Edexcel A-Level Accounting: Break-even analysis (YAC11)

This guide teaches topic 2.7, Break-even analysis, from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting (XAC11/YAC11) specification, Issue 2, September 2018, and works through learning outcomes 2.7.1 to 2.7.3. Because it is in Unit 2, Corporate and Management Accounting, it is Unit 2 (A2) only; it is not part of the International AS unit. Every firm and figure used here is fictional, and money is in dollars.

Course hub: Edexcel A-Level Accounting. Printable checklist: YAC11 topic checklist. For quick recall use the break-even revision notes, then test yourself with the break-even practice questions. Want to check your gaps before you start? Try a free 10-minute diagnostic.

Outcomes in this topic

Spec ref	What you need to do
2.7.1	Calculate fixed, semi-fixed, semi-variable and variable costs, selling price and net profit
2.7.2	Work out contribution, break-even point and margin of safety, and use them
2.7.3	Show break-even analysis on a graph: fixed costs, total costs, sales revenue, break-even point, margin of safety, angle of incidence, and the areas of profit and loss

The Unit 1 costing guide explains how each type of overhead behaves; here you use that behaviour to find profit at different outputs. The same cost split drives flexible budgets in the budgeting guide.

Cost behaviour and calculation (2.7.1)

• Variable cost: total cost moves in step with output, while each unit costs the same amount. Examples: raw materials, sales commission.
• Fixed cost: the total stays the same across the relevant range of output; the cost per unit falls as output rises. Examples: rent, insurance.
• Semi-variable cost: a fixed element plus a variable element. Example: a delivery contract with a monthly standing charge plus a rate per parcel.
• Semi-fixed (stepped) cost: fixed over a band of output, then jumps to a new level when a band is passed. Example: one extra supervisor for each block of output.

Splitting a semi-variable cost: the high-low method

Given a semi-variable cost at two output levels:

1. Take the highest and lowest output levels and their costs.
2. Variable cost per unit = (cost at high output − cost at low output) ÷ (high output − low output).
3. Fixed element = total cost at either level − (output at that level × variable cost per unit).
4. Check the fixed element using the other level. Both must agree.

Worked example 1: Pellory Lamps Ltd

Pellory Lamps Ltd makes desk lamps. Its monthly costs are:

• direct materials 13.40 per lamp and direct labour 7.80 per lamp
• factory rent and insurance 26,400 a month
• packing and dispatch, a semi-variable cost: 7,240 in a month when 2,800 lamps were made, and 9,580 in a month when 4,600 lamps were made.

The company budgets for 4,000 lamps a month and sets its selling price at total cost per lamp plus a mark-up of 25%. Maximum capacity is 5,000 lamps a month.

Step 1: split the semi-variable cost.

Variable part = (9,580 − 7,240) ÷ (4,600 − 2,800)
              = 2,340 ÷ 1,800 = 1.30 per lamp
Fixed part    = 9,580 − (4,600 × 1.30) = 9,580 − 5,980 = 3,600
Check         = 7,240 − (2,800 × 1.30) = 7,240 − 3,640 = 3,600

Step 2: total the variable and fixed costs.

Variable cost per lamp = 13.40 + 7.80 + 1.30 = 22.50
Fixed costs per month  = 26,400 + 3,600     = 30,000

Step 3: calculate the selling price. Total cost at the budgeted 4,000 lamps is (4,000 × 22.50) + 30,000 = 120,000, so the total cost per lamp is 120,000 ÷ 4,000 = 30.00. A 25% mark-up on cost gives a selling price of 30.00 × 1.25 = 37.50.

Cost per lamp depends on output, because the fixed 30,000 is spread over more or fewer lamps.

Step 4: calculate net profit at the budgeted output.

	$
Revenue (4,000 × 37.50)	150,000
Less variable costs (4,000 × 22.50)	(90,000)
Contribution	60,000
Less fixed costs	(30,000)
Net profit	30,000

Showing contribution as a subtotal is the quickest route to every break-even figure below.

Worked example 2: semi-fixed costs and more than one break-even point

Tolcarn Print Studio prints sports shirts. Each shirt earns a contribution of 6. With one press, fixed costs are 9,000 a month and capacity is 2,000 shirts. Above 2,000 shirts it must lease a second press and hire an operator, adding 4,200 a month (capacity 4,000 shirts).

Up to 2,000 shirts:  fixed costs 9,000   break-even = 9,000 ÷ 6  = 1,500 shirts
2,001 to 4,000:      fixed costs 13,200  break-even = 13,200 ÷ 6 = 2,200 shirts
Profit at 2,000 shirts = (2,000 × 6) − 9,000  = 3,000
Profit at 2,001 shirts = (2,001 × 6) − 13,200 = −1,194 (a loss)

So the studio breaks even at 1,500 shirts, makes a profit up to 2,000, falls back into loss from 2,001 to 2,199 shirts, and breaks even again at 2,200. On a graph the fixed cost and total cost lines jump upwards by 4,200 at 2,000 shirts. Always check that each break-even point lies inside its own band of output.

Contribution, break-even point and margin of safety (2.7.2)

Contribution is selling price less variable cost. It is the amount each unit adds towards paying the fixed costs; once fixed costs are covered, every further unit of contribution is profit.

Unit contribution  = selling price − variable cost (both per unit)
Total contribution = unit contribution × number sold
Net profit         = total contribution − fixed costs

The break-even point is the output at which sales revenue and total costs are equal, so there is neither profit nor loss. At that point total contribution exactly equals fixed costs.

Break-even output  = fixed costs ÷ unit contribution
Break-even revenue = break-even output × selling price
                   or fixed costs ÷ (unit contribution ÷ selling price)

Contribution ÷ selling price is often called the contribution to sales (C/S) ratio; use it when you have only revenue totals.

The margin of safety is how far budgeted (or actual) sales are above the break-even point. It shows how much sales could fall before a loss is made.

Margin of safety (units)   = budgeted units − break-even units
Margin of safety (revenue) = margin of safety units × selling price
Margin of safety (%)       = margin of safety ÷ budgeted sales × 100

Worked example 3: Pellory Lamps break-even figures

Using example 1 (price 37.50, variable cost 22.50, fixed costs 30,000, budget 4,000 lamps):

1. Contribution per lamp = 37.50 − 22.50 = 15.00.
2. Break-even point = 30,000 ÷ 15.00 = 2,000 lamps.
3. Break-even revenue = 2,000 × 37.50 = 75,000. Check: C/S ratio = 15 ÷ 37.50 = 0.4, and 30,000 ÷ 0.4 = 75,000.
4. Margin of safety = 4,000 − 2,000 = 2,000 lamps, which is 2,000 × 37.50 = 75,000 of revenue, or 2,000 ÷ 4,000 = 50% of budgeted sales.
5. Net profit check: margin of safety × contribution per lamp = 2,000 × 15 = 30,000, the same as the statement in example 1.
6. Lamps needed for a net profit of 39,000: (30,000 + 39,000) ÷ 15 = 4,600 lamps. This is within capacity of 5,000.

If a break-even or target-profit figure is not a whole number, round up; rounding down leaves a small loss.

What moves the break-even point

Change	Effect on contribution per unit	Effect on break-even point
Selling price rises	Rises	Falls
Variable cost per unit rises	Falls	Rises
Fixed costs rise	No change	Rises
Sales volume rises	No change	No change (margin of safety widens)

Break-even charts (2.7.3)

A break-even chart shows output (units) on the horizontal axis and dollars on the vertical axis, with three lines.

Line	Starts at	Slope	Pellory Lamps points
Fixed costs	Fixed cost figure on the vertical axis	Horizontal	(0, 30,000) to (5,000, 30,000)
Total costs	Fixed cost figure at nil output	Variable cost per unit	(0, 30,000) to (5,000, 142,500)
Sales revenue	The origin	Selling price per unit	(0, 0) to (5,000, 187,500)

Plot two points for each line, extend the lines to maximum capacity, then mark the crossing point and drop dashed lines to both axes. Title the chart and label both axes.

Label each feature the specification lists:

• Fixed costs: the horizontal line at 30,000.
• Total costs: the line starting at 30,000 on the vertical axis and rising by 22.50 for each lamp.
• Sales revenue: the line from the origin rising by 37.50 for each lamp.
• Break-even point: where the sales revenue line crosses the total costs line. Read off both values: 2,000 lamps and 75,000.
• Margin of safety: the horizontal distance between the break-even output and the budgeted output, 2,000 to 4,000 lamps. Mark it with a double-headed arrow along the output axis.
• Angle of incidence: the angle formed where the sales revenue line cuts the total costs line. A wide angle means each unit sold above break-even adds a lot of profit (high contribution per unit). A narrow angle means profit builds slowly above break-even.
• Area of profit or loss: the wedge between the two lines to the right of break-even is the area of profit; the wedge to the left is the area of loss. The vertical gap at any output is the profit or loss at that output. At 4,000 lamps the gap is 150,000 − 120,000 = 30,000 profit; at 1,500 lamps it is a loss of 7,500.

Reading the angle of incidence

Suppose Pellory raised its price to 40.00 with the same costs. Contribution rises to 17.50 and break-even falls to 30,000 ÷ 17.50 = 1,714.3, so 1,715 lamps. The revenue line is steeper, so it meets the total cost line sooner and at a wider angle. Profit is now more sensitive to volume in both directions.

What a break-even chart assumes

The straight lines assume that the selling price and variable cost per unit stay the same at every output, that fixed costs do not change within the range shown (unless a step is drawn in, as in example 2), and that everything made is sold. A bulk discount on materials, for example, would bend the total cost line, so the break-even point read from straight lines is an estimate.

Common errors

• Using the fixed element of a semi-variable cost as part of variable cost, or forgetting to add it to fixed costs.
• Using the selling price, not unit contribution, as the divisor for fixed costs.
• Rounding a break-even or target-profit result down.
• Expressing margin of safety as a percentage of break-even sales instead of budgeted sales.
• Starting the total costs line at the origin, or the sales revenue line at the fixed cost figure.
• Reading break-even where the revenue line crosses the fixed costs line.
• Ignoring a step in semi-fixed costs, so a second break-even point is missed.

Where to go next

• Condensed formulas and a self-test: break-even revision notes.
• Exam-style questions with worked answers: break-even practice questions.
• Not sure where your gaps are? Take a free 10-minute diagnostic.

Official syllabus

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting (XAC11/YAC11) specification, Issue 2, September 2018 (first teaching September 2015), Pearson Education Limited. Unit 2: Corporate and Management Accounting, topic 2.7 Break-even analysis.