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

These notes condense topic 2.7, Break-even analysis, of the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting (XAC11/YAC11) specification, Issue 2, September 2018. They cover outcomes 2.7.1 to 2.7.3 and are Unit 2 (A2) only. The break-even study guide has the full teaching and longer worked examples. The firms are fictional and money is in dollars.

Links: Edexcel A-Level Accounting hub, printable checklist, break-even practice questions, free 10-minute diagnostics. Cost types first appear in the costing notes for Unit 1.

2.7.1 Costs, selling price and net profit

Cost type	Total cost as output rises	Cost per unit as output rises	Example
Variable	Rises in proportion	Constant	Raw materials
Fixed	Constant (within the relevant range)	Falls	Rent of premises
Semi-variable	Rises, but from a fixed base	Falls	Water bill with a standing charge
Semi-fixed (stepped)	Constant within a band, then jumps	Falls within a band, jumps at the step	Hiring an extra van once orders pass a level

Method in steps: the high-low method

1. Pick the highest and lowest activity levels and their total costs.
2. Variable cost per unit = change in cost ÷ change in activity.
3. Fixed element = total cost at one level − (activity × variable rate).
4. Repeat step 3 at the other level as a check.
5. Add the fixed element to fixed costs and the variable rate to variable cost per unit.

Selling price and net profit formulas

What you need	Formula
Total cost	Fixed costs + (units × variable cost per unit)
Net profit	Revenue − total cost, or total contribution − fixed costs
Price at a mark-up on cost	Total cost per unit × (1 + mark-up %)
Price for a target net profit	Variable cost per unit + (fixed costs + target profit) ÷ expected units
Selling price from a chart	Revenue at any output ÷ that output

2.7.2 Contribution, break-even point, margin of safety

Term	Formula
Unit contribution	Price − variable cost, both per unit
Total contribution	Unit contribution × number sold
C/S ratio	Unit contribution ÷ price
Break-even output	Fixed costs ÷ unit contribution
Break-even revenue	Break-even output × price (or fixed costs ÷ C/S ratio)
Output for a target net profit	(Fixed costs + target) ÷ unit contribution
Margin of safety (units)	Budgeted units − break-even output
Margin of safety (%)	Margin of safety ÷ budgeted units × 100
Profit check	Margin of safety in units × unit contribution

Round break-even and target-profit units up to a whole unit.

Small reminder: Dunvane Ltd

Dunvane Ltd sells garden benches at 52 each. Variable cost is 31 per bench, fixed costs are 46,200 a year and budgeted sales are 3,000 benches.

Contribution per bench = 52 − 31             = 21
Break-even point       = 46,200 ÷ 21         = 2,200 benches
Break-even revenue     = 2,200 × 52          = 114,400
Margin of safety       = 3,000 − 2,200       = 800 benches (26.7%)
Net profit at 3,000    = (3,000 × 21) − 46,200 = 16,800
Check                  = 800 × 21            = 16,800

Semi-fixed costs: two break-even points

When fixed costs step up at an output level, work out a break-even point for each band separately. Keep a result only if it lies inside its own band. A step can push a profitable business back into a loss for a stretch of output just above the step.

2.7.3 Break-even chart checklist

Feature	How it appears
Fixed costs	Horizontal line at the fixed cost figure
Total costs	Starts at the fixed cost figure on the vertical axis; slope = variable cost per unit
Sales revenue	Starts at the origin; slope = selling price
Break-even point	Where sales revenue crosses total costs; read units and dollars
Margin of safety	Horizontal distance from break-even output to budgeted output
Angle of incidence	Angle between sales revenue and total costs lines at break-even; wide = high contribution per unit, profit grows fast
Area of profit or loss	Gap between the two lines: right of break-even = profit, left = loss

Method in steps: drawing the chart

1. Choose scales that reach maximum capacity and the largest revenue figure.
2. Plot two points for each line and join them with a ruler.
3. Mark the break-even point and drop dashed lines to both axes.
4. Mark budgeted output and show the margin of safety with a double-headed arrow.
5. Label the areas of profit and loss, every line and both axes.

Axes: output (units) along the bottom, dollars up the side. Title the chart and label every line.

Small reminder: reading Tewsley Cycles’ chart

The sales revenue line passes through (2,000 bikes, 90,000). The fixed costs line is at 21,600 and break-even is at 1,200 bikes.

Selling price          = 90,000 ÷ 2,000  = 45
Contribution per bike  = 21,600 ÷ 1,200  = 18
Variable cost per bike = 45 − 18         = 27
Profit at 2,000 bikes  = (2,000 − 1,200) × 18 = 14,400

The chart assumes a constant price, a constant variable cost per unit, fixed costs that do not change within the range shown, and that all output is sold.

Must-know distinctions

• Contribution vs net profit: contribution is before fixed costs; net profit is after them.
• Semi-variable vs semi-fixed: semi-variable has a fixed base plus a rate per unit; semi-fixed stays flat, then jumps.
• Fixed costs line vs total costs line: both start at the same point, but only total costs slopes upwards.
• Break-even point vs margin of safety: one is a level of output; the other is the gap between that level and budgeted sales.
• Mark-up vs margin: a mark-up is measured against cost; a margin is measured against selling price.

Quick self-test

1. Define margin of safety.
2. A delivery contract costs 400 a month plus 0.90 per parcel. Classify this cost.
3. A machine’s running cost was 2,980 at 1,200 machine hours and 4,100 at 2,000 machine hours. Find the variable rate and the fixed element, then the expected cost at 1,700 hours.
4. Price 18, variable cost 11, fixed costs 25,200. Calculate the break-even point in units and in revenue.
5. For question 4, budgeted sales are 5,000 units. By how many units could sales fall before a loss? Give this as a percentage of budget too.
6. For question 4, how many units give a net profit of 14,000?
7. For question 4, calculate net profit at 4,200 units.
8. Contribution is 9 per unit. Fixed costs are 12,600 up to 2,000 units and rise by 6,300 above that. Find both break-even points.
9. A business expects to sell 2,500 units. Variable cost is 26 per unit, fixed costs are 40,000 and it wants a net profit of 15,000. What selling price does it need?
10. What does a narrow angle of incidence tell you?
11. Where does the total costs line meet the vertical axis?

Answers

1. The amount by which budgeted (or actual) sales exceed break-even sales; how far sales can fall before a loss is made.
2. Semi-variable: a fixed 400 plus a variable 0.90 per parcel.
3. Rate = (4,100 − 2,980) ÷ 800 = 1.40 per hour; fixed = 4,100 − 2,800 = 1,300; at 1,700 hours: 1,300 + 2,380 = 3,680.
4. Contribution 7; 25,200 ÷ 7 = 3,600 units; 3,600 × 18 = 64,800.
5. 5,000 − 3,600 = 1,400 units; 1,400 ÷ 5,000 = 28%.
6. (25,200 + 14,000) ÷ 7 = 5,600 units.
7. (4,200 × 7) − 25,200 = 4,200.
8. 12,600 ÷ 9 = 1,400 units (inside the first band); 18,900 ÷ 9 = 2,100 units (inside the second band).
9. 26 + (40,000 + 15,000) ÷ 2,500 = 26 + 22 = 48.
10. Contribution per unit is low, so profit rises slowly once sales pass break-even.
11. At the fixed cost figure, because fixed costs are incurred even at nil output.

Where marks are usually lost

• Leaving the fixed element of a semi-variable cost out of fixed costs.
• Using price, not unit contribution, as the divisor.
• Rounding break-even or target-profit units down.
• Giving margin of safety as a percentage of break-even sales, not budgeted sales.
• Missing the second break-even point when a semi-fixed cost steps up.
• Drawing the total costs line from the origin.
• Reading break-even where revenue meets the fixed costs line.
• Leaving lines or axes unlabelled on a chart.
• Describing the angle of incidence without linking it to contribution per unit.

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.