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An example of cost-volume-profit (CVP) analysis

The following data relates to a new product due to be launched on the 1st May:

  • Selling price £20.00 per unit
  • Forecast volume 120,000 units
  • Variable costs £16.00 per unit
  • Fixed costs £300,000

We will apply the principles of CVP analysis to the following five situations, each has been treated as being independent of the other.

  1. Break-even point in units;
  2. Break-even point in units, if variable costs per unit increase to £17.00;
  3. Break-even point in £ sterling, if the fixed costs increase to £336,000;
  4. Minimum selling price to meet a profit target of £120,000;
  5. Volume of revenues required at a selling price of £19.00 per unit.

Finally, we will prepare a break-even chart using the original data.

The first step in tackling such a problem, is to calculate the total contribution and the contribution per unit.

  £ £ per unit
Revenues 2,400,000 20.00
less Variable costs 1,920,000 16.00
CONTRIBUTION 480,000 4.00
less Fixed costs 300,000  
Profit 180,000  

1. We calculate the break-even point by dividing the costs to be incurred, irrespective of the level of activity (i.e. fixed costs), by the contribution each unit will generate:

Break-even point (units)) = Fixed costs / Contribution per unit
  = £300,000 / £4.00
  = 75,000 units

2. Where the variable costs per unit change, so too will the contribution per unit:

  £ per unit
Revenues 20.00
Variable costs 17.00
Contribution 3.00

With an unchanged £20.00 selling price and a revised variable cost of £17.00 a contribution per unit of £3.00 will result. Assuming that the fixed costs remain unchanged at £300,000, the break-even point in units is 100,000 (£300,000 ÷ £3.00).

3. Break-even always arises where total cost equals total revenue. To find the break-even point in value, rather than volume, we first calculate the breakeven point in units, then multiply it by the selling price.

In this case, where fixed costs are £336,000 (with no other changes), the break-even point in units will be £336,000 divided by £4.00, which equals 84,000 units. Break-even in value can be found by multiplying 84,000 by £20.00, which equals £1,680,000.

4. The minimum selling price to meet a target profit is found from the sum of the contribution per unit plus the variable cost per unit. The contribution per unit can be found by dividing the required units into the sum of the fixed costs and the profit target. For example, we are told that the profit target is £120,000, added to fixed costs of £300,000 gives £420,000 (i.e. the contribution in value). The contribution per unit can now be found by dividing £420,000 by 120,000 units to give £3.50. Therefore, the minimum selling price is £3.50 plus the unit variable cost of £16.00 which equals £19.50.

5. The calculation of total volume to cover fixed costs and meet the target profit is similar to the approach used to determine the break-even volume. The only difference is that the profit target is added to the fixed costs in order to calculate the number of units (volume) required to cover fixed costs and to cover the profit target from a given contribution per unit.

In this case, the requirement is to identify the volume to cover fixed costs and profit assuming that the selling price per unit is decreased to £19.00. Where the selling price is £19.00, the unit contribution falls to £3.00:

  £ per unit
Revenues 19.00
less Variable costs 16.00
Contribution 3.00

The volume of sales under these circumstances, is found by adding the fixed costs of £300,000 to the profit target of £180,000 and then dividing the result by £3.00, to give 160,000 units.

Break-even analysis can also be plotted on a graph. The basic data required is total forecast volume, total revenues, total fixed costs and total variable costs. A break-even graph, using the original data from the previous example, is shown below.

One of the most difficult tasks when preparing a break-even chart is determining the intervals between the values (e.g. units of 15 for the volume). You must also consider the overall size of the graph, its position on the page and give it a suitable heading.

In the above graph, the following steps need to be taken:

  1. First, plot the total fixed costs, i.e. £300,000, a straight line across the page;
  2. Next, plot the total variable costs, i.e. £1,920,000, from £300,000 at zero units to £2,220,000 (£1,920,000 + £300,000) at 120,000 units;
  3. Finally, plot the total revenues, i.e. £2,400,000, from £0 at zero units to £2,400,000 at 120,000 units.

Break-even is the point where total costs equal total revenues. Also at this point, the total cost per unit equals the selling price per unit. To the left of the breakeven point, the total costs exceed the total revenues and represents the loss segment, while to the right of the break-even point the total revenues exceed the total costs and represents the profit segment.

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