P1 – Management Accounting CH5 – Break-even analysis

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Chapter 5 Break-even analysis Chapter learning objectives:

Lead Component Indicative syllabus content

C.2 Analyse short-term pricing and product decisions.

(b) Apply break-even analysis in multiple product contexts

• Multi-product break-even analysis, including break-even and profit/volume charts, contribution/sales ratio, margin of safety etc.

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1. Cost-Profit-Volume (CVP) analysis (break-even analysis) • CVP analysis is based on the concept of contribution.

• Contribution to sales (C/S) ratio

• Breakeven point

• Margin of safety

• Contribution = sales – variable costs

Breakeven Analysis or Cost-Profit-Volume (CVP) analysis is defined as the study of the effects on future profit of changes in fixed cost, variable cost, sales price, quantity and mix.

C/S ratio • C/S ratio is calculated as = !"#$%&'($&"# !"# !"#$

!"##$%& !"#$% !"# !"#$ or !"!#$ !"#$%&'($&"#

!"!#$ !"#"$%"

• C/S ratio is the proportion of its selling that a product contributes towards overheads and profit.

• A higher C/S ratio means after the breakeven point is reached profits will collect faster.

Break-even point

• The breakeven point is that level of production which yields neither profit nor loss.

• At the breakeven point total sales equal total costs (or total contribution equal total fixed costs).

• 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 𝑢𝑛𝑖𝑡𝑠 = !"#$% !"#$#!"#$%&'($&"# !"# !"#$

• 𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 (𝑟𝑒𝑣𝑒𝑛𝑢𝑒) = !"#$% !"#$#!/! !"#$%

Margin of safety • Margin of safety is the quantity by which sales can reduce before the business starts

making a loss.

• Margin of safety (units) = budgeted sales – breakeven point

• Margin of safety (% of budgeted sales) = !"#$%&%# !"#$! – !"#$%#&#' !"#$! !"#$%&%# !"#$!

×100%

• Expected profit = Margin of safety (units) x contribution per unit

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Test Your Understanding 1 CPV Margo produces high-end science calculators. Variable costs per unit is $34 and the selling price is $70. Fixed costs are $52,000 for the period.

Required:

1. What is the contribution per unit for the calculator? 2. If 2,000 calculators are sold, what is the total contribution? 3. What is the total profit and the profit per unit at this level of sales and also for the level of 500

and 5,000 units? What is the contribution per unit for each sales level?

2. Break-even charts Breakeven chart is a chart which indicates approximate profit or loss at different levels of sales volume within a limited range.

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3. Profit-volume chart

4. Multi-product break-even analysis • When an organisation manufactures multiple products weighted average C/S ratio is

calculated:

𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑆 𝑟𝑎𝑡𝑖𝑜 = 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒

• Then breakeven is calculated as:

𝐵𝑟𝑒𝑎𝑘𝑒𝑣𝑒𝑛 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 = 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠

𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑆 𝑟𝑎𝑡𝑖𝑜

• To determine revenue required for a target profit (for multiple products):

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝐹𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡𝑠 + 𝑇𝑎𝑟𝑔𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑆 𝑟𝑎𝑡𝑖𝑜

• It assumes that the sales mix will remain constant.

The Multi-product Profit-Volume Graph • One straight line representing constant mix of products.

• One curved line denoting that the most profitable products are sold first.

• Therefore, the graph shows two breakeven points – one for each line.

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5. Sensitivity analysis • Also called “what if?” analysis.

• It concentrates management attention on variables that are the most important for the decision under review.

• It makes use of spreadsheets and other software.

6. Advantages and disadvantages of CVP analysis

Advantages Disadvantages

Helps determine a target quantity. There may be different factors affecting profit.

Assists in understanding the relation between costs and revenue.

A change in any factor would render the whole analysis faulty.

Identifies the breakeven point (where losses can be prevented).

Its underlying assumptions limit its reliability.

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7. Solutions to Test Your Understanding

Solution to Test Your Understanding 1 CPV 1. Contribution per unit = sales – variable cost

$70 – 34 = $36

2. Total contribution = contribution per unit x number of units

$36 x 2,000 = $72,000

3. Total profit = total contribution – fixed costs

$72,000 – $52,000 = $20,000 Profit per unit = total profit / number of units

$20,000 / 2,000 = $10

Units 500 2,000 5,000

$ $ $

Sales 35,000 140,000 350,000

Variable Cost 17,000 68,000 170,000

Total Contribution 18,000 72,000 180,000

Fixed costs 52,000 52,000 52,000

Total profit (loss) (34,000) 20,000 128,000

Profit (loss) per unit (68.00) 10.00 25.60

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9. Chapter Summary