Breakeven Analysis

1 Introduction

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Breakeven analysis considers how profits change with changes in the level of activity of a business, and calculates what sales are needed in order for the business to be profitable.

Remember from chapter 6 (marginal costing) that contribution = sales revenue − variable costs, and profit = total contribution − fixed costs. Contribution per unit (selling price less variable cost per unit) stays the same whatever the volume, while fixed costs stay the same in total. Every extra unit sold therefore adds its contribution to profit.

2 Breakeven

Breakeven is the level of activity which gives rise to zero profit. Since profit is the difference between total contribution and fixed costs, breakeven is where the total contribution equals total fixed costs.

Breakeven volume (units) = fixed costs ÷ contribution per unit

Breakeven revenue = breakeven volume × selling price per unit (or fixed costs ÷ C/S ratio – section 4)

The same logic gives the sales needed for any target profit: the total contribution must cover the fixed costs and the profit.

Units for a target profit = (fixed costs + target profit) ÷ contribution per unit

3 Margin of safety

The Margin of Safety measures the percentage fall in budgeted sales that can be allowed before breakeven is reached.

Margin of safety = (budgeted sales − breakeven sales) ÷ budgeted sales × 100%

It is useful in identifying how big a problem any inaccuracy in the budgeted sales is likely to be.

It can also be stated in units (budgeted sales − breakeven sales) or in revenue, but a percentage is more meaningful: a shortfall of 50 units is serious on a budget of 300 units, and trivial on a budget of 5,000.

4 Contribution to sales ratio

The contribution to sales ratio (or C/S ratio) is calculated as follows:

C/S ratio = contribution ÷ sales (per unit or in total – the answer is the same)

Since the contribution and the sales revenue both vary linearly with the volume, the C/S ratio will remain constant.

Note: the C/S ratio is sometimes called the profit to volume (or P/V) ratio.

Because contribution is always the same fraction of sales, any contribution figure can be turned into the sales revenue that earns it:

Sales revenue needed = contribution needed ÷ C/S ratio

At breakeven the contribution needed is the fixed costs, so breakeven revenue = fixed costs ÷ C/S ratio. Where a business sells several products in a constant mix, the C/S ratio for the business as a whole is total contribution ÷ total sales.

5 Breakeven chart

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The breakeven chart plots total costs and total revenues at different levels of volume, and shows the activity level at which breakeven is achieved.

Volume (units) goes along the horizontal axis and costs and revenue ($) up the vertical axis. Three lines are drawn:

• Fixed costs – a horizontal line, the same at every volume.

• Total costs – starting at the fixed costs at nil volume and rising by the variable cost per unit.

• Total revenue – starting at nil and rising by the selling price per unit.

Where total revenue is above total costs there is a profit; below, a loss. Breakeven is where the two lines cross. The horizontal distance between budgeted sales and breakeven is the margin of safety. You will not have to draw the chart in the exam, but you must be able to read and interpret one.

6 Profit-volume chart

The profit volume chart shows the net profit or loss at any level of activity

Volume goes along the horizontal axis and profit (above the zero line) or loss (below it) up the vertical axis. Only one line is needed: at nil sales the loss equals the fixed costs, and profit then rises by the contribution per unit. Breakeven is where the line crosses zero profit.

7 The assumptions behind breakeven analysis

Breakeven analysis is a simple model, and its answers are only as good as its assumptions:

• costs can be split into fixed and variable elements

• fixed costs stay the same in total at every level of activity

• variable cost per unit and selling price per unit stay the same at every level of activity, so the cost and revenue lines are straight

• where there is more than one product, the sales mix stays the same

• everything that is produced is sold, so there is no change in inventory

In practice selling prices may have to fall to sell more, bulk discounts may reduce variable costs, and fixed costs may step up at higher volumes – so the results are best used within the normal range of activity.

8 Test your knowledge

Two quick checks before you move on: work through the flashcards to fix this chapter’s terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.