📚 Typical Example Questions Explained for IB & CIE Business | IB CIE 商务：典型例题详解
Mastering IB and CIE Business requires not just theory, but the ability to apply concepts to real-world scenarios. This article walks through eleven typical example questions, covering key quantitative and essay-style topics. Each section provides step-by-step reasoning, calculations where needed, and evaluative comments, demonstrating how to structure high-scoring answers.
掌握IB和CIE商务课程不仅需要理论，还需要将概念应用于实际情境的能力。本文通过11道典型例题，涵盖重要的定性和定量专题。每个小节提供逐步推理、必要的计算和评估性评论，展示如何构建高分答案。
1. Break-even Analysis | 盈亏平衡分析
A manufacturer has fixed costs of $60,000 per month. The selling price per unit is $25, and the variable cost per unit is $15. Expected monthly sales are 8,000 units. Calculate the break-even point and the margin of safety. Also discuss two limitations of break-even analysis.
某制造商每月固定成本为60,000美元，单位售价25美元，单位可变成本15美元。预计月销量为8,000件。计算盈亏平衡点和安全边际，并讨论盈亏平衡分析的两个局限性。
First, calculate the contribution per unit, which is the amount each sale contributes towards fixed costs and profit.
首先计算单位边际贡献，即每笔销售为覆盖固定成本和创造利润所作出的贡献。
Contribution per unit = Selling Price − Variable Cost per unit = $25 − $15 = $10
Then apply the break-even formula in units.
然后应用以数量表示的盈亏平衡公式。
Break-even point (units) = Fixed Costs ÷ Contribution per unit = $60,000 ÷ $10 = 6,000 units
The break-even revenue is 6,000 × $25 = $0,000. The margin of safety shows how far sales can fall before the business makes a loss.
盈亏平衡收入为6,000 × 25 = 150,000美元。安全边际表明销售额在出现亏损前可以下降的幅度。
Margin of safety (%) = (Actual Sales − Break-even Sales) ÷ Actual Sales × 100% = (8,000 − 6,000) ÷ 8,000 × 100% = 25%
Two important limitations should be discussed in an evaluative answer.
在评估型答案中应讨论两个重要局限性。
- Break-even analysis assumes that selling price and variable cost per unit remain constant at all output levels.
盈亏平衡分析假设售价和单位可变成本在所有产出水平上保持不变。 - It usually applies to a single product or a fixed product mix, so it becomes less reliable for multi-product businesses.
它通常适用于单一产品或固定产品组合，因此对多产品企业而言可靠性下降。
A strong evaluation would note that break-even is a static planning tool. It ignores changes in market demand, competitor reactions and the possibility that fixed costs may rise in steps. Therefore, it should be used alongside cash-flow forecasting and market research, not as a single decision-making method.
有力的评估会指出，盈亏平衡是一种静态规划工具。它忽略了市场需求变化、竞争对手反应以及固定成本可能阶梯式上升的可能性。因此，它应与现金流量预测和市场调研结合使用，而不能作为唯一的决策方法。
2. Investment Appraisal: Payback and ARR | 投资评估：回收期与平均报酬率
A business invests $200,000 in new machinery. Net cash flows are expected to be: Year 1 $50,000, Year 2 $60,000, Year 3 $70,000, Year 4 $80,000 and Year 5 $90,000. Calculate the payback period and the accounting rate of return (ARR).
某企业投资200,000美元购置新机器。预计净现金流为：第1年50,000美元，第2年60,000美元，第3年70,000美元，第4年80,000美元，第5年90,000美元。计算回收期和会计报酬率（ARR）。
For payback, calculate cumulative cash flow until the initial investment is recovered.
计算回收期时，先计算累计现金流，直到初始投资被收回。
- Year 1: $50,000
第1年：50,000美元 - Year 2: $110,000
第2年：110,000美元 - Year 3: $180,000
第3年：180,000美元 - Year 4: $260,000
第4年：260,000美元
The investment is recovered during Year 4. The remaining amount at the start of Year 4 is $200,000 − $180,000 = $20,000.
投资在第4年收回。第4年开始时尚未收回的金额为200,000 − 180,000 = 20,000美元。
Payback period = 3 + ($20,000 ÷ $80,000) = 3.25 years, or 3 years and 3 months
For ARR, first calculate average annual profit. Total cash flow is $350,000 over five years, so average annual cash flow is $70,000. Annual depreciation is $200,000 ÷ 5 = $40,000, giving average annual profit of $30,000. Average investment is $200,000 ÷ 2 = $100,000.
计算ARR时，先求平均年利润。五年总现金流为350,000美元，因此平均年现金流为70,000美元。年折旧为200,000 ÷ 5 = 40,000美元，平均年利润为30,000美元。平均投资为200,000 ÷ 2 = 100,000美元。
ARR = Average Annual Profit ÷ Average Investment × 100% = $30,000 ÷ $100,000 × 100% = 30%
Payback is simple and focuses on liquidity and risk, but it ignores cash flows after the payback date and does not consider the time value of money. ARR uses accounting profit and is easy to compare with target rates, but it also ignores the timing of cash flows and can be distorted by depreciation policies.
回收期简单易行，关注流动性和风险，但忽略了回收期之后的现金流，也没有考虑货币时间价值。ARR使用会计利润，便于与目标报酬率比较，但同样忽略现金流的时间分布，并可能因折旧政策而失真。
3. Cash-flow Forecasting | 现金流量预测
A firm starts January with $20,000 cash. January cash inflows are $50,000 and outflows are $65,000. February inflows are $70,000 and outflows are $55,000. Calculate the closing balance for each month and explain why a profitable business may still face a cash shortage.
某企业1月初现金余额为20,000美元。1月现金流入50,000美元，流出65,000美元。2月流入70,000美元，流出55,000美元。计算每月期末余额，并解释为什么盈利企业仍可能面临现金短缺。
January closing balance:
1月期末余额：
January closing = $20,000 + $50,000 − $65,000 = $5,000
February closing balance:
2月期末余额：
February closing = $5,000 + $70,000 − $55,000 = $20,000
The business survives January with a positive but low balance. A profitable firm can still run out of cash because profit is not the same as cash. Sales may be made on credit, so revenue is recorded before cash is received. Inventory may build up, tying up cash. Large one-off payments, loan repayments, dividends or rapid expansion can also drain cash.
该企业1月勉强维持正余额但数额较低。盈利企业仍可能现金枯竭，因为利润不等于现金。销售可能采用赊销，收入在收到现金之前就已确认。存货可能积压，占用现金。大额一次性付款、偿还贷款、支付股利或快速扩张也可能消耗现金。
In evaluation, a good answer distinguishes between liquidity and profitability. Cash-flow forecasts help managers identify shortages early, arrange overdrafts or delay payments. However, forecasts are only as good as their assumptions, and unexpected events such as late customer payments or supplier price rises can quickly change the position.
在评估中，优秀答案会区分流动性与盈利能力。现金流量预测帮助管理者尽早发现短缺，安排透支或推迟付款。然而，预测的质量取决于假设，客户延迟付款或供应商涨价等意外事件可能迅速改变局面。
4. Contribution and Profit Calculation | 边际贡献与利润计算
A product sells for $40. Variable cost per unit is $24 and fixed costs are $80,000. Calculate contribution per unit, contribution margin ratio, break-even output, and the output needed to achieve a target profit of $20,000.
某产品售价40美元，单位可变成本24美元，固定成本80,000美元。计算单位边际贡献、贡献率、盈亏平衡产量，以及实现20,000美元目标利润所需的产量。
Contribution per unit is the difference between selling price and variable cost.
单位边际贡献是售价与可变成本之间的差额。
Contribution per unit = $40 − $24 = $16
The contribution margin ratio expresses contribution as a percentage of selling price.
贡献率将边际贡献表示为售价的百分比。
Contribution margin ratio = $16 ÷ $40 × 100% = 40%
Break-even output is fixed costs divided by contribution per unit.
盈亏平衡产量等于固定成本除以单位边际贡献。
Break-even output = $80,000 ÷ $16 = 5,000 units
To earn a target profit, add the target profit to fixed costs and divide by contribution per unit.
要实现目标利润，将目标利润加到固定成本上，再除以单位边际贡献。
Target output = ($80,000 + $20,000) ÷ $16 = 6,250 units
Contribution analysis is useful for short-term decisions such as accepting a special order, deciding which product to prioritise when capacity is limited, or calculating the effect of a price change. However, it assumes costs remain linear and that fixed costs do not change. In the long run, all costs become variable, and capacity constraints, quality and brand image must also be considered.
边际贡献分析适用于短期决策，例如接受特殊订单、在产能有限时决定优先生产哪种产品，或计算价格变化的影响。但它假设成本保持线性且固定成本不变。长期来看，所有成本都会变为可变成本，还必须考虑产能限制、质量和品牌形象。
5. Price Elasticity of Demand | 需求价格弹性
When price rises from $20 to $22, quantity demanded falls from 1,000 units to 900 units. Calculate the price elasticity of demand (PED) and comment on the effect on total revenue.
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