Costs, scale of production and break-even
Introduced| English | Meaning |
|---|---|
| fixed costs/fɪkst kɒsts/ | Costs that do not change with output over the relevant period and production range. |
| variable costs/ˈveərɪəbl kɒsts/ | Costs that change as the level of output changes. |
| total cost/ˈtəʊtl kɒst/ | The sum of all costs of producing a given level of output, including fixed and variable costs. |
| average cost/ˈævrɪdʒ kɒst/ | Total production cost divided by the quantity produced. |
| contribution/ˌkɒntrɪˈbjuːʃn/ | Sales revenue minus variable costs, available to cover fixed costs and then provide profit. |
| break-even output/breɪk ˈiːvən ˈaʊtpʊt/ | break-even output |
| margin of safety/ˈmɑːdʒɪn ɒv ˈseɪfti/ | The amount by which actual or forecast sales exceed break-even sales. |
| diseconomies of scale/ˌdɪsɪˈkɒnəmiz ɒv skeɪl/ | Increases in average production cost as the scale of output grows. |
| economies of scale/ɪˈkɒnəmiz ɒv skeɪl/ | Falls in average production cost as the scale of output increases. |
Can selling more still leave a bakery making a loss?
- A bakery sells each cake for £10, but flour, packaging and other variable inputs cost £6 per cake. It also pays £80 of fixed costs 固定成本 each day.
- The difference between sales and costs determines profit. A break-even calculation helps the owner test a plan before producing more.
Classify costs for the same period
- Fixed costs do not change with output within the stated period and capacity, such as an agreed shop rent. Variable costs 可变成本 change with output, such as ingredients used per cake. A cost can change when capacity or the period changes.
- Total cost 总成本 = fixed costs + total variable costs. Average cost 平均成本 = total cost ÷ output. If variable cost is £6 per cake, the total variable cost of 25 cakes is £150; it is not £6.
Which is a fixed cost?
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An agreed rent is fixed within the stated period and capacity; it need not stay the same for every future building or lease.
Fixed costs are £120 per day and variable cost is £3 per unit. Find total cost at 40 units, in £.
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Total variable cost=3×40=£120. Total cost=£120+£120=£240.
A business has total cost £360 for 60 units. Find average cost per unit, in £.
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Average cost=360÷60=£6 per unit.
Find contribution 贡献 and break-even output 盈亏平衡产量
- Contribution per unit = selling price − variable cost per unit. Each cake contributes £10 − £6 = £4 towards fixed costs, then profit.
- Break-even output = fixed costs ÷ contribution per unit. For this bakery, £80 ÷ £4 = 20 cakes a day. At 20 cakes, revenue and total cost both equal £200, so profit is zero.
If all 25 cakes are sold, revenue = 25 × £10 = £250. Total cost = £80 + (25 × £6) = £230. Profit = £250 − £230 = £20. Alternatively, total contribution £100 minus fixed costs £80 gives the same £20. Contribution per cake is not profit per cake before fixed costs are covered.
Selling price is 12 and variable cost per unit is 8. What is the contribution per unit?
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Contribution = 12 − 8 = 4.
Fixed costs are 1,600 and contribution per unit is 4. What is the break-even output (units)?
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Break-even = 1,600 ÷ 4 = 400 units.
At the break-even point, the business makes:
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Revenue exactly equals total cost.
Construct and interpret the chart
- Put output on the horizontal axis and money for the same period on the vertical axis. Plot fixed cost as a horizontal line, total cost starting at fixed cost, and total revenue starting at zero.
- Use two points to draw each straight line. Here, at 0 cakes, total cost is £80 and revenue £0; at 40 cakes, total cost is £320 and revenue £400. The intersection is break-even. At any output, the vertical gap between revenue and total cost is profit or loss.
Test the assumptions behind break-even
$Q_{BE}=\frac{F}{p-v};\quad \pi=(p-v)Q-F$
Changing sales volume changes profit while fixed costs remain. The starting values match the lesson example.
A business sells all 50 units at £12 each. Variable cost is £7 per unit and fixed costs are £150. Find profit in £.
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Revenue=50×12=£600. Total cost=150+50×7=£500. Profit=£100.
A break-even chart has price £8 per unit. At output 30 units, what is total revenue in £ if all units are sold?
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Revenue=price×units sold=8×30=£240. The revenue line passes through the origin.
Interpret the margin of safety 安全边际
- Margin of safety = actual sales output − break-even output, assuming output is sold. At 25 cakes sold, it is 25 − 20 = 5 cakes. Sales could fall by 5 before the bakery reaches break-even.
- If the bakery sells only 15 cakes, the difference is −5: sales are 5 below break-even, not protected by a positive safety margin. Use the chart or calculate revenue and cost to find the loss.
Actual output minus break-even output is the margin of ______.
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It shows how far sales can fall before a loss.
Break-even sales are 240 units and actual sales are 310 units in the same period. Find the margin of safety in units.
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310−240=70 units.
Test a change before accepting it
- If the price rises to £11 and the variable cost stays £6, contribution becomes £5 and break-even falls to £80 ÷ £5 = 16 cakes. This does not prove profit will rise: customers may buy fewer cakes.
- If price equals variable cost, contribution is zero. With positive fixed costs, no sales quantity covers them in this model. When contribution is positive but sales are below break-even, continuing may still cover some unavoidable fixed costs; compare the actual alternatives before recommending closure.
The simple model assumes constant price and variable cost per unit, unchanged fixed costs within capacity, and that output is sold. Discounts, waste, extra equipment or lower demand can change the result. A break-even forecast is a planning guide, not a guarantee of sales or profit.
Fixed costs are £100 and contribution is £6 per unit. Units cannot be split. What is the minimum number of units sold to avoid a loss?
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Break-even is 100÷6=16⅔ units. At 16 units contribution is only £96; 17 units contribute £102, enough to cover fixed costs.
Price is £5, variable cost is £5 per unit, and fixed costs are £200. Which conclusion follows in the simple model?
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Every sale contributes zero towards the £200 fixed costs. Dividing fixed cost by zero does not give a finite break-even output.
Explain economies and diseconomies of scale 规模不经济
- Economies of scale 规模经济 reduce average cost as a business grows. Examples include bulk-buying discounts, spreading advertising over more units, cheaper borrowing, specialist managers, and more efficient machinery. Explain how the chosen change lowers cost per unit; total cost can still rise.
- Diseconomies of scale raise average cost as size grows. Poor communication, weaker employee commitment and coordination problems can create mistakes or delays. Growth therefore does not always reduce average cost.
A bakery doubles monthly output from 1000 to 2000 items. Total cost rises from £6000 to £10000 because bulk buying reduces ingredient cost per item. Explain whether this is an economy of scale and give one possible diseconomy as the business grows further.
Compare your calculation and reasoning with the criteria. Other recommendations can be valid when supported by the case evidence and a realistic condition.
Make a decision using the evidence
- Calculate the relevant contribution, break-even output, profit or margin of safety with fresh data. State the period, units and assumptions.
- For a recommendation, use the business's demand, capacity and costs. Explain a benefit, a risk and what extra evidence could change the decision.
Break-even means revenue equals total cost. Contribution helps cover fixed costs; the margin of safety measures the sales buffer. Scale and price decisions need cost evidence and realistic demand assumptions.
Price is 15, variable cost per unit is 9 and fixed costs are 1800. Sales are 420 units. What are the contribution, the break-even output and the margin of safety?
Contribution is price minus variable cost per unit. Break-even output is fixed cost divided by contribution. Margin of safety is sales minus that output.
A business has fixed costs 1800, price 15 and variable cost 9 per unit. What is its break-even sales output?
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Contribution is 6, and 1800 divided by 6 is 300 units. Other options — 400 units (the lesson example's result when fixed costs are 1600 and contribution is 4); 120 units (the margin of safety).
A café sells 500 meals at £12, with variable cost £7 per meal and fixed costs £1800 per week. A price rise to £13 is forecast to reduce sales to 400 meals. Compare forecast profits and recommend whether to raise price, explaining one limitation.
Compare your calculation and reasoning with the criteria. Other recommendations can be valid when supported by the case evidence and a realistic condition.
On paper, draw a break-even chart for price £8 per unit, variable cost £3 per unit and fixed costs £100. Use an output axis from 0 to 40 units. Label fixed cost, total cost, total revenue and break-even, then explain the position at 30 units.
Compare your calculation and reasoning with the criteria. Other recommendations can be valid when supported by the case evidence and a realistic condition.