It is possible to ascertain these by using a break-even chart or by using formulae.

Let us look at a basic accounting equation ie.

Sales - Total costs = Profit

or

Sales - ( Variable costs - Fixed costs ) = Profit

then

Sales - Variable costs = Contribution

Contribution is the excess of sales over variable costs and it represents the surplus available to meet the fixed costs. Once the fixed costs have been met any contribution left is profit.

At the break-even point the sales revenue generated covers the total costs and no more.

At the break-even point the contribution is sufficient to meet the fixed costs.

Contribution = Fixed costs

BEP = Fixed Costs

Contribution per Unit

P/V or C/S ratio = Contribution X 100

Sales

The P/V ratio indicates the % of contribution to sales.

Formulae:

1 Break-even point = Fixed costs/ Contribution per unit

2 Margin of safety = Break-even point(units) - The Expected Sales

3 Sales(units) to achieve a profit Fixed costs + Target profit

-----------------------------------

Contribution per unit

4 Profit volume ratio = Contribution x 100

----------------------------

Sales revenue

5 The Operating Gearing = Contribution / Profit

It is possible to present the profit volume relationship in a chart, a profit-volume chart. This chart dispenses with the need to draw cost and revenue lines and concentrates on the relationship between profit and output.

Revenues

and

Costs (£)

Output (units)

A break-even chart

P rofit

Output (units)

Loss

Limitations of cost volume profit analysis.

CVP analysis is based on a number of simplistic assumptions about cost behaviour which undermine the model’s effectiveness.

1 Costs can be divided into fixed and variable costs but in reality many costs have a fixed and variable element(semi-variable) and may not be easy to divide.

2 There is a linear relationship between output and costs and revenues.

The economists view tends to dispute this and presents a curvilinear

model.

3 The business has only one product or there is a specific constant product

mix.

4 The only factor influencing costs and revenues is output. Other factors

such as production efficiency and production methods may impact on output.

Example:

A company has sales of 120,000 units which sell for £1 with the variable costs 50p per unit. The fixed costs are £40,000. The management want to know the B/P point, the margin of safety and the profit. Solve graphically and by formula.