Fixed and variable costs, contribution and break-even

Costs can be sorted by what happens to them when the business makes more or fewer units.

Variable cost

A cost that rises and falls in step with output, such as materials. Twice the units, twice the cost.

Fixed cost

A cost that stays the same in total when output changes, such as rent.

Semi-variable cost

A cost with a fixed part and a variable part. Electricity is one: a standing charge, plus a charge for the power used.

A fixed cost stays the same in total, so the more units are made, the less of it each unit carries. A variable cost is the other way round: it changes in total, but it is the same for each unit.

That is why the cost of one unit falls when output rises. The variable cost of the unit has not changed. Only the fixed cost carried by each unit has fallen.

Contribution is the selling price of a unit less its variable cost. It is what each sale adds towards the fixed costs.

This way of counting is called marginal costing. Only the variable costs are treated as the cost of a unit. Fixed costs are treated as a cost of the month, not of the unit.

Total contribution is the contribution from one unit multiplied by the units sold. It pays the fixed costs first. What is left is profit.

• Total contribution is more than the fixed costs: a profit.
• Total contribution is equal to the fixed costs: no profit and no loss. This is the break-even point.
• Total contribution is less than the fixed costs: a loss.

1. Sort every cost into fixed, variable or semi-variable.
2. Split each semi-variable cost into its two parts. Take the month with the highest output and the month with the lowest. The variable cost of a unit is the difference between the two costs, divided by the difference between the two outputs. The fixed part is the total cost of one of those months, less its variable cost.
3. Add up the variable cost of one unit.
4. Take it from the selling price. That is the contribution from one unit.
5. Add up the fixed costs for the period.
6. Divide the fixed costs by the contribution from one unit. That is the break-even point in units.
7. Multiply the break-even units by the selling price. That is the break-even sales revenue.
8. Compare break-even with the sales that are planned. Budgeted sales less break-even sales is the margin of safety: how far sales can fall short before the business makes a loss.

The same sum finds the sales needed for a target profit. Add the profit wanted to the fixed costs, then divide by the contribution from one unit.

Pinewater Soaps makes one product, a gift box of soap. Each box sells for £26.00.

The contribution from one box is £26.00 less £12.00, which is £14.00.

The fixed costs are £5,600.00 a month: rent, a salary and insurance. The break-even point is £5,600.00 divided by £14.00, which is 400 boxes. At £26.00 a box, the break-even sales revenue is £10,400.00.

Pinewater plans to sell 550 boxes next month. That is 150 boxes above break-even, and each one adds its contribution to profit: 150 at £14.00 is a profit of £2,100.00. The margin of safety is 150 boxes.

In a slow month it sells 350 boxes. That is 50 short of break-even, so the loss is 50 at £14.00: £700.00.

For a profit of £2,800.00 a month, contribution must cover £8,400.00. Divided by £14.00, that is 600 boxes.

The break-even point moves when the fixed costs, the variable cost or the selling price changes. Work it out again with the new figures.

• Higher fixed costs: more units are needed to break even.
• A higher variable cost: the contribution from each unit is lower, so more units are needed.
• A higher selling price, with the same costs: the contribution from each unit is higher, so fewer units are needed.

Suppose the landlord raises Pinewater's rent by £700.00 a month. Fixed costs become £6,300.00. The contribution from one box is still £14.00, so the new break-even point is 450 boxes.

• Dividing the fixed costs by the selling price. The divisor is the contribution from one unit, because the variable cost of each unit has to be paid first.
• Putting a fixed cost into the variable cost of a unit. Rent does not rise when one more unit is made.
• Treating a semi-variable cost as all fixed or all variable. Split it first.
• Using the fixed cost for each unit from one month in another month. It changes whenever output changes.
• Dividing the margin of safety by the break-even sales to show it as a percentage. It is divided by the budgeted sales.
• Using an old break-even figure after a price or a cost has changed.

Work the answer forwards. At the break-even number of units, sales revenue less total variable costs must equal the fixed costs exactly.

For Pinewater: 400 boxes at £26.00 is £10,400.00. Their variable cost, at £12.00 each, is £4,800.00. The difference is £5,600.00, the fixed costs.

• The contribution from one unit is less than its selling price and more than nil. If it is nil or less, no level of sales breaks even.
• Profit at the planned sales comes out the same two ways: total contribution less fixed costs, and units above break-even times the contribution from one unit.
• The break-even point went the right way after a change: up for higher costs, down for a higher price.