by the prospect of higher profit.
供给定律指出，在其他条件不变的情况下，商品的市场价格上升，供给量通常会增加。生产者受更高利润前景的激励。
A higher price makes production more profitable, encouraging existing firms to produce more and new firms to enter the market. If the price of handmade candles rises, workshops may extend their hours or invest in faster equipment.
更高的价格使生产更有利可图，鼓励现有企业扩大产量、新企业进入市场。若手工蜡烛价格上涨，作坊可能延长工时或投资更快的设备。
The supply curve slopes upwards. Changes in production costs, technology, taxes or the number of sellers shift the entire supply curve.
供给曲线向上倾斜。生产成本、技术、税收或卖家数量的变化会使整条供给曲线平移。
Together, the laws of demand and supply determine the equilibrium market price – the point where quantity demanded equals quantity supplied.
需求定律与供给定律共同决定市场均衡价格——即需求量与供给量相等的点。
10. Opportunity Cost Principle | 机会成本原则
Opportunity cost is the value of the next best alternative foregone when a choice is made. It is a core concept that reminds us that every decision involves a trade-off.
机会成本是指做出某项选择时所放弃的次优选项的价值。这是一个核心理念，提醒我们每个决策都涉及权衡取舍。
It is not simply the money spent; it is the benefit lost from the option not chosen. For a student, the opportunity cost of studying Business for an hour might be the leisure time or the chance to revise another subject.
它不仅仅指花掉的钱，而是放弃的那个选项所带来的好处。对于学生而言，学习一小时商务的机会成本可能是休闲时间或复习另一门科目的机会。
In business, when a firm uses its factory to produce chairs instead of tables, the opportunity cost is the profit it could have earned from tables. This helps managers evaluate the true cost of decisions.
在商务中，当一家企业用工厂生产椅子而非桌子时，机会成本是原本生产桌子可获得的利润。这有助于管理者评估决策的真实成本。
Applying the opportunity cost principle encourages more thoughtful resource allocation. Even if a project makes a profit, if the alternative would have yielded a higher return, the decision carries an opportunity cost.
运用机会成本原则鼓励更审慎的资源分配。即使某个项目盈利，若其替代方案本可带来更高回报，该决策便存在机会成本。
Published by TutorHao | Business Revision Series | aleveler.com
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